Formulae and Methods connected with Lenses. 453 



But if v be the distance of the second principal focus of the 

 lens from the second surface, the value of k will be 



-Ml 



Hence f 2 p 



c= '— - or r=— '- v ; 



v + r c 



all the symbols on the right hand of this last equation are 

 known. 



This affords a very convenient way of practically mea- 

 suring the radius of curvature of the face of a lens, as a pool 

 of mercury is an easy way of producing the conditions. 



I have mentioned above in dealing with the index of 

 refraction of a liquid that a knowledge of this value is im- 

 portant ; and this optical method is in my opinion far superior 

 to that of the spherometer in making the determination. 



Those who may have followed the above remarks with care 

 will see that I strongly advocate those optical methods of 

 measurement which depend upon making a coincidence 

 between the position of an object and that of its image. 

 These coincidences may be determined with very great pre- 

 cision by any one accustomed to observation ; and the appa- 

 ratus required, though it may be made as elaborate as any 

 others, need be no more than the simplest. A small optical 

 bank about five inches long, a holder to slide up and down and 

 to carry a sharply-pointed piece of white paper, four square 

 inches of good plane mirror, a hand-lens of about 2 inches 

 focal length to determine coincidences, and a rule and calipers 

 to measure distances, are really all that is necessary to make 

 determinations of an accuracy far surpassing that in vogue at 

 present. 



I have examined a lantern-projector which professed to have 

 a focal length of 6 inches ( = 1 5*24 cm.). It actually possesses 

 one of 17"#1 cm. 



A microscope objective whose nominal value was 1J inch, 

 made by the most eminent optician in London, was measured 

 directly, and indirectly by taking its two component lenses 

 separately and measuring their focal lengths and the overlap 

 of their principal foci. 



The first method gave 1*347 ") • i c i i ,, 

 „ second „ ^355] inches focal length. 



The nominal value was therefore certainly in error by as 

 much as 10 per cent. 



