in which of course the suffixes to the sign of summation 

 denote the suffixes for y and y written out as in (40). 

 If <//;/ be constant ratio throughout, r say, then (40) 



But if r> be the same quantity for eacli ordinate, s say, 



g» = |{l*s A !ii + ^Z>n , ir^ + ui L.(*D 



I ( & + / y* I 



Thus, for convenience of computation, the former condition 

 is to be preferred, and if it could be secured, the series of 

 values of y for different values of q would be of equal weight 

 whatever the absolute values of y. 



The expressions for the error (40), (41) and (42) may be 

 required iu their absolute instead of their relative form: 

 they are then the absolute probable errors of q*, and for 



n =± 1 . V (43) 



Since the weigiit of any observation is proportional to 

 the reciprocal of the square of its probable error, we have 



to = l/p' (46) 



and the results for <f will therefore have the following 



(i) where the probable error is peculiar to each ordinate, 

 (ii) when it is a constant ratio of the length of the ordinate 

 (iii) when it is the same absolute amount. 



