THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



SEPTEMBER 1858. 



XVIII. On Equally Attracting Bodies. By Dr. T. A. Hirst*. 



II. On equally attracting Surfaces. 



1. A S in the former memoir f, we shall again find it convenient 

 -tJL to employ polar coordinates, the attracted point being 

 taken as pole, and to adopt the following as definitions : — 



Corresponding points of two orv more surfaces are those which 

 lie on the same radius vector. 



Corresponding tangent planes touch their respective surfaces at 

 corresponding points, and the normals at these points are corre- 

 sponding normals. 



If we allow ourselves, for the sake of brevity, to make use of 

 the term vector-plane for any plane through the radius vector at 

 any point, then the plane which contains both the radius vector 

 and the normal may be called the normal vector-plane of the 

 point under consideration, so that corresponding normal vector- 

 planes will pass through the same radius vector and contain 

 corresponding normals. 



Lastly, any cone having its vertex at the attracted point or pole 

 will be said to intercept upon two or more surfaces corresponding 

 portions or elements according as the dimensions of the cone are 

 finite or infinitesimal. Corresponding elements produced indefi- 

 nitely in every direction constitute, of course, corresponding tan- 

 gent planes. 



2. In each point of our surfaces we shall conceive matter of a cer- 

 tain density to be concentrated, and this matter will be regarded as 

 capable of acting at a distance — of attracting along the radius vec- 

 tor — according to the law of inverse squares. Amongst the infinite 



* Communicated by the Aiitlioi*. 

 t See I'hil. Mil}!;-, «■ ^- vol. xiii. p. .SO.'i. 

 Phil. Mag. S. 4-. Vol. 16. No. 106. Sept. 1858. M 



