Astronomical and Nautical Collections. 103 



2. Add together ; the log. sin. E ; the log. cos. d ; the log. cosec. 

 I, and reject 20 from the index ; look for the remainder among the 

 log. sines ; half the supplement of the corresponding arc will be 

 arc II. 



3. Let A + I be called S ; then add together the log. cosec. I ; 

 the log. secant. A ; the log. cosin. -V S + a; the log. sin. ^ . S — a, 

 and reject 20 from the index ; half the remainder will be the log. 

 sine of arc III. 



4. The difference of the second and third arcs will be arc. IV. 



5. Add together the log. cosin. A ; the log. cosin, D ; twice the 

 log. sin. IV; the constant logarithm 0.301030, and reject 30 from 

 the index ; subtract the natural number belonging to this logarithm 

 from the nat. cosin. A + U ; the remainder will be the nat. sine of 

 the true latitude. 



This Rule requires no distinction of cases. 



Rule II. 



To be used when the latitude and declination are of the same 

 name. 



1. Add together the log. cosin, D', the log. sin. i E ; and reject 

 ten from the index, look for the remainder among the log. sines ; 

 twice the corresponding arc will be arc I. 



2. Add together the log. sin. E; the log. cosin. d; the log 

 cosec. I, and reject 20 from the index ; look for the remainder 

 among the log. sines ; halfihe corresponding arc will be arc II. 



3. Let A + I be called S ; then add together the log. cosec. I, the 

 log. secant A ; the log. cosin. J- . S + a ; the log. sin. \ S— a, and 

 reject 20 from the index ; halfi\\Q remainder will be the log. sin. 

 arc in. 



4. The sum or difference between the second and third arcs will 

 be arc IV. (</) 



5. Add together the log. cosine A ; the log. cosin. D ; twice the 

 log. sin. IV. ; the constant logarithm 0.301030, and reject 30 from 

 the index ; subtract the natural number belonging to this logarithm 



