a8 4° Notices respecting New Books. 
dealing with a subject of vast extent, contains everything that may 
be regarded as essential to the electrical engineer, and is nowhere 
overloaded with theoretical developments which from the practical 
standpoint present but little interest. There are few books which 
we could so confidently recommend to the student of electro-— 
technology as Professor Gerard’s admirable treatise. 
Teoria Matematica dello Equilibrio det Corpi Elastici. Di RoBERTO 
Marcotonco. Ulrico Hoepli: Milano, 1904. Pp. xiv+366. 
Wirury the comparatively small compass of 366 pages of a pocket 
volume, Professor Marcolongo has succeeded in giving a fairly 
complete outline of the theory of elasticity. The first two chapters 
contain introductory mathematical matter, and deal with harmonic 
functions, Green’s theorem, and the Newtonian potential function. 
In Chapter III. we are introduced to the general principles under- 
lying the dynamics of a continuous body. Chapter LV. deals with 
the equations of equilibrium and motion of an isotropic elastic solid, 
Chapter V. with those of a non-isotropic solid, Chapter VI. with 
some general theorems, Chapter VII. withthe problem of Boussinesq 
and Cerruti, Chapter VIII. with the deformation of an isotropic 
sphere, Chapters 1X. and X. with St. Venant’s problem of the 
deformation of a cylindric shaft and the complementary problem, 
and the concluding Chapter XI. with the deformation of a crys- 
talline solid. To the advanced student of mathematical physics, 
Professor Marcolongo’s little book should prove most useful. 
Bibliography of Quaternions and Allied Systems of Mathematies. 
By ALEXANDER Macrartane, D.Sc., L.D., F.R.S.E. Printed 
at the University Press, Dublin. 
THIS important bibliography is published by the International 
Association for Promoting the Study of Quaternions and Allied 
Systems of Mathematics, of which Dr. Macfarlane is General 
Secretary. The matter is arranged under the names of the 
authors, and includes works, memoirs, and notes on quaternions 
and other systems of vector analysis, on Ausdehnungslehre, 
Universal Algebra, Complex Numbers, and Matrices. No pains 
have been spared by the compiler to make the list as complete as 
possible ; and all workers in those diflicult but growingly important 
departments of mathematics will find the booklet very useful for 
reference. T’o ensure accuracy and completeness every living author 
named received a proof of the bibliography, and Dr. Macfarlane 
had the gratification of getting corrections and additions from 
nearly all. Those who are interested in the history of this Inter- 
national Association will find the first steps chronicled in ‘ Nature,’ 
vol. lii., in an appeal from Kimura of Tokyo and Molenbroek of 
Leiden. 
