THE 

 LONDON, EDINBURGH x^o DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



MAY 1857. 



H 



XLIV. On Equally Attracting Bodies, By Dr. T. A. Hirst*. 



[With a Plate.] 



'OWEVER great the practical difficulties may be which 

 - have to be overcome in order to calculate the attraction 

 of a given body upon a given material point according to New- 

 ton's law of the inverse square of the distance, nothing is more 

 evident than that innumerable other bodies exist, differing from 

 each other in shape as well as situation in space, each of which 

 would attract the given point in precisely the same manner as 

 the given body. Taken in its widest sense, the problem to find 

 all such equally attracting bodies is clearly indeterminate ; by 

 introducing certain restrictions, however, this problem, by be- 

 coming capable of solution, will lead us to the detection of cer- 

 tain groups of bodies possessing the property in question. The 

 possible advantages arising from a determination, in an indepen- 

 dent manner, of such groups of bodies will at once suggest them- 

 selves ; at any rate they need not be cited in justification of any 

 attempt to solve a problem which has undoubtedly sufficient in- 

 herent interest. 



In confining ourselves for the present to one of the above 

 groups of equally attracting bodies, we propose to examine— 



I. Equally attracting curves, i. e. bars or wires of infinitesimal 

 thickness ; 



II. Equally attracting surfaces ; and 



III. Equally attracting solids j 



to the first of which the present communication will be restricted. 



* Communicated by the Author. 

 Phil. Mag. S. 4. Vol. 13. No. 87. May 1857. Y 



