(74.) In order to induce a general law from specific instances, and deduce the application of a law to a particular case by means of mechanical contrivances, we must take advantage of the geometrical arrangement of words formerly described, and denote each word by a cypher, and lastly then arrange them in such a manner that each cypher

may bear its proper relation to every other cypher.

(75.) The application of the geometric arrangement of cyphers may be best represented by any contrivance, the parts of which continually divide by a hinge joint into two portions. Nothing apparently can be more simple than this arrangement; though, practically, for large series, the details are so troublesome, that it has required much more labour to bring it into a working form than I had originally anticipated, owing to the difficulty which arises from the necessity of a large number of parts being compelled to move upon the other parts of the contrivance, which is absolutely necessary to the construction of the machine.

(76) I have before me, whilst I write, seven or eight varieties of these contrivances, some of which have their fixed points at the top of the geometric series, and some at the other extremity of the same. Perhaps the construction of the latter may be illustrated by a number of lines and letters as in the annexed diagram for a series of sixteen, thus:

abcdefghijklmnop

(77) In this case the fixed point of every line is at the bottom of the diagram, and each is represented as fixed upon a board. The whole is now shown as open, but it will be seen that when closed the act of opening any one of the lowest set would partially influence its corresponding cypher in the series above it. This form illustrates the principle exceedingly well, is simple in its construction, and by a proper use of readings is applicable in all

cases.

(78.) Upon the whole, however, perhaps the fixed point had better be placed at the upper part of the series, and as there are some difficulties in constructing it to work as a triangle, it may be arranged to shut up as a parallelogram.

(79.) If the action of the machine is desired to illustrate by its own mechanism, the principles, then the movements must be so arranged that the

spaces of the several series must open in a corresponding way, and this may be effected by constructing it as in the annexed diagram.

If, however, the action on the cyphers is only desired, then the mechanism may be arranged by a series of bars joined together by hinges at one of their extremities, and the different cyphers may be appended in their proper places in such a way that the mechanism may be concealed. This latter plan, is perhaps one which is the most applicable for a geometric series of high power.

(80.) I have constructed machines to work by a to and fro motion, by which a great number of elements can be packed parallel; but upon the whole, an action is perhaps better represented by one bar moving upon the others. Other contrivances may be made to work upon the periphery of a circle, so that the top of the series being placed nearest the centre, opens to but a small extent for a larger range of motion between any two bars at the bottom of the series.

(81.) This kind of motion, requiring whole series of movements to move upon other movements, is a

new requisite in mechanical contrivances; or at any rate I am unacquainted with its use amongst the machines which abound in this great metropolis.

(82.) When the vast extent of a machine sufficiently large to include all words and sequences is considered, we at once observe the absolute impossibility of forming one for practical purposes, inasmuch as it would cover an area exceeding probably all London, and the very attempt to move its respective parts upon each other, would inevitably cause its own destruction. Nevertheless, those lesser machines containing but a few elements, exemplify the principles of their operation, and demonstrate those laws of induction, deduction and relation, the right use of which cannot fail to render our thoughts more accurate, and our language more precise. The best form for the readings on the machine may be illustrated as below. When the machine is shut up it will appear as printed, and by cutting it diagonally, it will give a reading when open of either None, Some, All.

(83.) If we examine the results which can be obtained from the use of the relational machine, we observe that an action represented by an opening at any point represents a similar action upon every other element placed below it in the series, and also a partial action of every element having relation to it at the higher part of the series, hence the value of every expression, and its relation to other expressions, can be read off.

(84.) The machine, however, can do more than this; for two or more facts, or two or more assertions, can be represented by actions in a similar manner. Like the human brain, it is competent to give the resultant of any number of propositions be they ever so numerous, and show their mutual bearings upon each other.

(85). If the machine were sufficiently extensive to comprise every fact or principle which has been ascertained, then when any new fact is learnt it might be appended, and its bearings upon more general instances, or more particular cases, would be immediately shewn.

(86.) It is thus apparent that this mechanism gives an analogous representation of the natural process of thought, as perfectly as a human contrivance can well be expected to afford; but when we take into consideration the knowledge of the laws of