would pour upon the gudgeons and pistons of his engine acids instead of oil, just for a change, because this would be in opposition to his knowledge of the laws of mechanics, and spoil his machine. Yet he will pour wine and brandy, and tobacco juice into his stomach, and tobacco smoke into his lungs, which are infinitely more delicate organs than any thing of wood or iron.

If a dyer should use his old dyes over and over, and expect to produce fast and deep colors, or if the chemist should use acids over and over and expect to produce good salts, he would show himself so ignorant of his business as to lose employment. Yet men will breathe air over and over, and seem to expect that, by these imperfect means, they shall purify the blood.

If the laws of life were as well understood as the laws of matter, we should see no more mistakes in the management of our bodies, than we do in the management of our machinery; and if Physiology were as well taught in school and elsewhere as Natural Philosophy, its principles would be as familiar, and as ready for use.

The remedy then, for these evils and errors, is to incorporate the study of Physiology in the course of universal education. Give this science a prominence in all our schools, in proportion to its importance, to its bearing upon human health and human life. Then will men be saved great suffering, and be so far prepared to fulfil their natural destiny on earth.

NOTE. On account of the great length of the preceding Lecutre, and want of time, part of it was omitted at Hartford.

The readers of the Christian Examiner will here recognise many of the sentiments and some entire paragraphs which I published in that Journal for July, 1843, and which are here taken without acknowledgment. E. J.

DORCHESTER, Mass., Oct. 17, 1845.

In saying to you what I may be able to offer on the topic allotted to me, I need not occupy your time with remarking in general on the importance of the study of Arithmetic in schools: a study whose results are of universal application in common life; and the pursuit of which furnishes in a higher degree than any other one study, an easy and sure means for the discipline of the mind. Its various stages, too, are fitted for every variety of age, and for all degrees of mental power. Arithmetic, therefore, holds and should hold a prominent place among the studies of the common school. Perhaps it is not too much to say, that on an average one half of the time spent in study in our common schools is occupied with this branch. Besides the

liberal share of time uniformly allotted to it in the regular arrangements of the school, this study is a kind of reservoir into which are thrown the fragments of time not taken up with other things. It is the residuary legatee; or the old official, entitled to all the waifs and strays; so that in supposing that one half the time in common schools is occupied with arithmetic, I may have estimated it below, rather than above the truth. From this fact alone, if from no other from the amount of time employed in this branch of study—the subject before us invites our sincerest interest, and the best thoughts we can bring to it. A small saving in a boy's time, when he is one of a million, and the saving may be applied to the million as well as to one, becomes an immense gain: in the first place, because “time is money," and, secondly, because that time employed in vain, without fruit, is worse than the absence of money; it is counterfeit money.

The terms in which my subject is expressed, Intellectual Arithmetic, at once suggests to us the great change that has been wrought in the whole department of arithmetical instruction, within the recollection of most of those who are present. It is not many years since Intellectual Arithmetic began to receive any attention as a distinct object, in the studies of our schools. The only apparatus for arithmetical study was the slate and the old book, full of mysterious questions, and bristling with rules. In most cases the analysis of the principles involved in the operations was not attempted. The pupil was given

up to struggle on his way as he best could by rules, the sense or reason of which it was utterly beyond his power to comprehend. And it is no reproach to the teachers of that day to say, that, with few exceptions, they wrought in the formal and mechanical spirit that then prevailed. Why should they have been in advance of their time? To say, as is sometimes said, that the old system did, after all, make good arithmeticians, is claiming, as to the fact, the exception for the rule; and imputing success, when it did occur, to what was in reality an obstacle to such success, and not a help. No one was ever made an arithmetician by rules that seem entirely disconnected with an ultimate analysis of the properties of numbers. No generation, indeed, is destitute of some who will be distinguished in whatever branch of study invites their attention; but such owe their progress to something else than a system of rules whose application is, to such a mind, harder to discover than it is to do the work which the rules were intended to facilitate.

Having spoken thus of rules, perhaps I ought to say a word more, that I may not be misunderstood. There are cases in which the formula, by which a question is most readily solved, is reached by so long a process of reasoning, that, even by the aid of the most lucid statement, the analysis cannot be at once grasped by the mind. Here, manifestly, the reasoning must be dropped, and the formal rule employed, which expresses only its results. An instance of this kind, for ordinary capacities at least, may be