194 
NATURE 
[ Dec. 28, 1882 
ramifications which he has termed trees. This is a sub- 
ject which has applications to the theory of chemical com- 
binations, and it is one to which Prof. Cayley has already 
devoted attention, a long memoir of his upon it having 
appeared in the Report of the British Association for 
1875. Prof. Cayley also is the author of a short paper on 
certain imaginaries connected with the product of two | 
sums of eight squares. Among papers on general analysis 
should also be mentioned a determination by Prof. String- 
ham, of the number of possible finite groups of quater- 
nions, a group being defined as in the theory of substitu- 
tions; and a note by Mr. Story on non-Euclidean 
geometry. 
A number of papers relate to the differential calculus. 
There are two by Prof. Sylvester on the solution of classes 
of difference and differential equations. No less than 
four relate to development in series by Taylor’s and other 
expansion theorems and the forms of the remainder: 
these are by Mr. J. C. Glashan of Ottawa, Mr. McClin- 
tock, and Mr. A. W. Whitcom. Frof. Crofton gives some 
remarkable theorems involving symbols of operation, and 
Mr. J. Hammond considers the theory of general differentia- 
tion, a subject that received attention from Liouville, Pea- 
cock, and others half a century ago, but which has attracted 
but little notice in recent times. Mr. Franklin contributes 
a short note on Newton’s method of approximating to the 
roots of equations, and Mr. Glashan gives certain formulz 
relating to the change of the independent variable in 
differentiations. 
More than one whole number is devoted to a reprint of 
the late Prof. Benjamin Peirce’s valuable memoir on 
Linear Associative Algebra, of which only a small number 
of copies in lithograph were made in the author's life- 
time for circulation among his friends. This well-known 
paper was read before the National Academy of Sciences 
at Washington in 1870: it is here reproduced with notes 
and addenda by Mr. C. S. Peirce, the son of the author, 
and occupies 133 pages. Mr. C. S. Peirce himself, whc 
is known not only by his logical writings but by his stellar 
photometric researches, is also the author of two papers, 
the one on the algebra of logic and the other on the logic 
of number. In connection with this subject a paper by 
Miss Ladd on De Morgan’s extension of the algebraical 
processes should be noticed. 
There is a short bibliographical paper relating to 
Alhazen’s problem by Mr. Marcus Baker. The problem 
is from two points in the plane of a circle to draw lines 
meeting at a point on the circumference, and making 
equal angles with the tangent at that point. The 
author also gives an extension of the problem to the 
sphere. 
Only three papers belong to mathematical physics, 
One, by Prof. H. A. Rowland, relates to the general equa- 
tions of electromagnetic action, with application to a new 
theory of magnetic attractions and to the theory of the 
magnetic relation of the plane of polarisation of light. 
The other two are on hydrodynamics, they are by Prof. 
Rowland and Mr. Craig, and relate respectively to the 
motion of a perfect incompressible fluid and to certain pos- 
sible cases of steady motion in a viscous fluid. There are 
some notes on moving axes by Prof. Loudon of Toronto ; 
and Prof. Sylvester considers the theory of mechanical 
involution, which is the name he has given to the relation 
between six lines in space so situated that forces may be 
made to act along them whose statical sum is zero. 
Linkages form the subject of a paper by Mr. F. T, 
Freeland. 
Astronomy is represented by two papers: one by Prof, 
Newcomb, on a method of developing the perturbative 
function of planetary motion; and the other by Mr. G. 
W. Hill, on Hansen’s general formule for perturbations, 
The object of the former paper is to exhibit a method of 
effecting the development in powers of the eccentricities. 
The author remarks that in consequence of the complex 
character of the series this development has been but 
little used even in the cases of nearly circular orbits, when 
its application would be most convenient, but that, as the 
disturbing force is given as an explicit function of all the 
elements, it is of more interest to the mathematician than 
any other. In his method of development Prof. Newcomb 
directs especial attention to the expression of the co- 
efficient of each power of the eccentricity in terms of the 
coefficients of lower powers, and to the expression of the 
coefficient in each term involving, the perihelia of two 
planets as the symbolic product of coefficients involving 
the perihelion of one only. Mr. Hill’s paper contains a 
transformed form of Hansen’s expression for the pertur- 
bation of the mean anomaly, which is more simple and 
more convenient for computation. There is also a short 
note by Mr. Ormond Stone relating to formule in elliptic 
motion. 
The titles of the papers speak for themselves, and but 
little comment is needed. It will be seen that the two 
volumes represent a considerable amount of mathematical 
work, a fair proportion of which may have real influence 
on the advancement of the science. Some of the papers, 
as must evidently be the case, are needlessly pretentious 
in form, and the new matter they contain might be 
advantageously stated in less space. The effect of Pro- 
fessor Cayley’s visit to Baltimore is apparent in the 
papers which occur in the last number issued, and 
we believe that the lectures which he gave at the Johns 
Hopkins University will shortly appear in a future 
number. 
The dates which the numbers of the Journal bear are 
the dates when they ought to have appeared, assuming it 
to be published quarterly in March, June, September, 
and December, and not the dates when they did actually 
appear. Thus the last number issued bears date Decem- 
ber, 1881, but in the case of this number the inconvenience 
attending so great a discrepancy between the nominal 
date and the date of publication is partially remedied by 
the words “ Issued July 18, 1882,” at the foot of the last 
page. It seems a pity to retain the nominal dates on the 
wrappers, as they may be misleading. It will be difficult 
to regain the lost time, and there is but little advantage 
im stating the time when the number should have ap- 
peared. The volume and number and date of publication 
are all that need to be given. 
On the wrappers of the numbers of vol. iv. appears an 
announcement in which a prize of 1500 francs and a per- 
petual free subscription to the journal from its commence- 
ment are offered to the first person who, before January 1, 
1883, discovers and transmits to the Editor a valid proof 
or disproof of the proposition that a ground form and a 
syzygant of the same degree and order cannot appertain 
