From this balance deduct alfo 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 1,681,666,667, whereas it appears (the author has proved it in feveral parts of the work) that before they had only 1,666,666,666.

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 increafe of wages to the working clafs of the people; an increase required by justice, 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 burden of taxes heaped on us may be, the better we fhall 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 impofing new taxes, nor entertain any apprehenfion of being obliged to ftop in the midst 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 wifdom of practice and experience: but he appeals to the cafe of England for irrefragable proofs.

Towards the clofe of the laft 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, neverthelefs, 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 unfhakable fupport, 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 should 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 circumftances as call for extraordinary exertions of power and naturally intitle them to indemnity; wife enough, when there is a question of fupply, not to afk 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 fenfe of the different claffes of individuals, that may be affected by them, to make fuch a fettlement of their respective interefts, however oppofite they may be, that each may fuffer no more than the flight inconvenience which must attend the beft difcuffed tax and the mott judicioufly impofed.' [To be concluded in another article.]

ᏚᏂ .

ART. XX. Transactions of the American Philofophical Society, Vol. III. [Article concluded from the last 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. RITTENHOUSE was induced to attempt the fummation of

the powers of the fines, by its connexion with an elegant theorem discovered 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 af fiftance 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 fucceffive steps, 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 circumfcribing fquare. Confequently, collecting thefe elements together,

1. The fum of the fines is = r2.

=
=

r2
4.

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
We are tempted to make this fmall digreffion, because Dr.
RITTENHOUSE has invited Mr. Patterson to try the laft cafe,
and this without effect.

Art. 21.
Index Flore Lancaflrienfis 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 published 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 these 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 ufually 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

that opened near to the bafis of the internal cilia. He con cludes that the urn is a bi-fexual flower, and that the ufe of the cilia is to prevent the too rapid and impetuous emiffion of the pollen. In all this, however, there is much room for fancy.An engraving is annexed.

Art. 25. Letter from Major JONATHAN HART to Benjamin Smith Barton, M. D. containing Obfervations on the ancient Works of Art, the native Indians, &c. of the western Country.

These remarkable monuments are found near the Ohio, the Scioto, the Miami, and the other rivers which discharge themfelves into the magnificent Miffiffippi. Near Grave Creek, the works extend, at intermediate diftances, over the space of ten or twelve miles along the banks of the Ohio, and confift of fquare and circular redoubts, ditches, walls, and mounts, fcattered in every direction. Common Indian graves or cairns. occur in every part of the country. Whether these monuments were formed by the fame people who conftructed the former, which evince no fmall degree of civilization, feems doubtfal. Near to the river Mobile, are immenfe quantities of oyfter-fhells of a monstrous fize, which the natives use in making their earthen ware. Several petrifactions are found. There are unequivocal proofs, it is faid, that, in past ages, the waters of the Miffiffippi flowed 70 feet higher than at prefent. At the French Broad-river, are feen artificial characters of beafts, birds, &c. on the perpendicular rocks more than one hundred feet above high water. The Chickafaws fay that they came from the fetting-fun, and spent seven years on their journey, marching only a moon in each year. This tradition feems to corroborate the opinion that America was peopled from the north-east of Afia.

Art. 26. Account of fome of the principal Dies employed by the North American Indians. Extracted from a Paper by the late Mr. HUGH MARTIN.

To obtain the red colour, the Indians pound the roots of wild madder, and add the acid juice of the crab apple; the compound is put into a kettle of water along with the fubftance. to be died, and is kept fome time over a gentle fire. - The orange is procured from the root of the puccoon, or Sanguinaria Canadenfis, and fixed by the fame vegetable acid.-- They dye their bright yellow with the roots of a plant which grows fpontaneously in the weftern woods, has a ftem about a foot high, with a fingle broad leaf at the top, and bears a red berry refembling the raspberry.-Blue is obtained from the Indigo, and black from the Sumach, or from the bark of the white walnut.

Green

Green is prepared by boiling blue fubftances in the liquor of fmooth-hickery bark. This is their most expenfive dye, and therefore they carefully collect the fhreds of old green cloth, and add them to the colouring infufion.

Art. 27. Account of the beneficial Effects of the Caffia Chamachrifta, in recruiting worn-out Lands, and in enriching such as are naturally poor; together with a botanical Defcription of the Plant. By Dr. JAMES GREENWAY, of Dinwiddie County, in Virginia.

This plant, under the name of the bean, is highly valued in Maryland and on the eastern fhore of Virginia. A pint of the feed is fowed with every bufhel of oats. The oats are reaped in July; the beans next fucceed, flower in Auguft and September; and in October, when the feeds ripen, the pods burit with fuch elafticity as to fhed them fome distance around. The year following, Indian corn is planted; and thus maize and oats are cultivated alternately, without any manure, for the fpace of eight or ten years, until ground, which yields only five bushels per acre, becomes fo greatly improved as to produce fifteen. From this account, our readers will perceive the fort of hufbandry which prevails in America. The amelioration of the foil is owing to the rotation and the frequent recurrence of green crops.

Art. 28. Account of a Hill on the Borders of N. Carolina, fuppofed to have been a Volcano. In a Letter from a Continental Officer, refiding in that Neighbourhood, to Dr. J. Greenway, near Petersburgh, in Virginia.

This hill is fituated on the Dan-river, and is called by the people the Burfed-Hill. It appears, from the description, to have been the crater of a volcano. Traces are ftill vifible of the ftream of lava which flowed into the fubjacent valley.

Art. 29. Account of a poisonous Plant, growing spontaneously in the fouthern Part of Virginia. Extracted from a Paper by Dr. JAMES GREENWAY, of Dinwiddie County, in Virginia.

This plant grows on hilly barren grounds, and feems to be a fpecies of hemlock. A botanical defcription is here given of it, under the denomination of cicuta venofa. It is frequently miftaken for wild angelica, or eel-root. It has likewife the vulgar names of wild-carrot, wild-parfnip, and fever-root. Its noxious qualities were lately difcovered by an accident which nearly proved fatal. it feems to poffefs a moft powerful narcotic quality, by which it operates on the nervous fyftem, and deprives the patient of all fenfe and motion.

Art.