AND THE MEAN SPECIFIC GRAVITY OF THE EARTH. 
601 
the mean density of the earth is equal to *5076, is somewhat arbitrary, from this 
cause, that it is slightly dependent on the extent to which the calculation of the 
attraction is carried out. Had there not existed a marked difference in the mean 
height of the ground on the north side and on the south side of the hill, a smaller 
number of circles would have been sufficient. The existence of this attracting mass 
forbids our limiting the calculation to the visible extent of the hill ; we must, there- 
fore, in order to compare with what we have already obtained, extend the calculation 
to include a circle of about nine miles diameter round each station. 
We shall now, instead of drawing the circles at 500 feet apart, make the radius of 
the (w-f-l)th circle equal to ^ of the radius of the wth circle, so that they shall be in 
geometric progression. We have already drawn twelve circles round Arthur’s Seat ; 
the radius of the 13th circle will therefore be f ’SOOT 2 = (f) 6000 feet, that of the 
14th will be (1^)^6000 feet, and so on. Around each of the other two stations sixteen 
circles have been drawn, the radii of the 17th and 18th will therefore be (f)'8000 
and (|^)^’8000 feet, and so on. 
Now if h be the height in feet of any one of the compartments thus formed, we 
have shown that the resulting deflection in seconds is 
12'447 5280 
= 0-00003027^A. 
The following Table contains the sums of the heights of the surface for each of the 
additional rings : — 
station. 
17th. 
18th. 
19th. 
20th. 
21st. 
22nd. 
23rd. 
Total. 
South 
Station, 
2(4) north 
S(/t) south 
+ 2385 
+ 6060 
+ 1685 
+ 6870 
+ 935 
+ 8295 
+ 630 
+ 9010 
+ 465 
+ 8925 
+ 180 
+ 8175 
- 10 
+ 10060 
+ 6270 
+ 57935 
North 
Station. 
S(A) north 
S(A) south 
+ 520 
+ 4495 
+ 385 
+ 5045 
+ 277 
+ 5640 
— 15 
+ 6475 
- 200 
+ 8000 
— 320 
+ 8175 
- 375 
+ 8135 
+ 272 
+ 45965 
Arthur’s 
Seat. 
2(4) north 
2(4) south 
13th. 
14 th. 
15th. 
16th. 
17th. 
18 th. 
19th. 
20th. 
21st. 
+ 2643 
+ 4645 
+ 2245 
+ 5025 
+ 1624 
+ 5460 
+ 904 
+ 6080 
+ 548 
+ 7460 
+ 427 
+ 8485 
+ 148 
+ 8845 
— 92 
+ 8550 
— 132 
+ 9595 
+ 8315 
+ 64125 
Consequently the effective sums of the heights are, — 
South Station 2(A) = 5 1665 
Arthur’s Seat 2(A) = 558iO 
North Station 2(A) = 45693 
And therefore, multiplying by •00003027^^, the resulting deflections are, — 
South Station T565a^ 
Arthur’s Seat T691 x 
North Station T393a^ 
4 K 2 
