96 ANNUAL OF SCIENTIFIC DISCOVERY. 



ON THE RELATION BETWEEN THE INTENSITY OF LIGHT PRO- 

 DUCED FROM THE COMBUSTION OF ILLUMINATING GAS AND 

 THE VOLUME OF GAS CONSUMED. 



In pliotometric observations made to determine the illuminat- 

 ing power or intensity of street gas, it is the practice of observers 

 to compute their observations uj^on the assumed standard of 5 cubic 

 feet of gas, consumed for one liour; and in the constantly occur- 

 ring case of a variation from this standard, whether in the volume 

 of the gas consumed or in the weight of spermaceti burned, the 

 observed data are comj)Uted by tin; " rule of three," up or down, 

 to the stated terms. The standard sj)c'rmaceti candle is assumed 

 to consume 120 grains of sperm in one hour, a rate which is 

 rarely found exactly in actual experience. 



For example, a given gas, too rich to burn in a standard argand 

 burner at tlie rate of 3^ cubic feet to the hour, with an observed 

 effect of 20 candles' power. This result, previously corrected by 

 the same rule for the sperm consumed, is then brought to the 

 standard of 5 cubic feet by the ratio 3.5 : 20 = 5 : 28.57. 



The candle-power of the gas is, therefore, stated as 28.57 can- 

 dles, and the result has been universally accepted as a true ex- 

 pression of the intensity of the gas in question, or the relative 

 value of the two consumptions. 



In common with other observers, I have long suspected that 

 this mode of computation was seriously in error, as an expression 

 of the true intensity of illuminating llames, and that there were 

 other conditions, besides the volume of gas or weight of sperm 

 consumed, which must influence and greatly modify the results. 

 As most of these conditions are considered somewhat at length 

 in a paper on " Flame Temperatures,'''' prepared chiefly from re- 

 searches conducted by Professor Wurtz and myself, and presented 

 at the Salem Meeting of the Association, they need not be dis- 

 cussed in this connection. 



The results of many trials, made with the purpose of determin- 

 ing the value of these photometric rations, indicate clearly, that the 

 true ratio of increase in intensity in illuminating flames is, within 

 certain limits, expressed by the following theorem, namely: — 



T/ie intensiirj of gas fames, that is, illuminating power, increases 

 (within the ordinary limits of consumption) as the square of the 

 volume of the gas consumed. 



As the first ex))erimental demonstration of this theorem was 

 made liy Mr. William Farmer, the ])hotometric observer at the 

 ]\Ianiiattan (ias Co.'s works in New York, I })ropose to speak of 

 ' it as " Farmer's th(;orem." I am also indebted to Mr. Farmer, 

 a<id to Mr. Sabbaton, the well-known and courteous engineer of 

 \\w ^Manhattan CJas Light Company, for the free use of their ex- 

 perimental data, and the permission to employ them here. 



The fimdamcntal impoitance of this new mode of computation 

 will at once ap])ear, if, assuming it for the sake of illustration to 

 be ti-ue, we apply it to the case already given above, which then 

 becomes — 



3.5'^ : 20 = 5-^ : 10. 



