NAT ORE 
49 
THURSDAY, MAY 15, 1902. 
THE REPRINT OF STOKES’ PAPERS. 
Mathematical and Physical Papers, vol. iii. By Sir 
G. G. Stokes. Pp. viiit+451. (Cambridge University 
Press, 1901.) Price 15s. 
HE issue of the first volume of this work in the year 
1880 was the beginning of the valuable series of 
reprints of mathematical and physical papers for which 
we are indebted to the Cambridge Press. It was felt at 
the time that no more auspicious beginning could have 
been made, and the publication was widely appreciated ; 
but a gradual and increasing sense of disappointment 
supervened when, after the second volume, the continua- 
tion seemed to be suspended indefinitely. A third 
instalment has however now appeared, after the lapse of 
eighteen years, and although the regrets we have referred 
to cannot be altogether appeased, the contents of the 
volume will assure it of as hearty a welcome as was 
accorded to its predecessors. 
There is little to be said now by way of comment on 
papers which have, most of them, long ranked as classics. 
The volume opens with the memoir on pendulums. The 
first, or theoretical, part of this contains the germ of 
almost all that has since been written mathematically on 
the subject of viscosity. In addition to the main topic, 
viz. the effect of viscosity of the air on the linear vibra- 
tions of a sphere or of a circular cylinder, we find the 
theory of the oscillating disc employed in Coulomb’s 
experimental method (afterwards greatly improved by 
Maxwell), the calculation of the terminal velocity of a 
globule of water descending in air, and the general 
formula for the dissipation of energy in a viscous fluid, 
with (as an example) a discussion of the effect of viscosity 
on water waves. To appreciate fully the originality of 
this paper we must bear in mind that up to that time the 
subject had hardly advanced beyond the formulation of 
general equations ; moreover, that a good deal of the 
analysis here applied to special problems was new, and 
devised expressly for the occasion ; in particular, in the 
question of the oscillating cylinder an extremely difficult 
point in the theory of what are now known as Bessel’s 
Functions was resolved with great success and for the first 
time. The second part of the paper consists of a com- 
parison of the mathematical theory with Baily’s experi- 
ments on pendulums, and includes the first numerical 
estimate of the coefficient of viscosity (u) for air. The 
yalue thus obtained, although of the right order of 
magnitude, is considerably less than that now generally 
accepted ; and, indeed, for the experimental determina- 
tion of this constant the pendulum method would seem 
to be not specially appropriate. One source of uncertainty 
in the present determination is that » was assumed, on 
the strength of an experiment of Sabine, to be pro- 
portional to the density, whereas Maxwell has since 
shown that for the same gas p varies only. with the 
temperature. The author tells us that one reason for 
the long delay in the appearance of this volume has been 
a design of revising the calculations froin the point of 
view of Maxwell’s result. This design is now abandoned, 
but an interesting note is inserted, explaining how it 
comes about that the erroneous assumption had so little 
NO. 1698, VOL. 66] 
effect on the covsisfency of the results. Another note, 
which also now appears for the first time, deals with the 
question as to the existence of /wo constants of viscosity 
for a gas. The usual formal theory, which makes no 
appeal to molecular hypothesis, leads to stress-formule of 
the types 
du dv dw du 
em eM (Caen +2 , &e., 
Ras p (Z bay! z) be dx 
dw dav .¢ 
i > XC. 
fy: u( agin 4) Sri? 
involving the two constants A, #. The former of these is 
eliminated if we denote by / the #eam normal pressure 
about the point (*, y, 2), viz. we then have A= —§ p ; but 
the question remains whether the # thus defined is 
identical with the “pressure” referred to in the state- 
ment of the Boyle-Mariottelaw. The identity is assumed 
by most writers on the subject, and is supported by 
Maxwell’s molecular theory ; but it cannot be said that 
there is as yet any decisive experimental evidence on the 
point. There is a real physical question involved, viz. as to 
whether a wzdform: expansion or contraction of a gaseous 
mass does or does not involve dissipation of energy by 
viscosity. : 
The calculations of this memoir are, of course, based 
on the usual assumption that the terms of the second 
order in the velocities may be neglected. It has only 
lately been realised, thanks to a remark of Lord Ray- 
leigh, to what an extremely narrow range of velocities we 
are sometimes confined by this limitation. 
The next paper in the book discusses the effect of 
radiation of heat on the propagation of sound. It is 
shown that very slow and very rapid vibrations will alike 
be propagated without sensible thermal dissipation, the 
former with the “Newtonian” and the latter with the 
“Laplacian ” velocity, whilst for intermediate frequencies 
there would be a real degradation. The investigation is 
reproduced, and extended to include thermal conduction, 
in Lord Rayleigh’s ‘‘ Theory of Sound.” 
The memoir on the most general form of the equations 
of conduction of heat in crystals is remarkable historically, 
and also on account of the attention paid to the possible 
occurrence of the “rotatory” coefficients. These are 
finally dismissed as improbable, but their analogues have 
in recent times been appealed to to explain certain pheno- 
mena of electric conduction under magnetic influence. 
The remaining papers deal with optical questions. 
Those on the colours of thick plates and on the com- 
position and resolution of independent streams of 
polarised light are important applications of established 
principles of physical optics ; but the most notable in 
some respects is the great memoir on Fluorescence, with 
which the volume closes. This masterly analysis of the 
nature of the phenomenon was more fortunate than some 
of the author’s previous work in the attention which it 
immediately attracted, not only at home, but abroad.! A 
1 Prof. Stokes’ work on ‘‘ Attractions and Hydrodynamics" was long 
neglected on the continent. I recall a sally of Maxwell's in one of his 
early lectures at Cambridge. Incidentally he remarked (with, I think, 
some investigation of. Stokes in his mind), “ But foreign men of science 
don't read the Cambridge Transactions "; then, guessing from the smiles 
of some of the audience that his words might be taken ambiguously, he 
added very emphatically, ‘It would be a good thing if they did!” One 
particular instance of erroneous ascription has a curious vitality. In a 
book dated 1900 we read, *‘ Die Bewegung der Kugel in einer Fliissigkeit 
ist zuerst von Dirichlet behandelt,” and in another dated last year, ‘* Dies 
ist der von Dirichlet zuerst durchgefiihrte Fall.” Yet both works are written 
by highly accomplished authors, with a sense of mathematical history. 
D 
