4 ON THE REDUCTION OF THE 
In this formula each term, after the first, is relatively smaller 
than the corresponding term in (iv.); and if a is large, the terms 
b ¢t 
having sensible magnitude, are alternately positive and negative. 
Therefore the error, introduced by neglecting all terms beyond the 
first, is relatively less in (v.) than in (iv.); but, since B is not 
known until & has been determined, this formula could only be 
employed by successive approximation, and is therefore inconvenient. 
It may be seen by inspection that, in Table XIX.’, Be is very 
nearly equal oF : ate That this should be so, may be proved 
thus:— 
As already explained 
log — eh ee 
Bet cl Pam 6 10B 
ial 4 
t log 102 1 : 
10B-1 102 
Mt 2 
CaS 03! 
1028 " @aeetoe| 
2, 
108 ' gana); 
= — nearly, (vi.} 
B 
‘p= Bg N : nearly, as above stated. 
