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Instructions as to the relation of objects to each other were now entered on. A small box being placed on the table, one of the youths, at the request of the master, first named the different parts of it -- top, side, bottom, &c.; and subsequently the relation of objects as respects position in regard to it. For instance, when anything was placed upon it, the word "sur" was given, and so also "sans," "dedans," &c., according as the little object was put in these various situations in relation to the box. Here was an evident advance on the other exercises, showing an increased capacity of comprehension. The simple, natural, and easy way in which such knowledge was communicated, was at once strikingly applicable, and was also admirably calculated to excite the mental faculties, by extending the very limited range of comprehension bestowed on these unfortunates.

A model clock was now brought out. It was constructed so that the relative position of the fingers could be altered at pleasure. Under the direction of the tutor, the different hours of the day were indicated, as well as the fractional parts of an hour. The face of the clock, thus varied, was presented to several pupils, when the time was correctly and exactly stated by each. During the progress of these examinations, several of the boys advanced from the main body who had remained seated around the room. The few who thus left their fellows gathered round the table, and seemed to take interest as well as pleasure in the proficiency manifested by their brethren. Every now and then they approached the place where I was seated, and looked up inquiringly, as if desirous to know what I thought of their proceedings. That they were capable of entertaining such feelings, was made evident by several simple occurrences excited by passing events during my stay among them. Some amount of interest in each other was also shown, and the extent to which care was exercised by the improved over the more ignorant and wayward was undoubted. I was particularly struck on one occasion by the manner in which an elder boy led back to the seat his younger and more restless companion, in whom the system of education had not yet produced that power of self-control which most of the boys had attained. The youth who rendered this service to his neighbor had attracted my notice when I first entered the room. He presented every appearance of an idiot of the most hopeless class, to such a degree that I singled him out as one worthy of particular observation, with a view of ascertaining how far the functions of an intelligent being could be imparted to one apparently so forlorn. I may here mention, that at a subsequent stage of the proceedings this same boy advanced to the table, and appeared to take an interest in what was going forward. Observing a small note-book I held in my hand, he took it up, opened it, and after turning over a few leaves, returned it to me, as if his curiosity was satisfied.

The mode of communicating ideas of numbers, and of their corresponding signs, (figures,) was as simple and successful as the methods adopted of imparting a knowledge of the properties and positions of objects. The result of their tasks in this department showed how applicable such a system was to their feeble understandings. Several circular pieces of ivory were first placed on the table, and then divided into two unequal portions, so as to communicate the idea of quantity by requiring the pupils to say which was the larger and which the smaller portion. A certain number were then placed together, say three or four, and the question was asked -- How many are there? The answer being given, the attention of the pupil was directed immediately to a board on which were painted the figures, and opposite to each figure a corresponding number of circular spots of the same size as the pieces of ivory. He here saw the figure placed opposite the number of pieces before him, and the idea of number was produced; thus several sums in addition and subtraction were now undertaken, and in the execution of these, the board was sometimes used as a means of fixing attention and assisting the memory. The more proficient, however, readily replied to the various questions put to them without calling into operation the aid of the sense of sight. They answered correctly, and without hesitation, such questions as -- How many do 6 and 8 make? Take 3 from 9, and how many remain?

I was particularly struck with the burst of feeling produced in one of the junior pupils when foiled in the performance of his task. He was seated at the table on which were laid the pieces of ivory. These were first divided into two unequal portions, and he was requested to point out the greater and the smaller set. Three of the circles were then given to him, and he was desired to take from the others an equal number. Having performed these tasks, an even number were placed before him, with the request that he would divide them into two equal portions: this he proceeded to do by taking out very slowly and carefully the half of the number. An uneven number, consisting of nine pieces, were now given to him with a like request; this he tried to comply with as before, by separating four on each side: he then hesitated, re-examined his numbers, seemed perplexed, and at length finding, after a little pause, that he could not perform what was required of him, he burst into tears, and showed, by the difficulty which was experienced in assuaging his grief, how deeply he was capable of feeling both disappointment and vexation at his supposed inefficiency. This little incident told plainly of an important influence brought into operation. It explained how much could be done by acting on the amour propre. The grief at discomfiture, as well as the pleasure excited by success, showed that this power was used as a key to unlock dormant faculties, and to open the portals of intelligence.