TRANSACTIONS OF THE SECTIONS. 43. 
lay in the combination, A great step in this direction seems to me to have been 
ately made by Prof. Cooke, of the Harvard University of the United States (in a 
memoir which forms part of the fifth volume of the Memoirs of the American Aca- 
demy of Arts and Sciences), to extend and carry out the classification of chemical 
elements into families of the kind I allude to, in a system of grouping, in which the 
first idea, or rather the first germ of the idea, may be traced to a remark made by M. 
Dumas, in one of his reports to this Association, and which is founded on the prin- 
ciple of arranging them in a series, in each of which the atomic weight of the ele- 
ments it comprises are found among the terms of an arithmetical progression, the 
common difference of which in the several series are three, four, five, six, eight, and 
nine times the atomic weight of hydrogen respectively. So arranged, they form six 
groups, which are fairly entitled to be considered natural families, each group having 
common properties in the highest degree characteristic; and what is more remark- 
able, the initial member in each group possessing in every case the characteristic pro- 
perty of the group in its most eminent degree, while the others exhibit that property 
in a less and less degree, according to their rank in the progression, or according to 
the increased numerical value of the atomic equivalent. Generally speaking, | am a 
little slow to give full credence to numerical generalizations of this sort, because we 
are apt to find their authors either taking some liberties with the numbers themselves, 
or demanding a wider margin of error in the application of their principles, than the 
precision of the experimental data renders it possible to accord; so that the result is 
more or less wanting in that close appliance to nature which makes all the difference 
between a loose analogy and a physical law; but in this instance it certainly does 
appear that the groups so arising not only do correspond remarkably well in their 
theoretical numbers with those which the best authorities assign to their elements, 
but that it really would be difficult to distinguish the elements themselves into more 
distinctly characteristic classes by a consideration of their qualities alone, without 
reference to their atomic numbers. 
When we find, for instance, that the principle affords us such family groups as 
oxygen, fluorine, chlorine, bromine, and iodine self-arranged in that very order; or 
again, nitrogen, phosphorus, arsenic, antimony, and bismuth,-—-when we find that it 
packs together in one group all the more active and soluble electro-positive elements, 
hydrogen, lithium, sodium, and potassium, and in another the more inert and less 
soluble ones, calcium, strontium, barium, and lead, and that without outraging any 
other system of relations,—it certainly does seem that we have here something very 
like a valid generalization; and [ shall be very glad to learn in the course of any dis- 
cussions which may arise on such matters as may be brought before us in the regular 
conduct of our business from those more competent to judge than myself, whether I 
have been forming an overweening estimate of the value and importance of such 
generalizations. I will only add on this point, in reference to what fell from our 
excellent President in his address to the assembled Association last night, that 
this kind of speculation followed out, would seem to me likely to terminate in a point 
very far from that which would regard all the members of each of these family groups 
as allotropes of one fundamental one, inasmuch as the common difference of the 
several progressions which their atomic weights go to make up, are neither equal to, 
nor in all eases commensurate with the first terms of these progressions. For instance, 
in the chlorine group, the first term being eight, the common difference is nine, 
Something very different from allotropism is surely suggested by such a relation. It 
would rather seem to point to a dilution of energy of one primary element by the 
superaddition of dose after dose of some other modifying element; and this the more 
Beetely, since we find oxygen standing at the head of very distinct groups having 
very striking correspondences in some respects, and very striking differences in others. 
_ But all these speculations take for granted a principle, with which I must confess I 
think chemists have allowed themselves to be far too easily satisfied, viz. that all the 
atomic numbers are multiples of that of hydrogen. Not until these numbers are de- 
termined with a precision approaching that of the elements of the planetary orbits,—a 
precision which can leave no possible question of a tenth or a hundredth of a per cent., 
and in the presence of which such errors as are at present regarded as tolerable in the 
_ atomic numbers of even the best determined elements shall be considered utterly in- 
admissible,—I think, can this question be settled; and when such gigantic conse- 
