Aim and method of the present inquiry, 557. — The two fundamental problems, 558. — Prices should be treated as ratios, . 559. — When so treated the paradox of the arithmetic and harmonic means is resolved, 559. — Ratios are not fractional quantities, 561. — The completely weighted arithmetic mean is a ratio of aggregates, 563. — Geometrical representation of the price level, 563. — The method of least squares, 566. — The method of summation, 568. — Changes of the general price level, 568. — Effect of changes of the relative importance of trade in different types of commodities, 571. — Substitution of "dollar's worths" for physical units, 571. — Fisher's index number, 572. — Conclusion, 573.