STUDIES IN STATISTICAL REPRESENTATION. 



97 



a - i (y\ + 1J2 



tan p - y^y^t* 



Therefore /? 

 Also b 





Vi-ryi-Va-Vi 



y\) = 7-78 

 -47 

 117 



- 0-401 



8 tfl 



i/' 2 - y's - y\) sec £ 

 3927 x 1*17 x - 1*077 == 



B y'i-y's±y'szy'*_ sin p 



0*49 about 



y.i-yz-ys^y* 



•3727 = 0*7216 about. 



Hence 2 y = 43° 50' nearly 



and cos 2 y 



-*91 

 - - -47 X 

 and frequency is = 7*78 - 0*49 sin (x + 158° 7') 



- 0*49 sin 2 (x + 21° 55'). 

 Marriage fluctuation is of course profoundly affected by 

 the position of Easter in the year. 



11. Curves of temperature and suicide.— The application 

 of the formula for monthly fluctuations may be illustrated 

 by the following example. The monthly means of the mean 

 maximum and mean minimum temperatures for the different 

 capital cities of the Commonwealth were taken from volume 

 3 of the Commonwealth Official Year Book. The numbers 

 so obtained were corrected for unequal lengths of months 

 as explained in section 3 and then weighted by multiplying 

 by the populations of their respective States. The numbers 

 so obtained were added for the different months and divided 

 by the population of the Commonwealth. The resulting 

 numbers, which may be taken as approximately represent- 

 ing the monthly mean temperatures prevailing for the 

 great mass of people in the Commonwealth, are given in 

 the following table : — 



Dec. 



69-0 



Month 



Jan- 



Feb. 



March 



April 



May 



June 



July 



August 



Sept. 



Oct- 



Nov, 



Temp.Fah- 



711 



707 



68-4 



63-5 



577 



536 



51-8 



54-1 



57-7 



61-8 



65-6 



Turning now to equation (22) we have 



a = -^(71'1 + 70*7 -f + 69*0) = 62'08 



G— July 5, 1911. 



