124^. Astronomical and Nautical Collections, 



occasioned in the particles of the fluids velocities exactly equal 

 in their intensity, though opposite in the direction of the 

 motions. Let us at first suppose that two whole undula- 

 tions, moving in the some line and in the same direction, 

 differ half an undulation in their progress : they will then be 

 superinduced on each other through one half of their length, 

 or of their breadth, as we should say in speaking of the waves 

 of a liquid : but I here use in preference the term length as 

 applied ta; the interval between the two points which are 

 similarly affected by the motions of two consecutive undula- 

 tions. In the supposed case of the coincidence of one half of 

 each of the undulations, the interference will only take place 

 with respect to the parts so coinciding : that is, to the latter 

 half of the first undulation, and the preceding half of the 

 second : and if these two semiunJulations are of equal inten- 

 sity, since they tend to give, to the same points of the ether, 

 impulses directly opposite, they will wholly neutralise each 

 other, and the motion will be destroyed in this part of the 

 fluid, while it will subsist without alteration in the two other 

 halves of the undulations. In such a case, therefore, half of 

 the motion only would be destroyed. 



If now we suppose that each of these undulations, differ- 

 ing in their progress by half the whole length of each, is 

 preceded and followed by a great number of other similar un- 

 dulations; then, instead of the interference of two detached 

 undulations, we must consider the . interference of two sys- 

 tems of waves, which may be supposed equal in their number 

 and their intensity. Since, by the hypothesis, they differ 

 half an undulation in their progress, the semiundulations of 

 the one, which tend to cause in the particles of ether a mo- 

 tion in one direction, coincide with the semiundulations of 

 the other, which urge them in the opposite direction, and 

 these two forces hold each other in equilibrium, so that the 

 motion is wholly destroyed in the whole extent of these two 

 systems of waves, except the two extreme semiundulations, 

 which escape from the interference. But these semiundu- 

 lations will always constitute a very small part of tbe whole 

 series to be considered. •>«(; ^< '^^ 



This reasoning is obviously applicable to such systems only 



