[1] NOTE.—"I adhere to the term virtual, as it was in use before the term efficace which was recommended in 1889 by the Paris Congress to denote the square root of mean square value. The corresponding English adjective is efficacious; but some engineers mistranslate it with the word effective. I adhere to the term virtual mainly because the adjective effective is required in its usual meaning in kinematics to represent the resolved part of a force which acts obliquely to the line of motion, the effective force being the whole force multiplied by the cosine of the angle at which it acts with respect to the direction of motion. Some authors use the expression 'R.M.S. value' (meaning 'root mean square') to denote the virtual or quadratic mean value."—S. P. Thompson.
Fig. 1,235.—Maximum and average values of the sine curve. The average value of the sine curve is represented by an ordinate MS of such length that when multiplied by the base line FG, will give a rectangle MFSG whose area is equal to that included between the curve and base line FDGS.
Fig. 1,236.—Diagram illustrating "virtual" volts and amperes. The word virtual is defined as: Being in essence or effect, not in fact; not actual, but equivalent, so far as effect is concerned. As applied to the alternating current, it denotes an imaginary direct current of such value as will produce an effect equivalent to that of the alternating current. Thus, a virtual pressure of 1,000 volts is one that would produce the same deflection in an electrostatic voltmeter as a direct pressure of 1,000 volts: a virtual current of 10 amperes is that current which would produce the same heating effect as a direct current of 10 amperes. Both pressure and current vary continually above and below the virtual values in alternating current circuits. Distinction should be made between the virtual and "effective" values of an alternating current. See fig. 1,237. The word effective is commonly used erroneously for virtual. See note page [1,011].
The attraction (or repulsion) in electrostatic voltmeters is proportional to the square of the volts.
The readings which these instruments give, if first calibrated by using steady currents, are not true means, but are the square roots of the means of the squares.
Now the mean of the squares of the sine (taken over either one quadrant or a whole circle) is ½; hence the square root of mean square value of the sine functions is obtained by multiplying their maximum value by 1 ÷ √2, or by 0.707.
The arithmetical mean of the values of the sine, however, is 0.637. Hence an alternating current, if it obey the sine law, will produce a heating effect greater than that of a steady current of the same average strength, by the ratio of 0.707 to 0.637; that is, about 1.11 times greater.