568 



SCIENCE 



[N. S. Vol. XL. No. 1033 



i' : i" = r" : r (3) 



The amount of current passing through 

 two wires in parallel equals the sum of the 

 two separate currents. 



i = i'-{-i". (4) 



As an illustration, a rheocord, taking 2 

 amperes from a 110-volt main, has a resistance 

 of 55 ohms (formula 1) and 2 volts drop for 

 each ohm. Shunt in a 1.5 ohm signal magnet 

 on this line at two points, A and B, between 

 which there are 2 ohms and consequently 4 

 volts. The intervening resistance becomes by 

 formula (2) .85 ohm and is therefore reduced 

 1.15 ohms. The total line then has a resistance 

 of 53.85 ohms and a current of 2.04 amperes 

 (formula 1). Between A and B the voltage 

 becomes 2.04 X -85 or 1.75 (formula 1) and 

 the solving of equations from formulse (3) 

 and (4) shows the line amperage so divided 

 that .85 ampere passes through the line and 

 1.15 amperes pass through the instrument. 

 Accordingly, the magnet receives a current 

 of 1.75 volts and 1.15 amperes, which is suffi- 

 cient. But, should twelve such instruments 

 be connected to similar sections of the line, 

 the resistance would be reduced 1.15 ohms for 

 each section and 13.8 ohms for the twelve sec- 

 tions giving the line a resistance of only 41.2 

 ohms and a current increased to almost 3 

 amperes (formula 1). The point is that the 

 shunting in of too many instruments on a 2 

 ampere system would raise the amperage be- 

 yqnd the safe carrying capacity of the wire. 

 The danger in this case is eliminated by using 

 3 or 4 instruments only, which can be operated 

 across 8 or 10 ohms of resistance. Thus two 

 parallel 32-candle-power lamps connected in 

 series with 10 ohms of wire will furnish about 

 2 amperes and wiU operate instrument cir- 

 cuits of 1.5 or more ohms. Several such 

 systems are required for large classes and the 

 total amperage supply is necessarily high. 



Figuring with greater amperages on a single 

 line, it is found that an 11-ampere line will 

 accommodate sixty-five instruments on sepa- 

 rate shunts and keep the rise in amperage 

 below 15 per cent. This is easily determined: 



on a 10-ohm line carrying 11 amperes, let 

 there be between two points A and B a poten- 

 tial of 2 volts and a resistance of .18 ohm, each 

 ohm having a drop of 11 volts. With a 1.5 

 ohm instrument shunted in, there is found a 

 resistance of .16 ohm (difPering by .02 ohm 

 from the original .18 ohm), a potential of 

 1.76 volts, and a current through the instru- 

 ment of 1.2 amperes. Sixty-five instruments 

 averaging 1.5 ohms each, even when shunted 

 in simultaneously on separate sections, give 

 a total reduction of 1.3 ohms, and leaving 8.7 

 ohms in the line allow the passage of 12.6- 

 ampere current, which is an increase of 15 

 per cent, above the normal. But, as less than 

 twenty machines ordinarily are operating at 

 any instant, there can be a resistance not 

 reduced more than .4 ohm, a current not 

 greater than 11.5 amperes and hence an amper- 

 age rise not over 5 per cent. 



Third, Resistor Used. — Most of the electric- 

 ity passing through a line is transformed into 

 heat energy and the temperature of the con- 

 ductor rises until the heat generated by the 

 current equals the heat dispersed per unit of 

 time. This heat rise, other things being equal, 

 varies to a large degree inversely with the 

 amount of radiating surface, which again is 

 determined by the size, length and resistivity 

 of the wire as well as its actual resistance. A 

 large heat rise reduces the radiating surface 

 necessary, and for a short wire a high resistiv- 

 ity must be used. For a moderate heat rise as 

 150° F. the radiating surface becomes pro- 

 portionately larger and a correspondingly 

 moderate resistivity is demanded on a short 

 line carrying 5 or more amperes. Compara- 

 tive resistances of resistors range between 1 

 and 65 times that of copper. For a 2 ampere 

 system ordinary carbon lamps and any wire 

 of high resistance as B. «& S. No. 18 " Ni- 

 chrome " is satisfactory. In the " Multiple 

 Unit " system, which, carrying 11 amperes, has 

 10 ohms of resistance and is allowed an arbi- 

 trary heat rise of 160° F., the resistivity for 

 a line made as short as possible for compact- 

 ness is found to be about twenty times that 

 of copper. As an example No. 15 B. & S. 

 18 per cent. German silver wire 19 times as 



