394 



Dr. Edmund J. Mills on the 



the numerics, and of a treatise by Meyer and Seubert upon 

 the same subject in 1883, placed ampler data in my hands. 

 These have enabled me to calculate with considerable accuracy 

 the three constants required by the consecutive equations. 



If approximate trials be made with sets of contiguous 

 numerics, it will soon become evident that every numeric is 

 of the form 



K being some integral multiple of a number near to 15, 

 B being also near to 15, /3 the geometric factor, and x the 

 ordinal in the series. If K be taken as once, twice, thrice, 

 &c. 15, we shall have a succession of groups of numerics, and, 

 putting K = pl5, j> wn, l indicate their period. Lastly, we 

 can calculate the largest value of /3 which we may use in 

 common for all the groups, so as to make them interdependent: 

 this number will obviously be more accurately determined 

 than the other constants. The mean result from 37 numerics, 

 distributed in 9 groups, has been found to be /3 = '93727; for 

 this, without sensible error, we may write /3 = *9375 = 15/16. 

 It is probable that the equation 



y=pl5-15('9Z75) x 



includes the numerics of all known elements excepting 

 hydrogen. 



In the following comparison of theory with experiment, 

 I have depended mainly on Clarke's values : — 





G 

 #=15- 



roup I. 

 -15(-9375)*. 





Li . . 



X. 



. . 10 





7-01 



y calc 

 7-13 



Be . . 



. . 14 





9-09 



8-92 



Bo . . 



. . 20 





10-94 



10-87 



C . . 



. . 25 





11-97 



12-01 



N . . 



. . 42 





14-02 



14-00 





Group 



II. 







y=30- 



- 1509375)". 





. . 



X. 

 . . 1 





y- 

 15-96 



V calc. 

 15-94 



F . . 



. . 5 





18-98 



19-14 



Na . . 



. . 12 





23-00 



23-09 



Mg. • 



. . 15 





24-28 



24-30 



Al . . 



. . 25 





27-01 



27-01 



Si . . 



. . 32 





28-20 



28-10 



