on the Series of the Article " Cohesion." oil 



had made the depression less instead q{ greater : but he has not 

 attempted in the slightest degree to invaUdate the chain of argu- 

 ments, by which it is undeniably demonstrated, in the Journal of 

 the Royal Institution, that the depression must lie less than 

 •00418, for a tube of six-tenths of an inch in diameter, and that 

 it cannot therefore be either '00443 or -00431. 



While this simple computation remains uncorrected, it must 

 be allowed that Mr. Ivory's ingenious refinements have only fur- 

 nished him with tivo methods, both of which are in error to the 

 estent oi ten or tiuelue times the supposed unit, if not, like his 

 table in the Supplement, to the extent of twenty. It may how- 

 ever still be hoped, that his favourite "exponentials" may afford 

 him a third formula, which will again enable him to lisect this 

 error : and that he may have resolution to proceed in inventing 

 an infinite series nfseries^ approaching by degrees to the accuracy 

 of that, which was first applied to the solution of the problem by 

 the original author of the whole uivestigation, in its present form. 



My object in these remarks is triith, not victory ; for I do not 

 pretend to be a competitor for victory with Mr. Ivory in point of 

 analytical ingenuity. But what I do see clearly I will assert 

 boldlv; and will not give way to high authority, against that which 

 ajipears to me to be plain matter of fact. 

 I am, sir. 



Your very obedient servant, 

 London, 8th May 1821. ' S.B. L. 



Postscript. — Mr. 1%'ory ol)serves, that he has not been able to 

 accomplish what he had in view bv the employment of the Taylo- 

 rian theorem ; although he alludes to that part of the Elementary 

 Illustrations of the Celestial Mechanics, in which the way of ap- 

 plying the theorem to the problem in question is particularly 

 pointed out. It appears, therefore, that he was disposed to ob- 

 ject, for some unassigned reason, to the accuracy of that analysis: 

 for it is impossible to conceive that he could have felt any difli- 

 culty in following its steps, if he had approved it : and it becomes 

 necessary to show that the virtues of the " universal solvent " 

 have not, in this case at least, been exaggerated. 



For a tube six-tenths of an inch in diameter, the convergence 

 of the original series is amply sufficient, as far as | of an inch 

 from the axis, the high powers of \ being considerably smaller 

 than those of -r\-. We readily obtain from the Supplement, 

 p. 220, when x = \, the series .? = 3-G25 1 bx + 3-24 12 l^x^ 

 + I3-y b'x^, h being here supposed •4l(!0, ami bx = -\{)AO, 

 whence 5 = -37701 + -00304 + -00019 + [-00002] =38086; 

 the inclination l)eing 22° 23', the cosine -92463, and the tan- 



Vol.r,7. No. 277'. May 1821. 3 B gent 



