On ike Depression of Mercury in Glass Tules, 269 



hiav be confirmed. If two independent methods of computation 

 agree in bringing out the same numerical values, a greater proof 

 of exactness can seldom be obtained. Now having computed the 

 depressions in the table by the formula just set down, I have 

 found the same results as before, with slight differences in the 

 last place of figures, except in the cases of the bores 0-5 and 0*G, 

 in each of which a numerical error has been detected. In the first 

 instance, I = -b ; t = 3-0625 ; X = 3-546 ; then 



q = ""'I^S ^ .00815. 

 in the other instance, Z = 06; ^ = 4-41 5 A = 5-579; and 



o = "i^^ = -00431. 

 ^ l.x 



These results are confirmed by the new formula. The num- 

 bers in the table, viz. -00835 and -00443 are therefore both er- 

 roneous ; although the real state of the case is not on this ac- 

 count much altered, 



I may observe here that, in the long run, or for tubes large 

 enough, the expression, 



•01445 



will coincide with the formula given long ago by Laplace at 

 p. 65 of the Supplement to his Theory of Capillary Action. The 

 truth is, that A continually tends to a final expression as the bore 

 of the tube becomes greater ; and it is only when thatquantity has 

 attained its ultimate value that the two rules will coincide. La- 

 place's formula fails in giving an approximation near enough the 

 ttuth for tub&s contained in the table ; but it would be found to 

 have all the exactness to be wished for in larger tubes, lying be- 

 yond the scope of the table. 



In conclusion, sir, I am sorry that in this investigation I 

 was obliged to introduce such obnoxious quantities as expo- 

 nentials, &c., and I must express my regret that 1 could not ac- 

 complish what I had in view by means of the Taylorian Theorem, 

 that universal solvent of all analytical difficulties, as it has lately 

 been discovered to be. Believe me to be, &c. 



April 7, 1821. J. Ivory. 



XLIV. True apparent Right Ascension of Dr. Maskelyne's 

 36 Stars for every Day in the Year 1821. By the Rev. 



J.tjROOMy. 



[Continued from p. 19^.] 



1821. 



