4 
elaborate analysis is utterly wrong; and yet there 1s 
every ground for believing that even when steam is some- 
what superheated when leaving the boiler, even well- 
jacketed cylinders are never free from moisture. I am 
sorry to say that the Hirn analysis is often employed for 
cylinders with no jackets when the steam supplied is 
known to be quite moist. As an academic exercise, no 
one would object to the method of study if students were 
informed of its uselessness in most practical cases, but, 
unfortunately, this information is never given in treatises 
which advocate the method. 
If there is no leakage past the piston, we are sure that, 
from the beginning of the expansion to the release, we 
are dealing with the volume and pressure of a quantity 
of stuff which does not alter in amount. This is only a 
portion of an indicator diagram ; and, as I have already 
pointed out, our usual study of it is based upon an un- 
warrantable assumption. But what are we to say of men 
like Prof. Boulvin, who pile upon this Pelion, Ossas of 
further assumption for the sake of making pretty academic 
problems, and then publish the solutions of these problems 
as if they were of practical importance ? 
Of course we may, if we please, say that when steam 
is released to the condenser, we can imagine the whole 
change as occurring in the cylinder itself ; only we ought 
to remember that we are substituting a very simple 
hypothetical process fora very complicated reality, which 
has almost nothing in common with it. We ought to 
remember that the very pretty, beautifully complete, 
cyclic ¢p diagrams, which we obtain from childish as- 
sumptions, may get to be looked upon by students, and 
even by ourselves, as having a real meaning. 
The engineering teacher is much too apt to fill up the 
time of students with an elaborate and systematic course 
of instruction on a subject in which only a few lessons 
are essential, and, indeed, in which only a few lessons 
ought to be admissible. In some German schools we 
have systematic courses on graphical statics lasting 
whole terms or years. Courses on practical geometry 
are never supposed to be of use unless the student draws 
every imaginable kind of curve, draws every imaginable 
kind of intersection of surfaces. When some man who 
really thinks for himself has, after endless opposition and 
worry, convinced teachers that a certain kind of exercise 
is of value, his converts make his modest proposals 
into an elaborate academic system. There is no 
imaginable problem which does not become part of an 
elaborate course of exercise work. A student becomes 
wonderfully learned, but he loses the power to think 
things out for himself. Macfarlane Gray’s method of 
study may be made part of a student’s mental machinery 
in a few lessons, and in these few lessons it enables an 
elementary student to do easily what Hirn did with so 
much trouble ; but, in truth, its great value lies rather 
in its enabling students to work out for themselves the 
well-known results of Rankine and Clausius. They see 
at a glance that liquefaction accompanies adiabatic ex- 
pansion. They very quickly find the Z,v law of adiabatic 
expansion of steam of any wetness. They can calculate 
easily the work that would be done by a perfect steam 
engine using the Rankine cycle,:and many other im- 
portant things which the average student used to take 
on trust. Not only does the ¢p diagram enable one to 
NO. 1540, VOL. 60] 
NATURE 
_ [May 4, 1899 
| see at a glance the reasonableness of much that used to 
be very obscure, but it clears the ideas of men who still 
prefer to work algebraically. 
It is quite usual now in classes for students to prepare 
for themselves ¢p sheets on which not only are the ¢#p 
lines for a pound of water and a pound of steam laid 
down, but also lines of constant f and constant v and con- 
stant E for wet, and also for superheated steam ; and with 
these sheets many interesting problems may be worked. 
The ¢p sheets for a perfect gas, with lines of constant 
p, v and E, are even more valuable than such sheets for 
steam when one desires to convert an indicator diagram 
of a gas or oil engine into a ¢} diagram. But, indeed, 
the ¢p diagram is nothing like so valuable in gas engine 
work as in steam engine work, for rate of heat reception 
is quite easily obtainable from the /,v curve of a per- 
fect gas. When we also remember that all idea of time 
is absent from a ¢p curve, it will be seen that. practical 
gas engine people are not likely to make much use of it. 
Prof. Boulvin introduces his subject by a chapter on 
the laws of thermodynamics. He begins with—“ The 
study of the changes produced in bodies by heat is 
based upon certain /umdamental laws as the laws of 
Mariotte (or Boyle) and of Gay-Lussac (or Charles).” 
He defines absolute temperature as what is shown by an 
air thermometer, the zero of which is 273° C. below the 
ordinary zero. If adequate explanation were given, there 
might be no objection to these and other statements ; 
but I am inclined to think that the ordinary reader will 
find such an introduction misleading. I think that some 
difficulty would be cleared up if the author proved the 
truth of the fundamental equations for perfect gases, in- 
stead of merely assuming their truth; it would lead to 
a much simpler treatment of the next two chapters, 
Parenthetically, I would observe that he is quite mis- 
taken in thinking that a s#a// error in measuring clear- 
ance in a gas engine cylinder will lead to very wrong 
values of £ in the expansion curve, #v* constant. 
It would be interesting to know what the author means 
when, after speaking of Regnault’s value 0°48 for the 
specific heat of steam, he says, “and this is about the 
same value as it would have if treated as a permanent 
gas, and its density calculated from its molecular weight.” 
I think that there is almost no point of view from which 
this statement must not be regarded as absurd. 
On the whole, the author may be said to have given 
an account of the subject which it is worth while for a 
beginner to study, should he not be able to lay his hands 
on the several better accounts which have already been 
published in England. It is a pity that the translator 
did not think it worth while to alter Prof. Boulvin’s 
illustrations, for these have compelled him to use letters 
which will give trouble to the English student. Ran- 
kine’s letter # is universally used in England and America 
for entropy ; here we have S used instead. I am wrong 
in assuming that the use of the foreign illustrations com- 
pelled the translator to employ these letters ; for I see 
that he follows Prof. Boulvin in using 7 for latent heat, 
d for Regnault’s total heat ; and, of course, he uses A for 
Joule’s equivalent. In a book intended for English 
engineers, I think that either C.G.S. units or English 
engineers’ units ought to be used. In this translation 
we find the hybrid units of French engineers. 
