dent quantities or unconnected
events, which is the theory of probabilities." I am not ashamed, having the
British Association as a co-non-intelligent, to say I do not understand
this: there is a paradox in it, and the author should give further
explanation, especially of his negative quantity. Mr. Macleod has gained
{185} praise from great names for his political economy; but this, I
suspect, must have been for other parts of his system.

On the principles and practice of just Intonation, with a view to the
abolition of temperament.... By General Perronet Thompson.[320] Sixth
Edition. London, 1862, 8vo.

Here is General Thompson again, with another paradox: but always master of
the subject, always well up in what his predecessors have done, and always
aiming at a useful end. He desires to abolish temperament by additional
keys, and has constructed an enharmonic organ with forty sounds in the
octave. If this can be introduced, I, for one, shall delight to hear it:
but there are very great difficulties in the way, greater than stood even
in the way of the repeal of the bread-tax.

In a paper on the beats of organ-pipes and on temperament published some
years ago, I said that equal temperament appeared to me insipid, and not so
agreeable as the effect of the instrument when in progress towards being
what is called out of tune, before it becomes offensively wrong. There is
throughout that period unequal temperament, determined by accident. General
Thompson, taking me one way, says I have launched a declaration which is
likely to make an epoch in musical practice; a public musical critic,
taking me another way, quizzes me for preferring music _out of tune_. I do
not think I deserve either one remark or the other. My opponent critic, I
suspect, takes _equally tempered_ and _in tune_ to be phrases of one
meaning. But by equal temperament is meant equal distribution among all the
keys of the error which an instrument _must_ have, which, with twelve
sounds only in the octave, professes to be fit for all the keys. I am
reminded of the equal temperament which was once applied to the postmen's
jackets. The coats were all made for the average man: the {186} consequence
was that all the tall men had their tails too short; all the short men had
them too long. Some one innocently asked why the tall men did not change
coats with the short ones.

A diagram illustrating a discovery in the relation of circles to