324 On the Law of Reciprocity in Diffuse Reflexion. 



maximum but is mixed in sign. Suppose their respective 

 powers were + 2 dioptries and — 2 dioptries ; they will when 

 crossed not act as either a +4 dioptrie cylinder, or as a 

 —4 dioptrie cylinder, but can be made to act as such by 

 adding at choice either a -f 2 dioptrie spherical lens or a — 2 

 dioptrie spherical lens, to neutralize the refractive effects in 

 one or other of the meridians. When crossed at intermediate 

 angles the spherical lens required to neutralize, and so produce 

 the effect of a simple cylinder, would be of some intermediate 

 power. This is a slight inconvenience ; but a more serious 

 one exists in the circumstance that in rotating one about the 

 other the axis of the resultant cylindrical effect takes a varying 

 obliquity. This objection is not removed by rotating the two 

 lenses in opposite directions simultaneously. 



A more convenient combination to give varying degrees of 

 cylindricity is the following : — Let two lenses be ground, 

 each being a mixed equi-cylinder consisting of a concave and 

 convex ground at right-angles to one another on the opposite 

 faces of the glass. Two such mixed cylinders, if rotated with 

 equal motion in opposite directions, will give a varying 

 cylindricity of fixed direction in space. With the axes of 

 4- cylindricity coincident they give the maximum ; but when 

 each is rotated to 45°, one to the right, the other to the left, 

 their resultant is zero. In intermediate positions the value 

 of the resultant varies according to the square of the cosine 

 of double the angle through which either has been moved 

 (i. e. to the square of the cosine of the angle between their 

 axes), but it remains fixed in direction. When each is rotated 

 beyond 45° they begin again to act as a cylindrical lens, but 

 with the resultant axis of cylindricity negative in the fixed 

 direction in which formerly it was positive. An instrument 

 thus constructed may be graduated so as to be direct-reading. 



XXVIII. On the Law of Reciprocity in Diffuse Reflexion. 

 By Lord Rayleigh, F.R.S.* 



IN the current number of the Philosophical Magazine 

 (vol. xlix. p. 199) Dr. Wright discusses the question of 

 the amount of light diffusely reflected from a given area of a 

 matt surface as dependent upon the angle of incidence (i) and 

 the angle of emission (e). According to Lambert's law the 

 function of i and e is 



cos i cos e ; (1) 



and this law, though in the present case without theoretical 



* Communicated by the Author, 



