Ixvi Tablet ft 



n<l 



[\\.\V \ LVI 



The working origin was taken at 20, the centre of the group 1822. The 

 centre of the first group at 1'47 % is | (20- 1'47) = 3706 on the negative side of 

 the working origin and may be taken to contribute 56, + 206', 763, + 2830 



to the first, second, third and fourth moments respectively. The working unit 

 being b/ Q , the raw moment coefficients are: 



,'= -567,2191, i//= 7-703,4990, 

 v t ' = 28-982,5042, /' = 253-268,8730. 

 Whence transferring to mean and correcting, we have 



Mean = 22-8361, o- = 270156, 

 /<., = 7-298,428, /u 3 =16'238,780, /x 4 = 198-909,921. 



These lead to 



& = -678,295, ft = 3-734,20:2, 



*, = 2/8, - 3/8, - 6 = - -566,483, *, = - 1-052,180, 

 sk = -495,087, Distance from Mean to Mode = d = 1-337,508. 



These values, except the mean, are all in working units. Therefore in per- 

 centages of black : 



<r= 13-5078 and d = 6-6875. 



We can now find the probable errors of these constants. We first want ^, 

 from Table V, but 1086 is outside the limit of n. We therefore take ^, for 543 

 and have ^i = '02047, and we find ^ = '014,47. We can repeat our constants with 

 their probable errors 



Mean = 22-8361 '2765, <r = 13'5078 '1955. 

 Then from Table XXXVII, 



A = 37 : v^ 2,, = 4-70 + {j} [2] = 47 1 , 

 A -3-8: 



Hence for & = 37342 : VFS,, = 471 + - 



VJV^ = 4-83. 

 * 4 at and 11 at 3, giring a mean at 1-47 "/. 



