MATHEMATICAL SECTION. . 39 
Nov. 24. Transit circle. Nucleus sharp and stellar and about 
10th magnitude. 
Dec. 2. Transit circle. Seeing poor. Extremely faint. Like a 
12.5 magnitude star, surrounded by a large but faint nebula. 
Dec. 8. 9-inch equatorial and power 132. The diameter (in de- 
clination) of the outer envelope, from a micrometer measurement, 
was 2’ 21”, the seeing being noted a little better than on Noy. 22. 
Occasionally I think I see the inner condensed disc, but am not 
sure of it; also think that at times there is an indication of a more 
or less rounded outline to the head on the south preceding side, but 
it is unstable. Cannot be sure of anything like a tail, and indeed 
any definite form other than an irregular circle is, after all, largely 
a matter of imagination. 
The communication gave rise to some comment and discussion 
on the difficulties encountered in making satisfactory observations 
of faint comets and also on the resisting medium in space. 
Mr. Taytor called the attention of the Section to 
A SLIGHT MODIFICATION OF THE NEWTONIAN FORMULA OF 
GRAVITATION 
with which he had been struck in reading Mr. Bates’ paper on “ The 
Physical Basis of Phenomena” recently read before the General 
Meeting. (See vol. vii, p. 51.) 
[Abstract. ] 
There is a widespread fallacy—particularly displayed by those 
kinematists who fancy they have an exceptional insight into the 
“mechanism of gravitation,” that this influence is simply a 
radiant emanation, necessarily observing the geometry of radial 
space relations, having as such emanation the same total energy 
on all concentric spheres whatever their radii, as in the case of 
luminous radiation for example. Of course every well instructed 
astronomer and physicist knows that this is not so. In truth “the 
inverse square” is not geometrical—not a square at all, having no 
relation whatever to surface——kut simply an algebraical second 
power, very much like the familiar “velocity squared” (mv X 1, 
or momentum multiplied by velocity), which forms the measure of 
all kinetic energy and which no one supposes to represent a square. 
