49 6 ELEMENTS OF ELECTRICAL ENGINEERING. 



point of tangency. Show that eji is the least resistance which 

 will cause the arc to be stable with a current of / amperes and 

 an electromotive force of E volts across the arc. 



.Note. Plot the combined volt- ampere characteristic of the arc and the resistance 

 e\i in series, by adding to each ordinate of the given volt- ampere characteristic e\i 

 times the corresponding abscissa. This combined volt-ampere characteristic will show 

 a decreasing total voltage with increasing current (unstable) when the current is less 

 than /, it will be horizontal at the point corresponding to /, and it will show an in- 

 creasing total voltage with increasing current ( stable ) when the current is greater than 7. 



178. When the cost of electric power is 10 cents per kilowatt- 

 hour, what is the total cost of 1 ,000 candle-hours delivered by a 

 carbon-filament glow lamp costing 18 cents, giving an average 

 of 15 candles during its life of 600 hours, and consuming an 

 average of 54 watts ? Ans. 38 cents. 



179. At what price could an osmium-filament glow lamp be 

 sold to make the total cost of light 10 per cent, less than by the 

 use of the carbon-filament lamp specified in problem 178, the 

 osmium lamp giving an average of 1 5 J^ candles during a life of 

 1 , 500 hours, and consuming an average of 24 watts ? Ans. $4. 3 5 . 



180. An enclosed arc lamp costing 15 dollars is used 3,500 

 hours each year for street lighting. The depreciation of the lamp 

 is, say, 3 J^ dollars per year, including interest on its cost. The 

 lamp is trimmed and cleaned thirty-five times per year at a cost 

 of \y^ dollars. The lamp consumes 500 watts and delivers 225 

 spherical-candles of light. Find the total cost of 1,000 spherical- 

 candle-hours, the cost of power being 10 cents per kilowatt-hour. 

 Ans. 22.9 cents. 



Note. Power for street arc lighting should be reckoned at a cost very much less 

 than 10 cents per kilowatt-hour on account of the fact that the lights are operated 

 steadily for a long time each day. The cost of 10 cents per kilowatt-hour is here 

 specified in order that the result of problem 180 may be compared intelligently with 

 the result of problem 178. It is to be noted furthermore that 1,000 candle-hours 

 from a glow lamp means at present 1,000 mean -horizontal candle-hours, not 1,000 

 spherical-candle-hours. The latter is about 15 per cent, less than the former, so that 

 the result of problem 178 should be divided by 0.85 to make it strictly comparable 

 with the result of problem 180. 



Even though the cost per spherical-candle-hour be considerably less by the use of 

 an enclosed arc lamp than by the use of a glow lamp, the latter may be really cheaper 



