This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1917 edition. Excerpt: ...problem whether a maximum of a minimum occurs, or neither. For instance, if the problem is to determine the speed at which the efficiency of a motor is a maximum, the solution: speed=0, obviously is not a maximum but a mimimum, as at zero speed the efficiency is zero. If the problem is, to find the current at which the output of an alternator is a maximum, the solution i = 0 obviously is a minimum, and of the other two solutions, ii and t2, the larger value, %%, again gives a minimum, zero output at short-circuit current, while the intermediate value i gives the maximum. 101. The extremes of a function, therefore, are determined by equating its differential quotient to zero, as is illustrated by the following examples: Example 4. In an impulse turbine, the speed of the jet (steam jet or water jet) is Si. At what peripheral speed S2 is the output a maximum. The impulse force is proportional to the relative speed of the jet and the rotating impulse wheel; that is, to (S1-S2). The power is impulse force times speed S2; hence, P = kS2Sy-S2), (3) and is an extreme for the value of S2, given by-r-r = 0; hence, do 2 Si-2S2=0 and S2=y: (4) that is, when the peripheral speed of the impulse wheel equals half the jet velocity. Example 5. In a transformer of constant impressed e.m.f. Co = 2300 volts; the constant loss, that is, loss which is independent of the output (iron loss), is Pt-= 500 watts. The internal resistance (primary and secondary combined) is r = 20 ohms. At what current i is the efficiency of the transformer a maximum; that is, the percentage loss, X, a minimum? The loss is P= Pt +ri2 = 500+20i2 (5) The power input is Pi =et = 2300i;.... (6) hence, the percentage loss is, x P, ei' n and this is an extreme for the value of current i, ..