OF THE IRK, LOCOMOTIVE ENGINE. 523 
2,/ —1lx Aw die 
Therefore, by substitution, = 
ate mDag 
(2a) BI 
é xdt—e x dt 
By Integration, 2 of x A Ua 
=H ee Ae 5 ae ws 
al Neo auth bp cobaeh, 
a ee 
or— Awu cathy | oa ut 6D ; 
Dag ——— x (*D?++4) = e } ‘ cosd-+ysinSt +c 
But, when u=o, §=0, &t=o; &, therefore, c= — ' ;& 
fied 
Awu 
TIDagy 
XCD? +.4)=D—pe ei (2? cos usin® ) 
By Art. 7.¢=2. As also, by Art. 7, steam 
will continue to be generated, till the position of 
the fire-box becomes inverted; and, as during 
this time, from the escape of steam, at the fire- 
box, there will be a diminution of temperature, 
it is evident, that the steam, thus generated, will 
decrease in density; and it may, therefore, be 
supposed, with very little error, that the space 
occupied by the steam, in the boiler, at the time 
