of the Destructive Energy in Steam-boiler Eocplosionsi 335 



is seen that sum of second differences is sensibly equal to — first 

 of first differences. Thus I found the integral 



1131400, 

 which is the true measure of the energy of the 22 cubic feet of 

 water at the temperature which produces the pressure 60 lbs. to 

 the square inch, in a hot iron boiler, the units of the energy 

 being the metre and the kilogramme. 



15. If this be diminished in the ratio of 743-2 kilogs. (the 

 fictitious weight of water on which Professor Miller's calcula- 

 tions are made) to 597*1 kilogs. (the real weight of water), then 

 we shall have for the measure of the energy of the 22 cubic feet 

 of water at the same temperature, unassisted by the hot iron of 

 the boiler, 



909000; 

 and if we divide the two numbers by 22, we have for the energy 

 of one cubic foot of water at temperature producing a pressure 

 of 60 lbs. to the square inch, 



As surrounded by hot iron, 51400. (This is the practical 



value.) 

 Without influence from surrounding iron, 41300. (This 

 is the philosophical value.) 



16. 1 now proceed with the evaluation of the energy of gun- 

 powder. The formula applicable to cannon-experiments is given 

 in art. 4. Professor Miller referred me to a series of experiments 

 by General Didion, in his Trait e de Balistique, p. 485. These ex- 

 periments were made with cannon of four different bores, and 

 with eighteen different charges of powder in each cannon. The 

 first thing to be done was, to find by trial for each cannon, by 



W.V 2 



means of the formula >— — (which for a single cannon may be 



V 2 \ 



reduced to — J, what was the charge of powder in which the 



momentum produced bore the greatest proportion to the weight 



of the powder. It was found to be the following : — 



With ball of 12 kilogrammes, 1*500 kilog. of powder. 



807 „ 1-250 



6-08 „ 0-875 



4-05 „ 0-625 „ 



Then adopting these four for comparison among themselves, by 



W.V 2 . . . 



the formula — : — , it was found that the cannon in which the 

 w 



powder was most efficient was that with a ball of 6'08 kilogs. 



Here it may be desirable to state that the bore was 0*121& metre, 



the diameter of the ball 0-1182 metre, the length of bore 2*815 



