Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

362 PROF. LAMB, AN ELECTROMAGNETIC ILLUSTRATION OF THE THEORY
Hence if, = 1-0003, we have p = 2 x 10-4. This determines the product Va3, for
a gas such as oxygen or nitrogen under ordinary atmospheric conditions, but not N or a
separately. If in accordance with current mechanical estimates we take iV= 2 x 19,
we find a= 13 x 10-8 cm. Hence if X = 6 x 10-5 cm., we find
ka = 1'4 x 10-3,
so that, if ha = 7r, we must have
K = h2/kt2=5 x 106.
In a dense medium composed of the same molecules the formula (98) is replaced by
', -......................................... (99),
where the accents refer to the altered circumstances. Comparing, we have
~'-l2-1 2 p'
' = + 2 -1 (~ - 1)..................................(100).
PY~+ 2:3
The fact that the refractive indices of various substances in the liquid and in the
gaseous state have been found to accord fairly well with this formula shews that the
observed moderate values of K'(== -,2) for dense media, taken in the bulk, are not
incompatible with an enormous value of K for the individual molecules.
The formula (86) for the dissipation-ratio in the case of exact synchronism is
independent of any special numerical estimates. It can moreover be arrived at on
widely different hypotheses as to the nature of a molecule and of the surrounding
medium. Its unqualified application to an assenmblage of molecules arranged at ordinary
intervals may be doubtful, since with dissipation of such magnitude it may be necessary
to take account of repeated reflections between the molecules. It is clear however that
a gaseous medium of the constitution here imagined would be absolutely impenetrable
to radiations of the critical wave-length.
As regards the falling off of the absorption in the neighbourhood of the maximum,
the formula (95) in the case 2 = 1 would (on the numerical data given above) make
the absorption sink to one-half of the maximum when the wave-length varies only
by -00,000,000,028 of its value. The formula (89) would give a still more rapid
declension. The range of absorption in -a gaseous assemblage must however be far wider
than these results would indicate. So far as it is legitimate to assume that the
molecules act independently, the law of enfeeblerrment of light traversing such a medium is
E = E e-NI.........).................................( )
* This is Lorentz' result. Lord Rayleigh's investigations shew that it will hold approximately even if p' be
not a very small fraction.
1t Lord Rayleigh, i. c.