392 



Transactions of the Society. 



these requirements satisfied, it is obvious that the new lamp will 

 fulfil the condition of radiating through the given aperture the 

 required quantity of light in unit time. 



But, unlike the mirror, the lamp will radiate light not only- 

 through the aperture but also in every other direction, and the 

 radiation which passes the aperture will be only a fraction of its 

 whole output. If we calculate its whole output of light and 

 compare it with the whole output of its object lamp, we shall have 

 the means of determining their relative radiating surfaces, for we 

 know that both are burning at the same temperature, and therefore 



in unit time from unit 



giving off the 



same amount of 



light 



Fig. 82. 



surface. This comparison will be facilitated by the diagram 

 fig. 82 in which the two lamps are represented by two very small 

 radiant globes lying on the optical axis, and the aperture is repre- 

 sented by the circle in which two spheres intersect that are 

 described round the two lamps respectively. 



Now, it is clear that the new lamp r h if it is to send through 

 the aperture A A as much light as the old lamp e sends, must 

 produce more total light, for it wastes a larger proportion of what 

 it produces, and this waste is represented by the whole remaining 

 area of the sphere having a radius r v after allowing for the 

 aperture, whereas the lamp e only wastes the smaller quantity 

 represented by the surplus of the smaller sphere upon the radius 



