74 HISTORY OF MECHANICS. 



of composition cannot be applied in the same way ; 

 and, in this case, mathematicians were met by 

 some peculiar difficulties. 



One of these difficulties arises from the apparent 

 inconsistency of the statical and dynamical mea- 

 sures of force. When a body moves in a circle, the 

 force which urges the body to the center is only a 

 tendency to motion ; for the body does not, in fact, 

 approach to the center ; and this mere tendency to 

 motion is combined with an actual motion, which 

 takes place in the circumference. We appear to 

 have to compare two things which are heteroge- 

 neous. Descartes had noticed this difficulty, but 

 without giving any satisfactory solution of it 1 . If 

 we combine the actual motion to or from the center 

 with the transverse motion about the center, we 

 obtain a result which is false on mechanical prin- 

 ciples. Galileo endeavoured in this way to find the 

 curve described by a body which falls towards the 

 earth's center, and is, at the same time, carried 

 round by the motion of the earth ; and obtained an 

 erroneous result. Kepler and Fermat attempted 

 the same problem, and obtained solutions different 

 from that of Galileo, but not more correct. 



Even Newton, at an early period of his specu- 

 lations, had an erroneous opinion respecting this 

 curve, which he imagined to be a kind of spiral. 

 Hooke animadverted upon this opinion when it was 

 laid before the Royal Society of London in 1679, 



1 Princip. P. iii. 59. 



