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angle of resistance angular velocity arch axis beam body bordering upon motion capstan centre of gravity circumference co-efficient compression cord corresponding crank crank arm cubic foot curve cylinder deflexion described determined dimensions displaced fluid distance driving element epicycloidal equal equation equilibrium evident exceedingly small expended expression extrados formula friction given horizontal hypocycloidal inclination inclined plane inertia intersect involute lamina length limiting angle line of centres line of resistance load machine modulus moment of inertia neutral line number of units observing obtain oscillation parallel passing perpendicular pitch circle plane point of application point of contact portion position pulley Px and P2 quantity radius repre respect revolution revolve rupture side space stability supposed surfaces of contact taken to represent tension tion tooth unguent vertical vis viva viva voussoirs wall weight whence it follows whilst whole
Page 126 - VIII, leads to the following remarkable conclusion, easily fixing itself in the memory, that with the unguents, hogs* lard and olive oil interposed in a continuous stratum between them, surfaces of wood on metal, wood on wood, metal on wood, and metal on metal, when in motion, have all of them very nearly the same co-efficient of friction, the value of that co-efficient being in all cases included between 0,07 and 0,08, and the limiting angle of resistance therefore between 4° and 4° 35'.
Page 125 - When no unguent is interposed, the friction of any two surfaces (whether of quiescence or of motion) is directly proportional to the force with which they are pressed perpendicularly together ; so that for any two given surfaces of contact there is a constant ratio of the friction to the perpendicular pressure of the one surface upon the other.
Page 126 - The coefficient for the unguent tallow is the same, except in that of metals upon metals. This unguent appears to be less suited for metallic surfaces than the others, and gives for the mean value of its coefficient under the same circumstances -10.
Page 24 - ... BM, therefore am = bm ; hence the line ab will balance itself on C M. Similarly every other line parallel to AB will be in equilibrium on CM ; therefore the whole triangle ABC will balance itself on CM, and consequently the centre of gravity of the triangle is in C M. In like manner it may be proved that the centre of gravity of the triangle is in the line BN; therefore G the point of intersection of CM, BN is the centre of gravity of the triangle. Join MN; then, since...
Page 128 - ... in amount, but also in nature, from the friction of surfaces in continuous motion ; especially in this, that the friction of quiescence is subjected to causes of variation and uncertainty from which the friction during motion is exempt. This variation does not appear to depend upon the extent of the surface of contact; for, with different pressures, the ratio of the friction to the pressure varied greatly, although the surfaces of contact were the same. The slightest jar or shock, producing the...
Page 526 - ... collected into two unequal flanges joined by a rib, the greater flange being on the extended side, and the proportion of this inequality of the flanges being just such as to make up for the inequality of the resistances of the material to rupture by extension and compression respectively. Mr.
Page 37 - ... of the cylinder. Or it may be conceived to be generated by the motion of a circle, in a direction perpendicular to its surface, and always parallel to itself. 61. A cylinder is either right or oblique, as the axis is perpendicular to the base or inclined. 62. Every section of a right cylinder taken at right-angles to its axis, is a circle ; and every section taken across...
Page 127 - ... than the others, and gives for the mean value of its coefficient under the same circumstances -10. Hence it is evident that where the extent of the surface sustaining a given . pressure is so great as to make the pressure less than that which corresponds to a state of perfect separation, this greater extent of surface tends to increase the friction by reason of that adhesiveness of the unguent, dependent upon its greater or less viscosity, whose effect is proportional to the extent of the surfaces...
Page ix - The difference between the aggregate work done upon a machine during any time by those forces which tend to accelerate the motion, and the aggregate work, during the same time, of those which tend to retard the motion, is equal to the aggregate number of units of work accumulated in the moving parts of the machine during that time, if the former aggregate exceed the latter, and lost by them during that time, if the former aggregate fall short of the latter.
Page 675 - ... of the intervening rod each will be made to recede from the other by the same distance, and, by its contraction, to approach it by the same distance. But if they be placed on an inclined plane (one being lower than the other), then when by the increased temperature of the rod its tendency to extend becomes sufficient to push the lower of t!»- two bodies downwards, it will not have become sufficient to push the higher upwards.