176 
When a and 2 are small, the expansion may be s 
at the term containing the first power of =; putting 
2bE X, = Хо: | 
we again obtain eleven equations: et 
m, = (10 + va,‘ — рар) Xi + (2 va ° — tao) ) Xa "T 
from which the quantities X, and № are to ђе 2777 
after which 5 is found by the formula: T 
: № | 
етте 4 
The period of the variation R is given by the — 
25.8 * 
най ВВ ци ot al AR 
When 2 is, as in our case, equal to about four degree 
either method gives reliable results and therefore only Це. 
second, has been applied. Generally however the first 
will prove to be the more advantageous. When, however 
not very small, neither of the formulae (6) or (8) зїй 
an accurate representation of the values of the expanded functi 
sin ре : 
— = p — ро? + уз“ —— 506 + ele. 
Sunc 
because in formula (6) the value of the constants 15: 
А zz р — pb? + viz — 5166 + etc. 
В == — даџђЕ + 4276925 — Gazb^z^ + etc. 
C = — а?р + 62354223 - проза + ete. 
D Ah — 202580555 + ete. 
Е == — 152321222 
from which it is evident that the series ии by expat 
sion in ascending powers of р may be stopped at the ішігі ter 
only when bë is small; if therefore the formula (6) we Ç 
to give values for m not closely approximating to the quan" | 
m numerically found, this has to be considered as à P " 
that the approximate value of R according to which the ta 
tion has been effected (in our case 25.8) has not been 6 ве 
judiciously and a re-arrangement according to the appr 
value given by formula (10) will be necessary. 
