PHYSICS: C. BARUS 
43 
R = ry2^x 
(7) 
This method gives good results for lenses of all curvatures, however strong, 
as the tests made indicated. But it is not necessary to use the plate to obtain 
a fiducial reading, provided the system Gg carrying the lens g, is on good 
right and left slides. For in figure 4, let B be the angle between the plane of 
the tripod and the slides, and let three readings of A7V be taken for three 
preferably equidistant points /, c, v, of the lens, by sliding Gg over equal 
distances, r. Let the reading be 
and equations (4) and (7) apply as before. This method also gives good 
results even for short distances, r. 
3. Observations. — The use of the apparatus figure 1, with the strip of glass 
g to be tested sliding up or down, did not at first give satisfactory results, 
because the mirror mm' was too thin (2 mm. thick). It was found however, 
that on breaking contact at c during the sliding of g between successive posi- 
tions or by gently tapping the bar or standard G, very fair results were ob- 
tainable. There would have been no difficulty in using a thick glass mirror 
mm' (i inch or more) in which case the annoyance of flexure would have been 
negligible. But all difficulties were eliminated by using an independent arm 
to carry e, as stated above. Tapping at G before each observation is essential. 
The observations themselves must be omitted here. Tests of the degree of 
wedge-shape of long strips of glass from centimeter to centimeter of length, 
were made in detail, using both the screw and the ocular micrometer. Sim- 
ilarly, lenses of all focal lengths from a few centimeters to 100 cm. either con- 
vex or concave, were examined by the apparatus figure 3, with surprising ease 
and accuracy. The parts of the surfaces of such lenses may be explored to 
the fraction of a wave length, for successive circular patches of a cm. of 
radius, or less. 
Finally the spherometer method of figure 4 and equation (8) gave entirely 
satisfactory results. An application for the measurement of (elastic) micro- 
metric displacements will be discussed in a subsequent paper. 
y = N, y' = iV H- r tan ^ -f AA^ y" = N 2r tan 6 
(8) 
where AiV corresponds to Ax in figure 4. Hence 
2>'' - {y-\- y") = 2^N 
