88 
Dr. Young’s remarks on the reduction 
do not extend in a transverse direction, when we compress 
them in a longitudinal one, as is obviously the case with some 
soft elastic substances: but this objection is removed by the 
experiment on the sound of ice, which affords, either accu- 
rately or very nearly, the same resistance to compression as a 
portion of water confined in a strong vessel ; and this it could 
not do, if the particles of ice were allowed to expand laterally 
under the operation of a compressing force. 
Mr. Laplace’s conclusion, respecting the precise propor- 
tion of the densities, is indeed derived from another supposi- 
tion respecting their variation, and would be somewhat modi- 
fied by the adoption N of this theory ; it would not, however, 
be so materially altered, as by any means to invalidate the 
general inference. It would therefore be proper to revise 
the calculations derived from the lunar motions and the ellip- 
ticity of the earth, and to employ in them a variation of den- 
sity somewhat resembling that which is here investigated. 
Indeed without reference to the effects of compressibility, it is 
obviously probable that the density of the earth should vary 
more considerably in a given depth towards the surface than 
near the centre, although the calculation, upon Mr. La- 
place’s more simple hypothesis, of a uniform variation, is 
much less intricate. It would however be justifiable, as a 
first approximation, to reject those terms of the series which 
would vanish if n and x were very small, and to makey = 1 
+ ax 1 ; and indeed this formula has in one respect an ad- 
vantage over the series, as it seems to approach more nearly 
to the law of nature, in expressing a resistance somewhat 
greater towards the centre, where the density is most aug- 
mented: we have then, if the superficial density be to the 
