A slender and highly elastic spring of a like form is employed to produce a vibratory motion in the balance ring of a watch : one ex tremity of the spring is attached to the axle of the balance, and tho other to some part of its circumference: If a movement of small extent about the axle be given in one direction to the balance, the spring will be compressed near the axle, and, in the effort to recover its previous state, the balance-ring will be moved round in a contrary direction ; but the force of elasticity carries any point in the ring beyond the place which it occupies when the ring is in a state of rest ; and when that force is destroyed by the compression again produced in the spring, near the axle, the balance is made to return in the direction in which it was first moved. Thus an alternate motion iu the balance-ring is continued; the time of the vibrations, and con sequently the velocities with which the wheels revolve, depending upon the force of elasticity in the spring. The elastic power of the spring varies with the tension, and is directly proportional to the angle through which the spring is wound about the axle; and thus the vibrations of a spring, like those of a pendulum in a eyeloidal arc, are isochronous. [ELAsrrcrrr.] The length of the spring and the diameter of the balance are increased by heat and diminished by cold; consequently, without some Compensating power, the times of vibra tion will vary according to the changes of temperature.
When a carriage moving along a level road passes suddenly over an obstacle, so that a point in the circumference of the wheel is in contact with the obstacle, the centre of the wheel describes a circular arc about the point of contact as a centre ; and then, if the carriage is perfectly rigid, a portion of its velocity will be lost. In order to
maintain that velocity,amadditional force of draught would be necessary; and an expression for this additional force is investigated in Whewell's Mechanics' (art. 261, and the following). Part of this additional force is employed in counteracting the motion of ascent, and the re mainder, which is generally much the greater quantity, in diminishing the effect of the sudden change which takes place in the direction of the motion of the carriage. This latter part may be in a considerable degree removed by the use of springs ; for then, on the wheel meeting the obstacle, the suspended body of the carriage bending the springs by its weight, the centre of gravity of that body is made to describe a curve line, to which its previous rectilinear direction is a tangent ' • and thus the jerks which arise from movements in directions making finite angles with one another are avoided.
The force of draught required-in addition to that which is due to friction, when a stiff carriage passes over a roughly paved road, varies as the square of the velocity and the height of the stones directly, and as the radius of the wheel inversely.