1776. Mathematical Correspondence. 599 Mr. Hampshire the propofer, Theon, Cleonicus, λagure, and others fent algebraical folutions, but we received no conftruction but the very ingenious one before given. NEW MATHEMATICAL QUESTIONS. [76.] QUESTION I. By Mr. Ralph Taylor of Oldham near Manchefter. Given one angle of a fpherical triangle, and its oppofite fide; required a general rule for determining the other two fides of the triangle when they are the Complements of each other to 90 degrees. [77.] QUESTION II. By Arietis.* To determine the place and altitude of the nonagefima for all latitudes, by having that of a particular latitude, without beginning the work de novo. [78] QUESTION III. By Mr. Reuben Robbins. In a plane triangle, there is given the fum of the fides, the perpendicular, and the rectangle of the fegments of the base made by the perpendicular, to. determine the triangle. Arietis hath defired us to propofe the above queftion for the opinion of our many ingenious corresį ondents. I To the EDITOR of the LONDON MAGAZINE. SIR, War is various; man is various. The conqueror at the end of a war, has perhaps only won half of the many battles that were fought in the courfe of it; and the very men that gained one battle by their firmness, loft another by their panics. At Bunker's-hill, Quebec, Long land, and New York, we have fucceeded; at St. John's, Charlestown, and in the maintaining poffeffion of Boston, we have failed. But becaufe the laft action was in our favour, we think we are to fucceed in the next. But liberty takes a great deal of killing; and while Eaft and Weft are the Geographer's diftinction, the courage of freemen is the fame thing on both fides the Atlantic. The unexperienced cowardice of their mi litias, is now loft in a standing army; yet prejudice affimilating every thing to its preconceptions, an American's bravery is called his bold day, or the bravery of fafety and intrenchments; and if our own men are pricked on to action, we fay, the devil could not ftand the fire, the fituation was against us; or allow with compofure that an EngJifhman, like other men, may feel fear. As to Long Island, and the retreat 5 from Quebec, writers on war tell us, that an army retreating, is in a mea fure half defeated; that it is infinitely more difficult to preserve order in going from than to an enemy; that men always dread danger itself less than its confequences; and that more are killed in flight than in fight. The Provincials maintained their poft against (in reality) equal numbers, till they faw a fuperior number behind them; and the cutting off the retreat determined the day's action. This was a ftroke of Generalfhip, and may have important confequences I allow; but Putnam may recover his pafs, as Clinton has his ford, and the privates have only lived to fight again. The Americans are daily improving in arms, and in hatred; their country is a continued fortress; they are the native engineers in it; action will foon mark out their Generals; and their numbers are easily recruited. I repeat then, we fee only the beginning of forrows-benefit to neither-mifery to both. It will have little effect upon me to hear that the works at King'sbridge are forced they have laid their account in the poffibility of these things, and almoft expect them. 1 fhall only ask, Do the Americans defpond? Is more than one province conquered? Or can a single regiment march from one end of the continent to the other? Till General Howe can answer these quefti 600 Maxims on the Bravery and Cowardice of Troops. Nov. ons favourable to his country, I fay war is before him; a growing war, a war that may be joined in ilue, in a year or two, with a foreign war. When the ftates of Europe have all their arms in their hands, and have revenge or prey to fpurn them on, can we enfure their tranquillity for one year; or fuppofe that America cannot hold out the time that will be taken only to march through it? I look then, Sir, to the clofe of things. Every history, every memoir, telis me of hair breadth efcapes and apparent dangers; (hence our various anxiety in reading them)-fuch America may fuffer. But while the is united, and grows or keeps up her people, half Europe cannot conquer her laftingly, generally, or profitably. I fhall now introduce fome maxims from Saxe's Reveries, which have obvious application; and conclude with two very remarkable hiftories, one from the fame author, the other from D'Aubigné. Your readers will not think the whole long, and I shall amule thofe who are themielves no fighters. "The Chevalier Folard, fays Marshal Saxe, "fuppofes men to be the fame at all times, and always brave; without confidering that the bravery of troops is a variable and uncertain quality of mind. "The fame troops may most certally be defeated, even in intrench ments, which, if they were to begin the attack, would be victorious. This is an inftance which few have accounted for before in any reafonable manner; and it can only be ascribed to the weakness and imperfe&tions incident to human nature; there alone it is feated. If only ten men get footing upon a retrenchment, whole battali ons that have been pofted behind for its defence will abandon it. They no feaner fee a troop of horse enter within half a league of them, than they give themselves up totally to flight, and the defendants will no longer think of any thing but their own fecurity. Inftead of fationing your troops behind the parapet, it would be, much more prudent to post a single rank there, armed with pikes, whole bufinefs will be to puth the affailants back therewith, as faft as they attempt to mount. This your men will certainly execute, becaufe it is what they expect and are prepared for. If, moreover, you post bodies of infantry, at the distance of 30 paces in the front of the refrenchment, they will not be confounded at the approach of the enemy, from a confcioufnefs of their being stationed there for no other purpofe than to oppofe him; which, for that reason, they will do with proper vigour and refolution; while on the contrary, had they been all pofted within it, they would have fled at his appearance (giving themfelves up for loft).-It is, moreover, in a particular manner neceflary to perfuade your men, that they are by no means to depend upon the effect of their fmall arms, or to imagine their firing only will be fufficient to repel the enemy; but that the top of the parapet is the place where they will be required to exert themfelves. Thefe precautions will prevent their being furprised, or terrified to see him enter the ditch; for as it cannot be doubted, but that he (the enemy) will take a firm refolution to ftand their fire, which it is as certain that he will be able to go through; one ought therefore to expect, and be prepared for the confequence.' Thus, he remarks, we fee upon what nice diftinctions every thing in war depends, and how irrefiftibly weak mortals are governed by mere momentary caprice and opi. nion. "I shall only make ufe of one example amongst a thousand others, to enforce my opinion concerning this frailty of the human heart. After the French infantry, at the battle of Friedlingen, had repulfed the Imperialis with unparalleled fortitude; had to tally routed them, and purfued them through a wood into a plain, which lay on the other fide, fome one, upon the appearance of two squadrons, (which might be French for any thing that was known to the contrary) cried out, "We are cut off!" Upon which thefe victorious troops inftantly abandoned their triumphs, took to fight in the most dreadful contufion, without being either attacked or purfued by a single prion; repaffed the wood with the utmoft precipitation, and rever once halted till they had got be yond the field of batt e. Mahal Vil lars, togethet with the generals of the army, took all posible pains to rally them, but to no purpose; and yet the victory had not only been gained, but rendered at the fanie time fo complete, 1776 Review of New Publications. that no part of the enemy attempted to make the leaft appearance afterwards. Nevertheless we find, that thofe men who in one moment had difcovered fuch amazing intrepidity, were the fame whofe fears, the very next, betrayed them to a fhameful flight. It was from Marthal Villars himself I had the fact, and who related it to me at Vaux-villars, when he was fhewing me. the plan of his battles. And whoever has curiofity enough to search for more examples of this nature, may meet with a great many in the Hiftory of All Nations." .601 and running till want of breath obliged them to ftop, they stood still, staring at each other with furprise at their own cowardice, and fhame at having fo many witneffes of it, though every fpectator was at the fame time companion in the panic. Upon which, fays D'Aubigné, we agreed that God does not give fenfe and courage, he only lends it. But they were in fo different a ftate of mind the following day, that, with half that troop (D'Aubigné having fent the reft to the town of Sancerre, then befieged by the Catholics) he attacked 600 foldiers, who were returning by the Loire from the maflacre at Paris to Boifgency, and killed a great number of them." I fhall only give one more inftance from that gallant partifan, D'Aubigné; felected chiefly for the very remarkable expreffion contained in it. "When he heard the melancholy account of Thus there is a fear (in the law what was paffing at Paris, he had with phrafe) quod poteft cadere in virum forhim eighty of his foldiers, fome of tem & confiantem. Marthal Saxe fays, them of the most tried and approved that the confequences of this irrefiltcourage. As they were marching (we ible impulfe of the human heart were may fuppofe with great dejection of the principal motives that induced fpirits, and filled with horrid ideas, him to attempt his Reveries. His ideas fuggefted by the relation of the maffa- are retailed for prefent ufe and future cre of Paris) they heard one crying comfort by very loud at a distance: Whereupon they all betook themselves to flight, A A BYE-STANDER. An Impartial Review of New Publications. ARTICLE CLXXIV. Botanical Arrangement of all the Vegetables naturally growing in Great Britain. ByWilliam Withering, M. D. 2 v. 15s Cadeil. A judicious and well executed work. The beft that hath yet appeared on the fubject in this kingdom. Our author justly obferves, the oeconomical ufes of vegetables have been hitherto but little attended to by men, eminent for botanical knowledge. The theory of the fcience and the practical uses have been too much disjoined, it is time therefore to turn our acquifitions to fome ufeful purpose. The following extract we fubmit to our reader's confideration. "It is certainly a matter of the greateft confequence to determine what fpecies of plants are preferred by particular animals; for what is noxious to one animal is often nutritious to another. Thus the water cowbane is a certain poifon to cows; whereas the goat browfes upon it greedily. Monkf hood kills goats, but will not hurt hories. Bitter almonds are poifonous to dogs, but not to men. Parfley is fatal to fmall birds, while fwine eat it fafely; and pepper is mortal to fwine, but wholefome to poultry. Many experiments made with this view by Linnæus Nov. 1776. and his pupils at Upfal, are given in the fecond vol. of the Amanitates Academicæ. The refult of thofe that relate to the British plants will be found under the particular fpecies. Many of them were repeated ten and even twenty different times, and with the precautions mentioned below, which are here added for the fake of thofe who have leifure and opportunity to purfue thefe interesting enquiries further. When horfes, cows, &c. are faid to eat the plant, it means that they eat the leaves of the plant. Thus horfes and cows eat a great variety of graffes, but they only eat the leaves; for when left to their own choice they never touch the flowering ftems. Some plants are eaten early in the fpring, whilft young and tender, but are rejected in the fummer. The animals chofen for thefe experiments must not be over hungry, for an empty ftomach will compel them to feed upon plants which nature never defigned for them: nor fhould they be taken immediately out of the house; because after living a confiderable time upon dry food, they devour greedily every green vegetable that comes in their way. The plants offered them fhould be handled as little as poffible, for fome animals are very nice, and will re4 H fale 602 Review of New Publications. fufe the most agreeable food when defiled by fweaty hands. Throw the plant in question upon the ground; if the animals refufe to eat it, mix it with others that they are known to like, and if they ftill refufe it, the point is clear, especially if the experiment is repeated with different individuals. "The catalogue of infects that feed upon the different fpecies of plants, is confeffedly very imperfect; but it will ferve as a foundation for future obfervations of the fame kind. Perfection in thele matters is not to be attained at once. In its prefent state it may not be without its ufe. It will be feen that infects live chiefly upon the products of the tailer trees which grow out of the reach of quadrupeds, fuch as the Eim, the Pear, the Lime and the Oak; or upon the thorny and flinging plants which repel the attacks of other animals; as the Role, the Thistle, and the Nettle; or upon fuch plants as exift every where in great abundance as the graffes; or laftly, upon fuch plants as other animals will not eat, as the Dock, the Waterlily, the Figwort, and the Henbane. "Derham fuppoles, and with a degree of probability on his fide, that the virtues of plants may be difcovered by obferving what infects feed upon them. "Many people will be furprised to find fo little faid upon the medical virtues of plants; but those who are beft enabled to, judge of this matter, will perhaps think that the greater part of that little might have been omitted. The fuperftition of former ages, operating upon the ignorance of mankind, gave rife to miracles of every denomination; and the fafhion of combining a great váriety of ingredients with a defign to answer any particular purpofe, rendered the real efficacy of any of them extremely doubtful. The dreadful apprehenfions that men formerly entertained of poifons, made them fearful of employing fubftances that were capable of doing mifchief, and therefore they rejected those that were most likely to do good. A number of vegetables fit only for food, were fuppofed capable of producing the greatest alterations in the human body; and at length every common plant was efteemed a cure for almoft every difeafe. In this fitu. ation of things, little advantage can be reaped from the experience of former times, we fhall fooner attain the end propofed, if we take up the fubject as altogether new, and rejecting the fables of the ancient herbalifts, build only upon the bafis of accurate and well-conceived experiments. To facilitate the work as much as poffible, the following obfervations are added. "Certain plants, capable of producing very fudden and remarkable effects upon the human body, are called poifons. But poifons in fmall dofes are the best medicines, and the best medicines in too large cofes are Nov. CLXXV. Travels through France and Spain, in the Years 1770 and 1771. In which is particularly minuted, the prefent State of thofe Countries, respecting the Agriculture, Population, Manufactures, Commerce, the Arts, and useful Undertakings. By Jofeph Marshal, Efq. Vol. IV. 6. Corrall. Our traveller appears to be an accurate, fenfible, obferver, of the feveral things be profefies to defcribe.-And his obfervations if attended to, would be of more fervice to the community, than those of moft of our modern travellers, The following are fome of his reflections on cheapness of living in France, and the manufactures. "The cheapnefs of living in fome parts of France, cannot well be thought of, without fome reflections arifing on the comparison with England, which is fo much dearer; yet it is a certain fact, that more foreigners refort to Eugland than to France. Is not this furprifing? It cannot be the liberty of England that attracts low people: they are no judges of it. Great numbers of Frenchmen, in the lowest circumftances, go to England; moft certainly not on account of the government : they do not philofophize enough for that, I can attribute it to nothing but national wealth. Men will fly to countries where money is plentiful, almoft as naturally as the needle to the north. It matters not telling them that every thing is fo dear in rich countries, that 6d. a day at their homes, is as much as is. abroad. It is not that they cannot, but they will not comprehend this: they think that where there is fo much money ftirring, fome of it must come to their share; whereas, by staying at home, they are fure of getting nothing but their old pay. And this, I think, is a strong reafon against those who urge the danger of England lofing her manufacturers from the high prices of the necef faries of life. If they emigrate, it must be from is. to 8d. a day, which is fuch an obvious change, that no other confideration will make it up to them. But there is an other circumftance attending cheapness, which deferves to be confidered; where it arifes, as it generally does, from the lowness of national wealth, the employment of the poor mut be more uncertain and hazardous, and they muft experience a total want of it ofther than where |