January 21, 1897] 
NATURE 
267 
of each coefficient—that is to say, its order in the eccen- 
tricities, inclination, and solar parallax—can be written 
down by inspection, and is not modified by any integra- 
tion or other process that occurs in the computations. 
The order, however, in the ratio of the mean motions 
does not follow any simple law. 
that certain terms rise in importance on integration. 
The class of terms that behave thus is carefully pointed 
out in the book, and the fact that their consequent 
increase in importance is transmitted to the terms in 
gueue with them, thereby doubling the number of approxi- 
mations necessary, is noticed. As far as we know, the 
whole question has never been thoroughly gone into, 
so as to form rules whereby the order in the mean 
motions of every term may be estimated. It would form 
a fitting subject for a thorough investigation. For 
instance, with Delaunay’s notation, the term with argu- 
ment 2D is of order ”, the term with argument 2D —/ 
has been lowered by one order in » to me. The term 
in 4D + Z may be considered as made up of 2D + 2D + /, 
2D + (2D—Z) + 2/, or (2D—Z) + (2D—Z) + 3%, and its 
order will be wztz, 7°", me° in the three cases. Similarly 
the order of the term in 4D —/ is me and me. These 
are simple cases illustrating the fact that lower powers of 
m often occur than the power by which the characteristic 
part of the coefficient is multiplied. 
The treatise deals with four theories in some detail— 
De Pontécoulant’s, Hansen’s, Delaunay’s and Hill’s. 
Pontécoulant’s is an easy one to understand, and the 
author has attached to it his discussions of the constants 
and other points that are in reality common to all theories 
in variously modified forms. 
Hansen’s theory is an extremely difficult one, and 
Tisserand has entirely failed to give an intelligible | 
account of it. Prof. Brown, too, leaves something to be 
desired ; but we at least owe to hima remarkable sim- 
plification in an introductory lemma (recently published 
in the AJonthly Notices). The proof given by Prof. 
Brown is so simple, that its merit is only apparent to 
those who have read Hansen’s investigation of the same | 
point. Hansen’s theory is of a curious design: the 
inequalities are thrown upon the time or the mean 
longitude. Dr. Hill considers that the method was an 
outcome of an extension to all terms of a method used 
by Laplace for terms of long period. 
Delaunay’s theory is a gigantic task representing 
twenty years’ labour. His method is the variation of 
arbitrary constants, using canonical equations. Prof. 
Brown has considerably simplified the introductory 
analysis on which the theory rests, and has recently 
published a further simplification in the Proceedings of 
the London Mathematical Society. 
Dr. Hill’s theory is the most recent, and the simplest 
in form. It is, however, as yet far from complete. It 
was, as is well known, originated by some papers of Dr. 
Hill’s in the first volume of the American Journal and 
the eighth volume of the Acta Mathematica. In these 
papers Dr. Hill obtains the variation curve (that does 
duty as the intermediate orbit) and the motion of the 
perigee. The further development has been left almost 
entirely to Prof. Brown, who has published a series of 
papers in the American Journal. Among these is a 
paper of great analytical interest containing some 
NO. 1421, VOL. 55 | 
This is due to the fact | 
De | 
theorems that include two famous theorems of Adams’ as 
a special case. It is much to be wished that Dr. Hill’s 
theory should be completed. 
The book concludes with a short sketch of several 
other theories, and the methods used in computing 
inequalities other than those due to the sun. 
OUR BOOK SHELF. 
Chemistry for Engineers and Manufacturers. 
“ical /ext-book. 
A Prac- 
By B. Blount and A. G. Bloxam. 
Vol. i. Chemistry of Manufacturing Processes. 
Pp. 484. (London: C. Griffin and Co., Ltd., 1896.) 
Ir is stated in the preface that the sole object of this 
work is to give the reader a general view of the principles 
which underlie the several manufactures described. ‘lhe 
ground covered is very wide, so that in order to keep the 
book within reasonable limits a very condensed style has 
been adopted. The opening chapters deal with the 
manufacture of sulphuric acid and alkali, and the de- 
structive distillation of coal, wood, and bone, the account 
of coal-gas manufacture being especially well done, 
although the short account of methods of gas-testing is 
sketchy and inadequate, and might have been omitted 
with advantage. The subjects of artificial manures, 
petroleum, cement, glass and porcelain, sugar and starch, 
brewing and distilling, oils, resins and varnishes, are 
next dealt with. The soap and candle industry is dis- 
missed in nine pages, no account being given of the 
chemistry of the “cold process” of soap-making. in 
which the excess of alkali is eliminated by the subse- 
quent addition of ammonium salts, although most of the 
highest grades of toilet soaps are now prepared by this 
process. The chapter on dye-stuffs, which follows, con- 
tains a good synopsis of the chemistry of this subject. 
It is, however, too brief to be of much service to the dye- 
works chemist, and is certainly beyond the apprehension 
of the average engineer. ; 
The authors, indeed, are rather optimistic in their 
estimate of the chemical knowledge possessed by 
engineers, as chemical formule and equations are freely 
used throughout the book. Of the remaining chapters, 
those dealing with the preparation of pigments, leather, 
and explosives are the most important. In view of the 
growing importance of cyanide compounds in gold 
extraction, it is to be hoped that a little more space will 
be found for this subject in the next edition, no mention 
being made of the recent advances in the industrial 
applications of the well-known synthesis from alkalis, 
carbon, and gaseous nitrogen. The short bibliography at 
the end of the book will prove useful in following up the 
details of any particular subject. 
The Struggle of the Nations. By G. Maspero. Edited 
by A. H. Sayce, and translated by M. L. McClure. 
(Society for Promoting Christian Knowledge, 1896.) 
SoME time ago (see NATURE, No. 1310) we called the 
attention of our readers to the issue of a much enlarged 
and illustrated edition of M. Maspero’s work “ Histoire 
Ancienne des Peuples de l’Orient Classique” in a notice of 
the first volume, which appeared in England under the 
title of “‘ The Dawn of Civilization,” and we welcomed it 
as a book much to be desired. The second volume now 
before us is the next instalment of the edition, and we 
welcome it no less gladly; it is to be hoped that the 
intervals between the issue of the volumes will become 
shorter and shorter, and that the whole work may be in 
our hands in a few years. The period covered by the 
first volume extended from the time when we first have 
written records in Egypt and Western Asia (including 
Babylonia) to the end of the reign of the kings of the 
twelfth dynasty in Egypt, say about B.C. 2500; in this 
volume we are led from the time of Khammurabi and his 
immediate predecessors to the end of the twenty-first 
