February 13, 1902 J 



NA TURE 



353 



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

 p 

 is under all conditions <f(^i "^2)2, and this the more so the 

 greater the difference between \,^ and X^. Hence we deduce 

 lm---\p; 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 theoretical proof of the well-known pro- 

 perty of the observed spot-curve that the ascent is steeper than 

 the descent. 



To give some idea of the accuracy with which the above theory 



mical phenomena at the surface. Now these variations must 

 react on the development of eruptions and spots If the currents 

 are weak — viz, if the transfer of heat from the interior to the 

 surface is coniparatively small — the cooling of the atmosphere 

 must proceed rapidly, and hence the development of eruptions, 

 which are a direct consequence of this process of cooling, must be 

 energetic. At such times we have, therefore, to expect solar 

 cycles with a powerful display of dynamical phenomena. If, 

 on the other hand, the currents are intense — viz. if the heat- 

 supply from the interior is vigorous— the rate of atmospheric 



: of solar ^pots. 



: of solar spots (Sprtrer). 



can be made to represent the observed facts, I subjoin a plate 

 (Fig. I) in which the spot-curve, resulting from theoretical 

 considerations, is compared with Sporer's curve derived 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 Royal Observatory, Edinburgh. 



The theory also accounts satisfactorily for the existence of a 

 "great" period of solar phenomena. This greater cycle is 

 brought about by the influence of the surface fluctuations of tem- 

 perature described above on the intensity of the convection cur- 



cooling will be small, and we have then to expect cycles with 

 only a weak development of surface phenomena. 



Since the quantity a depends on the rate of cooling of the 

 atmospheric layers, it will attain high values at times when the 

 spot-development is powerful, and vice versd. Now the greater 

 o, the greater will be the difference between A,'- and Ao^ and, 

 consequently, the earlier must the time of maximum, /„„ occur. 

 Hence the position of the maximum in the spot period relatively 

 to the preceding minimum must depend on the greater or less 

 vigour of spot-development during the cycle, inasmuch as the 

 time of maximum must be the more in advance of the centre 



Fjg 2 Deviations of the Mean Anmisl Temperature from the Normal 



Koppuii flesalii from Trcpical Stations Kim^i Subttofial St3' 



rents which regulate the interchangeof heat between the interior 

 and the surface. It is inconceivable that in a gaseous body like 

 the sun, governed by a gigantic convection, changes of tempera- 

 ture of parts of its mass can be confined merely to the surface. 

 Hence we must conclude that the distribution of temperature 

 throughout a considerable part of the sun's bulk will be more or 

 less affected by the fluctuations of temperature at the surface, and 

 that consequently the intensity of the system of convection- 

 currents, which depend on this distribution of temperature, 

 must undergo variations similar to those exhibited by the dyna- 



NO. 1685, VOL. 65] 



of the period the greater the display of the dynamical pheno- 

 mena. This important conclusion, arrived at by purely 

 theoretical considerations, is amply corroborated by the facts. 

 I refer in this respect to a recent publication of Dr. W. Lockyer, 

 in which this peculiar shift of the maximum is pointed out as a 

 feature of the observed spot-curves. 



The object of this brief abstract being merely an exposition of 

 the main principles upon which I have ventured to build a new 

 solar theory, I shall not enter upon its various applications to 

 the phenomena connected with the periodic changes in the 



