352 Prof. L. Natanson on 



and (2) of the present paragraph, and neglecting all terms of 

 higher order, we get 



3iE-=£) = _ 2M _ (jfc _»_ Sn) ._^£ > . . (7a) 



liap> = .^_' M . w ,_ac?;, . (76) 



^f =-«a-f, (8.) 



^ = _n5-^p, (86) 



^=-«o-f' (8c) 



Thus, strictly speaking, the whole of our formulse only 

 apply to the case of extremely slow movements of the fluid. 

 It is easy to see that every chain of reasoning which, like 

 ours, starts from the fundamental ideas o£ the theory of 

 elasticity, must necessarily be subject to the same restriction. 

 It is, besides, known that among the theories of viscosity 

 hitherto proposed there is none perfectly general or rigorous. 



Equations (7) and (8) give by integration : — 



jp«-p = C«6-^-e-^ r^6'/ T {2w^+(&-A-fn)&>} 5 . (9a) 



Pw-P = (Vr^-e-^ I dt 6^{2nf+ (k- A-fn)»}, . (%) 



p„—p = G*fi-*? r - € -W! \dt€ t /' r {2rig + (k-h^%n)a)}, . (9c) 



Py^Qy.e-^-e-^^dte^na, ....... (10a) 



p zx = G zx e-^ T -€-^{dte t l T ?ib } (10b) 



p xy =Q xy e-^-e-^^dte^nc (10c) 



In these equations, e stands for the naperian logarithmic 

 base ; C xx , C yy , CL, Q> yz , C zx , C^ are functions of x, y, z, 



