98 G. H. KNIBBS. 



fi = 71*1 - 62*08 = 9*02, and the different values of r 

 are given in the following table : — 



fi r.> r :i r 4 n r 6 r 7 r 8 r 9 r i0 r n v vl 



+9-02 +8-62 + 6-32 +1-42 -4 38 -8-48 -10*28 -7'98 -4*38 -028 + 342 +6*92 



We can now make use of the equations already deduced 

 to determine the values of a x , 04 : a 2 , <* 2 * etc. From equation 

 (41) we obtain at once 



Hence cot (a, + 75°) = - 1*439 ; thus <*, = 70° 12'. 

 Then from (37)j we have 



eh = (R 2 + i? 4 + ^ 3 ^3) t^j cosec 15° cosec (^ + 75°) 



= 9*450 x *0218 x 3*864 x 11*951 = 9*513. 



From (33) and (34) a 2 = - 1*183; a 2 =65° 31' 

 From (30) and (31) a 3 = + 0*155; a 3 = 26° 6' 

 From (27) and (28) a 4 = + 0*099; a 4 =z 34° 30' 

 From (40) and (42) a 5 = - 0*046; « 6 =4° 36' 

 Lastly from (29), (29b) and (44), we have 



4- 4- -4- ' 4- 12 



f i T r 3 + r 5 + f 7 t r 9 f r a =- - a d cos « 6 



7T 



and if we assume that «<? = ; then a 6 = —0*047. 



The frequency is thus 

 = 62*08 + 9-513 sin (as + 70° 12') - 1*183 sin 2(a-+ 65°31') 

 + 0*155 sin 3(<e + 26° 6') + 0*099 sin 4(a + 34° 30') 

 - 0*046 sin 5(x + 4°36') - 0*047 sin Qx 



which will give the group means from which they were 



derived, as may be readily verified. 



The figures given in (4) representing daily number of 

 persons committing suicide in the Commonwealth during 

 the decennium 1900-09, may be taken by way of further 

 illustration of the analysis into periodic series, and by way 

 also of indicating the time-relation of the two series (see 

 also § 13 hereafter). 



