May 29, 1902] 
NATURE 99 
2 
occupies thirty-seven pages, and is divided into sections 
dealing respectively with determinants and elimination, 
symmetric functions, binary and other forms, enumerative 
functions with their generators,.and the theory of 
restricted substitutions. ° For the first time, perhaps, the 
methods of the English school have been discussed, in 
the same work, in conjunction with the symbolic calculus 
of Aronhold and Clebsch. Each method has its own 
special advantages, and the comparative study of both 
is very instructive. A good deal of space is devoted to 
Gordan’s important theory of transvectants and their 
reduction, and to Stroh’s recent extension of symbolic 
methods. Many parts of the article illustrate the value 
of the partition analysis as developed by MacMahon ; 
what he calls “the theorem of expressibility,” and the 
correspondence which he establishes between differential 
operation and partition operators, are real and fruitful 
contributions to mathematical science. This article is 
valuable, not only as a record of known facts, but also 
as suggesting new fields of research. The section on 
determinants contains little, if anything, that is not in the 
text-books ; if this had been suppressed, and some other 
topics treated at greater length, it would have been an 
advantage. 
“Astronomy” occupies twenty-eight pages, which 
contain a general account of some recent developments 
relating to the solar system, gravitational and theoretical 
astronomy, and the sidereal universe. In the section upon 
the planets, descriptions are given of progress in such 
subjects as the rotation periods of Mercury and Venus, 
the markings on Mars, the minor planet Eros, new 
satellites of Jupiter and Saturn, and Keeler’s proof of the 
discrete constitution of Saturn’s rings. The view that 
the dark regions on Mars are not oceans, as was formerly 
supposed, but the solid surface of the planet, is accepted, 
and also that which regards the canals or channels as 
not being physically continuous formations, but optical 
effects produced by more or less irregular differences 
in the minute shadings and colour tints on the surface 
of the planet. 
In the section on gravitational and theoretical as- 
tronomy, the chief advances recorded relate to apparent 
deviations from the law of gravitation exemplified by 
motions of the planetary perihelia and inequalities of the 
moon’s mean motion, and variation of latitude. The 
application of photography to celestial portraiture is 
briefly dealt with in the section on the fixed stars, and it 
is suggested that what is now required is a photographic 
survey of the heavens with the view of determining all 
the stars which have an appreciable parallax. Special 
attention is given to the structure of the sidereal universe 
and to systems of stars and clusters, but very little is 
said of spectroscopic advances in either connection. As 
progress in astronomy during the last quarter of a century 
means to a large extent progress in astrophysics, which 
depends almost entirely upon the spectroscope for its 
development, we assume that spectroscopic astronomy 
will be dealt with separately. The article certainly 
does not convey an accurate or adequate view of the 
physical and chemical aspects of the science, and it 
must be supplemented by one on celestial spectroscopy 
if the complete work is to be regarded as worthy of the 
intentions of the editors. 
NO. 1700, VoL. 66] 
To everyone familiar with astronomical progress during 
the past quarter of a century, the article will be dis- 
appointing ; for it is more of the nature of an essay than 
a contribution to an encyclopeedia. What is required in 
an encyclopzedic article upon any science is a concise 
and unbiassed summary of work and results, otherwise 
the contribution is misplaced. Measured by this 
standard, the article on astronomy fails entirely of its 
purpose, for it is both prolix and incomplete. Many 
small text-books contain far better statements of the 
position of astronomical science than is here given, 
because the authors have been to the trouble to become 
acquainted with the literature of the subject. This, how- 
ever, has evidently not been done by the writer of the 
article under notice, and the result is a contribution 
which will give readers very imperfect ideas as to pro- 
gress made since the contribution for the ninth edition 
was written. The new edition of the encyclopedia 
afforded an opportunity for giving a view of the vast 
amount of new material which has been accumulated by 
astronomers from unlooked-for sources, but instead of 
this inspiring survey we have a superficial essay upon a 
few points which have appealed to the writer. The 
article should have been a record of all essential advances 
of the science, whereas it is more remarkable for what is 
omitted than for what is included. 
Few articles in the ninth edition of the encyclopzedia 
could have required more extensive revision and addition 
than those devoted to zoological subjects. How great 
was the need for such revision, and how marked has 
been the progress in zoological discovery since the 
appearance of the former edition, is manifest by the 
articles in the volume under notice, which include the 
subjects “ Amphibia,” “ Amphioxus,” “Anatomy,” “ An- 
thropology,” ‘‘ Arachnida” and “ Arthropoda.” Some of 
these are in great part practically new treatises, while 
others, such as the one on anthropology, confine them- 
selves to the additions necessary to bring their prede- 
cessors up to date. The change of view that has taken 
place with regard to the relationships of the lower 
vertebrates will be manifest when the new and the old 
articles on amphibia are contrasted, while the advance 
in our knowledge of the structure of the extinct repre- 
sentatives of the latter is apparent by the amount of 
space allotted to this portion of the subject. The article 
on Amphioxus is entirely new, and occupies nearly four 
pages. 
The discoveries of modern histological methods of 
investigation are fully recorded under the heading of 
“ Anatomy,” while the Pithecanthropus is alluded to under 
“Anthropology,” and Mr. Henry’s method of classifying 
finger-prints receives mention in the article ‘“ Anthro- 
pometry.” The Funafuti boring and the inferences to 
be drawn therefrom are discussed in some detail under 
“ Anthozoa” ; while in “ Arachnida,” Prof. Ray Lankester 
adduces a long string of facts to show that the nearest 
living relatives of kingcrabs and trilobites are scorpions 
rather than crustaceans. Several of the authors had by 
no means an easy task before them in bringing up to 
date the work of their predecessors, but they all seem to 
have done their parts ina highly satisfactory manner. 
Finally, we may say that an earnest endeavour has been 
made by the editors to produce a work which represents the 
