Vol. 6, 1920 
PHYSICS: D. L. WEBSTER 
269 
ideal factors (11th line from bottom); but this decomposition holds for 
the case where '^'^(q:) contains only ideals of the first degree. Kummer 
has himself given {Crelle, 44, p. 120) the decomposition for the generalized 
function "^^(a) which may contain ideals of other degrees than the first 
and said decomposition is of a more general form than that which applies 
for ideals of the first degree. It would follow from these facts that in 
theorem IV, F{a) would necessarily contain factors of the first degree 
only. However, on page 67 of the 1857 memoir the theorem is applied 
to certain ideals QrM which are not proved to be of the first degree. 
Also, on page 54 it is stated without proof or reference that if m is not 
divisible by X-1 then 
where (f)(a) and <pi{a) are integers in ^l(a) such that (t>{a) = (i>i{a) (mod 
y + iy /jp^^ writer has not been able to find a proof of this any where 
in Kummer's papers. 
AN IMPROVED FORM OF HIGH TENSION D. C. APPARATUS 
By David L. Wejbster 
Dkpartme)nt of Physics, Massachusetts Institute of Technology 
Communicated by K. B. Wilson, March 6, 1920 
In a recent paper on X-rays in these ProcEeJdings, ^ I described a high 
tension D. C. outfit based on that of A. W. Hull, with certain changes of 
details. On further investigation it has appeared that one of these changes 
introduces a disturbing factor, which was not large enough to affect the 
results in that paper, or to be detected by the tests for fluctuation used 
at that time, but which might have been detectable if the choke coils in 
the apparatus had not had extremely high inductances. As I have re- 
ceived several inquiries lately about the best way to build such an outfit 
and the question is of importance to X-ray research workers, I am writing 
this note to call attention to the existence of this disturbing factor and the 
way to eliminate it in outfits with inductances and capacities not so large 
as those used here. 
In the arrangement described in the previous paper the principal A. C. 
components on the D. C. line had a frequency of 1000 cycles per second, 
twice that of the primary current, and the currents in both sides of the 
line increased and decreased in the same phase. The disturbing factor 
was the capacity of the transformer secondary, relative to the ground, 
that introduced components of current at 500 cycles, with opposite phases 
on the two sides of the line. Because of this phase relation, the 500 cycle 
components are difficult to choke off unless the middle points of the D. C. 
condenser lines are grounded, in which case the phase relation of each type 
