per ton, which is within the cost, including out-fits, it will amount to $701,000, the value of the cargoes will probably average $60,000 but to make the estimate within bounds, we will call them $50,000 each-$2.700,000, total, $3.101,000. CONNECTICUT. number of beautiful tunes. But the met wonderful part is, that on setting a spring, a picture on the top of the box rises slowly and discovers a bird ascending from below. The bird is of about an inch in length; of plumage the most rich, and yet the most natural. It sings with astonishing sweetness, During the year 1817, there were in Hart- and accompanies its voice with all those moford, 93 deaths; in New-Haven 77. NEW-YORK. By a report of the Commissioners of the Sinking Fund of the City of New-York, it ap pears that on the 10th of November, 1817, by the accounts of Commissioners, there was a balance in their hands of $125 12. The fishing in Lake Ontario has been more than commonly successful this season. The quantity of Salmon, Trout, White-fish, and Ciscoes taken in Chaumont Bay, and in the vicinity of Sackett's Harbour is estimated at 6000 barrels. NEW-JERSEY. The Legislature during their recent Session appointed a committee to report on the expediency of adopting measures to procure a revision of the State Constitution. PENNSYLVANIA. The Common Council of Philadelphia has presented Commodore Oliver H. Perry with an elegant sword, as a mark of respect for his skill and gallantry as a naval commander, and which was so conspicuously evidenced in his victory on Lake Erie in the late war. Mr. Oliver Evans has built a steam engine for the purpose of raising water to supply the city of Philadelphia. The contract was that it should raise 3,500,000 gallons of water, ninety-eight feet, in 24 hours. On the 26th and 27th ult. it was worked without interruption 20 hours, during which it was estimated that 3,556,401 galls. were raised, in doing which only 10 cords of oak wood were consumed. It seems that about 100 galls. were raised at every stroke, and that the average working was 214 strokes in a minute. The experiment was so satisfactory to the watering committee that they have reported the contract as fully completed by Mr. Evans. The United States mail coaches that run between Philadelphia and New-York are provided with a guard well armed, who will ride on the box with the driver; so that it will not only afford security to the mail, but also to the passenger. The way-mail is put in separate bags, after the European style, and is so arranged as not to detain the coach more than three minutes at each post-office on the road. The proportion of paupers in Philadelphia, during 1817, was estimated at one in every 114 persons. A Mr. Smith has been recently exhibiting in this State a curious piece of mechanism, said to be the work of an Italian artist. It consists of a box four inches long, three wide, and two deep-of fine gold. On one end is a snuff-box-on the other, a lid opens and discloses an eight day time piece, which besides striking the hours and quarters, plays a tions common to a living bird-its head turns from side to side-its little bill opens and its throat swells at every note, and its wings and tail spread and contract during its song. After finishing and repeating its strain, it drops upon its golden nest, descends to its retreat, and the lid gently closes to its place. Died At Philadelphia, Doctor Caspar Wistar, aged 56. He was long distinguished as a medical practitioner, and as a professor of anatomy. He was a man of general science, polished manners, and generous sentiments; and he died deeply lamented. Thursday, the 12th February, is recommended by the Governor of Maryland as a day of public thanksgiving and prayer throughout that State. A resolution has passed the Legislature of Maryland to appoint a committee of five to inquire into the expediency of taxing the of fice of discount and deposit of the Bank of the United States, established in the city of Baltimore. One hundred and fifteen thousand barrels, and four thousand three hundred and ten half barrels of flour have been inspected in the city of Baltimore, during the quarter ending Dec. 31, 1817. DISTRICT OF COLUMBIA. On the 1st January, 1818, the American Colonization Society held its first anniversary at the city of Washin ton. In the opening speech, by Judge Washington, it was stated that two agents, Messrs. Mills and Burgess, had been engaged to explore the Western coast of Africa, and to assist the United States in selecting a suitable district on that continent for the proposed settlement. The annual meetings of this society are hereafter to be held on the last Saturday in December. The officers for the present year are; the Hon. Bushrod Washington, President: Vice Presidents, Hon. William H. Crawford, of Georgia. Hon. Henry Clay, of Kentucky Hon. William Phillips, of Massachusetts. Col. Henry Rutgers, of New-York. Hon. John E. Howard, of Maryland. Hon. Samuel Smith, of do. Hon. John C. Herbert, of do. Joba Taylor, of Caroline, Esq. of Virginia. Gen. Andrew Jackson, of Tennessee. Robert Ralston, Esq. of Pennsylvania. Richard Rush, Esq. of do. Gen. John Mason, District of Columbia. Samuel Bayard, New Jersey. Balance in favour of the revenue 159,600 93 A meeting of the persons interested in the fisheries on the Potomac river, has been held for the purpose of petitioning the legislatures of Maryland and Virginia to forbid the use of Tide or Gill nets, which obstruct the passage of the fish, and kill and destroy a great many of them to no purpose. The memorial also remonstrates against the passage of steam-boats during the time of the spring fisheries-from the first of April to the middle of May. NORTH CAROLINA. The Legislature of North Carolina has passed a resolution directing an elegant sword to be presented to the infant and only son of the late Col. Benj. Forsyth, who fell at Odletown, Canada, June 22, 1814; and appropriating $250 annually, for seven years, for his education. A late Raleigh paper contains the following article. Among the numerous productions to which the soil and climate of North Carolina are favourable, it is found that the sugar cane may now be added-Several fine stalks, raised in Brunswick county, not far from Wilmington, are now in the possession of Col. Wm. Polk. of this city. They are from seven to eight feet in height, and although considerably dried, remained about two inches in diameter. The present is the second year of the experiment-only a few plantings having been at first obtained; but the enterprising gentleman who has made the attempt, calculates on making sugar his staple crop for the approaching year. The stalks. that I have seen are certainly very luxuriant; and I have understood from gen tlemen, acquainted with the culture and growth of the article, that there can be no doubt of its complete success in the lower parts of the State. SOUTH CAROLINA. The Legislature of South Carolina have ap pointed Maj. John Wilson, a civil and military en ineer for that State, and appropriated 50,000 dollars to open the Saluda, and other rivers. The salary of the governor of this State has been fixed at $4000. and that of the judges advanced from $2,372 to 3,500. The president of the State Bank receives $3000. About eleven o'clock on the night of the 10th of December a smart shock of an earthquake was felt, at the same instant, in nearly all the towns and settlements in the upper part of South Carolina and Georgia. GEORGIA. There have been some skirmishes between detachments of the United States troops and the Indians, in one of which, a party of 300 men under Col. Arbuckle, falling in with a small body of ambushed Indians, killed 8 or 10, and wounded several more, with the loss of 1 killed and 2 or 3 wounded; and in another, a small party under Lieut. Scott, passing in a boat ascending the Appalachicola were fired upon by a large number of Indians ambushed along the shore, and Lieut. Scott and most of his men were killed. Gen. Gaines, in a dispatch under date of Dec. 2d, 1817, says that the friendly chiefs inform him that the hostile indians on the banks of the Chatabochie have gone down to join the Seminoles and that all now remaining in that quarter are amicably disposed. A few days subsequent to the above date Gen. Gaines proceeded to fort Hawkins. The Legislature of this State, during its last session, appropriated $71,000 for improving the navi ation of several rivers, besides constituting a permanent fund of $250,000 for similar uses, and a like fund of the same amount for the support of Free Schools. An act also passed, subjecting the Branch of the United States in that State, to the same tax paid by the Banks chartered by the Legislature, viz: thirty one and a quarter cents on every hundred dollars of the capital stock. OHIO. Many of the families residing in the new settlements in America, to the south of the Gennessee country, on the bank of the great river Ohio, are supplied with shop goods from vessels which navigate it, and are fitted up with counters, shelves, drawers, in the sime manner as are shops on land, and as well stored as many of them with all kinds of goods that are in demand. On approaching a plantation, while they sail along the river, a horn or conch shell is blown to give notice of their arrival, when the planters, with their wives and daughters, repair to these floating shops, and select such things as they require; and make payment in the produce of their plantations, such as flour, cot LOUISIANA. the sugar estates of Louisiana are worth from A Millegeville paper says, that negroes on 600 to 1000 dollars yearly; and the sugar crops are worth from 20 to 150,000 dollars a year. the acre; and no sugar land sells for less than Sugar land close to the city, sells for $5000 800 the acre. Mechanics of all descriptions soon grow rich. Decent board is from 40 to to be used with discretion without any extra 60 dollars per month; but claret is allowed charge; house rent is high, and even naked lots on the front street, 60 feet rear, rent for 3 dollars a foot per month. The American population is increasing, and already balances the French in the legislature, there is a vast field open for persons fond of public life; the Creoles are averse to it, and the state pays her offices better than any of her sister judge of the supreme court 5000 dollars; instates. The governor has 7500 dollars a year; ferior judges in the city 4000, and those in the country 1500 and 2000: yet these salaries profits of a cultivated farm. are insignificant when compared to the TENNESSEE. The legislature of this state have passed an act for the improvement of the navigation of its rivers, and an act, in addition to a vote disapproving the introduction of a branch of the United States Bank, imposing a penalty of 50,000 dollars on the establishment of any such branch in the State. By a decision also, of the legislature, the seat of government is to be removed from Knoxville to Murfreesborough. ART. 16. MATHEMATICAL LUCUBRATIONS. Solution to the Prize Question of No. V. ty of the wind to that of the sail. It is Vol. I. by X. of New-Haven. I. Let manifest that the whole tendency of the wind on the oblique plane ab is to move it in the direction CH, perpendicular to ab. Hence resolving the force CH into CG, GH, whatever be the force of the wind on ab in the direction CH, its force in turning it round the axis in the direction FC, will be to it in the ratio of CG, GH. But it appears from the experiments of Dr. Hutton, (see Hutton's Dicty. Art. Resistance) that when an oblique plane, as ab, is confined to move in the direction of the wind DC, the resistance with a given velocity, varies nearly as sistance of the air to an oblique plane moving with any velocity, to be equivalent to the force which it exerts when it strikes with the same velocity on the place at rest. This is agreeable to the universal law of reaction; and although it appears from the experiments of Vince not to hold accurately in regard to a limited quantity of water, it may be taken as strictly true when applied to an indefinite fluid, like the atmosphere. The relative action of the plane and the fluid is manifestly the same, whether it be the plane or the fluid that is in absolute motion. Sv. 1 -x8 -3 1- -x21 x Sv. 1. -X 2 -x 2 =0. The foregoing formula would represent the effect of the wind, if its velocity relative to the sail were not changed by varying the angle DCa. But if the sail were placed in the direction FD, it is manifest that the wind would glide along the sail without producing any effect x dx.hl.x)= upon it. And in any other position, as FA, if F A be produced to E, it is plain that the relative velocity of the wind towards the sail in the direction DC will be to its whole velocity as DE: DC. In other words, the effect is the same as if the sail were at rest, and the wind moved with the velocity DE. But DE=DC-C E=DC_√1 — 2CF. or if the ratio of the velocities of the wind and sail be denoted by V and v, DE is as V r 3 dr_v V a -s dx + dx+ v This equation, by mul tiplying all the terms by 1 dx cancelling equal quantities, &c. is reduced —v √1 − x 2)a(1 — x − x ̄hl.x)=0. This equation may be reduced by approximation, when particular numerical values are assigned to V & v. If V:v:: 1:2, by anuming 6 as the value of the tangent of the angle of posi x 2 that in velocities not greater than those tion, (which will be more convenient than of windmill sails, the resistance is very to assume for r directly,) the error nearly as the square of the velocity. (See comes out +,0488. If it be anumed Gregory's Mechanics, Vol. 1 p. 554.) = = 6,1, the error is -,02086. Hence the effect when all considerations the common rule, we have 6,07 for Hence by are taken into view, (putting 1,842-a) the first approximation of the vale of and by a second operation, it comes out 6,055 nearly. When the tan- v:: 1: 3, gives DCa=83° 40'. In cases where the velocity of the sail these, the foregoing process derived from is so great compared with the wind as in the theory, which supposes the effect of experiment scarcely differs sensibly from the wind to be as the square of the sinc into the cosine of the angle of incidence. (See Maclaurin's Fluxions, Vol. 2, or Gregory's Mechanics, Vol. 1.) The resulting theorem for the maximum effect in theory is the following: ; which gives in the first of the two cases above, 810, 03', and in the second 830 484, exceeding those obtained from experiments by only 23 & 8 minutes respectively. The foregoing investigation gives the proper angle of incidence only for a narrow part of the sail at a certain distance from the axis; for it is impossible that all parts of the same sail should move with the same velocity. The extreme parts of the sail ought to be most turned towards the wind. If, for example, the extremity of the sail moves three times as fast as the wind, the rib ought to be set at 83° 40'; but at the length of the same sail from the axis, where the velocity is only twice that of the wind, the angle ought to be 80° 37'. I have chosen to deduce the solution of this question from the experiments of Dr. Hutton, rather than from those of Bossut, Vince, &c. because those of the latter were made with water as the re the velocity of the sail is equal to that of Ratio of vel. of sail 0 to 1 1 to 1 2 to 1 S to 1 Corresponding angles By this table the sails of a windmill relative velocities of the sails and wind are Solution to Ques. 10, by Analyticus. Let A the angle contained between the radius of the earth unity and the distance of the body from the centre of the earth; then will said distance -Sec A Cos A 1 and the absolute force of gravity at this distance will be which put o gives This question was ingeniously solved by X. of New-Haven, Mr. O'Conner and Mr. O'Shannessy. sisting medium. After a pretty extensive research, I can find no experiments which come so near the point in hand as The prize which is a set of the Magathose of Dr. Hutton; except those of Mr. Smeaton, which were actually made zine for one year, has been awarded to with wind-mill vanes on a small scale. X. of New-Haven for his very ingenious and elegant solution to the problem of But he does not attempt to draw from the windmill; a problem that has been his experiments any law of resistance, nor repeatedly discussed by many great madoes he appear to have regarded the pre-thematicians, but which is now for the cise ratio of the velocities of his sails first time resolved in such a manner as to render it useful to the public. round their axis to that with which they passed through the air. He nearly ascertained, in general, that an angle of position varying from the centre of the sail to its extremities from 71 to 83 degrees, produced, at a medium, the greatest effect. Prize Question by R. Adrain, to be solved in our No. for May next. It is required to investigate the general equations of the surface, at any point of which the sum of its inclinations to the plane of the horizon is a constant quantity; one of those inclinations being taken in a plane parallel to the meridian, and the other in a plane parallel to the prime vertical; and to point out the two simplest species of surface having the specified condition. ART. 17. REPORT OF DISEASES TREATED AT THE PUBLIC DISPENSARY, NEW-YORK, DURING THE MONTH OF DEC. 1817. FE ACUTE DISEASES. NEBRIS Intermittens, (Intermittent Fever,) 3; Febris Continua, (Continued Fever,) 4; Febris Infantum Remittens, (Infantile Remittent Fever,) 6; Ophthalmia, (Inflammation of |