VOL. LXXXI.] PHILOSOPHICAL TRANSACTIONS. 47 



n — I — m — p + \ , , ^ n— I — m— p— 1 n — I — m — p—2 

 ... xn-l -m-p. 5—^ . 3— ^1_ 



. . " ~ ~ '" ~ y ~ j — y^ gf{, which is the same as the co-efficient of the term 



a' X />"' X cP X di X &c. in the multinomial a-[-b-\-c-\-d-\- &c. raised to 

 the power n. 



The chance of any number of events a, b, c, d, &c. of which the numbers 

 are a, b, c, d, &c. happening /, m, p, q, &c. times respectively in a similar man- 

 ner to a's and b's happening in the preceding case will be . All the pro- 

 positions mentioned as immediately deducible from the preceding theorem, may, 

 mutatis mutandis, with the same ease be applied to more events a, b, c, d, &c. 

 If for a, h, c, d, &c. be substituted the same letters, increased or diminished by 

 any given quantities, the resulting equation will be equally true. 



X. yin Account of some Appearances attending the Conversion of Cast into Mal- 

 leable Iron. By Thomas Beddoes, M. D. p. 173. 



By an alteration lately introduced into our manufactories of iron, the reverbe- 

 ratory has been substituted instead of the finery furnace. The new process is 

 capable of being indefinitely varied. As in this method the changes undergone 

 by the metal during the first series of operations lie perfectly open to inspection, 

 a short description of them may not perhaps be unworthy the notice of philo- 

 sophical chemists. In little more than half an hour after it was put in, the 

 charge, consisting of 24-cwt. of grey pig iron, was nearly melted. The work- 

 man now began to stir the liquid mass: for this purpose he used sometimes an 

 iron lever, and sometimes a kind of hoe ; but he first turned the flame from off 

 the metal, which is done by letting down a damper on the chimney correspond- 

 ing to that with which ordinary reverberatory furnaces are provided, and by 

 raising the damper of a 2d chimney, which proceeds immediately from the fire- 

 place, and carries off the flame, current of air, &c. without allowing it to pass 

 into the body of the furnace. 



In 50 minutes from the commencement of the operation, the metal had be- 

 come, in consequence of the constant stirring, loose and incoherent ; it ap- 

 peared about as small as gravel ; it was now also stiff, and much cooled. 55™ 

 from the same period, flame turned on again. Workman keeps stirring and 

 turning over the metal ; in 3"' it becomes soft and semi-fluid ; flame turned off; 

 the hottest part of the mass begins to heave and swell, emitting a deep blue 

 lambent flame. The workman calls this appearance fermentation, l'' 1"" blue 

 flame breaking out over the whole mass ; heaving motion also general, l'' 13™ 

 metal full as hot, or, as was j udged, rather hotter than at the instant the flame 

 was turned off, though it is now a quarter of an hour since, l'' 18™ where 



