316 
PHYSICS: C. BARUS 
Proc. N. a. S. 
Turning first to the latter, it is astonishing to find that X and ^y, in 
spite of the marked ampHtude of radiant forces, make up a definite graph. 
In fact, if we omit the exceptional A^v = 25.7 (inadmissably large radiant 
forces), and X are nearly proportional. If this curve were known, 
di.y could be computed from X and vice versa. 
The values of T/2, as already intimated, were not accurately taken, as 
I did not anticipate relations like the present. Nevertheless figure 2 
adequately shows that these also make out a definite graph. 
If for instance = 13.4 cm.( about the mean value in the preceding 
paper), Ti = 758 sec. should be its equivalent and X log ^ = ,385 at the 
same time. If we take the vacuum period as Ti/^ l + \^/4ir^ it would be 
T = 750 sec. which happens to agree with the value taken in the report in 
question. 
6. Plenum. — In contrast with the preceding oscillations under conditions 
of high exhaustion, the results investigated for the case of the needle vibrat- 
ing in air under atmospheric pressure, are nearly aperiodic. The data 
for T, X, t^y, are all enormously larger. These values of X result from the 
continued drift of the position of equilibrium of the needle toward the di- 
rection in which it is deflected by the attracting weights M. In this re- 
spect the plenum results are quite different from the preceding under 
exhaustion. 
The motion of the needle in a plenum is peculiar. When the weights are 
exchanged, the needle falls from its high elongation to its low elongation in 
the time T/2. It then turns toward a new high elongation for a time (usually 
about T/4 sec. in length), after which it again moves toward low numbers 
by slow indefinite creeping, without again turning. Exactly the same phe- 
nomenon occurs when the needle rises from a low elongation toward a 
higher. In other words the needle may be said to oscillate about a position 
of equilibrium continually advancing in the direction of the deflection. 
7. Comparison with Theoretical Values of Frictional Resistance. — It is now 
desirable to endeavor to construe the values obtained for X and T by 
the aid of the familiar theory of the damped pendulum. If the needle be 
regarded as consisting of the two balls at its end, the frictional forces 
should be 6 XT? r v and therefore the frictional coefficient ^ is 6 tt t; r . If 
is the period of the damped needle and X its logarithmic decrement 
Tib = 2X, and therefore, X = 3 tt r Ti. Hence, if r = .23 cm., rj = .00019, 
Ti = 892 X log e seconds. In figure 2, however, not only is proportionality 
of T and X at long range excluded, but the factor would be twice as large, 
on the average. 
* Advance note, from a Report to the Carnegie Institution of Washington, D. C. 
^ These Proceedings, 8, pp. 13, 63, 1922. The present apparatus is essentially the 
same. 
