MAGNETIC INCLINATION AT GOTTINGEN. 651 
cosh sinh 
c= 90° = h + = 7° aA . 7 
sin 7 sin 2 
A cos A! Asin A! 
C= 900 =] hk =) oes 
sin 2 sin 2 
In the numerical calculation we may safely substitute for 7 the 
value 1 (f+ 9 +f! + g’), whereby in our example the equations 
will arrange themselves thus :— 
e = + 491" + 0:0026 ¢ — 1:0810 uw 
c = — 648 + 0:0034 ¢ + 1°0953 u. 
As the values of h and /! rest on twice as many positions as 
the values of f, 9, 7’, g', we should have, if we consider only the 
number of positions, to append to each of these equations the 
weight 2 sin 7”, the weight of each of the four equations in the 
preceding article being made = 1: but from the reasons pre- 
viously given (Art. 14) the determinations of / and /! possess 
considerably less trustworthiness, and the weight of all six equa- 
tions may therefore be taken as equal, by which the calculation 
will be rendered more simple. If we deduce from them in this 
manner the five unknown quantities, calculating according to the 
method of least squares, we find 
. i = 67° 40 55"! 
i= — 934 
a 211 
o == + 719 
c= = 880 
by which values all the equations are satisfied to one or two se- 
conds, a degree of agreement which must indeed be looked upon 
as merely accidental, as the data include a much greater amount 
of uncertainty. The values of u,c, c’ also deserve no confidence ; 
with the high dips of these regions the data are not suitable for 
a separation of those quantities with any degree of certainty. 
23. 
After this review of the different methods of calculation, I pasz 
to the principal object ; and shall first subjoin in a tabular form the 
observations made in the manner described in Art. 8. I place 
here only the quantities expressed by /, g,/’, g’, leaving out the 
partial results from which they have been deduced in the man- 
ner pointed out in Articles 11 to 13; these are omitted, partly 
on account of space, partly because the elements on which they 
depend had not the same value on different days by reason of 
