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little or nothing is gained by the more complicated
expression. But in some cases there
is a great gain. When, for example, instead of
saying that a particle moves we say that the
particle describes a line we introduce an abstraction
in the same manner as when we
talk of a dormitive virtue. But the advantages
here are manifest, since we may imagine
a filament to occupy the whole line at
once, and we may further imagine that
that filament moves in such a manner that at each moment it altogether quits the
line which it is momentarily occupying. Here again we may
introduce an abstraction and say that the
filament generates a surface. Then we
may imagine a material film to
occupy the whole surface at once, and may