82 PROCEEDINGS OF THE [Oct., 1875. 



er's table 11 is to be found in the negative portion of our Table, nor any one 

 (except B above mentioned) of tbe electro-negative third of table II, in the pos- 

 itive portion; in each of these portions, a few elements appear belonging to the 

 middle third of table II, which includes those of less decided electro-chemical 

 character than in the two other thirds. 



Those who desire to express approximately any one series by an equation of 

 the form IB+Qa, may easily do so, by properly choosing the constants P and Q, 

 and putting for a that number, witJi its sign, taken from the first column of 

 the table, which expresses the degree of atomic equivalence belonging to the 

 element whose atomic weight is required. For example, the atomic weight of 

 any element in series A is expressed approximately by 5 -I- 2a, in series B by 

 20-j-2a, in Cby 30-i-2a, in E by 82i+2ia, in G by 130+3a, the precise atomic 

 weight beiug given in many cases, the error, when occuring, being generally 1, 

 in two cases li, in one case 4. If it were worthwhile, values with fractions 

 might be given in each series to P and Q, by which the maximum error might 

 be much reduced, but then the sum of the errors would be distributed over all 

 the terms of the series, the results of the expression or equation being by a 

 small amount erroneous in each case. The numbers in the three series A, B, 

 and C maybe represented very closely by an arithmetical or equidifference series, 

 whose first term is 7 ( for Li ) and equidifference is 2, the errors nowhere ex- 

 ceeding 1 ; with first term 6. 6 and equidifference 2, the sum of the errors 

 would be -f- 0.2 and the errors would exceed 6.6 in but two cases the maximum 

 error being 0.9. So the numbers from 108 to 137 will be approximately repre- 

 sented by an equidifference series whose first term is 109 (for Ag) and common 

 difference 3, the error exceeding 1 for one element only. "With first term 

 109. 6, and same difference the algebraical sum of the errors will be reduced to 

 —0.2, but the errors would exceed 1 in two cases. Of course it is understood 

 that the series just mentioned furnish numbers to fill the gaps in Une +3 and 

 in line 0, although no Elements be there recorded in the Table, and it is some- 

 what remarkable that the numbers in the series which would correspond to line 

 +4, if it were used in the Table, answer equally well for line or group —4, 

 which lines are equally remote from the maxima of positivity or negativity ; 

 also numbers for +3 answer for —5. This wiU also be seen by using for series 

 A the expression 5+ 2a, for series B, 21+ 2a, for series C, 37+ 2a, instead of 

 those given above ; or taking the numbers actually recorded in the Table, Si 

 =28 which stands in line — 4 of series C, will numerically suit equally well for 

 hne +4 of series B ; Sn=118 which stands in line —4 of series G, will suit 

 very well for liae +4 of series F ; indeed as it is found near the middle of table 

 II, it might well be placed in line +4, but its proper place is in —4, because 

 of its relations with Ti as shown through Butile and Stannite, &c. 



The average difference for numbers on the same line in series B and C, and 

 also in A and B, is 16 ; for C and E, the difference is about 46, and between E 

 and G about 48 ( =3X 16 ). Hence Dumas' "triads " appear in series A, B, C, 

 on lines +1 and +2, and in series C, E, G, on each line except —4. If to 

 each of these last, we prefix the numbers corresponding in series B, we shall 

 have most of the sequences to which Dumas applied his equations of the form 



