3a 
book to be the outcome of a course of lectures to 
graduates intending to enter the teaching profession, 
in which Prof. Weber brings his long years’ experi- 
ence and profound knowledge to bear upon some of 
the subjects usually regarded as ‘‘ elementary.”’ 
The first volume contains three parts, Grundlagen 
der Arithmetik, Algebra, Analysis. The remaining 
two volumes are to deal with geometry, and applica- 
tions. The contents are what every teacher of elemen- 
tary mathematics should know and not teach. The 
authors have found some difficulty in defining the | 
range of subjects of discussion, but no limitation has | 
been imposed upon the methods employed. The first 
few pages deal with aggregates, and later we come 
to the logical reasoning upon which the introduction 
of irrationals and of imaginaries is based. The part | 
on algebra is chiefly concerned with theory of equa- 
tions and theory of numbers, and the third part with 
infinite series and products, including the most im- 
portant examples. Speaking generally, subjects of 
technical or practical interest are excluded, and only 
those presenting serious logical difficulties are dis- 
cussed in detail. 
The book is admirably printed and clearly arranged, 
and should prove a very useful and trustworthy com- 
panion to all who care for exact knowledge for its 
Re WeEon.. Ei: 
own sake. 
OUR BOOK SHELF. 
Stars and Sextants. By Sprigge, Doalk, Hudson and 
Cox. With an introduction by Lord Ellenborough. 
Pp. xxv+55. (London: J. D. Potter, 1903.) Price 
2s. 6d. 
Tuts book places in the hands of explorers, navigators, 
surveyors and others who use the sextant a simple 
means of finding its centring error. The centring 
error of a sextant at sea has hitherto been severely left 
alone on account of the somewhat tedious calculations 
necessary to find it. 
The method of obtaining the total error (and hence 
the centring error by applying the index error) by 
observing the distance between two stars when on the 
same vertical circle is mentioned in ‘*‘ Hydrographical 
Surveying,’’ by Sir William J. L. Wharton, in the 
second edition, 1898. The error thus obtained is owing 
to refraction not strictly accurate, unless the two 
stars are of equal altitudes at the time of observing. 
The best time for observing the distance between two 
stars, so that refraction may have the least possible 
effect and alter slowest with the time, is when the 
altitudes of the stars are equal. However, the error 
due to refraction in observing stars at different alti- 
tudes is not great when they are on the same vertical 
circle, and in finding the error of a sextant at sea it 
may be neglected, especially if the altitude of the lower 
star be above 30 degrees. 
The centring error can only be found for different 
points on the arc of a sextant by taking a large number 
of observations for each point and meaning the results. 
It.is to be hoped this book will induce many to take 
these observations, so that while learning the principal 
stars they may also become expert observers. 
NATURE 
[APRIL 7, 1904 
time a fictitious star rises and sets; (5) astronomical 
refraction corrected for barometer and thermometer; 
(6) notes on the stars. The descriptions and rules for 
using the tables are clear and simple, the figures are 
well arranged, and the type is very distinct. The 
temperature required for correcting the refraction 
should be taken by a Fahrenheit thermometer in a 
screen exposed to the open air. 
This book might lead a tyro to suppose that correct 
| time for obtaining errors and rating chronometers can 
only be obtained by equal altitudes of the sun, and only 
by a sextant of which the centring error is known; 
such is not the case. Time can be accurately obtained 
with a faulty sextant by observing sets of single alti- 
tudes both a.m. and p.m. of the sun, of stars both east 
| and west of the meridian and meaning the results. 
By another less known but very valuable method the 
time is obtained in less than half an hour, if the stars 
are properly selected, by taking the equal altitudes of 
two different stars on opposite sides of the meridian. 
Nothing must prevent the navigator from finding 
his position by stars. Take them at other times when 
possible, but always at twilight. 
VANSITTART Howarp. 
Engine Tests and Boiler Efficiencies. By J. Buchetti. 
Pp. xv+255. (Westminster: Constable and Co., 
Ltd., 1903.) Price ros, 6d. net. 
Tue volume before us is a translation, by Mr. Alexander 
Russell, of M. Buchetti’s well-known work ‘ Guide 
pour 1’Essai des Moteurs.’’ The object of the volume 
is to place before British and American engineers a 
record of Continental practice so as to render a com- 
parison possible with home practice, and in order to 
further this comparison the measures and tables have 
been converted to English units. 
The subject-matter is divided into nine chapters, and 
commences with well illustrated descriptions of the 
many indicators in use for testing steam and other 
engines. The important subject of mounting the in- 
dicator is then thoroughly dealt with, and this is as 
_it should be, since the accuracy of the results depends 
The book contains (1) ephemeris, 1904, with star | 
pairs of nearly equal magnitude; (2) distances of star 
pairs; (3) ex-meridian star pairs, with distances for 
every ten days; (4) semi-diurnal arcs for finding the 
NO. 1797, VOL. 69 | 
entirely on the fitting and the scientific arrangement 
of the gear; M. Buchetti appears to have taken in- 
finite pains to treat these details very thoroughly— 
there are many evidences of this right through the 
book. 
The same can be said of the treatment of the several 
types of brakes now in use. When dealing with 
properties of steam, we note on p. 180 one or two 
clerical errors under the paragraph on saturated steam. 
The author talks about ‘‘ If we compress the piston,”’ 
| &c., and further on in the next paragraph he says, 
‘“ When the piston is allowed to expand ’’; surely the 
word piston should read “saturated steam’? or 
ee Steam 7 
The brief chapter on the testing of steam turbines 
by the Hon. C. A. Parsons, F.R.S., is all too short; 
we should have welcomed more interesting details from 
the pen of this able experimenter and engineer. 
Taken as a whole, however, this book is full of 
interest. Students of steam and engineering should 
lose no time in obtaining a copy, since its contents are 
of the highest value to them. N. J. L. 
An English Grammar. By the Rey. S. Claude Tickell, 
A.K.C. Pp. 60. (London: O. Newmann and Co.) 
Price 2s. 
Tuis pamphlet of sixty pages is very unlike what is 
ordinarily understood by an English grammar. It 
opens with a paragraph of three lines headed 
“Analysis and Parsing Differentiated.’? Then comes 
