JuNE 1, 1899] 
MATORE 
99 
with this view, and yet to attach very high importance to 
the investigations now in evidence. They are concerned 
mainly with the processes of differentiation and inte- 
gration as applied to quaternions, and especially with the 
properties of Hamilton’s operator 
3h vd ray 3 
ax dy 
a branch of the subject which (as is well known) has 
exercised a great fascination on many distinguished 
cultivators of mathematical physics, from Maxwell down- 
wards. That Prof. Tait’s papers remain the primary, 
and indeed almost the sole, authority on such matters, is 
ample warrant for the present republication. For the 
rest, a few items gathered from the titles, such as 
Fresnel’s Wave-Surface, the Theory of Electrodynamics, 
the Theory of Strain, the Dynamics of Rotation, Green’s 
Theorem, Isothermal Surfaces, and Minding’s Theorem, 
will indicate the variety and importance of the subjects 
which Prof. Tait has sought to bring within the range of 
this ambitious calculus. 
Passing from this group, we have to notice an elabo- 
rate investigation on “ Knots,” suggested originally by 
Thomson’s theory of vortex-atoms. It deals with a 
branch of the Geometry of Position which few mathe- 
maticians (and those only of the ablest) have ventured 
to touch; and although the presentation disclaims any 
finality, there can be no doubt that Prof. Tait’s investi- 
gations must be accounted a solid and valuable, as they 
are an interesting contribution to the subject. 
It would be ungrateful to pass over a number of minor 
papers which are specially characteristic of Prof. Tait in 
respect of the symmetry and elegance of the mathematical 
treatment, or of the manner in which new light is thrown 
on well-worn topics. Of these the papers on Hamilton’s 
Characteristic Function, and on the Hodograph, may be 
cited as specimens. In this latter we find the now well- 
known representation of a small oscillation in a resisting 
medium as the projection of motion in an equiangular 
spiral, as well as several other results or modes of proof 
which have long become common property. It is 
pleasant to be reminded of their real source. 
A very attractive topic is treated alike with originality 
and elegance in the paper on “ Mirage.” 
There remain the experimental papers. Of these it may 
be sufficient to here say that those on Thermo-Electricity 
have long ranked as classics ; and that the paper on the 
pressure-errors of the Challenger thermometers is an 
interesting record of a laborious investigation undertaken 
to decide a very important practical question. 
Some readers may perhaps be disappointed to find 
that one side of Prof. Tait’s activity is not represented in 
these pages. He has in his time been engaged in many 
keen controversies, in which he has displayed the quali- 
ties of a “first-class fighting man.” One cannot but feel, 
therefore, great admiration for the restraint he has shown 
in omitting all traces of such incidents from the present 
record of his work. There is, in fact, only one paper 
which one would willingly have spared, and that for quite 
other reasons. ‘The lecture on “ Force,” with its insist- 
ence on what after all are verbal questions, is surely out 
of place in the present collection. The readers who are 
capable of following the /ecinzguwe of quaternions, or the 
NO. 1544, VOL. 60] 
intricacies of amphicheiral knots, do not need to be lec- 
tured on the looseness of newspaper language ; whilst 
the grave discussion as to whether force or energy has 
the greater title to rank as a “thing ” will hardly excite in 
them any other feeling than the amusement which (one 
suspects) may have been the real object of the whole 
discourse. 
The printing and general appearance of the volume 
are beyond praise. One might, indeed, protest that the 
format is a little foo luxurious. Many persons hold to 
the view that the octavo form adopted in the cases of 
Stokes and Thomson is far more handy and convenient 
for real work than the more imposing quarto. In the 
case of Cayley, the larger form was perhaps required by 
the nature of the subject-matter, with its long algebraical 
formulze ; but there is little in the present collection which 
could not witha little ingenuity have been accommodated 
in the smaller page. But such criticisms are, after all, 
somewhat ungracious. We conclude by thanking the 
University and Prof. Tait for this very acceptable volume, 
which we trust to see speedily followed by a second. 
And we venture to suggest to the University Press that 
an additional and welcome element of interest would be 
imparted to these reprints if they could be adorned with 
portraits of the authors, even when these are happily 
still amongst us. HORACE LAMB. 
OUR BOOK SHELF. 
Elementary Physiology. By Benjamin Moore, M.A. 
With 125 Illustrations. Pp. vi + 295. (London: 
Longmans, Green, and Co., 1899.) 
THIs book contrasts favourably with most others of its 
class. A simall treatise of three hundred pages on 
elementary physiology can scarcely avoid being super- 
ficial, and, from the students’ point of view, inadequate ; 
but to these inevitable shortcomings there are too often 
added, in books of the kind, the quite gratuitous defects 
of inaccuracy in statement and failure to keep up with 
the advance of knowledge. From faults of the latter 
description the work before us is practically free, and it 
may be commended with confidence to the junior student, 
who, as the author says, “‘is often plunged into a mass of 
detail, and gets so involved in this, that he loses sight of 
the main outstanding features of the subject.” Most 
teachers of physiology have probably had experience 
among their pupils of the mental condition here referred 
to. Lucid and concise in statement, Mr. Moore’s book 
manages to convey a large amount of accurate inform- 
ation in very smallcompass. It bearsample evidence of 
being no mere literary compilation, but the production of 
a genuine worker in physiology, whose mode of treat- 
ment is often striking and original. As might be ex- 
pected from the author, the book is especially strong in 
such matters as digestion, absorption and metabolism. 
The volume is in most respects so meritorious that it 
seems ungracious to call attention to its blemishes. 
These are, as arule, not serious. It would be unfair to 
find fault with a book of this kind for being dogmatic ; 
it is plainly not a fitting place for the discussion of con- 
troverted questions. The statement, however, on p. 14, 
with respect to the relations of cartilage and bone is dis- 
tinctly misleading. But with few exceptions the points 
that call for criticism concern the form of the book 
rather than its matter. Thus, the author is occasionally 
guilty of an awkwardness or inelegance of language that 
might easily have been avoided, and we cannot say that 
we approve of such colloquialisms as “harking back 
again to our simple type,”or “that bigger supply of 
