Cheapest Form of Light. 277 



while if we compare the total radiations (t. e. those directly 

 observed without the use of the glass) the contrast is still 

 stronger. 



It follows that the insect-light is accompanied by approxi- 

 mately one four-hundredth part of the heat which is ordinarily 

 associated with the radiation of flames of the luminous quality 

 of those which were the subject of experiment. This value is 

 confirmed by other methods which we do not give here. It 

 will conduce to a clearer comprehension of this if we exhibit 

 in a series of curves derived from our observations the spectral 

 distribution of one unit of energy in the gas-flame spectrum 

 (diagram 4, fig. 1) ; of the electric-arc spectrum (fig. 2) ; of 

 the sun (fig. 3) ; and of the insect (fig. 4). In all these the 

 abscissas are the same, the portion between 0^*4 and 0^*7 

 (violet to red) showing the part of the energy utilized in light, 

 while that from Qt'l to 3 th shows the part wasted as invisible 

 heat. The energy in each case being the same, the areas are 

 the same, except that owing to the relative importance of the 

 light heat-curve (fig. 4), only about ^o of the latter can be 

 shown in the limits of the plate. 



The curves in fig. 3 deal with luminous intensity only, and 

 give no means of drawing those economic conclusions which 

 appear to follow from our experiments, and which the curves 

 in diagram 4 supply. These curves all exhibit the spectrum 

 on the normal scale, from that easily visible, lying between 

 M, 4 in the violet and 0^*7 in the red, then to 3 M near the limit 

 of the glass-transmission. In the case of the first three, 

 representing spectra of the gas-flame, the electric arc, and the 

 sun, nearly all the energy lies above 3^ ; in that of the gas- 

 flame a considerable portion lies below 'd* (and still more in 

 that of the candle-flame, if that were shown, where most of the 

 energy would lie below 3^ or outside the limits of the drawing) . 

 The curves then, we repeat, represent equal amounts of energy 

 (which without sensible error we may assume to be all 

 exhibited as heat) and enclose equal areas. 



The total area represents in each case the expenditure of a 

 unit of cost in thermal energy, the area between (T*4 and 0^*7, 

 the proportion of this utilized as light; though, as we have 

 just stated, in the case of fig. 4, the representative of the fire- 

 fly spectrum, only a fraction of this can be shown (owing to 

 the limits of the drawing). 



Resuming, then, what we have said, we repeat that nature 

 produces this cheapest light at about one four-hundredth part 

 of the cost of the energy which is expended 'in the candle- 

 flame, and at but an insignificant fraction of the cost of the 

 electric light or the most economic light which has yet been 



