fituation or the bent of her genius, a fecond capital of at least 4800 millions like the first, and which ought now to be represented by other 240 millions of annual intereft, as lawfully due for the articles of expence peculiar to France, as the 240 millions that I have already mentioned would be for the capital really borrowed and absorbed by expences equal to those which England has vifibly incurred; expences which she cannot deny, fince they ftill annually coft her in intereft ten millions fterling. It may be faid, I ought at least to subtract from this grofs fum the million furplus employed in the useless measure of redeeming the annuities payable to the public creditors: but I fay no; because it is far from being an equivalent for the reductions of interest which England, as well as France, has permitted herself to make, but with which England cannot be as bitterly reproached, because she never forced the creditors to fubmit to them, as was the cafe in France: -but to return to the question. Thefe two fums of 240 millions of livres would make 480 millions of perpetual or irredeemable annuities, which France ought in all juftice to owe for the intereft on a capital of 9600 millions which she has actually borrowed. Here you will stop me and exclaim :-What! France owe at this moment 480 millions in perpetual annuities! France owe 360 millions over and above the 150 millions in perpetual and life annuities, which cannot be reduced to a lefs fum than 120 millions per annum! What! would you lay additional taxes on her to the amount of 360 millions annually, when the demand made of only 115 or 117 millions, which might have been reduced to 60 millions, has plunged her into the deplorable condition in which you now behold her! I hope that I do not weaken the objection. I will now endeavour to answer it, and, fhould it be found that my anfwer leads to a kind of new world greatly preferable to the old, I can only fay it is not my fault that it was not discovered fooner; the grounds for believing in its existence, which I have been giving every year for these ten years paft, are perhaps ftronger than thofe motives that determined Columbus to fet out in fearch of America. • I will begin my answer by asking a question. How comes it that England, with a population lefs by two-thirds than that of France, bears fo lightly, over and above her other burdens, the enormous weight of taxes neceffary for the payment of the intereft of her debt, amounting to 240 millions of French livres, always well paid? It is, you will fay, because she has an enormous mafs of capital, which he is conftantly employing as well in producing as in paying. This is unqueftionably true: but if you have fucceffively reduced from 5 to 4, then from 4 to 3, from 3 to 2, and then to I, without reckoning thofe brilliant occafions, when you completely emptied the pockets of your extorting bashaws;-if you, I say, have reduced a real capital of 9600 millions which you actually borrowed, to the 2400 millions reprefented by the 120 millions of perpetual annuities, you have then abfolutely and pofitively annihilated a capital of 7200 millions, which you actually had, and which you might have preferved, if you had on that head taken the fame fteps that were taken by England; who, by respecting the intereft of her debt, has preferved that immenfe 0 3 mafs mals of capital, which cannot be valued at lefs than 4800 millions of livres, the existence of which is well attefted by the intereft on it paid punctually to the day; while you can fhew only a capital that is rated too high, when it is faid to amount to 2400 millions; for you may talk of your 120 millions of perpetual annuities for fecuring the intereft on it, yet it is a truth which you cannot conceal, that thefe annuities never have been regularly paid! Let us fuppofe now that you had preferved this capital of 7200 millions which you have destroyed, and that you could exhibit the proof of its exiftence by fhewing the payment of a perpetual interest of 360 millions, which you could pay with as much cafe as England does her 240 millions, if like her you had laid on taxes in proportion as you borrowed; can you deny that these 360 millions regularly paid would prefent, in the general confumption, an article equal to this fum? Can you deny that, in plundering your creditors of this income of 360 millions, you have, by just as much, curtailed the expences into which they would have gone, if you had not plundered them? Can you deny that this decrease in their annual income has rendered a fimilar decreafe neceffary in the produce of the country? For, when the number of buyers falls off, the working part of the community must either produce fewer articles, or they will not be fo well executed as ufual, in order to indemnify themfelves: you have done both in France, while England, by following quite an oppofite line of conduct, has extended and improved both her agriculture and her manufactures. I certainly do not mean to propofe that you should now fubmit to bear the weight of thefe 7200 millions. ... but allow me to point out to you what would have been the confequence, had you respected the rights of your creditors, and fuffered that immenfe fum to continue part of the principal of your national debt. It is clear that 360 millions, which your creditors would have annually laid out, if you had not plundered them, would have neceffarily been followed by an annual reproduction of the fame value: but how much would thefe 360 millions of additional produce have added to the value of the old, in confequence of the ordinary re-actions of the taxes necessary to fecure the annual receipt of 360 millions? You will fee immediately, that they would have added at least 221 per cent. : 22 per cent. ought alfo to be added to the price of labour; and these two operations would be fufficient to reconcile and preserve, as entire as they could with, the interefts both of the labouring and the monied parts of the community. An addition of 22 per cent. to the price of the territorial produce, rated at 2500 millions, would raife them to the fum of 3,062,500,000. From this, however, you must deduct 22 per cent. the amount of the increased price of labour, which would raife the produce of induftry from 833,333,333 livres, to 1,020,833,333, making an increafe of 187 millions 500,000 livres. Deducting, then, the whole of the price of labour, the balance would remain as follows: Territorial produce Paid out of it for labour. 3,062,500,000 1,020,833,333 2,041,666,667 From From this balance deduct also 360 millions, the amount of taxes that would have been neceffary to pay the intereft of the 7200 millions which the nation ought in juftice to owe, but which the fpunged off, there would still remain to the proprietors of the territorial produce the fum of 1,681,656,667, whereas it appears (the author has proved it in feveral parts of the work) that before they had only 1,666,656,666. Thus they would have to receive 15,000,001, which would amount to an intereft of 8 per cent. on the 187 millions 500 thousand livres paid for increase of wages to the working clafs of the people; an increafe required by juftice, that they might not lofe any part of their enjoyments, by being obliged to bear their fhare of the additional taxes for raifing 360 millions per annum.' This doctrine (to which if there be any objection, it must be that it proves too much, by intimating that the more we get in debt, the richer we shall be; and the greater the bur. den of taxes heaped on us may be, the better we shall be able to bear it ;) will afford abundant comfort to the advocates for the present war, as it tells them that they need not be afraid of im pofing new taxes, nor entertain any apprehenfion of being obliged to ftop in the midft of the career for want of refources. Our author, however, is anxious to prove that he does not hold out falfe hopes; that, on the contrary, his calculations are founded on the unerring wisdom of practice and experience: but he appeals to the cafe of England for irrefragable proofs. Towards the close of the last century, (fays he,) from 1688 to 1697 the whole produce of the land in England amounted, according to the exact Mr. King, to no more than about 30 millions fterling. The price of labour was then eight pence a day. . . . During the fame period wheat was fome few pence more than 50 fhillings a quarter *Windfor measure. . . . About 80 or go years afterward wheat was not worth more than 40 fhillings a quarter: hence it appears that bread was neceffarily one-fifth dearer from 1688 to 1697, than it was from 1744 to 1780, and the produce of the land rofe from 30 millions to 72 millions fterling a year.... Thus it appears, odd as it may found, that the price of wheat may fall one-fifth in a century, while the territorial produce is more than doubled; for, in England, under this undeniable circumftance of the diminution of the price of wheat, the united enjoyments of the land owners and the labourers have actually increased in the fame proportion. In France, minifters were always able, without any uneasiness, to indulge in the intoxicating glory of regulating every thing, difpofing of every thing, doing every thing, without confulting any one, except their fubalterns in office, fome projectors no lefs defigning than greedy, but particularly the little cohort of favourites of the day; who, on their part, had nothing more to do than carefully to circumfcribe their prince, and intoxicate him with the unlimited extent of his power, the exercise of which they made him place in the hands Quere-Does the author mean Winchester measure ? of fuch admirable trustees.-In England, the King, who can do nothing without an affembly, that, in its turn, can do nothing without him, but who, when acting in concert with that affembly, can do every thing, this King of England who, in confequence of this limitation, used to be called in France a little bit of a King, (une portioncule de roi,) this King, nevertheless, whofe throne will not be deftroyed, until fociety fhall have been first diffolved, except in cafe he should endeavour to ftrengthen it by uniting in his own hands the powers, the divifion of which can alone form its unshakable support, or except in another cafe no lefs fatal to him and to his people, namely, that he fhould fuffer the flightest encroachment on his right of freely and fingly fanctioning laws, or of appointing those who in his name are to fee them carried into execution after they have received his royal affent-in England, I fay, the King is fo happily fituated, that it is impoffible for his minifters to conceal any thing from him that it is fit he fhould know; that they are obliged to be courageous enough to do every thing that their duty requires; circumfpect enough not to tranfgrefs the law, except in fuch preffing circumstances as call for extraordinary exertions of power and naturally intitle them to indemnity; wife enough, when there is a question of supply, not to ask for a larger fum than they know before-hand will abfolutely be wanted; and prudent enough, when taxes are once laid on, to leave it to the good fense of the different claffes of individuals, that may be affected by them, to make such a fettlement of their respective interests, however opposite they may be, that each may suffer no more than the flight inconvenience which must attend the best difcuffed tax and the moft judicioufly impofed.' [To be concluded in another article.] ART. XX. Transactions of the American Philofophical Society, Vol. III. [Article concluded from the left Appendix. See p. 576.] Art. 20. Dr. RITTENHOUSE, relative to a Method of finding the Sum of the feveral Powers of the Sines, &c. DR. R. RITTENHOUSE was induced to attempt the fummation of the powers of the fines, by its connexion with an elegant theorem difcovered by him, as he informs us, for determining the times of vibration of a pendulum in given arcs of a circle. Two cafes only he was able to demonftrate; the rest he has inferred from the approximation of feries and the law of continuity. That he was able to proceed fo far, without the affiftance of the Integral Calculus, argues no common share of fagacity and perfeverance. The folution of the problem de pends on the integration of the expreffion s'ds (,), (where r denotes the radius and s the fine of an arc,) in the cafe when s becomes equal to r; and this is performed by fuc ceffive fteps, the exponent, n, mounting at each interval by 2. A geometrical investigation, however, may be given as far as the the cubes of the fines. For, 1. The fine multiplied by the element of the arc is equal to the product of the radius by the element of the verfed fine. 2. The fquare of the fine multiplied by the element of the arc is, therefore, equal to the product of the radius, the fine, and the element of the verfed fine, or equal to the product of the radius and the element of the quadrant. 3. Hence, alfo, the cube of the fine multiplied into the element of the arc' is equal to the product of the radius, the fquare of the fine, and the element of the verfed fine, or equal to the product of the radius, and the fourth part of the element of the hemifphere augmented in proportion of the circle. to its circumferibing fquare. Confequently, collecting these elements together, 1. The fum of the fines is = r2. 2. The fum of the fquares of the fines is = r2 X arc of 90°. 3. The fum of the cubes of the fines is = 3r+. We are tempted to make this fmall digreffion, because Dr. RITTENHOUSE has invited Mr. Patterson to try the last cafe, and this without effect. Art, 21. Index Flore Lancarienfis auctore HENRICO MUHLENBERG, D.D. Dedicated to the Philofophical Society at Philadelphia, by the Author. We scarcely need obferve that this is the Lancaster of Pennfylvania. The catalogue contains nearly eleven hundred plants, denominated and arranged according to the Linnéan fyftem. Among the books confulted, is one thortly to be publifhed by Dr. MUHLENBERG, entitled Plenior plantarum defcriptio, cum calendario et ufu medico et œconomico. Art. 24. First Memoir of Obfervations on the Plants denominated Cryptogamic. By M. DE BEAUVOIS, Member of the Society of Sciences and Arts of St. Domingo, and Correfpondent Member of the Academy of Sciences of Paris. The object of thefe memoirs, of which the prefent confiders the moffes, is to extend the fexual fyftem of vegetables, and to confirm the lately difputed principle, omne vivum ex ovo. The author feems to have ftudied this curious fubject with enthusiaftic ardor. By affiduous obfervations, he difcovered that what naturalifts usually take for a filament fupporting the urn is a real tube, and that, within the epidermis of the urn or corolla, is the pollen, which furrounds the capfule containing globular feeds between the fibres of a fort of net. He was fortunate enough to detect nature in her operations. Having gently removed the opercule of the Hypnum velutinum, he perceived the cilia continually agitated by a convulfive motion, alternately approaching and receding, and ejecting their pollen in the space that |