256 Mr. S. Sharpe on the Solid of greatest Attraction. 



glass stool; they imagine that something formidable is about 

 to happen to them, when perhaps they have only to have the 

 electric stream drawn from the affected parts with a wooden 

 point. When the multiplicity of apparatus required in the 

 usual way to go through a series of experiments, and when 

 the expensive and brittle nature of the principal materials, 

 as well as their being often used in the dark, are considered, 

 I flatter myself that the simplicity and advantage of the 

 construction here I'ecommended, will be apparent to every 

 practical electrician ; at any rate a machine so constructed 

 will be found a very convenient " working tool." 

 I am, Gentlemen, yours, &c. 

 Dereham, Norfolk, July 15, 1830. G. DAKIN. 



XLII. On the Solid of greatest Attraction. By Samuel 



Sharpe, Esq.* 

 r V y O determine the form of the solid which attracts a body 

 ■*■ on the surface with the greatest force. 



The attraction of each particle of the solid must be resolved 

 into two parts, and that part rejected which is not towards 

 the centre of gravity of the solid ; and the solid is such that 

 every point of its surface attracts the body equally towards 

 the centre; otherwise the sum of the attractions might be in- 

 creased by removing that portion which attracts least, and 

 placing it beside that which attracts most. 



Let A (fig. 1.) the body attracted, be a point on the surface 

 of the solid. Fi.<r. 1. B 



A B ( ss a) the diameter through 

 A and the centre of gravity. 



A P ( = c) the chord joining A and 

 any attracting particle P. 



Then letting fall PN ( = 3/) perpen- 

 dicular on A B, A N ( = r) will be the 

 corresponding abscissa. 



The attraction of the particle at B = 



— r and of P = — , but in the direction 



a* c~ 



of the diameter (this latter) = -£-, and 



9 s 



therefore, — = a 2 , and the equation of the curve {x°~ + y*Y = 

 x a- Q.— E. I. 



c 2 



The curve may be easily drawn thus : make z = — ; then 



* Communicated by the Author. 



a 2 = 



