78 PROCEEDINGS OF THE [Oct., 1875. 



At the meeting of the British Association in 1851, * Dumas shewed that the 

 successive atomic weights of the members of a gToup, from least to greatest in 

 order, might in many cases be expressed by an equation of the form, <xA-j-5B 

 -\-cG ; in which A,B, and C were properly chosen constants for each group, A 

 being atomic weight of the first member, and a, b, c, might vary from member 

 to member, though in most cases a was constant and equal to 1 ; b was for 

 first member, c was for first two members and then might vary from member 

 to member, but were small numbers never greater than 7 or 8. He also shewed 

 that in several groups three of the members would form an arithmetical or 

 equidifference series, sometimes exactly, in general very approximately. These 

 sub-groups he called *' triads " but not in the sense in which that term is now 

 used in chemistry. These " triads" would of course be formed when in a 

 group three equations occurred, such, for example, as the following : 



A+B A+B A 



A+B+C or A+4B or A+B &c. 



A+B+2C A+7B A+2B 



In 18531 Gladstone discussed the same subject in an article on the " Numer- 

 ical Kelations of Atomic Weights, " using the numbers given in Gmehn's Hand- 

 book, in order "to avoid the objection that his mind had been biassed by 

 dwelling on the numerical relations." In 1854 J. P. Cooke arranged the ele- 

 ments in numerous groups or series by their numerical relations, and in 1857 

 Odliug considered these relations in an article % on the ' ' Natural Groupings of 

 the Elements, " using the numbers in Miller's Elements of Chemistry. 



In 1858 and subsequent years Dumas II pointed out the "parallelism" be- 

 tween corresponding members of a pair of groups, indicated by the nearly con- 

 stant difference between the atomic weights of corresponding elements in each 

 group, and shewed that this "parallelism" extended even to groups of com- 

 pounds. 



In 1858 Mercer § illustrated these relations in certain groups by diagrams, 

 laying down the atomic weights and their differences, by scale, as ordinates, or 

 parts of ordinates, to a line of abscissas. 



In articles inserted in Watts' Dictionary of Chemistry, in 1863 ^ and 1868, ^ 

 Odling again discusses this subject with the aid of later chemical views and 

 knowledge ; and in 1869 one writer in the American Supplement to the Chem- 

 ical News called attention to ' 'the pairing of the artiad and perissad Elements, " 



* Dumas, Sm. Jour., % XII, 275, 1851 ; 2, XXV, 267, 1858 ; 2, XXVI, 259, 1858. 

 t Gladstone, L. E. & D. Phil. Mag. 4 V. 313, May, 1853 wltn DeMorgan's Note on prob- 

 abilities of occui-rence. 



t Odling, it). 4 XIII, 423, 480, June and July, 1857 ; Report British Association, 



1858. 

 41 Dumas, Phil. Mag. 4 XVI, 209, Sept. 1858 ; Sill. JOUI'. 2 XXVII, 253, 1859. 

 S Mercer, Report British Assoc. 1858. 

 If Odling, Watts' Diet. Art. Atomic Weights, and Metals. 



