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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 caft- fuch 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 some great merit. But it suits not the in- improvements, it may become per. tended brevity of these obfervations, to fect.” 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 muft communicate. every part of Europe, and the Society, In another Review, we shall proceed in hopes of obtaining so desirable an in our account of this volume. We object, offered considerable premiums, have given very copious extracts from shich extended to persons residing in this work, as the improvements which any country whatever, To the honour it records reflect the higheit honour of this nation, a mode has been found on the Society, and on our nation.

ART. XXIX. Advice to the C'werfities of Oxford and Cambridge. 12mo. Kearney.

THE fame which the author of model yourself accordingly. You must the Advice to the Otticers of the put on a severe countenauce, speak British Army” acquired by his work roughly, and walk in fuch a manner as

a has induced another writer to attempt though you felt your confequence. "s the arduous talk”. of imitating You are next to take every method Swift. But

in your power to render yourself par"I hate c'en Garrick thus, at fcond hand,” ticular; this is peculiarly requisite to as Churchill faid of Holland. There every self-consequential man: make is always fomething awkward, fome- new laws, because there are not fuffithing unfinished in imitation. We cient already, or search into the statue frequently find ourselves impreiled book, and whateve law your predewith an idea of the fererul parts, but cetlors have passed over as needless, or yet, that nice cement which unites have thought to difficult to put in. every various particle, and forms a execution, do you be fure to fix upons complete whole, cannot be acquired. and order it to be, Itrictly observed.

How far the Buok of Advice which The less beneficial, or the more difis before us may be allowed to defend liked it is by the university, so much imida!ico, let our readers judge for the more it will enhance your authothemselves, by the following extracts: rity, in being able to put it in execu

« Tibe l'ice-Chance Ver. tion. Here are statutes in plenty, to The power annexed to your answer your purpose in this particular, ofice is vaft and almost unlimited; you and though time and culturns have, in have authority both to enact, and put the present ge, made them appear in execution what laws you please; rather absurd and ridiculous, that is you have fervants around you, ready tó too insignificant a reaton to be the guide obey your nod at a moment's warning: of your conduct: and by reviving thefe in mort, immediately on being, in

Natutes, which are moit contrary to veted with the office of Vice-Chan present afayes, yon will tho'y a proper culor, you should look upon yourfeif contempt ic: chain. as an entire new man, and begin to

" dress is chilly governed by

custoin,

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cuftom, I would attend to that par- · verely for the least fault, and extend ticularly; not by forbidding laced his authority to the very utmoft. - Here coats, and other tinsel finery, for this mould be his ne pins ultra; he must rale would not 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 anineasure for all wigy, curls, queus, num (for inost resident Fellow's have clubs, &c. &c. &c. reserving to myself some pupils) and is a profitable memthe right of wearing the largest wig, as ber of society, lee this be a fufficient being the greatest man in the university. recompence for any thing he may com

king llenry the Firit inade his arm mit within his cognisance, either in the standard of meature for a yard; contempt of his own authority, in deand as crery instance of arbitrary power fiance of the rules of the college, or should be adhered to as itrictly as pof- the statutes of the university. In Thort, sible, I would order, suppose, my little let him submit to any thing, if it will Yinger to be the length of every curl, be the mans of adding to his present and no queu, under pain of the fevereft 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 io racter of an active and arbitrary ma- those of fashion; which he ought to gistrate.”

contemn, as the parent of folly, and To the Fellows.

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 show his contempt of these, as if the the univerlity; his power, fo far as his whole world was inferior to him, and jurisdiction extends, bears almost 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 glect of which he has a power of in- own taste and learning: let him pour ficting a very severe punishment. 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 wifought to be thoroughly sensible of it, dom.-hould any one speak indiffeand endeavour, as much as poflible, to rently, such as concerning the weather, keep up his dignity: and in some things or any external object, merely for the he mar observe the rules laid down for sake of saying something, let him imthe proćtors; such as, if an under gra- mediately er.deavour to account for it duate neglects to cap him, to punith philofophically, quoting the opinion of luim feverely, keep him always stand- each author, from Copernicus 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 he 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 fubmifiive obedience; punish them fe- company, but thew chat he thinks it

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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 íuch behaviour ought a Fellow of a college, without a large Greek folio College to distinguish himself from the under his arm, appearing to mase, 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 fucceffive order of Fellows have another person, he should appear as if constantly observed with the most scru- he went merely to solve some deep pulous exactness! Let not, therefore, question of this kind, and suffer him. any one of you be so far forgetful of self 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 lourge away their To the Quiz.

time, which to him is so precious, and A Quiz, in the common accept- which he derotes constantly to ituds. 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 flow as mankind, it will be dificult to say itep, up and down the quadrangle; obwho shall be termed a Quiz, and who serving to choose that part opposite 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 room, he should be always myself, therefore, in the labyrinth of sure to put the outer door, that he opinions, fuffice 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 fhew fense, and, by the skilful alteration of them the folios which he has read, and a letter, produced the opinion of Ho- the notes, commentaries, criticisins, race in their favour; • Vir bonus eft &c. &c. which he has tranfcribed.quis."Others, by the contrary rule, Manuscripts of this latter kind he have held it in an opposite sense.

should firew all over liis 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 anotier, on each I believe this amphibious creature ori- table. ginally sprung; I conceive him to be “ The Lectures of the College should one of those dull, pedantic, fpiritless be his particular study, that he may be animals, who jog on in the same beaten able, in the eye of his tutor, to outtrack, pulled along, as it were, by mine the rest of his class. Should rules, and frightened, every fep he another person at lecture not be able adrances, with a continual terror of immediately to prove fome cry prosconces 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 defire 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 immediately:crery little 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 cafe. as much as possible, that of others, in If the person to whom the quer. the 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

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1783 PHILOSOPHICAL TRANSACTIONS.

445 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 answer two purposes; that it was much contrary to his

expecit may have the appearance of good- tation. nature on the one part, and shew his “ In his conversation he should knowledge and abilities on the other. assume the air of a pedant, by studying

." 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 most remote from common use." Punch in the puppet-New; 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 Bursar; the half farved.

Under Graduates, who are divided into “ 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 Philosophical Transactions of the Royal Society of London, Vol. LXXII. for the rear 1782, Part Ii. London. Davis and Elmiley.

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 shall now conclude.

algebra. The most that we find on it is VIII. a 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 Constantine 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 firit of them be obtained by a quadratić. 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. algebraift pleafes, even to a simple equaWe remember to have seen it, and thail tion, if it be proper; and, consequently, remark, that the modeít title he gave how to find the equal roots by division. it deserves to be imitated by other His theoreins are general, and are ilyoung authors. It was A Method lustrated by suitable examples. Mr. of folving Cubic Equations that have Simpson, indeed, at p. 49 of his equai Rosts, 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 proper judges of it.

doctrine of fluxions may be successfully Before Mr. Hellins, we had very applied to operations purely algebraical.

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

being, to the Book of advice.

2

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, 178z. proximations to the roots of equations The ingenious author of this paper in general. That use, it must be has published hele Further Confiderations, allowed, were it the only one, is fuf- in order to defend the litem which he ficient to repay the labour of investiga- laid down in a former memoir, arhich ting them; but if the equations that several of his friends had' afferted was have equal roots should hereafter be quite overturned by the fifth volume found not fo few as has been generally of Dr. Priestley, and by an experiment fupposed, the use of Mr. Heltins'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

from its nature will not essay is but a small part of a work, in admit of extract; and an abridged view which, if I ever should have leisure to of it would probably rather hurt than put a finihing hand to it, something forward his cause. 'We must, there inore on this subject may very posibly fore, refer thofe who have been fagappear. 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 stands by those 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 ditinils Liniai. By Mr. William André, Sure this article with observing, that by the geon. uitle of his paper, it appears that Mr. This paper, with which the rolume Hellins's provision 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 Niagail. Some further Confiderations on zine for August 1753. the Influence of the vegetable ling

This paper

EXTRACT OF A LETTER FROM MR. A. J. LEXELL, MEMBER
OF THE IMPERIAL ACADEMY OF SCIENCES AT PETERSBURGH, TO MR.
J. H. DE MAGELLAN, F. R. S. CONTAINING PARTICULARS RELATING
TO THE DIATH OF THAT GREAT MATHEMATICIAN THE LATE LEONARD
EULER. DATED SEPT. 30, 1783.
MY DEAR FRIEND,

in litele thought it would so foon with an apoplectic stroke, which on hare fallen to my lot, to have an-. a sudden deprived him of his fenfes. 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 judigement, so natural to him, until posed, and was taken with a giddiness the fatal moment that he was feised, in his head. On the 18th, at four as you will see by the conversation I

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