The London, Edinburgh and Dublin philosophical magazine and journal of science . The point B is supposed to travel from the point C, andtherefore a is the independent variable. D is a point in thisline of motion infinitesimally near to B, and BE isi a perpen-dicular from B upon the line A D. Then it is clear that if 6 is such a quantity that a = b shin 0, it will also be true thatc = b cosh 6, because * Communicated by the Author, the Hyperbolic Trigonometrical Functions of 6. 239 d shin 6 Also DB = Sa = shin 0=6. and ED = 8c = *\i6 = b. dd d cosh 6~~dd 86. =bcosh6 .86;86=b thin 6. 86
The London, Edinburgh and Dublin philosophical magazine and journal of science . The point B is supposed to travel from the point C, andtherefore a is the independent variable. D is a point in thisline of motion infinitesimally near to B, and BE isi a perpen-dicular from B upon the line A D. Then it is clear that if 6 is such a quantity that a = b shin 0, it will also be true thatc = b cosh 6, because * Communicated by the Author, the Hyperbolic Trigonometrical Functions of 6. 239 d shin 6 Also DB = Sa = shin 0=6. and ED = 8c = *\i6 = b. dd d cosh 6~~dd 86. =bcosh6 .86;86=b thin 6. 86. And the triangle BED being similar to the triangle A 0 B, BE _ DB = b. cosh 6~b ™ c c 2(BE 86=86. = 6. Therefore 6 can be obtained by summing such smallelements as BE, and dividing the result by b. BE, in fact,is that component of the motion of B which is at right anglesto AB. Fio- /fc/sz/vc £dg£ Suppose that at the point A there is a circular pin in adrawing-board, but capable of moving round a vertical axisexactly coinciding with the geometrical point A. In the head of this pin is a horizontal slot in which a barslides. This bar is enlarged at one end, as shown in the sketch,so as to carry a small wheel moved, by friction against theboard, about an axis exactly coinciding with the centre lineof the bar. It will be clear that the movement in arc of a point in thecircumference of this wheel will give the quantity 2 (BE) or6 . b if the point of contact of the wheel with the board iscarried along C B. If the circumference of the wheel isequal to b, the turns of the wheel will give 0, and these maybe given by arrangements (not shown in the sketch) similarto those in Amslers planimeter. 240 Mr. Gr. J. Parks on Heat Evolved or The enlargement necessary to carry the wheel may beconveniently made circular (at least in the portion remotefrom A) round the point B as ce
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
