James Henderson 
185 
where = -7= and ^„"', 0o'^ <^>o^. ••• are the third, fourth, fifth, etc. dift'er- 
ential of coefficients i-e. 1^ is really expressed in a series of tetrachoric functions, or 
F= 5 [t, - ySj V4! T, + /3, VF! T5 - /3, V6! Ts - ...j. 
ySs, /34, jSs, etc. along with M (the mean) and a Charlier calls the 'characteristics' 
of the distribution curve. Now he seems to think that generally the coefficients 
/Ss and will only be required and so he has tabled <^o{x), '^^^ , for x= 00 
CLOG QjOO ' 
to 3-00 at intervals of -01 and also for « = 4 (Tables III, IV and V on pp. 123—125) 
to four decimal places. With the series up to (84 the theoretical F-coordinate will 
be found, according to Charlier, but from our experience of tetrachoric functions 
we are exceedingly sceptical about the accuracy of such a result. In fact, we feel 
certain that the approximation will not be a good one. If the frequency curve 
be little different from the normal then possibly the approximation would not be 
very bad. 
The above investigation was undertaken by me at the suggestion of Professor 
Pearson and I am indebted to him for several hints. My grateful thanks are due 
to Miss I. M'^Learn for her assistance in the preparation of the diagrams. 
* Charlier defines the ' skewness' <S to be S = 3;83and the 'excess' E to be E = Spi. 
