OF ARTS AND SCIENCES. 29 



that this theory does not seem very probable. We shouhl also, in this 

 case, assume that the time of revolution was exactly equal to that of 

 rotation of the satellite. A second explanation would assume that one 

 portion of the disk of Algol was darker tiian the rest, so that when 

 the satellite entered the disk it would cut off the dark portion, or affect 

 the light less than when passing off and obscuring the brighter parts. 

 In this case we must assume that Algol does not rotate, or it would 

 show a variation independent of the eclipse by its satellite. Its axis 

 of rotation might be parallel to the path of the satellite and the varia- 

 tions in light on its surface be distributed in zones, but such a theory 

 seems improbable. The third explanation is that the orbit of the sat- 

 ellite is elliptical, and that the difference is due to the varying velocity 

 of the satellite. 



An analytical solution of this problem may be found by reducing 

 the observed light to distances of centres, either by interpolation from 

 the values computed above, or by successive approximations. The 

 case then becomes that of a binary stai", in which we have given the 

 period and a number of distances, but no position angles. It is of 

 course impossible to deduce the position angles of the peri-astron or 

 other point of the orbit, but its other dimensions may be determined. 

 The solution of this problem will be undertaken at another time should 

 the accumulation of observations of Algol and other similar stars 

 render it desirable. For the present, it will be sufficient to obtain 

 an approximate solution. The nature of the variation is not so 

 simple as would appear at first sight ; since the observed time of 

 increase equals that of diminution, we must assume that the apparent 

 motion, when compared with that in a circular orbit, is less at the 

 beginning and end, and greater in the middle of its path. The satellite 

 must therefore either pass its peri-astron during the eclipse, or it must 

 be approaching this point, so that the increased obliijuity of its path to 

 the line of sight will produce the apparent diminution in its motion. 

 An ellipse was constructed, having an eccentricity of 0.5 and divided 

 into thirty-two parts, corresponding to the position of the satellite at 

 the end of each thirty-second of its time of revolution. The eccen- 

 tric anomaly was derived from the mean anomaly by the tables of 

 Dr. Doberck, Astronomische Nachrichten, cxii. 275. 



As the time of eclipse is very nearly one eighth of that of revolu- 

 tion, four of these divisions correspond to the {)assage of the satellite 

 over the star. Laying this ellipse on a sheet of rectangular paper 

 and turning it around its focus, the effect of a change in the position 

 of the peri-astron could be determined. The problem is greatly sim- 



