File:Economic cycles- their law and cause (1914) (14763650815).jpg

Identifier: economiccyclesth00moor (find matches)
Title: Economic cycles: their law and cause
Year: 1914 (1910s)
Authors: Moore, Henry Ludwell
Subjects: Depressions Agriculture -- Economic aspects Supply and demand
Publisher: New York : The Macmillan Company
Contributing Library: University of California Libraries
Digitizing Sponsor: MSN

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e equationto the graph giving the course of rainfall in the OhioValley. The Equation to the Rainfall Curve It will be helpful to approach the algebraic descrip-tion of the cyclical movement of rainfall in the OhioValley, by observing how we obtain an increasinglyaccurate account of the actual rainfall by superposingthe constituent cycles. We shall use, as an index of therelative fit of the several curves, the root-mean-squaredeviation of the observations from each curve. If, as a preliminary step, the raw data of the courseof annual rainfall are examined, it is found that themean annual rainfall in the Ohio Valley is 41.19 inches,and the root-mean-square deviation about the mean is/S = 6.70 inches. If the long 33 years cycle is considered by itself, itappears that the root-mean-square deviation about the33 years curve is >S = 6.39 inches. The graph of the33 years cycle is given in Figure 4. Its equation is y = 41.19 + 2.88 sin (^ t + 328° 7V 22 Economic Cycles: Their Law and Cause
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Cycles of Rainfall 23 the origin being at 1839. This curve traces in boldoutline the general course of ramfall. It gives theground-swell of the rainfall movement. If the 8 years cycle is superposed upon the 33 yearscycle, the root-mean-square deviation about the curvebecomes S = 5.66 inches. The graph of the combinationof these two curves is traced in Figure 5. Its equation is 1/ = 41.19+ 2.88sin (1^^ + 328° 7)+4.13 sin (Ii + SIOMI), the origin being at 1839. A point of interest with regardto the flow of the curve is the rapidity with which itrises from the least minimum to the greatest maximum,and the slowness with which it then descends to thesubsequent least minimum. If the 8 years cycle and its semiharmonic of 4 yearsare combined with the 33 years cycle and its semi-harmonic of 16.5 years, the root-mean-square deviationabout the compound curve becomes *S=5.29 inches.The graph of the curve is given in Figure 6. Its equa-tion is 7/=41.19 + 2.88 sin(1^ i + 328° 7) + 2.25 sin (;*^^+

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