96 ON A SMALL CAPILLARY WAVE 



Hen^e the axis of the single resultant rotation passes through the 



. , , j- i 3(a>a?) 2(wy) 2(<oz) ,. 



point whose co-ordmates are % ) *f , ; / ; these are lnde- 



^i(co) 2,{m) 2(w) 



pendent of I, m, n, and this point therefore remains the same so long 

 as the magnitudes of the rotations, and the points through which 

 their axes are drawn are unaltered, whatever be the common direc- 

 tion of these axes ; by analogy this point might be called the Centre 

 of Parallel Rotations. 



OlS A SMALL CAPILLAR Y WAVE NOT HITHERTO 

 DESCRIBED. 



BY JOHN" LANGTON, M. A., 



VICE-CHANCELLOR OF THE UNIVERSITY OF TORONTO. 



Bead before the Canadian Institute, Vlth January, 1857. 



It is well known that the shape and velocity of waves, and the 

 different circumstances under which they are propagated, have at- 

 tracted considerable attention amongst men of science, not only 

 from the importance of the subject as connected with the theory of 

 tides, but also from its practical bearing in relation to the resistance 

 of fluids, and the best form for vessels which are destined to move 

 in them. An elaborate report upon waves was prepared by J. Scott 

 Russell, for the British Association, in 1844, the experiments de- 

 tailed in which have been the origin of some of the greatest im- 

 provements of the present day in ship-building, and have inseparably 

 connected the wave line with the name of Russell. Although this 

 report is principally devoted to the solitary wave of translation, 

 which gave rise to the investigation, it treats at less length of other 

 varieties, and may, I believe, be said to embody all that is known 

 upon the subject from observation. There is nothing, however, 

 amongst the waves there enumerated in any way resembling that 

 which I propose bringing under the notice of the Institute to-night, 

 nor have I elsewhere seen any account of its having been previously 

 observed. Amongst all the different kinds of waves, varying as 

 they do in dimensions from the great tidal wave, which, with an ele- 

 vation of only a few feet, rests upon a base of hundreds of miles in 

 extent, to the ripple which is raised by a summer's breeze, the wave 

 which I am about to introduce to you is, perhaps, the smallest. It 



