ON THE MATHEMATICAL THEORY OF FLUIDS, $51 



The circumstance of floating bodies rising vertically when 

 drawn with considerable velocities along the surface of water, 

 having attracted attention a few years ago, induced me to try to 

 explain the fact on mechanical principles, and accordingly, in a 

 paper published in the Cambridge Philosophical Transactions*^, 

 I have entered on a mathematical investigation which accounts 

 for such a fact, and shows in the instance taken, that when the 

 velocity of di-aught is uniform the rise is proportional to the 

 square of the velocity, in accordance with an experimental re- 

 sult obtained by Mr. Russellf. The inquiry is not pursued 

 further in that paper (though I believe it maybe done according 

 to the method there employed), the immediate object in view 

 being to gain confidence for the particular process of reasoning 

 adopted, which differs in some respects from that of previous 

 writers on fluid motion, by explaining to a considerable extent 

 a fact which had not before been shown to depend on received 

 mechanical principles. 



The problem of the resistance of the air to a ball pendulum 

 has been undertaken by M. Plana in a Memoir on the Motion 

 of a Pendulum in a resisting medium, {Turiii, 1835,) in which 

 the resistance of an incompressible fluid is first considered, and 

 then that of an elastic fluid; and in both cases the author finds, 

 as Poisson had done, that the loss of weight of the sphere 

 exceeds by just one half, the weight of the fluid it displaces. 

 The question, however, has not yet received a satisfactory solu- 

 tion, since theory has hitherto failed to account for one of the 

 leading circumstances of the case, viz., that the coefficient of 

 resistance is different for small spheres of different diameters. 

 This difference it appears would equally exist whether the balls 

 vibrated in a confined apparatus or in free air. 



The above particulars are mentioned for the purpose of calling 

 attention to parts of the theory of fluids which are still open to 

 improvement, and I may here state that one of the objects I 

 have chiefl)'^ had in view in this communication to the Associa- 

 tion, and in those preceding it, has been to bring into more notice 

 the mathematical theory of fluids and place it in its proper rank 

 among applied sciences. Judging from the very few contribu- 

 tions which have been made by Englishmen to this department 

 of science, it would appear to have been held by us in disesteem. 

 From the time of Newton till within these few years scarcely 

 anything was written upon it in this country. This neglect is 

 the less to be defended as there are few subjects in natural phi- 

 losophy which are not connected in some manner or other with 



• Vol. V. Part ii. p. 173. 



t Fourth Report of the British Association, p. j33. 



