Mercury in Glass Tales. 85 



convergent ; and its want of convergence in extreme cases might 

 be easily remedied, if it were necessary, by means of Taylor's 

 theorem ; but its convergence is already abundantly sufficient 

 to prove, that, in some instances, Mr, Ivory's numbers are er- 

 roneous, and not to the amount of " one unit in the last place 

 of figures" only, but to twenty times that amount, or to two 

 units in the last jolace but one. 



The depression in a tube of six-tenths of an inch in diametei, 

 for example, is made .00443, while in the article Cohesion it 

 stands either .00416, or .00413, according to the different bases 

 assumed from experiment. Now the series, computed for this 

 case (P.221), becomes .75 = .7160 -f .0254 + .0060 + [.0026], 

 the last term only being added from considering the ratios of 

 the preceding ; and it will appear upon examining the formation 

 of the co-efficients, that the first two numbers are determined 

 with perfect precision, and the third with a very small degree 

 of uncertainty ; so that the sum of the parts depending on 

 strict demonstration amounts to .7 160 + .0254 -1- .0050 = .7464, 

 diflfering from the whole supposed sura by ^ Jo only ; and if 

 we omitted altogether this undemonstrated part, we should 

 have, instead of .00416, about .00418, for the utmost possible 

 value of the depression in this case. Indeed, the first term of 

 the ultimate series alone affords a more correct result than the 

 whole of Mr. Ivory's approximation. 



It seems, therefore, manifest, either that Mr. Ivory has neg- 

 lected in his formulas some terms which ought to have been 

 comprehended, or that some numerical error has occurred in 

 one of the two computations. But considering that the tables 

 differ tliroughout from each other in a regular manner, the' 

 diversity can scarcely have arisen from any blunder of this 

 kind ; and it remains for Mr. Ivory, if he think proper, to ac-- 

 count in some other way for the paradox. 

 I am, Sir, 



Your very obedient servant, 

 Loudoji,Dec.M, 1820. S. B. I,. 



