270 PHYSICS: D. L. WEBSTER Proc. N. A. S. 
of current components is unchanged, but the 500 cycle voltage fluctuations 
on the first D. C. condenser are increased, and its 1000 cycle voltage fluc- 
tuations are reduced. To make this change we must remove the ground 
connection that was on the point A, figure 1, and ground the middle points 
of all the D. C. condensers as indicated by the grounds, G, and incidentally, 
we may as well ground the cores of the choke coils also. Since the 500 
cycle components have a phase relation opposite to that of the 1000 cycle 
ones it is well also to reverse the connections on the choke coils on one side 
of the line. This gives us the arrangement shown in figure 1. 
To compute the potential fluctuations, let I sin o)t be the current in the 
lead to either end of Ci, where co = 2% X 500 sec."~\ and we neglect har- 
monics. This gives potentials as indicated in the diagram, where 
{V -\- Vi) is the peak voltage of the transformer, 
and 
¥2(1 - C2Ma;2) /(I - C2MC02) 
CsZ^co^ 2CiC2LiL20)^ 
Here Ci, C2 and C3 are the capacities of the whole series condenser lines, and 
Li = 2L'i + 2Mi L2 = 2V2 + 2M2, and M is the mutual inductance 
between Li and L2. Because of the co^ in the denominator of Vs it is evi- 
dent that harmonics need not be considered, although for the 1000 cycle 
harmonic we must replace Li and L2 by 2L\ — 2Mi and 2L'2 — 2M2, re- 
spectively. To find / for a given value of the direct current I' is not easy, 
and the ratio of the two is not constant: But if the rise of voltage on either 
half of the first condenser occurred instantaneously it would not be greater 
than (27r/co)I' 2Ci \ and, if it took a whole half cycle it would not be less 
than half this amount. In practice, with heavy loads the rise appears to 
take a large fraction of a half cycle. The slower the rise is, the less of it 
we may ascribe to harmonics, and thus for an approximate value of I 
we may assume the rise to be 2Vi, and also to be somewhat greater than 
irl' /2Ciui. Thus / should be about 21' under such conditions, and measure- 
ments confirm this relation. 
This arrangement has the disadvantage of depending on a 500 cycle 
charging current in Ci instead of 1000. On the other hand, if the two sides 
of the line are symmetrical, there should be no 500 cycle fluctuation in 
the total potential difference between the ends of the line. In fact with 
the previous type of connection we might expect that if the ground wire 
was removed we should have likewise no 500 cycle fluctuation in the po- 
tential difference between the ends of the line, although both ends would 
fluctuate relative to the ground. But this conclusion is based on the 
assumption of perfect symmetry between the two ends of the line, which 
is liable not to occur. And although the 500 cycle fluctuation on the first 
