Colloquium publications.

ERRATA CORRIGE.

On page 35 in equation (9') change y to a. In all the formulae
and equations following on page 35 change y to: and f: to a.
On page 37 in equation (12) change y to: and f to a.
On page 39 in the second equation there should be an i as a
factor of each of the last two terms of the integrand.
Note to Art. 27 Lecture II.
The approach to the analog of Green's theorem is more clear
if done in the following way, and bears more relation to the
development with which we are familiar in calculus. The
meaning of equations (17) to (20) is perhaps not clear, as the
equations stand. But the invariant H,1 defined by (21):
(21) (V1 X V2)HW1l = WT1 X W2'
which may be rewritten in the new forms:
Hl, -= ([l.W1) (f' W1) + (a. Wl) (a. V1')
= - (f 3W1) (a.W V2') + (a. W1) ( W2')
as we see below, bears a noticeable relation to the scalar product
of two gradients which is subjected to the familiar analysis of
Green's theorem.
The forms just written however do not lend themselves to
the customary integration by parts. Let us then in these formulae replace the part which refers to say W1 and W2 by functions
(pi and p2 which depend on them (retaining meanwhile the quantities W1' and W2') and seek to write H~, in the form:
HqW = WI'* V1 + W2" V~2
or more generally, introducing an arbitrary point function
k(x, y, z),
(22) kH~ll, = W'. Vsl + W2' V',2
Green's theorem is merely the result of integrating both sides of
1