Geometrical Optics. 247 



7. Formula of the Lenticular Mirror. 



The lenticular mirror consists of a lens one face of which 

 is silvered, so that the light passes twice through the lens, and 

 suffers an intermediate reflexion at the silvered surface. If 

 the focal power of the lens be $ v and the curvature of the 

 mirror-surface be My then the total curvature which the 

 system impresses upon a plane wave will be equal to 

 2^ + 2^, and there will be a reversal of the direction of 



the light, so that ^ = _ 2 (<* l+ <%). . ..*.-. (19) 



8. A Dioptrie Spherometer. 



In order the better to bring to practical issues the method 

 of treating lens problems by curvatures, the author designed 

 a special spherometer. In this instrument the readings of the 

 scale are caused to indicate directly the dioptrics of the cur- 

 vature ; that is to say, one whole turn of the micrometric 

 screw corresponds accurately to a curvature having one metre 

 as its radius. In the particular instrument now exhibited 

 the pitch of the micrometric screw is 1 millimetre. To make 

 this correspond to a curvature of one dioptrie, the radius of 

 the contact-circle on which the three feet stand must be 44* 7 1 

 millimetres. For, by reference to fig. 1, it will be seen that 

 the radius PM of the contact-circle is such that 



(PM) 2 = AM.MB = 2rs- 5 2 , 



where s is the sagitta of the curve. Hence, if ?'=] 000 milli- 

 metres, and s=l millimetre, PM= \/l999 = 44'7102. The 

 screw itself is cut on a steel tube 8 millimetres in diameter. 

 The tips of the three feet and of the central point are of 

 phosphor-bronze, which does not scratch glass. The arms 

 carrying the three feet are girder-shaped, thin, deep ; so as to 

 be very firm vertically ; lateral flexure is immaterial. The 

 tips of the three feet are adjusted by filing to chisel-shaped 

 edges, forming little tangents to the imaginary circle of 

 contact. The divided circle is not, as ordinarily, cut upon a 

 flat plate, but is cut upon a thin cylinder of aluminium-bronze 

 affixed to the screw by a light spider with three arms. The 

 whole instrument weighs only 78 grammes. It was con- 

 structed for the author by Messrs. Nalder Brothers. 



The formula for the focal power of any lens (formula 

 no. (11), p. 244) consists of two factors — one depending 

 solely on the shape of the lens, the other upon its material. 



The latter factor, — — , is a mere numeric; whilst the 



