38 



C. V. L. Charlier. 



(' = — 11,32, 



and heuce is derived, taking the origin at the mean (= -\- 16. 80), 



1 = 3.38, 



= — 6.50, 



&, = +1.74, 



Cj = 212, 

 c,= 788. 



The form of the components and of the resultant curve is shown from fig. 18, 

 where I have used the same scale as Pearson for facilitating the comparison 

 with his curves. The value of a lies between the values, found by Peabson for 

 the two components. Though his values are rather unequal, we find that the agree- 

 ment in fig. 18 with the observed frequency curve is satisfactory. 



I have applied this method also to artificial mixtures of different pure lines 

 of the table V, and obtained acceptable results that at least may be used as a first 

 approximation to a more accurate solution. 



It is to be observed that the equation (48) coincides with the equation = 0, 

 which is required for the general solution. Hence it is no loss of time to begin 

 with this approximate method, which may be considered as an abridged method for 

 dissecting frequency curves. It must be remarked that the problem of dissecting 

 frequency curves into components is to a certain degree undetermined, there being 

 a possibility of an infinity of solutions. Under such circumstances it is often not 

 judicious to use too rigorous mathematical methods. Which may be understood in 

 just the same manner as it is not judicious to use too many decimals in nume- 

 rical calculations. It causes a temptation to overestimate the exactness of the result. 



Naturally this »abridged method » is only applicable when there are a priori 

 reasons for the assuoaption that the two components have nearly equal standard 

 deviations. There are many problems, where no such reasons exist. If we consider 

 for instance the frequency curve of the errors in astronomical transit observations, 

 we may divide the perturbative sources of error into two different groups. On 

 the one side we have the errors caused by psychological changes in the observer, 

 on the other accidental changes in the instrument and in the environs. It is 

 reasonable that the frequency curve may be considered as the resultant of two 

 (normal) curves, representing respectively the subjective and the objective errors of 

 observations. But there is no reason for the assumption that these two sources of 

 errors should have equal or nearly equal standard deviations. In such a case there 

 would be no meaning in the application of the abridged method. 



I have endeavoured to obtain, with the help of Engström, materials for 

 discussing the astronomical problem just now mentioned, which will no doubt furnish 

 an excellent instance relating to the importance of the problem to dissect a frequency 

 curve into unknown components. Up to this moment, however, I have not succeeded 

 in getting a frequency curve with a sufficient number of individual observations. 



