it will draw the thread from the position A C into the position A B, let B G be drawn perpendicular to A C. If B C reprefent the centrifugal force acting according to the direction B C, it is equivalent, as is commonly known, to two forces one of which is as GC, and acts according to the direction G C, which is contrary to that by which it defcends to O, the other is as G B, and acts according to the direction G B, which is no way contrary to the force of gravity, If therefore BC reprefent the total centrifugal force of the Body B, that part of it which directly opposes the force of gravity will be as GC: from whence it follows, that the decrease of gravity in going from the Pole to the Equator is always as the square of the co-fine of the Latitude: for draw B H parallel to the Axis P P, and because the triangles HCB, CDO are æquiangular, therefore HC is to CB as CO is to CD, or as QO is to CD, but QO is to CD as the decrease of gravity at Q is to the centrifugal force at C, and therefore HC is to CB as the decrease of gravity at Q is to the centrifugal force at C. But if CB reprefent the centrifugal force at C, GC will reprefent that part of it which acts directly against the force of gravity, and confequently the decreafe of gravity at the Equator is to the decrease of gravity at C as HC is to GC: now HC is to GC in duplicate proportion

of HC to CB, or of CO, or OQ to CD, by the 8th of the 6th of Euclid; and therefore the decrease of gravity at Q is to the decrease of gravity at C, as the fquare of CO is to the fquare of CD which was to be demonftrated.

From whence it is plain that if HC reprefent the decrease of gravity at the Equator, and GC its decreafe at C, then will GH represent the difference of these two diminutions, or the difference between the gravity at Qand the gravity at C, but HC is to HG in duplicate proportion of HC to HB, or of OC to DO, that is, the decrease of gravity at the Equator is to its increase at C, as the fquare of the radius is to the square of the fine of the Latitude.

By this alfo it will appear that the direction of heavy Bodies is not to the Centre of the Earth, as has been always fuppofed, For if we take a heavy Body and hang it by a thread, the thread produced will not pafs through the Centre any where but at the Poles and the Equator, for in the Figure the thread is carried by the centrifugal force of the Body B from the pofition AC, into the pofition A B where it will reft.

Now to determine the angle CAB which the line of direction of the Body makes with the line A C, let AN be drawn parallel to B C, and produce OB till it meet with it in N, and let us confider the Body B as drawn

by

by three powers according to three different directions BO BL and AB, the power which pulls it according to BO is its gravity, that which draws it according to the direction BL is its centrifugal force, and that which acts according to AB is the ftrength of the thread, by which the Body is hindered to move according to either of the other two directions, and therefore it is an æquilibrium with the other two powers, but by a Theorem which is demonftrated by feveral of the writers of Mechanics, but particularly by Monf. Hugens in his fmall Treatife De potentiis per fila trahentibus. If a Body be pulled by three different powers which are in aquilibrio with one another, according to three. different directions A B, BK, and BO, these three powers will be as the three fides of the Triangle ABN, viz. as AB, AN, and BN refpectively; or as A B, BC and AC: BN being very near parallel, and confequently equal to A C, fince they do not meet but at a great diftance. From hence it follows that the force of gravity is to the centrifugal force as, AC is to BČ: but a method has been already shown how the proportion of the force of gravity to the centrifugal force may be determined, and therefore the proportion of A C to BC, may be alfo determined, which at the Latitude of 51°, 46", is as 446 to 1. There fore in the Triangle ABC, the proportion of AC to BC is known and the angle A CB being

H 3

being equal to the angle COQ which is fubtended by the arch CQ the Latitude of the place, from thence by the Tables of Sines and Tangents the angle B A C may be known, which in the above mentioned Latitude is about five minutes.

From hence also it will appear that it is not the line AC, which being produced paffes through the Centre, but the line AB that is perpendicular to the curve PQ, for all the particles of the fluid will fettle themfelves in fuch a pofition that their lines of direction downwards must be perpendicular to the furface of the Body which they compofe, for otherwife the parts of the fluid would not be in an Aquilibrium one with another, and therefore altho' the lines of direction of heavy Bodies do not pass through the Centre of the Earth, yet are they still perpendicular to their Horizons, and upon this account there could arife no error in levelling of lines, and in finding the rifings and fallings of the ground.

Upon this account alfo it will appear that the furface of the Earth is not fpherical, for if it were, then would all lines drawn from the Centre be perpendicular to the furface of the Earth, fince it is the known property of a fphere that they must be fo, but I have already fhewed that it is not fo in the Earth, and therefore it is plain that the Earth is not a Sphere. That therefore I may enquire more particularly

particularly into the Figure of the Earth, I will refume my former hypothefis, that the Earth is compofed of an infinite number of Canals which communicate with one another at the Centre and are all equiponderant, of which we will confider two as OQ and ÓC, and let OQ ber, OD x and DC = y, let the abfolute gravity be called p, and the centrifugal force at the Equator n, OC is equal to x2+y, the weight of the Canal OQ is equal to the abfolute gravity of the whole canal, minus the centrifugal force of each particle contained in it, and because the centrifugal force of each particle is as its diftance from the Centre, and therefore it increases in an Arithmetical progreffion, the greatest of which is n, confequently the fum of all the centrifugal force is nr, but upon the hypothefis, that gravity is the fame at all diftances from the Centre, the abfolute gravity of the canal OQ is pr, and therefore its real weight upon the Centre OQ is pr-nr. After the fame manner the abfolute gravity of the canal OC is pxx+ but the fumm of the centrifugal forces of all the fluid in the canal OC is equal to the centrifugal force of the fluid in CD (as may be eafily proved from the confideration of inclined Planes) But the centrifugal force at C being to the centrifugal force at as CD is to OQ (that is, as y is to r) the centrifugal force at C will be equal

2

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