137 



coefficients are seminvariants, and the process explained in my memoir 

 on the Equation of Differences was therefore applicable, and hy means 

 of it, the equation is readily obtained. The auxiliary equation gives 

 rise to a corresponding covariant equation, which is given at the 

 conclusion of the memoir. 



III. "On Combustion in Rarefied Air/' By Dr. EDWARD 

 FRANKLAND, F.R.S. Received February 28, 1861. 



In the autumn of 1859, whilst accompanying Dr. Tyndall to the 

 summit of Mont Blanc, I undertook at his request some experiments 

 on the effect of atmospheric pressure upon the amount of combustible 

 matter consumed by a common candle. I found that, taking the 

 average of five experiments, a stearin candle diminished in weight 

 9 '4 grammes when burnt for an hour at Chamounix ; whilst its igni- 

 tion for the same length of time on the summit of Mont Blanc, 

 perfectly protected from currents of air, reduced its weight to the 

 extent of 9*2 grammes. 



This close approximation to the former number under such a 

 widely different atmospheric pressure, goes far to prove that the 

 rate of combustion is entirely independent of the density of the at- 

 mosphere. 



It is impossible to repeat these determinations in a satisfactory 

 manner with artificially rarefied atmospheres, owing to the heating 

 of the apparatus which surrounds the candle, and the consequent 

 guttering and unequal combustion of the latter ; but an experiment 

 in which a sperm candle was burnt first in air under a pressure of 

 287 inches of mercury, and then in air at 9 inches pressure, other 

 conditions being as similar as possible in the two experiments, the 

 consumption of sperm was found to be, 



At pressure of 28' 7 inches 7'85 grms. of sperm per hour, 



9-0 9-10 



thus confirming, for higher degrees of rarefaction, the result pre- 

 viously obtained. 



In- burning the candles upon the summit of Mont Blanc, I was 

 much struck by the comparatively small amount of light which they 

 emitted. The lower and blue portion of the flame, which under 



