+0 Mr. Ivory's Solution of a Geodetical Problem. 



In Dr. Young's paper, no reason is given why the refrac- 

 tions should be more exact when they are computed by the 

 assumption adopted than by any other. We may observe 

 here, by the by, that this mode of proceeding is at present not 

 uncommon in physical inquiries where the mathematics are 

 concerned ; the real difficulties being often got rid of, by a 

 phrase, or by some analogy, or by sliding in a formula to 

 serve as the basis of a calculation. In the present instance 

 we are referred to something that is said to be demonstrated 

 in the Journal of the Royal Institution. This probably al- 

 ludes to the passage at p. 148 of No. 31, to which I have al- 

 ready adverted in this Journal for April last. The reader 

 will find that nothing is proved ; and that the whole amounts 

 to the applying of the same assumption, viz. /« = 2, to another 

 of my general formulae, as indeed is very plainly implied in 

 the words of the passage. 



Dr. Young concludes his paper with giving a finite formula 

 of four terms, similar to that in the Nautical Almanac, by 

 which, he says, my table may be computed with great accu- 

 racy. Now this very fairly concedes every thing I have at 

 anv time said of the formula, and the method for the refrac- 

 tions in the Nautical Almanac. I have said that the method 

 does not emanate from any exact theory; that the formula is 

 empirical, and of no use till a table be produced, by means 

 of which the proper values are to be assigned to the indetermi- 

 nate coefficients. The formula will thus represent, to a cer- 

 tain degree of exactness, the French table, or that of M. Bes- 

 sel, or that of Dr. Bradley, or mine. But as it will represent 

 any table whatever, good or bad, it can be an authority for 

 none. The real foundation of the table in N. A. is the man- 

 ner in which the coefficients of the formula have been ob- 

 tained ; and not a word has escaped that can throw light 

 upon this point in all the discussions that have been sent forth 

 to the public quarterly in the Journal of the Royal Institution. 

 It appears that the table has been so constructed as to agree, 

 partly with M. Bessel's table, partly with that of the French 

 astronomers, and partly to fall between the two. In this man- 

 ner we can exactly appreciate the table ; whereas it is en- 

 veloped in mystery and obscurity when we regard it as a crea- 

 tion of the formula. 



July 10, 1824. J. I. 



VI. Analysis 



