ee 
May 4, 1899] 
NATURE 
> 
o 
The movement observed was in disaccord with the pre- 
diction of theory. In fact the major axis of Hyperion’s 
orbit, instead of moving, directly, round Saturn in a 
century, accomplished a revolution in the opposite direc- 
tion in the short period of eighteen years. 
Newcomb has proved that this rapid retrograde revo- 
ution is caused by the perturbing action of the next 
satellite Titan. 
- In the various volumes of “ The Astronomical Papers 
for the use of the American Nautical Almanac,” New- 
<omb has published a great number of memoirs. One 
<an follow step by step ‘the immense progress achieved 
in the execution of the vast project which he had taken 
upon himself to accomplish. 
It is difficult:to convey an idea of the considerable 
efforts, the sagacity which must be displayed, the 
numerous investigations which must be accomplished, 
in order to make known to a sufficient degree of approxi- 
mation the motion during a century of a body of our 
planetary system. Only those scientific men who have 
given themselves up to analogous studies can appreciate 
the enormous expenditure of physical and intellectual 
energy which must have been necessary to Newcomb in 
order to bring to a happy end the researches on the four 
planets nearest the sun. Newcomb has based his work 
on more than 60,000 observations, which he has com- 
pared with Le Verrier’s tables ; the perturbations have 
been calculated with great precision. While Newcomb 
has thus founded ‘theories of these planets on a more 
precise basis, his celebrated collaborator, Mr. Hill, has 
obtained the same results for the two planets Jupiter and 
Saturn. 
Henceforth, science will profit by the fruits of this 
immense labour, consisting of the tables of the planets 
Mercury, Venus, Mars and the Earth. In a special 
volume there are to be found various researches on the 
fundamental constants of astronomy. 
We have only been able to give a short sketch of 
Newcomb’s achievements; he is gifted with a pro- 
digious power of work, which is testified by the extra- 
ordinarily long list of his researches. 
' The reception which has been accorded to them by all 
€ompetent men points to their author as one of the most 
illustrious representatives of celestial mechanics. 
This activity has embraced the most diverse branches 
of astronomy. Not only has he given a great scope to 
the intellectual movement of his country, but he has also 
<ontributed in a very successful manner to elevate the 
level of the civilisation of our age, enriching the domain 
of science with beautiful and durable conquests. 
Lorwy. 
THE TEMPERATURE-ENTROPY DIAGRAM. 
The Entropy Diagram and its Applications. By J. 
Boulvin, Professor at the University of Gand, Belgium. 
Translated by Bryan Donkin. Pp. xii + 70. (London : 
E. and F. N. Spon, Ltd., 1898.) 
ANKINE’S “Thermodynamic Function ¢@” (defined 
by 4d = dH) is now called “ Entropy ¢.” The 
state of a pound of stuff which has only fluid stress and 
strain is completely defined when we know the values of 
any two of J, v,¢, E or ¢ [during change of state the two 
NO. 1540, VOL. 60] 
must not be merely # and /] where E is the intrinsic 
energy and @ is theentropy. When we say that E returns 
to its old value if we bring the stuff to the same state 
again, we state the first law of thermodynamics in its 
most general form. When we say that @ returns to its 
old value, we state the second law of thermodynamics in 
its most general form. 
A curve connecting the values of any two of the above 
coordinates will, therefore, completely define the chang- 
ing state of a pound of stuff. Rankine does not seem to 
have used the ¢7,f coordinates graphically, but he used 
them very much indeed in the algebraic form ; and the 
idea that a 4,@ diagram might be constructed was pub- 
lished by several mathematicians more than a quarter of 
a century ago. In truth, the idea was familiar to all 
students of Rankine, but until Mr. Macfarlane Gray 
began his crusade in favour of the use of the 4,p diagram 
in practical steam engine calculation, no other person 
had any idea of the changes that its use would effect. 
When a pound of water-stuff alters in pressure and 
volume in any assigned way, at what rate does it receive 
or give out heat? This is the problem that we used to, 
solve in the most laborious way ; and so troublesome was 
it that I question if anybody, not a lecturer, ever worked 
out more than one example completely. The problem 
was never put before any but the most advanced 
students. 
Now, thanks to Macfarlane Gray, this sort of problem 
is not only taken up and solved by the average student 
in the most elementary classes, but it is of all problems 
the one whose solution is most easily understood ; and it 
is through such work that we now most easily introduce 
the average student to the laws of thermodynamics and 
the properties of steam and water. For twelve years it 
has been one of the commonest of class problems to take 
an indicator (or f,v) diagram, and assuming a certain 
wetness of the steam at the beginning of the expansion, to 
convert it into a ¢p diagram. 
Prof. Boulvin has not added to our knowledge of theory 
or the practical application of the ¢p diagram, but in his 
well-known “Cours de Mécanique appliquée aux 
Machines,” in 1893, he made the method known to 
continental students, and exhibited the conversion of pv 
to ¢p coordinates in a fourfold diagram; whereas in 
England such a conversion has always been on one 
diagram. Our method has possibly been such that the 
result is confusing to all but the man who carries it out ; 
but this is the fault of all graphical methods of working 
problems. It has the merit of utilising the whole of a 
sheet of paper instead of one quarter of a sheet. The 
English method may be recommended to a student who 
wants an accurate answer. Prof. Boulvin’s method may 
be recommended to a lecturer who wishes merely to 
illustvate the connection between the 7,v and the 7p 
diagrams. 
The solution of the problem is really very misleading, 
for, invariably, the assumption is made that there is no 
moisture in the cylinder at the end of the exhaust. This 
assumption is the basis of the method used by Hirn and 
his numerous followers in that kind of study of the steam 
engine which is usually supposed to be complete. It 
does not seem to be understood that if there is any 
moisture in the cylinder at the end of the exhaust, Hirn’s 
