Engineering Mathematics; A Series of Lectures Delivered at Union College (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 Excerpt: ...S0. This is recorded in Table X B. In Fig. 46 are plotted the total exciting current i, its third harmonic i; , and the 9th harmonic?9. This method has the advantage of showing the limitation of the exactness of the results resulting from the limited num Fig. 46. ber of numerical values of i, on which the calculation is based. Thus, in the example, Table X, in which the values of i are given for every 10 deg., values of the third harmonic are derived for every 30 deg., and for the 9th harmonic for every 90 deg.; that is, for the latter, only two points per half wave are determinable from the numerical data, and as the two points per half wave are just sufficient to locate a sine wave, it follows that within the accuracy of the given numerical values of i, the 9th harmonic is a sine wave, or in other words, to determine whether still higher harmonics than the 9th exist, requires for i more numerical values than for every 10 deg. As further practice, the reader may separate from the general wave of current, io in Table XI, the even harmonics by above method, and also the sum of the odd harmonics, as the residue, then from the odd harmonics harmonic and its multiples, may be separated the third and in the same manner from i3 may be separated its third harmonic; that is, ig. Furthermore, in the sum of even harmonics, from i2 may again be separated its second harmonic, ?'4, and its multiples, and therefrom, is, and its third harmonic, i6, and its multiples, thus giving all the harmonics up to the 9th, with the exception of the 5th and the 7th. These latter two would require plotting the curve and taking numerical values at different intervals, so as to have a number of numerical values divisible by 5 or 7. It is further recommended to resolve this unsymmctrical e...