STUDIES IN STATISTICAL REPRESENTATION. 109 



number of marriages in the Lent period (6 weeks) preceding, 

 and to augment them in the preceding and following periods. 



It may be noted that for the fluctuations of annual period 

 in the marriage frequency, the great length of the Lent 

 period, viz., 6 weeks, has the effect of throwing the increase 

 of frequency as far back as February. The migration fre- 

 quency is frequently thrown back into March. Thus as is 

 evident from the preceding table and the diagram, decennial 

 means will clearly be nearly but not exactly comparable. 

 The data for a thorough study of periodic fluctuation would 

 in these cases have to be weekly groups. 



16. Connection between periodic series.— Correlation 

 between statistical results may be of two kinds, viz., (a) 

 rational, and (b) empirical. In the curves 2 and 3 in the 

 figure, where the fluctuations of suicide and temperature 

 are analysed by the expression in sin x and cos x only 

 (which in the nature of the case probably really represents 

 the general trend) the striking similarity is evident. That 

 suicide is accentuated in the summer and falls off in winter, 

 is thus indicated, and in the Northern Hemisphere the same 

 holds, that is to say the maximum period differs about six 

 months from that in the Southern Hemisphere. On com- 

 paring the two curves in sin x and cos x only, we find the 

 following results hold 



Temperature curve max. 71*61 at 19° 48' 



min. 52*55 difference 19°*06 



Suicide curve max. 0*3581 at 10° 44' 



min. 0*3001 difference 0*0580 



Since the mean for the suicide curve is 0*3291 and of the 

 temperature curve is 62*08°, and since moreover 0*0580/19*06 

 = 0*00304 we have the suicide curve almost exactly pro- 

 duced from the temperature curve by the formula 

 (71)... q = 0*3291 + 0*00304 (t - 62*08°) 



