450 Mr. T. H. Blakesley on some Improved 



If the lens constants are thoroughly known, we have an 

 equation of the form 



1 =^ + B. 



/L6 — 1 C 



where A and B are both constants. 



In practice it would be possible to determine A and B by 

 observing the values of c in the cases of two liquids whose 

 indices have been determined in other ways ; but it is not 

 necessary to take this course where a single lens is employed, 

 because in that case the radius r can be expressed in terms of 

 the focal length, the distances u and v of the principal foci 

 from the anterior and posterior surfaces of the lens, and the 

 thickness of the lens, the latter being easily measured by 



calipers. The formula for - then is 



f*-u Q v + df 



which can be inserted in the above equation. 



Or if a compound lens is employed, the value of r may be 

 determined by a spherometer; but this instrument does not 

 furnish the most accurate means of calculating such radii. 

 This point will receive attention below. 



A telescope is an arrangement of coaxial lenses, some 

 forming what is called the object-glass, others the eyepiece. 

 Each of these portions may be far from simple, but each must 

 have its own focal length and pair of principal foci. When 

 the second principal focus of the object-glass coincides w T ith 

 the first principal focus of the eyepiece, the focal length of 

 the combination is infinite, for the k of this problem is equal 

 to zero. This is often considered to be the position of adjust- 

 ment for viewing distant objects ; and in fact a telescope will 

 always have a very long focal length though the actual value 

 wall differ with different eyes. Xow if a telescope is in this 

 condition of adjustment, having an infinite focal length, we 

 may divide the system anywhere we please, and call one part 

 the object-glass and the other the eyepiece. All that is 

 necessary is that the dividing surface shall be a plane at right 

 angles to the common axis, or a sphere having its centre on 

 the common axis. The division itself may even take place 

 through one of the lenses. 



The two portions of the system thus formed will have the 

 following properties. 



The second principal focus of one of them will always 

 coincide with the first principal focus of the other. 





