768 
AECHDEACON PEATT ON THE DEFLECTION 
Katio of density at depth 50 miles to D = 1-170 
Eatio of density at depth 150 miles to D = 1-210 
Eatio of density at depth 250 miles to D = 1-353 
Eatio of density at depth 350 miles to D = 1-498 
Eatio of density at depth 450 miles to D = 1-646 
20. Multiply the lines in the last series of Deflections by these numbers, and we have 
our final results, as follows : — 
Table op Deflections, caused by an excess or defect of matter throughout a semi-cubic 
space of 4 millions of cubic miles, the mean density of the excess or defect being 
part of the density of the earth at the depth of the centre of the cubic space. 
Depth of the centre 
of the 
semi-cuhic space. 
Distance of the middle point of the space from A, measured along the chord to 
the surface. 
379 miles. 
581 miles. 
781 miles. 
980 miles. 
1173 miles. 
50 miles 
1-940 
0*835 
0-457 
0-248 
0-118 
160 miles 
1-621 
0-803 
0-456 
0-252 
0-120 
250 miles 
1-383 
0-782 
0-483 
0-272 
0*131 
350 miles 
1-067 
0-749 
0-490 
0-286 
0-142 
450 miles 
0-663 
0-713 
0-425 
0-277 
0-145 
The effect of this calculation is to show how much uncertainty must always attend 
the exact determination of the true vertical, a thing which is absolutely essential in the 
calculation of the curvature of the several portions of the earth’s surface. It will be 
observed that the supposed defect or excess of density has been assumed to be only 
_i_th part of the density of the earth where the hidden cause may lie. But a much 
larger fraction might have been chosen. Eocks at the surface of the earth, even of the 
same kind, differ considerably in their density according to the specimens examined. 
The following are examples 
Basalt 
Chalk 
Coal 
Dolomite 
Felspar 
Granite 
Gypsum 
Hornblende 
Hornstone 
Limestone 
varies through 
varies through 
varies through 
varies through 
varies through 
varies through 
varies through 
varies through 
varies through 
varies through 
f ths of its mean density, 
^th of its mean density. 
■Jth of its mean density, 
^th of its mean density, 
^g-ths of its mean density. 
|th of its mean density. 
•|-th of its mean density, 
■^th of its mean density. 
3 ^th of its mean density, 
fths of its mean density. 
These show how probable it is that the several portions of the earth’s interior, although 
preserving roughly the general average of density, according to their position, as required 
