152 Dr. E. J. Mills on the 



where n = 15, p is the periodic or group number (i. e. 1, 2, 

 3, &c, as the case may be) , and x is an ordinal integer. A 

 fair example of the accuracy of the theory occurs in Group II., 

 for which the equation is 





*/ = ' 



2x15- 



-i*(U)*i 







= 



30 • 



-15(-9375f. 





Element. 



X. 





y- 



y calculated 



. 



. 1 





15-96 



15-94 



F . 



. 5 





18-98 



19-14 



ISTa 



. 12 





23-00 



23-09 



Mg 



. 15 





24*28 



24-30 



Al . 



. 25 





27-01 



27-01 



Si . 



. 32 





28-20 



28-10 



On examining the above numbers, it will be seen that the 

 agreement between calculation and experiment is very striking. 

 The first, third, fourth, and fifth numerics are certainly known 

 to the first place of decimals ; and here the coincidence is 

 closest : the second and sixth are not known so accurately; 

 and here the coincidence is less close. Similar comments 

 might be made on nearly all the sixteen groups. 



As the differences between consecutive values of y diminish 

 with the increase of x, the verification of the theory is neces- 

 sarily dependent in the main upon low values of x. In about 

 46 cases the value of w is 20 or less, and the corresponding 

 values of y (having been well determined) agree well with 

 theory; but beyond the limit of x = 20, there are at least 15 

 cases of good determinations which also exhibit a very satis- 

 factory agreement. 



The difference y x —y 2 m an y group is equal to -88 ; 



,yio-yii =, 49; y 20 -y 2 i = '26. 



All these differences are greater than are found in ac- 

 curate determinations of numeric. Even the difference 

 3/42— y43 = '06 is perfectly accessible to refined experiment. 

 When, then, the theory agrees very closely with a long range 

 of experimental numbers which might apparently have had 

 any other values whatever, it may be regarded as having a 

 reasonable foundation. 



The following corrections, partly based on new data, enable 

 me to adduce additional evidence of the general correctness 

 of the theory. 



