648 GAUSS’S OBSERVATIONS OF THE 
and further calculation gives 
6) = a, ».0%, Abst 
i= 67 40 54 
Q-—c= 145 17 10 
Q Eoin tat 57 
£ = 0-0055111 
m 
L = 00055843. 
m™ 
The calculated values of h, k', computed according to these ele- 
ments, are 
h = 89° 49! 30" 
hi = 90 12 59, 
from which the observed values differ + 2'19"” and — 2! 11". 
19. 
In the absence of a direct determination of the relation of 
a - » We are constrained to make two arbitrary suppositions 
m 
instead of one. The two following modes have come into use 
by observers :— 
I. It is assumed that c = 0 and c = 0, whence we have for i 
the formula 
cot g' — cot f' — cot g + cot f 
ai cot g'.cotf— cotf’.cotg ~ 
This is the usual mode of proceeding when the needle is 
purposely loaded with a small weight, according to Mayer’s 
method. As in this mode readings are obtained at parts of the 
limb quite different from the place of the needle without weights, 
if the results do not show any considerable discordance, some 
satisfactory indication is afforded that the limb does not contain 
any magnetic particles. It is advisable to keep the loading 
within moderate limits, as otherwise the influence of errors of 
observation on the result would be unduly increased, and even 
the neglected c, c’, would have a sensibly prejudicial effect. 
II. It is assumed that m =m! and c=c!. This it will be 
seen is only a special case of the one treated of in the last arti- 
cle, and therefore the formula there given applies, A being made 
= 1. The formula (9.) for ¢ then assumes a form even somewhat 
more simple, namely,— 
