Traction, force of, on a railroad, 192 Tredgold,70 Trevithick and Vivian, Messrs., construct the first high-pressure engine used in this country, 148 U. United States, steam communication with, 274 V. Vacuum, production of, by experiment, 37 Vapour, elastic, force of, 35 Valves, Watt's method of working the, 109 W. Walker and Rastrick, Messrs., apparent discrepancy of their estimated expense of locomotive power, 189 Washborough takes out a patent for Watt's invention of the rotatory motion, 100 Water, sea, injurious to marine boilers, 245. How remedied by blowing out, 246 Watt, James, important discoveries of, 39. His acquaintance with Dr. Robinson and first experiments on the steam engine, 73. His subsequent improvements, 75. His method of condensation, 76. His first introduction of the air-pump into the steam engine, 77. Further improvements, 78. His difficulties, 78. Description of his single-acting engine, 80. His introduction to Dr. Roebuck, 88. Erects his first engine on the estate of the Duke of Hamilton, 88. After further improvements, obtains a patent for this engine, in conjunction with Roebuck, 88. His difficulties owing to Dr. Roebuck's failure, and subsequent connexion with Bolton, 88. Obtains an extension of his patent, 89. Ingenious invention of, to determine the rate of remuneration he should receive, 89. His invention of the parallel motion, 95. His method for producing a rotatory motion anticipated by Washborough, who takes out a patent for it, 101. His contrivance of the governor, 104. His method of working the valves, 109. His suggestion of the D valve, 113 Wood, Mr. Nicholas, 168 Woolf, Mr., his improvements in the steam engine, 134. Obtains a patent for the double-cylinder engine, 137 * * * * * JUST PUBLISHED, IN ONE VOLUME, 8VO. MATHEMATICS FOR PRACTICAL MEN; BEING A COMMON-PLACE BOOK OF PRINCIPLES, THEOREMS, RULES AND TABLES, IN VARIOUS DEPARTMENTS OF PURE AND MIXED MATHEMATICS, With their applications; especially to the pursuits of Surveyors, Architects, Mechanics, and Civil Engineers. With numerous engravings. BY OLINTHUS GREGORY, LL. D., F. R. A. S. "Only let men awake, and fix their eyes, one while on the nature of things, another while on the application of them to the use and service of mankind."--_Lord Bacon._ SECOND EDITION, CORRECTED AND IMPROVED. _Extract of a Letter from_ WALTER R. JOHNSON, _Professor of Mechanics and Natural Philosophy in the Franklin Institute_.