PROBLEMS. 495 



Ans. (a) 47 lamps ; () four times as many, because the area of 

 the light-absorbing surfaces in the larger room is four times as 

 great as in the smaller room ; (^65 lamps. 



. To specify the number of lamps required for illuminating a room as so 

 many per square foot of floor area, is to assume that the wall area is proportional to 

 the floor area, absorption coefficient being fixed in value. 



176. A direct-current arc lamp gives the following distribution 

 of light : 



Angle from vertical, 10 20 30 40 50 60 70 80 

 Candle-power, 290 440 670 1080 1220 1080 795 580 



Calculate the intensities of illumination at points along a level 

 open street distant h tan 10, h tan 20, h tan 30, h tan 40, etc., 

 horizontally from the lamp : (a) when the height, h, of the lamp 

 above the street is 1 5 feet, and () when the height, h, of the 

 lamp above the street is 50 feet. 



Express the intensities of illumination in " candle-feet," that is 

 in terms of the intensity of illumination produced by the beam 

 from a standard candle falling perpendicularly upon a screen at a 

 distance of one foot from the candle. 



Plot two curves showing horizontal distances from the lamp as 

 abscissas and intensities of illumination as ordinates. Sample 

 answer. Intensity of illumination of the surface of the street at a 

 distance of 26 feet horizontally from the lamp is 0.600 * 'candle- 

 feet " when the lamp is 1 5 feet above the ground. 



Note. The distance, d y in feet of one of the points on the street from the lamp is 

 equal to V h 2 -\- h 2 tan 2 where 6 is one of the angles given in the problem. The 

 sectional intensity of any one of the beams above specified, at distance d feet from the 

 lamp is equal to the candle-power of the beam divided by d 2 , this result being ex- 

 pressed in "candle-feet." Furthermore, one unit sectional area of this beam at the 

 given point on the street is spread over i/cos0 units of area of ground, so that the in- 

 tensity of illumination of the surface of the street at the given point is cos 6 times the sec- 

 tional intensity (in " candle -feet " ) of the given beam at distance d feet from the lamp. 



177. Draw a tangent to one of the volt-ampere arc character- 

 istics in Fig. 182, Chap. X, and let e volts be the intercept on 

 the volt-axis and i amperes the intercept on the ampere-axis, of 

 this tangent. Let E volts and 7 amperes be the coordinates of the 



