1889 - 90 .] Lord APLaren on Equation of nth Degree. 275 
(4) If /?a? 4 be > ax 5 , we have 
log {/L? 4 - ax 5 } = 0 = log /3 + log ( x 4 ) - A.oyg ; 
( 1 ). 
Also, 
ioga?=iog/3-ioga-m5; .... (2). 
whence 4mj + Xoyt = 5 log j3 - 4 log a ; ) Formula of 
In using formulae of reduction III. and IY. (1) the quantities 
Any and m are to be taken from the table of Logarithms of 
Subtraction. (2) If the result of inserting the numerical values of 
log a and log (3 is to make q negative, the formula is to be used 
with signs changed. 
For the equation of terms of contrary signs, a root can always 
be obtained from either of the formulae III. and IY. 
The first formula of reduction is the one to be used, or 
4 log a - 5 log f$ = 5 md + Any! . 
a = *02? ; £=-00694. 
(I.) 
log a = log ‘027 = 2*4436977 ; lo g£ = 3*8416377 
4 log a 7-7747908; 51og£ lT-2081885 
Subtracting 5 log £ 11-2081885 
4 log a - 5 log £ = 2 = 4-5666023 = 5 m^ + Aoyj . . . (a) 
Looking down the table of Logarithms of Addition for the nearest 
values of rrt and A.oy corresponding to 5 itl + Any = 4-56 or rq + \ Any 
= 0*9 1 we find, 
m = 0-90300 Any = 0-051 1625 
Prop, part, 9 Prop, part, - 98 
n\l -90309 Aoy® -0511527 
mi + i Xoyt = i log £ - log a = q. 
Eeduction IY. 
Example (1). 
a; 5 + Jx 4 = 36; or -027a? 5 + *00694£c 4 = 1. 
Add 5m! 4-51545 
4*56660 = 2, agreeing with (a). 
