SEXTANT AND PRISMATIC COMPASS SURVEY. 93 
and the angles B A C be equal to the latitude, then A C, the hypothenuse, 
will be equal to the difference in the longitude. 
Problem V .—Given the departure to find the difference of longitude. 
Also, if D B represent the distance, and C D the difference of latitude, 
then BCD will be a right angle, and B C the departure, nearly equal to the 
meridian distance in the middle latitude. If, then, in the triangle ABC 
the angle A B C be measured by that middle latitude, A B, the hypothenuse 
will be nearly equal to the difference of longitude between D and B. 
For the variation of the compass, it is convenient to take a bearing of 
the sun at sunset or sunrise; or, if this cannot be done, an azimuth of 
the sun at any time three hours before or after noon will answer equally 
A 
/ 
v 
D 
well. From the angular distance between the sun, when its own diameter is 
above the horizon, and any well-defined peak, measured with the sextant 
the true bearing can be obtained. 
To find the sun’s true amplitude for any day :—-to the log-secant of the 
latitude, rejecting the index, add the log-sine of the sun’s declinat'on 
corrected for the time and place of observation. Their sum will be the 
log-sine of the true amplitude. If the true and magnetic amplitudes be 
both north or both south, their difference is the variation; but if one be 
north and the other south, their sum is the variation; and to know 
whether it be easterly or westerly, suppose the observer looking towards 
that point of the compass representing the magnetic amplitude; then, if 
the true amplitude be to the right hand of the magnetic, the variation is 
east, but if to the left hand, it is west. 
