86 Professor J. A. Fleming [March 27, 



The loudness of the sound is represented by large amplitude in 

 the curve, and in the case of a musical note the pitch of the sound 

 by the distance from one hump to the next, this wave length being 

 large for deep notes and short for high ones on the musical scale. 



°This curve, whatever may l)e its nature, is called the waveform of 

 the sound, and the three qualities possessed by every sound — viz. 

 loudness, jntch, and quality or timbre— are represented in the curve by 

 the amplitude of height of the curve, by its wave length or distance 

 in which it repeats itself, and by the shape of the curve whether 

 regular or irregular. 



Since the transmitting telephone is a device for translating aerial 

 vibrations into electrical vibrations, we need another appliance for 

 investigating the wave form of the electrical current, which is created 

 in the cable, and this we have in that valuable instrument called the 

 oscillograph. In the form given to it by Mr. Duddell it consists of 

 a narrow loop of wire or two loops very tightly strained in the field 

 of a powerful magnet. To the loop is attached a little mirror, and 

 from this a ray of light is reflected, first on to a rocking mirror and 

 then on to the screen. When an electric current passes up one wire 

 of the loop and down the other it compels the wires to move in 

 opposite directions through the magnetic field, and tilts the attached 

 mirror to one side or the other. The ray is thus deflected, say, 

 vertically by the changes of current in the loop and horizontally 

 by the vibration of the rocking mirror. The combination of the two 

 motions makes the spot of hght on the screen describe a wavy curve, 

 which represents to the eye the wave form of the current. 



We have thus the means of delineating by the changing altitude 

 or ordinate of a curve these invisible motions of the air particles or 

 of the electrons in the wire which in reahty are longitudinal — that is, 

 in the direction of the motion of the wave. 



In the next place another prefatory explanation should be advanced 

 for the benefit of those who are not mathematicians. 



If we draw under one another any number of simple harmonic 

 curves having wave-lengths in the ratio of 1, 2, 3, etc., and various 

 amplitudes, it is quite an easy matter to place these constituent 

 curves one under the other in certain relative positions, and to plot a 

 new curve the ordinate of which at every point is the sum of the 

 respective ordinates of the conponent curves for the same abscissa. 

 AVe thus derive a complex periodic curve. On the other hand, the 

 inverse problem can also be solved. We can take any single-valued 

 periodic curve however irregular and find out the constituent har- 

 monic curves of which it is built up. 



Nearly a century ago (1822) Jean Baptiste Joseph Fourier, in 

 his classical work on the " Analytical Theory of Heat," which has been 

 aptly termed a mathematical poem, showed that any periodic curve 

 which is single-valued or not self-cutting can be built up by adding 

 together the ordinates of a number of sine curves having respectively 



