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

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C. Griffin, 1866 - Engineering - 312 pages
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Page 63 - 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 8 - The index of the common logarithm of a decimal fraction less than 1 is negative, and is one more than the number of noughts between the decimal point and the significant figures; and the negative sign is usually written above instead of before the index ; that is to say, for numbers less than 1 and not less than...
Page 164 - 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 249 - ... such a soft material could be the means by which tramcars are driven by shearing stresses seems an additional difficulty in the way of this suggestion. Mr. Larmor concludes that the stone support on which the mirrors were borne changed in its dimensions, as it was rotated, by an amount proportional to the square of the ratio of its velocity to the velocity of light, and he justifies this by showing that if matter consists of clusters of electrons, just such a change of dimensions would take place...
Page 147 - ... 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 120 - 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 205 - 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 79 - ... areas respectively by the volume s A, which is represented by O L. Those mean pressures, however, can be found by a direct process, without first measuring the areas, viz. : — having multiplied each ordinate, or breadth, of the area under consideration by the proper multiplier, divide the sum of the products by the sum of the multipliers, which process, when the common trapezoidal rule is used, takes the following form : add together the halves of the endmost ordinates, and the whole of the...
Page 127 - 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.
Page 120 - The theodolite being at a station in the station-line chosen, measure the horizontal angle from the station-line to any star which is not near the highest or lowest point of its apparent daily course, and take also the altitude of that star. Leave the vertical circle clamped, and let the instrument remain perfectly undisturbed until the star is approaching the same altitude at the other side of its apparent circular course. Then, •without moving the vertical circle, direct the telescope towards...

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