1871.] 



Ship's Place from Observations of Altitude, 



263 



that point of the column of values of b corresponding to half the comple- 

 ment of the assumed latitude ; this point will be on a level with one of 

 the numbers, or midway between that of two consecutive numbers, accord- 

 ing as the assumed latitude is even or odd : then use the compasses to 

 indicate pairs of co-hypotenuses equidistant in the vertical column from 

 the fixed point of the compasses, and try from one column to another until 

 co-hypotenuses approximately agreeing with the observed altitude and the 

 correct declination are found. It is easy to modify the rule so as to suit 

 cases in which the azimuth is an obtuse angle ; but it is not worth while to 

 do so at present, as such cases are rarely used in practice. 



The following examples will sufficiently illustrate the method of using 

 the Tables : — 



(1) On 1870, May 16, afternoon, at 5h. 42m. Greenwich apparent 

 time, the Sun's altitude was observed to be 32° 4' : to find the ship's place, 

 the assumed latitude being 54° North. 



The Nautical Almanac gives at 1870, May 16, 5h. 42m. Greenwich 

 apparent time, the Sun's apparent declination N. 19° 10'. On looking 

 at the annexed Table (which is a portion of the solutions of the 

 8100 right-angled spherical triangles) under the heading a = 56°, and 

 opposite b = 54°, the co-hypotenuse (representing the Sun's declination) 

 is 19° 11', and opposite b = 18° (differing from 54° by the complement of 

 the assumed latitude), the co-hypotenuse (representing the Sun's altitude) 

 is 32° 8', which are sufficiently near the actual values ; we therefore select 

 our sets of values from these columns as follows : — 



Co-hyp. A. 



56 : 



rl. 6=54 19 11 61 23 -Sun's hour-angle. 



6 = 18 32 8 78 14= Sun's azimuth (S. towards W.). 



2. 6 = 55 18 42 61 5 = Sun's hour-angle. 



6 = 19 31 55 77 37 = Sun's azimuth (S. towards W.). 



I 



from which we have the following : — 



o i o i 



Greenwich apparent time (in arc) 85 30 85 30 



Sun's hour-angle (1) 61 23 (2) 61 5 



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



Sun's altitude (observed) 32 4 32 4 



Sun's altitudes (auxiliary) (1) 32 8 (2) 31 55 



Diff. = - 4 +9 



Sun's declination from N. A. 19 10 19 10 



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



Diff = - 1 +28 



