His enquiries into evolutes enabled him to prove that the evolute of a cycloid was an equal cycloid, and by utilizing this property he constructed the isochronal pendulum generally known as the cycloidal pendulum.
Since the evolute of a cycloid is an equal cycloid the object is attained by means of two metal cheeks, having the form of the evolute near the cusp, on which the string wraps itself alternately as the pendulum swings.
If G was above M, the tangent drawn from G to the evolute of B, and normal to the curve of buoyancy, would give the vertical in a new position of equilibrium.
Now the line EK is not an arc of a circle, but is a curved line formed as the evolute of another curve ENC, which touches all the rays HL, GM, FO, etc.
A flush darkened Falk's pale face under the bandage, and with what dignity he could muster, he ignored our snickers.
Kipping was standing as they rowed, and so fiercely now did they ply their oars, casting to the winds every pretence of weakness, that the boat rocked from side to side.
The two sides of the evolute coil have unequal dimensions.
Each inductor in the form of a bar is connected to the next by means of two evolute spiral copper strips, one bending inwardly, the other outwardly, their junction being in some cases secured to a block of wood upon the shaft.
This coil differs from the evolute coil in that the two halves are of equal size, the parts which act respectively as upper and under inductor being of equal length.
In the same manner as described for evolute coils; when in position straight out coils appear as in fig.
Evolute connectors may be used for either lap or wave windings.
The balustrade of the platform consists of a simple diaper pattern of intersecting arcs with the familiar evolute band above and below.
The brackets are solid, of evolute spiral outline and beautifully hand carved.
The pleasing effect of the design at Seventh and Locust streets is largely due to appropriate use of the evolute spiral band.
Of more interest is the balustrade at Number 207 La Grange Alley with its evolutespiral band and slender ball spindles beneath.
Scroll work is conspicuous, as are rosettes, but a touch of individuality is given by a Grecian band instead of the more common evolutespiral above the diaper pattern.
When the refracting curve is a circle and the rays emanate from any point, the locus of the secondary caustic is a Cartesian oval, and the evolute of this curve is the required diacaustic.
If the second medium be more highly refractive than the first, the secondary caustic is a hyperbola having the same focus and centre as before, and the caustic is the evolute of this curve.
The evolute of this ellipse is the caustic required.
For a circle, when the rays emanate from any point, the secondary caustic is a limacon, and hence the primary caustic is the evolute of this curve.
It will at once be seen that Ez is less than Dx, and that since the normal at P is vertical and infinite, the evolute of DPE will consist of two branches xN, zM, to which the vertical normal PL is a common asymptote.
This point evidently lies upon the branch zM of the evolute in Fig.