ANALYSIS OP CURVES. 437 



R.M.S. Value. The R.M.S. or virtual value of the curve, 

 whose equation has been determined, can be obtained 

 from the maximum values of the component waves of 

 which it is formed. 



Thus, if the equation has been obtained in the form 

 e = E, sin (6 + &) + E 3 sin (3 + <t> 3 ) + E 5 sin (5 + < 5 ) 



+ . . . 

 where e is the instantaneous value of the quantity for any 



value of 0, 



then E 1} E 3 , E., &c., are the maximum values of the respec- 

 tive harmonics, and the R.M.S. value is given by the 

 expression 



/iTT&r + E* + . . .- 



e vlrt, - - - 



In the curve analysed above we have 



E l = 66, E 3 = 31, E 5 = 6, 

 and the virtual voltage is consequently 



/66 2 + 31 2 + 6 2 ~ /5353 -, 



volts - 



As mentioned on page 428, the actual value registered 

 by the voltmeter was 51-8 volts. 



