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 8, 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 a, 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 b, when the index 
marks p; the are o p measures the inclination of the two surfaces a 6, 
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. Toany . 
Y 
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 ¢, which (by what- 
ever means) fixes the position of the object; while an index ¢ can be 
either fixed to the inner c, or to the outer circle a, by clamping, or 
can move independently. First, the index 7 being clamped to c, then 
pointing to 0, while ¢ is directed to the object x; the part ¢ is then 
turned to y, while 7 moves over an arc 0 1, equal to that between x 
and y, and points tol. Secondly, 7 is clamped to a at 1, and un- 
clamped from c; ¢is moved back on x; 7is unclamped from a, and 
clamped toc; andi moving with 7 is directed to ¥; 7 consequently 
comes to 2, passing over an equal arc. Thirdly, the same operation is 
repeated, and 7 comes to 3, and so on for as many times as may be 
desired. The are read off in each instance will, from the errors of 
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