58 REPORT — 1853. 



Let us now endeavour from this table to discover the law expressing 

 the relation between the time and pressure, or between the time and tem- 

 perature *. 



The observations being made at intervals of one minute of time, and the 

 furnace being maintained at the same intensity, it may be presumed that the 

 quantity of heat communicated to the water was uniform, or that there were 

 equal quantities of absolute heat communicated to the boiler in equal times. 



The column of pressures gives the successive augmentations of pressure at 

 equal intervals, and the column of temperatures gives the corresponding 

 augmentations of heat as indicated by the thermometer. 



The column of pressures shows that the increments of pressure, in equal 

 intervals of time, increase with the temperature ; thus at or near '260° the 

 average increment of pressure is at the rate of 3'1 lbs. per minute ; at or 

 near 282°, it is 5*4 lbs. per minute; and at or near 326°, it is 7"1 lbs. per 

 minute. 



Mr. Ramsbottom's table of experiments indicates a similar result; thus at 

 or near 268° the average increment of pressure is at the rate of 4 lbs., 

 whereas at or near 304° it is at the rate of 5 lbs. per minute. 



The law, therefore, expressing the relation of time and pressure does not 

 appear to admit of assuming a simple form. But the case is different with 

 respect to the law expressing the relation of time and temperature. Thus if 

 T=temperature in degrees, and ^=the time in minutes at which this tem- 

 peratui'e is observed, estimated from the commencement of the experiments, 

 then 



T=axt+b (1) 



will give the relation between T and t with great precision where a and b 

 are constants, whose values, derived from these experiments, are a=4*44 and 

 6= -486. 



For example, let #=166, then 



T=4-44 X 166-486=251°, 



which exactly corresponds with the tabular value. 

 Again, let <=180, then 



T=4-44 X 180-486=313-2 ; 



in this case the tabular value is 313°. 

 Again, let <=18.5, then 



T=4-44 X 185-486=335°-4 ; 



in this case the tabular value is 335°*6. 

 From this formula we find 



.= I±m (2) 



4-44 ^ ^ 



If <(=the number of minutes which elapse between the temperatures T 

 and Tp then we find from 29 (I), 



T,-T=4-44/, ; (3) 



which shows that (he temperature increases with the time ; and presuming 

 that the heat of the furnace remained constant, this formula also shows that 



* I am indebted to my friend Mr. Tate for tUe mathematical analysis of this question. 



