ledge is a dangerous thing is one of the most fallacious
of proverbs. A person of small knowledge is in danger of trying to make his
_little_ do the work of _more_; but a person without any is in more danger
of making his _no_ knowledge do the work of _some_. Take the speculations
on the tides as an instance. Persons with nothing but a little geometry
have certainly exposed themselves in their modes of objecting to results
which require the higher mathematics to be known before an independent
opinion can be formed on sufficient grounds. But persons with no geometry
at all have done the same thing much more completely. {5}

There is a line to be drawn which is constantly put aside in the arguments
held by paradoxers in favor of their right to instruct the world. Most
persons must, or at least will, like the lady in Cadogan Place,[5] form and
express an immense variety of opinions on an immense variety of subjects;
and all persons must be their own guides in many things. So far all is
well. But there are many who, in carrying the expression of their own
opinions beyond the usual tone of private conversation, whether they go no
further than attempts at oral proselytism, or whether they commit
themselves to the press, do not reflect that they have ceased to stand upon
the ground on which their process is defensible. Aspiring to lead _others_,
they have never given themselves the fair chance of being first led by
_other_ others into something better than they can start for themselves;
and that they should first do this is what both those classes of others
have a fair right to expect. New knowledge, when to any purpose, must come
by contemplation of old knowledge in every matter which concerns thought;
mechanical contrivance sometimes, not very often, escapes this rule. All
the men who are now called discoverers, in every matter ruled by thought,
have been men versed in the minds of their predecessors, and learned in
what had been before them. There is not one exception. I do not say that
every man has made direct acquaintance with the whole of his mental
ancestry; many have, as I may say, only known their grandfathers by the
report of their fathers. But even on this point it is remarkable how many
of the greatest names in all departments of knowledge have been real
antiquaries in their several subjects.

I may cite, among those who have wrought strongly upon opinion or practice
in science, Aristotle, Plato, Ptolemy, Euclid, A