VOL. LXIX.] PHILOSOPHICAL TRANSACTIONS. 559 



the zero, which will appear no inconsiderable advantage to observers who know 

 how much easier it is to ascertain the contact of the external edges of two 

 images, than their perfect coincidence. A short explanation of the annexed 

 drawings will make the construction and the properties of this micrometer 

 obvious. 



I divided the small speculum of a reflecting telescope, of Cassegrain's con- 

 struction, into 2 equal parts, by a plane across its centre; and by inclining the 

 halves of the speculum to each other, on an axis at right angles to the plane that 

 separated them, I obtained 2 distinct images. The satisfaction I received on the 

 first trial was checked by the apparent impossibility of reducing this principle to 

 practice. The angular separation of the 2 images in this case being half the 

 angular inclination of the 2 specula, it required an index of an unmanageable 

 length, to allow the quantity of 1 second of a degree to become visible. Some 

 time afterwards, on revising the principle, 1 considered, that if both the halves 

 of the mirror turned on their centre of curvature, there could be no alteration 

 in their relative inclination to each other from their motion on this centre; and 

 that any extent of scale might be obtained, by fixing the centre of motion 

 at a proportional distance from the common centre of curvature. This will be 

 better understood from the annexed drawing. 



In fig. 8, pi. 5, A represents the small speculum divided into 2 equal parts; 

 one of which is fixed on the end of the arm b; the other end of the arm is 

 fixed on a steel axis x, which crosses the end of the telescope c. The other 

 half of the mirror a is fixed on the arm d, which arm at the other end termi- 

 nates in a socket y, that turns on the axis, x; both arms are prevented from 

 bending by the braces aa. G represents a double screw, having one part e cut 

 into double the number of threads in an inch to that of the part g: the part e 

 having 100 threads in 1 inch, and the part g 50 only. The screw e works in a 

 nut F in the side of the telescope, while the part g turns in a nut h, which is 

 attached to the arm b ; the ends of the arms b and d, to which the mirrors are 

 fixed, are separated from each other by the point of the double screw pressing 

 against the stud h, fixed to the arm d, and turning in the nut h on the arm b. 

 The 1 arms b and d are pressed against the direction of the double screw eg by 

 a spiral spring within the part n, by which means all shake or play in the nut h, 

 on which the measure depends, is entirely prevented. From the difference of 

 the threads on the screw at e and g, it is evident that the progressive motion of 

 the screw through the nut will be half the distance of the separation of the 

 2 halves of the mirror, and consequently the half mirrors will be moved equally 

 in contrary directions from the axis of the telescope c. 



The wheel v fixed on the end of the double screw has its circumference 

 divided into 100 equal parts, and numbered at every 5th division with 5, 10, &c. 



