922 General Notes. 
Now, if, in our hypothetical hollow sphere, we assume any point 
whatever, and draw a line through that point to the nearest and 
most distant points of the shell, this line will be a straight line, and 
the longest that can be drawn in the sphere ; hence it passes through 
the centre, and is the diameter. Now, pass a plane through this 
assumed point and perpendicular to the diameter, cutting the shell 
into two segments, corresponding to the two segments of the 
diameter made by the assumed point. 
Let R equal one segment of the diameter, and r equal the other; 
let Q equal the segment of the shell corresponding to R, and q 
equal the segment corresponding tor: then, since, by hypothesis, 
the density and thickness are everywhere equal, there results Q : q: : 
: 7’, and Q °? = q R’; but gravity varies in proportion to 
the duplicate ratios of the reciprocals of distance, R and r. t 
represent the gravity of the segment R? X q, and g represent the 
gravity of segment r° Q, at the assumed point, then we have G: 
1 1 
g::——:——-; therefore, G R? q =g r°’ Q. Now, since Qr 
Rg Q 
= q R? G = g: ie., gravity, at any point whatever, in this hollow 
point assumed: then will result G: gy: : R? : 1°; g = R? nM 
the centre r equals 0 and g = 0. They vanish together. _ 
As a matter of fact, however, this proportion and equation = 
true for two points only: viz., at the surface, when R = r, h 
the centre, when r = 0. y? Because the density varies wi 
the pressure, in the first place. Though the weight, i. e., the gravity, 
relative to that sphere alone, is greatest at the surface, in the hae 
of any given quantity of matter, yet, under the superimcum i 
pressure, the density of the inner sphere, composed of the sam 
matter, is greater than that of the entire sphere. : ‘ 
Again, the heavier matter, ie., the matter of the highest — 
ravity, during the process of free centralization, naturally 0. ys 
the nucleus of the sphere, throwing the lighter ma i 
surface, as we see in case of our earth. Thus, for two reasons, 
