MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
541 
IX. CALCULATION OF SOME OF THE CONSTANTS CONTAINED IN THE FORMULA 
OF THE PRECEDING SECTIONS. 
22. 1st. To find the numerical value of and n. It is evident that when D repre- 
sents the mean density of the earth, we should have 
(g’ 2 ) being the density of the shell’s outer surface, or in other words, the density of 
the first stratum solidified from the primitive fluid mass constituting the earth. To 
find D, I take a mean of the results of the best experiments which have been made 
for its determination, namely, of the experiments of Cavendish, Baily and Reich, 
or respectively of the numbers 5’48, 5‘68 and 5’44. The mean of these results is 
5*53 nearly. The density of granite, the crystalline rock which seems to form the 
base of all the sedimentary formations, is evidently that which must be used for (^ 2 *) 
This remark is important, because in all comparisons heretofore made of the mean 
and surface density of the earth, the mean density of the sedimentary rocks has 
been erroneously taken into consideration. From a comparison of the densities of 
granite obtained in different countries on the authority of different geological and 
engineering works, I have decided that the mean density of the rock cannot be less 
than 2*7. Adopting this value, the above equation becomes 
^(1 — W 2 cot ^ 2 ) = '6827 16, 
which is approximately satisfied by making 
14227 
= 16' 22". 
To find n, we have 
r? (^)w2 (^) 
]— ncotn 1—n^coin^ *682716 
Let (/c) = *7481, its least value found by experiment. Then 
'»g(r=;r5«s)=-0397i96. 
By trials I find that when w=154° 25', the quantity at the left side of the above ex- 
pression is *0396799, and when w=154° 24', it becomes *0398333; hence it lies 
between both of these values. 
When w=154° 24' 30", 
'»S:(rr^„)=-0397196, 
hence this value will serve for a first approximation. 
When (^)=*896, the greatest value found by experiment, we should have 
‘«s(t3W^5s)=-1180679. 
4 A 
MDCCCLI. 
