332 The Astronomer Royal on the Numerical Expression 



T + 0-00002 T 2 + 0-0000003 T 2 , where T for this instance 

 = 152*84), or 92182 calories. When all the steam has been 

 blown off, the 597*1 kilogs. of water are separated into # kilogs. 

 of steam at 100°, and (597*1 —x) kilogs. of water at 100°. [This 

 applies strictly when the steam has blown into a cylinder and 

 has driven a piston, because then there may be such intercom- 

 munication of temperature between the portions of steam as will 

 ensure that the final state of the steam is that of saturated steam 

 at 100°; it is probably true or very approximate when the steam 

 has blown out at different temperatures and has been lost in the 

 atmosphere.] To heat (597*1— x) kilogs. of water from 0° to 

 100° requires (597*1— x) x 100*5 calories; and to convert 

 x kilogs. of water at 0° into steam at 100° requires (606*5 

 + 0*305 x 100) x x calories (by a formula of Regnault's). Sup- 

 posing, then, that the amount of heat as measured by the num- 

 ber of calories is not altered by the blowing out from the boiler, 



92182= (597*1 -x)x 100*5 + 637x#, 

 whence x 3 the weight blown out as steam, =59*8. This, how- 

 ever, is equivalent to only 2*2 cubic feet of water, instead of 

 2*75, the quantity which Mr. Biddell found to have passed 

 away in steam. 



10. Professor Miller supposes the difference to be caused 

 principally by the heat of the mass of iron which surrounds the 

 water • any burning fuel which may have been left in the fire- 

 box would add slightly to its effect. It appears best therefore 

 to assume the experimental fact, and to infer from it what quan- 

 tity of heated water we ought to add (in investigations) to the 

 quantity of water really present in the boiler, in order to pro- 

 duce correctly the amount of water which in the experiment 

 was blown out as steam. Now 2*75 cubic feet of water at 100° 

 weigh 74*638 kilogs. Let y represent the number of kilogs. in 

 the bulk of water which may be considered equivalent to the 

 compound consisting of 22 cubic feet of water, the unknown 

 weight of iron, and the unknown quantity of fuel. To heat y 

 kilogs. of water from 0° to 152 0, 84 requires 154*38 xy calories; 

 and this is the amount of heat in the complex equivalent before 

 blowing off. To heat (y— 74*638) kilogs. of water from 0° to 

 100° requires (y — 74*638) x 100*5 calories; and to convert 

 74*638 kilogs. of water at 0° into steam at 100° requires 

 74*638 x 637 calories ; and the aggregate of this with the last, 

 or (y — 74*638) x 100*5 + 74*638x637, represents the number 

 of calories in the complex equivalent after the blowing off. 

 Making this equal to the number before blowing off, 



154-38 x y= (y-74-638) x 100*5 + 74-638 x 637, 

 whence y— 743*2. 



