364 NEWTON S PRINCIPIA. 



The motion of the fluid is propagated in all directions 

 with a. velocity equal to that of sound, and consists for 

 each molecule of two sorts of vibrations ; one whose 



st 



vibrations are very rapid, the time being TT sec, where 



c is the radius of the sphere, and a the velocity of propa 

 gation of sound. This will produce a sharp note, but in 

 sensible to the ear, because the amplitude of the vibrations 



_ ** 

 containing the exponential e * c rapidly decrease. The 



time of vibration of the other sort is equal to that of the 

 pendulum, and its magnitude decreases successively ac 

 cording to the same law that those of the pendulum follow. 

 These also will be insensible to the ear. 



We have now to test the correctness of the theory by a 

 brief comparison of its results with those of experiments. 

 Recur to our list of results. 



Theory teaches us that the resistance of the air is not in 

 sensible ; that the value of x does not depend on the interior 

 structure of the body, and it explains why x does not alter 

 much, being a fraction depending on the form of the body 

 and the external circumstances of the fluid ; it enables us 

 even to approximate to its true value. But it does not ex 

 plain why x is greater for small than large spheres, and the 

 very principles of the theory in regard to the motion of the 

 fluid in contact with the body is in opposition to certain ex 

 periments. Theory teaches also that the effect of the fluid is 

 not a resisting force varying as some function of the velocity, 

 but that its effect is simply to increase the inertia of the 

 body, and thus leaves the arc of vibration constant, which 

 is contrary to the commonest observations. Neither does 

 the theory explain the difference between the resistances in 

 hydrogen and air. 



The two important points of the motion are the time 

 and the length of the arc of vibration. Thus while the 

 ordinary theory of Hydrodynamics agrees in the main 



