What is the difference between λ and Λ with regard to molar conductivity? I came across these equations (boxed in red) in a book:


  $$
\begin{align}
&amp;\therefore &amp; t_\mathrm{c} &amp;= \frac{u_\mathrm{c}}{u_\mathrm{c} + u_\mathrm{a}}\\
&amp;\text{and} &amp; t_\mathrm{a} &amp;= \frac{u_\mathrm{a}}{u_\mathrm{c} + u_\mathrm{a}}
\end{align}
$$
  At infinite dilution,
  $$\text{Also,} \quad t_\mathrm{c}^\infty = \frac{u_\mathrm{c}^\infty}{u_\mathrm{c}^\infty + u_\mathrm{a}^\infty}$$
  Since, $\lambda_\mathrm{c}^\infty = u_\mathrm{c}^\infty\times F$ and $\lambda_\mathrm{a}^\infty = u_\mathrm{a}^\infty\times F$
  $$
\bbox[3px,border:1px solid red]{
\begin{align}
&amp;\therefore &amp; t_\mathrm{c}^\infty \times \Lambda_\mathrm{elecrolyte}^\infty &amp;= \lambda_\mathrm{c}^\infty\\
&amp;\text{and} &amp; t_\mathrm{a}^\infty \times \Lambda_\mathrm{elecrolyte}^\infty &amp;= \lambda_\mathrm{a}^\infty
\end{align}
}
$$


Where $t$ refers to the transport number of an ion, and the subscripts $\mathrm{a}$ and $\mathrm{c}$ refer to an anion and cation, respectively.

From what I've learnt, the uppercase lambda $\Lambda$ refers to molar conductivity. But then what does the lowercase lambda $\lambda$ stand for?

Different sections within the same book give different definitions for $\lambda$, one being 'ionic conductance' and another being 'ionic conductivity', and I'm pretty sure 'conductance' and 'conductivity' are not the same thing.

I did try looking it up online, but Wikipedia wasn't much help.
Look in the Wikipedia article Ion transport number.

Lower case lambda, $\lambda$, is the molar ionic conductivity

Upper case lambda, $\Lambda$, is the molar conductivity. 

$\lambda = t \dfrac{\Lambda}{\nu}$

Where $\nu$ is the number of ions for the cation or anion in the molecule. So $\ce{Na3PO4}$ would have 3 cations per molecule, but only 1 anion per molecule.