522 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
as a function of the latitude of that point, of the radii and ellipticities of the shell’s 
inner and outer surfaces, and of functions depending on the constitution of the shell 
and nucleus. Its value is not merely speculative, for it will be found to assist in ex- 
plaining certain apparent anomalies detected by observation in the variation of 
gravity at the earth’s surface, as well as in pointing out the limits assigned by obser- 
vation to the thickness of the solid crust. 
III. THE LAWS OF DENSITY OF THE SHELL AND NUCLEUS. 
8. The density f of a stratum of the mass when entirely fluid has been shown in 
Part I.* to depend on the pressure to which it may be subjected, and to the mole- 
cular properties of the fluid. The density of a stratum of the nucleus must evidently 
depend on the same circumstances, and hence we may assume its expression to have 
the same general form as for the entirely fluid mass, but yet containing variable 
indeterminate coefficients. 
If the solidification of the nucleus proceeded entirely from its centre to its surface 
no shell could at anytime exist, and as it will appear that it could not simultaneously 
solidify both from its centre towards its surface, and from its surface towards its 
centre, we can here consider only the latter case. When the solidification of the 
nucleus proceeds in this manner, its superficial stratum in contact with the inner 
surface of the shell will be the first to assume the solid state. As solidification must 
proceed very slowly from the slowness of the refrigeration of the entire mass, it is 
evident that the thickness of the stratum may be considered indefinitely small com- 
pared with the radius of the nucleus. Let its density in the fluid state be g>i, in the 
solid state ^ 2 , and let k being a function depending on the contraction of the 
fluid when solidifying. 
If, in conformity with the preceding remarks, we assume 
c, sin aw, 
0= , 
^ a 
c, and varying with a, the mean radius of the nucleus, we shall have to determine 
four quantities in order to arrive at a knowledge of the laws of density of the shell 
and nucleus. It appears, however, that the number of known conditions which these 
quantities must satisfy will not suffice for their complete determination, although it 
is possible to conceive how a new condition could be experimentally found by which 
the required number would be made up. For if the physical properties of the matter 
composing the earth’s interior resemble ’those of the matter at its surface, the form 
of k could be found with some degree of approximation, by a series of experiments 
on the contraction of fused matter at different densities resulting from differences of 
pressure. The conditions which can be at present determined are easily found thus : 
If the law of density of the shell be continuous, which must result from its mode of 
formation, and if the variations of a! and a, from refrigeration be neglected, we shall 
* Articles 6 and 7. 
