448 Mr. T. H. Blakesley on some Improved 



Let Uq, v be the positions of the principal foci of the first 

 system, and u ', v ' those of the second system, light being- 

 supposed to come from the right. 



— x *— -* *^— 



f» fi 



Let/j, f 2 be the two focal lengths, and the length from v Q 

 to Uq be k. 



Then the following rules fix the elements of the whole 

 united system. 



The new first principal focus is distant from u towards the 



f 2 

 right hand*—. 



A* 



The new second principal focus is distant from v towards 



the left hand 4-- 



f f 

 The new focal length is M~- 



K 



These rules are virtually equivalent to the following 

 statements: — 



The new first principal focus is conjugate by the first 

 system with the first principal focus of the second system. 



The new second principal focus is conjugate by the second 

 system with the second principal focus of the first system. 



The points w , i? ' are conjugate with one another. The 



travel of the principal focus from u to its final position 



being easily and accurately determinable by experiment, and 



f 2 

 having for its theoretical value '-^-, it may be employed in a 



variety of practical ways. 



The following example may illustrate how it may be used 

 to find the focal length of a lens in the absence of a magnifi- 

 cation apparatus. 



The tubes of a telescope retaining the object-glass, but 

 otherwise free from lenses, are placed vertically with the 

 object-glass downwards upon a plane mirror. Crossed silk 

 fibres are stretched across the open end, and the tubes are 

 adjusted till the image of these fibres is in the same horizontal 

 plane as the fibres themselves. The length of the tubes is then 

 found to be 25'95 cms An achromatic telescope object-glass, 

 whose principal foci are known to be 21/12 and 19*92 from 

 the convex and plane sides respectively, is placed upon the 

 upper end of the telescope -tube before mentioned, the plane 

 side being downwards. A minute triangle of white paper 



