Mr. T. S. Aldis on Goodricke's Theory of Algol 363 

 Now from (15) (16), since sinw' — sin u t = a 1 cos ^ cosu t , 

 Sco = ±e 2 cr(o J2 — o-' 2 ) sin u { cos u p 



V du J \dcr J du 



|* !^ C os 2 w( - /2 -3(7 2 )^a- ; 

 36 cos a v y 



§5= — -cos 4 wsin 2 2 



,400 



a f(o-' 2 -3o- 2 )Va- 



= ^^z cr 5 cos 4 w sin 2 2a. 



This will give an approximation to the truth when cr is not 

 very large. The coefficient ^^ae 41 is only 2*66 feet; and if cr 

 were, for instance, 10°, the maximum value of 8s would be less 

 than a hundredth of an inch. The difference between the lengths 

 of the two plane curves is of a higher order. 



Southampton, April 16, 1870. 



LIII. Goodricke's Theory of Algol By T. S. Aldis, M.A., 

 Late Scholar of Trinity College, Cambridge*. 



THERE are some consequences of this theory which I have 

 not seen noticed. The comparative light of Algol when 

 full and when eclipsed enables us to compute the relative size of 

 Algol and its satellite. The light varies from 25 to 9, about ; 

 and the disks are therefore as 25 to 16, and the diameters as 5 

 to 4. Knowing the time of eclipsing, we can easily compute the 

 distance, which on this scale is 27. Hence, knowing the periodic 

 time, the mean density is found to be one-fifth that of the sun. 

 This result is probable, as Algol is unquestionably brighter than 

 our sun, which would be the case naturally if Algol be less cooled 

 down or condensed. The gigantic size of the satellite is thus 

 easily explicable. Both it and Algol must undergo much con- 

 densation before they arrive at the condition of our system. 



The constant diminution of the period also naturally results 

 from the hypothesis. With such a low density for Algol, and 

 such a large satellite, the density of the latter must be very low. 

 It is indeed opaque, as is proved by spectral analysis, but pro- 

 bably in quite a gaseous state. It will therefore be very suscep- 

 tible to the influence of a resisting medium. This can be no 

 part of Algol's system ; for every part of that would gain, by 

 friction on the interior parts, velocity, till it revolved freely round 



* Communicated by the Author. 



