97 



when brought to bear upon the subject of mechanics ! All 

 writers up to this time — and among them are Newton and 

 Laplace — have stated and apparently proved, that the re- 

 sultant of two forces divided the angle between them into 

 parts, the sines of which were inversely proportional to the 

 adjacent forces. But our author has shown this to be all a 

 mistake ; that not the sines of the parts are inversely pro- 

 portional to the adjacent forces, but the parts themselves ! 

 Thus, if two forces of two and eight pounds 



respectively, w r ere acting at a certain point at right angles 

 to each other, the resultant according to Newton and others, 

 would make an angle of about 14° with the greater, but 

 according to Dr. Hickok, an angle of 18° ! 



A little further on in his discussion of this same law he 

 arrives at another conclusion which will startle mathema- 

 ticians of the old school. When two equal forces are acting 

 in diametrically opposite directions, he finds that in that 

 case they have a resultant at right angles with their com- 

 mon line. Thus, if two equal and diametrically opposite 

 forces were acting at a point 



c 



P, instead of destroying each other, as we know they would, 

 our author gives them resultants C, which squirt out in 

 every direction at right angles with the forces. At first we 

 were inclined to believe that this was a mere oversight, 

 made when the author's rational insight was less acute than 

 ordinary ; but we were astonished to find that he employs 

 [Trans, v.] 14 



