ON THE MOTIONS OF SIMPLE MASSES. 55 



equally true, if instead of the shortest distances, we substitute the distances 

 from the same plane, measured obliquely, in any directions always parallel to 

 each other. This property is peculiarly applicable to the consideration of the 

 centre of gravity, and affords also the readiest means of determining its place 

 in bodies of complicated forms. (Plate III. Fig. 32.) 



We have already seen that the place of the centre of inertia of two bodies 

 is not affected by any reciprocal action between tliem ; and the same is true 

 of the actions of a system of three or more bodies. We might easily apply 

 our experiment on the reciprocal action of two bodies to a greater number, 

 but we should throw no further light on the subject, and the mode of obtain- 

 ing the conclusion would be somewhat complicated. 



All the forces in nature, with which we are acquainted^ act reciprocally be- 

 tween different masses of matter, so that any two bodies repelling or attracting 

 each otlier, are made to recede or approach with equal momenta. This cir- 

 cumstance is generally expressed by the third law of motion, that action and 

 reaction are equal. There would be something peculiar, and almost incon- 

 ceivable, in a force which could affect unequally the similar particles of mat- 

 ter ; or in the particles themselves, if they could be possessed of such differ- 

 ent degrees of mobility, as to be equally moveable with respect to one force, 

 and unequally with respect to another. For instance, a magnet and a piece 

 of iron, each weighing a pound, will remain in equilibrium when their weights 

 are opposed to each other by means of a balance ; they will be separated with 

 equal velocities, if impelled by the unbending of a spring placed between thenij 

 and it is difficult to conceive that they should approach each other with une- 

 qual velocities in consequence of magnetic attraction, or of anj' other natural 

 force. The reciprocality of force is therefore a necessary law in the mathe- 

 matical consideration of mechanics, and it is also perfectly warranted by ex- 

 perience. The contrary supposition is so highly improbable, that the princi-. 

 pie may almost as justly be termed a necessary axiom, as a phenomenon col- 

 lected from observation. 



Sir Isaac Newton observes, in his third law of motion, that " reaction is 

 always contrary and equal to action, or, that the mutual actions of two bodies 

 are always equal, and directed contraiy ways." He proceeds, " if any body 



