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press, respecting the partiality of these examinations, plainly shows that there is a weak point somewhere. None such, we believe, appeared in Dr. Gregory's time.

During the professorship of Dr. Hutton there was interspersed a good deal relating to military subjects in his · Course, which, as far as we can judge, tended very little to the real wants of the military officer, if he studied with professional views alone; and had he not been under the necessity of making two volumes of his work, he would doubtless have left out much that he inserted upon gunnery, upon penetration of balls, &c. which, though good in its way, was not exactly a subject for class study. He would scarcely have dwelt at such length on the purely imaginary, and useless problem of projectiles in vacuo, which is only calculated to mislead the mind of such pupils as those who usually resort to the Royal Military Academy: and he might have, as the practical gunners now do, left out of consideration the path of the ball, and have merely formed a table of ranges for the several classes of guns, for specified elevations and charges. Many of his theoretical subjects have never been read in the Academy; and many others might as well have been omitted, if we may judge from the utter inattention with which they are treated by the officers in after life. With respect to the third volume of Hutton's Course, it was manufactured with the aid of paste and scissors, out of various tracts and works of Drs. Hutton and Gregory already before the world; well enough in their way, but sadly wanting in adaptation for forming a course for boys like those who constitute the mass of the gentlemen-cadets. In fact, we doubt whether half a dozen cadets had ever read each a dozen pages of that volume.

In 1836-7, Dr. Gregory, with the aid of Mr. Davies, published the eleventh edition of that work, many parts of which were much modified, and several new subjects, and new modes of treating others, were introduced into it. As a general course of mathematics it was an immense improvement upon the older editions. We do not take this upon hearsay, as, having looked much into mathematics, we can judge for ourselves; and certainly, we should be led to think, from our own views of what a military man may possibly want of mathematics, that it was also much better adopted to his use. Upon Dr. Gregory's resignation, and the accession of Mr. Christie to the Chair' in 1839, Hutton's Course was expelled from the walls of the Royal Military Academy; and the learned professor was thus enabled to accomplish a threat which he had not for

thirty yeras been at all scrupulous in making, with respect to Dr. Hutton, chiefly on the grounds of personal feeling. After five years, during which time there has been no text book for the use of cadets, and whose instruction had been during that period just what each master thought proper to give, the professor has presented them with 'An Elementary Course of Mathematics, for the use of the Royal Military Academy, and for Students in general, Vol. 1; comprising Arithmetic and Algebra’—and, what a course ! Were it not a book destined for the public service, we should, at a glance over a few of its pages, have consigned it to oblivion, as our cotemporaries in general have done; but as it is, we feel we should be guilty of a public wrong in so doing. The injury done to the service during this lengthened period of irregular and unconnected studies of the cadets, no one can estimate; but it is no secret that much dissatisfaction has arisen amongst the cadets, the masters, and the service itself. We would ask, is there any private office or place of business that would have put up with such irregularity? We have heard very free remarks—but we forbear to quote them—touching the imbecility of the authorities of the institution, in permitting the wrong-headedness of a pompous pedant to throw the system into almost irretrievable confusion.' We offer no opinion, as our knowledge of the facts is too vague to justify us in such censure; though in a public institution, devoted to public purposes, and supported out of the public purse, such allegations deserve the most serious attention and rigorous investigation.

We had been led to hope that after the loud heraldings of this promised work in circles which we have been in the habit of frequenting—the Royal Society tea-room amongst the rest—for four or five years, that we were at length to be blessed with a ‘Course of Mathematics' embodying all the excellencies of preceding Courses, and to be wholly unapproachable by any future writer, except by plagiarizing this. In fact, the world in general was apprised, that an intellectual chef d'ourre was about to be produced, another Pallas from the skull of another Jupiter! And magnificent, indeed, was the bearing of the 'thunderer,' when any allusion was made to the expected book.

We have it,—and, lo! what do we see? Six hundred large octavo pages upon immortal arithmetic and algebra alone! Why, this beats Professor Scott: and had we seen this before we reviewed the Sandhurst Course, we could not have so far wronged that author, as to consider his (as we then did) the ne plus ultra of absurdity and pretension. We have now got beyond the world's end-down, positively, into the sunless and dreary regions of old Tartarus himself. Truly this is an age of enterprise, and men venture as recklessly upon deeds of intellectual as mechanical daring.

Our procedure has always been the despised practice of reading the preface before reading the book; for we like to see what an author has to say for himself. It enables us in some degree to test the value of the book, by observing how far the writer has succeeded in carrying out his own intentions ; as also to observe, whether modest merit or bold pretension be the tone of the author. In the present case we see much to foreshadow the temper of the work; a tone of assumption is maintained, and a self-confidence, which, in our memory of prefaces, is without precedent, for when modesty does not really exist, there is usually a semblance of it; but here is neither the shadow nor the substance. We see, too, a hostile feeling evinced towards one of his colleagues which is most unbecoming ; and insinuations thrown out which we verily believe are utterly without foundation. Our conviction on this head led us to look through the work with some care; and seeing the same spirit displayed wherever the same name is mentioned-a name which it appears to be an object with Professor Christie to 'insinuate away'—we have taken considerable pains to investigate these charges, by an appeal to such authorities as are, in the scientific world, decisive. But more of this shortly.

The next thing that strikes us is the everlasting repetition of the various cases of the important pronoun of the first person ; it is absolutely overwhelming. I have undertaken’—I consider'-'I endeavour'-'I have dwelt—and so on. single paragraph of half a page it occurs no less than seven times ! It throws our own editorial plural unit' into the shade, and betokens that the Professor is at any rate ' upon good terms with himself,' whatever he may be with other people.

With respect to his opening statement we have no means of directly judging of its correctness; but the information which circumstances afford (and these are sometimes awkward things enough to deal with) we should be led to question its truth in the sense which most persons would attach to it. More is certainly implied than said—a species of composition in which our Professor, to do him justice, is well skilled. We shall, however, leave this to the discussion of those who know more than we do.

In the second paragraph is contained a most serious charge against the management of the mathematical studies precedent to the Professor's accession. It is neither more nor less than this,-that for a whole century the study of mathematics was

restricted to the acquisition of working rules and formula, which might occasionally be applied to professional objects.

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And are we to be told that this is all the cadets have done in the way of mathematics during the professorships of Simpson, Cowley, Hutton, Bonnycastle, and Gregory? If this be so, we need not wonder at the result, even as instanced in the case of our two friends of the Dublin steam-boat.

But we ask, how comes it to pass that Professor Christie, with his confessed knowledge of the inevitable scientific ignorance of young men so educated, has been so active in getting them dubbed ‘F.R.S.,' and in procuring them the appointments to the magnetic observatories, as he is understood to have been? Most persons will be led to infer that either the implied charge was a libel upon those who, not being able to reply to him, he can libel with impunity; or else that he has some singular notions respecting the nature of the duties he owes to the public and to the Royal Society: we are ignorant of his system of ethics, at any rate, if he can reconcile them to his own satisfaction; but the reconciliation will, probably, turn upon some studied ambiguity of expression.

In the last paragraph we are told, that his aim has been so to treat the various subjects, that a boy of fourteen years of age, with tolerable abilities, and having a strong desire to learn, should be able to master them by succession, without the assistance of an instructor.' That is, in other words, to dispense with the costly and useless asparatus of masters' at present employed in that Institution! They have much to thank him for, truly; and we hope they are duly grateful for his kind intentions. Still we pledge our reviewing life upon the result being far otherwise; and we feel confident that the said instructors' will find their difficulties, in rendering arithmetic and algebra intelligible to their pupils, increased to a great degree, by means of these ludicrously extended explanations of what other authors render clear by a few words. We will appeal to the masters themselves, if they dare but to speak audibly.

To be very methodical he begins with definitions, and to be unlike everybody else in something at least, he calls them with his accustomed brevity, "explanations of terms.' We shall content ourselves, and we expect our readers too, by quoting only three of them. :

•1. Under the term MATHEMATICs are comprehended those sciences which treat of magnitude, number, and quantity.'

*11. A postulate is a self-evident practical truth.'

• 18. Analysis, or the analytic method, is that by which a remote truth is discovered, by assuming that what is required to be done is done, and then, by reasoning from the more complex back to the more simple, finally arriving at a known truth. Analysis is the method usually employed in algebra.' (Algebra, by the by, is a term not 'explained in his present series. ]

Can any mathematician read these passages without a blush for the confusion of mind which they indicate in their author ? What is understood by quantity apart from magnitude and number? What can be meant by a self-evident practical truth? But as to analysis, we feel sure that not the least distinct conception of its nature could exist in the mind that so strangely mixes up mere fragments of the description of analysis applied to a theorem, with those of analysis applied to a problem. Poor unfortunate cadets ! and are you to learn analysis' from such a book, and without the aid of an instructor,' too?

We must, however, hurry forward, or our review will, like the book itself, occupy some hundreds of pages; but we are arrested at page 15, art. 54, and, to surmount the difficulty, we shall give it entire, in order that our readers may ponder on it at their pleasure :

• 54. From the inspection of this table [alluding to a previous addition table] it is evident that if two numbers are to be added together, it is indifferent which is considered as the number to be added to the other ; thus 7 added to 5 is the same as 5 added to 7; or making use of signs,

7 + 5 = 5 +7. We may, however, here point out the reason of this. 7 is 5 with 2 added, or 7 = 5 + 2; and, therefore, 7 with 5 added, or 7 + 5, is 5 with 2 added and 5 added,

or 7 + 5 5 + 2 + 5. But 2 added and 5 added is 7 added ; therefore, 7 with 5 added is the same as 5 with 7 added,

or 7 + 5 = 5 +7 Or thus :7 is 2 increased by 5 or 7 = 2 +5; and, therefore, 5 increased by 7 is 5 increased by 2 increased by 5,

or 5 +7 = 5 + 2 + 5; But 5 increased y 2 is 7, or 5 + 2 7 ; therefore, 5 increased by 7 is 7 increased by 5,

or 5 + 7 = 7 +5. Or thus :-on the principle that the sum of two numbers is the number of units in the one successively increased by the number of units in the other, which is in fact the only basis of all addition, in adding a greater number to a less, if the less be increased successively by an unit until it becomes equal to the greater, three will still be the number of units in the less to be added. This expressed by signs will be :

5 + 7 = (5 + 2)+ 5 = 7+ 5. Or we may refer this to the axiom, that every number is made up of the units in all its parts ; thus the number 12 is made up of the units in 5 increased by the units in 7, or the units in 7 increased by the units in 5.'

In order that this original and luminous exposition may obtain the immortality to which the author not only aspires, but evidently considers himself fully entitled, we shall simply enunciate it in a form adapted to the memory, thus :

CHRISTIE'S THEOREM.

7+ 5 = 5 +7.

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