220 REPORTS ON THE STATE OF SCIENCE. 



2 inches or 5 cm. diameter, the equivalent thickness of flame at 

 1 atmo. is 100 cm., and the intrinsic radiance for a flame of this 

 thickness has already reached within less than half per cent, of its limit 

 for an infinite thickness. The percentage loss due to radiation per 

 stroke will, therefore, vary inversely as the diameter in similar motors, 

 since E will be practically independent of the dimensions in all cases 

 which occur in practice. Since the rate of loss due to radiation 

 diminishes very rapidly with the time, the effect of variation in speed 

 on the radiation loss may be appropriately represented by a factor of 

 the type (A + B/n), where n is the speed in revolutions per minute, 

 as suggested in my paper already quoted at the beginning of the note. 

 From the rapidity of the radiation-loss during ignition it is clear that 

 the A term will be of considerable importance and will affect the com- 

 parison of similar motors of different sizes when running at the same 

 piston-speed (n inversely as D) in the manner explained in my paper. 

 I was convinced on general principles that this would turn out to be 

 the case, but without actually measuring the absorption coefficient it 

 was not possible to assert definitely that E would be practically indepen- 

 dent of the dimensions. 



The variation of the coefficients A and B with flame temperature 

 will be proportional to E, and will be of the nature already indicated. 

 This is corroborated by my analysis of Dr. Watson's observations in 

 a contribution to the discussion on his paper. * 



Absolute Value of Intrinsic Radiance. 



The absolute value of the intrinsic radiance of these flames was 

 determined by comparison with the radiation of a black body with the 

 same pyrometer. The black body temperature for six flames with full 

 air-supply, giving a deflection of 282 scale divisions with the galvano- 

 meter, was 679° 0. or 952° absolute, for a thickness of 16"8 cm. 

 This means that the intrinsic radiance of such a layer of flame is the 

 same as that of a black body at 679° C. 



Assuming the radiation from a black body at a temperature 6 Abs. 

 to vary as E 6 4 where E is the radiation constant, and has the value 

 5 - 32 x 10~ 5 ergs per sq. cm. per sec, or 1*273 x ]0 _1 ' 2 gm. cals. per sq. 

 cm. per sec, the radiation from a black body at 952° Abs. or 679° C. 

 would be 63 cals. per sq. cm. per min. 



The limiting value of the intrinsic radiance for infinite thickness 

 would be 105 cals. per sq. cm. per min. in case No. (1) with full air- 

 supply, and 83 cals. per sq. cm. in case No. (2) cones 2"5 cm. 

 high. These values would correspond approximately with the initial rates 

 of loss of heat by radiation per sq. cm. of surface in a gas-engine cylinder 

 filled with similar flames at corresponding temperatures. The higher 

 value gives a loss of 175 cal. per sq. cm. in the first tenth of a second. 

 Professor Hopkinson's experiments with a bolometer placed outside an 

 explosion vessel, in which the flame temperature was certainly a good 

 deal higher, give 0'315 cal. per sq. cm. lost in the first tenth 



Phjs. Zeit., 5, 1904, pp. 777-780, 



