76 G. H. KNIBBS. 



STUDIES IN STATISTICAL REPRESENTATION. 



Statistical Applications op Fourier Series. 



(Illustrated by the analysis of the rates of marriage, temperature, 

 suicide, etc.) 



By G. H. Knibbs, c.m.g., p.r.a.s., f.s.s., etc. 

 Federal Statistician. 



[Bead before the Royal Society of N. S. Wales, July 5, 1911.'] 



1. Fundamental nature of the problem. 



2. Correction for secular change of amplitude. 



3. Correction for unequal length of months. 



4. Corrections for unequal quarters and half years. 



5. Equalised months and years. 



6. Analysis of annual fluctuations, quadrimestral and quarterly 



results 



7. Annual fluctuations, monthly data. 



8. Quinquennial periods 



9. Tabulation of terms as far as 6x. 



10. Illustrations of applications of sine formulae marriage rates. 



11. Curves of temperature and suicide. 



12. Reduction of epochal angle to days. 



13. Determination of Lag in correlated phenomena. 



14. Analysis of sine and cosine curves. 



15. Periodicity affected by movable feasts. 



16. Connection between periodic series. 



17. Conclusion. 



1. Fundamental Nature of the Problem.— Whenever the 

 whole series of fluctuations in phenomena such as are 

 susceptible of numerical representation are, in general, 

 exactly repeated, or may be supposed to be repeated, dur- 

 ing equal periods of time, they may be arbitrarily repre- 

 sented by a formula of the following type. 



