410 
NATURE 
[Marcu 3, 1904 
As might be expected, the chapter on stereometry is 
mainly interesting for the account it gives of Archi- 
medes’s great discoveries. The brief section on analy- 
tical geometry shows how Fermat really invented the | 
method independently of Descartes. Parent appears to | 
have been the first to publish a treatise on analytical 
solid geometry; this was nearly seventy years after 
the appearance of Descartes’s ‘*‘ Géométrie.”’ 
The only other important section of the book is that 
on conic sections. It cannot be considered so good as 
some of the others; it does not deal with projective pro- 
perties at all, and thus does injustice even to Apollonius, 
to whom, rightly enough, a great part of the thirty-six 
pages is devoted. 
To profit by this history no advanced knowledge of 
mathematics is necessary; and it is to be hoped that | 
the author’s labours will be rewarded by the appreci- 
ation of many readers. G. B. M. 
THE PRACTICAL METHODS OF 
FRACTIONAL DISTILLATION. 
Fractional Distillation. By Prof. S. Young, F.R.S. 
Pp. xii+284. (London: Macmillan and Co., Ltd., 
1903.) _ Price 8s. 6d. 
ra his preface Prof. Young says that he wrote this 
book in the hope that the solution of the difficulties 
of fractional distillation might be rendered easier. He 
has written an eminently practical treatise on the sub- 
ject and one that cannot fail to be of considerable value. 
After an introductory chapter describing the neces- 
sary apparatus and the methods of carrying out a dis- 
tillation process, the vapour pressures and_ boiling 
points of liquids are first dealt with. Very little is 
known of the connection between the vapour pressure 
and composition of a mixture of two or more perfectly 
miscible liquids. The simple formula for the vapour 
pressure of a mixture of two perfectly miscible liquids 
A and B, 
pe mPs +(100 = 1)Py 
<3 
100 
where P, and P, are the two partial pressures and m 
the molecular percentage of the compound A, is only 
strictly applicable when the two components are closely 
related in chemical composition, when they have the 
same critical pressures and when the attraction be- 
tween the unlike molecules is equal to the geometric 
mean of the attractions between the lilke molecules. In 
certain other cases the deviations from the theoretical 
values are not large, but in the majority of cases the 
formula gives no approximation to the truth. Is it 
not possible that the deviations are due to the surface 
layer having a different composition from that of the 
bulk of the liquid, as is known to be the case with mix- 
tures of certain alcohols and water? 
In the chapter dealing with the boiling points of 
mixtures the cases of binary and ternary mixtures of 
minimum and of maximum boiling point are fully 
treated. There follows next an account of the constitu- 
tion of the vapour and liquid phases, including the work 
of Brown, Lehfeldt and Carveth; Brown found that in 
certain cases with two components the ratio of the 
masses of the two in the vapour phase was equal to 
NO. 1792, VOL. 69, 
| their ratio in the liquid phase multiplied by a constant, 
| while Lehfeldt showed that the logarithms of the ratio 
in the vapour phase were a linear function of the 
logarithms of the ratio in the liquid. In another 
chapter the theoretical considerations worked out by 
Duhem, Margules and Zawidski are briefly given. 
The next section deals with the methods of carrying 
out fractional distillations of simple and complex mix- 
tures, and also with the various forms of still heads 
which have been devised at various times. This is 
undoubtedly the most valuable portion of the book, 
inasmuch as it is drawn almost entirely from Prof. 
Young’s own work. The methods of fractional dis- 
tillation are described in detail, great stress being 
rightly laid upon the graphical expression of results. 
This may be done most easily by weighing the distillate 
obtained at various temperatures and plotting the 
values of dW/dT thus obtained against the temper- 
ature; it is in this way only that the distillation of a 
complex mixture can be properly carried out, for com- 
ponents present in only small quantities may otherwise 
easily be overlooked. Many forms of still head are 
described, amongst which the most efficient have been 
designed by Prof. Young himself. Tables are given of 
the relative efficiency of the various designs, as shown 
by the results obtained with mixtures of benzene and 
toluene, and of other substances. A chapter follows 
here containing descriptions of the various forms of 
still heads used in manufacturing processes. 
The remainder of the book deals in the main with the 
application of the methods previously described to cer- 
tain problems, as, for example, the quantitative 
| analysis of a mixture of liquids and the separation of 
| the components of a constant boiling mixture. 
Amongst the latter examples occurs the interesting 
case of the removal of the last traces of water from 
' alcohol by distillation after the addition of a small 
quantity of benzene. If the correct quantity of benzene 
has been added then there distils over the ternary 
benzene-alcohol-water mixture, leaving pure alcohol 
in the still. It is safer to add a slight excess of benzene, 
and in this case, after all the ternary mixture has come 
over, the remainder of the benzene distils as the binary 
benzene-alcohol mixture, leaving again the pure 
| alcohol. 
It is impossible to touch upon all the points of interest 
in this book. Its chief value lies in the fact that many 
examples are given of the various processes, mostly 
from Prof. Young’s own work. Moreover, a consider- 
able amount of hitherto unpublished matter is incor- 
Our thanks are due to the author for so 
EE. (G'ESB: 
porated. 
useful a work. 
A FRENCH MANUAL OF FORESTRY. 
Traité de Sylviculture. Exploitation et Aménagement 
des Bois. By Prof. P. Mbouillefert. Pp. 476. 
(Paris: Félix Alean, 1904.) Price 6 francs. 
| HIS is the second volume of a manual of forestry 
| the first of which was noticed in Narure of March 
| 20, 1903. The present volume treats of the utilisation 
| and management of woodlands, 361 pages being de- 
