234 



SCIENCE. 



[N. S. Vol. VIII. No. 191. 



leaves oflf and where physics begins. The 

 old controversy between the advocates of 

 the continuity and those of the discontin- 

 uity of matter is not dead, but only sleeps. 



It must be admitted that the conception 

 of the atom, as at present received, is not 

 without serious objections, and probably 

 many accept it as presenting fewer diffi- 

 culties than the theory of continuity. I 

 venture to suggest that the idea of a ma- 

 terial- limit, like that of space or quantity in 

 mathematics, avoids at least some difficul- 

 ties, so that we may define an atom as a 

 limit to which we approach as we subdivide 

 a given mass of any element, having refer- 

 ence to properties alone. Or, taking a 

 somewhat different mathematical concep- 

 tion, we may consider atoms as material 

 differentials of which the general integrals 

 which we term masses are made up, and in 

 this way we may connect purely material 

 with purely mathematical conceptions. The 

 conception of a limit or of a differential 

 avoids all hypotheses as regards form as 

 well as regards magnitude, and retains only 

 ideas of mass and kind. Conversely, I doubt 

 whether, for the purpose of instruction in the 

 calculus, any purely mathematical concep- 

 tion of limits or of differentials and inte- 

 grals gives as clear an idea of these as does 

 the comparison with physical or chemical 

 atoms and their aggregates. 



As all chemists know, we owe to Dalton 

 the first clear conception of the chemical 

 atom as distinguished from the atoms of 

 Leucippus and Democritus ; to Frankland 

 the conception of valence which shows us 

 what combinations of atoms can exist con- 

 sistently with the number of units of affinity 

 possessed by each individual atom, or, in 

 other words, in what manner groups of 

 atoms can form systems which are in stable 

 equilibrium. This conception includes that 

 of the chemistry of space, now so much em- 

 ployed in organic chemistry, as well as that 

 of the motions of atoms within the molecule, 



as yet almost without supporters. To the 

 conception of a defiuite number of units of 

 affinity recent chemistry has added that of 

 direction of action, statical according to 

 one school of chemists, dynamical according 

 to another. 



Within a comparatively short time atten- 

 tion has been directed to a large class of 

 compounds exhibiting very interesting prop- 

 erties and forming peculiar series, some of 

 which, at least, are made up of homologous 

 terms. This group has been called complex- 

 inorganic, because many of its members 

 form highly complex molecules of which no 

 analogues are known. 



I may here remark that Ostwald uses the 

 term ' complex ' to denote only those mole- 

 cules or groups of associated atoms which 

 are unitary and do not belong to the class 

 of double 'salts. I have not drawn this dis- 

 tinction in the present paper, because it is 

 not that which was originally proposed, and 

 because at present we are not able to sepa- 

 rate the two classes from each other, except 

 in a very limited number of cases. 



No one class of compounds appears so 

 well adapted to throw light upon the struc- 

 ture and modes of combination of mole- 

 cules. For this reason I have selected the 

 group as the subject of my address to- 

 day. 



In endeavoring to establish a plausible 

 theory of the constitution of the complex- 

 inorganic acids and their salts it will be ad- 

 vantageous to state first succinctly the prin- 

 cipal facts to be explained. These, I think, 

 are as follows : 



1. The teroxides of molybdenum and 

 tungsten possess, in a remarkable degree, 

 what may be termed a ' cumulative' charac- 

 ter, each being capable of forming series of 

 salts which contain a very large relative 

 number of molecules of the teroxide. In 

 this respect they stand alone, so far at least 

 as our present knowledge extends. Certain 

 other oxides share in this peculiarity to a 



