126 



BRUSH— DISCUSSION OF 



[April 24, 



conception to the case of the earth and moon. I have endeavored 

 to visuaHze Laplace's conception in Fig. 5, in which E represents the 

 earth, M the moon moving in the dotted Hne orbit in the direction 

 indicated by the large arrow, and lines NE the " gravific fluid " rush- 

 ing from all directions toward the earth. The orbital motion of the 

 moon continually carries her laterally against the stream of " gravific 



..-?^ 



Fig. 



Fig. 6. 



fluid," whereby she experiences a tangential retarding force, indi- 

 cated by the small arrow, just as if a less rapid flow of "gravific 

 fluid " came from that direction. Let the line MP represent the 

 direction and value of the retarding force in terms of the centripetal 

 force ME. Completing the parallelogram of forces, we find the line 

 of the moon's attraction shifted from ME to MO. Clearly this 

 would result in the moon taking an orbit in the form of a contract- 

 ing spiral which would ultimately bring her to the earth. At the 

 same time her actual velocity would continually increase (and her 

 angular velocity still more so) because of her falling toward the 



