THEORY OF ETHER 153 



cover the mirror, if large, with dull black paper, leaving a 

 small hole at the centre for observation. The needle is now 

 adjusted until the point of the image just touches the point of 

 the needle, and agrees with it in size. The coincidence must 

 be maintained when the eye is changed in position. 



When this adjustment is made, and the distance of the 

 needle-point from the mirror measured, it will be found to be 

 the same as the radius of the spherical surface of which the 

 mirror forms a part that is, the needle-point and its image 

 are at the geometrical centre of the reflecting surface. This 

 may be proved by using the spherometer to find the curvature 

 of the mirror. Knowing that the three fixed feet of the sphero- 

 meter are equidistant, and form an equilateral triangle of side I 

 (which may be measured), and the distance, a, through which 

 the centre leg has been moved, we get from Euc. iii. 35, if r 

 stand for the radius of the sphere of which a segment, of 

 thickness a, has been cut off by the plane of the triangle, 



, a 

 whence r = - + . 



Qa 2 



- is the radius of the circle circumscribing the triangle formed 



N/3 



by the legs, and corresponds with the distance a b in fig. 51, 

 b e corresponds with a, and db with 2r a. 



Half the distance thus found is called 

 the focal length, or the focus is a point mid- 

 way between the mirror and its centre of 

 curvature. 



When light passes through a transparent 

 body, it is changed in direction, except when 

 it is normal to the surfaces of entrance and Fig 51 



emergence. When the body is shaped like 

 a lens, certain properties, varying with the shape and material 

 of the lens, are the result of this change in direction of 

 transmitted light. 



