OF THE SOLID CRUST OF THE EARTH. 
337 
for deflections of the plumb-line do exist — such, for instance, as that near Moscow. 
Thus also in India a comparison of the amplitudes of arcs obtained by observation and 
by calculation shows the same. I have constructed the following Table to bring this to 
view. The data in the 1st, 2nd, and 3rd columns of numbers are derived from the 
Chapter on the Figure of the Earth in the volume of the British Ordnance Survey. 
Table I. 
Observed 
latitudes. 
Measured 
distances be- 
tween successive 
stations, in feet. 
Amplitudes between 
successive stations. 
Difference, 
or relative 
Deflections 
of plumb- 
Equivalent hori- 
Stations. 
Observed or 
astronomical. 
Calculated : 
a=20926184, 
b =20855301. 
deflection 
of plumb- 
line. 
line rela- 
tive to 
Punnae. 
force. 
+ means south. 
8 9 31 132 
o / // 
O / // 
// 
Retchapolliam ... 
10 59 42 276 
1029173-7 
2 50 1114 
2 50 10-32 
+0-82 
+0-82 
+0-0000040 g 
Dodagoontah 
12 59 52 165 
727386-3 
2 0 9 89 
2 0 1519 
-5-30 
-4-48 
-0 0000217 „ 
Namthabad 
15 5 53 562 
761813-4 
2 6 140 
2 5 55-48 
+5-92 
+ 1-44 
+0-0000070 „ 
Damargida 
18 3 15-292 
10734109 
2 57 21-73 
2 57 23-41 
-1-68 
- 0-24 
-0 0000012 „ 
Takal Ivhera 
21 5 51532 
1 105539-8 
3 2 36 24 
3 2 38-56 
-2 32 
-2-56 
-0 0000124 „ 
Kalianpur 
24 7 11-262 
1097364-9 
3 1 19-73 
3 1 13-62 
+6 1 1 
+3-55 
+0 0000172 „ 
Kaliana 
29 30 48 322 
1961138-0 
5 23 37 06 
5 23 41-65 
-4-59 
-1-04 
-0 0000050 „ 
I have calculated the amplitudes by means of the formula 
9 s r 
+ f 2C0S 
For finding such very small angles as the deflections, which are the differences of very 
much larger angles, no doubt the introduction of the square of the ellipticity would 
slightly modify the results in the last three columns ; but not so as to affect the use 
I shall make of them. It is seen from this Table (last column but one) that the 
deflections of the plumb-line, though small, are yet sensible quantities ; and they do not 
correspond with the heights of the neighbourhood of the several stations. 
The hypothesis, therefore, is not exact, but only approximately true, when applied 
generally, on a large scale. This, indeed, we might anticipate for other reasons. For 
example, if the crust below the ocean-beds has contracted or expanded at all (which no 
doubt it has) since it became too thick* to be able to adjust itself as it floated upon the 
* The late Hr. Hopkins pointed out that the amount of pi’ecession in the earth’s axis, caused by the disturb- 
ing force of the sun and moon, would be very different in amount as the solid crust was thin or thick ; and he 
made a calculation (Philosophical Transactions, 1839, 1840, 1842) based upon this idea, and showed that 
the crust must now he at least 1000 miles thick. M. Delaunay has lately read a paper before the Academy 
of Sciences controverting Mr. Hopkins’s idea — saying that the interior fluid must long ago have conformed 
to the motion of the crust in consequence of friction and viscidity, and be now moving with it as if the whole 
were solid. If the crust moved round a steady axis, this might be true. But this is not the case. The force 
which causes precession is continually tending to draw the earth’s pole towards the pole of the ecliptic — but 
does not move it in that direction, but, combining with the rotatory motion, causes it to shift through a small 
angle at right angles to the line joining the two poles. The extent of the angle must depend upon the force, 
the length of the infinitesimal portion of time, and the moment of inertia of the crust ; for the fluid, during 
this infinitesimal portion of time, will not have been able to acquire the new motion ; the crust, having no solid 
connexion with the fluid, will slip over it, with a twist. Suppose even that at the present instant the fluid were 
3 a 2 
