Wadsworth — Simple and Accurate Cathetorneter. 47 



An inspection of these two tables shows that in the case of 

 glass of the higher refractive index (n = 1'55), the maximum 

 value of d is only 0*2 per cent of f(<p), and since the maxi- 

 mum shifting of the image need never exceed l mm (if compari- 

 son is made on a mm. scale), the corresponding correction to 

 the tangent value is only - 5 ^Q mm and may be disregarded. In 

 this case we may read off the value of A directly on a straight 

 scale s s by means of a pointer, u, which consists of a thin 

 plate of glass or mica on which is ruled a fine radial line. The 

 distance ro from o, to the point of intersection of this line 

 with the longitudinal line s s on the scale, equals c'o tang <p and 

 hence is directly proportional to A. If we make c'o equal to 

 1T| t in mm., then each mm. on the scale ss corresponds to a 

 shifting of the image through ■^ r mm . For an angle of 30° 

 A^= \ t., hence for a shifting of l mm corresponding to this angle, 

 the plate P must be 5 mm thick, and the distance c'o therefore 

 about 89 mm as laid off in fig. 5. The scale s s of fig. 4 is grad- 



uated in 2 mm intervals so that such intervals correspond to 

 _^mm ? j-^j. jj. j s eag y to ge £ an( j reac [ t | ie p OS ition of the pointer 



to -jV div. or si/-'. 



In the case of glass of refractive index 1*5 the proportionality 

 between the scale readings obtained in this manner and the 

 value of A is not so exact, the error amounting in case of an 

 angle of 30° to nearly f of 1 per cent or to nearly O01 mm . 

 This is a quantity too large to be neglected. Poynting sug- 

 gests a very ingenious system of link work, whereby the read- 

 ings on the scale may be made directly proportional to A for 

 all values of <p ; but this, as he himself recognizes, is hardly 

 practicable on account of mechanical difficulties. We may, 

 however, obtain the desired result very much more simply. 

 An inspection of the values of d in Table I will show that 



