Stoney — Cause of Double Lines in Spectra. 593 



The "partials" or ultimate elements into wliich a sound-wave in air can be 

 resolved take the very simple form — 



x = a cos 6t. 



They are pendulous vibrations in a straight line, and we may regard each of 

 them as fully characterized if we can ascertain the values of its a and 6. These 

 are furnished by the intensity and pitch of the corresponding simple sound, which 

 can be determined experimentally by the use of resonators. 



This simplest form is also the form of the ultimate elements into which the 

 motions going on in the instruments of the orchestra are to be revolved. They are 

 all partials of the form x = a cos 6t, fully characterized when we can determine 

 a and 6. 



If, however, we want to make out what is the actual motion that is going on, it 

 is not sufficient to characterize its individual partials correctly, it is also necessary 

 to be able to combine them : and to do this we must know the phases in which 

 they all have been at some one instant of time. Now it is still a moot point 

 whether we can elicit any information about the phases from an analysis of the 

 resultant sound : we certainly cannot elicit enough of information in this way. To 

 acquire it we must have recourse to a study of the instruments from which the 

 sound has come, and, unfortunately, in the case of light we are in the predicament 

 of not being able to do what corresponds to this. 



Neither are the partials of the sethereal undulation so simple as in the case of 

 sound. Each sethereal partial is a pendulous elliptic revolution in the plane of the 

 wave, of the form 



X = a cos 6t, y = i sin 6t, 



or rather it is some change of varying electro-magnetic stresses that follows this 

 law. We may, however, for clearness and convenience, continue to speak of it as a 

 motion in the plane of the wave, it being understood that what is meant is some 

 change in the eether which follows the same law as the motion. Now to characterize 

 the above partial of such a motion, three quantities are requii-ed, «, I, and 6 ; and 

 what we can observe by separately examining its spectral line is not enough to 

 determine three quantities. The position of the Kne on the map of oscillation- 

 frequencies tells us the value of 6, its intensity determines a;^ -I- b"^, and this is all 

 that is given us by the examination of a single line. "We have enough, however, 

 if we independently know of some other equation between a and b. Thus from 

 Chap. II. we know that 5 = -f a for one of the two constituents of a double line, 

 and that b = — a for the other. In the case of double lines, therefore, the two cor- 

 responding partials of the motion in the aether are completely determined. Again, if 

 satellites arise in any of the ways pointed out in Chaj). II., when not due to cir- 

 cular, they are due to rectilinear vibrations. Here again, since b = o, the partial 



