Using these more complex mathematical methods, it is often possible to express the relationships more exactly. But no method, however far refined, will take the place of common sense market judgment. Nevertheless, it may be decidedly helpful to a better understanding of the normal working of supply and demand to use both hyperbolas and cubic curves on occasion. [Illustration: Chart illustrating the straight line as compared with the skew curve, for purposes of expressing the relation between hog receipts at Chicago and hog prices at Chicago. On the basis of the curve when the receipts are 45 per cent less than the secular trend corrected seasonally, the price should be 38 per cent over, and when the receipts are 42 per cent over the secular trend corrected seasonally, the price should be 33 per cent under. ] Other refinements of the mathematical study of hog prices may consist in working out the correlation coefficients between hog prices and receipts at six markets or eleven markets instead of using Chicago receipts alone. Work may be done looking into the relation between hog prices and potential supply as contrasted with the temporary or month-by-month supply. So far as the relation between hog prices and business conditions is concerned, it should be worth while to work out correlation coefficients between hog prices and the amount of new building, or hog prices and Dun’s index number. In fact, there are a great many measures of business activities which may possibly measure the demand for hogs better than bank clearings outside of New York City.[9] Some people may think it advisable to work out a correlation and line of regression illustrating the relation between hog prices and corn prices. This has been attempted, but it has been found that after the secular and seasonal trends are taken out of both corn prices and hog prices there is practically no relation between them. It is a curious commentary on our present marketing systems that corn prices and hog prices, while very closely related decade by decade, have very little influence on each other month by month. In other words, changing costs of production can have practically nothing to do with the month-by-month changes in the market price under our present economic system. Unusually high corn prices today are more likely to influence the hog prices of next year than the hog prices of today. After everything has been done which can be done by mathematical method, there will still be room for common sense judgment. But such judgment is best applied by men wise in market lore, men familiar with the technique of production, and who also are familiar with such mathematical methods as are here described. CONCLUSIONS BASED ON RATIOS AND MATHEMATICS OF SUPPLY AND DEMAND