A NEW SOLAR THKORY. 1(')9 



iiaturo of this process, couipollcd to overdo its work, and lo })resoi'vc 

 tiiiiilly too imicli eneriiv within. the star. 



Now, l)y this gradual overheatiiiu' of th(^ inner hiyers t\w vertical 

 teniperature-gradient iiiiist increase more and more, until it reaches a 

 deg-ree of steepness at which the permanence of a mechanical equilib- 

 rium l)ecomes impossil)le. In such a case the overheated gaseous 

 matt( !• will force its wayoutward and will break through the "'cloak'''' 

 of absorbing elements above it. lUit th(> overheated matter will not at 

 once obey its molecular impulse to escape^ into higher levels. We 

 nuist remember thiit there exists a powerful system of convection cur- 

 rents between the interior and the surface of the sun. and that the 

 overheated particles may for some time lie swept along the paths of 

 these currents and may thus be forcibly detained in levels inconsistent 

 with their increased temperature, so that their state of equilibrium is 

 rendered unstable. This will produce a tension which increases in 

 course of time until the upward tendency of the overheated particles 

 l)ecomes strong enough to overcome the resistance of the currents. 

 At such a critical moment even a slight disturbance will be sufficient 

 to induce the upward motion so long restrained, thus giving rise to a 

 solar eruption. The cause of a solar outburst is therefore to be found 

 in the temporar}' existence of an excessively great vertical tempera- 

 ture-gradient, caused V)v progressive cooling of the outer atmospheric 

 layers and the ensuing overheating of the inner photospheric layers. 



From this exceedingly simple principle we are able to deduce an 

 analytical demonstration of the periodicity of solar phenomena, which 

 explains all the characteristics of the sun-spot curve hitherto obs(n'ved. 

 Obviously, the problem consists in demonstrating the changes in the 

 amount of outward radiation which are caused, oti the one hand, 1)y 

 the increase of absorpti\e power of the atmosphere in conse(iuenc(^ of 

 its progressive cooling, and, on the other, b}^ the reduction of al)sorp- 

 ti\-e power of this same atmosphere in consequence of the "clarifying''"' 

 action of eru])tions which, b}' lireaking through the "veil,'' diminish 

 the munher of cooled absorbing elements at the localities of einiption. 

 I shall not enter upon this part of my investigation in the present note 

 beyond stating that it is a simple application of Ikniguer-Lambert's 

 fonnula for the (extinction of light and heat in an a))S()rbing mcMlium. 

 The energy -S* of the radiation leaving the u])pei' linnt of the atmos 

 phere is found hy the differential e({uation 



where t denotes the time reckoned from the moment when the i)hol()- 

 spheric layer ((^^ has attained its state of thermal equilibrium, and n 

 and /i re])resent constants, the former of which depends on the rate of 

 cooling of the atfnosphere, the lattei- on th(> action of the (M'uptions. 



