VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS. '255 



glass; as the greatest space pg is to the focal distance of the object-glass, as the 

 sum of the sines of the refractions of the prism is to the radius. 



There is a 3d way, and perhaps the best, of placing the prisms, so as to 

 touch each other along their sides which are at right angles to the common sec- 

 tions of their refracting planes. In this disposition of the prisms, the images 

 will be equally enlightened, namely, each with half the rays which fall on the 

 object-glass, wherever the prisms be placed between the object-glass and eye-glass. 



From what has been shown it appears, that this instrument, which may be 

 properly called the prismatic micrometer, will measure any angle that does not 

 exceed the sum of the refractions of the prisms, excepting only very small angles, 

 which cannot be taken with it, on account of the vanishing of the pencils of 

 rays at the juncture of the 2 prisms near the focus of the object-glass; that it 

 will afford a very large scale, namely, the whole focal length of the object-glass 

 for the greatest angle measured by it; and that it will never be out of adjust- 

 ment; as the point of the scale where the measurement begins (or the point of 

 o) answers to the focus of the object-glass, which is a fixed point for celestial 

 objects, and a point very easily found for terrestrial objects. All that will be 

 necessary to be done, in order to find the value of the scale of this micrometer, 

 will be to measure accurately the distance of the prisms from the focus, when the 

 instrument is set to measure the apparent diameter of any object subtending a 

 known angle at the centre of the object-glass, which may be easily found by ex- 

 periment, as by measuring a base and the diameter of the object observed placed 

 at the end of it, in the manner practised with other micrometers; for the angle 

 subtended by this object, will be to the angle subtended by a celestial object, or 

 very remote land object, when the distance of the prisms from the principal focus 

 is the same as it was found from the actual focus in the terrestrial experiment, as 

 the principal focal distance of the object-glass is to the actual focal distance in 

 the said experiment. 



It will, I apprehend, be the best way in practice, instead of I prism, to use 2 

 prisms, refracting contrary ways, and so divide the refraction between them, as 

 represented in fig. Q and JO. Achromatic prisms, each composed of 2 prisms 

 of fiint and crown glass, placed with their refracting angles contrary ways, will 

 undoubtedly be necessary for measuring angles with great precision by this in- 

 strument: and I can add with pleasure, that I find by experiment made with this 

 instrument, as it was executed by Mr. Dollond with achromatic prisms, ground 

 with great care for this trial above a year ago, that the images after refraction 

 through the prisms appear very distinct; and that observations of the apparent 

 diameters of objects may be taken in the manner here proposed with ease and 

 precision. 



Two or more sets of prisms mav be adapted to the same telescope, to be used 



