294 A SHORT HISTORY OF SCIENCE 



forces conjoined will describe the diagonal of a parallelogram, in the 

 same time that it would describe the sides, by those forces apart 



Of these laws, Pearson in his Grammar of Science remarks : 



The Newtonian laws of motion form the starting-point of most 

 modern treatises on dynamics, and it seems to me that physical sci- 

 ence, thus started, resembles the mighty genius of an Arabian tale 

 emerging amid metaphysical exhalations from the bottle in which for 

 long centuries it has been corked down. 



Passing to variable forces he discusses in particular the motion 

 of a body acted on by a central attractive force i.e. a force at- 

 tracting it towards a fixed point. He derives the law by which 

 equal areas are described in equal times, and shows that con- 

 versely, if equal areas are so described in a plane, the determining 

 force must be a central one. Turning to the consideration of or- 

 bits, he deals with the hypothesis of an elliptical orbit with the 

 attracting force at one of the foci, and shows that the attractive 

 force must vary inversely as the square of the distance from that 

 focus. The same result is obtained for the other conic sections. 

 These theorems applying to particles, he next shows that the action 

 of a homogeneous sphere on an external particle is the same as if 

 its mass were concentrated at its centre, so that the action of two 

 such spheres on each other is subject to the laws already derived. 



Comparing planetary motions with those of projectiles which 

 had been treated by Galileo, Newton says : 



That the planets can be held in their paths is evident from the 

 motions of projectiles. A stone thrown is deflected from the straight 

 line by its weight and falls describing a curved line to the earth. If 

 thrown with greater velocity it goes farther, and it could happen that 

 it described a curve of 10,100,1000 miles, and at last went outside the 

 boundaries of the earth, and never fell back. . . . 



The force of gravity for small distances being sensibly constant 

 in direction, causes motion in a path approximately parabolic. 

 For greater and greater ranges the change of direction of the 

 force must be taken account of and the path recognized as ellipti- 

 cal or hyperbolic. The laws as stated deal with the relations of 



