## The Mechanical Principles of Engineering and Architecture |

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### Common terms and phrases

a₁ angle of resistance angular velocity arch axes axis beam body bordering upon motion capstan centre of gravity circumference co-efficient conical surfaces cord corresponding crank crank arm cubic foot curve cylinder deflexion determined dimensions direction distance ditto driven wheel elongation epicycloidal equal equation equilibrium evident exceedingly small extrados fly-wheel force friction given horizontal hypocycloidal intersect involute lamina length limiting angle line of centres line of resistance load machine modulus moment of inertia moving n₁ n₂ neutral line numbers of teeth observing obtain P₁ P₂ parallel passing perpendicular pitch circle plane point of application point of contact portion position pressures applied pulley radii radius repre revolution revolve rupture screw space stability supposed surfaces of contact taken to represent tension tion tooth U₁ vertical vis viva voussoirs wall weight whence it follows whilst whole

### Popular passages

Page 14 - ... be equal to the sum of the moments of those which tend to turn it in the opposite direction about the same axis.

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 37 - GH is the length of the path descrilbed by G ; which is the first property of GULDINUS. 39. The above proposition is applicable to finding the solid contents of the thread of a screw of variable diameter, or of the material in a spiral staircase: for it is evident that the thread of a screw may be supposed to be made up of an infinite number of small solids of revolution, arranged one above another like the steps of a staircase, all of which (contained in one turn of the thread) might be made to...

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 substances 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...

Page 248 - ... According to a general (almost a universal) custom among mechanics, two different generating circles are thus used for striking the teeth on two wheels which are to act together, the diameter of the generating circle for striking the faces of the teeth on the one wheel being equal to the radius of the pitch circle of the other wheel. Thus if we call the wheels A and B, then the epicycloidal faces of the teeth on A, and the corresponding hypocycloidal flanks on B, are generated by a circle whose...

Page 472 - ... about an axis passing through its centre of gravity, and perpendicular to the plane in which the couple acts.

Page vii - Moral State and Moral Prospects of Society, being the substance of a course of lectures delivered to the students of the Theological Hall in Edinburgh, — " We know," says this distinguished philosopher, " that there is a mighty force of sentiment and natural affection arrayed against the law of primogeniture But here is the way in which we would appease these feelings, and make compensation for the violence done...

Page 377 - STONES.* A STRUCTURE may yield, under the pressures to which it is subjected, either by the slipping of certain of its surfaces of contact upon one another, or by their turning over upon the edges of one another ; and these two conditions involve the whole question of its stability.

Page 70 - Having given the mom.ent of inertia of a body, or system of bodies, about an axis passing through its centre of gravity, to find its moment of inertia about an axis, parallel to the first, passing through any other point in the body or system. Let...

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...