The Tangent Lens-Gauge. 257 



measured is placed on a board raised a couple of inches from 

 the table, and the inclined plates are allowed to rest upon 

 its curved surface, the other end of the instrument being sup- 

 ported on the point of an adjustable brass screw which passes 

 through the board from beneath. 



On examining the arrangement by reflected light, Newton's 

 rings can be seen at the two points where the plane surfaces 

 touch the sphere. Since the angle between the planes is 

 constant, the distance between the two points of contact is 

 directly proportional to the radius of the curved surfaces, 

 being in fact the chord of the angle which they subtend at 

 the centre of the sphere. The distance between the centres of 

 the two systems of Newton's rings is measured with a 

 micrometer microscope furnished with a vernier. Such 

 instruments, reading to -gV mm., can now be obtained at a 

 moderate cost, and are required for several purposes in a 

 course on practical physics. They should, however, be furnished 

 with a jointed arm so that the tube may be inclined from the 

 vertical — this I effect by unscrewing the microscope body 

 from the arm, and screwing in its place a short wooden plug 

 to the side of which I attach, with a small bolt and nut, a 

 brass plate carrying a split tube to hold the microscope, which 

 can by this means be fixed at any angle. 



Writing I for the distance between the two systems of 

 Newton's rings, and 6 for the angle between the normals to 

 the plane surfaces of the lens-gauge, the radius of curvature 

 of the sphere is given by the formula 



K = /-r- chord 6, 



and since is constant the calculation is extremely simple, 

 when once the value of chord 6 has been determined. There 

 are three methods by which this may be conveniently 

 effected : — 



(1) The tangent gauge may be applied to a sphere of which 

 the diameter has been accurately measured with the sphere- 

 meter. 



(2) The angle between the normals to the plates may be 

 determined with the goniometer, and the ratio found from a 

 table of chords. 



(3) A modification of the method sometimes used for find- 

 ing the index of refraction of glass may be employed. The 

 lens-gauge is supported vertically at one end of a drawing- 

 board, and a pin or needle P x fixed upright in the board a 

 few centimetres from it. Two other pins P 2 and P 3 are then 

 arranged at equal distances from the first, so that the reflexion 



Phil. Mag. S. 5. Vol. 43. No. 263. April 1897. X 



