76 
NATURE 
[May 25, 1899 
selection of examples well fitted to test the student’s 
progress. Many of these examples are of the familiar 
“academic” character, having little reference to natural 
phenomena ; but from time to time, and particularly in 
the chapter on central forces, we meet with problems of 
high interest and importance. The effect of planetary 
perturbations on comets and the disintegration of 
comets into meteor swarms may be specially mentioned. 
Then the question of the stability of orbits is discussed at 
considerable length. 
Here and there, however, a few points seem to call for 
remark. In § 222, Dr. Routh finds it convenient to in- 
troduce the term vector. It would have greatly facilitated 
his earlier work had he introduced the term at the very 
beginning. The conception of a vector quantity in 
mathematical physics is one which every student should 
get as soon as possible. It should be impressed upon 
his mind from the very start as something fundamental 
and far-reaching, and not merely as a convenient term 
enabling us “to avoid the continual repetition of the 
same argument.” 
The title of § 135 is “ Discontinuity of a centre of 
force”—a most extraordinary collocation of words, and 
absolutely misleading. There can be no discontinuity of 
a centre of force; the discontinuity (if the term be used 
at all) is in the incomplete mathematical expression of 
the solution. 
A certain looseness of expression is also apparent in 
the titles of §§ 186, 187, which are respectively, “ Work 
of a central force,” and “‘ Work of an elastic s¢vzzg.” 
In Chapter vii. Lagrange’s equations are introduced, 
and a variety of interesting problems in three dimensions 
discussed, e.g. motion of a particle constrained to move on 
a tortuous curve or on a surface. The case when the 
surface is an ellipsoid is investigated at considerable 
length, several of Liouville’s results being introduced as 
examples for solution by the student. 
Chapter viii. is devoted to “Some special problems,” 
a title, however, which is a most incomplete description 
of its contents.. The brachistochrone may, in a sense, 
be called a special Arob/em, but, as developed by Tait, 
Townsend and others, its theory is of a very general 
character, and abounds in ¢Aeovems of great interest. 
Following this there is a fairly complete discussion of the 
motion of a particle relative to the earth when the earth’s 
rotation is taken into account—a problem of no small im- 
portance. After a few sections on inversion and con- 
jugate functions, the final “special problem” taken up 
is Hamilton’s theory of action. We doubt if any student, 
not otherwise instructed, could gather from Dr. Routh’s 
pages the great importance of Hamilton’s contributions 
to general dynamic theory. On p. 394 we read : 
“These are called the Hamiltonian Equations of 
Motion” ; but there is no direct reference whatsoever 
to Hamilton, and in the index, under Hamilton’s name, 
we find references to “‘ Law of force ina conic” and to 
“ Hodograph,” but none to “Action”! In a book, one 
of whose really valuable features is its system of historic 
notes, such an omission is inexplicable. In_ striking 
contrast there is fz// recognition of the merits of Jacobi, 
who, as Hamilton himself expressed it in a letter to 
Andrews, “enriched by his comments” Hamilton’s 
theory. One recommendation the student will do well to 
NO. 1543, VOL. 60] 
follow: let him refer to his ““ Thomson and Tait.” The 
enunciation of Tait’s problem (p. 401) contains a mis- 
print which reduces the statement to an absurdity. 
It is a reproach frequently cast by literary men that 
scientific writers lack style. There is not much scope 
for a cultivation of style in a mathematical treatise, but 
surely we have a right to expect good English. In the 
book before us there occurs with painful frequency the 
fault of the misrelated participle. On p. 7, an indefinite 
“it” is found “assuming the principles of the differ- 
ential calculus”; on p. 145, a (dynamic) couple is re- 
presented as “remembering” something; on p. I50, 
the work done by forces is found capable of “selecting 
some geometrically possible arrangement,” and so on. 
By way of general summary we may, in conclusion, 
remark that, although the first chapter is open to serious 
criticism, and the book is somewhat marred throughout 
by a looseness of diction, Dr. Routh’s “ Treatise on the 
Dynamics of a Particle” is an important contribution to 
the literature of the subject. To the working student 
its value is enhanced by a well-selected stock of ex- 
amples, many of which appear for the first time in a 
formal treatise. Some of the problems specially con- 
sidered are of high interest, and the solutions in many 
cases are of practical value. In a word, the book fully 
sustains the reputation of its author as an experienced 
teacher, now bringing forth from his treasure-house 
things old and new, and appealing to a wider circle of 
ardent disciples who will be found wherever the English 
tongue is heard. GuiGrke 
MANUALS OF INORGANIC 
CHEMISTRY. 
Qualitative Chemical Analysis. By Chapman Jones. 
Pp. 213. (London: Macmillan and Co., Ltd., 1898.) 
Practical Inorganic Chemistry for Advanced Students. 
By Chapman Jones. Pp. 239. (London: Macmillan 
and Co., Ltd., 1898.) 
Advanced Inorganic Chemistry. By G. H.Bailey, D.Sc., 
Ph.D. Edited by William Briggs, M.A. Pp. 
(London: W. B. Clive, 1898.) 
HE first of the above books appears as one of the 
well-known series of “ Manuals for Students.” The 
tradition of these books is that they are not primarily 
written for a syllabus, but rather that an author has here 
an opportunity of developing his own ideas, and pro- 
ducing a book which has individuality. We turn, there- 
fore, with considerable interest to this addition to an 
already abundant literature to see how far the author has 
contributed anything new or valuable to analytical 
teaching. As far as we can gather, the great defect 
which Mr. Chapman Jones believes to attend the study 
of analysis is that the student’s mind is apt to get filled 
with a knowledge of isolated reactions, whilst really 
“ the use of such exercises, as are given in the laboratory, 
is to the would-be chemist exactly what the practising of 
exercises and scales is to the young musician. The aim 
is not merely to perform the exercise, but to do it in such 
a manner that it shall be practice in a thoroughly sound 
method of work.” 
It appears, therefore, that Mr. Chapman Jones sets his 
mind essentially on producing a correct executant. 
LABORATORY 
222 
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