28 
DYNAMICS: OLD AND NEW. 
(1) Lecons sur la Dynamique des Systémes 
matériels. By Prof. E. Delassus. Pp. xii+ 421. 
(Paris: A. Hermann et Fils, 1913.) Price 14 
francs. 
(2) The Theory of Relativity. By Prof. R. D. 
Carmichael. Pp. 74. (New York: John Wiley 
and Sons, Inc.; London: Chapman and Hall, 
Ltd:, 1913.) Price 4s. 6d. net. 
(1) “HIS volume is the result of an experi- 
x ' ment made by the author to improve 
on the usual methods of introducing students to 
the study of dynamics. The first respect in which 
this has been essayed is in presenting the subject 
from the beginning in a general form, instead of 
beginning with those problems which are geo- 
metrically most simple. Thus the volume has 
rather the appearance of a treatise on what is 
usually known as analytical dynamics. But the 
object which the author has in view is not so much 
the development of the advanced analytical theory, 
which becomes largely a study of differential equa- 
tions, as a unification of method which shall ob- 
viate the feeding of the student on a multiplicity 
of isolated problems in which the dynamical pro- 
perties are essentially of the same type. 
Special attention is paid to the class of systems 
the equations of motion of which can be integrated 
by quadratures. An elaborate study is made of two 
special questions in respect of which the author 
considers wrong notions to be prevalent. The first 
of these is the assumption usually made in respect 
of a unilateral constraint, such as that which occurs 
when a body rolls or slides on another body, that 
the constraint will cease to be conformed to at 
the moment when the force required to maintain 
it vanishes and changes sign; examples are given 
in which the assumption that this is true where 
there is more than one point of contact between 
two bodies leads to wrong conclusions. 
The other point which is called in question is 
the assumption, which the author considers to be 
often tacitly made, that if the constraint imposed 
On a system is realised by means of auxiliary 
bodies of negligible mass, these auxiliary bodies 
have no influence on the motion of the system. 
An example given is that of a heavy particle con- 
strained to move in a horizontal plane by attach- 
ment to an axis bearing two weightless wheels 
which roll and slide respectively on a fixed hori- 
zontal plane. It is clear that if the wheels and 
axis have ever so little inertia and are set in motion 
with a rotation about the vertical, the particle 
cannot describe a straight line, but the example 
points to such an obvious objection to the assump- 
NO."23 05, VOL. 93| 
NATURE 
[Marco 12, 1914 
tion referred to that it is dithcult to believe that 
as a general rule it has really been commonly 
asserted. 
(2) After reading this careful course on classical 
dynamics, it is an abrupt transition to the first 
book published in English on the principle of 
relativity, and to read of a revision of the funda- 
mental concepts, not only of space and time, but 
also of mass. Prof. Carmichael sets out to 
give a popular account of the way in which these 
magnitudes are regarded by the exponents of this 
most up-to-date of generalisations, without going 
into the details of its origin in electrical theory. 
The project is well carried through, but it seems 
doubtful whether even yet the public mind is 
prepared to face the shock of the postulate (p. 20) : 
“The velocity of light in free space, measured on 
an unaccelerated system of reference S, is inde- 
pendent of the velocity of S.”’ But less objection 
seems to be taken to one of the consequences of 
the assumption of the complete relativity of all 
physical phenomena, namely, the dependence of 
the mass of a body upon its velocity, in spite of 
its reducing the status of Newtonian mechanics to 
that of an approximate theory. 
The reason for this is probably that experiment 
seems to have demonstrated without doubt that 
the mass of the electron must be admitted to be 
variable, and we can find no reason for denying 
the possibility of the mass of any body varying 
within the limits of error admitted by astronomical 
theory. 
The real obstacle to the acceptance of the theory 
of relativity is the carrving over of a conception 
| of space and time, which is based on, or rather 
part of, Newton’s dynamical theory into regions 
where that theory is certainly no longer tenable 
in its entirety. Prof. Carmichael’s book deals 
entirely with these fundamental matters and will 
help to make more familiar a more logical and 
less metaphysical view of space and time in their 
physical bearing. 
NEW ZEALAND: THEN AND NOW. 
(1) Camp Fire Yarns of the Lost Legion. By 
Col. G. Hamilton-Browne. Pp. xiii+3or. 
(London: T. Werner Laurie, n.d.) Price 
$25) OA. Met: 
(2) Social Welfare in New Zealand. 
Lusk. Pp. viii+287. (London: 
Heinemann, 1913.) Price 6s. net. 
By Hugh H. 
William 
HESE two hooks present a most vivid pic- 
ture of the progress which has occurred 
in New Zealand during the last fifty years. The 
