76 NATORE [ NOVEMBER 26, 1903 
The work thus covers the domain of general It might also be suggested here that the diagram 
astronomy, with, however, one notable exception, | of the solar spectrum (p. 75) should be placed hori- 
namely, the omission of all reference to new stars! | zontally and not vertically, as this latter position would 
The reader is thus left entirely ignorant not only of 
the facts that such bodies as Nova Auriga, Nova 
Persei, Nova Geminorum, &c., ever existed, but of 
the various hypotheses put forward to explain the 
sequence of the interesting and important phenomena 
which are so characteristic of them. 
This omission is, however, not the only blot which 
mars this book, for unfortunately errors of Eaten? 
kind are by no means uncommon. 
Those who have taught astronomy know how im- 
portant it is to give the student a correct idea of the 
difference between “ rotation ’’ and ‘‘ revolution,’’ so 
that the beginner may clearly grasp the facts that the 
former is responsible for our day and the latter for our 
year. 
For a popular work, such as this, the definition of 
rotation could scarcely be more clearly explained than 
is done under the heading ‘“ rotation ’’? in Webster’s 
Dictionary (1902) :—‘‘ The act of rotating or turn- 
ing, as a wheel or a solid body on its axis, as dis- 
tinguished from the progressive motion of a body 
round another body or a distant point. Thus, the daily 
turning of the earth on its axis is a rotation; its annual 
motion round the sun is a revolution.’’ 
With these definitions before us the following ex- 
tracts from the book under review may be of interest. 
On p. 11, for instance, the reader is told that ‘ the 
earth is not at rest, but revolves unceasingly around 
an axis .. .,’’ and on the same page that “ this real 
vevolution of the earth, with the apparent revolution 
of the stars which it causes, is called the diurnal 
motion... .’? Again, on p. 19 we read, “as the earth 
revolves on its axis... .” 
If the author had expressly stated that his definition 
_of “rotation ”’ referred to points on the earth’s surface 
and not to the earth as a whole, then the above state- 
ments might be valid, but as he makes no mention of 
this, the beginner will undoubtedly become perplexed 
as regards these motions. 
A little further on (p. 35) a description is given of 
how the obliquity of the ecliptic produces the changes 
of seasons. Unfortunately (line 9) the word ‘ orbit ”’ 
is printed instead of “ axis,’ an error which by no 
means renders the explanation very clear. 
Another difficulty which the beginner will have to 
Overcome occurs on p. 57, where the illustration show- 
ing the axes on which a telescope turns is placed on 
its side. Apropos of the incorrectness of diagrams, an 
error occurs in the drawing of the path of the rays 
(p. 68) illustrating the principle of the Nieuiioaign re- 
flecting telescope. Here the “ flat’’ or ‘‘ secondary 
mirror ’’ is placed outside the focus of the large re- 
flector, so that the rays which after reflection from 
the latter fall on it are divergent and not convergent. 
In this chapter it is stated that ‘“‘ the largest mirrors 
so far successfully made and used have been about 
four feet in diameter.’? The author does not seem to 
be aware that the late Dr. Common constructed, 
mounted, and used a mirror measuring five feet in 
diameter. 
0. 1778, VOL. 69] 
“ 
tend rather to confuse than to enlighten beginners 
when they are confronted later with terrestrial or 
celestial spectra. 
On p. 114 a rather perplexing statement is made :— 
if we imagine ourselves standing exactly on a pole 
of the earth, with a flagstaff fastened in the ground, 
we should be carried round the flagstaff by the earth’s 
rotation. a 
To the writer of this notice it seems that the flag- 
staff would travel round the observer if the observer 
be standing exactly on a pole of the earth as is stated; 
of course, it is meant that the flagstaff should be placed 
on a pole and the observer near it, but the reader has 
good cause to be puzzled. 
A point which calls for special attention when giving 
our readers an idea of the contents of this book is the 
extreme poorness of the illustrations. One would 
have thought that advantage would be taken of the 
wealth and excellence of astronomical photographs 
that are now available, and the facility and accuracy 
with which they can be reproduced; but this is not 
the case. 
Sun-spots are represented by a single drawing made 
many years ago; comets are illustrated by four draw- 
ings made by G. P. Bond, instead of by some of the 
beautiful photographs secured at recent appearances. 
Further, Bond’s drawing of Donati’s comet is so badly 
reproduced that probably the original artist would 
not be able to recognise it; the frontispiece, an im- 
pression of the solar corona of 1900, is decidedly 
feeble. The reader is not shown either a_ stellar 
spectrum or a reproduction of Hale’s fine spectro- 
heliograph photographs, or even a spectroscope or 
objective prism telescope. 
From the above remarks it will be gathered that 
the book before us is not the best that could be placed 
in the hands of a beginner, and it seems a pity that 
more trouble was not taken in its production. 
HISTORY OF ELEMENTARY MATHEMATICS. 
Geschichte der Elementar-mathematik in  system- 
atischer Darstellung. By Dr. Johannes Tropfke. 
Erster Band. Pp. viii+332. (Leipzig: Veit and 
Co., 1902.) Price 8 marks. 
HE great work of Moritz Cantor has made him, 
as it were, the Gibbon of mathematical history. 
But the extent of his subject has prevented him, as a 
rule, from entering into detail, and there are many 
things of great interest about which it is not easy to 
get information without laborious research. The 
history of mathematics is being studied, and its value 
is recognised, not only by those who make it their 
special domain, but by an increasing number of 
practical teachers, so that there is both a demand for 
books dealing with various parts of the subject in 
different degrees of detail and a school of historians 
ready to supply them. 
Dr. Tropfke’s work is not exactly a popular treatise. 
He has limited himself to the range of elementary 
