206 ON POECES OP ATTRACTION TO SEVERAL CENTRES. 



The younger Euler (J. A. Euler) lias a paper in the Berlin 

 Mem. 1760, p. 250, upon the action of a central force de- 

 creasing as the distance, in the case of the attracted body's 

 descent towards the centre, and states the reason of this 

 problem being insoluble except by arcs or logarithms. He 

 finds that taking a = the height from which the descent 

 begins, f = that at which the centripetal force is equal to 

 the gravity of the attracted body, the time of descent to- 



wards the centre is = =r -- , y being the distance 



' 



= =r -- , 

 SfJ 



from the centre.* 



* This Tract is from Appendix in. and IV. to the Analytical View of 

 the Priucipia, pp. 424, 421. 



