A STUDV OF CORUELATIOXS AMONG TERRESTRIAL TEMPERATURES. 375 



It is not necessary to compute tlie value of to from these data because it is evidently 

 evanescent, the mean coming out with an imaginary value. In fact the values of A 

 as they come out in the last columns of the table are less than their probable errors 

 by amounts smaller than could be expected, except as the result of chance. There 

 is therefore no evidence of any irregular fluctuation having a period between ten 

 days and several years. 



§ 15. Search for Variations Synchronous with the Sun's Synodic Rotation by the Method of 



Time-correlation. 



Granting the existence of variations in the solar constant it is extremely improb- 

 al)le, and indeed almost inconsistent with any theory of what is going on in the sun, 

 to suppose them to take place simultaneously over the entire photosphere. We should 

 expect them to be mostly confined in each case to some limited region ; then, when this 

 region became visible from the earth, we should experience a change in the solar heat, 

 which would reach its maximum or minimum when, in consequence of the sun's rota- 

 tion, the meridian of the hot or cool region of the photosphere passed the middle of 

 the sun's disc as seen from the earth. After this the effect would diminish, and would 

 disappear entirely as the region disappeared from our sight on the sun's western limb, 

 to be renewed when it reappeared on the eastern limb. Thus we should have a fluc- 

 tuation in the terrestrial temperature having the period of the sun's synodic rotation. 



Were the period of the rotation a well-defined constant, and were the excess of 

 temperature in any region of one hemisphere permanent, the effect could be deter- 

 mined in the same way that we have determined that of the solar spots, by forming 

 equations of condition for the coefficients expressing the amplitude of the resulting 

 fluctuations. But there are two conditions which would render this method illusory. 

 The first is that, owiiag to the different periods of rotation in different parallels of solar 

 latitude, there would be no one invariable period of the phenomenon. The other 

 impeding condition is that we must expect such deviations of temperature within any 

 region of the sun to be temporary, lasting only a few weeks or months, and then dis- 

 appearing, to reappear in some other region of the sun. Then the effect would appear 

 entirely non-periodic if followed during long intervals of time, and could be detected 

 only Ijy the statistical methods already developed. If the change of solar temperature 

 ordinarily disappeared before a rotation was completed, the effect would be entirely 

 irregular and non-periodic. But if it continued through one or more solar rotations, 

 as would probably be the case, then the effect would be temporary fiuctuations of 

 temperature having the period of the synodic rotation, but changing their epoch from 

 time to time, and thus annulling each other if we treated them as continuous through 



