NEWTON S PRINCIPIA. 255 



determined, but it was found to be greater than a third 

 part of the whole resistance of the lesser pendulum. 

 When this third part is subtracted, the ratio 7 J to 1 be 

 comes 7 to or 10 to 1, a ratio not very different from 

 llyf to 1.&quot; Since the resistance of the thread is of less 

 moment in greater globes, Newton also tried the experi 

 ment with a globe whose diameter was 18| inches. He 

 found the resistance on this globe to be 7 times that on 

 the first globe, whose diameter was 6J inches ; but the 

 squares of the diameters are in the ratio of 7.438 to 1. 

 The difference of these ratios is scarcely greater than 

 what might arise from the resistance of the thread. 

 Therefore the parts of the resistances which are in swift 

 motions when the globes are equal as the squares of the 

 velocities, are also when the velocities are equal as the 

 squares of the diameters of the globes. &quot;We shall find 

 occasion to modify this conclusion in another chapter. 



In order to determine the manner in which the resist 

 ance depended on the density of the fluid, Newton calcu 

 lated the resistance made to a body oscillating in water 

 and in air, and found that that part which is proportional 

 to the square of the velocity (and which alone it is neces 

 sary to consider in swift motions) is proportional to the 

 density of the medium. &quot; This is not perfectly accurate ; 

 for more tenacious fluids of equal density will undoubtedly 

 resist more than those that are more liquid, as cold oil 

 more than warm, warm oil more than rain water, and 

 water more than spirits of wine. But in liquids which 

 are fluid enough to retain for some time the motion im 

 pressed upon them by an agitation of the vessel, and 

 which being poured out are easily resolvable into drops, 

 the rule will be pretty accurate, especially for large bodies 

 moving with a swift velocity. 



&quot; Lastly, since it is the opinion of some that there is a 



