PLANING CAST-IRON — PO- of lengthening and shortening a pen

LISHING PLATE-GLASS. dulum by so easy a method, and with “ 'The machine for planing cat- such degree of accuracy, as to solve iron piates: and also the engine or the problem in a manner nearer truth mill for polishing plate-glass, by horse, than had ever been done before, and wind, or water, are inventions of very renders it probable, that, with somegreat merit. But it suits not the in- improvements, it may become pertended brevity of these observations, to feci." defcribe the several excellent machines A gentleman, well known to men in possession of the Society, which will of science for his skill in mechanics be belt understood by viewing them in and mineralogy, has since completed the repository."

what this candidate began. The acWEIGHTS AND MEASURES. count will be published. Let us not,

The discovery of an univerfal therefore, anticipate any further the standard of weights and measures has pleasure which fo important a discovery long been wilhed for by the learned in met communicate. every part of Europe, and the Society, In another Review, we shall proceed. in hopes of obtaining fo desirable an in our account of this volume. We object, offered considerable premiums, have given very copious extracts from which extended to persons residing in this work, as the improvements which any country whatever, To the honour it records refcet the higheit honour of this nation, a mode has been found on thc Society, and on our nation.

Art. XXIX. Advice to the Cuerfities of Oxford' and Cambridge. 12 moe Kearsley.

THE fame which the author of model yourself accordingly. You must the “ Advice to the Officers of the put on a severe countenauce, speak British Ariny" acquired by his work roughly, and walk in such a manner as has induced another writer to attempt though you felt your consequence. " the arduous talk" of imitating “ You are next to take every method Swift. But

in your power to render yourself par. " I hate e'en Garrick thus, at second hand,” ticular; this is peculiarly requisite to as Churchill faid of Holland. There every felf-consequential man: make is always something awkward, fome- new laws, because there are not fuffithing unfinished in imitation. We cient already, or search into the statute frequently find ourselves impreiled book, and whateve law your predewith an idea of the fereral purts, but ceilors have passed over as needless, or yet, that nice cement which unites have thought too difficult to put in every various particle, and forms a execution, do you be fure to fix

upons complete whole, cannot be aequired.

and order it to be, Itrialy observed. How far the Book of Adiice which The less beneficial, or the more dif is before us may be allowed to defend liked it is by the university, so much imitation, let our readers judge for the more it will enhance your authotheinfelses, by the following extracts: rity, in being able to put it in execu

To the l'ice-Chancellor. tion. Here are statutes in plenty, to “ The power annexed to your answer your purpose in this particular, office is vaft and almost unlimited; you and though time and custoins have, in have authority both to enact, and put the present age, made them appear in execution what laws you please; rather absurd and ridiculous, that is you have fervants around you, ready to too insignificant a reaton to be the guide obey your nod at a moment's warning: of your conduct: and by reviving thofe in short, immediately on being in

fiatutes, which are most contrary to vested with the office of Vice-Chan-, prefent ufanyes, you will lhov a proper cellor, you should look upon yourseif contempt to th-in. as an entire new man, and begin to " its drets is chielly governed by Custom, I would attend to that par- · verely for the least fault, and extend ticularly; not by forbidding laced his authority to the very utmost. - Here coats, and other tinfel finery, for this should be his ultra; "he must rale would net be sufficiently fingular now yield to a principle no less urgent to bear a date in the annals of your than the former; viz. felf-intereft. reign; but I would attack the head- If an under graduate pays him, as tupiece at once, and make a standard of tor, but eight guineas addition per anineafure for all wigs, curls, queus, nuin (for inof resident Fellow's have clubs, &c. &c. &c. reserving to myself some pupils) and is a profitable memthe right of wearing the largeit wig, as ber of society, let this be a fufficient being the greatest man in the university. recompence for any thing he may com

"King Ileary the First inade his arm mit within his cognisance, either in the standard of meature for a yard; contempt of his own authority, in deand as every instance of arbitrary power fiance of the rules of the college, or should be adhered to as strictly as pos. the statutes of the university. In Thort, sible, I would order, suppose, my little let him submit to any thing, if it will finger to be the length of every curl, be the means of adding to his present and no queu, under pain of the severest finecures, or of keeping those which penalty, to exceed the length of my he has got. great one.

Thus, you will have the If, in the long vacation, he should whole university under the command condesvend so far as to visit his friends, (you may say) of your little finger; and and mix a little with the world, let have the credit of executing the full him be sure to keep up his college power of your office, with the cha- rules and manners, and not yield to racter of an active and arbitrary ma- thofe of fashion; which he ought to gistrate.”

contemn, as the parent of folly, and To the Fellou's.

mere child of whim and fancy. - -Let A Fellow of a College is a person his whole demeanour and conversation of very high rank and consequence in Tow his contempt of these, as if the the univerfity; his power, fo far as his whole world was inferior to him, and jurisdiction extends, bears allmoft an that true and proper manners were only unlimited fway. The Under-Graduates to be learned in a college library.of the College are put under submissive Let him not fail, however, to catch obedience to his command, for a ne- the first opportunity of thowing his gleet of which he has a power of in- own taste and learning: let him pour flicting a very severe punithment. His forth his sentiments in abundance, with only business is, to eat, drink, and quotations from old Greek and Latin deep; his only care, the means of fil. authors, and tell his long, dry, legending up his idle hours.

dary tale; this will give him, in the * As we have just said how conse- opinion of the ladies, the character of quential an office this is, a Fellow deep knowledge, and profound wifouglit to be thoroughly sensible of it, dom.-hould any one fpeak indiffeand endeavour, as much as possible, to rently, such as concerning the weather, keep up his dignity: and in some things or any external object, merely for the he mai observe the rules laid down for sake of saying something, let him imthe pročtors; such as, if an under gra- mediately er.deavour to account for it duate neglects to cap him, to punish philosophically, quoting the opinion of liim severely, keep him always stand. each author, from Copemicus down to ing, and the like I would only advise Ferguson. Now and then, however, him at the same time, that, as his pow- he may attempt to shake off the Fellow, er is rather of less extent than the and let the company see can be any former, so he ought to keep exactly to thing, by telling a merry story which its limits, ifi quodam prodine tenus, fed happened at college fifty years ago: non datur ultra.-He should have all as soon as he has finished, he should the dependant members in absolute, not wait for the approbation of the submisive obedience; punish them fe- company, but thew chat he thinks it

3 La

an extraordinary good thing, by raising all the morning, let him not ftir, on a laugh louder than all the rest.-By any account, within the walls of the such behaviour ought a Fellow of a college, without a large Greek folio College to distingujih himself from the under his arm, appearing to mafe, cioud of other mortals. How con- every step he advances, on some intritemptible! how insignificant! is the cate point of dispute, or on some subfashion and custom of the world; when ject the most dry and remote from comcompared to those rules, which have mon observation. antiquity for their origin, and which " When he wants to lounge with cach'fuccessive order of Fellows have another person, he should appear as if constantly observed with the most scru- he went merely to folve some deep pulous exactnefs! Let not, therefore, question of this kind, and suffer him. any one of you be so far forgetful of felf to be detained not without the these rules, as to give them up for those greatest difficulty; with a continual which whim firit invented as a pattern complaint of the idieness and folly of for ignorance and folly.”

others, who can so lounge away their To the Quiz.

time, which to him is so precious, and " A Quiz, in the common accept which he devotes constantly to study. ation of the word, fignifies one who " Whilst his room is cleaning out, thinks, speaks, or acts differently from let him handle his folio again, which the rest of the world in general.' But, should be always ready for that puras manners and opinions are as various pose, and march, reading, with llow as mankind, it will be difficult to say itep, up and down the quadrangle; obwho shall be termed a Quiz, and who serving to choose that part oppolite his thall not; each person indiscriminately tutor's window, and to have his hook applying the name of Quiz to every one open towards the latter end. - When who differs from himself: not to lose he is in his rooin, he should be always myself, therefore, in the labyrinth of sure to shut the outer door, that he opinions, suffice it to say, that those may appear to avoid loungers, taking to whom the term has most commonly particular care, at the fame time, to been applied have held it in a good let every one in who comes; to few fense, and, by the skilful alteration of them the folios which he has read, and a letter, produced the opinion of How the notes, commentaries, criticisins, race in their favour; Vir bonus eft &c. &c. which he has tranferibed.quis." -Others, by the contrary rule, Manuscripts of this latter kind he have held it in an opposite sense. Mould firew all over his room; and

But, to confine myself within the keep his folios, some open, and some precincts of the university', froin whence piled up, one upon another, on each I believe this amphibious creature ori- table. ginally forung; 1 conceive him to be “ The Lectures of the College should one of those dull, pedantic, spiritless be his particular study, that he may be animals, who jog on in the same beaten able, in the eve of his tutor, to outtrack, pulled along, as it were, by mine the rest of his class. Should rules, and frightened, every fiep he another person at lecture not be able adrances, with a continual' terror of immediately to prove some cry piosconces and impositions. Influenced in blem in Euclid proposed to him by his his conduct rather through a dread of tutor, let him be fure, by whispering, punishment, than through a real desire gesture, and features, to thew all preof doing what is right.

fent that he is perfectly acquainted with " A Quiz, therefore, ought, by it, and able to folve it iminediately. every litele art and appearance, to en

It will not be amiss to fet down a few hance his own merit, and depreciate, rules to be observed in the above case. as much as possible, that of others, in If the person to whom the querthe opinion of those who are placed in tion is put should hesitate a little, and authority over him.

not give an immediate answer, he " If he is tired of being in his room should, in that case, whisper it to his next neighbour, but it must be in such else a side-shake, with a grin and a manner, that every one present, par- squint; signs that he thought him very ticularly his tutor, may be sure to hear lucky in hitting upon the point, and it. This will anfwer two purposes; that it was much contrary to his expecit may have the appearance of good- tation. nature on the one part, and few his “ In his conversation he should knowledge and abilities on the other. assume the air of a pedant, by studiving

: “ If he gives a wrong answer to the it long before he attempts to speak, question, he should in that case be pre- and taking care always to select words pared with as many signs and antics as the moft remote from common use." Punch in the pupper-hew; he should The persons, who are honoured with move about in his chair, figh, gape, this author's advice are, The Vicegrin, extend his front, and contradict Chancellor; the Proctors; the heads of the side part of his face, like a man Colleges; the Fellows; the Burfar; the half farved.

Under Graduates, who are dividedinto “If a right answer be given, he the Quiz, the Rapht, and the Buck; should then give a nod of affent, ac- and the Cook. companied with a very gentle smile, or

Art. XXX. The Plilosophical Transactions of the Royal Society of London, Vol. LXXII. for the Hear 1982, Parı li. London. Davis and Elinlley.

Concluded from page 333.) WE have already given an account little on the subject of extracting the of the first leven papers in this volume. equal roots of an equation by pure We ihall now conclude.

algebra. The most that we find on it is VI. new Method of finding in Mr. Maclaurin's treatise on Algebra, the equal Roots of Equations by di

where it is shown that when any equavision. By the Rev. John Hellins, tion' has two equal roots, it may be Curate of Conftantine in Cornwall. depressed one dimension; and, conse:

In the introductory paragraph, Mr. quently, its solution will be rendered Hellins informs us, that the theorems more easy. For instance, if the equacontained in these papers were the pro- tion were a biquadratic one, one of the duction of his younger years, when equal roots might be had by a cubic Algebra was his favourite tłudy, having equation; or if it were a cubic equabeen invented by him about twelve tion, one of its equal roots might years since; and that the first of them be obtained by a quadratic. But Mr. was published, as a specimen of this

Hellins thews how to reduce such method of extracting the equal roots equations to any lower dimension the of an equation, about eleven years ago. algebraist pleases, even to a simple equaWe remember to have feen it, and thail tion, if it be proper; and, consequently, remark, that the modest title he gave how to find the equal roots by division. it deserves to be iinitated by other His theoreins are general, and are ilyoung authors. It was “ A Method luftrated by suitable examples. Mr. of folving Cubic Equations that have Simpson, indeed, at p. 49 of his equai Roots, by division.” For though Fluxions, 2d edit. has given a very the method was new to him, yet, as we elegant fluxionary method, not only of are well informed, he thought it too knowing whether any proposed equamuch presumption in a young man,

tion has equal roots;

but also the under twenty, to call any of his in- number of such roots, and likewise ventions new, until they had been ac- how to find them: but this is a conknowledged as such by those whose fideration of a higher nature. It is not, years and extensive reading render chem however, the only instance in which the

doctrine of Auxions may be fuccessfully Before vír. Hellins, we had very applied to operations purely algebraical.

It We must refer those who are art of a College," and wish to be a quainted with this order of

being, the Book 01 Advice,

proper judges of it.

It has been supposed that the num- dom on the Animal Creation. By ber of equations that have equal roots John Ingenhousz, Counsellor to the is but small, and confequently, that Court, and Body Physician to the Emthe chief use of the rules for finding peror, F. R. S. &c. their roots, is to obtain limits and ap

Read June 13, 1782. proximations to the roots of equations The ingenious author of this paper in general. That use, it must be has publishedthese Further Confiderations, allowed, were it the only one, is suf- in order to defend the stem which le ficient to repay the labour of investiga- laid down in a former memoir, arbich ting them; but if the equations that several of his friends had' afferred was have equal roots should hereafter be quite overturned by the fifth volume found not so few as has been generally of Dr. Priestley, and by an experiment fupposed, the use of Mr. Hellins's quoted in Mr. Cavallo's book upon ait. theorems will become more extensive. The experiments which are here de

The concluding paragraph, as it fcribed, were made by Dr. Ingenhousz, fuggests that Mr. Hellins has other in the presence of several friends, in a improvements by him in this branch of hot-house of the botanical garden, in science, we will give in his own words. the winter 1782. • I beg leave to add, that this Thort This


from its nature will not essay is but a small part of a work, in adınit of extract; and an abridged riew which; if I ever should have leisure to of it would probably rather hurt than put a finishing hand to it, something forward his caufe.' We must, there more on this fubject may very posibly fore, refer thofe who have been ftagappear. In the mean while, I hope, gered by the authorities of Prieities this little piece will be candidly viewed and Cavallo to the memoir, as it Itands by thofe who have more leisure and in the Transactions. butter abilities for studies of this kind.” X. A Microfcopic Defcription of We heartily with Mr. Hellins leisure the Eyes of the Monocuius Polyphemus to finish his work, and thall dimifs Linzi. By Mr. William André, Sure this article with observing, that by the geon. sitle of his paper, it appears that Mr. This paper, with which the rolume Hellins's proviñon is a curacy; we concludes, has already been inserted ia cannot but lament that science and this miscellany. The reader will find ingenuity has found no better encou- it, in the department allotted to laragement.

tural History, in the London Magaix. Some further Confiderations on zine for August 1783. the Influence of the vegetable ling

EULER, DATED SEPT. 30, 1783.
HEN I wrote to you last, I o'clock in the afternoon, he was ftruck

with apoplectic stroke, which on hare fallen to my lot, to have an-. a sudden deprived him of his senses. nounced to you the melancholy news He lay until eleven o'clock the same of the death of our great and incom- evening, when he died. He retained parable EULER. On the 16th of Sep- all that presence of mind, and solidiry tember he found himself much indif- of judgement, so natural to him, until posed, and was taken with a giddiness the fatal moment that he was seised, in his licad. On the 18th, at four as you will see by the conversation I


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