16 



C. V. L. Charlier. 



As to the controls it is to be remarked that the control (c), being a mere 

 transposition of the terms, must give full agreement between the tivo results to the last 

 cipher. As to the control of the second part of the calculus, through (i), a diffe- 

 rence between the first and the second value of v^' may amount to some units 

 of the last cipher. The difference in the example is 0.008, and hence rather great, 

 and is probably caused by the neglected decimals in h'^. There is, however, no 

 reason to make the calculation with more decimals. 



All multiplications and divisions (partially also the additions) are performed 

 with the aid of a calculating machine (I use for the present a machine of Odhners 

 construction). 



The five parameters hence have the following values: 



1x0=2000, 



h = — 0.499, 

 a = -|- 1 .681, 

 p3 = — 0.0848, 

 = -\- 0.0046. 



For comparing the observed values of the frequency with the theory we must 

 calculate the values of œ^, œ.^, corresponding to the different classes. From 

 tables B, C, D at the end of this memoir we obtain the values 



11 



0 



1 



2 



3 



4 



f) 



X 



— 3.5 



— 2.5 



— 1.5 



— 0.5 



+ 0.5 



+ 1.5 





— 2.07 



— 1.49 



— 0.893 



— 0.296 



+ 0.296 



+ 0.893 



'h 



+ 0.047 



+ 0.131 



+ 0.268 



+ 0.382 



+ 0.382 



+ 0.268 





— 0.124 



— 0.163 



— 0.527 



— 0.329 



-|- 0.329 



+ 0.527 



tr 



— 0.204 



— 0.712 



— 0.308 



+ 0.947 



+ 0 917 



— 0.308 



n 



ß 



7 



8 



9 



10 





X 



+ 2.5 



+ 3.5 



+ 4.5 



+ 5.5 



+ ().5 







-f- 1.-186 



+ 2.07 



+ 2.68 



+ 3.27 



+ 3 86 





'fi, 



+ 0.131 



+ 0.047 



+ 0.011 



+ 0.002 



+ 0.000 





'h 



+ 0.153 



— 0.124 



— 0.123 



— 0.048 



— 0.011 





'h 



— 0.712 



— 0.204 



+ 0.126 



+ 0.102 



+ 0.031 





We hence derive the following values of the calculated frequencies compared 

 with the observed ones. 



Number of glands (m) 



0 



1 



2 



3 



4 



5 



6 



7 



8 



9 



10 



Observed frequency 



15 



209 



365 



482 



414 



277 



134 



72 



22 



8 



2 



Calculated ,, 



43 



166 



369 



494 



427 



2(34 



136 



67 



26 



8 



1 



Tlie results are illustrated by fig. 6 on plate II. 



