feveral thus fainter traces of feveral difpofitions, are often difcernible in a countenance, which yet receives its principal expreffion and general form from one affection-that it is not only by the prevalence of fome of them in comparison with the reft, that the paffions produce diverfities of temper among mankind; but that the general tone of all the paffions occafions a fuitable peculiarity.

Though the paffions be the most immediate caufes of the varieties of temper, he further obferves, that the understanding has not only fome influence on every peculiarity of temper, but also that fome peculiarities of it cannot be at all explained without taking into the account the turn and degree of the understanding; nay, that fome peculiarities of temper are occafioned almost wholly by the form of the intellectual powers-that fome men have a propenfity to obferve accurately, without any formed defign, whatever comes in their way; that this propensity lays the foundation of an attentive turn; that a heedless temper arifes from the want of this propenfity-that fome men have reasoning minds; that whatever object is before them, they place it in every attitude, view it in every light, and inveftigate all its confequences; that this turn of understanding lays the foundation of a confiderate, provident temper, and the contrary turn, of a thoughtless, rafh, improvident temper ;-that the fame temper may, in different men, proceed from different caufes, and even oppofite tempers may proceed from the fame caufe.

Having explained the origin and the nature of the variety of tempers among mankind, in his firft fermon, he proceeds, in the fecond, to fhew the neceffity of our governing, each his own peculiar temper, and to point out the ill confequences of neglecting it. In the third, he fhews how the duty of governing the natural temper ought to be performed, and to explain what is implied in the government of it; but we must refer our Readers to the fermons themselves, where they will find this important fubject treated in a masterly manner.

The Sermon on conftancy in religion, &c. is a very judicious difcourfe, and contains fome observations which we do not remember to have feen fo happily illuftrated by any other writer, The Doctor fhews very clearly, that, by deviating from virtue, we can obtain no fecurity against thofe afflictions and forrows which are common and even univerfal in human life.

The fubjects of the other fermons are-Juftice the Decorum of the Character of Judges, preached at the affizes-the firft Promife of the Redeemer-the Promise of the Redeemer to Abraham-the Old Age of the Righteous honourable-Virtuous Solicitude-Regard to pofitive Inftitutions effential to Goodness of Character-Redeeming the Time-the Truth of Christianity confirmed, &c.-the Power of virtuous Refolutions-the Advantages of the Virtuous for the Enjoyment of external Good

the Houfe of Mourning more improving than the House of Feasting.

ART. XII. Account of the PHILOSOPHICAL TRANSACTIONS, Part II. for the Year 1779, concluded.

MATHEMATICAL.

Article 32. On the Preceffion of the Equinoxes produced by the Sun's Attraction. By the Rev. Mr. Ifaac Milner, M. A. and Fellow of Queen's College, Cambridge.

HE purport of this ingenious paper is, as Mr. Milner

on the molt

foundation, the philofophical principles on which the mathematical calculations of this moft interefting problem are founded, than to illuftrate the method of calculation itself, although he has not altogether neglected the latter. And he fhews, contrary to the opinions of fome, that the refult will be very different if the calculation be founded on a fuppofition that the earth is a mass of fluid matter, under the form of an oblate spheroid, from what it will be if fuppofed a mass of matter, perfectly rigid, under the fame form.

Having established, in the clearest and most incontestable manner, the first principles, he proceeds, by a very short and elegant calculus, to enquire into the quantity of the annual preceffion of the equinoxes, caufed by the attraction of the fun, and finds it to be 21′′ 6", agreeing exactly with the result which Mr. Simpfon has given us in his Mifcellaneous Tracts, published in 1757, as well as with feveral other authors who have written fince that time, and which is fomewhat more than double the quantity affigned to it by Sir Ifaac Newton, at P. 476 of his Principia, Edit. 1726.

Mr. Milner next enquires into the cause and feat of Sir Ifaac's error; and concludes that it is not where Mr. Simplon has fuppofed it to be, namely, in affuming as principle, which he does in his 39th propofition of the 3d book, "That if a ring, encompaffing the earth at its equator, but detached therefrom, was to tend or begin to move about its diameter with the fame accelerative force, or angular celerity, as that whereby the earth itself tends to move about the fame diameter through the action of the fun, that then the motion of the nodes of the ring and of the equator would be exactly the fame.'

But, fays Mr. Milner, if the error be not here, it will be afked, where is it then to be looked for? To this question he does not appear to be abfolutely prepared with an answer, but feems to think, with Father Frifius, in contradiction to what has been advanced by Simpson, that it lies in Newton's fuppofing.

that

that the motion of the nodes of a ring would be the fame, whether the ring were fluid, or confifted of hard rigid matter; and also the fame with the motion of the nodes of a fatellite moving upon the furface of the earth in the plane of its equator, and making one revo lution in the time of a fyderial day. But he intimates, that at fome future opportunity he may further confider this matter.

We rather marvel why, when he is enumerating the feveral authors who have investigated this curious fubject, he should take no notice of one of the most valuable papers that have been offered to the public upon it; hamely, Art. 15. Part I. of the Philofophical Transactions for 1777.

HYDROSTATICS.

Article 37. A Treatise on Rivers and Canals. By Theod. Aug. Mann, Member of the Imperial and Royal Academy of Sciences at Bruffels.

This long paper, which takes up more than 100 pages of the Tranfactions, is divided by the Author into fix fections, befide the introduction.

In the firft, he treats of the different purposes for which canals are made, and gives a fhort account of the principal authors who have written on the subject.

In the second, he diftinguishes between natural and artificial rivers, as he terms them; that is, rivers whose channels are dug by hand, but which have not their waters kept up by fluices or flood-gates; and those again from fuch as have their waters kept up by these means, and which, alone, he calls canals. He defines fuch terms, ufed by himself in this paper, as have not been made ufe of by others before him, or that have been ufed in a lefs determinate fenfe than he chufes to confine them to; and delivers the laws by which waters, flowing in rivers and canals, act; referring to the authors mentioned in the first fection, for the demonftrations of thefe laws.

PP

He next enumerates the several inherent caufes of the acce. leration and retardation of the motion of water in rivers and canals; he fhews by what means this motion may be either augmented or diminished circumftances require; and he explains divers methods of ing the velocity of the current, and finding whether the water flows fwifteft at the top or bottom of the ftream. From the principles thus laid down, he deduces various means of preventing and remedying the defects and inconveniencies which muft neceffarily happen to rivers, &c. in a series of years, from the reiterated action of the water on their banks, and many other, as well natural as accidental causes and explains the nature and caufes of inundations; why they are more frequent in fome rivers than others, and always lefs frequent in large than fmall ones; at the fame time fhewing how they may be prevented, or at leaft rendered lefs frequent,

where

where the object will anfwer the expence.

He concludes

this fection with fome remarks on the confluence of rivers, and on the feparation of the fame river into many branches, as is ufual in large rivers especially, near their mouths, or influx to the fea; and explains the effects which thefe circumftances have on the velocity of the currents, inundations, &c.

In this fection he investigates the laws which obtain when currents running in oppofite directions meet; and he obferves that, when two equal currents of homogeneous fluids meet in oppofite directions, there is firft a fwelling and rifing up of them, at the point of rencounter; then follows a revulsion and counter-current of each equally back again, so as to bring the whole to an equilibrium.'

If the two oppofite currents are unequal, either in force or in quantity, or both, there will fill be a fwelling and revulfion of each back again; but it will be diminished in the greater current, and augmented in the lefs, in proportion to the quantity by which the one furpaffes the other; and the point of rencounter of the two currents will have a flow and progreffive motion in the direction of the ftronger, the degree of velocity thereof being always in a direct ratio of the force and quantity of one above the other.

"If the fluids in oppofite currents be not homogeneous, as is the cafe between fea and river water, that which has the leaft fpecific gravity will swim upon the other, and continue to follow its first direction, until fuch time as the heavier fluid fhall have communicated its motion to all the parts of the lighter. But the lighter fluid will not lofe its' former motion and direction at once, but in a decreafing feries, the law of which will vary according to the greater or lefs fpecific gravity in the two fluids, until the whole of the lighter has acquired the velocity and direction of the heavier, which buoys it up.

The time and space required for a greater current of falt water to communicate its motion and direction to an oppofite one of fresh wa ter, will be but very little, fince they differ in fpecific gravity only

parts, which the falt is heavier than the freth. It would require much greater between water and oil, and ftill much more between quickfilver and oil, and fo on. The elements for determining them in every cafe might be found by a proper number of experiments.

Let the two currents be equal or unequal in force and velocity, but nearly of the fame fpecific gravity, if we fhould suppose, at the fame time, that their furfaces are not upon a level, but that the one is higher than the other (as is conftantly the cafe in all fluices that open to the fea, except at the moment when the furface of the tide is on a level with the furface of the water in the canal behind the fluice), this circumftance entirely changes both the cafe and effects. It is certain, on this fuppofition, that the overplus of velocity and elevation in the higher current, though it fhould be the leffer, will make the waters in the lower and greater current reflow upon themselves, until they come to a level and equilibrium with thofe in the upper current; fince these, by the laws of univerfal gravitation, cannot flow back from a lower to a higher level, but muft defcend according to the declivity of their furfaces. "If the currents are of very dif

ferent

ferent fpecific gravity, they will come to an equilibrium according to the law laid down above; but their greater or leffer quantity and velocity will produce little or no effect in this case.

Now, as the running of two currents in oppofite directions, after their rencounter, and beyond the limits laid down above, is incompatible with, and contradictory to the laws of nature, and confequently impoffible, we may draw this ufeful conclufion, which becomes important during inundations, and especially during the annual overflowing of the low grounds in flat countries; to wit, that if the fluices next the fea, against which the tide flows, be fhut only a quarter of an hour before the flood has rifen to the level of the water in the canal, not a drop of water can enter the faid canal, nor even into the fluice itself; because both the progreffive motion of the point of rencounter of the two currents, and the over-fwimming of the fresh water upon the falt, will be always without the fluice and towards the fea, fo long as the furface of the tide is below the level of the water in the canal. Many fluice-mafters, for want of knowing or confidering this, are accustomed to fhut their gates next the fea a little after half flood, under the pretence of preventing, by this means, the falt water from getting into the canal, and communicating thereby with the waters which overflow the low grounds in many places during the winter, which would be of great detriment to the foil. Through this falfe perfuafion, they lofe no inconfiderable part of that time every day, which they might fafely employ in drawing off the waters which overflow and incommode low and flat countries, almost every winter and rainy feafon, as is the cafe in the Dutch and Auftrian Netherlands;' as well as many parts of the counties of Norfolk, Cambridge, and Lincoln, and other parts of England..

Section IV. contains an account of fundry experiments made by the Author, at the request of Mr. Needham, Director of the Imperial Academy of Sciences at Bruxelles, for determining the different velocities which the fame floating bodies will have in different depths of water, when urged by the fame force. Dr. Franklin, in a letter to Sir John Pringle, written so long ago as the year 1769, has fhewn, that it is well known amongst people accustomed to work boats on canals, that there is a confiderable difference in the fwiftnefs of their motion, according as they float in a greater or lefs depth of water; and that the water being fhallow is of itself fufficient to retard the motion of a boat, notwithstanding its keel may not touch the bottom of the canal. The reafon he affigns for it is evident; for a boat cannot advance its own length without difplacing a quantity of water equal in mass to the space which the boat occupies under the furface of the fluid. The water fo difplaced must return, and pass underneath and by the fides of the boat; fo that the less depth and breadth of water there is in the canal, the more in proportion it muft rife up and prefs against the boat, and of courfe retard its motion.

The refult of the experiments here related by Mr. Mann is as follows:

When