426 
ME. C. W. MEEEIFIELD ON A NEW METHOD OE APPEOXBIATION 
log sina;=9'0206346 
log cos^=9‘9975988 
log^=5-9969834 
ar. CO. log ^=0'9785662 
log ^^^=5-9937830 
2nd correction — 1 4 
log sin^a:=8-0413 
log 2 = 0-3010 
log#=5-9970 
log (2 sin^ a7)=4-3393 
2sin’^^= 21,800 
t sin 2a? 
log 21670 = 4-33585 89113 
log r. =4-68557 48668 
log ^=9-02143 37781 
Z= +9 85786 
log y= 9-02153 23567 
2a? 
-= 985,8 
log ^=5-9937816 
U +493 
1007,6 
-^=-993,1 
log wA=5-9938309 2nd correction 
log 0^=9-0214338 
ar. CO. log (-|7r—o^)= 9-8339439 
14,5 
The comma cuts off the 
eighth decimal. 
log 302330 = 5-48048 12441 
logr'=4-68557 48668 
log (+r~o;) 
correction 
0-16605 61109 
-70666 
log correction= 4-8492086 
log(+r-y)=0-16604 90443 
Verification . — The numbers corresponding to these logarithms of y and of +r— y are 
0-10508 29743 and 1-46571 33525, the sum of which, to the very last figure, is 
exactly -^tt. 
25. To find from lo^y. —Let log |^=log^+p, and log y=log a;+^ ; 
( ^QCC \ 1 Ci 
j nearly. This formula obviously fails where y is 
near unity ; in this case log cannot be had with great accuracy, unless y itself be 
given absolutely. All the cases of niay be included in the above formula by 
giving proper signs to p and q. It may save trouble to remark that x must not always 
be taken to the extreme limit of the Table, because log(^+l) and log (^ — 1) have also 
to be taken out. As an example, let 
log?/=0-36290 63835 
log^=0-36285 93030 
+4 70805 
log ^=5-6728411 
ar. co.log(d?^ — 1)= 9-3647540 
5-0375951 
log?r=0-3628593 
log 2 = 0-3010300 
5-7014844 
2nd correction= — 1225 
0^=2-306, 0^+1 = 3-306, o;-l=l-306 
log(^+l)=0-51930 28492 
log(o--l)=0-11594 31769 
sum: 
=0-0001090 
135 
2nd corr“= 0-0001225 
:0-63524 60261 
difierence= 0-40335 96723 
-p= -5 02761 
log ^=0-40330 93962 
logp=5-7013619 
