into circuit: the result being that the temperature of the strip varies only between very narrow limits, and that the current itself is rendered very uniform, notwithstanding considerable variation in its force, or in the resistance of the lamp, or other extraneous resistance which it is intended to regulate. It might appear at first sight that, in dealing with powerful currents, the breaking of contacts would cause serious inconvenience in consequence of the discharge of extra current between the points of contact. But no such discharges of any importance actually take place, because the metallic continuity of the circuit is never broken, and each contact serves only to diminish to some extent the resistance of the regulating rheostat. The resistance coils, by which adjoining contact springs are connected, may be readily changed, so as to suit particular cases; they are made by preference of naked wire, in order to expose the entire surface to the cooling action of the atmosphere. In dealing with feeble currents, I use another form of regulator, in which disks of carbon are substituted for the wire rheostat. The Count du Moncel, in 1856, first called attention to, and Mr. Edison more recently took advantage of, the interesting circumstance that the electrical resistance of carbon varies inversely with the pressure to which it is subjected, and by piling several disks of carbon one upon another in a vertical glass tube, a rheostat may be constructed which varies between wide limits, according as the mechanical pressure in the line of the axis is increased or diminished. Fig. 4, Plate 5, represents the current regulator based upon this principle, and the foot-notes below the figure furnish the explanation of parts. A steel wire of say 0.3 milim. diameter is drawn tight between the end of a bell-crank lever (L) and an adjusting screw (B), the pressure of the lever being resisted by a pile of carbon disks (C) placed in a vertical glass tube. The current passing through the steel wire, through the bell-crank lever, and through the carbon disks, encounters the minimum resistance in the latter so long as the tension of the wire is at its maximum; whereas the least increase in temperature of the steel wire by the passage of the current causes a decrease of pressure upon the pile of carbon disks, and an increase in their electrical resistance; it will thus be readily seen that, by means of this simple apparatus, the strength of small currents may be regulated so as to vary only within certain narrow limits. The apparatus described in figs. 1 to 3, Plate 4, may be adapted also for the measurement of powerful electric currents-an application which is represented by figs. 5 and 6, Plate 5. The variable rheostat is in this case dispensed with, and the lever (L) carries at its end a pencil (P) pressing with its point upon a strip of paper drawn under it in a parallel direction with the lever by means of clockwork. A second fixed pencil (D) draws a second or datum line upon the strip, so adjusted that the lines drawn by the two pencils coincide when no current is passing through the sensitive strip. The passage of a current through the strip immediately causes the pencil attached to the lever to move away from the datum line, and the distance between the two lines represents the temperature of the strip. This temperature depends, in the first place, upon the amount of current passing through the strip, and, in the second place, upon the loss of heat by radiation from the strip; which two quantities balance one another during any interval that the current remains constant. If C is the current before increase of temperature has taken place; R the resistance of the conductor at the external temperature (T); H the heat generated per unit of time at the commencement of the flow; R' the resistance, and H' the heat, when the temperature T' and the current C' have been attained; Then by the law of Joule H'=R'C'. But inasmuch as the radiation during the interval of constant current and temperature is equal to the supply of heat during the same interval, we have by the law of Dulong and Petit— But TT represents the expansion of the strip, or movement of the pencil m, and considering that the electrical resistance of the conductor varies as its absolute temperature (which upon the Centigrade scale is 274° below the zero Centigrade) according to a law first expressed by Helmholtz, and that we are only here dealing with a few degrees difference of temperature, no sensible error will be committed in putting the value of R for R', and we have the condition of equi or, in words, the current varies as the square root of the difference of temperature or ordinates. For any other condition of temperature T" we have S S and (C'2—C')=('T'”—T—T+T)=(T" —T′) R R' but for small differences of C" and C' we may put (C"2-C'2)=2C" (C”—C′), that is to say, small variations of current will be proportional to the variation in the temperature of the strip. In order to facilitate the process of determining the value of a diagram in webers or other units of current, it is only necessary, if the variations are not excessive, to average the ordinates, and to determine their value by equation (1), or from a table prepared for that purpose. The error committed in taking the average ordinate instead of the absolute ordinates, when the current varies between small limits, is evidently small, the variation of the ordinates above their mean value averaging the variations below the same. 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