NATORE 
THURSDAY, MAY 14, 1885 
SIR WILLIAM THOMSON’S “MATHEMATICAL 
AND PHYSICAL PAPERS” 
Mathematical and Physical Papers. By Sir William 
Thomson. Vols. I. and II. (Cambridge University 
Press. 1882, 1884.) 
VERY one interested in the study of physics of the 
more profound kind will welcome this collection of 
essays by the celebrated natural philosopher, so many of 
which, hitherto scattered throughout various periodicals, 
difficult to gather together, or even wholly inaccessible to 
readers out of the reach of large public libraries, are yet 
of decisive importance for those chapters of the science 
to which they refer. With the two volumes now before 
us, in conjunction with the late publication, “ Reprint of 
Papers on Electrostatics and Magnetism,” the collection 
is now completed down to the date of February, 1856. 
Vol. II. contains, besides, all that the author has written 
on the Transatlantic Telegraphs, which, according 
to the strict order of time, might have been looked 
for in later volumes. The first volume begins with 
a series of essays, for the most part of a mathe- 
matical nature, ranging from the year 1841 to 1850. 
So far as these essays relate to physical problems, their 
chief interest turns on the difficulties connected with the 
analytic method. These difficulties were, however, even 
at that early period, treated by the youthful author with 
great skill, and under comprehensive points of view. 
The problems are, in part, geometrical and mechanical, 
referring to lines of curvature, systems of orthogonal 
surfaces, principal axes of a rigid body, &c. Most of 
them, however, deal with the integration of the differen- 
tial equations, on which is based the doctrine of thermal 
conductivity and potential functions. The latter, asis well 
known, form the mathematical foundation of a large num- 
ber of chapters in physics—the doctrine of gravitation, 
of electrostatical distribution, of magnetic induction, of 
stationary currents of heat, of electricity and of ponder- 
able fluids. By treating all these problems collaterally 
and rendering concretely in some what in others appears 
in the highest degree abstract, the author has succeeded 
in overcoming the greatest difficulties, and we can only 
recommend every student of mathematical physics to 
follow his example. A field particularly favourable for 
the exercise of his powers was opened up to Sir W. 
Thomson by the phenomena, newly discovered by Fara- 
day, in diamagnetic and weakly magnetic bodies, crystall- 
ine as well as uncrystalline. These our author rapidly 
and easily succeeded in arranging under comprehensive 
points of view. One great merit in the scientific method 
of Sir William Thomson consists in the fact that, follow- 
ing the example set by Faraday, he avoids as far as 
possible hypotheses on unknown subjects, and by his 
mathematical treatment of problems endeavours to ex- 
press the law simply of observable processes. By this 
circumscription of his field the analogy between the dif- 
ferent processes of nature is brought out much more> 
distinctly than would be the case were it complicated by 
29) 
| From the year 1848 and onwards there follows a long 
series of important investigations into the fundamental 
problems of thermo-dynamics. These start first with 
Saadi Carnot’s conclusions respecting the mechanical 
functions of heat arrived at before J. P. Joule had ex- 
perimentally demonstrated the equivalence of heat and 
mechanical energy. At the time when Carnot published 
his investigations heat was, by the majority of physical 
scientists, deemed an imponderable substance capable of 
flowing from one body to another, of entering occasionally 
into a more intimate kind of union with ponderable matter, 
and becoming, so to say, chemically united with it, under 
changes in the state of aggregation and under chemical 
processes. According to this older view temperature 
signified as much as the pressure under which the im- 
ponderable fluid stood in the warm bodies. In the case 
of a great number of thermal processes heat, in point 
of fact, acts entirely like a substance, showing the con- 
stancy of quantity, which is the most characteristic 
criterion of substances. In this way large sections of 
the doctrine of heat, embracing great bodies of facts, 
could very well be treated under the substantial concep- 
tion of this agent—such, for example, as the exchange of 
heat between different bodies, the confinement and libera- 
tion of latent heat, the chemical production of heat. Al] 
that was necessary to render the substantial conception 
of heat apparently satisfactory was but to leave out of 
account all cases in which other forms of work are pro- 
duced by heat or in which heat is produced by such. Cases 
of this kind then known were indeed very few, whereas the 
sections of the doctrine of heat already referred to were 
exactly those which till towards the middle of this century 
engaged the attention of natural philosophers. Carnot’s 
highly acute investigation was an attempt to bring the phe- 
nomena likewise of the performance of work by means of 
heat into harmony with the assumption of the substantial 
theory of heat. The result of this endeavour was remark- 
able enough, He showed, namely, that heat was capable 
of performing mechanical work only when a quantity of it 
passed from a body of higher temperature into another 
body of lower temperature. A complete analogy thus 
seemed to be established between heat and those gases 
which through their pressure are capable of performing 
work, expanding, as they do, and abating their pressure in 
a measure corresponding with their expansion. The heat 
of a warm body corresponds n a manner with a com- 
pressed gas; it diffuses itself in space, passing into neigh- 
bouring bodies, to the lowering of the temperature of the 
body in which it was originally compacted. 
Carnot’s deductions, although based essentially on the 
erroneous assumption that the quantity of heat was 
constant like that of a substance, proved in reality correct 
so far as they respected transitions of heat within very 
narrow limits of temperatu... They cease, however, to 
be strictly accurate when they are extended to wider 
intervals of temperature, for in that case finite parts o 
the transferred heat become transformed into work and 
no longer continue as heat. We now know through the 
experiments of Joule that heat does not possess the abso- 
lute constancy of a substance, but only the relative con- 
| stancy of an equivalent of work which, to be sure, can 
widely-diverging ideas respecting the unknown interior | 
mechanism of the phenomena. 
VOL. XXXII.—No. 815 
neither be produced from nothing nor come to nothing 
| but is yet capable of being transferred into other forms of 
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