true, that words are to the mind itself the necessary instruments of thought, yet, in my apprehension, it cannot well be denied, that in some of its operations and intellectual reaches, the mind is greatly assisted by its own contrivances with respect to language.  I refer not now to the communication of knowledge; for, of this, language is admitted to be properly the instrument.  But there seem to be some processes of thought, or calculation, in which the mind, by a wonderful artifice in the combination of terms, contrives to prevent embarrassment, and help itself forward in its conceptions, when the objects before it are in themselves perhaps infinite in number or variety.

19.  We have an instance of this in numeration.  No idea is more obvious or simple than that of unity, or one.  By the continual addition of this, first to itself to make two, and then to each higher combination successively, we form a series of different numbers, which may go on to infinity.  In the consideration of these, the mind would not be able to go tar without the help of words, and those peculiarly fitted to the purpose.  The understanding would lose itself in the multiplicity, were it not aided by that curious concatenation of names, which has been contrived for the several parts of the succession.  As far as twelve we make use of simple unrelated terms.  Thenceforward we apply derivatives and compounds, formed from these in their regular order, till we arrive at a hundred.  This one new word, hundred, introduced to prevent confusion, has nine hundred and ninety-nine distinct repetitions in connexion with the preceding terms, and thus brings us to a thousand.  Here the computation begins anew, runs through all the former combinations, and then extends forward, till the word thousand has been used nine hundred and ninety-nine thousand times; and then, for ten hundred thousand, we introduce the new word million.  With this name we begin again as before, and proceed till we have used it a million of times, each combination denoting a number clearly distinguished from every other; and then, in like manner, we begin and proceed, with billions, trillions, quadrillions, quintillions, etc., to any extent we please.

20.  Now can any one suppose that words are not here, in some true sense, the instruments of thought, or of the intellectual process thus carried on?  Were all these different numbers to be distinguished directly by the mind itself, and denominated by terms destitute of this artificial connexion, it may well be doubted whether the greatest genius in the world would ever be able to do what any child may now effect by this orderly arrangement of words; that is, to distinguish exactly the several stages of this long progression, and see at a glance how far it is from the beginning of the series.  “The great art of knowledge,” says Duncan, “lies in managing with skill the capacity of the intellect,