AgCl. The average wave-length of the residual radiation* was found to be 81.5 μ (v=3-68 × 1012). (N1+N2)v=11 × 21-5 × 1012.

The value of

was

PbCl. The average wave-length in this case* 91.0μ (v=3·30 × 1012), giving (N1 +2N2)v = 18 × 21.2 × 1012. When such large integers are involved, it is always possible to find an integer which will give a concordant value for v

HgCl. The average wave-length observed was 98.8μ (v=3·04 × 1012). Taking N1=80, N2=17, we find

(N1+N1)v=14x 21.0 × 1012.

AgBr. For this salt* =1127μ (v=2·66 × 1012), and (N1+ N2)v=103 × 20‍8 × 1012.

CaCO3. The case of cale spart is interesting as it contains three elements, whilst only two bands have been recorded, a strong band at 93.0μ (v3-23 × 1012) and a weaker at 116.1μ (v=258 x 1012). It is found that the strong band must be assigned to calcium, giving Nv=3× 21.5 × 1012, the weaker to oxygen, giving Nv = 1 × 20·7 × 1012.

In a later paper Rubens and Wartenberg‡ have given the wave-lengths for two ammonium salts and three compounds of thallium.

NH Cl. The observed wave-lengths are very nearly the same as those for NaCl, being 54.0μ (v=5.56×1012) and 46 3μ (v=6·48 x 1012) respectively. This is what might be expected if the group NH be regarded as a compound radicle replacing Na, for the "molecular number" of ammonium (7+4) is the same as the atomic number of sodium (11). Taking the first line as associated with the NH group, Nv=3 × 20·4 × 1012, whilst the second line gives for the chlorine atom Nv=5 × 22·0 × 1012.

NH Br. Here again two wave-lengths have been observed, 62.3μ (v=4·82 × 1012) and 55·3μ (v=5·42 × 1012). The former line must be associated with bromine, giving Nv=8×21.1× 1012; the latter with the ammonium group, yielding Nv 3 x 200 × 1012.

TICI. The mean wave-length recorded is 91.6μ (v=3·27 x1012). The atomic number of thallium being 81 and that of chlorine 17, we find Nv=15 × 21·4 × 1012.

TIBr. For the bromide the mean wave-length is 117·0μ (v=2.56 x 1012). In this case we find Nv 14 x 21.2 x 1012. TII. For the iodide the mean wave-length is 151-8μ (v=1·98 × 1012), giving for Nv the value 13 × 20·4 × 1012.

Rubens, Preuss. Akad. Berlin, vol. xxviii. p. 513 (1913).

† Rubens, D. P. G. V. vol. xiii. p. 102 (1911).

Rubens and Wartenberg, Preuss. Akad. Berlin, p. 169 (1914).

Thus for the halogen derivatives of thallium the interesting result is found that the "frequency numbers" (15, 14, 13) diminish by unity in passing from chloride to bromide and from bromide to iodide.

It must be stated that the suggestion which attributes the two absorption bands of NaCl, KCl, KBr to separate atoms is not a new one*. Nernst is of opinion that it was a mere coincidence" a very curious and misleading one indeed "that calculations of the specific heat on that supposition gave quite good results. Rubens was unable to find two bands in the case of AgCl and PbCl2, and came to the conclusion that the two apparent bands were due simply to water vapour, which has a great number of absorption bands. If this conclusion be accepted the results quoted above will require modification in the sense that the "molecular number " must be employed instead of the atomic number; but the proposed relation will still hold good. Thus for NaCl we find Nv 8 × 20·6 × 1012, for KCI Nv=8×20·1×1012, and for KBr Nv=9×21.6 × 1012.

It would appear probable that the relation here discussed applies only in the case of the longer residual rays, having a wave-length greater than say 20μ. For shorter wave

lengths, corresponding to a higher frequency, the value of the product, Nv, is so large that ho real test of the proposed relation can be obtained. It is unfortunate for our present purpose that although the residual rays from quartz in the region of 9 and 13μ have been measured with considerable accuracy, the longer waves have not as yet been determined accurately; we know only that quartz shows strong selective absorption for the region between 60 and 80μ.

It may be worthy of mention that water vapour has an absorption band at 143 μ, which is the wave-length corresponding to a frequency 210 × 1012 sec.-1, that is the frequency here denoted by v. Further, the vapour of carbon dioxide has an absorption band at 14-1μ. It would be of interest to know whether other substances show absorption in the same region.

The possibility of deducing the wave-length of the infra-red radiation from the elastic properties of the solid has been discussed by Madelung and by Sutherland. By considering a cubical space-lattice the former obtained for the wave-length the expression

Cf. Nernst, The Theory of the Solid State,' p. 80 (1914).

where M1, M2 are the masses of the atoms, K is the compressibility, and D the density. This may be compared with Einstein's formula. Rubens and Wartenberg have shown that this formula gives results in moderately good agreement with their observations.

They have also obtained fair agreement by employing modified form of the equation of Lindemann, viz.

MM, V
M1+M2 T

where V is the molecular volume and T, the meltingpoint.

In both formule the constant must be determined empirically.

The results of this and preceding papers support the following conclusions:

(1) The forces binding the atoms in the molecule are similar in character to those which bind the molecules of the solid, that is the forces of chemical affinity are of the same nature as the forces of molecular cohesion*.

(2) There must be something of a discrete character in the nature of these forces, in order to account for the occurrence of integral values of n. The simplest hypothesis is to assume that the forces arise from the presence of valency electrons. As it is probable that these forces act only in definite directions, it is a plausible suggestion that the linkages between the atoms are constituted by Faraday tubes of force, which would then be regarded as physical entities. The fundamental frequencies, v, and VE, would depend on the properties of the unit tube of force. It has been pointed out by Prof. Nicholson† that such a view seems to be required in order to explain the relations between the frequencies of spectral series. Attention may also be drawn to an important article by Sir J. J. Thomson on the Forces between Atoms and Chemical Affinity, in which chemical valency is discussed from the same standpoint.

Compare Nernst, 'The Theory of the Solid State,' pp. 4-9 (1914); Langmuir, Ann. Chem. Soc. Journ. vol. xxxviii. p. 2221 (1916). + Nicholson, Phil. Mag. vol. xxvii. p. 541, vol. xxviii. p. 90 (1914). ↑ J. J. Thomson, Phil. Mag. vol. xxvii. p. 757 (1914).

XLVII. On Wood's Criticism of Wien's Distribution Law. By HAROLD JEFFREYS, M..1., D.Sc.*

IN

N the February number of the Philosophical Magazine, pp. 190-203, Mr. F. E. Wood offers a criticism of Wien's law of the distribution of energy in the spectrum of a radiating gas. If λ denote the wave-length and the absolute temperature, Wien's law is that the energy of the part of the radiation with wave-lengths between λ and λ+ dλ is

Wood shows from the same

where C and k are constants. assumptions as Wien that the omission of a factor by Wien in his first equation led to an error in the final result and that the correct formula based on these hypotheses is

With reference to this law it must be noted that the total radiation is obtained by integrating pdλ from zero to infinity, and as this must by Stefan's law be proportional to 1, it can easily be shown that Ck in Wood's equation is not a constant, but is proportional to 0-1. As Wood's argument is involved and in places somewhat obscure †, I offer an alternative proof which is shorter and appears to be equally satisfactory subject to substantially the same assumptions. If N be the total number of molecules in a mass of gas, the number whose absolute velocities lie between v and v + dv is

where is a velocity whose square is proportional to the temperature. Then Wien's first assumption is that the wave-length and intensity of the radiation emitted by a molecule depends on alone. If e be the rate of emission

*Communicated by the Author.

†The argument at the foot of p. 197 and the top of the next page implies that the number of molecules with velocities between v and v+dv is kv20 ̃3 ̧ ̄lv2 dv2 instead of kv20 − 2 e 2.0 dv.

- lv2

The introduction of an ideal type of gas on p. 198, with the notion of corresponding velocities, is unnecessary; so is the use of the meaningless law 10=constant, which requires such careful interpretation that it is more difficult to apply than the second and third hypotheses of the present paper, expressed in equations (5) and (14), which are equivalent

to it.

of energy by a molecule of velocity, that emitted by all the molecules whose velocities lie between v and v+dv is (2)

dR=4(x, 0)dλ=4Nπ ̄3x ̄3⁄4v2€ e ̄v21⁄4a2 dv,

where e is a function of v only.

Now the total radiation for all wave-lengths together is obtained by integrating this from v=0 to v∞, and must by Stefan's law be proportional to 04, and therefore to a. We have thus an integral equation for e. Assume that e(v) can be expanded in powers of v for all values of v, so that

and that the series av+2-2/a2

term.

anv"

0

(3)

e can be integrated term by

Then R can be expressed as a power series in a, thus:

By hypothesis R is equal to Ncas, where c is an absolute constant, and therefore all the a's are zero except ag.

Hence

Thus the distribution of energy with regard to the molecular velocities is completely found from the first assumption alone, and all that is now required is to determine the relation of the velocity to the wave-length.

At this stage a further assumption is needed; and this will be that the graph of 4 against λ for any temperature can be derived from that for any other temperature by homogeneous strain in two dimensions. In other words, if the temperature be changed from 0 to 20, or, what is the same thing, if a be replaced by ka, two numbers a and b will exist, so that

for all values of λ, where a and b are functions of k alone. Now it is evident from (4), by putting 2=f(x), that (, ) is of the form

(6)

where F and fare at present unknown, but are connected by a differential relation.