276 Proceedings of Royal Society of Edinburgh. [sess. 
II. The Equation of Solution is, as above (1), - log^ = ^-{Aoy 4 
+ log a} 
log a = 2-44369 
Xoyl -05116 
2-49485 
i{log a + Xoy} =1-69897 = log” ; whence i = -5 ; x = 2. 
This value evidently satisfies the given equation. 
Example (2). 
x 5 - \x£ = 10 ; or TOa? 5 - '025a? 4 = 1. 
The third formula of reduction is the one to he used, or 
4 log a - 5 log p = 5ttl4 - hoyl [a= TO ; /? = * 025. 
I. 
log a = log TO = 1*0 ; log /? = log *025 = 2*39794 
4 log a, 4-0000 51o g/3 9-9897 
Subtracting 5 log /3 9-9897 
4 log a- 5 log /3 = 2 = 4-0103 = 5111 - Xoyl (a). 
The nearest tabular values in the table of Logarithms of Sub- 
traction are 
m! 0-81640 Xoyl *07192 
Pp. 4 The proportional part is insensible 
0*81644 in the result. 
5rn,4 4*08220 
Subtracting Xoy® '07192 
5rri4 _ A-oy®, 4-01028, which agrees with the value given by (a ) . 
II. The Equation of Solution is , log x = ^{ Xoyl - l°g a } 
Xoyl, 
0-07192 
Verification. 
- log a, - 1 -0 
Xoyl — log a, 1-07192 
^-{ A.o 7 4 — log a} = log x -214384 
a = 1-63825 
a 5 11-8010 
Also log x 5 
logic 4 
1-07193 
0-85754 
x 4 , 7-2035 ) 
i, 1-8009 J i x4 
1-8009 
10-0001 
