24 Mr. Ivory on deducing the Difference 



other nations, have been obhgcd to modif}' that system of 

 writing, to adajit it to their own languages. He adds, that 

 the details of these alterations are to be found in a late me- 

 moir of M. Remiisat, inserted in the 8th volume of the Me- 

 moirs of the Institute of France (Academy of Inscriptions and 

 Belles Lettres), pp. 34—69. Thus I have the good fortune to 

 have M. Champollion and M. Remusat on my side, to some 

 extent, at least, though to liihat extent I cannot exactly tell, 

 as the volume of the Memoirs of the Institute above referred 

 to, has not yet reached this country, at least that I know of. 

 I am very anxious to see it, as I have no doubt that the subject 

 will have been treated in a very profound and scientific man- 

 ner, by so able and learned a writer as M. Remusat. I beg 

 leave to refer you to it, for further information on this inter- 

 esting topic. P. S. D. 



III. On the Method of deducing the Difference of Longitude 

 from the Latitudes and Azimuths qftwoStatiojis on theLartlCs 

 Surface. By J. Ivory, Esq. M.A. F.R.S. 4-c.* 



I 



NOW proceed to deduce the consequences that result 

 from the equations (A) at p. 433 of the last Number of 

 this Journal. Conceive the planes of the meridians of the two 

 stations on the earth's surface, to be prolonged to meet the 

 sphere circumscribing the terrestrial spheroid, and, in the great 

 circles of the sphere, take two points having the same latitudes 

 with the terrestrial stations ; let /3' denote the arc of a great 

 circle passing through the two points, and there will be formed 

 a spherical triangle of which the three sides are 90° — X, 90° — A', 

 /3' ; the angle opposite to |3' will be w the difference of longi- 

 tude ; and if we put ju. for the angle opposite to 90°— X', and 

 [jJ for that opposite to 90°— A, we shall have, by spherical tri- 

 gonometry, 



sin a . , I „ 



+ cos w sm A — cos A tan A' =0, 



tan fi 

 sin a 



+ cos M sm A' — cos A' tan A = 



tan fi 



Subtract these equations respectively from the equations (A) 

 above cited ; then 



~,. , , sin u cos X o . / y-v 



Sm (u,—m) X -. : = T.e^ A'Q 



^' ' sin ^ sin m cos K ^^ 



t~\' / I i\ sin w cos ^' „ y-. 



Sin(m' — u.') X -. — — — ; = .c- A Q. 



^ sill f. sin m cos A. 



* Conimiinicatcd by the Author. 



But, 



