Simple and Accurate Cathetometer. 131 



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

 value of 8 is only 02 per cent, of/ ((/>), and since the maxi- 

 mum shifting of the image need never exceed 1 millim. (if 

 comparison is made on a miliim. scale), the corresponding 

 correction to the tangent value is only 3-^ millim. and may 

 be disregarded. In this case we may read off the value of A 

 directly on a straight scale 5 s by means of a pointer, w, which 

 consists of a thin plate of glass or mica on which is ruled a 

 fine radial line. The distance ro from 0, to~the point of inter- 

 section of this line with the longitudinal line s s on the scale, 

 equals c'o tang </>, and hence is directly proportional to A. If 

 we make c'o equal to 17J t in millim., then each millim. on 

 the scale s s corresponds to a shifting of the image through 

 i^y millim. For an angle of 30° A=i-£, hence for a shifting 

 of 1 millim. corresponding to this angle, the plate P must be 

 h millim. thick, and the distance c'o therefore about 89 millim. 

 as laid off in fig. 6. The scale §5 of fig. 5 is graduated in 



Fig. 6. 



2 millim. intervals so that such intervals correspond to ^ 

 millim., but it is easy to set and read the position of the 

 pointer to j 1 ^ div. or -jIq millim. 



In the case of glass of refractive index 1*5 the proportion- 

 ality 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 j of 1 per cent, or to nearly O'Ol 

 millim. This is a quantity too large to be neglected. Poyn- 

 ting suggests a very ingenious system of link-work, whereby 

 the readings on the scale may be made directly proportional 



K 2 



