300 REPORTS ON THE STATE OF SCIENCE, ETC. 



Our freshly synthesised molecule, therefore, will be able to absorb or radiate 

 its own molecular quantum and also the quanta characteristic of its two 

 atoms. It will, on examination by absorption spectra methods, exhibit its mole- 

 cular frequency together with the two atomic frequencies. Again, in making 

 the first assumption that an elementary atom is characterised by a quantum of 

 energy associated with the shift of an electron from one orbit to another, there 

 is no need to restrict the atom to the possession of only one such electron. There 

 may be several electrons of the same type, and as two or more of these niay 

 simultaneously undergo change of orbit, the atom will be capable of absorbing 

 1, 2, 3, etc. of its characteristic quanta at one time, and therefore will exhibit 

 the corresponding frequencies. Our freshly synthesised molecule therefore will, 

 on examination, be found to exhibit the molecular frequency of 3.0137x10'= 

 and the atomic frequencies of ?iX 1.674x10" and ?! X 1.37x10", where 



1 792u 

 R = l, 2, 3, etc. These correspond to the wave-lengths of 99.7 ju, , and 



_ ^ . This sets an upper limit to the two series of atomic frequencies, for, 'as 



n 

 will be seen, they converge at the 18th and 22nd terms respectively in the 

 molecular frequency. 



It follows from the foregoing that the energy lost in the combination of 

 atoms depends on the size of their atomic quanta, and that these quanta have 

 a very important significance. It may be noted in passing that the actual 

 amount of energy evolved in the formation of the freshly synthesised molecule 

 from the two atoms is small, and for one gram-molecule amounts to 

 1.98xl0-'''x6.23xl0=V4.17xl0', where 6.23x10=' is the Avogadro constant and 

 4.17x10' is the mechanical equivalent of heat. The total energy, therefore, 

 evolved in the formation of the freshly synthesised molecule when expressed as 

 calories per gram-molecule is 296. 



Although in the first assumption it was stated that an elementary atom 

 is characterised by one energy quantum, there is no reason against an atom 

 being characterised by two or more quanta of different sizes. It is probable 

 that in some atoms there are two or more electrons, each of which requires 

 a different amount of energy to shift it from one orbit to another. In view of 

 the quantitative basis now given to the combination of atoms, it is very 

 reasonable to suggest that the valency of an atom is the measure of the number 

 of different atomic quanta associated with that atom. The natural corollary 

 follows that the position of an element in the series of electropositivity is 

 determined by the size of its largest atomic quantum. 



The simplest case of tlie combination of two monovalent atoms was considered 

 above, and it is now possible to deal with the next simplest case — namely, the 

 synthesis of a molecule AB2 from three atoms. Let the bivalent atom A be 

 characterised by two quanta. 11x10-'* erg and 9x10-'* erg, and let the atom B 

 be characterised by the quantum 7x10-'* erg. The first stage in the combina- 

 tion will be the formation of the molecule AB, with the establishment of the 

 atomic group quantum of 2x11x7x10-'* erg or 1.54x10-'* erg. The second 

 stage will be the formation of the molecule AB2 with the formation of the 

 second atomic group quantum of 2x9x7x10-'* erg or 1.26x10-''' erg. Both 

 of these two atomic group quanta \vill be characteristic of the complete mole- 

 cule, which can only gain or lose energy as a whole in terms of the true 

 molecular quantum. ■ This molecular quantum will naturally be twice the least 

 common integral multiple of the two atomic group quanta^ — that is to say, 

 2x1.386x10" or 2.772x10" erg. This molecular quantum is four times the 

 least common integral multiple of the three atomic quanta. This molecule differs 

 from the simplest case of a binary molecule formed from two monovalent atoms 

 in that it is characterised by two atomic group quanta as well as by the atomic 

 quanta and the molecular quantum, and will be endowed with the corresponding 

 frequencies. For the same reason as was given above for atomic frequencies 

 there will also be series of atomic group frequencies, and therefore the total 

 number of frequencies exhibited by this molecule will be as follows : three 

 series of atomic frequencies, nx 1.674x 10", nxl. 37x10", and 71X1.0655x10". 

 where n = \, 2, 3, etc.; two series of atomic group frequencies, n x2.3'i4x 10'= 

 and 71x1.918x10'=; one true molecular frequency, 4.22x10". The first and 



