3. _Phosphuretted hydrogen and hydrogen; also carburetted hydrogen and hydrogen, and carburetted hydrogen and carbonic oxide._ The notation being as above, we have _x_ + _y_ = _w_, and 2_x_ + ½_y_ = _g_ (see page 171): and, 2_g_ - _w_ 4_w_ - 2_g_ _x_ = -----------, and _y_ = -----------. 3 3 4. _Olefiant gas and carburetted hydrogen._ The notation being as above, we have _x_ + _y_ = _w_, and 3_x_ + 2_y_ = _g_; whence _x_ = _g_ - 2_w_ and _y_ = 3_w_ - _g_. 5. _Carburetted hydrogen, carbonic oxide and hydrogen._ Let _x_ = carburetted hydrogen, _y_ = carbonic oxide, _z_ = the hydrogen, _g_ = the oxygen spent in the combustion of _w_ volumes of mixed gas, and _a_ = the carbonic acid produced. Then _x_ + _y_ + _z_ = _w_, _x_ + ½_y_ + ½_z_ = _g_, and 2_x_ + _y_ = _a_. whence we have 2_g_ - _w_ 3_a_ - 2_g_ + _w_ _x_ = -----------, _y_ = ----------------- 3 3 and _z_ = _w_ - _a_. 6. _Olefiant gas, carburetted hydrogen and carbonic oxide._ Let _a_ = the olefiant gas, _y_ = the carburetted hydrogen, and _z_ = equal the carbonic oxide, _g_ = the oxygen entering into combination, and _a_ = the carbonic acid produced; also _w_ = the whole volume as before. Then we have _x_ + _y_ + _z_ = _w_, 3_x_ + 2_y_ + ½_z_ = _g_, and 2_x_ + _y_ + _z_ = _a_. Whence _x_ = _a_ - _w_, _y_ = 4_w_ - 5_a_ + 2_g_ -------------------, 3 and _z_ = ⅔(_w_ + _a_ - _g_). 7. _Superolefiant gas,[29] carburetted hydrogen, and carbonic oxide._ [Footnote 29: A gas found in oil and coal gas. See Manchester Memoirs, vol. 4 (new series), page 73.] Let _x_ = volume of superolefiant, _y_ = volume of carburetted hydrogen, _z_ = volume of carbonic oxide, _g_ = the oxygen combining, _a_ = carbonic acid produced, and _w_ = volume of mixed gas. Then _x_ + _y_ + _z_ = _w_, 4½_x_ + 2_y_ + ½_z_ = _g_, and 3_x_ + _y_ + _z_ = _a_. Whence _x_ = _a_ - _w_ ----------, 2 _y_ = 3_w_ - 4_a_ + 2_g_ ------------------, 3 and _z_ = 3_w_ - 4_g_ + 5_a_ -------------------. 6 8. _Superolefiant gas, carburetted hydrogen, carbonic oxide, and hydrogen._ This is the mixture of gases obtained by a red heat from coal and oil, after being freed from carbonic acid, &c., by the usual means. This mixture requires a very complicated formula, in consequence of the specific gravities of the gases entering into the calculus. The importance of the subject however may be an apology for the labour.