258 Tlie Tangent Lens-Gauge. 



of each in the plane opposite is exactly in a line with it and 

 the first pin. 



In the triangle ~P 1 P 2 P 3 , 



P x P 2 = p x P 3 by the construction, 

 and ZLP 2 PiP 3 =^ 



so that chord = ^&. 

 r 1 r 2 



It is best to place the eye at some distance from the pins, 

 which should be as fine as possible, and strongly illuminated. 

 A large drawing-board should be used. 



Using this method, which is obviously the least accurate, 

 and measuring the distance between the points of contact 

 with a cheap micrometer microscope reading to ^V mm -> I 

 find it easy to get results within one per cent, of the truth. 

 It is important, especially in working with artificial light, to 

 focus the microscope accurately upon the actual surface of the 

 lens, as the Newton's rings are visible without any striking 

 alteration of appearance some distance beyond the focus, and 

 under these circumstances a large collimation error is intro- 

 duced. A small correction, constant for each instrument, 

 must be made for refraction. This is found by subtracting 

 the actual length of a short rod as measured in air from its 

 apparent length as seen through the glass plates. In the 

 instrument I have made it amounts to fa mm. 



My object in designing the tangent lens-gauge was to pro- 

 vide a simple and cheap form of apparatus by which students 

 could measure the curvature of a lens in order to determine 

 its index of refraction. The instrument lends itself readily to 

 teaching purposes. It affords an opportunity of using the 

 goniometer, and familiarizes the student with Newton's rings. 

 It illustrates a geometrical principle, and while by the third 

 method it is rendered independent of the spherometer and of 

 the goniometer, the results so obtained can easily be checked 

 by the more accurate methods. It has a greater range than 

 the spherometer, and can be used for lenses of from 2 cms. 

 to 2 metres focal length, the percentage of error being smaller 

 in the latter case than in the former, owing to the greater 

 distance between the points of contact. It is, in fact, con- 

 siderably more accurate for such lenses than the majority of 

 cheap spherometers. 



With lenses of short focus the Newton's rings are so small 

 that students sometimes have a difficulty in finding them. 

 In such cases it is best to search for them with a hand lens 

 while applying gentle pressure to the gauge. With long 



