ONE:"So far you have made it quite plain," Leona murmured, "but I fail to see that all the rest was easy."In the driving gearing of planing machines, conditions which favour the reversing movement are high speed and narrow driving belts. The time in which belts may be shifted is as their speed and width; to be shifted a belt must be deflected or bent edgewise, and from this cause wind spirally in order to pass from one pulley to another. To bend or deflect a belt edgewise there will be required a force in proportion to its width, and [133] the time of passing from one pulley to another is as the number of revolutions made by the pulleys.
TWO:Motion or power may be varied to almost any degree by the ratio between the pistons of pumps and the pistons which give off the power, the same general arrangement of machinery answering in all cases; whereas, with gearing the quantity of machinery has to be increased as the motive power and the applied power may vary in time and force. This as said recommends hydraulic apparatus where a great force is required at intervals, and it is in such cases that it was first employed, and is yet for the most part used.Disjunction is, in truth, the primordial form of all reasoning, out of which the other forms are successively evolved; and, as such, it is common to man with the lower animals. You are taking a walk in the country with your dog. You come to a stream and jump over it. On measuring the distance with his eye, the animal is afraid to follow you. After waiting a little, he first runs up stream in search of a crossing, and, finding none, returns to look for one in the opposite direction. Failing there also, he comes back once more, and either ventures on the leap or makes his way home by some other route. Now, on considering the matter a little more382 closely, we shall find that hypothetical reasoning takes its rise from the examination of each separate alternative presented by a disjunctive premise. A plurality of courses being open to us, we consider what will ensue on the acceptance or rejection of each. The dog in our illustration thinks (after a canine fashion) that if he jumps he may fall in; if he does not, he will be left behind. Hector will not take refuge within the walls, because, if he does, Polydamas will triumph over him; nor will he offer terms of peace, because, if he does, Achilles will refuse them. Once more, categorical reasoning is developed out of hypothetical reasoning by the necessity of deducing consequences from a general rule. Hector must have argued from the known characters of Polydamas and Achilles, that in certain circumstances they would act after a certain manner. We may add, that this progress of conscious reasoning is a reproduction of the unconscious logic according to which life itself is evolved. All sorts of combinations are spontaneously produced, which, in consequence of the struggle for existence, cannot all survive. Those adapted to the conditions of life are selected, on trial, at the expense of the rest; and their adaptation or non-adaptation is determined in accordance with categorical laws. Furthermore, the framing of a disjunctive proposition necessitates the systematic distribution of possibilities under mutually exclusive heads, thus involving the logical processes of definition, division, and classification. Dialectic, as Plato understood it, consisted almost entirely in the joint performance of these operations;a process which Aristotle regards as the immediate but very imperfect precursor of his own syllogistic method.276 You cannot, he says, prove anything by dividing, for instance, all living things into the two classes, mortal and immortal; unless, indeed, you assume the very point under discussionto which class a particular species belongs. Yet this is how he constantly reasons himself; and even demonstrative reason383ing, as he interprets it, implies the possession of a ready-made classification. For, according to him, it consists exclusively of propositions which predicate some essential attribute of a thingin other words, some attribute already included in the definition of the subject; and a continuous series of such definitions can only be given by a fixed classification of things.
