162 MALUS. 



added to the perfection of the English instrument by 

 giving it the principle of repetition.* He desired thus to 



other object having two plane surfaces a and b, capable of reflecting 

 light, is fixed at the centre of a graduated circle, to its index i. It is 

 first brought into such a position that the image of an object x, by re- 

 flexion from the surface o, is seen by the eye coincident with another 

 object y, seen directly; the index marking 0. It is then turned round 

 till the same thing is observed with the surface 6, when the index 

 marks/); the arc op measures the inclination of the two surfaces a >, 

 since the surface b now occupies the same position with respect to the 

 circle which a did before. Translator. 

 * The principle of " repetition " may be thus briefly stated. To any 



graduated circular instrument intended for measuring the angular 

 distance of two objects x Y, there is added an inner circle c, moving 

 about the same centre, to which is fixed the part t, which (by what- 

 ever means) fixes the position of the object; while an index i can be 

 either fixed to the inner c, or to the outer circle a, by clamping, or 

 can move independently. First, the index i being clamped to c, then 

 pointing to 0, while t is directed to the object x; the part t is then 

 turned to y, while i moves over an arc o 1, equal to that between x 

 and Y, and points to 1. Secondly, i is clamped to a at 1, and un- 

 clamped from c; t is moved back on x; i is undamped from , and 

 clamped to c ; and t moving with i is directed to Y ; i consequently 

 comes to 2, passing over an equal arc. Thirdly, the same operation is 

 repeated, and i comes to 3, and so on for as many times as may be 

 desired. The arc read off in each instance will, from the errors of 



