177 
In this case however, when š is not very small, the tedious 
labour of a re-arrangement might be avoided by adding terms, 
containing the higher powers of 2, to formula (8) and substitut- 
ing for £ the value: 
54-34 
in which & denotes the very approximate value indicated by 
the results of the additions: if for instance a maximum value is 
found Гого = + 5 this value of š, is given by the equation: 
_ 0.05 X27 
25.80 x 20.85 | 
By substituting this value and rejecting the terms containing 
the higher powers of 4, the eleven equations are again reduced 
to the first degree and, by repeating the operation, the 
approximation may be continued as far as convenient. 
>, — 
$4 ke 
= 
5. Аз the amplitudes of the periodical variations are very 
small, it has been deemed advisable to apply the usual method 
of control by dividing the ten groups into two equal parts and 
comparing the results. In order to effect this in such a way 
that a possible influence of the frequency of sunspots may be 
excluded as completely as possible, the two groups have been 
formed by combining the five odd and the five even numbers 
of groups separately. Instead of the formula (4) we find for 
the even numbers: 
де: (2555-0995 (nz + C 4- 599 x 12.9 5 + 5 ga) ...(11) 
sin (774 Е ＋ ра) 
lor the even numbers: 
x, Sn 5 (774 E + pz) 
sin (774 Е + ра) 
for the first series the difference between two subsequent 
arguments must be: 
sin (na + C+ 269 X 12.95 + 4 ра) ...(12) 
5 a = 20246 
lor the second series: 
4 a = 16957! 
The quantity š is calculated in the same way as has been 
42 
