612 Lord Rayleigh on the 



limits his investigation to the case in which the squares of 

 the velocities can be neglected 



... radius of globe X velocity ... 



<«' e - diffusivity 7er y Sma11 )' 



in which it is manifest that the steady motion is the same 

 whatever the viscosity ; but it is manifest that when the 

 squares cannot be neglected, the steady motion is very dif- 

 ferent (and horribly difficult to find) for different degrees of 

 viscosity. 



" In your p. 62, near the foot, it is not explained what V 

 is ; and it disappears henceforth. — Great want of explanation 

 here — Did you not want your paper to be understandable 

 without Basset in hand ? I find your two papers of July 

 /92 pp. 61-70, and Oct./93 pp. 355-372, very difficult 

 reading, in every page, and in some go ly difficult. 



"pp. 366, 367 very mysterious. The elastic problem is 

 not defined. It is impossible that there can be the recti- 

 lineal motion of the fluid asserted in p. 367 lines 17-19 from 

 foot, in circumstances of motion, quite undefined, but of some 

 kind making the lines of motion on the right side different 

 from those on the left. The conditions are not explained for 

 either the elastic-solid *, or the hydraulic case. 



" See p. 361 lines 19, 20, 21 from foot. The formation of 

 a backwater depends essentially on the non-negligibility of 

 squares of velocities ; and your p. 367 lines 1-4, and line IT 

 from foot, are not right. 



" If you come to the R. S. Library Committee on Thursday 

 we may come to agreement on some of these questions." 



Although the main purpose in Kelvin's papers of 1887 

 was not attained, his special solution for a disturbed vorticity 

 in case (i.) is not without interest. The general dynamical 

 equation for the vorticity in two dimensions is 



Df-dt^ dx dy V ^ ' ' W 



where v( = fi/p) is the kinematic viscosity and \/ 2 =d 2 /dx 2 

 + d?/dy 2 . In this hydrodynamical equation £ is itself a 

 feature of the motion, being connected with the velocities 

 u, v by the relation 



t-*(| 7 £> < 2 > 



* I think Kelvin did not understand that the analogous elastic problem 

 referred to is that of a thin plate. See words following- equation (5) of 

 my paper. 



