26 THE SPECIFIC HEAT OF WOOD. 



theoretical frequency curve which is formed by the ordinate over the 

 average specific heat. The way in which the empirical curve differs 

 from the true curve indicates the presence of a systematic error which 

 tends to make the individual results too low by a varying amount. 

 It was the exaggerated prominence of this error which led to the 

 rejection of the results of eight runs under the procedure followed on 

 page 20. 



The nature of the error is learned by reviewing the apparatus and 

 methods employed. There is no reason to doubt that its origin lies 

 in the loss of heat during the transfer of the specimen from the oven 

 to the calorimeter. In other words, the assumption made in all 

 calculations that the hot specimen reached the interior of the calo- 

 rimeter at the same temperature as that indicated by the thermometer 

 in the oven before its removal is not entirely justified. The effect of 

 this error is to make the average 0.325 too low; judging from an 

 inspection of the curve the true value lies near 0.327. The error in 

 the result 0.325 due to this systematic error is about one-half of 1 

 per cent, and the corrected value 0.327 contains a residual systematic 

 error of about the same magnitude or smaller. 



The chance error of the result is readily calculated according to 

 the theory of probability. The probable error of a single result is 

 obtained by the following formula, in which d is the amount by which 

 each individual result differs from the average of the results, and n 

 is the number of results averaged : 



probable error = 0.67V - 

 \ n 



This calculation gives 1.3 per cent for the probable error of a single 

 result. The probable error of the average varies inversely as the 

 square root of the number of results averaged. Thus for the average 

 of 100 results the probable error is one-tenth that for a single result, 

 or one-tenth of 1 per cent. 



The sum of the two errors, or six-tenths of 1 per cent, measures the 

 reliability of the result secured for the specific heat of wood between 

 106 C. andOC.; viz, 0.327. 



