[ 34-4. ] 



LV. Reply to the Observations of Mr. Riddle and Mr. Hen- 

 derson on Mr. BuRNs's Mode qfjind'mg the Latitude hij 

 Double Altitudes. By James Burns, £55-. 

 To the Editor of the Philosophical Magazine and Journal. 

 Sir, 

 T^HE remarks made by two of your Correspondents on my 

 -■■ method for solving the problem of double altitudes seem 

 to call for some reply on my part, as they both appear to have 

 misunderstood the foundation and object of it. In the first 

 place then, INIr. Riddle thinks that I " misapprehended the 

 nature of the problem altogether," and asserts that I have as- 

 sumed data, which, in nautical practice, cannot be obtained, 

 viz. the horary angles or apparent time, and the iyiterval. Now 

 Mr. R. ought to have known that those angles can be always 

 had, by means of the valuable Horary Tables first published 

 bv that distinguished astronomer j\I. Lalande in 1793; and 

 he ought to have seen that mj' method posttdated the use of 

 such tables, which I distinctly stated in the outset. Hence 

 it is very plain, that where those tables are used, the problem 

 of double altitudes becomes a matter of mere curiosity, and 

 that the importance which is attempted to be attached to it 

 vanishes. However, the formulas which 1 have given in my 

 method will be the best verification of them, whether the ob- 

 server would find his latitude by single or double altitudes. 

 When I mentioned the chronometer, I did so (it must be evi- 

 dent to any one that understood the question) not for the pur- 

 pose of deducing from it the ajiparent time, but merely to de- 

 termine the interval. In this last point only, Mr. R. seemed 

 to comprehend the proposed method. If the above-named 

 tables were introduced into the modern compilations of navi- 

 gation published in this country, it would be an essential im- 

 provement, as mariners would by their use be saved the trouble 

 of practising the method of double altitudes, especially by rules 

 which not one out of a hundred could practise, and not one 

 out of a thousand could understand. — Besides, if there were 

 no such tables in existence, the horary angles which, these 

 gentlemen imagine, cannot be 



ascertained at sea, can be al- ..-■--,'•., 



ways had by calculation, as ,.••' ,' '-•, 



well as the latitude, as follows: ,■■' J. 



Let P be the pole, Z the S'^'.' •' " ^"""--v 



zenith, S 5 the sun's parallel ; "'••... ,' x'^ 



and let us suppose PZ the co- "■•-.^ • ,,.'** 



latitude nearly known, as it \ I ...♦'''' 



generally will be; and then c *' 



we have a spherical triangle, 



of 



