DUE TO THE WEIGHT OE CONTINENTS. 
209 
or 
A= 
IT 1 
2{i +1) 2 +1 
' i(i + 2)(2i— l) 
i—1 
a 2 —(}+1 )(2i+ 3)r 2 
i(i + V){2i + ^)a?r i 2 
— +1 )(2i + 3) — i 
3 
(V 2 —1)(2^ + 3) 
This value for A requires of course multiplication by appropriate factors involving 
the height of the continents and gravity. 
Even when i is no larger than 6. (41) differs but little from ir { ~ 2 (a Qj —r 2 ), at least for 
values of r not very nearly equal to cl 
A clearly reaches a maximum when 
H- 
o 
O 
(f 3 — 1) (2^ -h 3) 
For large values of i this maximum is nearly equal to 2 {{i —2 )/i} li 1 ci i 
From these formulas the following results are easily obtained. 
Table V. (a). 
i— 
2 
4 
6 
8 
10 
12 
Maximum value of A ... 
2'526 
1-118 
•959 
•894 
•859 
•836 
Value of r/a when A is max. 
0 
-714 
•819 
•867 
•895 
•913 
Plate 20, fig. 4, shows graphically the law of diminution of stress-difference for 
the even zonal harmonics, the vertical ordinates representing stress-difference and the 
horizontal ones the distances from the surface or from the centre of the globe. 
In order to find a numerical value of these maximum stress-differences which shall 
be intelligible according to ordinary mechanical ideas, I will suppose the height of 
each of the harmonics at the equator to be 1500 meters. On account of the small 
density of the superficial layers in the earth, this is very nearly the same as supposing 
that in the earth the maximum height of the continents above, and the maximum 
depth of the depressions below the mean level of the earth are each about 3000 meters. 
In the summary at the end I shall show that there is reason to believe that this is 
about the magnitude of terrestrial inequalities. 
Then by (33) we have to multiply the maximum stress-differences in the above 
table by 2(i-l)ivh/(2i-\-l), in order to obtain the stress-differences for the supposed 
continents in grammes or tonnes per square centimeter. 
Now w= 5'66 and A^l'SxlO 5 according to the above hypothesis as to height of 
continent; and the coefficient in i is of course different for each harmonic. 
By performing these multiplications I find the following results. 
MDCCCLXXXTT. 2 E 
