MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
509 
but 
hence 
whence, finally, 
A=J-, 
oin-w” ' A < ' 
smn 
?>(«)= 
45 
■(-S) 
8M 
If this expression be written in the form 
45 K 
8 
then Q=Yq K, and (5.) will become 
^ 9 m'K. 
^—10 7 ^- 
( 11 .) 
In making use of either (6.) or (11.), a quantity P is introduced which depends 
upon certain numbers obtained from observation. One of these numbers is the ratio 
of the earth’s mass to that of the moon, and some uncertainty seems yet to exist as 
to its value*. The results obtained from using in (6.) or (11.) the different values of 
this number, which may be obtained by different methods, are much affected by their 
differences. 
In order to compare equation (6.) with that used in the Mecanique Celeste for 
finding the earth’s ellipticity, the following calculations have been made. 
If the equation in the Mecanique Celeste be used, we shall have 
If equation (6.) be used. 
17 
5 17_ 1 
-C— 305 
1 
T7_ 1 
^ — -C— 308 
-11 17_ 1 
n — j 2 ^r, E — 
■317’ 
The value of P which has been used in the application of (6.) is that which is given 
in equation (k.), Livre V. of the work of M. De Pontecoulant. 
9. After the formation of the external shell of the earth, the entire mass composed 
of that shell and of the internal fluid nucleus, may be supposed to rotate about an 
axis not differing much in position from the present terrestrial axis of rotation. If 
the angular velocities of the shell and nucleus about this axis were from any cause 
MDCCCLT. 
* Pontecoulant, Th^orie, &c., tom. iv., Note 3, p. 651. 
3 u 
