ON OPTICAL INSTRUMENTS. 329 



inch of any surface, occupies, at twice the distance of the surface from the 

 luminous point, the space of four square inches, the intensity of the light 

 diminishes as the square of the distance increases. We can judge with 

 tolerable accuracy of the equality of two lights by the estimation of the 

 eye, but we cannot form any idea of the proportions of lights of different 

 intensities : if, however, we remove two sources of light to such distances 

 from an object, that they may illuminate it in equal degrees, we may con- 

 clude that their original intensities are inversely as the squares of their 

 distances. Count Rumford's * photometer performs this very conveniently, 

 by casting two shadows of a given object near each other, on the same 

 surface, the lights being removed to such distances that the shadows 

 appear equally dark. (Plate XXVII. Fig. 387, 388.) 



For determining the refractive density of solids, it has been usual to form 

 them into a prism, and to measure the angular deviations which they 

 produce ; and for fluids, to inclose them either in a hollow prism, or between 

 two meniscus lenses, and to measure the angular deviations produced by 

 the prisms, and the focal distances of the lenses. But in most cases, Dr v 

 Wollaston's apparatus t is far preferable to both these methods: it is 

 arranged for ascertaining the angle at which light, moving within a certain 

 dense transparent substance, begins to be totally reflected from the common 

 surface of that substance and the solid or fluid which is to be examined. Thus, 

 if we first measure the angle at which light begins to be totally reflected 

 from the posterior surface of a prism of glass, in contact with air, we may 

 readily determine its refractive power ; and then, having caused a drop of 

 a fluid to adhere to that surface, or fixed a solid to it by a small portion of 

 some fluid denser than itself, we may observe, as we turn the prism round 

 its axis, at what angle the drop or spot begins to disappear, and may thence 

 calculate the refractive density of the substance ; and even without actual 

 measurement of the angle, we may readily compare the disappearance of 

 the drop or spot with that of others placed near it, of which the properties 

 are known. Dr. Wollaston has, however, rendered the process still easier 

 and more simple, by employing a rectangular prism of glass, with sights 

 fixed to a jointed frame, of such a construction as to enable him to read off, 

 by a vernier, without any calculation, the index of the refractive power of 

 any substance less dense than glass. (Plate XXVII. Fig. 389.) 



All instruments strictly optical are employed for forming an image of an 

 external object : the simplest are mirrors and lenses, which form a single 

 image only, either actual or virtual, and sometimes depict it on a surface 

 calculated for receiving and exhibiting it. Other instruments repeat the 

 image once or more under several forms, in general enlarging it con- 

 tinually ; and these are either microscopes or telescopes, which present us 

 with great diversity in their arrangements, and in the appurtenances sub- 

 servient to their uses. 



It is a general rule, that when an image of an actual object is formed by 



any lens or speculum, if the rays converge to an actual focus, the image is 



inverted ; but erect, if they diverge from a virtual focus, and the object 



and image subtend equal angles at the centre of the lens or speculum. 



* Ph. Tr. 1794, Ixxxiv. 67, f Ibid. 1802, p. 365. 



