464 PHILOSOPHICAL TRANSACTIONS. [aNNO 1754. 



Obs. 8. — ^Though tlie centres of the segments may be drawn from their coin- 

 cidence, by removing the segments in any direction whatever ; yet the most con- 

 venient way for this purpose is, to slide their straight edges one along the other, 

 till they are removed, as the figure in the margin represents them : 

 for thus they may be moved without suffering any false light to 

 come in between them. And by this way of removing them, the 

 distance between their centres may be very conveniently measured, 

 viz. by having a Vernier's division fixed to the brass work, that 

 holds one segment, so as to slide along a scale on the plate to 

 which the other part of the glass is fitted. 



Obs. Q. — As the images of the same object are separated by the motion of the 

 segments; so those of different objects, or different parts of the same object, 

 may be made to coincide. Suppose the sun, moon, or any planet, to be the 

 object ; their two images may, by this contrivance, be removed till their oppo- 

 site edges are in contact : in which case the distance between the centres of the 

 two images will be equal to the diameter of either ; and so of any other object 

 whatever. 



Obs. 10. — This divided glass may be used as a micrometer, 3 different ways. 

 In the first place, it may be fixed at the end of a tube, of a suitable length to 

 its focal distance, as an object glass ; the other end of the tube having an eye- 

 glass fitted as usual in astronomical telescopes. 2dly, It may be applied to the 

 end of a tube much shorter than its focal distance, by having another convex 

 glass within the tube, to shorten the focal distance of that which is cut in two. 

 Lastly, it may be applied to the open end of a reflecting telescope ; either of the 

 Newtonian, Gregorian, or Cassegrain construction. And though this last me- 

 thod is much the best, and most convenient, of the three ; yet as the first is the 

 most natural, as well as the easiest to be understood, it will be proper to explain 

 it fully, and to demonstrate the principles on which this micrometer is con- 

 structed, by supposing it made use of in the first way : which being done, the 

 application of it to other methods will be readily understood. 



Having thus, by the foregoing observations, given a general idea of the nature 

 and effects of this divided object-glass, Mr. D. proceeds to demonstrate the prin- 

 ciples from which the measures of the angles are to be obtained by this instru- 

 ment, by the following propositions. 



■ Prop. I. Suppose a divided object-glass fixed at the end of a tube, according to 

 the first method, and the tube directed to the object intended to be measured ; 

 and suppose also the segments removed from their original position, as directed 

 under Obs. 8, till the opposite edges of the two images are seen in contact at the 

 focus of the eye-glass : then the angle subtended by the distance between the 



