PART II. 



LECTURE XXI. 



ON HYDROSTATICS. 



THE mechanical properties and affections of fluids, and the laws, and 

 phenomena of their motions, are to be the subjects of the second division 

 of this Course of Lectures. Although these properties are in reality 

 derived from the same fundamental principles as the doctrines of pure 

 mechanics, they are yet in great measure incapable of being referred, in a 

 demonstrative and accurate manner, to the operation of simple and general 

 causes. We are therefore frequently under the necessity of calling in the 

 assistance of experimental determinations ; and for this reason, as well as 

 others, the science of hydrodynamics may with propriety hold a middle 

 rank, between mathematical mechanics and descriptive physics. In treat- 

 ing of the mechanics of solid bodies, we are able to begin with axioms or 

 self-evident truths, almost inseparable from the constitution of the human 

 mind ; to deduce from them the general laws of motion, and to apply these 

 laws, with little chance of error, to every combination of circumstances in 

 which we have occasion to examine their consequences ; and it requires 

 only a certain degree of attention and of mathematical knowledge, to be 

 perfectly convinced of the justice of all our conclusions, without any 

 reference to experimental proof. But here our abstract reasonings begin to 

 fail ; and whether from the imperfection of our modes of considering the 

 mechanical actions of the particles of fluids on each other, or from the 

 deficiencies of our analytical calculations, or, as there is more reason to 

 suppose, from a combination of both these causes, all attempts to reduce 

 the affections of fluids to a perfect mechanical theory have been hitherto 

 unsuccessful. At the same time it will appear, that by a proper mixture 

 of calculation with experiment, we may obtain sufficient foundations for 

 all such determinations as are likely to be of any practical utility. 



The whole of the subjects, which will be classed under the denomination 

 Hydrodynamics, may be divided into three general heads ; Hydraulics, 

 Aoustics, and Optics ; terms which are sufficiently understood, as relating 

 to the common properties of fluids, to sound, and to light ; but which do 

 not allow of a very strict definition, without a still further division. The 



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