170 



A NEW SOLAR THEOEY. 



The integ-ral of this e({uatioii will thus give us the changes in the radiat- 

 ing- power of the sun toward a point in the universe. Considering that 

 the intensity of the dynamical phenomena at the solar surface must 

 depend on the excess of energy preserved to the sun beyond what he 

 requires for the maintenance of thermal equilibrium at r/,,, we arrive at 

 the following theoretical equation for the frequency of eruptions and 

 spots : 



where ^> is the period and 



/\i = —\a-\- x/i^"^ + aft 

 \ — — h:Oc — y/\a^ -\- afS 



It is readily seen that /• starts froiu zero at the moment t=o^ and that 

 it reverts to zero at the moment t=2^- Between these two moments ;' 

 attains a maximum, and we find the time when this occurs from the 

 equation. 



^,(Ai-A,.)'' 



.Alt' 



Aj 1 - e^-^" 



Now, it can be shown that the right-hand side of this equation is 

 under all conditions <.e''-'''^~^-^~_, and this the more so the greater the 

 difference between \{' and A/. Hence we deduce 2^„i<i_/^/ i. e. , the 

 ascent from zero to the maximum must take place in an interval of 

 time shorter than half the period. This constitutes the first theoret- 

 ical proof of the well-known property of the observed spot-curve that 

 the ascent is steeper than the descent. 



To give some idea of the accuracy with which the alxne theory can 

 be made to represent the observed facts, 1 sul)join a plate (iig. 1) in 



90 

 80 



I 2 3 4 5 6 7 8 9 10 11 Vcars. 



TAeoreCccai curyes of soiar spots. Obsert'ed curves ofioCar spots(SpbrerJ. 



which the spot-curve, resulting from theoretical considerations, is 

 compared with Siwrer's curve dei'ived from observation. A full 

 description of the method by which the theoretical curve has been 

 obtained will be given in a paper shortly to be published as part of 

 the first volume of the Annals of the Koyal Observatory, Edinburgh. 



