PHYSICAL CURVES. 93 



another than down any other form of curve or straight line. 

 The other name for the cycloid, the curve of equal times, 

 means that if a pendulum bob is constrained in some way to 

 vibrate in a true cycloidal curve, the vibrations of the pendu- 

 lum will be isochronous no matter what the amplitude of 

 vibration. It is commonly said that this is so of the ordi- 

 nary pendulum, but this is not true, although a very close 

 approximation is reached when the angle of vibration is 

 small. 



The Spiral . — The spiral is the curve described by a point 

 which while revolving around a fixed centre continually 

 approaches or recedes from that centre under some given law. 

 There may be, of course, a number of different kinds of 

 spirals. One of the most interesting of spirals is that which 

 would be described by a body moving under a central force 

 in the presence of a resisting medium. In this case the body 

 would gain in lineal velocity and slowly wind in to the centre 

 of force. At one time it was thought that Encke's comet, 

 one of the periodical comets, was showing an unexplained 

 increase in velocity and was moving in such a spiral path. 

 It was therefore assumed that the presence of a resisting 

 medium in planetary space was indicated. Later observa- 

 tions, however, do not seem to have confirmed this theory. 



The Helix. — This curve differs from the preceding curves 

 in that it is a curved line in three dimensions instead of two. 

 It is such a curve as is described by a body revolving in a 

 circle at the same time that the plane of the circle moves per- 

 pendicularly to itself. The path of the end of a propellor 

 blade illustrates this motion. The helix is supposed to be 

 indicative of the form of wave met with in the luminiferous 

 ether in circulary polarized light. 



The Sine Curve. — The sine of an angle is equal to the 

 vertical projection of a moving radius in a circle whose radius 

 is unity. By sine curve is meant the curve which would be 

 plotted by setting off equal angles along a horizontal line and 

 at each point erecting a perpendicular eciual to the sine of 



