Re: Why "harmonic"

From: The World Wide Wade (waderameyxiii_at_comcast.remove13.net)
Date: 08/11/04 

Date: Tue, 10 Aug 2004 19:36:43 -0700

In article <waderameyxiii-0408EC.18362006082004@news.supernews.com>,
 The World Wide Wade <waderameyxiii@comcast.remove13.net> wrote:

> In article <cf0vqf$f1g$1@nntp.itservices.ubc.ca>,
> israel@math.ubc.ca (Robert Israel) wrote:
>
> > In article <cf0kpk$adf$1@nntp.itservices.ubc.ca>,
> > Robert Israel <israel@math.ubc.ca> wrote:
> > >In article <cf0i6j$ipn$1@panix2.panix.com>,
> > >Lee Rudolph <lrudolph@panix.com> wrote:
> >
> > >>The World Wide Wade <waderameyxiii@comcast.remove13.net> writes:
> >
> > >>>Laplace's equation. They were given the name "spherical harmonics" by
> > >>>William Thomson (Lord Kelvin) and Peter Tait in 1879.
> >
> > >>The Oxford English Dictionary gives the year of Thomson and Tait's
> > >>coinage of "sphereical harmonics" as 1867.
> >
> > >That should be "spherical", of course
> >
> > >The term "harmonic analysis" is also attributed to Thomson and Tait.
> > >T & T first came out in 1867 and went through a number of different
> > >editions, which may explain the discrepancy. Apparently there was
> > >a book by Ferres entitled "Spherical Harmonics" published in 1877,
> > >so the 1879 date would be too late.
> >
> > I didn't find T & T in our library, but I did find "Life and Scientific
> > Work of Peter Guthrie Tait" by C.G. Knott, which makes it clear that
> > the appendix on "Spherical Harmonic Analysis" was indeed in the
> > first edition. He also quotes from a letter Maxwell wrote to Tait
> > in December 1867: "I believe you call Laplace's Coeffts Spherical
> > Harmonics."
>
> Thanks Robert. In our book we write "The term 'spherical harmonic' was
> apparently first used in this context by William Thomson (Lord Kelvin) and
> Peter Tait (see [12], Appendix B)." The reference [12] is
>
> William Thomson (Lord Kelvin) and Peter Guthrie Tait, Treatise on natural
> philosophy, Cambridge University Press, Cambridge, 1879.
>
> So from that I assumed 1879 was the year of birth of "spherical harmonics".
> I'm not sure why we cite the 1879 edition of that book. I'll ask my
> coauthors.

It looks like we simply missed the earlier date of 1867. Thanks again to
Robert and Lee for pointing this out. If there is a third edition of
Harmonic Function Theory, we'll certainly fix that.

Incidentally, if anyone would like a pdf file of "Harmonic Function Theory"
by Axler, Bourdon, and Ramey (yep, a pdf of the entire book, 2nd edition),
you can find it here:

            http://www.axler.net/HFT.html

(Pay no attention to the warning on the cover page about having to purchase
the book, etc.) Comments and criticism welcome!