Problem of finding the Latitude. 371 



error of consequence to the navigator. But in fact, if great 

 accuracy be desired, the change of declination may be easily 

 allowed for in practising the method of Douwes, as stated 

 below. 2. That, except under great limitations, the latitude 

 computed may be further from the truth than that by the 

 reckoning. But Dr. Brinkley's method entirely obviates this 

 objection. His method is intended to correct and extend the 

 results obtained by the original method of Douwes, even for 

 cases where it would otherwise be quite useless. 3. The 

 length of the computation has also been objected to, but unless 

 it be repeated two or three times, it is shorter than the direct 

 can be made, and it possesses no ambiguity embarrassing to 

 those not conversant in spherical trigonometry. By Dr. Brink- 

 ley's method it rarely indeed happens that two operations are 

 necessary. 



Dr. Brinkley has given the following method of allowing for 

 the change of declination. 



Having computed the middle time by the method in the re- 

 quisite tables, or by the common log. tables, add to it half the 

 interval to get the time furthest from noon. Or use the esti- 

 mated time when the observation furthest from noon was made ; 

 add together (three places of log. are sufficient), the sine of 

 time furthest from noon, the secant of the altitude belonging to 

 this time, and the cosine of the lat. by account ; look for the 

 sum among the log. sines, and take out the corresponding cosine, 

 which is to be added to the log. of the change of declination in 

 minutes. The sum is log. of the correction of the altitude 

 furthest from noon. This is to be added to that altitude when 

 the sun at the other observation is nearer the elevated pole ; 

 otherwise subtracted. The altitude so corrected is to be used 

 instead of that observed, and the declination to be used is that 

 at the observation nearest noon. The computed latitude found 

 is to be corrected by Dr. Brinkley's rules in the Nautical Al- 

 manac 1822. 



It will rarely occur that the time is not known with sufficient 

 exactness for this correction of the altitude made to obviate the 

 effect of the change of declination. Thus the correction will be 

 easily had for tlie direct method. 



