f 81 j 
XVI. On the Problem in Nautical Astronomy for finding the 
Latitude by Means of two Olservations of the Sun’s Altitude 
and the Time elapsed between them. By James Ivory, 
A.M. F-R.S. 
Tue method generally practised in the British Navy for solving 
this problem was invented by Douwes, an examiner of sea officers 
and pilots at Amsterdam, who proposed it to the English Admi- 
ralty in 1740. It is however no more than a very limited solu- 
- tion; since it can only be applied with the desired success to 
correct the latitude by account when one of the observations is 
very near the meridian, or when the middle time is very little 
different from half the interval between the two observations. 
In all other cases one application of the rules will hardly lead to 
a result sufficiently near the truth; and a series of approxima- 
tions obtained by repeated operations generally converges so 
slowly that the method is of little practical utility unless it be 
assisted by some other artifice. 
Dr. Brinkley of Dublin, so long ago as 1791, gave a method 
of correcting the result found by one operation of Douwes’s rules, 
which, unless in particular circumstances, is abundantly exact 
for nautical purposes. The same astronomer has since reconsi- 
dered the subject ; and, in the Nautical Almanac 1822, has re- 
duced his method to easy formule comprehending every case 
that can occur in practice. If this improved method be liable to 
objection, it is on account of the length and embarrassment of 
the calculation. 
Delambre in his Astronomy (vol. iii. chap. 26) has examined 
the different methods that have been proposed for solving this 
problem with his usual industry and accuracy. After a careful 
examination of the different processes with respect to the length 
of the calculation and the exactness of the result, he inclines to 
reject all the indirect methods, and to give the preference to the 
direct and rigorous solution obtained by the rules of spherical 
trigonometry. ‘T'wo elaborate articles in the Conn. des Tems, 
1817 and 1822, written by the same astronomer, are intended 
to add strength to his opinion. In these he particularly ex- 
amines the effect produced by supposing, as is usually done, that 
the sun’s declination is equal to the mean quantity between the 
two observations and suffers no variation in the elapsed time ; 
and he shows that the error arising from this source may be 
equal to the sun’s change of declination. The error may no 
doubt be obviated by allowing for the variation of this element 
of the calculation *; but a new rule is required for this purpose, 
* Delambre's Astronomy, vol. iii. chap. 26. § 110. 
Vol. 58, No. 280, Aug. 1821. L which 
