794 Transactions of the Society. 



interference of an eye-piece, the visual angle of the dissipation- 

 circles of that image, taken for the place of the posterior principal 

 focus, is the same for every position and amplification of the image, 

 and is a constant quantity in every system. 



This proposition shows the method of estimating numerically 

 the degree of optical perfection in objectives. The constant visual 

 angle defined above (which I shall denote by the letter u in the 

 following discussion) exhibits an exact measure of the smaller or 

 greater dissipation of the rays inherent in a given construction, 

 and one which is independent of the various accidental circum- 

 stances under which an objective performs. 



(c) Suppose now the angle u (the inherent angular dissipation 

 of the light) to be given for a certain objective, and an image 

 projected by that objective to a distance A from its posterior prin- 

 cipal focus (which focus is generally in composite systems not very 

 far from the back surface). The linear dissipation of the light in 

 that image will be 



6 = A M, 



whilst the amplification of the object is 



. " = 7- 



This objective-image being observed by means of an ocular of 

 a focal length cf), and a virtual image being projected to a distance 

 I from the eye-point (the distance of distinct vision) the linear 

 amplification N" to which the objective-image is submitted will be 



and the total amplification of the ultimate image > 



N = N' N" = ^ , 

 f'P 



which is the general and strict formula for the determination of 

 the power of a compound Microscope by means of the focal lengths 

 of objective and ocular, and the distance A, which I shall call the 

 optical length of the tube. * 



* As the focal length of a composite system is always the quotient of the 

 linear amplification N of the image, by the distance of that image from the 

 posterior principal focus of the system (which is in the case of the Microscope 

 the place of the Kamsden circle above the ocular, or the eye-point, very 

 approximately), we have the focal length of the entire Microscope 



^-N- a:' 



where the length A may be defined now as the distance between the posterior 

 principal focus of the objective and the anterior principal focus of the ocular, 

 because this latter focus must coincide with the objective-image (very approxi- 

 mately at least) in order to obtain the ultimate virtual image at a considerable 

 distance. 



