HISTORY OF THE ATOMIC THEORY. 193 



** According to the paragraphs quoted, the following is 

 the series of the alkaline earths in their relation to muriatic 

 acid : — 



" Little as the niembers of this series appear to follow any 

 certain order, it is nevertheless decidedly the case; at the 

 same time the inquiry into the law of these series is one of 

 the most difficult problems which stcechiometry gives us to 

 solve, and if we do not go to the inquiry with sufficient prac- 

 tical and theoretical exactness, we shall not succeed in our 

 inquiry into these laws or orders (of the numbers). And 

 now, to inquire into the law of the series before us, let 

 us first seek the difference between each member and its 

 successor, and we obtain 858—734=124, 1107—858=249, 

 3099— 1107=1992. Let us then use the first difference to di- 

 vide the two following differences, and we obtain ff|=2+TiT, 

 -W**=16rST. Then let us see if one quotient allows of divi- 

 sion by the other, that is, let us divide IG+xfr by 2+1-^4. If 

 we bring divisor and dividend under the same denomination of 

 124, this will be \6-{-Thi=^iW- and 2-|-^T=flf; therefore 

 •W6^?aV-=W9«- and 249 is contained exactly 8 times in 1992, 

 consequently Wi^=S. From this it is clear, that when we 

 have the first difference 124i=-j^, all the succeeding differ- 

 ences may be so divided by it that nothing remains; the half 

 here mentioned is only t-tH-^ in 858 parts=0.0006 and still 

 less in the other members of the series, it is, therefore, of no 

 importance; it is impossible in experiments to arrive at 

 such minuteness, at the same time in calculating the pro- 

 portion to 1 000 parts, it was necessary to throw away small 

 unimportant fractions, otherwise it would be needful to use 

 an enormous number of figures in order to designate the 

 quantities. Now H^ X 2 = 249; and ^P X8= 1992, con- 

 sequently 734-h^l^ = 858i, 734+*«^+ = ?^X2=lI07i ; 734 



2C 



