17 
of the numerator will be the quantity of black employed, 
which we may denote by b, so that the first term would 
become — The second term multiplied by n may be 
written in the form the limiting value of net is b, so 
that this term becomes ^ ; since it contains a term which 
ultimately vanishes it will disappear, so a fortiori all the 
remaining terms. So that we should get as the residual 
_ l 
white area Ae a 
This simple form of expression for the white area has been 
suggested by Mr. James Heelis in a letter to me. The atomic 
constitution of matter seems a bar to its perfect acceptance. 
It does not seem likely that we can so divide matter as to 
arrive at 0. In this, as in many problems, physical con- 
ditions- place limits to mathematical generalities. Never- 
theless, on account of the extreme smallness of atoms there 
will be no sensible difference whether we use this formula 
or the one suggested by me, which takes into account the 
atomic constitution of matter, for in the term 
pnp pn$ 
£ A -¥As-&c. 
the second term of the expansion — first term x ^ 
This will be so small as not to be sensible, and may therefore 
be neglected— and so, a fortiori, the remaining terms.. The 
above remarks will apply to the mixtures of other colours 
as well as black and white. 
“ On some early anticipations of Heliographic Signalling,’' 
by William E. A. Axon, M.RS.L. 
The use of the heliograph . in war is likely to gain ground. 
Nature (April 29, 1880, vol. xxi., p. 617) gives an instance 
in which a message was flashed by this means as speedily 
as by the electric telegraph. The following description is 
