An experienced operator can work very rapidly with this little apparatus, which has been constructed with much care and ingenuity, and which enters into a series of special mechanisms that is always of interest to know about.

The manufacturer was advised to construct his apparatus so that it could be run by foot power, but, after some trials, it was found that the addition of a pedal and the mechanism that it necessitates was absolutely superfluous, the apparatus working very well such as it is.—­La Nature.

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[Continued from SUPPLEMENT, No. 567, page 9057.]

RADII OF CURVATURE GEOMETRICALLY DETERMINED.

By Prof.  C.W.  MACCORD, Sc.D.

NO.  VII.—­PATH OF A POINT ON A CONNECTING ROD.

The motion of the connecting rod of a reciprocating steam engine is very clearly understood from the simple statement that one end travels in a circle and the other in a right line.  From this statement it is also readily inferred that the path of any point between the centers of the crank and crosshead pins will be neither circular nor straight, but an elongated curve.  This inference is so far correct, but the very common impression that the middle point of the rod always describes an ellipse is quite erroneous.  The variation from that curve, while not conspicuous in all cases, is nevertheless quite sufficient to prevent the use of this movement for an elliptograph.  To this there is, abstractly, one exception.  Referring to Fig. 22 in the preceding article, it will be seen that if the crank OH and the connecting HE are of equal length, any point on the latter or on its prolongation, except E, H, and F, will describe an exact ellipse.  But the proportions are here so different from anything used in steam engines (the stroke being four times the length of the crank), that this particular arrangement can hardly be considered as what is ordinarily understood by a “crank and connecting rod movement,” such as is shown in Fig. 23.

The length DE of the curve traced by the point P will evidently be equal to A’B’, the stroke of the engine, and that again to AB, the throw of the crank.  The highest position of P will be that shown in the figure, determined by placing the crank vertically, as OC.  At that instant the motions of C and C’ are horizontal, and being inclined to CC’ they must be equal.  In other words, the motion is one of translation, and the radius of curvature at P is infinite.

To find the center of curvature at D, assume the crank pin A to have a velocity A_a_.  Then, since the rod is at that instant turning about the farther end A’, we will have D_d_ for the motion of D. The instantaneous axis of the connecting rod is found by drawing perpendiculars to the directions of the simultaneous motions of its two ends, and it therefore falls at A’, in the present position.  But