text:
\section{Introduction}

The number of strongly lensed sources found in individual
observational programs can be used to constrain the cosmological
constant (e.g., Turner 1990). Using statistics of optical
lensing programs, various  studies have now derived
upper limuts on the present day value of the
 cosmological constant (Kochanek 1996a;
Chiba \& Yoshi 1997; Cooray et al. 1998a). As discussed
in the literature, however, lensed source search programs
at optical wavelengths can be affected by
systematics arising from effects due to extinction and
reddening  (e.g., Malhotra et al. 1996), and
issues related to completeness (Kochanek 1991).
Such effects, especially extinction for which there is no
 clear consensus, cannot easily be quantified in
cosmological studies with gravitational lensing statistics.
At radio wavelengths, neither of these effects are
likely to affect the statistics (see, Falco et al. 1998),
including completeness,  when flux-limited systematic
surveys are carried out.
Also, high resolution interferometers such as the VLA and  MERLIN allow
detection of lensed sources with image separations much smaller than
that allowed by ground-based optical telescopes.
Thus, statistics from lensed radio source surveys
 are generally preferred over the optical ones
to obtain cosmological parameters.

Recently, Falco et al. (1998) studied the statistics of lensed radio sources
in the Jodrell Bank-VLA Astrometric Survey (JVAS; Browne et al.
1997; Patnaik et al. 1992) sample of
2500 flat-spectrum sources brighter than 200 mJy at 5 GHz.
They were able to derive a 2$\sigma$ lower-limit on the mass density of
the universe of $\Omega_m > 0.27$ ($0.47 < \Omega_m < 1.38$ at 1$\sigma$).
Recently, the number of strongly lensed radio sources has steadily increased
 with results from the  Cosmic Lens All Sky Survey (CLASS), which has
observed $\sim$ 6500 flat-spectrum sources during the first two sessions of
 its observations using the VLA.
The total number of currently confirmed lensed radio sources
from these observations amount to six: B1608+656
(Myers et al. 1995), B2045+265 (Fassnacht et al. 1998), B1933+503 (Sykes
et al. 1998),
B0712+472 (Jackson et al. 1998a), B1600+434 (Jackson et al. 1995),
B1127+385 (Koopmans et al. 1998). The CLASS  is a collaboration between groups
at Jodrell Bank, Caltech, Dwingeloo and Leiden, and is an extension  to
the previous JVAS by observing
flat-spectrum sources ($\alpha \geq -0.5;
S_\nu \propto \nu^\alpha$) down to a flux density limit of 30 mJy
at 5 GHz.

Here, we calculate the expected number of lensed radio sources in the
CLASS sample of $\sim$ 6500 sources
 for different cosmological parameters, and constrain
these parameters by comparing the predictions with the observations.
In Sect. 2, we discuss our calculation and its inputs,  including
the redshift distribution for background
radio sources and the luminosity  distribution
of foreground lenses.  In Sect. 3, we present our resulting constraints on
cosmological parameters, and in particular on
$\Omega_m-\Omega_\Lambda$, as well as
on the redshift distribution of the faint radio sources.
In Sect. 4, we discuss the potential effect of
systematic errors in the predicted and observed rate of strong
lensing.  Finally, in Sect. 5, we summarize and discuss future prospects for
tighter constraints. We follow the conventions that the Hubble
constant, $H_0$, is 100\,$h$\ km~s$^{-1}$~Mpc$^{-1}$, the present normalized
mean density of the universe $\Omega_{m}$ is $8 \pi G \rho_m/3 H_0^2$,
and the present normalized cosmological constant $\Omega_\Lambda$ is
$\Lambda/3 H_0^2$.
In a flat universe, $\Omega_m+\Omega_\Lambda=1$. We have simplified the
notation by not including the subscript '0'
usually taken to denote the present day values of these quantities.

\section{Expected number of strongly lensed sources}

\subsection{Calculational method}

Our present calculational method is quite similar  to that of Cooray
et al.
(1998a; hereafter CQM), in which
we calculated the expected lensing rate in the Hubble Deep Field (HDF;
Williams et al. 1996),
as implied by various photometric redshift catalogs for HDF sources.
A comparison between the observed number of lensed sources in the HDF and
the predicted number, allowed us to
calculate the present value of $\Omega_m-\Omega_\Lambda$.
We follow a procedure similar to CQM by first establishing the
redshift distribution of the observed CLASS sources, and then by
using the standard lensing
calculations to estimate the expected number of strongly
lensed radio sources present in this sample.

In Fig.~1, we show the flux density
distribution of CLASS sources. Except for a
handful of sources with flux densities greater than 200 mJy,
most of the observed sources follow a
 distribution that sharply rises around 30 mJy. This is
only an observational artifact due to the 30 mJy cutoff imposed on
the initial source selection. Since the source sample was selected based on
previous Green Bank 5 GHz surveys  (e.g., Gregory et al. 1996)
and that we are now using the measured flux densities
from CLASS VLA snapshot
maps at 8.4 GHz, the presence of sources with flux densities
less than 30 mJy at 8.4 GHz suggest that the current CLASS sample includes
a small number of non-flat spectrum radio sources; The CLASS definition
with respect to flat spectrum sources is based on an upper frequency point
at 5 GHz rather than 8.4 GHz. Sources with flux densities
less than 30 mJy are also expected
given uncertainties in the Green Bank survey flux density measurements
 and the possibility for intrinsic flux density variation
between Green Bank and CLASS survey epochs.
The total number of radio sources in the publicly available catalog
of CLASS sources\footnote{http://www.jb.man.ac.uk/$\sim$njj/glens/class.html} during the first two sessions is 6528.

\begin{figure}[ht]
\vspace{6cm}
\caption{The flux density
distribution for CLASS sources. We have only shown the
distribution of sources with flux densities less than 150 mJy, where
most of the sources are found}
\end{figure}

As discussed in Falco et al. (1998), one of the main problems associated
with lensed radio source statistics is the non-availability of redshifts
for radio sources. However, it has also
been shown by Falco et al. (1998), and previously by Kochanek (1996b),
that the radio sources exhibit a strong correlation between their redshift
and flux density distributions.
Thus, even though complete redshift surveys may not exist,
it is still possible to construct with existing data
a statistically accurate redshift distribution for a given radio flux density.
This assumes that the correlation between redshift and flux
density distribution remains to be valid at flux levels
lower than observationally studied.
Since redshifts cannot be determined exactly for individual
sources, each of the
assigned redshifts at a given flux density will have an uncertainty
which can be accounted when
calculating cosmological parameters. Also, since the CLASS radio source
sample is substantially large, on average, the modeled redshift distribution
can be expected to represent the true redshift
distribution. Since no new radio source redshift surveys
have been published recently,
we use the parameterization of the flux$-$redshift relation
in  Falco et al. (1998)
to calculate the probable redshifts
of CLASS sources. For each redshift, we also assign
an uncertainty based on the error in the parameterization
presented by Falco et al. (1998; see, their Fig.~ 4).
Since no redshift surveys exist for radio sources with flux densities
less than  $\sim$ 200 mJy, we use the extrapolation of the flux$-$redshift
distribution to estimate the redshifts of these sources.
However, we assign
a slightly higher uncertainty for these redshifts than expected from the
simple extrapolation presented in Falco et al. (1998).
We assume that the model A in Falco et al. (1998) is the mean
redshift distribution, while models B and C, with an increase in
uncertainty, represents our higher and lower redshift distributions,
respectively. With redshift and flux density for each source, we calculate
the radio luminosity, $L$,  and its uncertainty. We do not consider any errors
in the flux density measurement as these
are likely to be small compared to the ones associated with
the lensing calculation.

In order to calculate the lensing rate for radio sources, we model the
lensing galaxies as singular isothermal spheres (SIS) and use the
analytical  filled-beam approximation (e.g., Fukugita et al.
1992). At redshifts $z \leq 4$, the analytical filled-beam
calculation  in Fukugita et al. (1992) agree to better than 2\% with
numerical calculations (e.g.,  Fig.\ 1 in Holz et al. 1998).

Gravitational lensing statistics are
affected by the so-called ``magnification bias'' (Kochanek 1991)
in which the number of lensed sources in the
sample can be different from an unlensed sample down to the same flux density
level. Thus, any calculation involving
lensed source statistics should account for the magnification bias
and associated systematic effects.
The effect of this bias, whether to  increase or decrease the number
of lensed sources, depends
on the slope of the number counts.
The magnification bias is
particularly pronounced in quasar lensing
surveys (Maoz \& Rix 1993), because the faint end of the
quasar luminosity function rises steeply, increasing the number
of lensed sources.   In Sect. 2.2, we discuss this effect
for radio sources based on the flat-spectrum radio luminosity
function.

Following CQM, if the probability for a source at redshift $z$ to
be strongly lensed
is $p(z,\Omega_m,\Omega_\Lambda)$, as calculated
based on the filled-beam equation, we can write the
number of lensed sources, $\bar N$,  as (see, also, Maoz et al. 1992):
\begin{eqnarray}
\bar N = & \sum_i p(z_i,\Omega_m,\Omega_\Lambda) B(L_i,z_i) g(\Delta \theta,\Delta f) \nonumber \\
 & \equiv \sum_i \tau(z_i) \;,
\end{eqnarray}
where $B(L_i,z_i)$ is the magnification bias for a radio source
at redshift $z$ with luminosity $L$, and $g(\Delta \theta,\Delta f)$ is
the selection function
defined based on image separation, $\Delta \theta$, and flux
ratio, $\Delta f$,
between components of the strongly lensed sources.
Here, the sum is over each of the radio sources in our sample.
The index $i$ represents each object; hence, $z_i$ and $L_i$ are,
respectively, the redshift, and the  rest-frame luminosity of the $i$th
source.

For simplicity, following Kochanek (1996b), we assume that
the selection function is simply a uniform function in the range
$0\farcs3 \leq \Delta \theta \leq 6\farcs0$, such that all lensed
sources in this range are recovered.
For the SIS model, the fraction of lensed sources
in this range of image separations is
0.917 (e.g., Kochanek 1996b). We have assumed that the image separation,
$\Delta \theta$, under the SIS assumption for foreground galaxies is
given by $\Delta \theta = 8 \pi (\sigma/c)^2$, where
$\sigma$ is the velocity dispersion of the foreground lensing
galaxies, and that the characteristic velocity dispersion for
a $L^*$ galaxy, $\sigma^*$, is 220 km s$^{-1}$ (see, Eq.~22 in Kochanek 1996b).
Given that the observations are carried out to a much lower flux
density level than the flux density of the observed source,  and that the
candidate lensed sources are selected when flux  ratios between strong
components are $\leq$ 10 (Browne et al. 1997),  it is likely that the
selection function is independent of the flux  ratio between
lensed images. For SIS models, the fraction of lensed sources with
image flux ratios $\leq$ 10
is 0.9997,  and thus, for the purpose of this calculation we take
$g(\Delta \theta,\Delta f)$ to be a constant with numerical value of 0.916.

\subsection{Magnification bias for radio sources}

The bias, $B(L,z)$, can be calculated based on the radio
luminosity function for background sources at redshift $z$, $\Phi(L,z)$:
\begin{equation}
B(L,z) = \frac{ \int_{A_{\rm min}}^{\infty} \Phi(L/A,z)\, P(A)\, dA\, d(L/A)}{\Phi(L,z)\, dL},
\end{equation}
where $P(A)dA$ is the probability distribution of amplifications $A$.
The GHz radio luminosity function for flat-spectrum sources,
and its evolution,
is still not well determined observationally.
For the purpose of
the present paper, we follow the work of Dunlop \& Peacock (1990),
where luminosity
functions are calculated for sources at 2.7 GHz. Since we are
dealing with a sample of flat spectrum sources, we can safely assume
that the 1 to 10 GHz luminosity function is equivalent to that
at 2.7 GHz.
We use the pure luminosity-evolution model (PLE) for flat-spectrum
sources, which is motivated by optical
quasar and X-ray AGN luminosity functions (e.g., Boyle et al. 1987):
\begin{equation}
\Phi(L,z) = \Phi_0 \left[ \left(\frac{L}{L_c(z)}\right)^{\alpha_1^*}+\left(\frac{L}{L_c(z)}\right)^{\beta_1^*}\right]^{-1},
\end{equation}
where $\alpha_1^*$ and $\beta_1^*$ are the
 faint and bright end slopes of the luminosity
function with respect to the critical, or break, luminosity $L_c$.
For the purpose of this paper,
the quantity $L$ is the radio luminosity (in W Hz$^{-1}$ sr$^{-1}$).
Since this luminosity function is defined in terms of an
element $d\log L$ instead of the $dL$ required in Eq.~2,
following King \& Browne (1996), we rewrite the
luminosity function in terms of a linear element, with new
slopes $\gamma_1$ and $\gamma_2$ below and above the critical luminosity:
\begin{equation}
\Phi(L,z) = \frac{\Phi_0}{L_c(z) \ln 10} \left[ \left(\frac{L}{L_c(z)}\right)^{\gamma_1}+\left(\frac{L}{L_c(z)}\right)^{\gamma_2}\right]^{-1}.
\end{equation}

The critical
luminosity, $L_c$, has been found to evolve with the form:
\begin{equation}
\log L_c(z) = a_0 + a_1 z + a_2 z^2.
\end{equation}
In Table~1, we list each of the coefficients.

\begin{table}
\caption[]{The adopted luminosity function for  radio sources
assuming a pure luminosity evolution model based on
Dunlop \& Peacock (1990)}
\begin{flushleft}
\begin{tabular}{cc}
\noalign{\smallskip}
\hline
\noalign{\smallskip}
Parameter & Value \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
Log($\Phi_0$/Mpc$^{-3}\Delta$ Log L$^{-1}$) & -8.15 \\
$\alpha_1^*$ & 0.83 \\
$\beta_1^*$  &  1.96 \\
$\gamma_1$  &  1.83 \\
$\gamma_2$  &  2.96 \\
$a_0$    &    25.26 \\
$a_1$    &   1.18 \\
$a_2$    &   -0.28 \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{flushleft}
\end{table}

Since we are using the SIS model, the minimum
amplification, $A_{\rm min}$, is 2 and the probability distribution
for amplifications, $P(A)$, is $8A^{-3}$ (see, e.g., Maoz \& Rix 1993).
The magnification bias can  be written as (Maoz \& Rix 1993):
\begin{equation}
B(L,z) = \cases{8\left(\frac{L}{L_c}\right)^{\gamma_2-3}\left(\frac{1}{3-\gamma_1}-\frac{1}{3-\gamma_2}\right)+\frac{2^{\gamma_2}}{3-\gamma_2}, & $L > 2 L_c$; \cr
\frac{2^{\gamma_1} \left(\frac{L}{L_c}\right)^{(\gamma_2-\gamma_1)}}{3-\gamma_1}, & $L_c  < L < 2 L_c$; \cr
\frac{2^{\gamma_1}}{3-\gamma_1}, & $L_c  > L$. \cr }
\end{equation}

In Fig.~2, we show the magnification bias as a function of radio
luminosity using
the luminosity range for most of the sources in the CLASS Survey. For
sources  with luminosities such that $L(z) \leq L_c(z)$,
the magnification bias is simply determined by the slope $\gamma_1$
and is numerically equivalent to $\sim$ 3.04.

\begin{figure}[ht]
\vspace{6cm}
\caption{The calculated $B(L,z)$ vs. $L$ for sources at
redshifts, $z$, of 0.5 (solid), 1 (dashed) and 1.5 (dotted) and 2
(dot-dashed). When $L(z) \leq L_c(z)$,
the magnification bias is a constant determined by the slope of
the lower end of the luminosity function $\gamma_1$}
\end{figure}

\subsection{Properties of lensing galaxies}

The probability of
strong lensing depends on the number density and
typical mass of lensing galaxies.  For singular isothermal spheres,
this factor is conveniently represented by the dimensionless parameter
(Turner, Ostriker \& Gott 1984):
\begin{equation} F\equiv
16\pi^3n_0R_0^3\left(\sigma\over{c}\right)^4\; .
\end{equation} Here $n_0$ is the number density of galaxies, $R_0\equiv
c/H_0$, and $\sigma$ is the velocity dispersion.  The
parameter $F$ is independent of the Hubble constant, because the
observationally inferred  number density is proportional to $h^3$.  We
can estimate $F$ at a given redshift from the galaxy luminosity
function, which we describe based on the Schechter function (Schechter 1976),
in
which the comoving density of galaxies at redshift $z$ and with
luminosity between $L$ and $L+dL$ is:
\begin{equation}
\phi(L,z)\, dL=\phi^*(z)\left[L\over{L^*(z)}\right]^{\alpha(z)}
e^{-L/L^*(z)}\, dL\;.
\end{equation}
In order to relate velocity dispersion,
$\sigma$, with luminosity, we assume a dependence between
absolute magnitude, $M$, and $\sigma$ of the form:
\begin{equation}
-M = a + b \log \sigma,
\end{equation}
which is known as the Faber-Jackson relation for early-type galaxies
(Faber \& Jackson 1976) and the Tully-Fisher relation for spiral galaxies (Tully \& Fisher 1977).

Thus, using Eqs.~8 and 9, Eq.~7 can be written as (Fukugita \& Turner 1991):
\begin{equation}
F= \frac{16 \pi^3}{c H_0^3} \phi^* \sigma_*^4 \Gamma\left(\alpha+\frac{10}{b}+1\right)\; ,
\end{equation}
where $\Gamma$ is the normal gamma function and $\sigma^*$ is given
by the characteristic magnitude $M^*$: $-M^* = a +b \log \sigma^*$.

To estimate $F$, we use a recent determination of
the foreground galaxy
luminosity function by Zucca et al. (1997) based on
observations of 3342 galaxies in the ESO Slice Project (ESP).
A comparison between the ESP luminosity function and
the ones previously used in
lensing statistics calculations (e.g., Kochanek 1996, Falco et al. 1998)
suggest no large variations. Thus, we expect our $F$ parameter
to be within the uncertainty of previous $F$ parameter estimations.
However, we note one change in our estimate for $F$ from a
recent study of lensed source
statistics: We consider lensing galaxies to be composed of
both early-type as
well as spiral galaxies. This is contrary to the recent suggestion by
Chiba \& Yoshi (1998) that spiral and dwarf-type
galaxies do not contribute to the observed lensing rate.
We argue against this possibility simply based
on the observational data, where
spiral galaxy lenses have been found
(e.g., B1600+434 in the present CLASS sample, Jaunsen \& Hjorth 1997;
Koopmans et al. 1998).
Zucca et al. (1997) find that  the
luminosity function for galaxies is represented by a Schechter
function with parameters:
\begin{eqnarray}
M^*_B= & -19.61^{+0.06}_{-0.08}\; ,\qquad \alpha=-1.22^{+0.06}_{-0.07}\; ,\qquad  \phi^*=0.020 \pm 0.004 \ h^3{\rm Mpc}^{-3}\; .
\end{eqnarray}
These parameters agree with the recent estimation of the
luminosity function of known lenses (Kochanek et al. 1998; see their Fig.~4).

In order to derive the characteristic velocity dispersion $\sigma^*$
for the observed $M^*$, we use the following Faber-Jackson and Tully-Fisher
relations:
\begin{eqnarray}
-M_B^\ast + 5\log h &=& (19.37 \pm 0.07) + 10 (\log \sigma_E^\ast - 2.3)
   \qquad \mbox{\rm for E} \nonumber \\
-M_B^\ast + 5\log h &=& (19.75 \pm 0.07) + 10 (\log \sigma_{S0}^\ast - 2.3)
   \qquad \mbox{\rm for S0} \nonumber \\
-M_B^\ast + 5\log h &=& (19.18 \pm 0.10) + (6.56 \pm 0.48) (\log \sigma_{Sp}^\ast - 2.05) \qquad \mbox{\rm for Sp},
\end{eqnarray}
as presented by de~Vaucouleurs \& Olson (1982) for early-type galaxies (E/S0)
and Fukugita et al. (1991) for spiral galaxies (Sp).
To estimate the overall $F$ from individual contributions,
we use the galaxy fractions presented by Postman \& Geller (1984)
with ratios E:S0:Sp=12$\pm$2:19$\pm$4:69$\pm$4. These
ratios also agree with the relative numbers of spiral and
early type galaxies in the Southern Sky Redshift Survey
(Marzke et al. 1998).
In Table~2, we list these parameters and estimate for $F$ using the
luminosity function from the ESP survey.

\begin{table}
\caption[]{$F$ value based on the ESP luminosity function}
\begin{flushleft}
\begin{tabular}{cccc}
\noalign{\smallskip}
\hline
\noalign{\smallskip}
Type & Fraction & $\sigma^*$ & $F$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
E  & 0.12 $\pm$ 0.02 & $210^{+10}_{-11}$ & 0.009 $\pm$ 0.004 \\
S0 & 0.19 $\pm$ 0.04 & $194^{+12}_{-10}$ & 0.010 $\pm$ 0.003 \\
Sp & 0.69 $\pm$ 0.04 & $131^{+15}_{-14}$ & 0.006 $\pm$ 0.004 \\
Total &             &                   & 0.026 $\pm$ 0.006 \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{flushleft}
\end{table}

The best estimate for $F$ is 0.026 $\pm$ 0.006, with a relative
contribution of 31\% from spiral galaxies. Such a spiral
galaxy contribution agrees with the estimate by
Helbig (1998) that 2 of the
6 known lensed CLASS sources are due to foreground spirals.
This observation also justifies our inclusion of
spiral galaxies in the $F$ parameter estimation.

Our estimate for $F$ is
a factor of 2.5 higher than the value used by Chiba \& Yoshi (1998).
According to Kochanek et al. (1998), the two luminosity functions
used by Chiba \& Yoshi (1998) are the two models most
discrepant with the luminosity function from known lenses.
Using a low $F$ value can decrease the number of expected lensed sources
 enhancing the significance of
a cosmological constant in producing strongly lensed sources.
In order to obtain reliable estimates of the cosmological parameters
based on statistics of lensed sources, as well as for comparative
purposes, a consistent value of $F$ is needed among different studies.
We note that our estimate for $F$ is consistent with previous
estimates by Kochanek (1996a,1996b) and Falco et al. (1998).
Since there could be additional errors,
we allow for a slightly higher uncertainty (30\%)
and take $F$ to be 0.026 $\pm$ 0.008. This estimate
for $F$ is factor of four less than the value we recently estimated
for gravitational lensing in the HDF (CQM). This was both due to
the factor of 2 higher number density of sources in the HDF as suggested
by its luminosity function (Sawicki et al. 1997) and our partly incorrect
assumption that all such sources are elliptical galaxies.
The revised constraints on cosmological parameters from HDF lensing
rate based on a more appropriate $F$ value could
be found in Cooray et al. (1998b).

We calculate the expected number of  lensed sources by
first estimating the redshift, luminosity and lensing rate
for individual CLASS sources
as a function of cosmology, with luminosity
used to account for the magnification bias.
We also vary the redshift according to flux$-$redshift correlation
and recalculate the expected number of strongly lensed sources.
In Fig.~3, we show the
expected number of strongly lensed radio sources in the CLASS survey
as a function of $\Omega_m$ and $\Omega_\Lambda$ when the mean redshift is
considered:  A universe dominated with $\Omega_\Lambda$ has
a higher number of multiply-imaged sources than a universe
dominated with a large $\Omega_m$. As shown in Fig.~3,
$\bar N$ is essentially a function of the combined
quantity $\Omega_m-\Omega_\Lambda$, which is mainly
due to a coincidence; the exact dependence is a function of
background source redshifts.
For background source redshifts in the range 1 to 3,
the curves are essentially $\Omega_m-\Omega_\Lambda$.
 We can use this degeneracy in the
lensing rate (e.g., Carroll, Press \& Turner 1992; Kochanek 1993)
to constrain $\Omega_m-\Omega_\Lambda$ rather than
$\Omega_m$ or $\Omega_\Lambda$ individually.
In Table~3, we list the expected number of strongly lensed radio
sources along the  $\Omega_m+\Omega_\Lambda=1$ line  as a function of
$\Omega_m-\Omega_\Lambda$. The error bar accounts only for the uncertainty
in redshift. We account for the error in $F$ when cosmological
parameters are estimated, which is facilitated by the
fact that the number of expected lensed sources
is directly proportional to $F$.

\begin{figure}[ht]
\vspace{6cm}
\caption{Expected number of lensed radio sources, $\bar N$
as a function of $\Omega_m$ and $\Omega_\Lambda$.
$\bar N$ is constant along lines of constant $\Omega_m-\Omega_\Lambda$,
allowing for direct constraints on this quantity. Shown here
is the expected number of lensed sources for model A
in Falco et al. 1997}
\end{figure}

\begin{table}
\caption[]{Predicted number of lensed radio sources in the CLASS survey}
\begin{flushleft}
\begin{tabular}{cc}
\noalign{\smallskip}
\hline
\noalign{\smallskip}
$\Omega_m-\Omega_\Lambda$ & $\bar N$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
-1.0 & $55.1^{+8.0}_{-22.5}$\\
-0.8&  $30.7^{+2.4}_{-10.8}$\\
-0.6& $21.5^{+1.3}_{-7.0}$\\
-0.4& $16.6^{+0.8}_{-5.2}$\\
-0.2& $13.5^{+0.5}_{-4.1}$\\
0.0&  $11.3^{+0.4}_{-3.8}$\\
0.2& $9.7^{+0.3}_{-2.8}$\\
0.4& $8.5^{+0.2}_{-2.4}$\\
0.6 & $7.6^{+0.1}_{-2.2}$\\
0.8 & $6.8^{+0.1}_{-1.9}$\\
1.0&  $6.2^{+0.1}_{-1.8}$\\
\noalign{\smallskip}
\hline
\end{tabular}
\end{flushleft}
\end{table}

\section{Constraints on cosmological parameters}

\subsection{Observed number of lensed radio sources}

As listed in Sect. 1, the CLASS survey has produced six new lensed sources
during the first two sessions of its observations from a sample
of 6500 sources. We assume this number to be our canonical case.
However, to account for the possibility that a subsample of lensed sources
has been missed, possibly due to unaccountable selection effects and
other biases in the lens search strategy, we consider the
possibility that there are total of  ten strongly  lensed sources
within this sample and study the variation in cosmological
parameters from the canonical case. We also study the case when
there are four lensed sources.

\subsection{Constraints on $\Omega_m-\Omega_\Lambda$}

We follow CQM to constrain the quantity $\Omega_m-\Omega_\Lambda$ by
comparing the observed and predicted number of lensed radio sources.
We adopt a Bayesian approach, and take a uniform prior for
$\Omega_m - \Omega_\Lambda$  between -1 and +1, since
we do not yet have a precise determination of
this quantity, and because  we do not wish to consider cosmologies in
which either $\Omega_m$ or $\Omega_\Lambda$ lie outside the interval [0,1].
For values outside the interval of -1 to +1 in $\Omega_m-\Omega_\Lambda$,
we  assume an a priori likelihood of zero.
We do not constrain $\Omega_m$ or $\Omega_\Lambda$ separately;
thus, no prior is required for these quantities.
Since the prior for $\Omega_m - \Omega_\Lambda$ is uniform,
the posterior probability density is simply proportional to the
likelihood.

As derived in CQM, the likelihood ${\cal L}$ --- a function of $\Omega_m - \Omega_\Lambda$ --- is the probability of the data, given $\Omega_m -
\Omega_\Lambda$. The likelihood for $n$ observed sources (at redshifts
$z_j$) when $\bar N$ is expected is given by:
\begin{equation}
\langle {\cal L}(n)\rangle =\prod_{j=0}^n \tau(z_j) \times e^{- \bar N} \times
\left(1 + \sigma_{\cal F}^2 \left[ \frac{\bar N^2}{2}-n\bar N +\frac{n(n-1)}{2}\right]\right) \; .
\end{equation}
Here, $n$ is the observed number of
strongly lensed radio sources, while $\bar N$ is the
expected number of lensed sources for a given cosmology.
We have also taken into account the uncertainty in $F$ by defining
${\cal F} \equiv F/0.026$ and taking ${\cal F}$ to have a mean of unity
and standard deviation $\sigma_{\cal F}=0.3$ allowing for a
30\% uncertainty in $F$.
The factor ${\cal F}$ is then an overall correction to the
expected lensing rate, due to a systematic uncertainty in $F$.

In order to constrain $\Omega_m-\Omega_\Lambda$, we also need the
redshifts $z_j$ of the observed lensed sources. Using Table~1 of
Jackson et al. (1998b),
we obtained redshifts for 4 sources. For the 2 sources with no known
redshifts, we assume a source redshift of 1.5, consistent with other
four redshifts as well as the predicted redshift distribution for
radio sources in the CLASS sample. Changing these redshifts to
reasonably different values do not change our constraints
on the cosmological parameters greatly. We assume that there
are 4, 6 and 10 lensed sources in the CLASS sample.
This is primarily to study the variation in cosmological
parameters with the observed number of lensed sources.

\begin{table}
\caption[]{95\% confidence lower limits on $\Omega_m-\Omega_\Lambda$}
\begin{flushleft}
\begin{tabular}{cc}
\noalign{\smallskip}
\hline
\noalign{\smallskip}
Case &  $\Omega_m - \Omega_\Lambda$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
n=6, $z_{\rm mid} $& -0.29 \\
n=6, $z_{\rm low}$ & -0.58 \\
n=6, $z_{\rm high}$& -0.23 \\
n=10, $z_{\rm mid}$& -0.58 \\
n=10, $z_{\rm low}$& -0.90 \\
n=10, $z_{\rm high}$& -0.52 \\
n=4, $z_{\rm mid}$& -0.08 \\
n=4, $z_{\rm low}$& -0.28 \\
n=4, $z_{\rm high}$& -0.04 \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{flushleft}
\end{table}

In Table~4, we summarize our 95\% confidence lower limits
on $\Omega_m-\Omega_\Lambda$ for the three cases, with
$z_{\rm mid}$, $z_{\rm low}$, and $z_{\rm high}$ representing
the mid, low and high values for the redshift distribution
of radio sources. The cumulative probabilities
for observing six lensed sources with the three different estimates
of the redshift distribution is shown in Fig.~4.
As shown and tabulated, our lowest 95\% confidence on
$\Omega_m-\Omega_\Lambda$ is -0.58.
Accordingly, in a flat universe with $\Omega_m+\Omega_\Lambda=1$,
$\Omega_\Lambda < 0.79$ (95\% C.L.).
If the true redshift distribution for faint radio sources
is represented by the high end allowed by the flux$-$redshift
parameterization, then
$\Omega_m-\Omega_\Lambda > -0.23$ and $\Omega_\Lambda < 0.61$
(95\% C.L.). If there are ten lensed
sources in the present sample of $\sim$ 6500 sources in
the CLASS survey, assuming that four lensed sources have
been missed by current searches,
then $\Omega_\Lambda < 0.95$ (95\% C.L.). These results
are consistent with previous lensing statistics
with a 95\% confidence upper limit
on $\Omega_\Lambda$ of 0.57 (Kochanek 1996a) and
cosmological parameters based on high redshift
type Ia Supernovae (Riess et al. 1998).
However, these
limits, especially when $n=6$, are marginally inconsistent
with recent estimates of the cosmological parameters based on the combined
cosmic microwave background (CMB) power spectrum analysis
and the high redshift supernovae (Lineweaver 1998; however,
see, Tegmark 1998), with the
current best estimate for
$\Omega_m-\Omega_\Lambda$ of $-0.38 \pm 0.18$ (1$\sigma$).
To be consistent, we need more than the currently known six
lensed sources within this CLASS sample or a lower
redshift distribution for faint radio sources
than allowed by current studies ($z \leq 1$, see below) if there
are six or less lensed sources.
The case for a low redshift distribution can be rejected based
on the observed distribution of redshifts for known lensed sources.

As presented in Table 4, our lower limit on $\Omega_m-\Omega_\Lambda$
varies widely with the used parameterization of flux$-$redshift
relation for background radio sources. Since the number of sources
at the lower flux density end are quite large for the CLASS sample and that
the redshift distribution at this low flux density end
is not known, it is necessary that the redshift distribution
be accurately determined to obtain firm limits on cosmological parameters.
This can be carried out in two ways:
observational determination based on spectroscopic observations
of optical counterparts of radio sources with flux densities
less than 150 mJy or theoretical determinations based
on the number counts and other information (e.g.,
Jackson \& Wall 1998).

A comparison of Fig.~3 and Table~3, suggest that an upper limit
to $\Omega_m-\Omega_\Lambda$ can also be calculated,
in addition to the lower limit.
Since the number of lensed sources does not vary greatly
when $\Omega_m-\Omega_\Lambda >0$,
such an upper limit is  weak compared to constraints from other
cosmological probes. Also, this upper limit from lensing lies
outside the current range of interest in $\Omega_m-\Omega_\Lambda$ of
-1 to +1, and will depend on what one assumes for a prior
likelihood.
Also, flat cosmologies where $\Omega_m-\Omega_\Lambda$ is greater
than +1 are incompatible with current constraints on
cosmological parameters (e.g., White 1998). Therefore, we do not
attempt to calculate an upper limit to
$\Omega_m-\Omega_\Lambda$, hence a lower limit to $\Omega_\Lambda$
in a flat universe, using current lensing statistics.

Since the CLASS survey is expected to observe a total of
$\sim$ 10000 sources, it is possibile that the current
constraints on cosmological parameters may be improved.
In order to investigate this possibility, we used the full catalog
of $\sim$ 10500 sources publicly available from
the CLASS collaboration, which includes sources
that are planned to be observed, as well as the $\sim$ 6500
sources in the current sample.
The present constraints on $\Omega_m-\Omega_\Lambda$ do not vary
greatly when the true number of lensed sources for the whole
sample remains to be
what is obtained based on the current observed lensing rate.
If for some reason, the additional sample of $\sim$ 3500
sources were to contain twice as more lensed sources than
currently expected, then cosmological parameter estimates
change to be consistent with a high $\Omega_\Lambda$.
However, since this is not likely to be the case, unless the source
selection process is heavily affected systematics,
 an increase in the source sample is not likely to
improve the radio lensing constraints on cosmological
parameters greatly.

\subsection{Constraints on $\Omega_x-w$}

Recent studies have suggested the
existence of a scalar field as viable alternatives to the cosmological
constant
(see, e.g., Caldwell, Dave \& Steinhardt 1998)
 with an equation of state of the
form $w=P_x/\rho_x$, where $P_x$ and $\rho_x$ are the pressure and
density of the scalar-field,
respectively. Then, as the Universe expands
$\rho_x
\propto a^{-3(1+w)}$, where $a$ is the scale factor with $a=(1+z)^{-1}$.
The vacuum energy or the cosmological constant corresponds to
$w=-1$, while texture or tangled strings correspond to $w=-1/3$.

We modified  our lensing probability calculation
to account for the scalar field, and recalculated the likelihoods
using the same technique as above. We assume
a flat universe, and take $\Omega_m+\Omega_x=1$, where
$\Omega_x$ is the present day normalized energy density of
th scalar-field component. We assume a prior in which $\Omega_x$ is
uniform between 0 and +1. Our new constraints are summarized in
Fig.~5 on the $\Omega_x-w$ plane. The 95\% and 68\% upper limits
({\it thick solid lines}) from gravitational lensing
are labeled 95\% GL and 68\% GL respectively.
The 95\% confidence. upper limit on $\Omega_x$ can be written as
$\Omega_x \la (1.2 -0.5 w^2) \pm 0.05$.

In addition to lensing constraints, we also
show the resulting constraints on $\Omega_x$ and $w$
based on type Ia
supernovae at high
redshifts (95\% SN) as recently
studied by Garnavich et al. (1998; {\it dot-dashed
lines}) and constant  age  lines of the Universe
as a function of $H_0t_0$ ({\it dotted lines}).
For a Hubble constant, $H_0$, of 65 $\pm$ 10 km s$^{-1}$ Mpc$^{-1}$
(Riess et al. 1998) and a minimum age of the Universe,
$t_0$, from globular clusters
of $12.5 \pm 1$ Gyr (Chaboyer et al.
1996), a conservative lower limit on $H_0t_0$ is $\sim 0.8$ ({\it
dashed line}). For an age of the universe of $\sim$ 15 $\pm$ 2 Gyr,
$H_0t_0 \sim$ 0.90 to 1.15.
These three cosmological probes, Type Ia supernovae,
age and lensed sources, qualitatively agree with each other
when $0.5 \la \Omega_x \la 0.8$ and $w \la -0.4$.
These combined results rule out tangled strings with an equation of
state of the form  $w=-1/3$ as the scalar-field component.

As studied by Turner \& White (1997), the combined large scale structure,
age and supernovae data are consistent with $w\sim -0.6$ when
$\Omega_m \sim 0.3$ to 0.4. The constraints on $\Omega_m$ primarily
comes from the clustered mass-density in galaxy clusters
based on observed baryonic mass
combined with a nucleosynthesis determined baryonic
mass density of the universe,
$\Omega_b = (0.019 \pm 0.001) h^{-2}$ (e.g., Burles \& Tytler 1997),
resulting in $\Omega_m = (0.28 \pm 0.07) h^{-2/3}$ (Evrard 1997).
In Fig.~5, We have outlined a conservative
lower limit on the known matter content
considering these and similar measurements.
Even with known matter considered,
there is still a large region left on the $\Omega_x-w$ plane
to form a flat universe
allowing various possibilities for the physical nature of the scalar-field
component.
In future, constraints on the equation of state of the
unknown scalar-field component is
likely to be improved based on CMB anisotropy and
large scale structure data combined with standard cosmological
probes such as high redshift supernovae and gravitational lensing statistics
(see, Hu et al. 1998).

\subsection{Constraints on $\langle z \rangle$}

Since redshifts for radio sources with flux densities less
than 150 mJy are not accurately known, we can use the observed
lensing rate with an assumed  cosmological model to
constrain the redshift distribution of background
sources. This approach is very similar to
the one used by Holz et al. (1998) to constrain the redshift distribution
of gamma-ray burst sources detected by BATSE based on lensing
statistics.
For the purpose of this calculation, we vary the
redshifts of the background sources with flux densities less than 150 mJy,
while keeping the rest fixed at the appropriate redshifts as determined
earlier. Since we are only interested in an upper limit to the average
redshift of  faint radio sources,
we calculate lensing probabilities
as a function of $\langle z \rangle$, the {\it effective} average redshift,
under the assumption that all sources are at this redshift. This
methodology parameterizes our ignorance of the faint radio source
redshift distribution (see, Holz et al. 1998 for a discussion).
However, this assumption is incorrect given that at a given flux
density level, radio sources have a rather broad distribution in redshift.
Nevertheless, our approach is to suggest a possible upper
limit to the mean redshift of this distribution, assuming that
the distribution is not shaped such that more sources are at higher
redshifts than suggested by the mean. Since the lensing rate is
highly nonlinear in redshift, a slowly
decreasing distribution with increasing redshift can increase
the lensing rate faster than the assumed average value.
In general, our upper limit
underestimates the true average redshift.

In Table~5, we tabulate the 68\% confidence upper
limit on the redshift of the  subsample of sources
with flux densities less than 150 mJy and assuming that the
total number of lensed sources in the current CLASS sample is
either 6 or 10. This upper limit on the redshift is again
a function of $\Omega_m-\Omega_\Lambda$. If there are
6 lensed sources in the present CLASS sample, then
 $ \langle z \rangle
\, <\, 1.4 + (\Omega_m-\Omega_\Lambda) \pm 0.1$ (68\% C.L.).
Since the observed redshift distribution of known lensed sources in
the CLASS sample are between 1.3 and 1.6 (see, Table 1 in Jackson
et al. 1998b), cosmological
models where $\Omega_\Lambda$ is greater than 0.8
in a flat universe are disfavored.

\begin{figure}[ht]
\vspace{6cm}
\caption{Cumulative probability distribution for $\Omega_m-\Omega_\Lambda$,
if there are six strongly lensed sources assuming that the redshifts
are distributed according to model A of Falco et al. (1998) ({\it solid}),
higher ({\it dashed}), and lower ({\it dotted}) from this mean (see,
Sect. 3). The intercepts with the horizontal line show the
95\% confidence lower limits on $\Omega_m-\Omega_\Lambda$ (see, also,
Table~4)}
\end{figure}

\begin{table}
\caption[]{68\% upper limit on  $f_{\rm 8.4\, GHz} \leq 150\, {\rm mJy}\,$ source redshift distribution as a function of $\Omega_m-\Omega_\Lambda$}
\begin{flushleft}
\begin{tabular}{ccc}
\noalign{\smallskip}
\hline
\noalign{\smallskip}
$\Omega_m-\Omega_\Lambda$ & $n=6$ & $n=10$  \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
-1.0 & 0.57 & 0.84 \\
-0.4 & 1.05 & 1.39 \\
 0.0  & 1.44 & 1.78 \\
 0.4  & 1.83 & 2.24  \\
 1.0  & 2.37 & 2.88 \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{flushleft}
\end{table}

\begin{figure}[ht]
\vspace{6cm}
\caption{Constraints on the $\Omega_x-w$ plane based on gravitational lensing,
high redshift Type Ia supernovae, and globular cluster ages.
We have assumed a spatially flat universe such that
$\Omega_m+\Omega_x=1$. The dotted lines are the constant $H_0t_0$ values,
with $H_0t_0 \sim 0.8$ (dashed-line)
for the minimum age of the universe. The solid lines are the upper limits
based on gravitational lensing statistics at the 68\% and 95\% confidence.
the 95\% confidence contours from high redshift type Ia supernovae
are shown as dot-dashed lines. If the universe is flat, we can put an
upper limit on $\Omega_x$ based on the known matter content of the
universe as outlined and discussed in text}
\end{figure}

\section{Systematic errors}
As presented in Table~4,
a major uncertainty
comes from the unknown redshift distribution of faint
radio sources with flux densities less than 150 mJy. Thus,
it is unlikely that the current observational data
on radio sources would be useful to constrain
the cosmological parameters based on  CLASS results, unless
the redshift distribution for its sources is properly
established. Since the redshift and flux density
distributions for radio sources
are strongly correlated, it is not necessary that redshifts for all $\sim$
6500 sources be known. However, redshifts for a representative
subsample of CLASS sources are much needed. The determination
of redshifts would involve the process of optical identifications
and spectroscopic observations; a task that would take a considerable amount
of telescope time and man power to complete.
However,
as a result of this study, where we have shown
the strong variation in cosmological
parameters with a change in redshift distribution,
it is necessary that the true redshift
distribution be used to constrain the cosmological parameters.
We strongly recommend that a subsample of sources be
defined from the CLASS catalog  and be followed up optically to obtain
redshifts. The determination of redshifts would also aid
in the estimation of a reliable luminosity function for
faint radio sources,
which can be used to improve the calculation associated
with the magnification bias.

In addition to redshift distribution, the selection function for  lensed radio
source discovery process is badly needed. For the present calculation,
we have assumed that all lensed sources with image separations
between 0.3 and 6 arcsecs are recovered. However, the selection
function is likely to be complicated; it is much easier to
recognize a four-image lensed source than a doubly-imaged
lensed source. An initial study of such biases
as applied to the JVAS survey could be found in King \& Browne
(1996). However, as discussed earlier, since radio lens
statistics are much 'cleaner' than the optical ones, we do not
expect biases and selection effects to make a big difference
in present constraints on the cosmological parameters, unless
the selection function is heavily affected by such effects.
Nevertheless, King \& Browne (1996) found that the JVAS survey
contains at least a factor of 2 less doubly imaged sources
than expected from SIS and external shear models. Such a result,
if also confirmed for CLASS survey, suggests
the possibility that a large number of doubly-imaged sources
has been missed by the search process or that a bias not yet understood
affects the observations.

Apart from background sources, an understanding of the foreground lenses
is clearly needed. Use of different $F$ values by neglecting
certain galaxy populations can lead to rather diverse results,
as was recently demonstrated by Chiba \& Yoshi (1998).
Current
deep and wide-area redshift surveys are likely to
increase our knowledge on the foreground lenses and their
composition over the next few years.
A consistent description
of foreground lenses are also needed for the comparative purposes
between optical and radio lensed source sample studies.
Currently, however, this task is complicated
by individual studies suggesting different values for
the $F$ parameter, resulting from
different luminosity functions used to describe foreground lenses.
With increasing knowledge on the foreground lenses, an ideal approach would be
to use the luminosity function determined from known
lensing galaxies (e.g., Kochanek et al. 1998), including the
variation of their number density with redshift.

\section{Summary and conclusions}

Using flux density distribution for a sample of $\sim$ 6500 radio sources
observed during the first two sessions of the Cosmic Lens
All Sky Survey, and the observed number of
strongly lensed sources within this sample,
we have constrained the cosmological parameters.
We have considered the possibility that there are total of
six (as observed), four or ten lensed
sources within this sample to investigate the changes in our
constraints on the cosmological parameters.

We find that the expected number of lensed sources is primarily
a function of $\Omega_m-\Omega_\Lambda$. A comparison of the
predicted number of lensed sources with
the observed number allows us to constrain
its current value.
Based on the current determinations of the
redshift distribution for radio sources, our 95\% confidence lower
limit on $\Omega_m-\Omega_\Lambda$ is between -0.58 to -0.23
depending on the assumed model for the redshift distribution of
faint radio sources. For a flat universe with $\Omega_m+\Omega_\Lambda=1$,
then, $\Omega_\Lambda < 0.61$  to 0.79 (95\% C.L.). If there
are ten strongly lensed sources, the 95\% confidence lower limit
on $\Omega_\Lambda$ is between -0.90 and -0.52.
These limits are in agreement with previous limits based on
gravitational lensing (Kochanek 1996a, 1996b; Falco et al. 1998), and
are not in conflict with estimates based on high redshift supernovae
(viz., $\Omega_m - \Omega_\Lambda\sim -0.5\pm 0.4$ [Riess et al. 1998]).

As has been performed recently in various papers,
combining $\Omega_m-\Omega_\Lambda$ results from high redshift
supernovae measurements with
$\Omega_m+\Omega_\Lambda$ results from CMB power spectrum analysis
constrains $\Omega_m$ and $\Omega_\Lambda$ separately, with
much higher accuracy than the individual experiments alone.
We note that gravitational
lensing constraints on $\Omega_m-\Omega_\Lambda$ should also be
considered in such an analysis, to obtain a consistent picture
on the present cosmological parameters.

In addition to the cosmological constant, we have also studied
the possibility of a scalar field responsible for the
additional energy density of the universe. We have shown our
constraints on the $\Omega_x-w$ plane.
If there are six strongly
lensed sources in the present CLASS sample,
gravitational lensing statistics allow us to rule
out the region with $\Omega_x \ga (1.2 - 0.5 w^2) \pm 0.05$ (95\% C.L.).
We study the region allowed using combined constraints from
gravitational lensing statistics,
high redshift Type Ia supernovae distances and limits on
the age of the universe from globular clusters.
We have also considered the current estimates on the known
matter content of the universe.

Since we have assumed a redshift distribution for
radio sources to constrain cosmological models, alternatively,
we can constrain the redshift
distribution of faint radio sources based on the observed
gravitational lensing rate and an assumed cosmological model.
If there are six strongly lensed sources, the 68\% confidence
upper limit on the redshift distribution of flat-spectrum
radio sources with flux
densities less than 150 mJy at 8.4 GHz is
$ \langle z \rangle \, <\, 1.4 + (\Omega_m-\Omega_\Lambda) \pm 0.1$.

In order to obtain a much tighter estimate on $\Omega_m-\Omega_\Lambda$,
it is essential that the redshift distribution for radio sources at the
faint flux density levels be observationally
determined. Also, estimates of the flat-spectrum radio luminosity function
and the selection function in lensed source
discovery process are needed to complete the story.
We strongly recommend that statistically complete
optical spectroscopic programs be carried out to
obtain redshifts of faint background radio sources.
Until such redshifts are obtained, it is unlikely that a major
improvement could be made with respect to radio lensing constraints
on cosmological parameters.

\begin{acknowledgements}

I thank members of the CLASS collaboration for making their source
catalog publicly available, Phillip Helbig for useful correspondences,
and Jean Quashnock, Cole Miller, Andr\'e Fletcher, and John Carlstrom
for useful discussions. I would also like to thank the anonymous
referee for  constructive comments on the paper.
This work was supported in part by the
McCormick Fellowship at the University of Chicago,
and a Grant-In-Aid of Research from the National Academy of
Sciences, awarded through Sigma Xi, the Scientific Research Society.

\end{acknowledgements}

redpajama_set_name: RedPajamaArXiv


text:
My Life On-Purpose
How to Live My Life Better
Find Your Purpose
I'll Do It Myself (DIY)
Become a My Life Member
Poured Wisdom
The On-Purpose Puzzle
Explore Your Possibilities
On-Purpose: Uniquely Me
Presenter Exam
Power Up!
My Leadership
My Training Program
On-Purpose.com
2-Word Purpose App Tutorial
Are You Still Living in Trial and Error Mode?
This On-Purpose® Minute may rattle your cage a bit as I challenge what might be a hidden and unproductive point of view coloring your daily experience. More importantly, it may be setting the trajectory of your life far lower than it was designed to be.
Trials and errors in life are inevitable, but "trial and error" does not need to define our life approach.
As clarity around who you are comes to light, you'll discover a greater sense of peace despite the circumstances. Yes, the trials and errors will still come, but they won't toss you about as they have in the past. Be clear about who you are and whose you are.
The On-Purpose Approach is a strategic approach where you think and plan in order to advance that which is most important to you. If things go "wrong," then chances are you're able to better isolate the problem, address it faster and better, and get back on track.
In trial and error mode, everything appears to blow up all at once. Panic sets in as the matter appears to be overwhelming. The temptation is to throw up one's arms a quit. And this, unfortunately, begins another round of trial and error with lessons for improvement unlearned, confidence shaken, and more time passing. Done repeatedly it's a tragic waste of a human life.
How does "Trial & Error Living" affect us?
Here's a true account of a business client from years ago. My client came to me down and discouraged because his business was losing money and he wanted to sell it soon before the bottom fell out.
In reviewing the business, I realized that if he were to sell it there were a few things he could do to "window dress" or clean it up for sale that would make it far more appealing to a buyer. In anticipation of the sale, we began to make some of these small changes and tweaks to his systems.
Two months later, my client called to say he no longer wanted to sell the business because it was making money again; he was thrilled and wanted to keep it. Oddly enough, about a year later, he called me wanting to sell the business again because it was losing money again albeit after a substantial growth in sales.
We went through the same cycle—cleaning up a few things for the sale and the revenues turning around. It happened yet a third time in 18 months. The third time, however, the pattern of his emotional swings rather than the business matters caught my attention.
His business was basically sound, but there was something "wrong" with the business owner. Why was he on such an emotional roller coaster? The pattern was apparent—when the business showed bottom-line profits, he was happy. When the business showed bottom-line losses, he was sad.
It struck me that his emotional well-being was tied to a monthly financial statement. The P&L report literally colored his world in 30-day increments. Good news—good life. Bad news—bad life.
That's interesting, but here's where it got fascinating. I asked him if he knew how to read a financial statement. Of course not. He knew sales was the top number and profit and loss was the bottom number but everything in between was meaningless to him.
In effect, his emotional stability was tied to what was seemingly a random event—profit or loss.
He was a hard worker, but some months he made money and other months he lost money—it all appeared to be random to him. He was living in trial and error mode.
I gave him a basic primer on financial statements and had him enroll at the local community college in a course called "Finance for Non-Financial People." Once he understood his financial statements, he gained control of his business and, frankly, his emotions were not subject to the seeming randomness of the financial well-being of his business.
Within two years he had doubled his business.
He doubled it again by buying out his closest competitor.
He ran his business for another 10 years and eventually sold it for a handsome sum and is still living a good life off the profits he made.
He moved from trial and error to being proactive. Instead of running from his problems and ignorance, he ran into them and became educated.
Here's the point: trial and error mode isn't necessarily random.
Once we realize our contribution to the "randomness," we can actually take action to make our lives much more predictable and emotionally stable and calm. Look around to see if the "randomness" is affecting other people or if they seem to be on top of it. If others have it mastered then that's a clue to you that you're self-selecting trial and error over leadership and learning.
Improve your odds of success by looking for ways to reduce your variables.
Be strategic instead of stuck in trial and error mode.
Certainty isn't possible, but do your share to improve your chances of success and you'll grow as a person and find life isn't so crazy after all.
Sometimes the greatest benefit of a business advisor like me or a life coach isn't what we know technically. Rather it is our outside perspective to look into your life and simply ask, "Why are you doing it that way?"
So, why are you living in trial and error mode when you could be on-purpose?
Will My Life Make A Difference?
One of Life's Great Questions is, "How Can I Make A Difference?" It is an important question because it generally reflects an early mile-marker on the road toward a life of meaning, significance, and purpose. Realistically, it is a road filled with character-building potholes and detours for all but the fortunate few who scrape by relatively unscathed with the proverbial "stuff" happens.
Asking the question is an indicator of getting beyond oneself and thinking about the well-being of others. Here's the beginning of maturity. Age is irrelevant because the desire to make a difference is an attitude of the heart.
Making a difference with one's life is a process of becoming a leader. While a heroic act may have a defining element of difference-making and reveal strength of character in a moment, true difference making is a way of life being lived in service.
Few us will ever have that truly heroic moment of a dramatic rescue. In fact, our contribution is more likely in the ordinary, seemingly mundane, aspects of life. This is being a player in the game of life–a daily contributor. Placing yourself into the life of others at home, at work, or at play are all opportunities to give expression to your purpose is subtle ways, often far from the public eye or accolades, but nevertheless still heroic.
Purpose is the Essential Ingredient
Your 2-word purpose statements begins with a generic set-up of, "I exist to serve by …." Purpose is the primary source for the flow and development of your "difference making" capability and delivery. This matters over time as much as it does in a single act.
In fact, failing to act or to be the hero can be devastating to our psyche. Playing games of "what if" and "if only I had" are inevitable but ultimately counterproductive. Instead of being riddled with guilt or despair prepare for the next moment, the next and the next to be difference-making in the best sense of the concept.
Over the years, many a person has told me, "At some point in my life, I figured I needed to make a change in my life. I've discovered that my purpose is to make a difference." While celebrating this important statement, I'll ever so gently press and ask, "Have you considered how you are uniquely called to be a difference maker?" My hope is to move them toward a more specific understanding and depth of seeing their greater contribution in more specific terms.
You have the benefit of knowing your purpose in 2-words. It doesn't any more specific than this. Leverage your advantage over your old, "I don't know my purpose" self, to invest in giving your purpose greater expression in every life account. The inevitable byproduct of such gain is an attitude of gratitude and the overflowing desire to better serve others in any moment the opportunity presents itself. Watch, more often than not, you will be the right person at the right time.
To make a difference, first make a life for yourself.
Failure + Success = Growth
Success is fleeting. So is failure! Much like the weather, success and failure are bound to be in constant change and motion. The current climate of your life does not define you. In fact, such changing conditions are essential ingredients to growth. Your conditions have an effect on your circumstances, but you are not defined by your conditions.
Your 2-word purpose defines you best. It is your best, most pure sense of identity. Here, you are either off-purpose or on-purpose. This carries no judgment of success or failure, only information so you can adequately adjust so you are on-purpose, truer to who you are.
The success-failure only viewpoint ultimately undermines being an on-purpose person in creation. This overly simplistic binary approach doesn't account for the nuances of possible alternative outcomes. The win-lose only scenario too often raises the stakes beyond reasonable pressure. On one hand, this extrinsic pressure can motivate one to be super prepared to achieve success. On the hand, in the very moment when success or failure is on the line, the building pressure can overwhelm and cause one to choke resulting in failure.
Seeing success and failure as natural parts of your growing and improvement process is a healthy attitude. This isn't to say that we're to seek failure over success. Instead, factor in the opportunities found within "failure" as the alternative positive results of your endeavors. Such middle outcomes will redeem what might otherwise appear to be over dramatized as "a total loss."
Only we can inflict total loss on ourselves. Within the "I Grow" introduction page, you can read my story of Don Budge, the first person, who truly gave me permission to lose as a tennis player, yet win in the process. For me to grasp that losing is an essential part of the long-term process of growing into a champion was freeing, especially when the person teaching this lesson is the first ever Grand Slam tennis champion.
Success and failure are typically external measures of expectations, goals, status, bank accounts, and other such extrinsic rewards. While there's nothing inherently wrong the desire to material success and social standing, these are not the true measures of who you are.
Do you feel like a failure?
Choose How You Frame "Failure"
How you frame failure is more important to your overall wellbeing than any particular success-failure event. If you allow failure to define you as a "loser," then you will condition yourself to be just that. Weighting one's attitude and spirit to the point of discouragement and negativity will create the very outcomes and personality that fails. Oddly, you are winning at self-defeating because you've chosen it.
What if you embrace a different perspective? What if your perspective, not your current circumstance, is the problem? Stop looking outward and downward. Begin looking inward and upward to the freshness of the On-Purpose approach. This holds the key to flourishing. Start by knowing your purpose, owning it, and looking for ways to give it greater expression.
Edison's Edge on Invention
Thomas Alva Edison, the great inventor, saw "failure" as information. (See the video clip "I Haven't Failed" by my actor friend, Frank Attwood, who portrays Edison.) How many times have you tried and "failed" only to discover you were one step closer to success?
Gene Kranz, NASA Flight Director, in the movie Apollo 13 is attributed with saying, "Failure is not an option," in the face of saving the crew in space. When failure isn't an option, then what are the options?
Work-arounds
Fresh and exciting options must open up!
When we live scared, then we live to avoid losing instead of playing to win. Such defensiveness means we will lose more often because opportunities will not come our way, but we'll never know what we've missed. We'll cry foul or conspiracy or glass wall or some other blame game. With this irresponsible mindset, the best we can do is hold steady or lose ground. A shaky self-defeating cycle is set up that once set in motion gains momentum and without intervention will overwhelm us with despair or worse.
Here's what to do. Learn to play with reasoned abandon, a healthy (not full) detachment from failure or success. Rather, embrace the growth opportunity. Reasoned abandon may sound like an oxymoron, but it isn't. It means that we're disconnected specifically to the end result, so we're able to be actually more highly focused on the matters at hand. This frees us to live for the sheer joy and moment, yet be aware that what we're doing in the moment matters. Athletes call it being in "the zone." It is preparation and hard work intersecting with opportunity and pleasure to produce meaningful results.
Try this and in time you'll grow through your experiences and be on your way to true success. Turning "failures" into successes is what it means to be on-purpose person in creation.
The Sling Shot and The Bucket List
https://mylife-onpurpose.com/wp-content/uploads/2008/06/Glenn-Kevin-Sling-Shot.mp4
Glenn Hettinger, AIA and founder of the amazing home book series, Distinctive Homes of America, and I have been friend since 1982. We get together once or twice a year to just hang out, eat together, and do mutual business consulting for one another. Although, Glenn gets the better end of that deal! ; )
Because Glenn lives in the Jacksonville, FL and I'm in Orlando, we often meet at Daytona Beach as a middle spot. It was here where Glenn took my photo with the rainbow in my hand. But, that's not why this photo matters. It was what happened after this shot was taken.
That, my friends, is The Sling Shot.
Glenn said to me, "One time in my life, I would like to do something like that before I die." Oh my gosh, that's all I needed to hear. "Let's do it then, Glenn," I said. "It's like the movie, The Bucket List, grab opportunities when you can. And so on June 24, 2008 around 7:30 PM, Glenn scratched one adventure item off of his 'Bucket List" by parking are bottom in a big bucket and being flung high into the air.
What a privilege to be able to participate in such a simple request. And to have a bucket list buddy as well.
What about you? Do you have a bucket list – a list of things you would like to do, see, achieve before you die? Who do you know that has a dream that you can contribute to making it happen? Seize the moment and give it your best shot… sling shot that is!
Making A Difference?
"I wish I could believe that one person could make a difference."
Comedic Actress
"If you feel rooted in your home and family, if you're active in your community, there's nothing more empowering. The best way to make a difference in the world is to start by making a difference in your own life."
"One person can make a difference. In fact, it's not only possible for one person to make a difference, it's essential that one person makes a difference. And believe it or not, that person is you."
Robert A. "Bob" Riley
66th Governor of Alabama
email: info@on-purpose.com
© 2021 On-Purpose Partners
On-Purpose Home

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Posted 5:22 pm, May 31, 2019, by Tribune Media
MONROE COUNTY, Ind. — Months before the 12-year-old son of circus promoters died in Indiana – emaciated and covered in bruises – investigators in their previous Florida hometown found no evidence of abuse.
A haunting photo shows 12-year-old Eduardo Posso sitting in a chair, smiling after investigators said they found no signs of abuse or neglect in December, 2018. Eduardo died nearly 6 months later, and authorities say there is now evidence of extreme abuse.
Police arrested Eduardo's father, Luis Posso Jr., and stepmother, Dayana Medina Flores, Friday following the boy's death.
"Every time I tried, nobody would want to listen," Aurea Esmerlda Garcia, his mother, said.
Garcia said she didn't have custody of Posso, but tried to speak up when she thought something wasn't right.
"I went crazy. I didn't show him anything, but I was thinking in my mind, 'what can I do? Oh my God I have to do something because this is not right,'" she said.
Investigators believe the family traveled promoting circuses and arrived in Bloomington, Indiana just days before his death. They said the family previously lived in Myakka City, Florida, a rural area of Manatee County. Garcia said she didn't know they had left.
"You know looking back at it, we feel very confident that we did everything that we could to find signs of abuse and neglect and they did not exist at that time," said Randy Warren, a public information officer for the Manatee County Sheriff's Office. "Certainly nothing to the level of what would have occurred in his life in the last couple of weeks or months."
Warren said their office had investigated five allegations from different sources, including Eduardo's biological mother. They were in March 2017, September 2017, November 2017, February 2018 and November 2018.
Some incident reports showed concerns about bruises.
An incident report from September 2017 showed Luis Posso's mother as the reporting party. The report stated she complained Eduardo was hit several times on his head. Investigators stated during interviews with Eduardo and his parents it was stated he hit his cheek on his knee while trying to do a flip on the trampoline. Investigators wrote the case was unfounded, and no crime occurred.
Another incident report from November 2018 showed allegations Eduardo was hit in the face causing a bruise. The report states "this is a circus performer family. Investigation shows the child obtained the bruise during juggling practice. Case is unfounded."
Warren said multiple investigators found no signs of abuse or neglect.
"We go into the home do a very thorough investigation, checking the conditions of the home, looking at the attitude, mood of everyone that's involved, those that are being accused, speaking extensively with the victim, with siblings, looking for physical evidence that matches whatever that claim is and in every one of these cases after thorough work they had no signs no marks no signs of neglect or abuse," he said.
Warren said the last time they saw him was at the conclusion of an investigation December 3 when the photo of him smiling, sitting in the chair was taken.
"The child Eduardo was able to talk to us and denied that there had been any abuse, he was seemingly healthy, seemingly happy," Warren said.
A spokesperson for the School District of Manatee County said that month Eduardo was withdrawn to be home schooled.
"So we just don't know what happened from the time he moved in December to the time they reached your county in Indiana," Warren said.
Investigators with the Monroe County Sheriff's Office said they were called to Bloomington Hospital last Friday where Eduardo was pronounced dead. His stepfather and mother had driven him there when he wasn't breathing. The coroner said he was bruised, severely emaciated and weighed only 50-55 pounds with zero percent body fat.
"We believe within the past year things seemed to have gotten more severe," Monroe County Detective Lt. Jennifer Allen said.
Authorities said during a search of the Bloomington motel room where Posso and Flores stayed with Eduardo and his other siblings, they found wrist and ankle restraints, chains and a dog training shock collar. They said they found images on a cellphone of him in restraints with a dog shock collar on his neck in the bathtub. Investigators said both denied withholding food. Investigators said Posso admitted to some sort of abuse but did not admit to using restraints.
Investigators said Indiana DCS wasn't involved until they called Friday.
Investigators said the other children in the home appeared to be in relatively good health. They were placed with child services.
According to the Centers for Disease Control and Prevention, at least one in seven children have experienced child abuse or neglect in the past year. In 2017, it's estimated 1,720 children died from abuse and neglect.
"We know the dynamics that play into abuse are really complicated and often times people make reports and they feel like they're not followed up on or they feel like the outcome is not what they were hoping for I would encourage those people to continue to make those reports if they have those concerns," said Emily Perry, the executive director of Susie's Place Child Advocacy Centers.
Perry said signs of physical abuse can include marks and injuries that don't have a good explanation or in places where a child wouldn't typically bruise from playing or running around. Other signs can be children who are being isolated or who have significant changes in behavior.
"What we typically see in cases where maybe there's been abuse over an extended period of time, we see if there's been reports of concern and there hasn't been an effective intervention. There's times where that perpetrator may feel empowered by that, that they have ultimate control over that situation and no one will ever intervene or bring safety to that child. So we can see abuse escalate in those situations," Perry said. "It's another reason why you know kids need adults in their lives to be paying attention to them and need to continue to make those phone calls."
The question for Eduardo's mother now is what happened between the picture of him smiling and the day he died, and is it possible signs were missed?
"You have to see there's something wrong there, just don't go in and say, 'oh you're fine' and that's it," Garcia said.
Both Posso and Flores are expected to have initial hearings Friday. They're each behind bars on $500,000 bonds.
FOX 2 News is Everywhere You Go!
Streaming TV, podcasts, FREE apps, social media and much more! Click HERE to CONNECT with FOX 2 News.
Dangerous heatwave to arrive after remnants of Hurricane Barry pass through St. Louis
7-year-old girl drowns, driver in critical condition after vehicle goes into a pond in Warren County
Hazardous material leaks on I-55 following tractor-trailer accident
US House votes to condemn President Trump's racist tweets
Sheriff: Boy was restrained in bathtub with shackles, dog shock collar before death
Great-grandmother says California boy who died suspiciously begged not to be reunited with birth parents
Jeffrey Epstein allegedly hired private investigators and engaged in a campaign of intimidation against accusers in Florida
Pam Hupp deal leads to reopening of Betsy Faria murder investigation
A 12-year-old girl contracted a flesh-eating bacteria while on vacation in Florida
Man wore werewolf mask while terrorizing girlfriend's sleeping 2-year-old, sheriff says
'Maybe Mommy didn't mean to hurt me,' 5-year-old told doctor of possible abuse months before he was killed
Just minutes away from Columbine, students tried to stop another deadly school shooting
12-year-old Indiana girl contracts deadly flesh-eating disease during Florida vacation
DNA credited for breakthrough as man charged with Angie Housman's murder
Accused Angie Housman killer facing new sodomy charges
Woman on honeymoon becomes 10th U.S. tourist to die after Dominican Republic vacation
She FaceTimed her mom after a night out and then vanished. Her remains were found 6 months later
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But now that you've read our reviews, you're sure to want toys of your own. Check out where you can buy the toys and the companies who make them.
Amazon had a much better selection when they were partnered with Toys Я Us: now they let far too many scalpers sell things through their shops. Still, the site backs up its transactions, so you won't get cheated (other than the high prices).
TRU suffered just as much as Amazon when the two split: their site is hard to navigate and has misleading item listings. They've been getting better, but they're still not very good.
The toy store in the mall, KB is the biggest national toy chain. They're a bit expensive, but their discount sales can't be beat!
Comicshops are the main outlet for Diamond Distributors, and thus often have exclusives you can find nowhere else. Stop in and ask for a copy of Previews, the catalog of upcoming releases.
The world's biggest auction site, eBay sellers often have that hard-to-find figure you need to complete your collection.
A great toy merchant site. Caters to the MOC crowd by offering figures with Standard and High grading.
Lots of exclusives, plus a "free shipping" section.
Discounts on busts, statues, action figures and comics.
Toy Rocket offers a huge supply of new stuff as well as older, off the market toys. They seem to have a nice mix of mass-market and specialty product, but the prices are very high.


Video ads are an increasingly important component of digital advertising. A video is an effective way to give potential customers a visual representation of the product or service being sold. Also, the creator can take any number of creative routes to decide how best to showcase what is being sold: telling a story, making a funny recommendation, demonstrating how the product works, etc. However, videos can only talk once someone presses play. First, videos have to be found. That's where SEO comes in.
"To help viewers find their videos, B2B marketers must maximize the use of text," says Marcus Sheridan in his article, "How to Maximize Your Reach with Video SEO." To do this, Sheridan recommends posting the video's transcript along with the footage online. That way, search engines can pick up on key words when someone performs a search, making it easier for the casual internet surfer to find. To further increase the video's visibility, enhance your clients' SEO power by adding more words. Add titles, captions, and descriptions to broaden the variety of words search engines can pick up. The video will then have an even better chance of reaching a greater number of relevant viewers.
Transcripts also aid the potential customer who may not be able to watch a video. The person may not have the time to actually watch the whole thing or maybe they're someplace where they can't turn on the sound. Posting the transcript gives people who would potentially pass a video by the opportunity to receive its message through reading.
Another way to increase a video ad's SEO is to post the content or links to the video on multiple channels. Social media and blog posts referencing the video will only increase the number of media search engines and internet surfers who can find the video, and it's also a good way to advertise the video a bit. In the social media and blog blurbs, reel in viewers with brief descriptions of how the video will be relevant to its target audience. Having a better idea of what consumers will be watching is bound to give the video a higher click through rate.
Sure, there are a lot of advertising media that do just fine on their own, video included. But why not give it a little bit more of a boost to put it ahead of the competition's ads? Talk with your video advertising clients about their video/SEO strategies today.


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October 3, 2017 October 3, 2017 lyttleton Leave a comment
They said it would be difficult.
They weren't lying.
It can't be overstated, moving to a new country is a Herculean task, like scaling a brick wall with your bare hands.
Since my arrival in Madrid, just over a month ago, I have faced a slew of speed bumps and a not inconsiderable number of road blocks. My limited (read: pathetic) Spanish ability has been my greatest impediment, for sure, but hardly the only one. Some challenges are simply a matter of learning cultural differences and adapting; others, though, are intrinsically more complex.
Emily arrived almost two weeks ago, and less than 48 hours after deplaning, we were onto the apartment flat search. We had a hard deadline: Our AirBnB was only booked until October 1st. If we didn't have a place by then, we'd be scrambling to book short-term housing (another AirBnB or a hostel), an expensive proposition that would only exacerbate the financial obstacle inherent to finding a new home.
Madrid in September is much like Boston in September, in that the city is awash in new arrivals, both students and teachers. Lots of rooms open up and there's a mad dash to lock down a place to live before someone else takes it. In that way, Madrid is also similar to Brooklyn. So, take the two most difficult moves of my 10 Cities endeavor and combine them into one, and that's basically this last week.
There were a number of housing options to consider. The first, which is the most common for expats, was for Emily and I to book our own separate rooms. There are various websites and apps for flat searches, with the most often recommended (at least by our fellow expats) being Idealista. Others include Fotocasa and the Badi app, that one specifically designed for finding individual rooms. (Craigslist, my go-to in the States, is all but useless here.)
The benefit of renting a room is that you generally don't need to sign a lease or pay an agency fee. Of course, there are plenty of risks inherent in not being on a lease, and as someone who has moved into another person's abode on numerous occasions, I know firsthand how often those arrangements tend to turn into "This is my home, you're just renting a room here" situations.
Emily and I had come here with the intention of rooming together as we had in Boston; unfortunately, it's nearly impossible to find someone renting multiple rooms within the same flat. It happens, but they tend to be dorm-like situations where they specify only men or only women.
With room rentals out, we agreed that our best bet was finding a flat of our own. In the weeks before Emily's arrival, I'd done a fair amount of research on what two-bedroom flats were available. For anything that didn't look like a serial killer's lair, we were going to have to lay down a hefty pile of euros.
Fortunately, in my time here in Madrid, I had met many expats who were similarly on the search for a place to live. It was true, a two-bedroom flat was going to be costly, but if we added a third roommate we could mitigate some of the upfront costs while also decreasing the number of buried bodies we'd have to sleep on.
I spoke to two new friends who were interested in being our third roommate if we found the right place. The first was the one of the first people I met in Madrid, Calla, originally from Kentucky, currently in Madrid to teach English (unless stated otherwise, you can pretty much assume every American I'll mention is here to teach English). She was staying in a flat with a mixed group of semi-locals and had been on her own unfruitful housing search since before my arrival. Her search had nearly netted her a place to live on a few occasions, but each time one factor or another had undercut the candidate home and she had passed.
The second potential roommate was another new arrival who I had met through Calla, Megan from New Jersey. Her situation was similar to Calla's in that she had a semi-definite place to live, and could extend her stay if she needed to. She also had other potential arrangements, but I kept her in mind just in case. In a new country, it never hurts to keep one's options open.
Thus, waking up on Saturday morning, eight days before we had to be out of our AirBnB, Emily and I expanded our search to three-bedrooms. There were dozens of options on Idealista. To each one with promise, I would send a Google-translated email and then Emily would call. Though not fluent, Emily's Spanish is head-and-shoulders better than mine, so the responsibility for direct communication fell entirely on her.
By Sunday afternoon, we had contacted over two dozen different flats. Unfortunately, Madrid is a city that takes its weekends seriously, so few of them were returning calls. At the end of searching on Sunday night, we had only one viewing lined up, a three-bedroom near Prosperidad with a suspiciously small-looking living room.
The woman on the phone told us the viewing would be at noon, but recommended we show up early because it would essentially be first come, first serve.
"So, we should be there at 11?" Emily asked. The woman laughed. No, not quite that early.
We Americans are perhaps a bit overzealous, especially compared to Spaniards. As I was told by a Spanish man I met a couple weeks earlier, in Madrid, no one is on-time, ever. "Early" means arriving when you said. Arriving American-early (i.e. before the agreed upon meet-up time) is seen as weird, even for a job.
We decided to arrive at 11:50 just to be safe. That Monday morning, before the viewing, we happily received return calls on some of our other messages. We lined up two more viewings for later in the evening. By the day's end, we'd see a total of five.
We arrived at the Prosperidad flat by 11:45, believing we'd be in the frontrunning, but unfortunately, we weren't the only Americans on the prowl. A small crowd had already gathered outside the building. By the time the woman arrived to show the flat – at 12:15 – the sidewalk was full of potential renters. As our naïve optimism deflated, Emily and I returned to our phones to continue our search.
We liked it; didn't love it. The three bedrooms were large (the largest of any we saw in our search), but its "living room" was really just a wide hallway they had stuck a couch in. Still, we agreed, if the place were offered to us, we'd take it.
The next flat on our viewing list was the only one we found that wasn't being rented out by an agency. An older couple were privately renting out their own place. Emily and I both loved the spot, a well-maintained three-bedroom with an actual living room and a kitchen. We tried our hardest to be charming (well, Emily did; I mostly stood around staring blankly as the conversation switched from Spanish to English and back again).
The couple was sweet, but as we left, we each had the impression that we hadn't matched up to whatever indefinite measure they were using to judge possible tenants. Still, if offered, we'd take the place in a heartbeat (basically, this was how we felt above every place, especially as the day progressed and we grew increasingly pessimistic).
Our third stop of the day was mostly a lark, a fifth-floor, five-bedroom that was being rented at the same price as all the three-bedrooms we'd been looking at. I'd sent a message earlier in the morning, not expecting a response, but while Emily and I stopped for a beer – because that's what you do here – she got a call asking if we could stop by. We had time to kill before two other viewings, so we said we'd come right over and check it out.
As had been my suspicion, most of the bedrooms were on the smaller side. There was one "master" bedroom with a double bed, massive closet space, and its own private terrace. Otherwise, there were two half-sized rooms with fold-away beds, one closet they were trying to pass off as a bedroom, and a fourth, isolated room off of the kitchen that appeared to be the servant's quarters. It was an ideal home for a family with small children, so even though it had a large kitchen and one of the biggest living rooms we'd seen, we weren't sure it could work for us.
One plus in its favor, though, was that we could offer it to both Calla and Megan. We could afford the place with just three of us, but a fourth roommate would make the cost sharing even better and would make the landlord feel more secure with us.
The fourth flat Emily and I saw was immediately our favorite. It was spacious and very modern looking, with average-sized bedrooms and a nice location just a few minutes' walk from Parque de El Retiro. As Emily haltingly made her way through an all-Spanish conversation with the agent in a suit, though, it started to become clear, even to my clueless ears, that it was going to be an uphill battle to lock down this, or any flat.
Our fifth and final viewing of the day only confirmed those fears. Now 6:30 in the evening, Calla was able to join us. Unfortunately, one of the prerequisites for renting the space was that we have job contracts in Spain, something none of us had or would have for at least a few more weeks. It was clear that almost everywhere we hoped to live would have a similar requirement. Collectively, we had sufficient funds to pay rent and put down extra deposits, if required, but the rental agents were mostly uninterested in seeing our financial statements. No job contract, no flat.
There's been a lot of these this week.
After a full day of viewings and walking the city, the three of us dejectedly went for beers and one-euro sandwiches at 100 Montaditos. I was trying my hardest to focus on what we could accomplish, despite the major hurdles, but it was hard not to see the day as a failure. I concluded that if we hadn't found a place by Wednesday evening, we'd have to all go separate ways and hopefully find rooms on our own in less than four days.
Our discount sandwiches and beers led to, "Hey, want to grab another drink," which eventually snowballed into buying bottles of wine and whiskey and drinking until sometime past three in the morning. By the time Emily and I woke the next morning, hungover and weighted down by a pound of cream cheese and crackers we had drunkenly ate before crashing, our housing perspectives were looking even dimmer.
We spent the day in our beds searching for more flats and sending out our collective financial information to each agent who had given us their email address. We thought – hoped (prayed!) – that if we deluged them with our overwhelming proof of financial solvency, one of them might just say, "Okay, fine, take the flat, jeez!"
With no viewings lined up for the day, all we could do was send out messages while the whiskey/cream cheese ball in our guts slowly oozed out of our pores.
To our amazement, in late afternoon we received a somewhat confusing but ultimately wonderful message: We could come by the office and put down a 300€ deposit for the five-bedroom. If we wanted it, it was ours (of course, it wasn't really that simple, but we were sinking).
I hastily created a group Whatsapp message with Calla and Megan and told them our news: If they both wanted, we could all move in together. They, of course, would need to see the place for themselves to decide.
We arranged for the four of us to view the flat the next morning at 9 am. Unfortunately, there wasn't much time to decide. Emily and I had a viewing for a three-bedroom that evening, but otherwise, we'd been wholly unsuccessful getting any responses the day before and we were rapidly running out of time.
In a turn of events that will surely never be brought up again, Calla overslept and missed the viewing, so it was just Megan joining us. We "facetimed" with Calla while walking the flat (isn't technology kind of crazy?) so she could "see" the place for herself, but it wasn't the same.
After the viewing, with the agent needing to return to the office, the four of us met for a drink at a nearby café. We hashed out the pros and cons (con: small bedrooms; pro: not homeless) for over an hour. The decision was toughest for Calla who hadn't seen the place, but all of us were in a similar position, and taking the place was essentially an all-or-nothing situation (they wouldn't sign it over to just three of us).
I feel you, Screaming Face Eyes
Through some uneasiness, the four of us agreed: We'd take it.
As if it were that easy. Since none of us had job contracts, we had to throw down a giant pile of cash to secure the place; like, a Scrooge McDuck's money bin amount of money. In hopes of bringing down the cost, we offered a first-born child, but it turns out a) none of us have children and b) apparently child-based payments have fallen out of favor here in Europe. Who knew?
We managed to scrounge together enough money between the four of us that the agency eventually just said, "Yeah, whatever, take the keys, get out of our office, we're tired of looking at you." We did it.
No, it's not a perfect place. There have already been some hiccups (no hot water; insufficient number of building keys), and there will surely be more (which I'll document at a later date, I'm sure), but the important thing is, we have a place to live. We have a home.
Life in Madrid can begin in earnest.
It's been an arduous trip so far, and surely will continue to be, but my life on the road has taught me an important lesson: Take your victories where you can.
Moving, TravelAinBrB, alquilar, alquilar en espana, Apartment Search, Badi, Espana, Flat Search, Fotocasa, home, Housing, Idealista, Madrid, New Home, Renting, Renting in Spain, Spain, Travel, Travel Living
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Visiting Clergy
Photos – Recent Events
Photos – Churches Used
Photos – 30th Anniversary
Annual Church Meeting
Help in Andorra
If someone dies in Andorra
– Safeguarding
Other matters..
Saint George – an icon
This page will be used to show our visitors and talk a little about their backgrounds and experiences. Now that we have become a worship centre of St George's Barcelona, we have the big advantage of being able to welcome their chaplain, Revd John Chapman, each quarter and his ordained wife, Revd Deborah Chapman, even more frequently.
REVD DEBORAH CHAPMAN:
Deborah came to visit us in 2016 and has been instrumental in helping us find a way forward for the next three years, a way forward that includes up to ten visits a year from Revd Deborah
Born in a small town in Massachusetts, the first of 5 children, my parents took me to Argentina when I was a year old. This is how I grew up bilingual, with Spanish as my first spoken language. I have lived in five different countries in Latin America, as well as various places in the U.S., U.K., Spain, France, Papua New Guinea and most recently, in Sharjah (UAE). I am now a cleric with Permission to Officiate in the Archdeaconry of Gibraltar, accompanying my husband John who is the Chaplain at St George's Barcelona.
John, from Scotland, and I met in 1977, at the London Bible College, after I had moved to London in 1976 to study linguistics and then theology, having been accepted as a Bible translator with Wycliffe Bible Translators. We married in 1980, and thereafter worked together in Christian mission with the International Fellowship of Evangelical Students (1979-1991), and Latin Link (1991-2002) before both of us became ordained Anglican Deacons then Priests. I served in the Willesden Area of the Diocese of London from 2005-2013, before moving to the UAE for a year in 2013 and then on to Barcelona in 2014.
I accepted Jesus Christ as my Lord and Saviour one night when staying in a hotel in Copacabana, on the shores of Lake Titicaca in Bolivia – my apologies if you need an atlas to work out where that is! I was 16 at the time. Nothing has brought me more satisfaction in life than allowing my Lord to guide me into that fullness of life that He promises in John 10.10. My husband John and our two married children and their spouses – Matthew (and Belinda) and Kirstin (and Elliot) are a huge part of the full life He has given me, as is the pleasure of serving Him as an ordained minister. I also enjoy walking, swimming, reading, writing, painting, cooking and being an occasional academic.
REVD CANON MEL SMITH:
Mel came back to visit us in 2015 and agreed to start providing us with simple services recorded on CD for us to use for our second service each month. He came back again in 2016 to see how we were doing and how the CDs had been working, and then went away and produced more. He was back with us again in April 2017 and has been producing still more CDs for us to help us out for the second services for the rest of 2017.
Mel writes – I grew up in a pit village on the edge of the North Staffordshire Potteries. After sixth form I went on to study for a degree in Theology at King's College, University of London. After five years at King's I went straight on to ordination in my home Diocese of Lichfield and I retired from paid ministry four years ago . Most of my adult life has been lived in the Black Country, to which Kasia, my wife, and I moved when I was first ordained. We've been there ever since, apart from a three year spell in North Mallorca. Kasia and I have two children – Chris(topher), who's a musician, runs a recording studio and is a Trainee Minister in the Assemblies of God, and Helen, who works as a trainer and consultant caring for those with learning difficulties. For most of my ordained ministry my prime focus has been on building the Body of Christ by encouraging and enabling church people to discover a personal relationship with Jesus and to be blessed by God's Holy and Life-Giving Spirit. Since retirement I have enjoyed being able to give more time to biblical studies and, as a result, I have found that some of my opinions and attitudes have begun to be challenged and changed – praise God!
REVD. PAUL NEEDLE:
Paul came back to visit us for Harvest Festival in October 2014 and then came back again in 2015 and 2016. Then he said he had run out of harvest themed sermons, so instead of harvest time, he visited us in July and September in 2017. While John and Deborah Chapman enjoy a three month sabbatical in 019 he will join us again twice in 2019 – in June and August.
Paul is a Northamptonshire lad who went to Wellingborough Grammar School, when David Frost was a prefect. He was ordained in 1970 and served two curacies in Bradford and Pudsey (West Yorkshire). During that time he drifted into religious broadcasting with BBC Radio Leeds. From there a full time broadcasting career took him to commercial radio in Bradford, Peterborough and his home town of Northampton. He became News Editor and later Station Manager.
In 1985 he was appointed Director of Broadcast Journalism at City University in London. During his ten years there he also became Vicar (non stipendiary) of two country villages in Northamptonshire and worked as a freelance with BBC Radio Northampton. His radio work included five years hosting the religious Sunday Breakfast show and he still contributes to that programme occasionally, including doing a couple of them from his home in Spain. In 1996 he became Communications Officer for the Diocese in Europe, handling media matters, editing The European Anglican and updating the website news pages.
Paul and his wife Lynda came to the Costa Azahar, on the Mediterranean coast just north of Valencia, in 1997 when he became the first Priest-in-Charge of a small church which had just been granted a constitution and part of the Diocese in Europe. St Christopher´s now has three worshipping congregations along a 60 mile stretch of coast – each with its own drop-in centre where locals are made welcome and books, clothing and bric-a-brac are sold to support the church ministry. He retired as Vicar at the end of February 2012 and he and his wife divide their time between England and their Spanish home.
His interests include transport – trains, buses and canal boats, music (he plays in a jazz quartet), reading, and currently researching local history from the Spanish Civil War.
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Intex Aqua Star L Android Smartphone was launched in February 2015. It is priced in India at Rs. 7199 ($105.87), running on the Mediatek MT6582M processor with Mali-400MP2 GPU. The phone has 1 GB RAM and 8 GB of internal storage which is expandable using microSD, up to 32 GB.
The Aqua Star L has a 5 inches FWVGA, 480 x 854 pixels IPS display with a pixel density of 196 ppi. Coming to cameras, it has a 8 MP rear camera and a 2 MP front camera for selfies. It has a microUSB port for data syncing and charging. There is a accelerometer sensor present on the Aqua Star L. It is a dual SIM smartphone with support for 3G, USB OTG, Wi-Fi, FM Radio, Bluetooth and GPS too.
The Aqua Star L runs on Android OS, v5.0 (Lollipop) and all this is powered by a 2000 mAh battery.


Sometime in mid to late January a subtle change begins to creep into the minds of most people who live north of the 30th parallel. Frankly, we're tired of winter and ready for some sunlight. The beach seems to be a good place to dream of – maybe even a Caribbean island, say Barbados?
Recently, my wife and I were fortunate enough to spend a little time cruising around this tropical island – what an adventure! Our rental car seemed to come from a prior generation – complete with rusted body and 40 horse-power engine. The rental car 'agent' (actually a 17 year old surfer dude) gave us a map and said everything is easy to find – no problem, you'll have a great time.
By the time we returned the car, we were missing a couple of hubcaps – and maybe even some other parts that had fallen off during our drive on the rough roads. Did we get lost? Of course. There are no road signs in Barbados so you never really know what street you're on. Did we have a great time? Absolutely!
The beaches in Barbados are spectacular – the people very friendly. The weather – 82 degrees Fahrenheit – 28 Celsius – it was paradise.