590 MATHEMATICAL QUESTIONS folved, &c. App, An univerfal ANSWER to the GEOMETRICAL QUESTION. Viz. 39,4786 LPX P2, plus 39,4786 mi. P{ x P + P p + p2 the folidity. And when L25, ?=8,544, P = 94,248 and 75,3984 feet, it is 9312,06857 cubick feet, For 1XP 2 39.4786 L P 4x P2= tic. The SOLUTION to the QUESTION in September laf, p. 416. ROM the femi-perimeter substract each fide feparately, and the continued product of the four differences, will exhibit the fquare of the area when a maximum: Thus 9X13X17X 1937791194,399074 the greatest area. But in order to delineate the figure when the area is a maximum, it is abfolutely neceffary to find a diagonal, which may be effected by the following "1 THEOREM... Multiply the fum of the fquares of the fides above the diagonal by the rectangle of the fides under it: Alfo multiply the fum of the fquares of the fides under the diagonal by the rectangle of the fides above it; and the total of those products being divided by the total of the said rectangles, will give the fquare of the diagonal required. N. B. Thefe excellent theorems I inveftigated, without confidering the trapezium as inscribed in a circle; and the first was published in the Gentleman's Diary for the year 1744: But that for a diagonal I have lately deduced, and here prefent it as a New-Year's Gift to all true lovers of arts and sciences. JAMES HEMINGWAY. Some mens heads are as easily blown away as their hats. If the commending others well, did not recommend ourfelves, there would be few panegyricks. Mens vanity will often difpose them to be commended into very troublesome employments. The defiring to be remembered when we are dead, is to fo little purpose, that it is fit men should, as they generally are, be disappointed in it. Nevertheless, the defire of leaving a good name behind us is fo honourable to ourselves, and fo ufeful to the world, that good fenfe must not be heard against it. Heraldry 1752. LEGACIES of the late Bishop of Gloucefter. Heraldry is one of those foolish things that may yet be too much despised.com The contempt of fcutcheons is as much a difeafe in this age, as the over-valuing them was in former times. There is a good ufe to be made of the moft contemptible things, and an ill one of thofe that are the most valuable. The following Particulars of the laft Will and Teftament of Dr. MARTIN BENSON, late Bishop of Gloucefter, appear worthy of publick Regard. 591 to which confiderable fubfcriptions were ASTLY, I am defirous of cafting in my mite out of the fubftance which the goodness of Providence has been pleafed to bestow upon me, towards B the relief and benefit of such of thren as are in want of it. my bre And as the first regard is due to the fouls of men, and as I, by my facred profeffion, have a more particular obliga tion upon me in this refpect, I leave to the Society for the Propagation of the Gofpel in America 20l. and I farther leave C to the fame fociety 50l. to be added to the fund for fettling bishops in our plantations, hoping that a defign fo neceffary and unexceptionable, cannot but be at lait put in execution. And I leave to the Society for promoting Christian Knowledge 401, one half to be applied to the Eastern miffion. And I leave to the Correfponding So. D ciety for erecting and maintaining Proteftant Working Schools in Ireland 201 and I humbly beg of God to blefs and profper all fuch good defigns and endeavours for preferving and promoting piety, virtue, and true religion in the earth. I leave, in the next place, 100l, to Richard Dalton, and Thomas Uthwat, Efqrs. requesting them to put it out to intereft in the funds, or otherwife, as they shall think proper, and to apply the intereft towards the maintenance of Mr. Allen, fo long as they shall think fuch affiftance neceffary for his fupport; and after his death, or after the time they fhall judge him to live not in want of that fupport, I defire and direct them to give 50l. of this fum to the Hofpital of St. Luke for lunaticks; and the other 50l. to that of incurables at Bedlam. I leave alfo zol. to the Westminster Infirmary in James street, ten to the curables, and ten to the incurables. And I again most humbly implore the Almighty and All merciful Power, who is able to afford all help, to compassionate and fuccour all thofe, who are any where in any distress, whether of mind, body, <or eftate. E Likewise I leave rol, to be diftributed by the rector of Cradley, at his difcretion, to the poor of that place wherein I was born. Likewife I leave 50l. to the mafter and officers of the Charter house, where I had the bleffing to receive my education, to be difpofed of in any way, as they shall judge moft proper † for the fervice of the fcholars there. Likewife I leave to the dean and chapter of Chrift-Church, in Oxford, of which college I had the bleffing to be a ftudent, the fum of 100l. to be difpofed of in whatever way they fhall judge proper for the fervice of that college. 4 From the INSPECTOR, Dec, 16. MONG the earliest of mankind, a promife was as facred as the most F binding obligation An affertion was of equal weight with the most folemn ap. In the fimplicity of those peal to heaven. times, mens words corresponded with their intentions, because they were the offspring of their thoughts; and their actions answered to their words, becaufe they were of the fame origin. Men were not yet accustomed to fraud; and the word, or the more awful affeveration, were always fulfilled; becaufe that which they engaged would have been done, whether they had been given or not on the occafion.. When I leave alfo 50l. to the building of the Infirmary at Newcastle, and defire that it G may be applied in particular to the finishing or ornamenting, or in any way to the fervice of the chapel there. And whereas I had attempted to set up an Infirmary in the city of Gloucester, In Herefordfire. the time of bis life. The good bishop bad been a confiderable benefactor to the fcholars in 592 Origin of OATHS, and fad Abuse of them. When the children of thefe happier fathers became divided into different ranks, actuated by different views, and under the influence of different interes, the promife, or the affurance, were no longer. Locked upon as mere declarations of what had been done, or what was intended to be done; they were now confidered not A as fimple affertions, but as teftimonies" and obligations. While they were credited, they often deceived; interest and wuth could not fubfifl together. The ins tercourfe between man and man could not be kept up to mutual advantage, without thefe evidences and engagements, and thefe were found invalid. Some expedient was neceffary, and they had recourfe to a bold one: They made the perfon, on whofe word any thing of importance depended, fwear by the living God that it was true. This form of confirmation was to them awful in the highest degree, for they were religious: They trembled to make the allegation under fo folemn an appeal; and they who had trembled to make, dared not to break it. Here was the origin of that facred form of attestation, the oath. Men, who could not be credited in an earthly court, appealed to a higher tribunal; they looked up to that above, and while they called upon the God of heaven and earth to hear their words, and as they were falfe or true, to reject or to receive them; they placed fo much upon the forfeiture, that there remained no doubt of their fidelity. App: must often fwear, fay what credit is to be given to it on this foundation; în general, none.) The oath in thofe times, when it was in truth that of which it is now the thadow, when it was the proof of right and was never administered, but under the Wrong, was held facred and awful. It most folemn forms; and was never permitted to be taken, but upon the most important occafions. How is it now?. That familiarity, which in all things is the parent of indifference, here has praduced the utmost of its influence, contempt. There are no fubjects to trivial on which an oath is not administered; Binone fo contradictory on which it is refurfed, no character fo black that is not admitted to take it; and what is worse, there is none fo bad, whofe atteftation in this form is not received as evidence of truth, except he have been already convicted of perjury, an exception that fearce difpute men fly to the magiftrate and happens twice in an age. In every trivial make oath; and thofe to whom the obligation is of no validity, expe& it to be received as a fanction by others: On every occafion of intereft men are ex pected, nay, in many they are compelled, to ufe this folemn credential, where it is known they break it. The oaths of ofregard them? The oaths of voters at fice, who ever fo much as pretended to elections, who is it that does not know they are violated as they are taken ? D Perhaps it had been better for the world, if this cuftom had never been in troduced. There is no doubt but much good accrued from it in the ages when it was first established, but in thofe which E have paffed fince, it is most probable, that while a neglect of religion has taken from this manner of affeveration all its force, it has greatly injured religion. F It is wonderful, that thofe who faw this facred test devifed upon the principle, and fupported by the authority of religion, fhould continue, and thould render it more frequent, at a time when religion was no longer regarded by the greater part of those to whom it was administered. It is atonihing, that the most important things should be decided by it, at a time when the validity and obligation of it, with many on whofe teftimony that deci fion depended, was nothing. As piety is the fource and the foundation of all that G awe which an oath infpires; the force of an oath, with regard to those who take it, will be exactly proportioned to the degree of their piety: And let thofe, who look into the lives and characters of fuch as One would imagine, that thofe in power form of many oatlis, impofed by autho looked upon all this as trivial. The very rity, is fach as renders them incompatible of the prefent time; and yet they are unwith the customs and the establishments altered: The words calculated for an earlier period are not changed; And tho all things are changed which they concern, the man who is to have the advantage, muft fwear to them. cafes, where but a moderate fhare of duty In other is required, a vast deal is implied in the They receive it notwitliftanding; and they oath on which men receive the charge. difregard it all. It is impoffible the whole fhould be complied with: It is not expected, even by thofe who propofe it, that it should: And cuftom authorizes the neglecting all. (See p. 575-) What is the confequence? Oaths are power: Thofe who would be awed by taken by thofe over whom they have no them, decline them. The offices to which they are appointed as preparatory, and nerality of mankind, devolve on those many of which are important to the ge who will not regard the obligation. "Men, Whe 1752. Extracts from the SCHOOL of MAN. who have honesty to discharge the most important truft, but have confciences too fenfible, and minds too firm, to engage for more than they shall execute, or than fhall be expected of them, are Aut out of the lift, from among whom they are to be chofen, not who will perform, but who will undertake them. " If the admitting paths in evidence, from those who pay no regard to the ap peal, interrupt much of the justice, that would otherwife be done to men oppreffed and injured by the form of our most excellent laws; the annexing thefe antiquated or inconfiderate oaths to offices of importance, is a much greater injury It robs the nation of the fervice of the best men in it, only because they are fo. No period has seen so many grievances redreffed as the prefent: None has enjoyed a tranquillity, under which thefe things might fo well come into confidera tion. This is of the first rate in its na ture and in its confequences, and alluredly it will not be neglected. of Some EXTRACTS from the Translation TH HIS book is digefted by the author into difcourfes upon various fubjects, and by giving fatyrical, tho' perhaps true characters of many of the first A 593 too credulous young man! How up happy have been the confequences! his fuggeftions have been a law to you. He commanded you to cross the fea; you did fo, without helitating: He fent you almost alone in the midft of your numberlef's enemies, who, to a man, rofe up against you, and baffled your attempts and with what difficulty did you escape? In a word, Auguftus betrayed you; and behold how foon he has changed his note! Betake yourself, fays he, whither you pleafe, I can harbour you no longer; George, Frederick † and Francis I will tal upon me: The fear of that outweighed all your pathetick remonftrances of hoBnour and religion: All you have now to do, is to fet out immediately, or worke may befal you: What can you hope for after fuch an abrupt defection? The play is over, and the curtain dropped: Hatte off the stage; ftifle all remembrance of the fplendid fchemes which fo lately fwelled your afpiring heart: Serenely Cexchange the military robe for the thep herd's coat. Instead of governing ferocious men, tend fubmiffive heep: Let. the branches of the beech form a canopy for thy throne, and the verdure of na→ ture fupply the place of a carpet: Take the crook for thy feepter; thy courage, let it be levelled at the wolves, and let sank in France, he introduces many ex- Dur flock be benefited by your exemplary sellent moral precep's. Upon education he fays, How many capped Senecas do we fee, no more than the infamous tools, or at best, the first confidents of their pupils? Shall I not deferve a reward in preventing them from being their corruptors? And a little further he adds, "To relieve the diftrefs of a friend, and properly to educate a fon, is more than giving. them life. To preferve life, to learn the virtuous enjoyment of it, is more than having received it, at a time we were infenfible of it." Upon religion he fays, "To give only in expectation of acknowledgment, that is man's way; but to heap benefits even on the ungrateful, to prevent them, to do them good against their will, in this, O my God, I behold thee: But who can imitate thee ?" virtues. Hafte thee away then; Canft thou be infenfible that a market is made of thee? But if in thy flight, thine enemies and Auguftus fhould come into thy mind, beware of wishing him any; rather thank him for not using you worse.' A little further he gives us this paragraph, Says a friend, Terona is a Eftar of the firft magnitude in the sphere of learning; if you have a mind, I will give you a fight of him to-morrow; i know a houfe where he is to be feen: Softly, I am at a lofs; Do you mean fome ftrange creature? Why, no; I am talking of that prodigy of erudition Terona, anfwers my friend: Oh! go on then. Well, are you for feeing him to-mor Frow? Fair and foftly, fay I again: What fort of a man is Terona? Is he a good parent? or fit to make a friend of? Why, replies my friend, he has indeed played loofe with fome perfons, and has expofed in epigrams others, whofe kindness to him demanded another kind of treatment; as to his religion, we will wave it: How ever, he is an admirable genius; his compofitions are fo animated, fo-well, my friend, favour me with his works: As for himself be is no more than the copy of a man; the original will be welcome Upon honour he has this bold para- King of France. ↑ King of Pruffia. to me. " Some 594 Extracts from the SCHOOL of M AN. Some pages further he fays, "So then, Cræfus, after three years confinement, you are your own man again; inftances of the like have been, yet it is a notable efcape, and I with you joy: A word to the wife is enough, your conscience intimates, that it is not of your innocence, but that you were fo deeply involved as to be able to compaís a pardon. Grease your lawyer, that is one way, though he was not the main inftrument; it is owing to your unbounded monopolies and oppreffions, that your head is upon your shoulders. He who has where with to buy a caufe, is in a fair way to carry it." App What are those which begin with uneafiness, and terminate in remorfe? Surely no better than real pains, coloured with a bewitching varnish. In a word, the pleafures which religion allows, are the real fupports of nature; and it is the genuine offspring of the former who alone do hoAnour to the latter; whilft all others depreciate it, as a rugged tyrant, and traduce this favourite child of heaven as an enemy to the deity. Upon the fummum malum, or chief evil, he most justly obferves, that as virtue is our chief good, vice must be our chief evil. In fhewing the feveral mistakes of mankind in relation to this, he fays: "There is Lycoris † juft appearing in the gay world, like an opening rofe; (carce were the firft leaves difclofed, when Guniphilus caft his eye upon her. Should I say he was fmitten with her, it would be a thunderclap. to Melania, who three years ago left her hufband to live with him; to be fure, handfome prefents have been made, if not And towards the end of this difcourfe B he gives us this useful advice, after having told the story of Jacob and Efau : "Whoever is under the unhappy neceffity of making any propofal to another, should let nothing of himself be feen; let him cover his eyes and put a bridle upon his tongue: If he lays open his weak fide, he may be fure to be fqueezed to his very Ca fettlement for life. Melania had cerfoul. There is no fafety till our irregular appetites and fancies are brought under; every one about us is on the catch to turn them agan ft ourselves: I tremble to think what difafters they bring upon us. Inftead of ridiculing Efau, let us do better; let his example put us upon our guard; D fome Jacob or other may find a way to fupplant us in our birth-right. Upon the fummum bonum, or chief good, he fays: "Let me explain myfelf: The fummum bonun imports a fixed determinate object, and fo univerfal as intirely to engrofs us, and leave us not the flighteft attention to any other circumstances. In that fupreme object all our thoughts muft E center; it muft employ our reflections; from it our defires, our affections, our likings must not prefume to ftray: Does not this fufficiently exhibit what is the fummum bonum; or must I speak more plainly? To what can fuch an extenfive definition appertain, but to virtue? It evidently is virtue alone which can rid us of all those extravagant defires, which disturb the enjoyment of fubordinate goods; therefore the fummum bonum is virtue." F And he afterwards adds thus: It is a current faying, that, to extinguish the paf fions, is to deftroy nature; their brutality only it is that religion profcribes; all its injunctions tend to their exaltation and G refinement: It confults our fatisfaction, may I not fay our delight, in abridging us only of criminal pleafures, and confequently permitting us the beft, the most exquifite, fuch as are without alloy. tainly been difcarded, when, most fortunately for her, an English lord fteps between, vafly outbids Guniphilus, and carries off the blooming Lycoris that fame night. Never any perfon, Guniphilus, did thee a better turn than this lavish rival With Lycoris you had been an undone man. : And this difcourfe he concludes thus The careffes of a lovely woman do much more hurt than all the clamours of the obftreperous. The latter I grant to be in fupportable, yet is the former most to be feared: From her all vices are derived; the is the engine of all misfortunes; and to be the hufband of fuch a one makes the cafe worfe; duty and religion fo linking us to her careffes, that they cannot be hunned or eluded without a kinď crime. A fine woman, beloved, and ungovern-' able, with a spirit difdaining the curb of reafon, what a fcourge! what a curfe what an evil what a fummum malum! even to the worthieft man! and the more he is fo, the more is he to be pitied. Upon ambition, after telling the story of Haman, he concludes thus: "Power is no more than a loan from fortune, which the often bestows on us to require it again with fevere intereft. Ye great ones, turn your eyes, towards Haman's catastrophe; and learn that an exalted ftation begets enemies in greater numbers than flatterers." In his difcourfe upon the world he fays, "A great lord is one who has keepers to knock on the head with impunity all who prefume to catch a hare • M. de la Bourdenaye. † Madam. Luce, a young actress, upon |