MOTION AND RESISTANCE OE FLUIDS. 



equally in all directions, produces effects of such an extraordinary 

 nature as to surpass the power of investigation. The indefinitely 

 small corpuscles of which a fluid is composed, probably possess the 

 same powers, and would be subject to the same laws of motion, as 

 bodies of finite magnitude, could any two of them act on each other 

 by contact; but this is a circumstance which certainly never takes 

 place in any of the aerial fluids, and probably not in any liquids. 

 Under the circumstances, therefore, of an indefinite number of bo- 

 dies acting on each other by repulsive powers, or by absolute con- 

 tact, under the uncertainty of the friction which may take pl-ice, 

 and of what variation of effects may be produced under different 

 degrees of compression, it is no wonder that our theory and expe- 

 riments should be so often found to disagree. 



Sir Isaac Newton seems to have been well aware of all these diffi- 

 culties, and therefore in his Principia he has deduced his laws of 

 resistance, and the principles on which the times of emptying vessels 

 are founded, entirely from experiment. He was too cautious to 

 trust to theory alone, under all the uncertainties to which he appears 

 to have been sensible it must be subject. He had, in a preceding 

 part of that great work, deduced the general principles of motion, 

 and applied them to the solution of problems which had never be, 

 fore been attempted; but when he came to treat of fluids, 'he saw 

 it was necessary to establish his principles on experiments ; prin- 

 ciples not indeed mathematically true, like his general principles of 

 motion before delivered, but, under certain limitations., sufficiently 

 accurate for all practical purposes. 



The principle to be established in order to determine the time of 

 emptying a vessel through an orifice at the bottom, is the relation 

 between the velocity of a fluid at the orifice and the altitude of the 

 fluid above it. Most writers on this subject have considered the 

 column of fluid over the orifice as the expelling force ; whence some 

 have deduced the velocity at the orifice to be that which a body 

 would acquire in falling down the whole depth of the fluid - 9 and 

 others that acquired in falling through half the depth, without any 

 regard to the magnitude of the orifice; whereas it is manifest from 

 experiment, that the velocity at the orifice, the depth of the fluid 

 being the same, depends on the proportion which the magnitude 

 x)f the orifice bears to the magnitude of the bottom of the vessel, 

 supposing, for instance, the vessel to be a cylinder standing on its 



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