33$ 
Mr. Manning's new Method 
II. To find the h. 1. of any Number , whole or mixt. 
Rule. Reduce the given number (if necessary ) to a whole 
or mixt number less than 2, by setting the decimal point after 
the first significant figure, or if the given number be 10 or a 
power of 10 after the first o; and then dividing by 2 (if 
necessary) till the integral part is 1.* * 
Find the h. 1. of this reduced number by the last rule, and 
add to it or subtract from it as many times the h. 1. of 10 as 
the decimal point was removed places to the left or right ; 
also add to it as many times the h. 1. of 2 as there were divi- 
sions by 2. The sum is the h. 1. required. 
Ex. hi. To find the h. 1. of 10. 
~ = 1.25, whose h. log. is found in the last example to be. 
,223143551306 
h. 1. 2 3 = 2,079443541911 
h. 1. 1 0 2,3 02585093217 
Ex. iv. To find the h. 1. of 5548748 to 6 Places of Decimals. 
4)5-.548748 3 x h. 1. ~ = ,316081546 
1.387187 
1387187 
1.2484683 
12484683 
1.12362 147 
112362147 
Toi 1259323 . . 
10112593 
1.001146730 . . 
1001 146 
1 .000145584 
uh.l.“= ,010050335 
ixh.1.— = ,001000500 
decimal of last 
remainder = ,000145584 
.3 h. log. 1.387187 = >3 2 7 2 779$5 
6 x h. 1. 10 = 13,815510559 
.1 2 x h. 1. 2 — 1,386294361 
jlog. required 1 5.529082885 
last remainder. 
• Three divisions by 2 will always suffice. 
