486 Notices respecting New Boohs. 



would intersect for the value h = l, but this is far beyond the 

 range within which the above relations hold. 



If we consider the values of S* for different positions of 

 the centre of gravity of the beam, i. e. for different values of 

 r' or of p, we shall obtain different hyperbolas of the type 

 (7) whose centres lie on OA. The constants of these hyperbolas 

 vary directly as Oi; and as they can be determined graphi- 

 cally for curves plotted from experimental values of the 

 sensitiveness, the position of can readily be obtained. 



Fig. 8 gives a set of such hyperbolas obtained by means of 

 the balance referred to at the beginning of this note. The 

 mass of the beam is over 200 grins. The deflexions were 

 observed by means of a telescope and scale. The vertical 

 scale of the diagram represents deflexions in cms. caused 

 by a load of T J mgm. at one end of the beam. The hori- 

 zontal readings are taken from the graduated head of the 

 adjusting screw. The position of derived graphically 

 from the 1st and 3rd curves corresponds to 106°. Using this 

 value, and the constant of the 2nd curve obtained graphi- 

 cally, the centre of this curve is found to correspond to 

 46°*7 instead of 48°'8 as obtained from the curve alone. 

 This gives an indication of the degree of approximation of the 

 experimental values to the theory. 



LV. Notices respecting New Books, 



A Simplified Method of Tracing Rays through any Optical System. 

 By Lujdwik Silberstein, Ph.D. Pp. vii + 37. Longmans, 

 Green & Co. Price 5s. net. 



r PHIS little book deals with a subject which is of the utmost 

 -*■ practical importance to all concerned with optical instruments. 

 By using throughout the vectorial method the author has effected 

 a considerable simplification of what is usually a laborious and 

 complicated task, namely, the following of a ray through a system 

 composed of any number of lenses, prisms, and mirrors. The 

 knowledge of vectors required to enable the reader to make 

 effective use of the book can be obtained in a few hours by anyone 

 possessing the mathematical acquirements of the average worker 

 in optics. The deduction of the vectorial form of the refraction 

 (which really includes the reflexion) formula and the transfer 

 formula for spherical surfaces occupies only a few pages, and the 

 rest of the book is devoted to showing how the formulae may 

 be applied to numerical cases, and to expounding the author's 

 dyadic operator for multiple reflexions. Jt is an original and 

 suggestive little book, and we note with interest that it is written 

 from the research department of Messrs. Hilger, whose name 

 stands for so much in the realm of optical instruments. 



