4 Lord Kelvin on the 



all directions through the surrounding ether. The rears 1 

 of the last of these waves leave the atom, at some time after 

 its acceleration ceases. This time, if the motion of the ether 

 outside the atom, close beside it, is infinitesimal, is equal to- 

 the time taken by the slower wave (which is the equi- 

 voluminal) to travel the diameter of the atom, and is the 

 short time referred to in § 4. When the rears of both waves 

 have got clear of the atom, the ether within it and in the 

 space around it, left clear by both rears, has come to a steady 

 state of motion relatively to the atom. This steady motion 

 approximates more and more nearly to uniform motion in 

 parallel lines, at greater and greater distances from the atom. 

 At a distance of twenty diameters it differs exceedingly little 

 from uniformity. 



§ 6. But it is only when the velocity of the atom is 

 very small in comparison with the velocity of light, that 

 the disturbance of the ether in the space close round the 

 atom is infinitesimal. The propositions asserted in § 4 and 

 the first sentence of § 5 are true, however little the final 

 velocity of the atom falls short of the velocity of light. If 

 this uniform final velocity of the atom exceeds the velocity 

 of light, by ever so little, a non-periodic conical wave of 

 equi-voluminal motion is produced, according to the same 

 principle as that illustrated for sound by Mach's beautiful 

 photographs of illumination by electric spark, showing, by 

 changed refractivity, the condensational -rarefactional dis- 

 turbance produced in air by the motion through it of a rifle 

 bullet. The semi-vertical angle of the cone, whether in air 

 or ether, is equal to the angle whose sine is the ratio of the 

 wave velocity to the velocity of the moving body *". 



* On the same principle we see that a body moving steadily (and, 

 with little error, we may say also that a fish or water-fowl propelling 

 itself by fins or web-feet) through calm water, either floating on the 

 surface or wholly submerged at some moderate distance below the sur- 

 face, produces no wave disturbance if its 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 J ; 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 the 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 minimumi 

 velocity of waves, in a letter to William Froude, published in ' Nature ' 

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

 the following is extracted. u [Eecently, in the schooner yacht Lalla 



