  This paper aims to develop the theory of Ford spheres in line with the
current theory for Ford circles laid out in a recent paper by S. Chaubey, A.
Malik and A. Zaharescu. As a first step towards this goal, we establish an
asymptotic estimate for the first moment $\mathcal{M}_{1,I_2} (S) =
\sum\limits_{\substack{\frac{r}{s},\frac{r'}{s'}\in \mathcal{G}_S \\ consec}}
\frac{1}{2\lvert s \rvert ^2} + \frac{1}{2\lvert s' \rvert ^2}$ where the sum
is taken over pairs of fractions associated with `consecutive' Ford spheres of
radius less than or equal to $\frac{1}{2S^2}$.

Number Theory