which are evolved in Coal-Mines. 133 



from which the four unknown quantities may he determined 

 by elimination. We thus have : 



_ (4 g + 2 y — 3 I) m + (3 $ — 3 y) b — 3 c m + (2 y — 2 £,) a 

 ~ 8 — 3 a + 5 y — 32 



_ ( 4 « — 6 y + 3 3) m + {l — y)b — cm + (4 y — 2 a. — 2 5) a 

 f — 3a — /3 — 5y + 32 



_ (2 a + 6 /3 — 3 I) m + (8 — 3« + 2 g) & — 5 cm + (2« — 43 + 2 S) a 

 • V ~ 3« — — 5y + 3S 



_ (3y — 3 a — 3fi)m + (3« — g — 2y) b + 3 c«t + (2 g — 2y )« 

 *— — 3 a — /S — 5y + 32 



If we now substitute for the specific gravities of the four 

 inflammable gases, the values determined with so much accu- 

 racy by Dulong and Berzelius, we have the following nume- 

 rical co-efficients in the preceding equations : 



_ 2.0674 m + 1.2645 b — 3 c m — 0.8276 a 

 W ~ 0.6196 



_ 0.137 m — 0.4215 6+ cm — 0.1372 a 



* ~ ~~ 0.6196 



— 3.0326 m — 2.7271 b + 5 c m + 1.7924 a 



* ~ 0.6196 



_ 1.4478 m + L8841 — 3 c m — 0.8276 a 

 z ~ ~ 0.6196 



If we compare the two equations for m and a with one an- 

 other, it is easy to see that a combination of the four inflam- 

 mable gases is only possible when 2 tny a ; for only in that 



1 3 



case is 0^4 2 *)> ^ If. on the other hand, should 2m^«, 



1 3 



there will be 2 ~ w + <> * -^- ^' anf ^ tn i s combination is then 



not possible. 



If we apply this to the results of our analysis in the deto- 

 nation-tube, we have 2. 1/ 1.9535, and the combination would 

 consequently be possible. But it is here that the detonated 

 gas consisted entirely of inflammable gases, or at least that the 

 quantity of the latter was between 0.97675 and 1. As in all 

 such cases only small differences are under consideration, let 

 us make m = l, and we have a = 1.9535, 6 = 1.0399 ; and c has 

 been found =0.5769. If we employ these values in the above 

 equations, we obtain : 



