16 
PHYSICS: C. BARUS 
introduced is thus a decrement and is twice the 2 e cos (45° — a) of each mir- 
ror. Thus the total correction to be subtracted from the equation is after 
reduction 2 R (1 — cos a) ( 1 + tana). Hence the equation becomes ultimately 
n\ = 2 R (sin a + cos a — 1). 
To the second order of small quantities, if i = 45° is the angle of incidence, 
and An the normal displacement of M', 
AN/Aa = R(l + Aa/2)/cos I 
As all the mirrors receive the light on their silvered sides, M originally 
compensates N if the mirrors are identical in thickness and glass. But the 
transmission at 3 varies as the angle of incidence changes from i = 45° to 
45° — a. The glass path here decreases by e (sin i — cos i tan r) Aa, 
where e is the plate thickness, r the angle of refraction. The path difference 
as above reckoned has thus been increased by this amount and this quantity 
is to be added to the right hand member. The effect will not usually exceed 
a few per cent of the air path difference, and the ratio is the same as above. 
3. Ocular Micrometer. — It has been stated that the motion of the fringes 
across the field of the telescope, T, is astonishly swift. Hence it is often de- 
sirable to insert a micrometer here, as the displacement of fringes can thus be 
much more accurately and easily measured than at the micrometer along the 
normal of the opaque mirror, M' , of the interferometer. If the latter is of the 
type using an auxiliary mirror, mm, figure 1, the fringes may even be estab- 
lished of a size to correspond with the ocular micrometer, by rotating the 
auxiliary mirror; but this is not usually necessary. A good ocular plate 
micrometer was at hand dividing the width of field (about 1 cm.) into 100 
parts, the divisions being 0.1 mm. One- tenth of this is easily estimated by the 
eye in view of the strong eye lens. The light from the collimator at L should 
completely fill the field, a condition which may be fulfilled by suitably placing 
the former, modifying its objective. After completing such preliminary ad- 
justments with the fringes, made very sharp and the ocular scale equally so, 
this is to be placed at right angles to the fringes. Let Ae denote their dis- 
placement measured in centimeters on the ocular scale and AN (cm.) the dis- 
placement of the opaque mirror M' of the interferometer. The question is 
whether Ae and AN are nearly enough proportional quantities for practical 
purposes. A number of such standardizations were carried out throughout 
1 cm. of Ae, two of which are shown in detail in figure 3. The fluctuation of 
data is due to air currents across the interferometer. It was not easy to ob- 
viate these, and it was not thought necessary for the present purposes. Other- 
wise the data would have been smooth. There is no doubt that a linear rela- 
tion may be assumed. In curve a the readings of the interferometer micro- 
meter increase, in curve b they decrease. If the means be taken from doublets 
far apart the ratios are 
(a) AN/Ae = 0.00310; (b) AN/Ae = 0.00310, 
