612 SCIENTIFIC RECOKD FOR 1885. 



of homogeneous light is unim])ortaut so loug as the fourth power of the 

 angular seuii-aperture does not exceed the ratio of the wave length to 

 the focal distance ; a condition satisfied by a lens of 3 feet focus pro- 

 vided that the aperture be less than 2 inches. He has now discussed 

 the accuracy of focus necessary for sensibly perfect definition, and has 

 reached the result that a displacement from the true focus will not 

 impair definition, provided it is less than the product of the wave length 

 by the square of the ratio of the focal length to the semi-aperture. 

 Hence the linear accuracy required is the same whatever the absolute 

 aperture of the object glass may be, provided that the ratio of aperture 

 to focal length be preserved. Experimental results confirmed closely 

 this theoretical conclusion. [Phil. Mag., October, 1885, Y, xx, 354.) 



D'Ocagne has shown that if the two sides of a square and the diag- 

 onal be divided into the same number of equal parts, and a straight 

 line be drawn from the point on one side corresponding numerically to 

 one of the conjugate focal distances through the number of the division 

 on the diagonal representing the principal focal length, this line will 

 cut the other side at a point representing numerically the other conju- 

 gate focal distance. Conversely any right line whatever drawn through 

 a point on the diagonal corresponding numerically to the principal 

 focus of a lens cuts the sides at points representing its conjugate foci 

 as it moves about this point as a center. In practice a rod may be 

 pivoted at the given center. {J. Pliys., December, 1885, II, iv, 555.) 



Kayleigh has described a monochromatic telescope which is a modi- 

 fication of Maxwell's color box. In this well-known instrument light 

 passes through a slit in the focus of a collimating lens and traverses in 

 succession this lens, a prism, and another lens, by which it is brought to a 

 focus upon a plane surface in which is a movable slit, the eye placed be- 

 hind this slit receiving light approximately monochromatic. If now, in 

 addition, a lens be placed just behind the first slit so as to bring some 

 distant object into focus at a convenient distance from the eye this 

 object will be seen by the light that would enter the eye in the simple 

 color box. The instrument is to be used to compare lights of different 

 colors for practical purposes. [Phil. Mag., June, 1885, V, xix, 446.) 



Malcolm kas adjusted his binocular glass to eyes of different focal 

 lengths by arranging one of the eye-pieces so that it can be moved 

 through a small range in or out by turning a milled bead. An index 

 arrangement is attached by which a given setting may always be repro- 

 duced. The unaltered tube is brought to the most perfect focus pos- 

 sible in the ordinary way, using only one eye. Then the other tube is 

 used with the other eye and focused accurately with its own adjustment, 

 the oth^r remaining unchanged. {Piril. Mag., June, 1885, V, xix, 461.) 



3. Dispersion and Color. 



Wiillner, in 1883, showed that the index of any transparent substance 

 could be very exactly represented in terms of wave length by a formula 

 giv^n by him. Since that time he has compared the experimental r§- 



