August 19, 1886] 
reader shall be above reproach, so that if he further 
pursues the subject treated of, he may, at least, not be 
hindered or misled by erroneous definitions or ideas 
placed before him at the outset. 
The work before us, when it has been subjected to a 
slight revision, will fairly satisfy the conditions of an 
elementary text-book which is at once strictly scientific 
in its ideas and rich in practical applications. 
Indeed, the practical portion of the work is, as was to 
be expected, very good. The portions dealing with 
mechanism are well suited to illustrate the scientific 
principles, and will be found very useful. 
We shall confine ourselves to pointing out some of the 
blemishes which disfigure the theoretical portion. 
P. 1. “ When the tendency which force exerts to move 
a body is counteracted, so that the body remains at rest, 
the force is commonly called a pressure.” It may be 
safely said that no such limited use is ordinarily made of 
the term pressure. 
P. 2. The statement that two lumps of sugar placed in 
contact on a table do not adhere, because “the attraction 
emanates from their centres, which may be an inch 
apart,” is not altogether conducive to sound notions. 
In p. 19 we have the usual definition of the measure of 
a variable velocity, viz. “the space which would be de- 
scribed in a unit of time if the body retained throughout 
that unit the velocity which it has at the instant con- 
sidered.” When will people find out that this definition 
really defines nothing? It is truly Gladstonian in its 
elusiveness. Of course we find exactly the same 
“definition” of variable angular velocity (p. 62), variable 
acceleration (p. 99), and variable pressure (p. 176). 
In p. 26 we havea most confusing exposition of New- 
ton’s Second Law. What, for instance, is the beginner to 
understand by this >—‘‘ Since we are dealing with a body 
in motion, itis clear that we may consider (1) the weight 
of the body to be constant, and its velocity to vary; (2) 
the weight of the body to vary, and its velocity to remain 
constant.” The discussion of this law seems to show 
that its object is entirely misconceived by the author. 
For, while the law aims at giving a complete measure of 
Sorce, the author merely deduces from zt (by reasoning in a 
circle) a definition of momentum, his discussion ending 
with the words, “Hence, quantity of motion = (mass) 
(velocity).” 
Again, in p. 28,.“the explosive force of powder in a 
gun is actzom, and the momentum generated in the pro- 
jectile is veactzov.” This is plainly open to the objection 
of equating force to momentum—a most mischievous 
notion. 
In p. 48 the full meaning of the centre of parallel forces 
is by no means brought out, and the rule for finding its 
distance from a given line is incorrect: “ Multiply each 
force into its perpendicular distance from a given line,” 
&c. The rule ought to be enunciated with reference toa 
plane, and not to a ézze, and instead of the unmeaning 
term “distance of a force from the plane” we should say 
‘distance of its point of application from the plane.” 
It is surely incorrect to say, as in p. 61, that “it is the 
universal practice to appropriate the Greek letter o 
(omega) for expressing the unit of angular velocity.” 
It is very important to distinguish, in the mind of the 
beginner, between force and fower. In p. 72 power is 
| remember that the 
NATURE 359 
Jo 
correctly defined as [time-] rate of doing work; but the 
language immediately following loosens this idea. Thus, 
“the number 33,000 foot-pounds is the zsz¢ of horse- 
power.” There is tautology in the expression “ Watt 
estimated that the sustained work of a horse continued 
for one minute would raise 33 000 lbs. through one foot in 
one minute.” Again, the term fower is used in p. 94 to 
designate a force applied to a machine. 
In p. 73 the principle of work as applied to equilibrium 
is thus enunciated: “If a system of bodies be at rest 
under the action of any forces, and be moved a very little, 
no work will be done.” It may well be doubted whether 
this enunciation is explicit enough to give a useful idea 
of the great statical principle. Indeed, the cases selected 
for illustration bear out in no way the proviso that the 
bodies must “ be moved a very little.” 
Passing on to p. 98, we find acceleration of velocity 
discussed, and we have the formal definition: “the unit 
of acceleration adds a velocity of 1 foot in 1 second,” 
which, as the words stand, has absolutely no meaning. 
The beginner ought to be taught that acceleration has a 
double reference to time, and it should never for a moment 
be spoken of otherwise than as “feet per second per 
second,” or “miles per hour per minute,” or by some 
other equivalent phrase. In p. 102, g is spoken of as 
32°2 feet per second. 
Finally, in p. 113 the beginner is introduced to the 
discussion of a compound pendulum formed by a straight 
uniform bar. Its time of oscillation depends on a radius 
of gyration. What idea is our beginner likely to have of 
this? The definition of £, the radius of gyration of the 
bar 4B about an axis through its centre of gravity, G 
(p. 114), is quite erroneous—“ let £® be the sum of the 
squares of the distances of each particle of A from the 
point G.” This sum is, of course, infinite. What is 
meant by £? is the zea square of distance from G. But 
clearly such a question is wholly unsuited to beginners. 
The book concludes with a large collection of examples, 
taken from the Science Examinations, which will be 
useful to students. GEORGE M. MINCHIN 
OUR BOOK SHELF 
Mémoire sur les Volumes moléculaires des Liguides, avec 
un Avant-propos. By Hermann Kopp. Pp. 47.« 
(Heidelberg : C. Winter, 1886.) 
THIs is a dvochure one-third of which is devoted to an 
“avant-propos” explaining why the paper does not appear 
in the Annales de Chimie e¢ Physique, and making certain 
statements relating to M. Berthelot’s recent work, “ Les 
Origines de lAlchimie.” The remaining part contains a 
discussion of a paper on molecular volumes of liquids 
which appeared in the Azales. In 1869 Prof. Kopp 
published, in succession to his “ Geschichte der Chemie,” 
a volume of “ Beitrage” to the history, explaining more 
fully the principal epochs in chemical history, more espe- 
cially in relation to alchemy. In 1885 M. Berthelot pub- 
lished his work, which had occupied more or less of his 
attention since 1869. Its general character is very similar 
to the “ Beitrage,” though much less complete, and Kopp 
complains that no reference whatever is made to his book. 
Berthelot, in reply, states that he was unaware of the 
existence of the “ Beitrage,” yet he quotes references to 
works in which this “cahier” (as he calls it) is repeatedly 
mentioned. The oversight is a very grave one, when we 
“cahier” is a contribution of over 
