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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 bv electric spark, showing, by changed refractivity, the condensational-rarefactional 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 (andr 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 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 watery; 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 observaticns for an experimental determination of the minimum velocity of waves, in a letter to William Froude, published in ‘ Nature 7 for October 26, and in the Phil. Mag. for November 1871, from which the following is extracted. “ [Recently, in the schooner yacht LaUa
§ 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 condensational-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 irrota-tional, 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 condensational-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 o£ >§ 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 of the very general question pointed out in § 3 as needing answer. Another part, fundamental in the
u Rookh\ being becalmed in the Sound of Mull, I had an excellent u opportunity, with the assistance of Professor Helmholtz, and my u brother from Belfast [the late Professor James Thomson], of deter-£i mining by observation the minimum wave-veloeity with some approach u to accuracy. The fishing-line was hung at a distance of two or three u feet from the vessel’s side, so as to cut the water at a point not sensibly u disturbed by the motion of the vessel. The speed was determined by u throwing into the sea pieces of paper previously wetted, and observing u their times of transit across parallel planes, at a distance of 912 centi-il metres asunder, fixed relatively to the vessel by marks on the deck and u gunwale. By watching carefully the pattern of ripples and waves which u 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 u and presenting appearances which proved them to be waves of the il 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 u glassy ” ; though there was wind -enough to propel the S2hooner at speed varying between £ mile and 1 mile per hour.