NATURE 



\Nov. 2, 1871 



mum wave velocity for sea-water may be expected to be 

 not very different from this. (It would of course be the 

 same if the cohesive tension of sea water were greater 

 than that of pure water in precisely the same ratio as the 

 density.) 



About three weeks later, being becalmed in the Sound 

 of Mull, I had an excellent opportunity, with the assist- 

 ance of Prof Helmholtz, and my brother from Belfast, of 

 determining by observation the minimum wave velocity 

 with some approach to accuracy. The tishing-line was 

 hung at a distance of two or three feet from the vessel's 

 side, so as to cut the water at a point not sensibly dis- 

 turbed by the motion of the vessel. The speed was de- 

 termined by throwing into the sea pieces of paper pre- 

 viously wetted, and observing their times of transit across 

 parallel planes, at a distance of 912 centimetres asunder, 

 fixed relatively to the vessel by marks on the deck and 

 gunwale. By watching carefully the pattern of ripples 

 and waves, which connected the ripples in front 

 with the waves in rear, I had seen that it in- 

 cluded a set of parallel waves slanting oft' obliquely 

 on each side, and presenting appearances which 

 proved them to be waves of the critical length and cor- 

 responding minimum speed of propagation. Hence 

 the component velocity of the fishing-line perpendicular 

 to the fronts of these waves was the true minimum 

 velocity. To measure it, therefore, all that was necessary 

 was to measure the angle between the two sets of parallel 

 lines of ridges and hollows, sloping away on the two sides 

 of the wake, and at the same time to measure the velocity 

 with which the fishing-line was dragged through the water. 

 The angle was measured by holding a jointed two- foot 

 rule, with its two branches, as nearly as could be judged, 

 by the eye, parallel to the sets of lines of wave-ridges. 

 The angle to which the ruler had to be opened in this 

 adjustment was the angle sought. By laying it down 

 on paper, drawing two straight lines by its two edges, 

 and completing a simple geometrical construction with a 

 length properly introduced to represent the measured 

 velocity of the moving solid, the required minimum wave- 

 velocity was readily obtained. Six observations of this 

 kind were made, of which two were rejected as not satis- 

 factory. The following are the results of the other four : — 



Velocily of Deduced Minimum 

 Moving Solid. Wave-Velocity. 



51 centimetres per second. 23 'o centimetres per second. 



38 „ „ 23-S 



26 ,, ,, 23-2 ,, ,, 



24 ,. .. 22-9 ,, 



Mean 23^22 



The extreme closeness of this result to the theoretical 

 estimate {23 centimetres per second) was, of course, merely 

 a coincidence, but it proved that the cohesive force of sea- 

 water at the temperature (not noted) of the observation 

 cannot be very difl'erent from that which I had estimated 

 from Gay Lussac's observations for pure water. 



I need not trouble you with the theoretical formula: just 

 now, as they are given in a paper which I have communi- 

 cated to the Royal Society of Edinburgh, and which will 

 proljably appear soon in the PJiilosopJiical Magazine. If 

 23 centimetres per second be taken as the minimum speed 

 they give 17 centimetres for the corresponding wave-length. 



I propose, if you approve, to call ripples, waves of 



lengths less than this critical value, and generally to 

 restrict the name waves to waves of lengths exceeding it. 

 If this distinction is adopted, ripples will be undulations 

 such that the shorter the length from crest to crest the 

 greater the velocity of propagation ; while for waves the 

 greater the length the greater the velocity of propagation. 

 The motive force of ripples is chiefly cohesion ; that of 

 waves chiefly gravity. In ripples of lengths less than half 

 a centimetre the influence of gravity is scarcely sensible ; 

 cohesion is nearly paramount. Thus the motive of ripples 

 is the same as that of the trembling of a dew drop and of 

 the spherical tendency of a drop of rain or spherule of 

 mist. In all waves of lengths exceeding five or six centi- 

 metres, the effect of cohesion is practically insensible, and 

 the moving force may be regarded as wholly gravity. 

 This seems amply to confirm the choice you have made of 

 dimensions in your models, so far as concerns escaping 

 disturbances due to cohesion. 



The introduction of cohesion into the theory of waves 

 explains a difficulty which has often been felt in consider- 

 ing the patte»n6 of standing ripples seen on the surface 

 of water in a finger-glass made to sound by rubbing a 

 moist finger on its lip. If no other levelling force than 

 gravity were concerned, the length from crest to crest 

 corresponding to 256 vibrations per second would be a 

 fortieth of a millimetre. The ripples would be quite undis- 

 tinguishable without the aid of a microscope, and the 

 disturbance of the surface could only be perceived as a 

 dimming of the reflections seen from it. But taking 

 cohesion into account, I find the length from crest 10 crest 

 corresponding to the period of gsa °f ^ second to be rg 

 millimetres, a length which quite corresponds to ordinary 

 experience on the subject. 



When gravity is neglected the formula for the period 

 {P) in terms of the wave-length (/), the cohesive tension of 

 the surface (T), and the density of the fluid (p), is 



P = 



Vs 



where 7* must be measured in kinetic units. For water 

 we have ;> = i, and (according to the estimate I have taken 

 from Poisson and Gay Lussac) T = 982* X '074 = 73. 

 Hence for water ., „ 



V^ ^ t 



21-4 



P = 



^2 77 X 73 



When / is anything less than half a centimetre the error 

 from thus neglecting gravity is less than 5 per cent, of P. 

 When / exceeds 5^ centimetres the error from neglecting 

 cohesion is less than five per cent, of the period. It is to 

 be remarked that, while for waves of sufficient length to 

 be insensible to cohesion, the period is proportional to 

 the square-root of the length, for ripples short enough to 

 be insensible to gravity, the period varies in the sesqui- 

 plicate ratio of the length. 



William Thomson 



iVIr. Froude having called my attention to Mr. Scott 

 Russell's Report on Waves (British Association, York, 1844) 

 as containing observations on some of the phenomena 

 which formed the subject of the preceding letter to him, 

 I find in it, under the heading "Waves of the Third Order," 

 or, " Capillary Waves," a most interesting account of the 



* 982 being the weight of one gr, 

 metres per second. 



I kinetic units of force-centi- 



