Page:Electricity (1912) Kapp.djvu/215

Rh hypotenuse. Let us assume that instead of making the calculation for one vector only, we make it simultaneously for two, such as A and A1, situate at right angles to each other. Since we count each vector twice over, the result will also be twice the true value. We have now to form the sum of AB2 and A1B2, but by the axiom just mentioned, this is always equal to the square of the vector itself. Since this is the same for all positions, the mean is the same as each part, but since we counted each vector twice, the mean is twice the real value. The square of the effective value of the current is therefore one-half of the square of the crest value, or the effective value is found by dividing the crest value by the square root of 2. This is 1.4, and 1 divided by 1.4 is 0.71. We thus find that the effective value of an A.C. is 71 per cent. of its crest value. The same relation applies of course also to the e.m.f, The same reasoning which has here been applied when discussing the passage of the A.C. through the lamp, also applies to its passage through any measuring instrument adapted for A.C. Amperemeters and voltmeters give the effective values, not the crest values. In the case of an incandescent lamp, the product of the current shown on such an