Sept. 6, 1888] 



NA TURE 



459 



assumed that the axes of the molecules in the crystal are all 

 parallel. 



Thomson arrived at a different result, which the author attri- 

 butes to his having assumed the product of the denominators 



c x + c 2 - mJT 2 and c x l + c 2 - „] to be sensibly a constant, 



and therefore considered only the manner in which T enters into 

 the numerators. 



It is easy to see that similar results will be obtained for 

 molecules consisting of any number of shells. 



§ 7. Spectra of Chemical Compounds. 



In considering chemical compounds it is necessary to make a 

 clear distinction between atoms and molecules, and henceforward 

 the author uses the term atom to denote a system of shells such 

 as is described in § I, and employs the term molecule only for a 

 combination of two or more atoms having their external shells 

 close together. The author restricts his investigations to di- 

 atomic molecules. 



A molecule will then be capable of executing stationary vibra- 

 tions without disturbing the ether, similar to those of an atom, 

 and will therefore also have its critical periods ; but their values, 

 in the case of the molecule, will depend on the direction of the 

 disturbance. A diatomic molecule may be considered approxi- 

 mately as consisting of a series of concentric prolate spheroidal 

 shells having their longer axes coincident with the lines joining 

 the centres of the spheres. 



There will be two principal series of critical periods, corre- 

 sponding respectively to disturbances propagated in the direction 

 of the longest axis or of any of the shortest axes. If the direc- 

 tion of propagation of a disturbance differs slightly from one of 

 these axes, the corresponding lines of the spectrum will only be 

 slightly displaced, and in this way well-defined bright lines will 

 be replaced by bright bands sharply defined on one side and 

 indistinctly on the other. If two of these bands overlap on 

 their indistinct sides, a band may be produced of equai 

 brightness throughout, and having both its sides sharply 

 defined. 



This gives an explanation "of the well-known experimental 

 fact that the spectra of chemical compounds usually consist of 

 bright fluted bands, sometimes accompanied by distinct bright 

 lines, and riot of bright lines only. Conversely, if the spectrum 

 of a gas contains bright bands, it will be natural to infer that it 

 is a chemical compound. This would lead us to suppose that 

 oxygen, sulphur, nitrogen, phosphorus, carbon, and silicon are 

 really compound bodies — a conclusion which receives independent 

 confirmation from other points of view. 



The theory does not lead to any simple law, such as has often 

 been sought after, for determining the spectrum of a compound 

 from the spectra of its constituents, but it throws a good deal of 

 light on the subject generally. 



The differential equations to determine the motions of the 

 shells within an atom differ from equations (1) only in virtue of 

 the core itself being supposed to be in motion, so that the last of 

 these equations will become — 



4tt- dt- 



= Cj (xj _ 1 - Xy) - cj + 1 {Xj - xj + 1) 



(23) 



the difference consisting only in the presence of xj + i, which was 

 supposed equal to zero in equations (1). 



If we discard the assumption that the mass of the core is so 

 great relatively to that of the shells in an atom that the centre of 

 gravity of the system may be identified with that of the core, the 

 condition x, -4 \ = o will be replaced by the more general one — 



m i x 1 + m^c % + . . . + my +ix/+.i = 6 . . . (24) 



which determines the value of d-xj + ^dt-, which is wanting in 

 the system (23). 



From (2), (3), an! (23) we obtain the system — 



— r il = a ^ x \ + c -2 X -2 



™~ C.-y-X-y — il„~\ .) "J" t*l*V'} 



.(25) 



where, as before, a t - — m t /T 2 - a - c,- + i. 



These, together with (24), form a set of/ + I linear equations, 

 which are sufficient to determine the 7+1 unknown quantities 

 x v x. 2 , . . . Xj 4 1 in terms of the given quantities | and T 2 . 



Replacing £, m, x, c, j by 77, n, y, e, k respectively, we obtain 

 a similar set of equations to determine the vibrations of the 

 second atom. If the outer shells of these two atoms are in 

 contact, x l must be equal to y lt unless the disturbance is such 

 as to effect a separation, xt and y, being corresponding displace- 

 ments from the common centre of gravity. Writing x for the 

 common displacement of the shells in contact, equations (25) 

 assume the form — 



- c Y ri = b^x + e»y« 



- e. 2 x = b,y. 2 + e&t 



- e^y, -1 = b K y K + e m +\y t 



The condition that the common centre of gravity of the two 

 atoms may remain at rest will therefore be — 



(«! + n^)x + m 2 x 2 + m 3 x 3 + . . . + mj 4 1 xj 4 1 



+ ' i -j.y-i + • • . +«,+ij,+i =0. . . . (27) 



(25), (26), and (27) form a system of j + k + I equations to 

 determine the same number of unknowns, x, x. 2 , . . . Xj± u 

 r]. 2 . , . 77*41, in terms of the known quantities {, 77, and 'P. 

 £ is determined as before by equation (2), and gives the vibration of 

 the ether at the point where the ray impinges on the first atom. 

 The axis of a molecule may be at any angle with the impinging 

 ray, and 77 will give the ether vibration at the point where a ray 

 parallel to the first strikes the second atom. For a given period 

 and wave-length, £ and 77 will therefore in general be in different 

 phases. 



In the case of vibrations parallel to the axis of the molecule 

 we shall have £ = 77, supposing all the parallel rays impinging 

 on the molecule to be in the same phase. The ratio „r/£, re- 

 quired for the determination of n" will then be the quotient of 

 the second and first minors (viz. the coefficients of zi x ahd tc) of 

 the determinant of order j + k + 2 given below, in which the 

 first row is completed by arbitrary quantities. 



This will always be the case applicable to the determination of 

 the light emitted by a molecule. 



The equation | = o, which determines the critical periods of 

 the molecule, will then be obtained by equating the coefficient 

 of u to zero, and as a* and hi are linear functions of T- 2 , the 

 resulting equation will be of the order j + k. Therefore, for 

 vibrations parallel to the axis, the number of critical periods of 

 a diatomic molecule is equal to the sum of the numbers of 

 critical periods of its constituent atoms. This number may be 

 diminished if x = o while xj£ and u 2 remain finite. 



If a single ray only is considered, as at the limits of illumina- 

 tion, 77 may be taken equal to zero for any given value of | ; it 

 is only necessary to put e x = o in the first column of the deter- 

 minant. This will, however, not affect the equation £ = o. 



If the impinging ray is parallel to the axis of the molecule, 

 in which case the vibrations will be perpendicular to it, the two 

 atoms will be differently affected by the vibrations of the ether, 

 for, in the case of the first atom, | is again determined by (2), 

 or more generally by the equation — 



£ = «cos(- t -_J 



where X is the abxissa of the atom ; and if r and S are the radii 

 of the two atoms we shall have for the second atom — 



it = a cos ( 



V T 



X + r + s 

 A 



) 



Now the r.tdii of the atoms are supposed to be very small 



