R. G. WEST ON LTSSAJOUs' CURVES. 39 



being free from the tendency to twist, and so alter the relative 

 lengths of the pendulums ; also as eliminating any real or apparent 

 effect of unequal lateral tension of the strings. I believe the next 

 stage was Mr. Tisley's happy combination of the movements of two 

 separate pendulums in a single point, as described by him to the 

 British Association in 1873. Following this was an exact and 

 scientific explanation of the curves by Dr. C. Giebel in the " Zeit- 

 schrift fur die gesammten Naturwissenschaffen," Bd. xiv., October, 

 1875. In the "Loan Collection of Scientific Apparatus," in 1876, 

 an instrument embodying some new features was sent by the Institute 

 for Physical Science of the University of Halle ; and later, Mr. 

 Browning has introduced a cheap form of the apparatus, which he 

 calls the Sympalmograph, and has issued an interesting pamphlet 

 in connection with it. There is also a description of Mr. Tisley's 

 machine in " Engineering" for the 6th February, 1874, and he has 

 since produced a cheaper form of it. I will proceed to describe 

 briefly the Compound Pendulum Apparatus, by which these curves, 

 in their ordinary form, are produced. Two pendulums are sus- 

 pended so that their planes of vibration are at right angles to each 

 other. From a point in each pendulum above the point of suspen- 

 sion there proceeds an arm, connected at one end with the pendulum 

 by means of a ball-and-socket joint, the other extremities of these 

 arms meeting in a glass tube-pen, which traces a line representing 

 the resultant of the motions of the two pendulums. This is sub- 

 stantially the instrument as originally brought out by Mr. Tisley. 

 In Mr. Browning's Sympalmograph, the details differ in several re- 

 spects, chiefly in the connecting arms being attached by means of 

 a Hook's universal joint below the points of suspension of the 

 pendulums. If either pendulum is set vibrating separately, the pen 

 will trace an arc of a circle, of which the radius will be the arm 

 attached to the other pendulum, and the centre the point of that 

 attachment. For the present let us consider these as straight lines. 

 Now, suppose the pendulums adjusted to vibrate exactly in the same 

 periods of time, or, as it is usually put, tuned to strict unison, and 

 that they are started exactly together. It is clear that the pen will 

 trace a diagonal line, the resultant of the rectilinear motions, and 

 this line will be repeatedly retraced as the vibrations die away. The 

 angular direction of this line will vary according to the relative ampli- 

 tude of the vibrations of the two pendulums. Directly, however, 

 you leave this simple set of conditions, by starting one pendulum 



