182 On the Reduction of Circummeridian Altitudes of the Sun. 



The most probable ellipticity by the pendulum-experiments 



appears to be, from my calculations, 0*00330 



The same, from my comparison of degrees . . . 0*00322 



Mr. Ivory's investigations give from arcs 0*00324 



Laplace adopted 0*00326 



Mean of the whole 0*00327 



It is probable that Mr. Ivory's ellipticity, or 0*00324, is the 

 most accurate of the whole, and may safely be adopted as that 

 to which it will ultimately converge, since it satisfies all the 

 most accurate arcs hitherto measured with extreme precision. 



But the most extraordinary circumstance attending all these 

 comparisons is their discrepancy from those of Mr. Professor 

 Airy, of Cambridge, who finds from Captain Sabine's pen- 

 dulum-experiments 0*003474 ; and still more so the result of 

 his comparison of arcs, which is 0*003589 ! these arcs being 

 the very same as those which Mr. Ivory and I have employed. 

 To what cause then must this discordance be attributed ? Can 

 it be supposed that the Professor has committed an error 

 either in his investigations, or in his calculations, or in both ? 

 In such an important investigation it would be most desirable 

 to see the whole scrutinized with great care, and this scrutiny 

 would come with a better grace from the Professor himself than 

 from any other individual. I am, Gentlemen, yours, &c. 



Edinburgh, June 18, 1828. WlLLlAM GALBRAITH. 



XXX. On the Reduction of Circummeridian Altitudes of the 



Sun*. 



PROFESSOR GAUSS's ingenious method of effecting the 

 usual reduction of circummeridian altitudes of the sun not 

 having yet been noticed in any English work, the following 

 deduction of the same will perhaps deserve a place in the 

 Philosophical Magazine. Let 



<p= the latitude of the place of observation. 

 8= the sun's declination at noon. 

 J8 = the change of the sun's declination in 24 hours at noon 

 expressed in seconds. 

 — t = the number of seconds any observation was taken 



before noon. 

 + t =z the number of seconds any observation was taken 

 after noon. 

 0= the observed altitude of the sun for the time /. 

 M = the meridian altitude of the sun. 



* Communicated by the Author. 



We 



