Mathematical formulation of price-making factors is necessary in order to know when extraordinary or strategic considerations are influencing the market. The mathematical methods are highly technical, and in order to explain most clearly we shall follow a specific problem thru from beginning to end. The problem is to determine the price of hogs from hog receipts (supply) and from business conditions (demand). To represent business conditions, we are using bank clearings outside of New York City. The actual figures for heavy hog prices at Chicago are given in the Appendix. Hog receipts at Chicago and bank clearings outside of New York City are given on pages 81 and 82. The problem is to evolve from these figures the law of hog prices. The first step is to determine the secular or long-time trend of these figures. Find, for example, the secular trend of such a series as: 1901 2 1902 3 1903 2 1904 5 1905 2 1906 6 1907 4 1908 6 1909 6 From looking at these figures, we know that the secular trend slopes upward, starting with about 2 in 1901, reaching 3 or 4 by 1905, and 5 or 6 by 1909. To express the matter with mathematical accuracy, the method as applied to this series is as follows: First add all the figures together. Answer in this case, 36. Then divide by the number of figures—in this case 9. Thirty-six divided by 9 gives 4, which is the value of the secular trend for 1905, which is the central year. The year 1904 is the −1 year, 1903 the −2 year, 1902 the −3 year, 1901 the −4 year, and in like manner 1906 is the +1 year, 1907 the +2 year, 1908 the +3 year and 1909 the +4 year. Multiply the minus years by their respective values: −1 by 5, −2 by 2, −3 by 3 and −4 by 2, and also the plus years, +1 by 6, +2 by 4, +3 by 6 and +4 by 6. The totals are −26 and +56, or a net of +30. Now the sum of the squares of −1, −2, −3, −4, +1, +2, +3 and +4 is 60. Sixty divided into 30 gives .5, which is the rate of movement of the secular trend each year, or if, as we found, 4 is the secular trend value for 1905, then 3.5 is the value for 1904, 3.0 for 1903, 2.5 for 1902, and 2.0 for 1901, and in like manner 4.5 for 1906, 5.0 for 1907, 5.5 for 1908 and 6 for 1909. The secular trend is a straight line, and the actual goes above and below the secular trend in more or less wave-like fashion. In Chart I, the straight line is the secular trend of heavy hog prices at Chicago for 1903–1916, and the irregular line fluctuating above and below is the actual price of heavy hogs. BANK CLEARINGS OF THE UNITED STATES OUTSIDE NEW YORK CITY. (7 ciphers omitted)