Notices respecting New Books, 231 



are two uprights about 10 feet high, with a crosspiece B fast- 

 ened firmly to them. At intervals of 3 inches along this cross- 

 piece are inserted violin-pegs, each peg carrying a light string 

 with a heavy ball of 1 inch diameter attached. Before fastening 

 the strings to the violin-pegs, each string is passed through a 

 small hole in the projecting base of the crosspiece, so that the 

 length of the pendulum is determined by the distance of the 

 ball from the base of the crosspiece. C is a light wooden box 

 deeper at one end than at the other, with a number of compart- 

 ments corresponding to the number of pendulums. The box 

 C is attached at the ends to two radial arms, one of which, D, 

 is seen in the figure. Cords are also attached to C running 

 over pulleys, by which the box C may be raised and lowered. 

 These cords would confuse the figure if introduced ; and their 

 action can be easily realized. 



Suppose it be wished to illustrate a plane wave. The box 

 C is raised, and the pedulums are placed one in each compart- 

 ment so that they are all drawn on one side. By means of the 

 cords the box C is gently lowered, when the pendulums are 

 successively released and the wave formed. 



To illustrate the sound-wave, the box C is removed from the 

 radial arms and is hung vertically underneath the crosspiece 

 B ; one or two of the pendulums (to the left, say) are removed, 

 and the others placed in the compartments as before ; only now 

 each pendulum, instead of being drawn from under the cross- 

 piece, lies still underneath, but to the left of the vertical line let 

 fall from each point of support. On now allowing the box to 

 fall slowly, the pendulums are released successively and a wave 

 of condensation and rarefaction is formed. 



In conclusion I should acknowledge the assistance of Mr. H. 

 F. Marshall, of Birmingham, who has rendered great service in 

 simplifying the mechanical arrangements of the apparatus. 



Birmingham and Midland Institute 5 

 January 1876. 



XXIX. Notices respecting New Boohs. 



Theorie des Formes Binaires par le Chev. F. Faa de Bruno, Docteur 

 is Sciences de VUniversite de Paris, Professeur a VUniversiU de 

 Turin. Turin : Libraire Brero, 1876 (8vo, pp. 320, with Appen- 

 dices). 



THIS work contains the substance of the author's lectures deli- 

 vered at the University of Turin, and is designed to put 

 within the reach of students a knowledge of the Modern Higher 

 Algebra, or the Algebra of Linear Transformations. It has so far 

 the same aim as Dr. Salmon's ' Lessons introductory to the Modern 



