JANUAKT 22, 1915] 



SCIENCE 



115 



may not arise from other causes thaa 

 changes in velocity. This disturbing ques- 

 tion is one that frequently recurs to the 

 mind of the astronomer. Happily, in this 

 case it can be answered in the negative 

 without hesitation. The presence of the 

 third body necessitates a light equation 

 similar to that imagined by Chandler, but 

 now of course with a period of less than 

 two years and with a small amplitude. 

 This amplitude can be computed in ad- 

 vance; we find that it amounts to about 

 five minutes of time. I have examined the 

 rich photometric material on this star ac- 

 cumulated in the second half of the nine- 

 teenth century and have found that this 

 light equation is actually present. This 

 seems to leave no doubt that the shift in 

 the spectrum lines is nothing other than an 

 effect of velocity and that the system of 

 Algol contains at least three bodies, only 

 one of which is visible in even our most 

 powerful telescopes. 



It is at this point that the man at the 

 telescope must turn to the mathematician 

 and ask him whether this third body can 

 in any way produce the long inequality in 

 Algol's period, that is, in the time that 

 elapses between successive eclipses. If 

 this should be found not to be the case, 

 what dynamical explanations are possible 

 other than those already tested and re- 

 jected? 



The answer to these questions would 

 doubtless apply to other eclipsing vari- 

 ables, for many of these show similar in- 

 equalities in their periods, though as yet 

 in only one other case has the presence of 

 a third body been demonstrated. 



A somewhat similar problem is presented 

 by the so-called secondary oscillations that 

 have been announced for certain spectro- 

 scopic binaries. If we observe the veloci- 

 ties in a system as carefully as we can, we 

 may draw a curve that expresses the rela- 



tion between time and velocity. Curves 

 of this sort from various stars will differ 

 widely from each other, but all must con- 

 form to certain restrictions, which are in 

 fact those that follow from Kepler's laws. 

 Now for the majority of binaries this is 

 found to be the case, and by assuming that 

 the orbit of the body we have observed has 

 certain dimensions, shape and situation, 

 the velocity curve can be represented 

 within the limits that the accuracy of the 

 observations leads us to expect. But 

 this is not always so : a number of spectro- 

 scopic binaries were found for which the 

 velocity curve did not conform to simple 

 elliptic motion. It was then assumed that 

 the system must contain a third body 

 whose attraction causes perturbations in 

 the place and in the velocity of the bright 

 component that we observe. By adopting: 

 suitable mass and distance for this body 

 it was found possible to represent the ve- 

 locity curve fairly well. Too much em- 

 phasis should not be placed upon such a 

 representation, however; the assumption 

 of a third body is very much like the adop- 

 tion of additional pairs of Fourier terms 

 in an empirical formula, and it would 

 have to be a velocity curve of very com- 

 plex form that did not resemble, within 

 plausible limits, one of the great variety 

 of curves that so many terms would yield. 

 It has developed recently that many of 

 the cases in which secondary oscillations 

 were appeirently present could be ex- 

 plained as a systematic error of observa- 

 tion. This is caused by the presence on 

 the plates of the spectrum of the fainter 

 component which sometimes blends with 

 that of the brighter in such a way as to 

 distort the measures. Leaving out of ac- 

 count all the stars whose secondary oscil- 

 lations can be explained in this way, we 

 find that practically all the remaining 

 cases are also variable in their light, but 



