228 
HINTS TO TRAVELLERS. 
take away the parts for 10" or 20" ; add 10" or 20" accordingly, and also 
the seconds corresponding to this last remainder. 
Example 1.—Find the arc to the log tangent 9’127945. 
o r It 
Given .. .« 
WJ 
00 
O 
Next less 
294 
IO 
Parts .. .. 
8 
Rem. 
Arc req. 7 38 48 
Example 2.—Find the arc. to the log. cosec. 10*881005. 
0 ' " Given.10.881005 
7 33 o Next greater .. .. 10*88143; 
428 
20 Parts. 318 
7 Rem.. no 
Arc req.7 33 27 
When greater precision than that afforded by the parts is required, the 
log. sine, &c., or the arc may be found by means of the proportional part 
of the diff. between two terms, or for 80". 
The log. cosec. is the arith. compl. of the log. sine. 
The log. cotan. is the ar. co. of the log. tan. 
The log. sec. is the ar. co. of the log. cosine. 
The log. tan. is the sum of the log. sine and log. secant; thus all may 
be obtained from the log. sine. 
Table XXVII. Proportional Logarithms .—These logarithms are given 
to every second of time, or arc, for 3h. or 3°. The Table is entered with 
the hour or degree and the minute at the top, and the second at the side; 
thus the prop. log. of 1° 2' 27" or of lh. 2m. 27s. is 4597, that of 1m. 2s. 
is 2*2410. The index 0 proper to quantities above 19m. (or 19') is 
suppressed for convenience* 
To find the prop. log. of an arc under 18', to T the. tenth of a second. 
Put the proper index, and find the decimal part due to ten times 
the arc. 
Example .—Find the prop. log. of 7' 13"’7; the index of 7' 13" is 1; the 
