230 
HINTS TO TRAVELLERS. 
59° 41' 40" Under 59° and against 40" we find 168 parts, and against 
41' the cosice is 504779 ; subtracting the 168 from this 504611, which is 
negative because the proposed angle is greater than 90°. Since the sine 
of any angle is the cosine of its complement, the sine of an angle may be 
obtained from this table, by taking out the cosine of the defect from, or 
the excess above 90° The sine of 50° 37' 27" is, for instance, the same 
as the cosine of 39° 22' 33" : and the sine of 149° 41' 40" is the same as 
the cosine of 59° 41' 40". The tangent of an angle is its sine divided by 
its cosine, and may be also readily found from this table. 
3, Required the angle whose cosine is 568293 : 
By the table .. .. . 568j2j = 55 22 
Given cosine.56829 j 
_ /' 
Parts for secs. 30 = 7-5 
.Angle required is 55 0 2 1' 5. 
If the cosine given had been negative — 568293, the supplement of 
this angle, namely 124° 37' 52" *5, would have been the angle to which 
that cosine belongs. 
Tables XXIX and XXX.—These tables contain the corresponding 
divisions of Time and Arc. 
Table XXXI. Acceleration.— This is the change of the sun’s mean 
Right Ascension in a mean solar day. It is employed in reducing the 
Sidereal Time at mean noon to the Green. Date, and in converting Mean 
Time into Sidereal Time. 
The Acceleration is itself a portion of Sidereal Time. 
Table XXXII. Retardation .— This is the change of the sun’s mean 
Right Ascension in a sidereal day. It is employed in converting Sidereal 
Time into Mean Time. 
The Retardation is itself a portion of Mean Time. 
Table XXXIII. Parallax in Altitude of a Planet .— The Table is 
entered with the Planet’s Horizontal Parallax at the top, and its Altitude 
at the side; and the corresponding seconds taken out. 
To compute a Term. Enter the Traverse Table with the alt. as course 
and the hor. par. as disk, and take out the D. Lat. 
Table XXXIV. Diminution of the Moon's Horizontal Parallax for the 
Spheroidal Figure of the Earth .— The Table is entered with the Horizontal 
