342 
PHYSICS: C. BARUS 
around the needle provoked by small differences of temperature, resulting for 
instance from illumination. If the possible accuracy of deflection measure- 
ment is to be of any value, therefore, the apparatus must be kept in the dark 
except during observation. Fortunately the achromatic fringes require little 
light. Even then a closed case which can be exhausted of air is essential, for 
such radiometer forces as may enter would in any event be differential, seeing 
that the mirrors are symmetric and the illumination is not subject to alterna- 
tions like the forces on m. It is probable that in case of the above regular 
method a thicker quartz fiber and a greater distance R would conduce to the 
best results since AN is the least difficult quantity to determine. 
The question may now be asked whether it is not possible in the present 
case to determine gravitational attraction in terms of the acceleration of balls 
resulting. With an ocular micrometer this would not be difficult as the 
fringes move slowly enough that the position can always be sharply specified. 
But with a needle of long period in vacuum, the screw micrometer would 
also be available. If there is no damping we may write 
yMm/R 2 — ax — 2ma 
where a is the acceleration, and a the torsion coefficient, referred to x the dis- 
placement of m, at the time t, supposing the needle starts from rest, and the 
gravitational force is applied at / = 0. If at the outset we may put X = 
at 2 /2 
yMm/R 2 = X(at 2 + 4m) /t 2 
an equation whose interesting feature is this, that if / is kept very small (which 
should be possible with an ocular micrometer «and the achromatic fringes, a 
fine quartz fiber presupposed) the term involving / may be neglected and the 
experiment interpreted as a case of uniformly varied motion in which 
y = 2R 2 a/M 
Thus for instance if R = 5 cm., M = 10 3 grams and y = 6.7 X 10~ 8 and if t 
= 100 seconds is admissible, a = 1.3 X 10~ 7 cm. /sec. 2 and the distance tra- 
versed in 100 seconds would be 0.0065 cm., well measurable on the interfer- 
ometer, quite so if the work is done reciprocally and the interference fringes are 
used individually. The theoretical error will be a minimum if m is as large as 
the fiber can safely carry and t as small as possible. On the other hand X 
is independent of m and if t is to be kept small, the result may be compensated 
in a large M/R 2 . The measurement is thus to consist in keeping the fringes at 
zero by moving the micrometer screw for the small interval t during which 
the weight M acts. The constant y would then follow from the micrometer 
reading, M and R only, all other quantities entering secondarily, as correc- 
tions. The experiment seems well worth while. 
