360 Astronomical and Nautical Collections. 



parallax p = 59' 27"; whence we find the tabular corrections 

 of the altitudes + 51' 33', and — 30', the difference of the 

 apparent altitudes 32° 9' 22", the difference of the true altitudes 

 31° 17' 19', and the tabular logarithmic difference 9.996735 

 — . . 16 = 9.996719. The computation will stand thus ; 

 Verse sine 7n ^ s 153399 



d 491351 



Difference 337952 Log. 5.528855 



+ L. D. 9.996719 



Number 335407 Log. 5.525574 



Verse sine diff. tr. alt. + 145437 



Verse sine true distance 480844 58° 43' 28' 



We have here only about nine references to tables, four of 

 them relating to verse sines with seconds ; and the result is 

 free from all error and ambiguity. 



B. Mendoza's Method at length. 



Mr. Mendoza finds an angle b, of which the logarithmic cosine 

 is equal to the logarithmic difference lessened by the logarithm 

 of 2, which, in the last example, becomes 9.695689, whence 

 b zz 60° 14' 55" : he then takes the sums and differences 

 w» + s + 6, vi + s — b, d + b, and d — b, and adds their 

 verse sines to that of the supplement of the sum of the true 

 altitudes. The operation will stand thus, observing that the 

 verse sines of arcs above 90° may be easily found from a table 

 of sines. 



1.833725 + 17" 45 



101078 27 57 



1.494953 29 122 



000102 21 1 



1.050593 35 169 



394 



V. s. 58° 43' 28" (4).480845 

 This process has three more references to tables with seconds 

 than the last, and has therefore no advantage in its independent 

 form; but Mr. Mendoza's great Tables give at once the angle b, 



