18 
PHYSICS: C. BARUS 
if AN = ANo is constant and also X, we may then write 
A<p = di/dn = — X/2 AN 0 sin i. 
Furthermore if AS is the angular displacement of fringes 
A0 = nA<p = - (AN /ANo) cot i, 
if n\ is replaced by its value and AN is small compared with AN 0 . If it is 
not, since AN 0 involves AN, we must state the case thus: 
J^AiVo + AiV 
dN/dNa, 
ANo 
or on integrating and expanding the natural logarithm 
- AS = cot i [AN /ANo -(AN/AN 0 ) 2 /2 + . . .] 
and Ae = LAd. 
In the above measurements 
A<p = LA<p/L = 7.2 X 10- 4 
whence apart from signs 
ANo = \/2Aq> sin i = 0.06 cm., nearly, 
whereas the maximum displacement AN throughout the whole series (equiva- 
lent to the telescopic field width) does not exceed AN = 5 X 10~ 3 cm. Hence 
(AN/ANo) 2 /2 may here be neglected to about 1/300 and (again apart from 
signs) since i = 45°, 
Ae = L(AN/AN 0 ) = 325 AN, 
as it should be; i.e., the relation of Ae and AN is practically linear, if the dis- 
placement AN is not excessive or goes beyond the equivalent of field width. 
As the determination of ANo is inconvenient we thus come back to the 
practical equation already used, or 
AN /Ad = \/2A<p cos i, 
or if Ld<p — be and Ae and be are the fringe displacement and the fringe breadth 
measured on the same ocular micrometer, 
AN/Ae = X/2 be cos i, 
With this deduction the equations of long distance interferometry, etc., 
form in terms of be the fringe breadth and the fringe displacement Ae which 
may be recorded here, d being the distance, 
Aa = (\/2Rbe)Ae; d = (bRbe/\)/Ae. 
4. Collimator Micrometer. — For many purposes even better conditions 
are obtainable by replacing the slit of the collimator by a plate glass microm- 
eter. The magnification in such a case is usually greater and since the tele- 
scope now contains no fiducial lines, it need not be fixed, but may be shifted 
