Mr. Henderson on Mr. Burns's Nautical Problem. 283 



Habitat C. B. S. G. H. H. 



Floret verno tempore,more affinium. 



0^5. H. concuvce simillima habitu et magnitiidine, 

 tbliis forte niinoribus, aristula longiore, paiicioribus 

 (sive adhuc iiuUis) propaginibus, uno singular! excepto 

 in summo scapi floriferi, quae in nostro exeniplo per 

 annum ultrave persistit. Distinguitur optime foliorum 

 plana pagina. 



angustifolin. H. (slender-leaved) foliis lorato-attenuatis ar- 

 1 0. cuatim patenti-recurvis perviridibus, apice subcarinatis ; 

 carina orisque creberrime denticulatim exasperatis. 



Habitat C. B. S. G. H. %. 



Floret Junio, affinium more. 



Obs. H. chloracanthce Nob. proxima, at minor, foliis 

 multo angustioribus, patentioribus et longioribus s. 

 3 — 4-uncialibus, subtiis convexis, supra planioribus, 

 seepiiis linea elevata longitudinali centrali ; marginali- 

 bus denticulis minutissimis, et inarmato oculo vix con- 

 spicuis. 



XLV. On Mr. Burns's Method of Jinding the Latitude by 

 Double Altitudes. By Thomas Henderson, Esq. 



To the Editor of the Philosophical Magazine and Journal. 



Sir, 

 ¥ N your Number for September, art. xxx. there is professed 

 *- to be given a short, direct, and accurate method of finding 

 the latitude at sea by double altitudes and the time between. 

 But I believe that the following considerations will show, with- 

 out difficulty, that this method is altogether inefficient, and 

 produces erroneous results, which may often lead to serious 

 consequences. 



The author first assumes the trigonometrical formula for 

 determinhig the altitude of a celestial body by means of the 

 latitude, declination, and horary angle, on which the solution 

 of this problem in the Requisite Tables depends, and which be- 

 ing transformed gives the well-known equation for expressing 

 the cosine of a side of a spherical triangle in terms of the sines 

 and cosines of the opposite angle and the other sides. Tliis 

 equation, which Delambre and other late writers make the 

 foundation of all spherical trigonometry, might have been as- 

 sumed at tmce, without being detluced from one of its own 

 corollaries. The author next finds an et|uation for determi- 

 ning ihe latitude from the observed altiludes and the times or 

 horary angles, which, he says, from tiic improved state of our 

 N n 2 chronometers 



