As this example is rather curious, I have thought it worth while to Thus: Since V and A, are constant, spaces described by the reciprocating

give the complete solution of it. they are in the proportion of the piece and the point whose radius is unity upon the first axis; and as one revolution of the latter corresponds to a complete double oscillation of

be the corresponding value of in the driving curve, we have

will give the driving curve. In the following Table a sufficient number of values are computed to enable these two curves to be laid down by points.

The radius of the follower, however, vanishes at two points of the circumference, the form of its curve resembling that of the figure 0. These points correspond to the passage of the crank over the dead points, where, as it communicates for the moment no velocity to the reciprocating piece, the velocity of the crank must become infinite to maintain the conditions of the problem, which requires a constant velocity in the reciprocating piece, and therefore no loss of time in the change of direction. All which being practically impossible, it is necessary to alter the figure of the curve at these points, and reduce it to the form, shortening the points of the driver accordingly; teeth may then be added to these curves in the usual manner.

xxxi

NOTE to page 361.

THE following mode of communicating an aggregate velocity to a worm-wheel, ought to have been inserted at page 361, as a mixture of sliding and rolling contact.

In fig. 198, let the axis of motion of the worm-wheel B be supposed fixed in position. Then, if the endless screw or long worm Aa revolve, it will communicate a rotation to the wheel B in the usual manner, at the rate of one tooth of the latter for each turn of the former. Again, if an endlong travelling motion without rotation be communicated to Aa, it will now act as a rack upon the teeth of B. If, therefore, the two motions of rotation and travelling be communicated to the endless screw, which can be done in various ways from two sources, the wheel B will receive the aggregate motion, and its angular velocity be affected accordingly. For example, let the screw revolve uniformly, and at the same time travel back and forwards through a small space endlong, the wheel will then revolve with a hobbling motion, making a short trip in one direction and a long trip in the other direction continually.

ERRATA.

22, line 6, for ...we should find in like manner the velocity of Q triple that

of P. And...

read ...M being now the moving point and P the fixed point, we

should find in like manner the velocity of Q triple that of M.

And M being again the fixed point... (Vide Chap. VI.)

278, line 2, for Chapter, read Class.

284, line 11, for DIVISION D, read DIVISION E.

393, line 5 from bottom, for velocity, read velocity-ratio.

397, line 3 from bottom, for not, read not necessarily.

PRINCIPLES OF MECHANISM.

INTRODUCTION.

1. EVERY machine is constructed for the purpose of performing certain mechanical operations, each of which supposes the existence of two other things beside the machine in question, namely, a moving power, and an object subjected to the operation, which may be termed the work to be done.

Machines, in fact, are interposed between the power and the work, for the purpose of adapting the one to the other.

2. As an example of a machine whose construction is familiar to all, the grinding machine so commonly seen in our streets may be cited, in which the grindstone is made to revolve by the application of the foot to a treadle.

Here the moving power is derived from muscular action. The operation is carried on by pressing the edge of the cutting instrument, which is the subject of it, against the surface of the grindstone, which is caused to travel rapidly

under it.

The arrangement and form of this surface, and its connexion with the foot in such a manner that the pressure of the latter shall communicate the required motion to the former, is the office and object of the machine.