280 SECTIONAL TRANSACTIONS .—A*. 
it is possible to regard (1) as an equation for 8, inasmuchas (1) is only possible 
Gf, e.g., I(x) is everywhere > 0) for a unique value of 8, given O(z). 
By forming the Fourier transforms of both sides of (1) it is possible from 
examination of the zeros of the periodogram to find 8, and by a second 
Fourier transformation to compute J(z). For example, if g(t) is +/(1 — ?”), 
on) 
the transform | O(#) cos ut dt must vanish whenever uB is one of the zeros 
— 00 
of F;(x) ; hence, since u is known at these zeros, B is determined. 
(2) If the probability of a quantity having a magnitude between x and 
x -+ dx is f(«)dx in one ‘ measurement,’ the probability of asum s to s + ds 
from m measurements is f;,(s)ds, where 
(02) 
Firs) = | n—z (s + t)f(t)dt. 
Co 
The computation of f,(s), in successive steps, is very laborious, but if the 
transform g(u) of f(x) be constructed, 
I 
Co 
g(u) = ESI F(t) cos ut dt, 
—oo 
taking f(—t) = f(t), then f,,(s) is obtained rapidly and simply as 
on) 
{/(2n) } na g"(u) cos ut du. 
—0o 
In illustration the method is applied to the probability of a given score 
after a given number of rubbers at contract bridge. 
Incidentally the method offers a convenient proof of the theorem that the 
distribution function for errors the result of a large number of small errors 
tends to the Gaussian law as the number of independent sources of error 
tends to infinity. 
Dr. W. L. Marr.—Desargues configurations from a quintic curve (10.50). 
If P is a point such that the lines joining P to five fixed points are tangents 
to a cubic curve at these five points, the locus of P is a quintic touching the 
conic of the five points at these points and passing through the other fifteen 
points of intersection of the lines joining them. ‘The quintic can, however, 
be defined uniquely, and more simply, by these contacts and incidences, 
instead of as a locus. 
If six points are given on a conic, there are ten points P such that the 
lines joining P to the six points touch a cubic at these points. The ten 
points can be found as the relevant intersections of two quintics, but they 
can be shown independently to form the 103103 configuration arising in 
Desargues’ theorem on perspective triangles, whence it follows that six 
quintics associated with six points on a conic have ten common points form- 
ing a Desargues configuration. If P is one of these ten points, three other 
of the points are on the polar of P for the conic. ‘This result enables us to 
construct the configuration from one of the quintics and one of the ten 
points, and we find that the point can be chosen arbitrarily on the quintic— 
that is, that one quintic is the source of a single infinity of the 10,103 
configurations. 
