ORii — Stability or InstaUlity of Motions of a Viscous Liquid. 79 



all speeds the resistance could be represented as the sum of two terms, one 

 varying as the velocity and the other as its square ; the latter was attributed 

 to the action of the ends of the rotating cylinder, and was found to become 

 smaller and smaller as the ratio of the length to the width of the annulus 

 increased. 



[I take this opportunity of making a few corrections in Part I. : — 



p. 15, 1. 8, for "m" read "m^". 



p. 1 5, 1. 3 from foot, for " a " read " any ". 



p. 25, 1. 25, for "^" read"/3". 



p. 31, 1. 19, for "= " read " = ". 



p. 35, 1. 17, for " r' read " I". 



p. 35, last line, for " (^5 - 1)2" read "(-/5 - l)/2 ". 



p. 40, I would withdraw the opinion expressed in the final sentence which 

 begins on this page. 



p. 42, 1. 21. In keeping with the last change, I would insert "lb and" 

 before " mb ". 



p. 47, et seq. Just as the analysis of Art. 21 is simpler than that of 

 Art. 20, so, in the disturbance discussed in Art. 18, the 

 investigation is simpler when ka is very small, the other 

 extreme case from that chosen. 



The following electric analogy may illustrate instability of fluid motion : — 

 In two dimensions vorticity represents electric density — stream-function, 

 potential. Take a shearing stream with embedded positive and negative 

 electric charges, arranged, as an extreme and simple case, like rectangles on a 

 chess-board, the sides parallel to the direction of the stream being much 

 longer than those across it, and the bounding-planes being kept at zero 

 potential. Let the charges, like the vorticity, flow with the stream. AYhen 

 sheared so that original diagonals run right across the stream, the potential 

 at most points towards mid-stream is much greater than originally, owing to 

 the altered distribution of the charges.] 



[ir=^] 



