STUDIES IN STATISTICAL REPRESENTATION. 



85 



Years. 



1901 

 1905 

 1909 

 etc. 



1902 

 1906 

 1910 

 etc. 



1903 

 1907 

 1911 



etc. 



1904 

 1908 

 1912 

 etc. 



Equalised 

 Month. 





Beginning of 



Equalised Months. 





January- 



Jan. 



0-A- 



0-A- 



0H 



February 



Jan. 30-iV 



30±£ 



30H 



31A* 



March 



Mar. m 



2-A 



9 e 



1H 



April 



April 1-fg- 



1* 



lis. 



1 1 6 



ItV 



May 



May 1H 



2 



2-±- 



^16 



1-A- 



June 



June l-j^ 



ItV 



X 1 6 



Otf 



July 



July lit 



Art 



9 2 



1* 



August 



Aug. lfe- 



1 1 6 



1 1 6 



OH 



September 



Sept. 0-iV 



OH 



1 



0x% 



October 



Oct. OH 



liV 



1-iV 



U l 6 



November 



Nov. 0^ 6 - 



W 



Oif 



U 16 



December 



Dec. O-Jf 



1* 



1* 



0--2- 



January 



Jan. 0-i- 6 - 



OiV 



Oif 







* Feb. OJfe. 



That is, the beginniDg of the equalised month or year 

 will fall regularly into a new position each year in the cycle 

 of four years, but this position will be repeated four years 

 later. In allowing for change of absolute or relative num- 

 bers for each month the principles already indicated may 

 be followed. 



6. Analysis of annual fluctuations. Quadrimestral and 

 quarterly data.— A large number of statistical results may 

 be more or less approximately represented by fluctuations 

 which have an annual period ; the simplest instance being 

 those whose instantaneous value is representable by 



(10) y =a + bsinfc + fi) 



the integral of which is 



(10a) Y = /{a + bsin(x + p)}dx = ax - bcos(*+£) 



