290 
mission of heat, corrosion, &c., and to the various methods 
for producing draught, with a discussion of the ad- 
vantages and disadvantages of the various systems. 
On p. 45 there is a slip, probably arising in conver- 
sion of units: it is stated that 5°89 lbs. of oxygen are 
needed to burn a pound of carbon; the figure should be 
2°67 lbs. In discussing the possibility of the utilisation of 
the heat passing away up the funnel for warming either the 
feed water or the air before it passes into the furnace, 
there is a somewhat cur ious remark about the heat wasted 
in condensing the exhaust steam from an engine by cold 
water in the condenser, the author stating that so far “‘no 
remedy for this evil” had been proposed. Surely it has 
been forgotten that since the engine can only convert 
into work a small portion afterall of the heat it receives, 
there must be rejection of heat in the condenser or else- 
where. In discussing the effects of corrosion in tubes, it 
is laid down as an axiom that only solid drawn tubes 
should be used, on account of the liability of the welded 
tube to suffer injury by corrosion along the line of weld, 
a remark which is sadly significant after the late disaster 
toa boiler in H.M.S. Zervrzéle, and the finding of the 
Court of Inquiry. 
The next two parts deal in detail with the older forms 
of marine boilers, the Scotch boiler mainly, and the newer 
tubulous or water-tube boiler. Very full descriptions are 
given in the second section of the more important details 
in a cylindrical boiler, especially in regard to the tubes 
and to the stays, and the section concludes with a 
valuable table of weights, space occupied, &c. 
The third section, on water-tube boilers, is the most 
complete and the most interesting, as was to be ex- 
pected, the tubulous boiler now reigning almost supreme 
in the French navy, and its use in the French mercantile 
marine being fairly large. Three classes of such boilers 
are described in three separate chapters—the limited 
circulation class, type Belleville ; the free circulation, 
types Niclausse, Babcock-Wilcox, &c. ; and lastly the 
accelerated circulation, types Normand, Thorny croft, 
Yarrow, &c. 
In each chapter practically every boiler of the class 
under description which has been actually tried in prac- 
tice is illustrated and briefly explained, while very full 
detailed descriptions are given of one or two of the 
important forms, such as Belleville, Niclausse, Thorny- 
croft, &c., with much valuable information as to their 
performances under steam. 
The last chapter in Part iil. is devoted to an able 
summary of the advantages and disadvantages of the 
tubulous type of boiler, mainly, of course, from the point 
of view of the marine engineer; interesting contrast- 
ing figures of comparative weights, costs, &c., per 
square foot of grate render this chapter one of the most 
useful in the book. It is surprising how cheap these 
apparently complex water-tube boilers are, averaging 
32/. per square foot of grate surface. 
The four chapters in Part iv. are devoted to descrip- 
tions of boiler mountings and fittings, in particular to the 
automatic feed arrangements, so essential to many water- 
tube boilers; in these chapters the illustrations are 
very good. 
The book undoubtedly is the most complete work on 
the subject issued in English up to the present, and is 
NO. 1552, VOL. 60] 
NATURE 
[JuLy 27, 1899 
well up to date; it should prove a valuable work of 
reference, not only to the marine engineer, but to the 
intelligent layman who takes an interest in the efficiency 
of our navy. The water-tube boiler, much as Mr. Allen 
may dislike it, has come to stay; in our navy it will 
gradually displace the old Scotch boiler, and we should 
be surprised if it does not eventually make headway in 
the mercantile marine. : 
Any one reading the book and anxious to ascertain 
the trend of opinion amongst English marine engineers 
on this important question should consult the papers 
read a month or two ago before the Institution of Civil 
Engineers by Mr. Milton and Sir John Durston. 
lly 514 
OUR BOOK SHELF. 
The Elements of Euclid. With Notes, &c., by I. Tod- 
hunter, D.Sc, F.R.S. New edition, revised and 
enlarged, by S.L. Loney, M.A. Pp. vilit+332, cxxxij. 
(London : Macmillan and Co., 1899.) 
Essentials of Plane and Solid Geometry. By W. Wells, 
S.B. Pp. vilit392. (London: Isbister and Co. 
Boston, D.C. : Heath and Co., 1899.) 
WITHOUT altering the general character of the well- 
known text-book with which he has had to deal, Mr. 
Loney has succeeded very well in bringing it up to date. 
The appendix has been enlarged by the insertion of 
sections on poles and polars, harmonic ranges, inversion, 
coaxal circles, &c.; the number of exercises has been 
doubled, and, what is more important, the really valuable 
exercises have been starred and hints given for the solu- 
tion of many of them. To teachers of the conservative 
school this new edition ought to prove very acceptable. 
Mr. Wells’ book is of quite another stamp. The 
author belongs to the progressive party, and makes no 
scruple of using hypothetical constructions or any ab- 
breviations he finds convenient. In treating of parallels 
he uses Playfair’s axiom, and the discussion of ratio and 
proportion is distinctly arithmetical. The exercises are 
numerous and often accompanied by figures ; hints for 
solution are also given in many cases. Mr. Wells writes 
in a fresh and independent manner, and his book seems 
very likely to interest a student and develop any geo- 
metrical power he may have in the right way. 
In another edition the author will, we trust, suppress 
the appendix (p. 386), which is almost entirely vitiated by 
an error of reasoning. Mr. Wells proposes, for instance, 
to prove that the circumference of a circle is less than 
the perimeter of any circumscribed polygon, and pro- 
ceeds thus: “Of the perimeters of the circle and of its 
circumscribed polygons, there must be one perimeter 
such that all the others are of equal or greater length.” 
He then proves that, given any circumscribed polygon, 
we can construct another ene with less perimeter ; and 
then infers the truth of the proposition. As a matter of 
fact, the statement quoted above is not justifiable; the 
perimeters of the polygons form a manifold, and this does 
not necessarily contain a least element ; indeed, Mr. 
Wells shows that it does not. There may be a definite 
lower limit to the perimeter of a circumscribed polygon : 
even then, Mr. Wells brings forward no argument to show 
that this lower limit exists ; still less that it is equal to the 
circumference of the circle. Strictly speaking, he brings 
the circumference of the circle into no relation of equality 
or inequality with any of the polygons: it just stands by 
itself at the end asat the beginning. It is as if one said: 
“We have a set of quantities x, 1°3, 1°33, 1°333, &c. ; one 
of these must be at least equal to any of the rest. But 
this cannot be any of the decimals, because if we choose, 
