to possess some knowledge
of algebra and of geometry, which Herschel did not possess, but of which
he made himself master in a very short time.

In 1766, Herschel obtained the appointment of organist to the Octagon
Chapel at Bath. This was a more lucrative post than that of Halifax, but
new obligations also devolved on the able pianist. He had to play
incessantly either at the Oratorios, or in the rooms at the baths, at
the theatre, and in the public concerts. Then, being immersed in the
most fashionable circle in England, Herschel could no longer refuse the
numerous pupils who wished to be instructed in his school. It is
difficult to imagine how, among so many duties, so many distractions of
various kinds, Herschel could continue so many studies, which already at
Halifax had required in him so much resolution, so much perseverance,
and a very uncommon degree of talent. We have already seen that it was
by music that Herschel was led to mathematics; mathematics in their turn
led him to optics, the principal and fertile source of his illustrious
career. The hour finally struck, when his theoretic knowledge was to
guide the young musician into a laborious application of principles
quite foreign to his habits; and the brilliant success of which, as well
as their excessive hardihood, will excite reasonable astonishment.

A telescope, a simple telescope, only two English feet in length, falls
into the hands of Herschel during his residence at Bath. This
instrument, however imperfect, shows him a multitude of stars in the sky
that the naked eye cannot discern; shows him also some of the known
objects, but now under their true dimensions; reveals forms to him that
the richest imaginations of antiquity had never suspected. Herschel is
transported with enthusiasm. He will, without delay, have a similar
instrument but of larger dimensions. The answer from London is delayed
for some days: these few days appear as many centuries to him. When the
answer arrives, the price that the optician demands proves to be much
beyond the pecuniary resources of a mere organist. To any other man this
would have been a clap of thunder. This unexpected difficulty on the
contrary, inspired Herschel with fresh energy; he cannot buy a
telescope, then he will construct one with his own hands. The musician
of the Octagon Chapel rushes immediately into a multitude of
experiments, on metallic alloys that reflect light with the greatest
intensity, on the m