390 PROF. H. L. CALLENDAR, PREFACE TO 



tf'tf, denoted by dO for brevity, is the observed change of temperature of the flow Q 

 due to the supply of electric energy EC in watts. Q is given in grammes per second. 

 The heat supplied per gramme per degree rise EC/QcZ0 is the most convenient 

 quantity to calculate in the first instance. The observed value has to be reduced, as 

 subsequently explained, to allow for slight variations in the temperature limits 

 Q' and 0". The reduced values corresponding to the range 103" C. to 113 C. are 

 denoted by X and are employed in calculating the results for S, h and k in the usual 

 formula for the continuous-flow method, which may conveniently be expressed by the 



following equation : 



X = 



The greater part of the heat-loss, represented by hd9 watts, appears to be independent 

 of the flow and proportional to the rise dd, but there is usually a small term kdO/Q 

 varying inversely as the flow, due to conduction and other similar causes. X may be 

 regarded as the unconnected value of the specific heat, which always appears to increase 

 with diminution of the flow, but tends to a limit coinciding with S as the flow is 

 increased. From the values X 15 X 2 , for any pair of flows Q 1} Q 2 , reduced to the same 

 range dQ if necessary, we obtain immediately by eliminating h, 



S = (QiXj Q 2 X 2 )/(Q 1 Q 2 )-(-AyQjQ g = S ia + &/QiQ 2 , 



where S 12 is the value of S obtained by neglecting k as is often done. If three flows 

 are available, designated by the suffixes 1, 2, 3, in descending order of magnitude, we 

 may eliminate k by finding S, 3 , and obtain, 



S = S ia + (S ia -S aa )Q : ,/(Q 1 -Q 3 ) = (S ia Q 1 -S a8 Q 3 )/(Q 1 -Q 8 ). 

 The values of k and h are easily obtained from the relations, 



k = Q 2 Q 3 (S-S S3 ), h = (X s -S)Q 3 -Jfe/Q 3 , 



in which the smaller flows are preferably employed as giving the largest differences. 



It will be observed that the complete expression for the specific heat, S, as deduced 

 from the values of X for three flows by the above method, may be put in the following 

 symmetrical form, 



S = X 1 Q 1 2 /(Q 1 -Q 2 )(Q 1 -Q 3 ) + X 2 Q 2 2 /(Q 2 -Q 3 )(Q 2 -Q 1 ) + X 3 Q 3 2 /(Q 3 -Q 1 )(Q 3 -Q a ), 



which is useful in estimating the effect of errors of observation. Thus if the flows 

 Qi Qa, Qs, are in the ratio 4:2:1, the terms depending on X 1; X a , X 3 , are approxi- 

 mately in the ratio 8:6:1, which shows that the accurate determination of X 3 is much 

 less important than that of X x or X 2 . Further, since each product XQ is independent 

 of Q, the effect of percentage errors in the measurement of the flows are in the same 

 proportion as the corresponding X terms in the expression for S. Thus an error of 



