Prof. Hare's improved Eudiometrical Apparatus. 183 



We shall then have for every observation the following equa- 

 tion : 



O + at 2 -bt = M 



t_ 15*. »in 1" cos <p . cos 2 7 



where a = . . \ ^ : b = 



sin (<p-$) ' 86400 



Let — =t seconds; and we shall have + a(t— t) 9 = 



M+tfT 2 , where the part on the right is the same for every 

 observation, t being independent of t. This equation shows 

 that the greatest, O, will belong to t—r = 0, or t = t, and will 



exceed the meridian-altitude M by ar 2 [ = -£-\ or that r 



seconds after noon the sun will attain his highest altitude 

 M + tfT 2 , to which every observed altitude may be reduced by 

 the addition of the single term a [t—r) 2 ; t—r will evidently 

 be the number of seconds elapsing between the observation 

 and the moment of the sun's highest altitude. This moment 



is found by this equation: r (= - — ) = A , '* m \ , 



J n \ 2a/ 100 . cos <p . cos $ \ 



log. N = 0*0257289, and r is positive in the ascending, and 

 negative in the descending signs. Prof. Schumacher publishes 

 annually a table of the values of t for every tenth day of the 

 year, and every degree of latitude from 36° to 60°. It is un- 

 necessary to add, that the quantities a (£— t) 2 for every obser- 

 vation, and the constant quantity ar 2 , are calculated by the 

 assistance of the well-known tables of Delambre, Dr. Young, 

 and others. 



We entirely avoid, therefore, by this method, the calcula- 

 tion of the term bt, or the change of declination for every ob- 

 servation. M. Von Heiligenstein, who has explained this me- 

 thod in Prof. Schumacher's Astr. Nachrichten, No. 134, has 

 neglected the quantity «t 2 , which indeed never amounts to 

 0"*25 ; but it is clear that this is not correct, and that where 

 great accuracy is required it certainly ought to be taken into 

 consideration. J. L. T. 



XXXI. Improved Eudiometrical Apparatus. By R. Hare, 

 M.D. Professor of Chemistry in the University of Pennsyl- 

 vania. 



[Concluded from page 134.] 



Of the Barometer-Gauge Eudiometer by Phosphorus. 



A HOLLOW glass spheroid A, of which the vertical dia- 

 ■*-*• meter is 11 inches, the horizonal diameter 9 inches, is 

 cemented into a brass socket which screws into the Same place 



as 



