194 MEMOIR OF DR. D ALTON, AND 



4.A^+ jLApjj _|.AjjL xjLa=3099i. In order better to understand 

 all, let us make 734=a, -^^=6, then 734=0!, 858^=a-f 5, 

 ll07i = a-\-b-^2b = a-{-Sb, 3099^=a+b-{-2b^\eb=a-\-\9b, 

 From this the quantitative series appears in the following 

 order : — 



MURIATIC ACID. 



ALUMINA.. MAGNESIA. LIME. BARYTA. 



a a-\-b a+3 6 a+19 6 



" Now this series remains always the same, even when we 

 put a higher or a lower number for the mass of the determining 

 element, for if the mass of the determining element is n times 

 greater or n times smaller, then, in the first case, all the 

 terms w^ould be n time& greater; that is, multiplied by n; and 

 in the latter case n times smaller or divided by n, and the 

 order of the differences would remain always the same ; 

 because what occurs with one of the differences must occur 

 also with the others, if otherwise the determining element 

 must still be considered as such. When this series is atten- 

 tively considered, we observe that the difference of the suc- 

 cessive terms is a mathematical product of the first difference 

 b with an odd number. According to it the quantities in which 

 the hitherto known alkaline earths assert their neutrality with 

 muriatic acid are terms of a real arithmetical progression, the 

 terms of which are found, when the product of a certain 

 quantity with an odd number is added to the first term, only 

 that between them many odd numbers, such as 5, 7, 9, 11, 

 13, 17, are left out. This is more remarkable, as the differ- 

 ences which the first term makes with the succeeding ones 

 may be represented entirely by odd numbers ; for one need 

 ©nly suppose that the mass of the determining element is 

 divided by J, then all the terms of the series would be at once 

 divided by b, and appear in the following form : — 



