420 
Notices of Booh. [July, 
ments approach to accuracy as nearly as is possible. Messrs. 
Goodeve and Shelley have given an interesting account of the 
instruments, accompanied by good plates and woodcuts. 
The Theory of Sound. By Lord Rayleigh, M.A., F.R.S., for- 
merly Fellow of Trinity College, Cambridge. Vol. I. 
London : Macmillan and Co. 
Every student of the mathematical theory of sound has felt the 
exceeding meagreness of the information on the subject within 
his reach. The ordinary text-books treat of Sound merely by 
way of an appendix to Dynamics and Hydro-dynamics, and con- 
sequently limit themselves to the most elementary parts of the 
theory, with scarcely a hint as to the existence of a mass of 
important recent investigations sufficiently numerous and valu- 
able to require a separate treatment of the whole subject. The 
book before us is the first instalment of a work intended to re- 
medy this deficiency, and certainly, so far as the range of this 
first volume extends, achieves a success. 
After some valuable preliminary remarks on the ordinary 
theory of musical notes as due to vibrations, amongst which is 
to be found a remarkably clear expose (p. 17) of the reasons for 
supposing the sensation of a simple tone to be due to a simple 
harmonic vibration, the author proceeds to describe various 
appliances for investigating the rapidity of the simple vibrations 
which may be present in any compound vibratory motion, illus- 
trating at the same time the laws of superposition of small 
motions without interference, and showing very clearly the nature 
of the interference effedt, in a simple case, of the superposition 
of motions which are so great that the squares and higher powers 
of the disturbance cannot be neglected — an effedt which shows 
itself in the production of vibrations whose periods are the 
doubles, sum, and difference of the periods of the originals. 
The application of the method of generalised co-ordinates to the 
problem of small vibrations about an equilibrium position is then 
discussed, and the main part of the work consists of the appli- 
cation of the results to the detailed examination of the vibrations 
of strings, bars, membranes, and plates. This discussion con- 
tains all that is most important in the work of recent investi- 
gators, amongst whom Lord Rayleigh holds a foremost place. 
The theory of sound is perhaps somewhat uninteresting as 
yet to the general mathematical reader, but it is full of interest 
to the investigator on account of the facility and delicacy of the 
acoustical tests which can be applied to verify theoretical deduc- 
tions, and the author has taken care to supply this element of 
interest in this work by constant exhibition of the results of a 
