340 Essay on the Theory of Attraction. 



are often noticed in strong electrical discharges with a powerful 

 machine, especially where the electric fluid has to be diffused 

 on or amongst imperfect conductors. 



Probably these or similar phenomena are not uncommon 

 in the torrid zone, where it is said the coruscations of light- 

 ning are frequently seen in the sky when there are no clouds; 

 but as similar appearances are rarely, if ever, observed in this 

 neighbourhood, I have been induced to draw up the foregoing 

 account in the hope that if similar phsenomena have been no- 

 ticed, some description of them may be given by other writers. 



Manchester, September 30, 1850. 



XLII. Essay on the Theory of Attraction. By John Kin- 

 nersley Smythies, Barrister-at-Law of 'the Middle Temple. 



To the Editors of the Philosophical Magazine and Journal. 



3 Oakley Square, London, 

 Gentlemen, October 14, 1850. 



I ADMIT that my essay noticed in your last Number con- 

 tains a serious error. I now perceive that wherever <£ 

 (the function of the distance, according to which the attractive 

 force varies) occurs in an equation, the term involving it is 

 multiplied by a function of the distances and angles, which is 

 zero for all positions of the bodies, so that <fi may have any 

 value consistently with the equations containing it. The cor- 

 rection of this error requires that sections 11, and 13-18 in- 

 clusive, and some short references to them, should be cancelled: 

 the remainder will be free from this error. 



Till I read your notice, I supposed that my equation be- 

 tween the ten mutual distances of five points in space was 

 new; and having since referred to Carnot's memoir, I find 

 that the labour I spent on the solution of that problem is 

 not wholly lost, since my demonstration is much shorter 

 and less laborious for the reader than Carnot's. When all, 

 in which I have been anticipated or have erred, shall have 

 been deducted from my essay, I venture to express my hope 

 that something new and true will still remain. By the publi- 

 cation of this short statement in your Magazine you will much 

 oblige, Gentlemen, 



Your obedient Servant, 



J. K. Smythies. 



