594 
ON THE DEFLECTION OF THE PLUMB-LINE AT ARTHUR’S SEAT, 
Let (yj and (y*) be the sums of the errors of observation at S and A, of a star of 
the first set, the same quantities being- accented for other stars. Let (a*), (aj repre- 
sent corresponding quantities for stars of the second set, (|8„), ((3^) and (sj, (g^), (gj the 
same quantities for the third and fourth sets of stars. 
Then L and N are affected with the errors 
L 
N 
^ d+e h + k 
^ f+ff 
h+k ^ 
n-\-p 
p-^rq 
From these expressions we may derive, finally, the following : if E be the probable 
error of an observation, the probable error of ^i-l-|M<<p2 is 
j^j7j^2|M(MH-K^)+2PMK-2jt/,(K(HM-K^)-l-P(HM-|-K^))-l-//.^(H(HM-K^)+2PKl 
where 
P=2- 
npq 
n^p){p + q) 
The values of H, M, K, P, L and N are found to be 
H= 168-93 M = 168-52 K=46-06 
L =362-40 N = 182-20 P =49-34, 
whence we obtain 
^j=17"*00 (p,=25"-53 (p,-j-<p,=42''’53. 
Now the value of E is to be deduced from the differences between the individual 
and mean results given by the different stars. The sum of the squares of these 
errors is found from the whole of the observations to be 712-1, hence the mean square 
of an error of observation (1263 obs.) is 0-56, and the probable error of an observa- 
tion consequently =0"-50 ( = -67\/0'56). 
We have therefore the probable error of equal to 
^^|520-48— 544-66 |(/.-l-522-04 ^"|' = 0"-043|l — 1-046 
so that the probable errors of (p, and (p^ are each equal 0"-043. 
As the differences of latitude are the quantities principally required, we may append 
these amplitudes to any one of the observed latitudes. Thus making use of the 
observed latitude of the South Station, namely 55° 56' 26"-69, there will result by 
applying the above most probable amplitudes the following latitudes ; — 
Latitude ofS=55° 56' 26"-69 
„ „ A =55° 56' 43"-69 
„ „ N=55° 57' 9"-22. 
The last two latitudes differ from those in the first table by about a quarter of a 
second each. 
