- 
had Pcs this text to supply a course 
that will equip the student for work in calculus 
and engineering, without burdening him with a 
mass of detail useful only to the student of mathe- 
matics for its own sake. The result is a very 
attractive little book. The author has picked out 
the easy and fruitful bits of his subject without 
concerning himself greatly whether the topics 
chosen are conventionally elementary or advanced. 
He gives us a book very different from the stock 
“analytical conics,” for the conic falls into its 
place among other curves, and is not studied under 
a microscope. For example, we have nothing 
about the equation of the tangent to a conic; 
presumably the author would take tangents after 
dy/dx. On the other hand, we have sections on 
periodic functions, empirical equations, parametric 
representation, co-ordinates in space, surfaces. 
The book is one that might very well be used 
with a class of intelligent non-specialists in their 
last two years at an English public school, at a 
stage when the function of mathematics is to 
broaden their outlook. It would serve equally 
well as an introductory course for a specialist. 
' The book is full of pleasing practical touches— 
e.g. “But on other problems, notably in work with 
alternating currents, an interpretation can be 
given to the process of extracting the square root 
of a negative number, and then such results are 
entirely real.” 
(2) Most English text-books on the calculus are 
fairly well provided with exercises, but anyone 
who wants more will find a good collection here. 
The sets on maxima and minima are especially 
practical. Students of foreign fashions in nota- 
tion will note the absence of sin-1; arc sin is used 
instead. The hyperbolic functions have not found 
admission, which seems a pity. The sets of exer- 
cises are prefaced by brief directions and plain 
warnings; the directions however are, from an 
educational point of view, too much in the way 
of rules—e.g. “To find d?y/dx® (when x and y 
are given as functions of t) use the somewhat 
cumbersome formula 
Bs. (22 dy dy ef) (ey. 
dx? \dt° dt? * dt? }/\ dt]? 
etc.” (p. 29). On p. 81 the precise meaning of 
“in general” is not clear in the sentence: “ Ex- 
pansion into series is, in general, useful in calcu- 
lations only when the series is convergent.” 
(3) This book contains many more tables than 
are commonly used in British class-rooms—e.¢. 
cubes and cube roots, tables of x}, n®, xt, 3, 7, 
areas and circumferences of circles, volumes of 
spheres, circular segments, chords, etc., together 
with five pages of weights and measures (from 
which it appears that the American yard differs 
from the British yard, being defined as 3600/3937 
metres). On the other hand, there is no full table 
of secs and cosecs. Sine and cosine share a 
table, as do tan and cot. The “arguments ” are 
given to three significant figures, or for every 
ten minutes in the trigonometrical tables. There 
are no difference columns, and to obtain a fourth 
NO. 2449, VOL. 98] 
NATURE 
89 
significant figure, or the intermediate degrees, it 
is necessary to interpolate. Some of the functions 
are given to four significant figures, some to five; 
the principle underlying the choice of four or five 
is not mentioned. The author has broken with 
the curious tradition (the origin of which we should 
like to know) that ten should be added to the log 
of a circular function. 
For British schools this book will probably be 
considered to contain too much in one way and 
too little in another (e.g. difference columns). The 
type is too small for young eyes. 
(4) This book contains chapters on household 
accounts, commercial arithmetic, business letters, 
soils, manures, crops, live-stock, foodstuffs, dairy- 
ing, mensuration, levelling, brickwork and build- 
ing construction, water supply, work and power, 
measurement in the field. The explanations of 
arithmetical processes are undistinguished and 
sometimes old-fashioned (e.g. inverting the multi- 
plier in contracted multiplication). But we 
imagine that this is not the part of the book in 
which the author is most interested. The descrip- 
tion of all practical matters concerning farms and 
farmers is well written, and the numerous examples 
have a most realistic and practical appearance. 
How much more interesting it must be to find 
the volume of a “mangel pie” than of a mere 
prism ! C.\G: 
OUR BOOKSHELF. 
Aids to Bacteriology. By C. G. Moor and William 
Partridge. Third edition. Pp. viii+278. 
(London: Bailli¢re, Tindall and Cox, 1916.) 
Price 3s. 6d. net. 
Tuts well-known little book, now in its third edi- 
tion, contains an extraordinary amount of informa- 
tion within a small compass, though necessarily in 
a condensed form; in fact, the whole range of 
subjects included under the term ‘‘ Bacteriology ”’ 
is covered by it. Migula’s classification of the Bac- 
teria now replaces that of Heuppe, and as regards 
bacterial mutability, the authors remark that this 
is largely of academic interest, and that in practice 
species tend to crop up fairly true to type. , Anti- 
bodies, apparatus, culture media and methods of 
examination are surveyed, and all the principal 
pathogenic bacteria and protozoa are described, 
In addition, the moulds, yeasts, fermentation, 
and enzymes are dealt with as well as the bacterio- 
logy of water, milk and other foods, air, soil and 
sewage, and disinfection and disinfectants; little 
seems to have been missed and few errors occur. 
It is a pity that B. perfringens as a synonym for 
B. Welchii is not mentioned, for it is so commonly 
used now. Agricultural bacteriology has two or 
three pages devoted to it, including nitrogen fixa- 
tion, nitrification and sterilisation of soil. The 
filterable viruses are dealt with, and some recent ~ 
work on the meningococcus and other topics is 
referred to in a brief appendix. Altogether we 
may congratulate the authors upon having com- 
piled an exceedingly comprehensive and useful 
little book. 
