ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 767 



glass, due to the stress, produces in the vertically polarized ray an up- 

 wards deflection, 9 X = x radians, and in the horizontally polarized 



ray a deflection, 9 2 = — ^= — radians, where t is the thickness of the glass, 



I the second moment of area of the cross-section about the " neutral 

 axis," and C x and C 2 are the stress-optical co-efficients for the vertically 

 and horizontally polarized rays respectively ; the stress-optical co-efficient 

 for any ray being the increase in the index of refraction for unit tension, 

 or, what is equivalent, the additional retardation introduced per unit 

 thickness per unit tension. In the above, M is reckoned positive when 

 the slab is bent concave downwards. The author gives full details of his 

 apparatus and of his numerical results. 



Southall's Principles and Methods of Geometrical Optics.* — In 

 this work of C2G pages, James P. C. Southall has compiled for the 

 English-speaking student a treatise based largely upon the most recent 

 writings of German investigators. He expressly acknowledges his 

 obligations to Czapski's epoch-making book, Die Theorie der Optischen 

 Instrumente nach Abbe, and to M. von Bohr's Die Theorie der Op- 

 tischen Instrumente, i. (Berlin, 1904). References to many of the 

 most important contributions to optical literature, French and English, 

 as well as German, of the last fifteen years are freely made. The older 

 writers are also frequently quoted. The author does not hesitate to 

 demonstrate his theorems by the help of modern geometry. Thus in 

 Chapter V. (Reflexion and refraction of paraxial rays at a spherical 

 surface) and Chapter VII. (Geometrical theory of optical images) he 

 makes great use of the properties of harmonic ranges and of conjugate 

 planes. In Chapter XII. he deals with Seidel's extension of Gauss's 

 methods, whereby the inclusion of terms of a higher order in the series- 

 developments made it possible to derive certain elegant and entirely 

 general formulas in a simple way. These formulae enable one to perceive 

 almost at a glance how the faults in an image formed by a centred system 

 of spherical refracting surfaces are due partly to the size of the aperture, 

 and partly also to the extent of the field of view. Prism-spectra and the 

 chromatic aberrations of dioptric systems are included under the head of 

 " Colour phenomena" in Chapter XIII. 



The work is a very valuable contribution to the study of optics, and 

 should do a great deal to bring an English reader abreast of the latest 

 continental developments. 



(6) Miscellanecms. 



Method for Testing Screws.j — J. A. Anderson shows how a screw 

 may be tested quite independently of the divided head or end bearings. 

 Consider a screw whose error is a simple periodic one, so that the relation 

 between the distance x advanced by a perfectly fitting nut and the an- 

 gular rotation 9 of the screw is x = c6 -\-b sin 9, where c and b are 



* Macmillan Co., Ltd., Loudon and New York, 1910. 



f Johns Hopkins Univ. Circular, No. 2 (1910) pp. 14-19 (1 pi.). 



