268 Dr. Hirst on Equally Attracting Bodies. 



property, and then indeed they are identical with the two sur- 

 faces already considered in art. 16. 



26. A second particular case, of more interest than the last, 

 arises from the hypothesis 



0= cos 6, and $= tan ^, 



by means of which the equations (22), art. 24, become 



- = ^=^[log (sin e . sin (/>)] . ^i[log (tan 6 , cos 0)], 



ri _ c'l _ '^ [log (sin 6 . sin ^)] 



Cj ~ /•', "" '^j [log (tan ^ . cos </))] * 

 If wc transform to rectangular coordinates by means of the 

 forumliic 



a; = 7' cosO, 



y = r sin 6 . cos (p, 

 ^•z::^ sin 6 . sin 0, 



and replace the functional symbols '^ log, ^P, log by the equally 

 available symbols "^j ^j, the above equations assume the simpler 

 forms. 



■\^ 



I—'' i_ 



© 



*.(!) 



!3) 



27. Instead of examining the nature of the surfaces here re- 

 presented, we will particularize still further by assuming 



If, at the same time, wc confine our attention to the two surfaces 

 (?•) and (/-j), the formulae (23) take the forms 



g=c^A^ 



(I)'] 



(24) 





and the surfaces represented are both cunoidal, inasmuch as they 

 are generated by the motion of a line which always cuts the 

 5r-axis perpendicularly. 



28. One of the most interesting cases of such equally attract- 



1 



