3G6 Lord Kelvin [April 27, 



§ 7. If, for a moment, we imagine the steady motion of the atom 

 to be at a higher speed than the wave velocity of the condensational- 

 rarefactional wave, two conical waves, of angles corresponding to the 

 two wave velocities, will be steadily produced ; but we need not occupy 

 ourselves at present with this case, because the velocity of the condeu- 

 sational-rarefactional wave in ether is, we are compelled to believe, 

 enormously great in comparison with the velocity of light. 



§ 8. Let now a periodic force be applied to the atom so as to cause 

 it to move to and fro continually, with simple harmonic motion. By 

 the first sentence of § 5 we see that two sets of periodic waves, 

 one equi-voluminal, the other irrotational, are continually produced. 

 Without mathematical investigation we see that if, as in ether, the 

 condensational-rarefactional wave velocity is very great in comparison 

 with the equi-voluminal wave velocity, the energy taken by the con- 

 densational-rarefactional wave is exceedingly small in comparison 

 with that taken by the equi-voluminal wave ; how small we can find 

 easily enough by regular mathematical investigation. Thus we see 

 how it is that the hypothesis of § 3 suffices for the answer suggested 

 in that section to the question, How could matter act on ether so as 

 to produce light ? 



§ 9. But this, though of primary importance, is only a small part 



velocity is less than the minimum wave velocity due to gravity and surface 

 tension (being about 23 cms. per second, or -44 of a nautical mile per hour, 

 whether for sea water or fresh water) ; and if its velocity exceeds the minimum 

 wave velocity, it produces a wave disturbance bounded by two lines inclined on 

 each side of its wake at angles each equal to the angle whose sine is the minimum 

 wave velocity divided by the velocity of tlie moving body. It is easy for anyone 

 to observe this by dipping vertically a pencil or a walking stick into still water 

 in a pond (or even in a good-sized hand basin), and moving it horizontally, first 

 with exceeding small speed, and afterwards faster and faster. I first noticed it 

 nineteen years ago, and described observations for an experimental determination 

 of the minimum velocity of waves, in a letter to William Froude, published in 

 1 Nature' for October 26, and in the Phil. Mag. for November 1871, from which 

 the following is extracted. "[Recently, in the schooner yacht Lalla BookK], 

 " being becalmed in the Sound of Mull, I had an excellent opportunity, with the 

 " assistance of Professor Helmholtz, and my brother from Belfast [the late 

 " Professor James Thomson], of determining by observation the minimum wave- 

 " velocity with some approach to accuracy. The ti*hing-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 disturbed by the motion of the vessel. The speed was determined by 

 " throwing into the tea pieces of paper previously 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, included a set of parallel waves 

 " slanting off obliquely on each side and presenting appearances which proved 

 " them to be waves of the critical length and corresponding minimum speed of 

 " propagation." When the speed of the yacht fell to but little above the critical 

 velocity, the front of the ripples was very nearly perpendicular to the line of 

 motion, and when it just fell below the critical velocity the ripples disappeared 

 altogether, and there was no perceptible disturbance on the surface of the water. 

 The sea was " glassy " ; though there was wind enough to propel the schooner 

 at speed varying between J mile and 1 mile per hour. 



