Mr. Riddle on Mr. Burns's Nautical Problem. 251 



Indeed, Mr. B. altogether misapprehends the nature of the 

 problem : for he assumes, as known, not only the interval of 

 time between the observations, but the ti-ue aj>parcnt time at 

 each obsc}-vatiofi, both of which data, he says, may be obtained 

 with the greatest exactness from the improved state of chro- 

 nometers. 



Now it may be observed on this, — that if the apparent time 

 at either observation were known, the other observation and 

 time would be superfluous data ; as the problem would then, 

 without their aid, become one of the simplest in nautical astro- 

 nomy. But it is not, as Mr. B. has incautiously inferred, the 

 object of chronometers to point out the time at atiy place at 

 which an observation may be made ; but to show, at any instant, 

 what the time is at some individual meridian : and therefore, 

 though the interval in mean time may be correctly obtained 

 from a chronometei', the actual times as shown by a chrono- 

 meter may differ in any way from the apparent times at the 

 place oj observation ; — it is sufficient for the computer, if he 

 know the Greenwich time nearly enough to take out the de- 

 clination with requisite con-ectness. The times A.M. and P.M. 

 in the examples which Mr. B. has re-computed are by no 

 means intended to represent the true apparent times of obser- 

 vation ; their only use is to determine the elapsed interval, and 

 to find, with the aid of the estunated longitude, the approxi- 

 mate Greenwich time for determining the declination. 



In fact, Mr. Burns has proposed to himself the solution of 

 one problem ; and he has, unknowingly, given the solution of 

 another, — and of one for which, in nautical practice, the ne- 

 cessaiy data cannot be obtained. 



I have only to add, that I believe the simplest solution of 

 this useful problem that has yet been given, was deduced by 

 myself from formulae that were first investigated by Mr. Ivory. 

 This solution was first published in the PhilosophicalMagazine, 

 and has been copied into other works in general use among 

 nautical men. It is direct, accurate, and perhaps as concise 

 as from the nature of the problem any solution of it can be ex- 

 pected to be. Mr. Burns's proposed solution, as we have seen, 

 is not a solution to the pi'oblem at all. 



The true answers to the examples which Mr. Burns has 

 recomputed, are 27° 59' 16", and 9° 59' 32". 



The same answers by Dr. Brinkley's approximate method 

 of solution, are 27° 59', and 10° 1'. 



Mr. Burns makes the answers 27° 0', and 8° 58' ; and he 

 notices the discrepancies between his results and Dr. Brink- 

 ley's with a maik of admiration. The diflerence is certainly 

 I i 2 remarkable ; 



