AND THE MEAN SPECIFIC GRAVITY OF THE EARTH. 
599 
one of which will be, putting x for the unknown ratio of the density of the hill to the 
density of the earth, 
500 ,, 1 . 
I^=^^Xl2"*447XY^sin2, 
so that the total deflection is equal to 
0"-0982 2 (sin s)x. 
At each of the three stations, the first ring of 500 feet was subdivided by rings at 
the distance of 100 feet; the result is shown in the following Table : — 
South Station. 
Sums of Sines. 
1st Ring, 
100 feet. 
2ncl Ring, 
200 feet. 
3rd Ring, 
300 feet. 
4th Ring, 
400 feet. 
5th Ring, 
500 feet. 
S(sine) for Prisms South of station ... ... 
S (sin g) for Prisms North of station 
-1*796 
+ 1*689 
-11-294 
+ 5-448 
-11-808 
+ 7*705 
— 11-360 
+ 9-038 
-10-001 
+ 8-845 
S(sin e)=78*984 Deflect North. 
Arthur’s Seat. 
S (sin e) for Prisms North of station 
2 (sin g) for Prisms South of station 
-7*118 
-3-524 
-11-281 
- 9*164 
— 11-845 
- 8-603 
— 12-014 
- 7-436 
-11*719 
- 6-421 
2(sing)=18'829 Deflect South. 
North Station. 
2 (sin g) for Prisms South of station 
2 (sin g) for Prisms North of station 
+ 4-867 
-2-002 
+ 4-347 
-8-038 
+ 3-159 
-8-856 
+ 2-179 
—8-424 
+ 1-932 
-6-973 
2 (sin g) = 50'777 Deflect South. 
By drawing twelve rings at 500 feet apart round the centre station, and sixteen rings 
round each of the other two stations, the results contained in the following Table are 
obtained : — 
Stations. 
2 
(sin e). 
2nd 
Ring. 
3rd 
Ring. 
4 th 
Ring. 
5th 
Ring. 
6th 
Ring. 
7 th 
Ring. 
8th 
Ring. 
9th 
Ring. 
lOth 
Ring. 
nth 
Ring. 
12 th 
Ring. 
13 th 
Ring. 
14 th 
Ring. 
15th 
Ring. 
l6th 
Ring. 
South 
+ 6-614 
+3-187 
+ 1-088 
+0-025 
-0-095 
-0-088 
-0-418 
-0-926 
-1-004 
-1-037 
-1-004 
-0-908 
-0-843 
-0-828 
-0-806 
Station. 
x. 
- 6-299 
-3-531 
-2-536 
-2-026 
-1-713 
-1-488 
-1-309 
-1-149 
-0-985 
-0-844 
-0-729 
-0-625 
-0-539 
-0-472 
-0-434 
Arthur’s 
-10-560 
-7-996 
-5-850 
-4-656 
-4-474 
-4-570 
-4-209 
-3-839 
-3-467 
-3-119 
-2-883 
Seat. 
2, 
- 5 148 
-6634 
-7-715 
-6-425 
-5-295 
-4-549 
-3-994 
-3-587 
-3-234 
-2-931 
-2-667 
North 
- 4-644 
-3-094 
—2-859 
-2-361 
-1-954 
-1-623 
-1-422 
-1-258 
-1-176 
-1-117 
-1-048 
-0-996 
-0-941 
-0-935 
-0-894 
Station. 
2. 
+ 2-009 
+1-695 
+0-978 
+ 1-028 
+1-195 
+0-745 
-0-361 
-0-747 
-0-671 
-0-604 
-0-575 
-0-558 
-0-525 
-0-488 
-0-449 
where 2„ signifies 2 (sin z) for the prisms north of the station, 
2, signifies 2 (sin a) for the prisms south of the station. 
4 K 
MDCCCLVI. 
