1. A geometric property of the Farey series, discovered by L. R. Ford (1) is used in this note for the construction of a new path of integration to replace the circle carrying the Farey dissection, first introduced by Hardy and Ramanujan in their classical paper (2). This new path of integration will bring about an essential simplification in the treatment of the partition function and, in general, in the determination of the coefficients of modular functions of nonnegative dimension. It seems to me that the new path exhibits more clearly than the Farey arcs do the different contributions of the approximation functions near the roots of unity. Moreover, only two estimations have to be performed, and they are direct consequences of the obvious statements (3.2) and (4.1) concerning the circle over the diameter 0 to 1. Ford's theorem referred to above can be enunciated as follows: If in a complex r-plane we mark the points corresponding to the reduced fractions h/k and draw about the points