Notices respecting New Books. 513 



out the sliding supports may be used for finding the focal 

 length and principal points of a convex combination. 



It would, no doubt, be easy to construct the apparatus so 

 that the same screw could move both the pair of sliding sup- 

 ports and the pair of micrometers independently. But it 

 seems a simpler method, after first finding the principal foci, 

 to obtain with only one of the convex lenses an image of its 

 cross wires on a suitably placed screen, by rays passing 

 through both the lens and the combination. The position of 

 the conjugate focus of this image can then be found by moving 

 the combination out of the axial plane and obtaining the image 

 of the cross wires formed by rays passing through the convex 

 lens alone. The distances of these conjugate points from the 

 principal foci are then measured, and the focal length is given 

 by the formula dd'=f 2 . 



A support of the kind described above, furnished with a 

 convex lens and cross wires, would be required in many cases 

 for determining the focal or symmetric points of positive or 

 negative systems ; but in no case would a knowledge of the 

 focal length of the lens or any calculation involving it be 

 necessary. 



LXV. Notices respecting New Books. 



Higher Geometry, containing an Introduction to Modem Geometry 

 and Elementary Geometrical Conies. By ~W. J. Macdoxald. 

 (Edinburgh: J. Thin; 184 pp.) (i.) 



Supplement to " Euclid revised" being an Introduction {within the 

 limits of Euclidian Geometry) to the Lemoine and Brocard Points, 

 Lines, and Circles. By E. C. J. Nixox. (Oxford : Clarendon 

 Press ; pp. 378-426.) (ii.) 



Pitt Press Euclid, iii.-iv. By H. M. Tatloe. (pp. 167-326.) (hi.) 



Geometrical Deductions. Book I. By J. Blaikie and W. Thom- 

 son. (London: Longmans ; pp. viii-|- 138.) (iv.) 



WE have grouped these elementary geometrical Text-books 

 together and briefly indicate their contents. 



(i.) is a short course which the author has used in his own 

 classes for many years, so that it represents what an experienced 

 teacher has found suitable for junior pupils. It deals with the 

 fundamental theorems of Harmonic pencils and " Cross Eatios " in 

 a clear manner, and after a brief look at Linkages introduces the 

 student to the simpler properties of the Conic Sections. The book 

 furnishes a good introduction to Housel, Dr. C. Taylor, and other 

 writers on the subject. 



(ii.) is an account, of the Circles and Lines discussed, with proofs 

 that must satisfy the most rigid adherent of Euclidian methods. 

 This little pamphlet will do much, we feel sure, to make this 



Phil, Mag. S. 5. Vol. 31. No. 193. June 1891. 2 



