Method of determining Curvature of Spherical Surfaces. 223 



angles to itself until the coincidence is obtained. The vertex 

 of the spindle then lies on the axis of the table. Since the 

 projection of the axis of the spindle on the plane of the board 

 has been made parallel to the edge of the board, the axis of 

 the spindle intersects that of the table for all positions of the 

 board along the scale. These adjustments may, of course, be 

 made once for all, but for purposes of instruction it is best 

 that each student should make them for himself. 



§ 7. The face-plate is now attached to the spindle and the 

 lens or mirror to be tested is fixed to the adjustable plate by 

 wax. In the case of a lens, the back surface should, for 

 convenience, be smeared with a mixture of lamp-black and 

 vaseline or be coated with black varnish to stop reflexion at 

 that surface. The spindle is then rotated and some object is 

 observed by reflexion at the spherical surface. If the rotation 

 cause a motion of the image, the three adjusting screws are 

 manipulated until the image remains stationary when the 

 spindle is revolved. The centre of curvature then lies on 

 the axis of the spindle. During the adjustment the table- 

 top is clamped so that it cannot rotate. 



A piece of ground glass with a fine vertical line drawn 

 on it forms a convenient object ; the glass should be well 

 illuminated. A fixed microscope may be used to facilitate 

 the adjustment. The spindle is turned into the position in 

 which the image of the vertical line is as far to the right as 

 possible. The plate carrying the surface is then made to 

 move as nearly as possible about a vertical axis by turning 

 the appropriate screw or screws, so that the image moves to 

 the left through the proper distance. The success of the ad- 

 justment is then tested by rotating the spindle ; if necessary 

 a second adjustment is made. 



The preliminary adjustments are now complete. If they 

 are only nearly but not quite perfect, the errors which they 

 cause in the radius of curvature as found by this method will 

 be very small, since these errors of radius depend on the 

 second powers of the errors in the preliminary adjustments. 



§ 8. The board carrying the lathe-head is now set into the 

 " first position " in which the centre of curvature of the 

 surface lies on the axis of revolution of the table. The 

 ground glass with the vertical line is set up in such a position 

 that the image of the vertical line which is observed in the 

 microscope is formed by rays which fall nearly normally 

 upon the surface. If the image move when the table is 

 turned backwards and forwards about its axis, the board 

 carrying the lathe-head is moved along the scale until 

 the image remains at rest. The centre ol' curvature then 



