HI8T0KY OF THE ATOMIC THEOKY. 195 



<* In this case the first term would be-r* and if it were all 

 expressed in numbers then would -f- =THf?=-Wir=5-l-fH' 

 and the mass of the determining element ^^^-^V^i^^^W 

 =8r4ir. In this way all the members are obtained in numbers, 

 when 1, 3, and 19 are added to the first term WaS and the 

 elements observed which are designated by these figures. It is 

 very probable that the terms -^ +6, -f-+7, -f +9, -f- +11, 

 _£_-fl3, _«_-|-15, -«_+ 17 are wanting in the series, and the 



b b b 



reasons for considering this probable, will be shewn in a suit- 

 able place. 



" Preliminary determination of the order of the alkaline 

 earths which enter into neutrality with vitriolic acid, 

 § XXIIL, p.33. 



** If we put in order the amount (mass) of alkaline earths 

 which stand in neutrality with 1000 parts of vitriolic acid, 

 in the manner adopted with muriatic acid, the following 

 series of quantities is obtained : — 



" In order to discover the law of this series let us, as in the 

 former case, subtract the first term from all the succeeding, 

 and we receive 796—616=180; 1053—616=437, 2226—616 

 =1610. Let us see now if the first difference can so divide 

 all the rest, that nothing, or at least very little, remains, then 

 HJ=2+T^, -VW=8-Mia. As nothing can be discovered 

 here on account of the variety in the remaining fractions, 

 let us divide every difference by 90 as the half of the first 

 difference, and we obtain -W=2, W^=5, -»-|J^=18— f^. The 

 fractions here are not so considerable as before, although too 

 large to be thrown away. Until, therefore, we are able to 

 complete the order let us make 616=616, 796=616—2.90,* 

 1053=616+5.90— H, 2226=6164-18.90— i^." 



• 2.90 means 2 X ^0. 



