;152 UNDULATORY TIIEOUY OF LIGHT. 



sensibly so,) wlictlicr the molecular moveiueut be large or Hinall. This last fact 

 we leani experimentally, thougli it may be deduced from considerations entirely 

 theoretical, as will presently be shown. 



A molecular movement, like what lias just been diiscribed, may b(! called a 

 trvmor. A succession of tremor,^, swelling and sinking in magnitude, each so 

 excessively brief that their successive differences arc comparatively null, consti- 

 tutes an ^mdulatlon. ksuch a succession of tremors must bo produced in the air 

 by a vibrating sonorovis body. Take, for instance, one of the steel springs of a 

 musical box. It traverses, in its vibration, but a very minute portion of spac*e, 

 and its duration occupies an equally minute portion of lime. But as, at the end 

 of its path, its velocity is, for an instant, zero, while, in the middle, it is very 

 great, we know, from the general jn-inciples laid down above, that, at interme- 

 diate points, it must have as many intermediate values as it is possible to imagine 

 points, and we are abb;, moreover, to give a delinite mathera;itical expression to 

 those values. These various velocities, beginning and ending with zero, and 

 passing through an intermediate maximum, will be successively imparted to the 

 stratum of particles of air which is in conta,ct with the spring. From this stra- 

 tum they will be transferred to the second, from the second to the third, and 

 so on. 



And here, to the clear understanding of this subject, it is necessary to take 

 into consideration a very imjjortant fact, viz., that, how(;ver rapid may bo the 

 motion of the spring, the trctnors which th(i air takes up from it advance with a 

 velocity vastly greater. Let us suppose, for in^^tance, that the spi'ing makes a 

 thousand simple vibrations, or five hundred double vibrations, in a second, which 

 is somewhat below the number corresponding to th(! tenor C. and that the 

 amplitude of each vibration, measured between the cxtremi! limits of its excur- 

 sions iu both directions from the position of equilibrium, is one twentieth of an 

 inch. In one second after beginning to vibrate it will have described only fifty 

 inches, but in the mean time the tremor generated by its first movement will 

 have passed over eleven hundred and thirty feet. In this case, accordingly, the 

 tremor will have more than two hundred and seventy tim(!S the mean velocity 

 of the vibration. Thus, while the spring is advancing from its first zero of 

 velocity to its maximum, a distance of one-fortieth of an inch, the first .and 

 feeblest tremor which it excited will have; reached a point nearly seven inches 

 in advance, of it, and the stratum next befori! it wdl be receiving the most ener- 

 getic tremor which it is capable of im])arting. When it reaches the second 

 zero the first tremor will be fourteen inches in advance, the middle or maximum 

 will be s(!ven inches in advance, and the stratum next it will have just received 

 a minimum impulse corresponding to the first. Were the spring to remain in 

 this position, the undulation would pass on, leaving the air in its vicinity at rest. 

 But as it instantly commences its return, it withdraws from the stratum in con- 

 tact with it the support it afforded against the repulsive forces of the more ad- 

 vanced particles; and accordingly that stratum follows the spring, producing a 

 rarefaction, or increase of distance, between the first and second. The repellent 

 foi'ces between the first and second strata will thus be diminished, so that those 

 between the second and third will predominate. The second stratum will con- 

 sequently follow the first, and in like manner each successive stratum throughout 

 the fluid will successively move backward toward the one before it; or a tremor 

 will affect every stratum of particles, as in the case before considered, but will 

 differ froni that in this ])nrticular, viz : that, in the latter case, the particles arc 

 moving in one direr/ ion, while the tremor is advancing iu the contrary direction, 

 whereas in the case W(; first considered the movement of the particles is the 

 scune in direction with that of the progress of the tremor. 



It is easily seen that the whole series of tremors produced by the return 

 vibration will generate an undulation equal m length to the foimer, and differing 

 from it only iu the direction of mocemcnt of the particles. This is called the 



