[From the Cambridge Philosophical Society Proceedings, VoL I. pp. 173 175.] 



X. On the Elementary Tlieory of Optical Instruments. 



THE object of this communication was to shew how the magnitude and 

 position of the image of any object seen through an optical instrument could 

 be ascertained without knowing the construction of the instrument, by means 

 of data derived from two experiments on the instrument. Optical questions 

 are generally treated of with respect to the pencils of rays which pass through 

 the instrument. A pencil is a collection of rays which have passed through one 

 point, and may again do so, by some optical contrivance. Now if we suppose 

 all the points of a plane luminous, each will give out a pencil of rays, and 

 that collection of pencils which passes through the instrument may be treated 

 as a beam of light. In a pencil only one ray passes through any point of 

 space, unless that point be the focus. In a beam an infinite number of rays, 

 corresponding each to some point in the luminous plane, passes through any 

 point ; and we may, if we choose, treat this collection of rays as a pencil 

 proceeding from that point. Hence the same beam of light may be decomposed 

 into pencils in an infinite variety of ways ; and yet, since we regard it as the 

 same collection of rays, we may study its properties as a beam independently 

 of the particular way in which we conceive it analysed into pencils. 



Now in any instrument the incident and emergent beams are composed 

 of the same light, and therefore every ray in the incident beam has a 

 corresponding ray in the emergent beam. We do not know their path within 

 the instrument, but before incidence and after emergence they are straight 

 lines, and therefore any two points serve to determine the direction of each. 



Let us suppose the instrument such that it forms an accurate image of a 

 plane object in a given position. Then every ray which passes through a given 



