TRANSACTIONS OF SECTION A. 



493 



r= -. Hence for this value ofy the second term within the bracket in Lord 

 m 



(P T 

 Rayleigh's formula is infinite unless, for the same value of y, -j—^ vanishes. 



We evade entirely the consideration of this infinity if we take only the case of 



a layer of constant vorticity f- = constant from y = o to y = a\, as for this case 



JO 



the formula is simply ^;' = m" v, hut the interpretation of the infinity which 



occurs in the more comprehensive formula suggests an examination of the stream- 

 lines by which its interpretation becomes obvious, and which proves that even in 

 the case of constant vorticity the motion has a startlingly peculiar^ character at the 

 place where the translational velocity is equal to the wave-velocity. This pecu- 

 liarity is represented by the annexed diagram, which is most easily understood if 



we imagine the translational velocities at y = and ?/ = n to be in opposite direc- 

 tions, and of such magnitude that the wave-velocity is zero ; so that we have the 

 case of standing waves. For this case the stream lines are as represented in the 

 annexed diagram, in which the region of translational velocity greater than wave- 

 propagational velocity is separated from the region of translational velocity less 

 than wave-propagational velocity by a cat's-eye border pattern of elliptic whirls. 



9. Supplement to a Paper on the SyncJironism of Mean Temperature and 

 Rainfall in the Climate of London. By H. Courtenay Fox, M.B.C.S. 



In the Report of the British Association for 1879, page 277, is an abstract of a 

 paper on the above subject which I had the pleasure of reading last year. The 

 rainfaU-data which I tlien used were of two kinds — namely, first, the monthly 

 rainfall at the Royal Observatory back to the year 1841 ; and, secondly (for the 

 years 1813 to 1840), the rainfall for every month collected by Mr. Dines from 

 sundry observations about London. After I had presented this paper, Mr. Glaisher 

 kindly favoured me with a table of the monthly rainfall at Greenwich, going back 

 to the year 1815. 



I have since gone carefully through my paper with it, and am glad to state 

 that the results which I ventiu-ed to ofler to the Association are, with small excep- 

 tion, fully confirmed. 



Conclusion No. 1 is confirmed, with the exception that February loses the 

 svnchronism of cold with dry, although that of warm with wet is retained. 



Conclusions Nos. 2 and 3 are confirmed. 



Conclusion No. 4 ; — The results for April and November are unchanged. The 

 four remaining months, though in some respects they presented ' slight ' tendencies 

 to the association of extremes of rainfall and temperature, were more or less 

 indefinite in character. This is still the case as regards March, September, and 

 October, but in May the tendency is for the synchronism of cold with wet to 

 prevail. 



