32 Mr. C. V. Boys on Measurement of 



mally — that is, have left the lens and returned to it as a 

 parallel beam ; therefore the card is at the principal focus. 

 For a plane glass surface a piece of plate glass blacked at the 

 back, or the surface of a prism may be used. The observations 

 of the distances F and / can be easily and accurately made ; 

 then the radius of curvature may be found from the formula 



as I shall presently show. 



Before doing so, however, I think it well to describe the 

 most accurate method of observing the distances F and /. The 

 card with the pin-hole is convenient ; but it is difficult to find 

 the place with great accuracy where the focus is most sharply 

 defined, and to measure the distance when found. All diffi- 

 culty is completely avoided by the following plan: — Take a 

 piece of thin sheet metal, of the size and shape shown in 

 PI. I. fig. 1, and fix in front of it, in the position shown by 

 the dotted line, a small reflecting-prism, so that, when a small 

 bright flame is placed on one side of the prism, a beam of 

 light leaves the slit in the plate. Replace the card by this 

 plate and prism, and move the lens till the aerial image of the 

 slit is formed in the corner, close by the edge of the prism. 

 To examine the position of the image with greater precision, 

 an ordinary positive eyepiece will be found convenient. When 

 the image and the slit are equally distant from the lens, there 

 will be no relative movement on moving the eye ; if there is 

 relative movement, the distance between the lens and the plate 

 must be increased or diminished according as the plate or the 

 image appears to move with the eye. When the distance has 

 been properly adjusted, it is easily measured by resting a scale 

 on the continuation of the lower edge of the slit, and moving 

 it till it touches the surface of the lens. The position of the 

 edge of the prism or of the slit may then be read with great 

 accuracy; and it will be found that, on repeating the obser- 

 vations several times, a discrepancy more than a tenth of a 

 millimetre between any of the measures need not occur. 



Instead of observing the position with an eyepiece, the 

 Foucault plan may be adopted. Place the eye immediately 

 behind the edge of the prism, so that all the light forming the 

 image enters the eye. Move the prism laterally towards the 

 image, which of course moves to meet it, and observe whether 

 the light which fills the lens dies away uniformly, or whether 

 it seems to retreat from one edge of the lens. If the retreat 

 is in the same direction as the movement of the prism-plate, 

 the distance is too small ; if in the opposite direction, too 



