Journal . rs,vol. i, p. 135, on a correction sometimes required in curves professing to represent the connection between two physical magnitudes ). The correction is this. Plot the curve givenby the quantities like ic/x, , values averaged over a range,say, + h: such values might be given, for example by a linethermopile of width 2h used to measure temperature along aspectrum. Let R (Fig- 1) be any point on the false curve soobtained. Let PM, QX be ordinates at the distances +hfrom the ordinate Rm. Join PQ cutting R7?i in S. Take Upequal to one-third of RS. Then p is the corrected point,p a
Journal . rs,vol. i, p. 135, on a correction sometimes required in curves professing to represent the connection between two physical magnitudes ). The correction is this. Plot the curve givenby the quantities like ic/x, , values averaged over a range,say, + h: such values might be given, for example by a linethermopile of width 2h used to measure temperature along aspectrum. Let R (Fig- 1) be any point on the false curve soobtained. Let PM, QX be ordinates at the distances +hfrom the ordinate Rm. Join PQ cutting R7?i in S. Take Upequal to one-third of RS. Then p is the corrected point,p and S always lying on opposite sides of R, It Avill be notedthat in this construction PM and QN are, in the actuarial case,unknown quantities, representing bounding ordinates of aw-gTOwp. In Lord Rayleigh^s case, since many values—overlapping values—of w/x are obtained by observation, the?oidinates may be supposed for graphic purposes to be known. 138 A Note (111 Mr. Kin (/a method of Graduation [ The proof given is as follows : Let y denote an ordinate oftlie true curve ; then +/( y . dJi where //o is the ordinate of the true curve at m and .Vo is theabscissa of m. That is area = 2;.^./o+^^j. But if y be the ordinate of the observed curve, by definitionwe must have 2hyQ equal to this area. That is and, generally,Hence , h^ d-i/ _ /i2 d^y y =y + 6 dx- d-y _ d-y li- d*ydx^ dx^ 6 * h^/(Py\ _ h^fd^ _ h^ ^?/^aKdxV ~ G \da^ Q da:*) _ li d-y~ Q di^ 1920.] and its relation to Graphic Method. 131^ if we may neglect the term in h^. Whence finalh- But S»i=i(PM + QN) 2v dxf, dx-i, 2 1/ , dy -, d^ii Ir2v^ Clef,, (/,/- 2 , d-i/ h- , .. = y«+rf^9 (4) Therefore, since S?7i = //„ —KS, ,Vn = ?yo+ oRS (5) As pointed out above, to get this correction Lord Rayleighused two points which, in the actuarial case, cannot besupposed to be known. Let the figure be extended, and letAB, CD (Fig. 2) be the ordinates of the false curve atdistances of +2/i from R?>i. By the same line of ar
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