428 ANALYSIS OP CURVES. 



The function then becomes finally : 

 e = F, sin (0 + &) + ^ 3 sin (30 



As an illustration of this method of analysing a curve, 

 its application to the curve in Fig. 204 may be given. 



This curve was obtained by the method described in 

 Experiment XV. from a small Pyke & Harris inductor 

 alternator, having 7 inductors. The armature was con- 

 nected to a condenser having a capacity of 6 micro-farads 

 in series with a single incandescent lamp. The curve 

 was plotted from readings taken at the terminals of the 

 lamp. The K.M.S. volts of the alternator were 80, those 

 across the lamp 51 '8, and across the condenser 61 '5. 



Table II. shows the method adopted for entering up 

 the observations and calculated figures. It will be seen 

 that there are several modifications from the form of 

 Table I. ; these were made in order to enable logarithms 

 to be used for the multiplication. 



In. the case of the fifth harmonic, logarithms were not 

 used on account of the comparative simplicity of the 

 values of sin 5 6 and cos 5 0. 



A separate column for values of the cosines was not 

 considered necessary, since the column of logarithmic 

 sines may be used, taking values of 90 -- 0, instead 

 of B, &c. 



The method of obtaining the first form of the equation 

 given at the foot of the table will be clear from the 

 description already given. The following calculation 

 shows the steps for arriving at the second, simplified, 

 form of the expression : 



As seen from the first form of the equation 

 .4 1 = 66 B,= - 0-073 



A l sin 0+ B, cos e = V **+&?. ' sin {0+tan ^(jf 

 66* -I- (0-073)'. sin (0 + tan ~ 1 -^ 



= 66 sin (0- OP 4') since tan 4' = -00112 = 



66 sin 6, practically. 

 similarly, 



A = 22- ( J6 5, = 20-72 



