1900.] on the Dynamical Theory of Heat and Light. 365 



for the sake of simplicity, to tho suggestion of a spherical atom pro- 

 ducing condensation and rarefaction, with concentric spherical surfaces 

 of equal density, but the same total quantity of ether within its 

 boundary as the quantity in an equal volume of free undisturbed 

 ether. 



§ 4. Consider now such an atom given at rest anywhere in space 

 occupied by ether. Let force be applied to it to cause it to move in 

 any direction, first with gradually increasing speed, and after that 

 with uniform speed. If this speed is anything less than the velocity 

 of light, the force may be mathematically proved to become zero at 

 some short time after the instant when the velocity of the atom be- 

 comes uniform, and to remain zero for ever thereafter. What takes 

 place is this : 



§ 5. During all the time in which the velocity of the atom is being 

 augmented from zero, two sets of non-periodic waves, one of them 

 equi-voluminal, the other irrotational (which is therefore condensa- 

 tional-rarefactional), are being sent out in all directions through the 

 surrounding ether. The rears 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-rarefac- 

 tional disturbance 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 surface, produces no wave disturbance if its 



