THE AID OF THE ACHROMATIC FRINGES. 11 



Tests made with another piece of plate glass (the auxiliary mirror provided 

 with an independent cross-arm and the apparatus gently tapped before obser- 

 vation), gave the results following: 



Position 40.8 35.6 37.7 39.8 40.7 cm. 



io'A]V 15.8 40.6 30.7 21. i 16.7 cm. 



They are constructed in figure 6. Hence per unit of length of plate 



= 0.00239 cm. Ax = 0.00186 cm. 



As the micrometer read to about io~ 4 cm., a corresponding error in the indi- 

 vidual data is inevitable. 



Tested within 5 mm. by the ocular micrometer (scale-part equivalent to 

 AJV = 46X io~ 6 cm.), the mean displacement was about 50 scale parts, so that 

 per centimeter of length A7V = 0.0023 cm. The results for so small a length are 

 complicated by the difficulty of securing the same lateral position as well as 

 the same longitudinal position, since the thickness changes in both directions. 

 Lateral sliding, which is equivalent to lateral flexure of the contact lever is 

 particularly to be guarded against, but it vanishes on tapping. 



Experiments were now made with the design figure 3, except that the mirror 

 mm' was left free, while a special arm (conical tube) parallel to mm' carried the 

 stylus e. Although small fringes were used, the behavior of the apparatus as a 

 spherometer was quite satisfactory. The three set-screws h, h, h were equi- 

 distant on a circle of radius r 1.08 cm. Sliding the lens g (about 5 cm. in 

 diameter) so that its center and the outer parts of four quadrants lay succes- 

 sively under the pin e, the readings obtained after gentle tapping were 



Top. Bottom. Right. Left. Center. 



io 8 AAT = 2.oo 2.00 2.05 2.05 2.00 cm. 



The screw micrometer was thus not sufficiently sensitive to register 

 inaccuracies. 



The apparatus used as a spherometer gave for: 



Plate. Lens. Plate. 



A]VXio' = 28.5 23.2 28.4 cm. 



so that the height above the plate corresponded to 

 io 3 A./V=5.2 cm., or io 3 A.n; = 4.o4 cm. 



If R is the radius of curvature of the lens, 



r 2 (i.o8) 2 



The fringes, however, were here too fine to admit of greater precision. In 

 another experiment with somewhat larger fringes, the data were 



Lens. Plate. Lens. 



o s = 10.48 15-52 IO -53 



