The name is absent

Rectilinear Drawing          71

e =(cos φ- г sin φ)e ,

and then proceeding essentially as in the case m = 1 treated
above.

We therefore content ourselves with stating the final
result and giving in an appended Note the series of re-
ductions involved. The reader who wishes a more detailed
deduction will find it in my article referred to at the outset.

In the case of a given harmonic distribution function of the
mth order,

F_m(r, θ) =F_m(r) cos τnθ+G_m(r) sin mθ,
where H_m(r) =F_m(r) +iG_m(f) is supposed to vanish to the
{m-l)st order at r =Q so that H_m(r)∕r^m~' remains finite, there
exists a corresponding continuous distribution function.

fm(s, <p) =f_m(s) COS mφ +gm(ʃ) sin m<f>,
likewise harmonic of the mth order, if and only if the integral
in the equation

<_v, ⅛ ^{im d} f^sH (^+Vu^-∖y + {u-^u^-F)^m
(5) h_m(s) _Ts j_o 77_m(∕)-------------------------dt,

J-

is continuous and admits a continuous derivative as to s, in
which case the unique solution is derived by setting h_m(s') in
(5) equal to f_n(fi) +ig_m(s).

10. EXPLICIT SOLUTION IN THE N0N-HARM0NIC CASE

In virtue of the known relationship between continuous
functions and their Fourier series we are now in a position
to formulate the general solution of our problem:

If the given continuous density function F(r, 0) be expanded
in a Fourier series

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