The Cambridge and Dublin Mathematical Journal, Band 5Macmillan, 1850 |
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a² a² angles angular points apparent double points ARTHUR CAYLEY axes bifocal chord centre circuit coefficients common tangent cone confocal surfaces conic conjugate plane conjugate point constant contains coordinates cos² curve of double curve of intersection denote determined drawn edge of regression electrical points ellipsoid equal roots equation expression four function generatrix geodesic line Hence hyperboloid integral line of curvature meet obtain octahedron osculating plane P₁ pair paraboloid parallel pascalians perpendicular plane of contact point of intersection points of contact quantity reciprocal right line second degree passing second order semi-major axis sides six points stationary points straight line supposed symbols tangent plane Theor theorem third degree touch triangles values vertex µ² µ³
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Seite 130 - In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal...
Seite 250 - 087 feet. Hence the work developed during an entire stroke is •087 xp foot-pounds. Now this is developed by the descent from 0° to - f of the quantity of heat necessary to melt a cubic foot of ice; that is, by 4925 thermic units, the unit being the quantity of heat required to raise a pound of water from 0° to 1° centigrade.
Seite 251 - ... 087 x p. Hence t = -00000355^ .............. (1). This, then, is the desired formula for giving the freezing point - t° centigrade, which corresponds to a pressure exceeding that of the atmosphere by a quantity p, estimated in pounds on a square foot. To put this result in another form, let us suppose water to be subjected to one additional atmosphere, and let it be required to find the freezing point. Here p = one atmosphere = 2120 pounds on a square foot; and therefore, by (1), t = -00000355...
Seite 131 - ... always on the left, or, according to the notation of this note, from the non-accented to the accented terminal letter of each of the given lines ; and it is clear that the constant sum of the areas of the triangles is equal to the area of the closed circuit ; the term ' area' being used in the extended sense explained by Professor De Morgan in the paper which follows, if the circuit be
Seite 250 - Now, when 1'087 cubic feet of ice are melted, one cubic foot of water is formed. Hence, if EF be taken equal to '087 feet, F will be the position of the piston when one cubic foot of water has been melted from ice, that is, the position at the end of Process 1, the bottom of the cylinder being at a point A distant from F by rather more than a foot. Let FG be the compression during Process 2, and HE the expansion during Process 4. Let ef be parallel to EF, and let Ee represent one atmosphere of pressure...
Seite 245 - ... that temperature. The change, then, which takes place is, that a certain amount of work is given from the hand to the air, and a certain amount of heat is given from the air to the water of the lake. In the next place, let the bottom of the cylinder be placed in contact with the mass of water at 0°, which is proposed to be converted into ice, and let the piston be allowed to move back to the position it had at the commencement of the first process. During this second process, the temperature...
Seite 244 - Eointed out to me a curious conclusion to which he had been ;d, by reasoning on principles similar to those developed by Carnot, with reference to the motive power of heat. It was, that water at the freezing point may be converted into ice by a process solely mechanical, and yet without the final expenditure of any mechanical work. This at first appeared to me to involve an impossibility, because water expands while freezing; and therefore it seemed to follow, that 'if a quantity of it were merely...
Seite 266 - Diminished Determinant" in Postscript to this paper. f As we know d priori by virtue of a theorem given by M. Cauchy, and which is included as a particular case in a theorem of my own, relating to Compound Determinants, ie Determinants of Determinants, which will take its place as an immediate consequence of my fundamental Theorem given in a Memoir about to appear. The well-known rule for the multiplication of Determinants, is also a direct and simple consequence from my theorem on Compound Determinants,...
Seite 251 - ... tables deduced in the preceding paper from the experiments of Regnault, we find that the quantity of work developed by one of the same thermic units descending through one degree about the freezing point, is 4'97 foot-pounds. Hence, the work due to 4925 thermic units descending from 0° to - t° is 4925 x 4-97 xt foot-pounds.