In this case cross _dividing_ gives a constant quotient, _e.g._, 8 ÷ 3 = 4 ÷ 1·5. Since the upper scale is now a scale of reciprocals, the ratio is really O ⅛ ¼ ─────────── D 1·5 3 Footnote 6: These lines should not be brought to the working edge of the scale but should terminate in the horizontal line which forms the border of the finer graduations, their value being read into the calculation by means of the cursor (see page 55). Footnote 7: The same principle may be applied to the cursor. Footnote 8: Philosophical Transactions of the Royal Society, 1815. ------------------------------------------------------------------------ _BY THE SAME AUTHOR._ LOGARITHMS FOR BEGINNERS. “An extremely useful and much-needed little work, giving a complete explanation of the theory and use of logarithms, by a teacher of great clearness and good style.”—_The Mining Journal._ 1s. 8d. Post Free. THE INDICATOR HANDBOOK. Comprising “The Indicator: Its Construction and Application” and “The Indicator Diagram: Its Analysis and Calculation.” Complete in One Volume. 7s. 10d. Post Free. “Mr. Pickworth’s judgment is always sound, and is evidently derived from a personal acquaintance with indicator work.”—_The Engineer._ POWER COMPUTER FOR STEAM, GAS AND OIL ENGINES, Etc. “Accurate, expeditious and thoroughly practical.... We can confidently recommend it, and engineers will find it a great boon in undertaking tests, etc.”—_The Electrician._ 7s. 6d. Post Free. ------------------------------------------------------------------------ ADVERTISEMENTS. LOGARITHMS FOR BEGINNERS For a full and intelligent appreciation of the Slide Rule and its various applications an elementary knowledge of logarithms is necessary. All that is required will be found in this little work, which gives a simple, detailed and practical explanation of logarithms and their uses, particular care having been taken to elucidate all difficult points by the aid of a number of worked examples. Seventh Edition, 1s. 8d. Post Free. POWER COMPUTER for STEAM, GAS, AND OIL ENGINES, Etc. Gives The Indicated Horse-Power of Steam, Gas, and Oil Engines—The Brake Horse-Power of Steam, Gas, and Oil Engines—The Size of Engine Necessary to Develop any Given Power—The Mechanical Efficiency of an Engine—The Ratio of Compound Engine Cylinders—The Piston Speed of an Engine—The Delivery of Pumps with any Efficiency—The Horse-Power of Belting—The Rim Speeds of Wheels, Speeds of Ropes, Belts, etc.—Speed Ratios of Pulleys, Gearing, etc.