602 
ON THE DEFLECTION OF THE PLUMB-LINE AT ARTHUR’S SEAT, 
We see from this that the assumption of y being constant for the three stations was 
not very erroneous, though the difference is perceptible. 
We shall now form the equations for x and y, remarking that y is not now the 
same quantity that was before represented by that symbol, and that the assumption 
of its being constant for the three stations is now almost unobjectionable. Taking 
into consideration the deflections before obtained, the total deflections south at each 
of the stations will be — 
South Station (1*565 — 4*265)a?= — 2*700a? 
Arthur’s Seat (0*708-1- l'691)a:;= 2*399 j: 
North Station (3*845 -1-1 *393).r= 5*238^ 
Hence the equations are, — 
?/ — 2*7000^ — 2*44=0 
3/4-2*3990?— 5*25 = 0 
3/4-5*2380?— 6*51=0, 
which give for the most probable values of x and y, 
o?=*5173 3/=3*8820. 
By substituting these values in the equations, they show the errors 
4-0"*04; — 0"*13; 4-0"*08, 
showing that the above values agree very well with the observations. From a com- 
parison of the errors of these equations with those previously solved, it would appear 
that the probable error of this value of x is considerably less than that of the value 
(*5076) then obtained. The two values, however, are as close as could be expected. 
We shall adopt, therefore, as most probable, so far as resulting from these observa- 
tions, a?=*5173. 
We may estimate the probable error of this quantity dependent upon the probable 
errors of the observed amplitudes thus ; writing the three equations in the form 
y-\-ax-\-a!=Q 
y-\-bx-\-h' — 0 
y-\-cx-{-d =Q, 
we have 
[a—b) {a' — b') + {b — c) {b' — c') + {c—a){c' — a') 
{a—b)'^+ (6— c)^+ {c—a)^ 
If now X be the observed latitude of the South station, X„ Xj, X3 the geodetic latitudes 
of the three stations, — 
fl^ = X — X, 6^ = X4 ~^i“'X2 C?^ = X-}-<Pi4“*P2*~^3 
a'— Z>'=X2— Xi— (p, 
fc'— £?'=X 3 — X2— <p2 
d — a^=Xi — X3 4 -<Pi4"?’2- 
