\v 



xcix 



Illustration (iii). We will now take a case in which the probable error of the 

 mode is less than that of the menu, namely 3653 observations on the degree of 

 cloudiness at Breslau*; here represents a clear sky and 10 one wholly covered 

 with cloud. The data run : 



Degrees of Cloudinesn at Breslau. 



We have Mean = 6-829,181, Antimode = 4*827,034, 



yu a = 18-29987, 0- = 4-277,834, 



A = -611,2252, ,= 1-741,445. 



Seeking these values in Table XV we find that the value for /9, lies just outside 

 the Table. But it is perfectly easy to complete the Table here. The value of the 

 ratio for /9j = -7, # 2 = 1'7 is clearly zero. To obtain that for & = 1'7, y9i= '6, all we 

 need do is to consider the differences along the diagonal below the zeros. Thus : 



Here the quantities in square brackets are extra- 

 polated, and we see that '2004 is the value we 

 require at & = '6, /9 2 = 1*7. 



,= 2004, ^io = 0, 2 01 = '41 93, z u = '' 



= 88775, x = '41445, i/r = -58555, 

 give us, using the Hyperbolic Interpolation formula (a), 



Zex = -88775 x -58555 x '2004 + -11225 x -58555 4- -0000 

 + 11225 x -41445 x -2072 + -41445 x -88775 x -4193 



= -25844. 



67449 x 4-277,834 

 Probable Error of Mean = - 



V3653 



= 04774. 



Hence Probable Error of Mode = -25844 x -04774 



= 01234. 



We have therefore Mean = 6'8292 '0477, 



Antimode = 4-8270 -0123. 



Proc. It. S. Vol. xn. pp. 287290. Data taken from Hugo Meyer's Anleitung zur Bearbeitung 

 meteorologiacher Beobachtunyen filr die Klimatologie, Berlin, 1891, S. 108. There is clearly some error 

 about grade 8; no such "lump" occurs in similar Greenwich observations. 







