524 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
Cl being indeterminate, hence 
, j dq, C\]i\ d^q. 
consequently (23.) becomes after substitution and differentiation with respect to «i. 
(24.) 
neglecting terms of the second order, and making Ci — 1 = — c'. 
If we assume CgUnd Wg being constants, and make gi=l— «iWi cotaiWi, 
</ 3 = 1 — ffiWa cot «iW 2 (24.) becomes 
but as and h are evidently identical, we shall obtain after reduction 
( 25 -) 
whence 
2\i-m 
^“ 5^2 , 
in which 
q =\ — w cot w, §- 2 = 1 — ^2 cot W 2 J 
n being the value of Wi at the surface of the entirely fluid mass, and (k) the value of 
k determined by experiment at the surface under atmospheric pressure. 
But from ( 22 .) we have 
(27.) 
hence for the determination of we obtain 

In obtaining these results, some assumptions had to be made which in the absence 
of experimental data can be considered only provisional ; but it will be satisfactory 
to perceive that the results themselves seem to be in accordance with what we would 
expect from known physical laws. When ai= 0 , ^i= 0 , §' 3=0 and k=\, its greatest 
value, k consequently increases as the thickness of the shell increases, or as the 
density of the surface stratum of the nucleus increases. But the cubical contraction 
is equal to the cubical dilatation of the mass if reduced again to the fluid state under 
the same pressure, and by a recognized physical principle the dilatation of a body is 
equal to its resistance to compression, or inversely proportional to its compressibility. 
But the compressibility of a stratum of the nucleus decreases as its density increases, 
hence the above result appears to be in conformity with an observed physical law. 
