The London, Edinburgh and Dublin philosophical magazine and journal of science . ge Greenhill, theelement PQRS (p. 647) consists of the two circular arcsPQ, US, having the pole A as centre, and two other arcsQR, PS, described by the tracer about the fixed joint H ascentre. In this case the records of the wheel along QR andPS cancel. Further, it is obvious that QR and PS may be any twosimilar curves whatever and the same method applied forthe records of the wheel, which will, in general, partlyslip and partly roll, along QR and PS will cancel andthe total record and area described will be the s
The London, Edinburgh and Dublin philosophical magazine and journal of science . ge Greenhill, theelement PQRS (p. 647) consists of the two circular arcsPQ, US, having the pole A as centre, and two other arcsQR, PS, described by the tracer about the fixed joint H ascentre. In this case the records of the wheel along QR andPS cancel. Further, it is obvious that QR and PS may be any twosimilar curves whatever and the same method applied forthe records of the wheel, which will, in general, partlyslip and partly roll, along QR and PS will cancel andthe total record and area described will be the same in allcases. Slip-Curves of an Amsler Planimeter. 143 The theory of the instrument having been established byany one of the various methods when the pole is outsidethe area to be measured, it can be applied at once to thecase in which the pole is inside the area by a simplemethod which I have described in the Mathematical Gazette(July 1911). This may be briefly indicated by reference to the figure,in which, for simplicity, the curve is shown wholly outsidethe Draw any arbitrary curve PS from the curve to the base-circle. Starting at P, take the tracer round the boundaryPQ RP, in the positive (clockwise) direction, along PlS,round the base-circle SU TS in the positive (this time, anti-clockwise) direction, and finally back along SP. The record is clearly the area of: the portion of the curveoutside the base-circle. But this record is merely that whichwould be obtained by taking the tracer round the boundaryPQ RP, for nothing is recorded round the base-circle andthe records along PS and SP cancel. Hence by suppressingthese motions and taking the tracer once round the boundaryin the usual way, the instrument gives the excess of thearea of the curve over that of the base-circle. Similar reasoning can be applied when the curve lieswholly inside or partly outside and partly inside the base-circle. Yours faithfully,Technical College, Bradford. J. A. ToMKINS. [ U4 ] X
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
