TRANSACTIONS OF SECTION F, 751 



standard deviations. But this correlation will clearly only give an indication of 

 the correspondence of the general moTements of two ciirve? : vrhereas the minor 

 movements may be intimately connected, although the general movements may be 

 quite different. It appears possible to slightly modify the usual method of correla- 

 tion so as to eliminate the general movement in the special case — of very frequent 

 occurrence — where the phenomena exhibit a regular periodic fluctuation, and to 

 correlate the oscillations. All that is necessary for this purpose is to replace the 

 deviations from the average of the whole series in the above formula by the devia- 

 tions from the trend, or curve of instantaneous averages. To determine this trend, 

 note the number of observations (p) in a complete phase ; the instantaneous 

 average at any particular point is represented by the average of the ^j observations 

 of which that point is the middle one. 



As an illustration the method may be used to determine which of the sets of 

 figures, quoted by the Registrar-General in his annual reports for comparison with 

 the movements of the marriage-rate, is most intimately connected with it, viz., 

 imports, exports, total trade, wheat prices, or amount cleared at the Bankers' 

 Clearing House. The marriage-rate is now lower than formerly, whereas the 

 trade per head has increased : there is thus no correspondence between the general 

 movements, and correlation by the usual method about the average merely confirms 

 this. But the marriage-rate (and four of the other phenomena to be examined) 

 shows fairly regular oscillations with a period of about nine years. Replacing the 

 average of the whole period in these various series by the trend, the * average ' for 

 any one year being the average of the nine years of which it is the middle, we can 

 thus ascertain what correspondence there is between the oscillations of these 

 curves. By correlating the marriage-rate with the trade, &c., of the previous and 

 following years, of half a year earlier, &c., other correlation coefficients are 

 obtained : if these are plotted on a diagram it will easily be seen that there is a 

 point of maximum correlation. This gives a measure of the lag of the marriage- 

 rate behind the trade-curve, the point of maximum correlation indicating the 

 period with which the marriage-rate is most closely connected. 



It is thus found that the total trade per head and the amount of clearing are 

 most intimately connected with the marriage-rate, the exports per head is 

 almost as closely, and the imports per head less so, although the correspondence 

 with all four is very close. There is on the other hand no connection between the 

 price of wheat and marriage-rate nowadays. As regards lag, the marriage-rate 

 is now just half a year behind the total trade, three quarters of a year behind the 

 exports, and about one and a quarter year behind the clearing. 



It is noticeable that in 18G1-75 the marriage-rate was only a quarter of a year 

 behind the total trade and export curves, indicating that it now responds a little 

 more slowly to the general prosperity. It is interesting to observe that this defer- 

 ment of a quarter of a year (as compared with total trade) corresponds very fairly 

 with the deferment indicated in the marriages by a consideration of the ages at 

 marriage. 



5. Joint Discussion with Section L on Economics and Commercial 

 Education, opened hy L. L. Price. 



In the middle of the nineteenth century the economist exerted a dominant 

 influence over British public opinion, but by the close of the century that influence 

 had become less considerable. The stir now arising on commercial education 

 offers a fresh opportvmity for asserting the claim of Economics to a distinct place 

 in the education of the citizen ; and two circumstances favour the advance of the 

 claim. On the one hand, the inner history of economic study affords reason for 

 believing that the old controversies, which created such noise, are dying or dead ; 

 that the criticism, which has been busy, has been accompanied by a considerable 

 amount of constructive work ; and that the popular antithesis between the ' old ' 

 and the ' new ' schools has lost its meaning, if it is supposed to represent irrecon- 

 cilable feuds. On the other hand, economic guidance is more urgently required in 

 practical affairs ; for many questions coming to the front of popular discussion are 



