The object of this paper is to show how some formulae in Analytic Number Theory, in particular, the formula for N(T), the number of zeros of the Zeta-function between t = 0 and t = T, are easy deductions from the Generalised Poisson-Jensen formula. A similar method, using Green's function instead of the general function g(s) of § 2, has been published by F. and R. Nevanlinna (Math. Zeitschrift, 20 (1924), and 23 (1925), but the result contained in (vi) below appears to be new, although the writer has not been able, as yet, to make any effective use of it. It is clear that other applications could be made, but it seems sufficient to give here an indication of the method. The notation throughout is the usual one, and the references are to the Cambridge Tract by E. C. Titchmarsh on “The Zeta-function of Riemann”. Finally, I am indebted to the referee for the reference to the papers of F. and R. Nevanlinna.