a new Method of determining the Latitude. 365 



than two years after the observations given in that letter were 

 made and computed froin. 



The method of Gen. E. is even more like mine than { was 

 likely to anticipate, as it is absolutely the same, both in principle^ 

 and in all its practical details. The only diifeience, if a dif- 

 ference it can be called, is in tliis, that I deduce the latitv.de each 

 day from separate observations of th.e uj)per and lower linios of 

 tlie sun, taken alteinatcly ; by which means any faultv habit of 

 estimating the contact is prevented from vitiating the result. In 

 Gen. B.'s two exampies this precaution is not observed; and it 

 is easy to perceive that, in consequence, each of his results 77iai/ 

 be affected by a coinmon error incident to his method of esti- 

 mating the contact. .Setting this aside, however, as a circum- 

 stance from vvhicii, in the case of so excellent an observer, no 

 error of any moment wliatever will probably arise, the absolute 

 identity of his method and mine is beyond all (|uestion. 



Gen. B. computes the declination for the instant ol each ob- 

 servation, so do 1 ; he reduces each altitude to the meridian se- 

 parately, so do I ; he deduces the latitude from each altitude 

 thus reduced separately, so also do I ; and the theorem bv which 

 he calculates the reduction to the meridian is the same as that 

 which I use for the same purpose. His theorem isy"(the reduc- 



. 2 sin- :t P /cosH.cosDX , tt • i i • i i~v 



tion) = — ,,.= ' . ( — — , , ^, ) ; where H is the latitude, D 

 ' 1' \cos(H + D)/' ' 



the declination, and P the horary angle. 



My theorem is z (the reduction) = — —, — . sin PS . sin PZ . 



cosect ZS ; where PS = the polar distance, PZ= the colat., and 

 ZS = the meridian zenith distance. Now vers. P= 2 siu^ ^P^ 



sin PS = cos H, sin PZ = cos D, and cosect ZS = -^-pi^T^.. 



' ' sill (11 + D)* 



The theorems are therefore the same; only the one which I used 

 is a little more convenient in form. But on tlie subject of the 

 tlteorem I dare sav neither of us fancies that he has made any 

 discovery. 



Though the absolute identity of the two methods in every par- 

 ticular is, to say nothing else, a very curious circumstance; I have 

 no reason to believe tliat Gen. B. has availed iiimself of any thing 

 that 1 iuive done on the sul)jcct, notwithstanding the publication 

 of my letter took place, probably, loni^ before his communication 

 was written. I understand he has of late chiefly resided aljroad; 

 and even wiien in this ctmnuy he probably may not s-c tlie work 

 in whicii my letter appeared. 



But 1 cannot help thinking it exceedingly singular, that his 

 jjapcr should have been printed in so respectable a pul)licalion, 

 without a hint from any one connected with the work, that how- 

 ever 



