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[Nov. 12,
Mr. H. Bateman

A second transformation of some interest is obtained by interchanging m with n and μ with ν. This changes


that is

f(x, y, z, w)


Putting w = ict and changing the sign of z, the formulæ for the transformation are

where, now,

If V = F(x, y, z, t) is a solution of

the function F(X, Y, Z, T) is also a solution, and, if U = f(x, y, z, t) is