264 



Sir W. Thomson on the Determinatian of a [Jan. J 9, 



This example is represented graphically in the first diagram annexed. 

 The second set of values could have been selected equally well from the 

 contiguous columns (a = 5 7°), which on trial will be found to give an 

 almost identical result. 



Again, (2), on 1870, May 16, afternoon, at 5b. 42m. Greenwich ap- 

 parent time, the Sun's altitude was observed to be 30° 30' : to find the 

 ship's place, the assumed latitude being 10° North. 



The Sun's declination from N. A. is N. 19° 10', and the half comple- 

 ment of the assumed latitude 40°. By a few successive trials, a=56° will be 

 found to contain values of co-hypotenuses approximately equal to the Sun's 

 declination and altitude at the time, and which are equidistant from 40° ; 

 we therefore select the following sets of values from this column as 

 follows : — 



Co-hyp. A. 



( 1. b = o4 19 11 61 23 = Sun's hour-angle. 



| 6 = 26 30 10 73 32= Suns azimuth (N. towards W.). 

 a = 56° \ 



I 2. 6 = 55 1 8 42 61 5 = Sun's hour-angle. 



{ b = 27 29 53 72 58 = Sun's azimuth (N. towards W.). 



from which we have the following : — 



O I O I 



Greenwich apparent time (in arc) 85 30 85 30 



Son's hour-angle (1) 6123 (2) 61 5 



Diff. = Longitude 24 7 W. 24 25 W. 



Sun's altitude (observed) 30 30 30 30 



Sun's altitudes (auxiliary) (1) 30 10 (2) 29 53 



Diff. = + 20 +37 



Sun's declination from ]S T . A. 19 10 19 10 



Sun's decimations (auxiliary) (1) 19 11 (2) 18 42 



Diff. = - 1 4-28 



In this case the sun passes the meridian to the north of the ship's 

 zenith, the azimuth, from the Tables being less than 90°, is measured from 

 the north towards the west. In this case also the second set of values 

 might have been taken from a = 57°, which will be found on trial to give 

 a position nearly identical with the above. 



This example is represented in the second diagram annexed. 



Again, (3), on 1870, May 16, afternoon, at 5h. 42m. Greenwich ap- 

 parent time, the Sun's altitude was observed to be 18° 35' : to find the 

 ship's place, the assumed latitude being 20° South. 



The Sun's declination from N. A. is N. 19°- 10', and the half complement 

 of the assumed latitude is 55°, to be used because the Sun's declination and 

 the assumed latitude are of different names. Proceeding as in the previous 



