7H2 



d^h 7 ^dy 



( 



where y is determined bj 



W 2 ^ dr ^ ' 





or 



rfr 



;/ gives the change of Ihe temperature. 



By »the formulae (1) and (2) the change of A witli the time is 

 determined, when the quantity /?, which determines the original con- 

 dition, is known as a function of?*. We may, for instance, assume a 

 density distribution such as Emden has calculated for a gaseous 

 sphere in equilibrium, but supposing a mucii iiigher temperature at 

 each point than beloi»gs to an equilibrium form of this kind. The 

 original conditions must be such that A continually increases^ owing 

 to the strong force of expansion which is working all the time 

 towards the outside in consequence of the high temperature. This 

 will cause the tenq^erature of each layer to fall in a ratio which 

 is given by the quantity //, and in consequence the luminosity will 

 decrease. The most external coldest layers, which absorb the light 

 of the central parts, will move towards us with great rapidity ; this 

 e.cplains tvhij hi all new stars, as soon as the lufht begins to decrease, 

 the dark absorption-lines are displaced strongly toioards the violet — 

 a phenomenon which it has been attempted in vain to explain by 

 a rapid approach of tiie whole star, or by diflterences of pressure. 



Even when the initial conditions are simple, the equations (1) 

 and (2) are difficult to integrate. An attempt to find the course of 

 the change by mechanical quadrature failed through the fact that 



II • • ^y 



small variations in y come out greatly increased in -^, and tliere- 



dr 



fore also in the L that is found and the subsequent values for y, 

 so that each step gives an increasing inaccuracy, which, after inte- 

 gration through a few units of time, makes the results quite un- 

 reliable. On this account we have not succeeded in explaining the 

 periodic variation in brightness — which both in Nova Persei and 

 Nova Aquilae began to appear after the star had decreased 4 classes 

 of magnitude — by special initial conditions. 



On the other hand the general mean course of the process may 

 be calculated. The question may be asked: is it possible for the 



