FOR DETERMINING THE MEAN DENSITY OF THE EARTH. 
337 
of measure. In all the preceding formulae, c must now be made =1. The earth’s 
radius corresponding to Harton is then 1662T7, its attraction at the lower station 
47r f SttI 
is y X 1662T7xD, or 69625 xD, and at the upper station j 69625— y^xD. The 
attraction of the shell upon the upper station, or the difference of attractions of the 
indefinite horizontal stratum upon the upper and lower stations, is 47rxd. The for- 
25 
mula applicable to the depression of the sea will be —xd; and that applicable to any 
other elevation or depression will be ^ ^ . ^here all linear measures are to be 
referred to the mine-depth as unit. 
58. On my making known that information on the inequalities of the ground would 
be required for the final calculations, the Mayor and Corporation of South Shields 
directed that the necessary surveys should be made, and the execution of this work 
was entrusted to Christopher Thompson, Esq., Surveyor for the Corporation. This 
gentleman entered fully into ray views, and, after the proper surveys for elevation, 
furnished me with a map extending about three miles in all directions round Harton, 
with the elevations above high water in feet marked at numerous points. I found that 
a line might be drawn, nearly ten depths distant from the upper station, touching the 
cliffs of Tynemouth and the cliffs south-east of Harton, and ranging for some distance 
along the coast of Durham. I therefore drew a line parallel to this at ten depths 
distance from the upper station, and divided the whole country into squares (with 
sides of one depth each) whose sides were parallel and perpendicular to this. These 
squares I grouped as appeared most convenient, as will be seen in the Map, Plate XII. 
fig. 4 (the principal object being to secure a proper representation of Jarrow Slake 
and the Valley of the Tyne), and adopted for each group the elevation in feet above 
high water which Mr. Thompson’s elevations of special points suggested. The 
elevation of the upper pendulum-station was 74 feet. Consequently, the vertical 
measure which was to be used for computing the ^‘volume” in the formula above 
was 
Elevation — 74 
1256 ‘ 
Of this formula, a small table was prepared. The quantity g was 
measured graphically from the map, and \/ f-\-\ was formed graphically from it. 
59. Adopting for the sea, so far as its effects are principally sensible (and con- 
ceiving the water replaced by an equivalent quantity of ground with surface lower 
than the sea), the elevation — 15 feet, to which corresponds 
“1256“ 07087, 
1256 
the factor of d applicable to the depression of the sea beyond the straight line at 
distance 10 is 
-2 X -07087 
10 
= —•014174. 
2 Y 
MDCCCLVI. 
