272 ON THE GENERAL LAWS OF OPTICAL INSTRUMENTS. 



Geometrical Optics, as conceived by Cotes and laboured by Smith, has fallen 

 into neglect, except among the writers before named. Smith tells us that it 

 was with reference to these optical theorems that Newton said "If Mr Cotes 

 had lived we might have known something." 



The investigations which I now offer are intended to show how simple and 

 how general the theory of instruments may be rendered, by considering the 

 optical effects of the entire instrument, without examining the mechanism by 

 which those effects are obtained. I have thus established a theory of " perfect 

 instruments," geometrically complete in itself, although I have also shown, that 

 no instrument depending on refraction and reflexion, (except the plane mirror) 

 can be optically perfect. The first part of this theory was communicated to 

 the Philosophical Society of Cambridge, 28th April, 1856, and an abstract will 

 be found in the Philosophical Magazine, November, 1856. Propositions VIII. 

 and IX. are now added. I am not aware that the last has been proved before. 



In the following propositions I propose to establish certain rules for deter- 

 mining, from simple data, the path of a ray of light after passing through any 

 optical instrument, the position of the conjugate focus of a luminous point, and 

 the magnitude of the image of a given object. The method which I shall use 

 does not require a knowledge of the internal construction of the instrument and 

 derives all its data from two simple experiments. 



There are certain defects incident to optical instruments from which, in the 

 elementary theory, we suppose them to be free. A perfect instrument must 

 fulfil three conditions: 



I. Every ray of the pencil, proceeding from a single point of the object, 

 must, after passing through the instrument, converge to, or diverge from, a 

 single point of the image. The corresponding defect, when the emergent rays 

 have not a common focus, has been appropriately called (by Dr Whewell) 

 Astigmatism. 



II. If the object is a plane surface, perpendicular to the axis of the 

 instrument, the image of any point of it must also lie in a plane perpendicular 

 to the axis. When the points of the image lie in a curved surface, it is said 

 to have the defect of curvature. 



III. The image of an object on this plane must be similar to the object, 

 whether its linear dimensions be altered or not ; when the image is not similar 

 to the object, it is said to be distorted. 



