## Useful Rules and Tables Relating to Mensuration, Engineering, Structures, and Machines |

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acting angle angular approximate axis base beam body breadth British calculate called centre centre of magnitude circle circular common computed correct corresponding cube cubic curve cutting decimal denote depth diameter difference direction distance divide division draw engine equal example feet figure foot force fraction give given gravity greater greatest half head heat horizontal inch intervals iron joint length less load logarithm mean measure Metres middle mile minute motion multiply nearly opposite parallel perpendicular places plane position preceding pressure proportional quotient radius ratio represent resistance resultant root RULE side slope solid speed square square inch steam straight line stress subtract surface tangent temperature thickness thrust triangle uniform unit velocity vertical volume weight wheel whole yard

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Page 140 - Each of the three forces is equal and opposite to the resultant of the other two; and each pair of forces are equal and opposite to the components of the third. Hence this rule serves to resolve a given force into two parallel components acting in given lines in the same plane.

Page 59 - To find the area of a trapezoid. RULE. Multiply half the sum of the two parallel sides "by the perpendicular distance between them : the product will be the area.

Page 225 - XVI. — To reduce the inertia or mass of a machine to the driving point. Multiply the weight of each moving portion of the machine by the square of the ratio of its velocity to the velocity of the driving point ; and add together the products; the sum will be the weight of the mass which, if concentrated at the driving point, would require the same force to produce a given change in its speed, in the course of a given time or of a given motion, that is required by the actual machine.

Page 4 - ... between 1 and 10 is obtained by moving the decimal point of the number (actual or implied) the required number of digits. The power of 10, for a number greater than 1, is positive and is one less than the number of digits before the decimal point in the original number. The power of 10, for a number less than 1, is negative and is one more than the number of zeros immediately following the decimal point in the original number. Hence...

Page 123 - ... the ratio of the mass of a given volume of the substance to the mass of an equal volume of water, in which case it is equal to the specific gravity. In its application to gases, the term THE INTENSITY OP PRESSURE. 121

Page 277 - ... by the difference between the pressures in the boiler and cylinder, multiply the square root of the quotient by the speed of the piston in feet per minute, and by the square of the diameter of the cylinder in inches, and divide the product by 15000. From this we obtain the proper area of the steam passages for the particular cases that may demand our consideration. For safety take the minimum difference between pressures in cylinder and boiler with maximum pressure in the cylinder. Let the diameter...

Page 251 - ... stream relatively to the ship in knots; the real slip, or part of that speed which is impressed on that stream by the propeller, also in knots ; and the constant 5-66/or sea-water, or 5-5 for fresh water.

Page 96 - Then, without moving the vertical circle, direct the telescope towards the star, clamp the vernier-plate, and by the aid of its tangent-screw follow the star in azimuth with the cross wires until it arrives exactly at its former altitude, as is shown by its image coinciding with the cross wires; then measure the horizontal angle between the new direction of the star and the station-line...

Page 181 - A live load is one that is put on suddenly, or is accompanied with vibration ; such as a swift train travelling over a railway bridge, or a force exerted in a moving machine.

Page 103 - To find the sides of a rightangled triangle in whole numbers, take two unequal whole numbers: then the sum of their squares, the difference of their squares, and twice their product will be the three sides.