518 REPORT^— 1902. 



chromosphere from the continuous overlapping spectrum of the sun. This sepa- 

 ration is accomplished hy applying spectroscopes of great resolving powers. In 

 the Fourier analysis resolvhig power corresponds to the interval of time which is 

 taken into account ; hence, to discover periodicities of small amplitude we must 

 extend the time interval of the observations. 



I believe that the curve which connects the intensity with the period will play 

 an important role in meteorology. It is a curve which ought to have a name, and 

 for want of a better one I have suggested that of 'periodograph.' To take once 

 more barometric variations as an example, it is easy to see that just as in the case 

 of white light the periodograph would be zero for very short, and probably also for 

 very long periods. There must be some period for which intensity of variation is 

 a maximum. Where is that maximum ? And does it vary according to locality ? 

 The answer to these questions might give us valuable information on the difference 

 of climate. Once the periodograph has been obtained, the question of testing the 

 reality of any special periodicity is an extremely simple one. If h be the heiglit 

 of the periodosrapb, the probability that during the time interval chosen the 

 square of the Fourier coefficient should exceed kh is e~'-\ If we wish this quantity 

 to be less than a million /,• must be about eleven ; so that in order to be reasonably 

 certain that any jjeriodicity indicates the existence of a truly homogeneous varia- 

 tion the square of the Fourier coefficient found should not be less than eleven 

 times the corresponding ordinate of a periodograph. 



I have calculated in detail the periodograph of the changes of magnetic declina- 

 tion at Greenwich, taking as a basis the observations published for the twenty-five 

 years, 1871-95. It was not perhaps a very good example to choose, on account of 

 the complications introduced by the secular variation, but my objpct was to test 

 the very persistent assertions that have been made as to the reality of periodic 

 changes of 26 days or thereabouts. The first suggestion of such a period came 

 from Hornstein, of Prague, who ascribed the cause of the period to the time of 

 revolution of the sun round its axis. He only discussed the records for one year's 

 observations, but the evidence he offered was'sufficient to impress Clerk Maxwell 

 with its genuineness. Since Ilornstein's first attempts a great many rough and 

 some very elaborate efforts have been made by himself and others to prove a similar 

 period in various meteorological variations. The period found by different com- 

 putors differed, but there is a good deal of latitude allowed if the rotation of the 

 sun really has an effect on terrestrial phenomena, because the angular velocity of 

 the visible solar surtace varies with the latitude. Hornstein himself and some of 

 his followers deduced a period not differing much from i'G day. s, while Professor 

 Frank liigelow, using a large quantity of material, finds 26-68 days, and Eckholm 

 and Arrhenius return to 26 days, or, as they put it more accurately, to 2.5-929 days. 

 The two latter investigators do not, however, adopt the idea that this periodicity 

 is due to thi' rotation of the sun. None of these periods can stand the test of 

 accurate investigation. 



As the result of my calculations I can definitely state that the magnetic decli- 

 nation at Greenwich shows no period between 25'5 and 27'5 days having an 

 amplitude as great as 6", The influence of solar rotation on magnetic variation 

 may therefore be considered to be definitely disproved. 



The intensity of the periodograph increases rapidly with the period, and minute 

 variations are therefore more easily detected in short than in longer periods. Six 

 seconds of arc forms about the limit of amplitude which can be detected in twenty- 

 five ye.ys of observation when the period is about 26 days, and from what has 

 been said above the amplitude which can be detected will be seen to vary inversely 

 with the square root of the time interval. For periods of about 14 days an ampli, 

 tude of 3" is still distinguishable with the material I ha^e used, and such 

 ah amplitude is actually found for a period which has half the synodic month .ns 

 its time. The chance that this apparent variation is due to an accidental coinci- 

 dence is one in 2,000, and I cannot therefore as.sert its definite existence 

 beyond all possibility of cavil. But it is surely significant that of all the periodic 

 possible between 12-3 and 18 7 days that gives the highest amplitude which 

 pojncides witli jialf the synodic revolution of the moon. That it is at all possible 



