Prof. Challis on the Principles of Hydrodynamics. 231 



from the mean and extreme epochs, would produce a faithful 

 record of the mean diurnal state in any part of the globe. He 

 could also thus ascertain the mean daily state at sea by observing 

 at 5 11, 5, 11, which might without much error be referred to 

 the 'ship's place midway between 8 a.m. and 8 p.m., or at the 

 place about 3 p.m. If^ moreover, observations were taken at 

 6 0, 6, 13, the horary velocity of increase or decrease would be 

 ascertainable; and fi-om a number of records of this nature we 

 might eventually find the theoretical formulse for geographical 

 position and season of the year in the open sea, where local in- 

 fluences nearly vanish, and general laws are therefore sooner per- 

 ceptible. 



23 Walpole Street, Chelsea, 

 January 7, 1851. 



XXXII. On the Principles of Hijdrodynamics : with a Reply to 

 the Arguments of Professor Stokes. By the Kev. J. Challis, 

 M.A., F.R.S., F.R.A.S., Plumian Professor of Astronomy and 

 Experimental Philosophy in the University of Cambridge. 

 [Continued from p. 38.] 



BY the previous discussion it appeared, that in three instances 

 in which the two ordinary general equations of hydi-odyna- 

 mics were used in the ordinary way, contradictory results were 

 arrived at, which showed that a logical fault had been committed. 

 I proceed now to point out the reason of these contradictions, and 

 the course which the investigation ought to have taken. 



The principles maintained in the following argument may be 

 thus expressed in general terms : — 



(1 ) When a mass of fluid is disturbed m any manner, the 

 motion at any point depends both on the immediate action of the 

 disturbing cause on the fluid, and on the action of the parts ot 



the fluid on each other. i . n ^i, ^j„ 



(2 ) The law of the latter action is independent ot the mode 

 of disturbance, and must be ascertained previous to the conside- 

 ration of particular cases of motion. 



(3 ) To ascertain the law of the mutual action of the parts ot 

 a fluid on each other, the new general equation (3.), investigated 

 in Proposition VI., is necessary. .„ , ^ j 



Accordhig to these views, the right coui-se will be to endeavour 

 to deduce from the general equations the mode of action ot the 

 parts of the fluid on each other, prior to the apphcation ot the 

 same equations to particular cases of motion. 



In commencing this inquiry, I remark, first, that since Mrfi/r) 

 =udx + vdy + wdz, the right-hand side of this equality is an 

 exact difl-erential if \ be a function of ^lr and t. This analytical 



