600 
ON THE DEFLECTION OF THE PLUMB-LINE AT ARTHUR’S SEAT, 
Hence we obtain — 
South Station. 
2„-2,= +27-636 
Arthur’s Seat. North Station. 
+3-441 +28-994. 
In order to obtain the whole effect at each station, we must add to these the fifth 
part of the sum of the sines in the first ringf of 500 feet at each of these stations : 
these are, respectively, 15-797, 3-766, 10-155 ; so that we have — 
At South Station . . . 2 (sin s) =43-433 
At Arthur’s Seat . . . 2 (sin 2 )= 7'207 
At North Station. . . S(sin £)=39-149 
Consequently, 
Deflection at South Station =4"-265x North 
Deflection at Arthur’s Seat =0"-708 j? South 
Deflection at North Station =3"-845 x South. 
Comparison of observed and calculated Deflection. 
We may now determine a value of x by the comparison of the observed effects of 
the action of the hill upon the amplitudes, with the calculated effects in terms of x. 
The equations thus obtained are 
4-973 x= 2-81 
8 - 110 a:= 4-07, 
whence 90503 j?=46-982 
x= -5191. 
This solution contains tacitly the assumption that the effect of the general south 
deflection is equal at each of the three stations; if we put 3 / for this quantity expressed 
in seconds, then the following equations will result from the comparison of the ob- 
served and geodetical latitudes, together with the calculated but unknown deflections 
in X, 
y — 4-265 X — 2-44=0 
3/+0-708^— 5-25=0 
3/+3-845 a?— 6-51=0, 
which give 3 /= 4"-68 and x=-5076. 
These quantities give, when supplied in the equations, the following errors : 
+ 0"-08; — 0"-21; +0"-13; 
SO nearly are the observations represented by these values of x and y. 
Extension of the Calculation of Deflection. 
The result just obtained, namely, that the ratio of the density of Arthur’s Seat to 
