Rev. J. Challis on the Elliptkities of the Platiets. 203 



true for the earth. Let us see what will follow from sup- 

 posing this equation to be generally true. If the mean den- 

 sity of the earth be d, then M = — , and q^ = —— — -.. 



Now the velocity (V) of propagation in a medium in which 

 p = k'-[^ — l), is -^ i/2 8, where the density is S. This 



may be shown by a separate consideration of this particular 

 case, or be inferred from a general proposition respecting the 

 velocity of propagation, which I gave in the Phil. Mag. and 

 Annals of Philosophy, for May 1830*, where it was proved 

 that if p + C = a^g^"*"", V may be found from the equation 



V2_ a^ §»(!+«) = 0. We have then, -—^ = -^ ; 9« = 



^S^ J o o 25 TT^ 3gC^8 XT T 1 U 



"V^J and q-c, or -^ = ^^-^. Now Laplace has 



calculated that according to this theory the ratio of the mean 

 density to the density at the surface of the earth is 2*42 ; and 

 according to our supposition the same ratio holds true for the 

 planets. 



Therefore if D = the mean density of the planet, ^^ — -r = 



25 TT^ X 2*4'2 



— — - — —— = 5\ nearly. Hence if u = the velocity of pro- 

 pagation in the material which composes the nucleus of the 



V beinff calculated 



earth, -^ = 5^ or v = J -^ 



from this, is found to be 10*13 times the velocity of propaga- 

 tion in air : — a result far from being improbable. Generally, 



gc^D ga „,, V c /~D /c^D a 



~%n — r = ^V-. Whence — = —^/-j- = ^/ —r-. — 



\ ad v^ V a s/ d W a^ d ' c 



m being the mass of the planet, M of the earth. 



* I have there shown that, the vclnciti/ of uniform 2}''0])agatioii 



the velocity in tlie medium rriL- .• i ^i ^ .- ^ 



= ^-= -. — y — -; — ; : — . 1 his equation bears the same relation to 



Najjenan log. oj the density 



the propagation of motion, as the equation, uniform velocity = -~. — —, to 



motion itself, and will not seem unimportant to those who consider tliat 

 the one ph;uuomenoii is nearly as frei|uent as the other. As the projiosi- 

 tion is quite new, and in some degree contradicts the received mode of 

 detenniiiing the velocity of propagation, it is not likely to meet with iin- 

 inediale attention : 1 have therefore adverted to it here. 



2 D 2 Tlie 



