320 Prof. F. Zollner on the Temperature and 



elevation*, it appears that the simplest supposition is that the 

 liquid surface required by this theory of the sun-spots is identical 

 with that out of which the protuberances burst forth. The ra- 

 dius of this surface r will be r = R — 8" when R signifies the 

 sun's radius expressed in seconds; or taking R at the mean 

 distance of the sun to be 16', we have r=15' 52". According 

 to Hansen, the mean solar parallax is 8"*9] 5 ; hence we have 

 r = 680,930,000 metres, or 8"= 5,722,500 metres. In order, 

 therefore, to be able to obtain a numerical value for the mini- 

 mum temperature in the space from which an eruption of the 

 height of 1*5 minute breaks out, we have only to substitute the 

 following values in equation (5) : 



r= 680,930,000, H = 64,370,000, A= T J„ * = 3'409, 



Hence we find ^ = 40690°. 



If we give H double the above value, or suppose an eruption 

 of 3 minutes (as not unfrequently occurs) to take place, we have 

 a minimum temperature ti = 74910°. 



We may, however, now inquire whether we are justified in 

 taking the extreme heights of observed protuberances as values 

 for H in our formula, H signifying the height to which a body 

 thrown out from the sun's surface would rise without resistance. 

 If we have really to do with rising masses of glowing hydrogen, as 

 is indeed sufficiently proved, this rise may take place, according to 

 Archimedes's principles, like air heated and made specifically 

 lighter than the neighbouring parts. It is, however, clear that 

 the two conditions of motion will produce a very different effect 

 as regards the time in which the moving masses will reach a given 

 height. "Without going more specially into these conditions, it 

 is plain that the time which a protuberance needs in order to 

 rise to a given elevation H, by virtue of the principle of Archi- 

 medes, will under all circumstances be greater than that needed 

 to rise to the same height H when moving under the influence 

 of a certain initial velocity and encountering no resistance. 



An exact observation of the length of time which a rising pro- 

 minence takes to reach a given elevation will give a means of 

 deciding whether or not the elevation is reached by the action 

 of the first-mentioned cause; and unless this is proved to be 

 likely, this elevation cannot be used as an integral part of the 

 above formula. 



According to the hypothesis which we have made, the outlet 

 whence the protuberance emerges from the glowing layer of 



* I have mentioned this theory, five years ago, in my * Photometricai 

 Researches/ p. 245, 'and also in the Vierteljahrsschrift d. Astron. Ges. 

 Jahrgang iv., H. 3. p. 172; and it is my intention to develope it in a spe- 

 cial memoir. 



