DETERMINATION OF WAVE FORM 669 



turntable may be caused to make k complete displacements 

 along the ways while the table makes one complete revolution. 

 The point P is thus guided in the manner already suggested. 



When the sine components are to be determined the crank is 

 placed so that the carriage is at its maximum displacement, 

 at the lower end of the ways, when = 0. If the cosine terms 

 are desired the carriage is started at its mid-position when 8 = 0. 



By the use of the proper system of change gears the coefficient 

 of any harmonic, either odd or even, is readily determined with 

 all the accuracy needed in electrical engineering work. 



The oscillograph is readily adapted for obtaining curves plotted 

 in the peculiar manner necessary for the construction of the tern- 

 plat e; the oscillogram is taken on a plate which is rotated about 

 an axis perpendicular to its plane. If undeflected the spot of 

 light traces the base circle abc from which the displacements are 

 measured. 



From the oscillogram one can readily detect the presence of 

 even harmonics, for if they are absent all the " diameters" are 

 of equal length and equal to the diameter of the base circle abc. 



Experimental Analysis: Laws Method. 12 When dealing with 

 potential difference and current waves it is possible to determine 

 the various coefficients experimentally as will be seen from the 

 following. 



The coefficient A k is twice the mean product between + IT and 

 TT of the curve /(0) and the curve sin kd; B k is twice the mean 

 product of /(0) and cos k6, between the same limits. The deflec- 

 tion of an electrodynamometer is proportional to the mean prod- 

 uct of the currents in the fixed and movable coils. Conse- 

 quently, if the wave to be analyzed, of frequency/, is led 

 through the fixed coil while a sinusoidal current wave of fre- 

 quency /,/ and maximum value A' k is sent through the movable 

 coil, the deflection of the instrument will be proportional to A k or 

 to B k according as the zero point of the unknown wave coincides 

 with the zero point of the sine wave or with the maximum of 

 the sine wave. The deflection will be proportional to C k if the 

 ph.Mse of the sinusoidal current is a^usted until the deflection is 

 a maximum. 



In order to carry out the analysis, the machine from which the 

 sinusoidal current is derived must be driven from the shaft of 



