NOVEMBER 17, 1899. ] 
as a correct and a fruitful method of discussion 
of thermodynamic problems and phenomena. 
A number of books and papers in elaboration 
of this system have recently appeared, and of 
these we take up several for review together. 
The titles of papers in the list given in the foot- 
note* are added as containing the earliest and 
most important applications of this method of 
study of the efficiencies of the heat-engines, and 
the latest addition to the algebraic discussion 
of the abstract theory of entropy-diagrams. 
The little book issued by Professor Reeve 
contains one of the clearest and most complete 
explanations of the temperature-entropy dia- 
gram that we have met with. The purpose of 
the publication is the presentation of a new di- 
agram in which the author has introduced some 
modifications of the form proposed by Boulvin 
and, as it is thought, thus made the work of 
preparation for entropy-temperature analyses 
much less troublesome than formerly ; obvi- 
ating the necessity of detailed computations 
for each analysis. With this diagram at hand, 
it is thought that ‘‘the entropy method, once 
understood, will be found to reveal with sur- 
prising speed and facility factors in steam- 
engine economy hitherto only to be estimated, 
at best, and that only at the expenditure of 
tedious labor.’’ This paper was originally pub- 
lished in the interests of the engineers; but it 
cannot fail to have equal interest and value for 
those engaged in the study of mathematical 
physics and abstract thermodynamics. The 
diagram is well made, its explanation is ad- 
mirably satisfactory, and the text is printed 
with equal excellence. The diagram consists 
of a sheet divided into four quadrants, of which 
one is devoted to quantities involving pressure- 
temperature determinations, the second to those 
* Belpaire, Th., ‘Bulletin de l’Academie royale de 
Belgique,’ 1872. Gibbs, J. Willard, ‘Trans. Conn. 
Academy of Arts and Sciences,’ 1873. Linde, C., ‘The 
Refrigerating Machine of To day’; Trans. (Munich, 
1875), A.S. M. E, 1893. Gray, Macfarlane, ‘ Trans. 
Inst. Naval Archts.,’ 1889 ; Inst. C. E., 1889; Inst. 
Mech. Eng’rs., 1889. Willans, P. W., ‘Steam-En- 
gine Trials’; Minutes Proc. Inst. C. E., 1888-1893. 
Sankey, H. R., Proc. Inst. M. E., 1891; Proce. Inst. 
C. E., 1895-6. Durand, W. F., Jour. Am. Soc. Naval 
Engineers, May, 1898, Sibley Journal, 1898. 
_ SCIENCE. 
129 
related to entropy-temperature problems; the 
third gives entropy-volume quantities, and the 
fourth pressure-volume measurements. On 
these four sections of the sheet are laid down 
with care and accuracy the corresponding curves 
for water and steam, unity-weight in each case, 
and printed upon the sheet are also the heads 
for entries of all necessary data from observa- 
tion at an engine trial, in the reduction of 
which this method is to be employed. The 
method of use of the system and of the diagram 
in its applications to heat-engines is very fully 
and lucidly described and illustrated. 
The chart and its text will, unquestionably, 
be found to be very useful and helpful to every 
engineer seeking to enrich his work by the re- 
sults of this system of exploration of the ther- 
modynamic and the thermal and the dynamic 
phenomena of heat-engine performance. 
Mr. Golding’s ‘Theta-Phi Diagram’ and 
its illustrations of practical application of the 
Gibbs system of treatment of thermodynamic 
problems also find place in the work of 
the engineer employed in the investigation 
of the performance of engines, whether the 
working fluids be steam, gas, oil- 
vapor. The author employs geometrical rather 
than algebraic methods, where choice is al- 
lowed; illustrating the fact which will prob- 
ably be observed by all familiar with the mat- 
ter, that the designer and constructor, the me- 
chanic in whom the art is inborn, is almost in- 
variably a geometrician rather than an alge- 
braist. The utility of the method presented is 
considered beyond doubt, and, as Mr. Robinson 
remarked in discussing a paper by Mr. Willans, 
whose disciple, Mr. Golding, evidently is, ‘‘ Up 
to a certain point, the practical man might 
ignore the present paper and others like it; but 
if he aspires to design economical engines, he 
might derive more good from the study of, say, 
Mr. Macfarlane Gray’s ‘Theta-Phi Diagram’ 
than from many portfolios of working draw- 
ings.’’ In fact, the study of current practice, 
in working drawings, simply reveals the rela- 
tive forms and proportions of well- and ill-de- 
signed engines and throws little light upon the 
causes and remedies of faults of construction or 
defects of practice. The author acknowledges 
indebtedness to the earlier writers, Boulvin, 
air or 
