"284: Mr. Henderson on Mr. Burns's Nautical Problem. 



chronometers and other instruments may be known with the 

 greatest exactness. But he must be aware that, if the horary 

 angles can be ascertained at sea with such precision, two alti- 

 tudes are not necessary for finding the latitude, one only 

 with its horary angle being sufficient. It is well known, how- 

 ever, that it is impossible to determine, with the requisite ac- 

 curacy, the times or horary angles at sea, independent of a 

 knowledge of the latitude or longitude ; and accordingly all 

 the solutions of the jiroblem of double altitudes hitherto given 

 suppose only the difference of the horary angles, or the elapsed 

 time, to be known. The serious errors produced upon the 

 latitude from a defective knowledge of the horary angles will 

 be seen by differentiating the author's equation, or even by 

 considering the two examples which he has computed. For 

 his final equation is identical with Dr. Brinkley's equation (S), 

 which again is the algebi'aic exj)ression of Douwes's rule for 

 computing the middle time between the observations, or the 

 horary angles from a supposed latitude by account. See Dr. 

 Brinkley's paper, p. 14, annexed to the Nautical Almanac for 

 1822, where the coefficient 2 has, from a typographical error, 

 been omitted in the denominator of the second member of the 

 equation. The horary angles, which the author has assumed 

 in his examples, being the approximate values found by Dr. 

 Brinkley from the first operations by Douwes's method, when 

 substituted in our author's formula they of course give for 

 latitudes the quantities assumed by the Doctor for the latitudes 

 by account. This is evidently going round in a circle ; and 

 yet it is from the results derived from this process that the 

 method of solving this problem, proposed by one of our first 

 mathematicians and astronomers, is asserted to give errors of 

 one degree of latitude. In this manner it might be convicted 

 of errors to any amount. 



Navigators will always prefer short and easy methods of per- 

 forming the astronomical problems requisite at sea, and there- 

 fore it is incumbent upon those who publish such methods to 

 be well assured of their accuracy. It is to be regretted that 

 our author had not taken the trouble of computing his ex- 

 amples in the direct trigonometrical manner ; for then he would 

 have at once discovered his error, and the censure, which he 

 seems to pass upon the methods hitherto proposed (several of 

 them by the most eminent mathematicians and astronomers of 

 Europe), would have been spared. 



I am, sir, yours, &c. 



Leopold Place, Edinbuicli, TiiOMAS HENDERSON. 



Oct. 14, 1825. 



XLVI. Ex- 



