146 THE SUN-SrOT PEEIOD. 



It apppears that — ^ — = 0.5 dz 0.06. There seems to be a remark- 



ably constant proportionalit}^ between the total number of sun spots 

 and the summation of the temperature departures for all of the periods 

 reviewed. 



6. From the result just given it seems to follow that we may assign 

 to the arbitrary sun-spot frequency numbers of Wolf a physical sig- 

 nificance expressing the mean relation between sun-spot frequency and 

 terrestrial temperatures. Thus 1 Woli number corresponds to 0°.01 

 X 0.5 = 0=.005 C. 



Finally, from this discussion we are able to state detinitel}" the fol- 

 lowing law, which is also in agreement with the results of Koppen: 



The mean terrestrial temperature is subject to a period identical 

 with tliat of sun-spot frequency, and the effect of the presence of sun 

 spots is to diminisli the mean temperature of the earth, so that the 

 curve of mean temperature departures runs parallel with an inverted 

 curve of sun-spot frequency." 



III. 



It may now ])e inquired how far the result just reached might be 

 theoretically predicted. It is known that sun spots radiate less than 

 equal surfaces of the adjoining photosphere. This may be visually 

 observed from a comparative study of sun-spot and photospheric 

 spectra, which indicates a strong general absorption over the sun 

 spots. It has also been shown by the bolometric observations of 

 Langley, who reached the result that the umbra of an average spot 

 emitted onh^ 61 per cent as nmch radiation as equal areas of the adja- 

 cent photosphere. Again, at the time of maximum sun spots the 

 thickness of the absorbing laj'er of the chromosphere is increased, 

 which tends to diminish the radiation of the sun. Still, there are also 

 present at this time many faculte which radiate more strongly than 

 other portions of the photosphere. The effect of the faculas tends to 

 offset the absorption of the more opaque chromosphere, and we may 

 assume as a first approximation that the two effects compensate each 

 other, leaving only the influence of sun spots themselves to consider. 



From the researches of Zenker,^ based upon several different methods 

 yielding concordant results, the mean temperature of the earth's sur- 



«This law has been deduced from the discussion of observations made exclusively 

 at tropical stations, for these alone present a sufficient regularity of climate to per- 

 mit of the detection of such small temperature variations as are here in question. 

 But it would seem to be legitimate to extend the application of the law to the whole 

 surface of the globe, for it is impossible to conceive that a variation of the solar 

 radiation could influence temperature over half tlie surface of the earth without 

 affecting the remainder. 



'5'Thermische Aufljau der Klimat. Halle (Leipzig), 1895. 



