8 



Weight of the Central Nervous System of the Frog 



This table gives the original tabular number, sex, body-weight (without ovaries 

 in the case of the females), length from tip of nose to tip of longest toe, observed and 

 calculated weights of the central nervous system, together with the percentage by 

 which the calculated departs from the observed weight; the observed weight being 

 always considered as the standard. The conditions under which these measurements 

 were made are given in full in an earlier paper (Donaldson, 1898, pp. 323 ff. ). In 

 the foregoing table the records in each case are for single observations. When the 

 averages of the weights of the central nervous system, observed and calculated, are 

 determined, it is seen that the average of the observed weights is 212, while that of 

 the calculated is 211, thus giving a difference of only 0.4: per cent. That this small 

 difference is the expression of discrepancies that are only slight is indicated by the 

 fact that, if the entire series of records be divided into three groups, formed respect- 

 ively by the first eleven, second eleven, and last twelve, and the difference in the 

 average values of the observed and calculated weights be taken for each group, we 

 obtain the percentage differences given in the following table: 



TABLE II 



To show the average percentage differences in the values of the observed and calculated weights of the 

 central nervous system in three groups, formed from the records in Table I. 



It is thus seen that the percentage difference between the averages does not in any 

 group exceed 1 per cent, and consequently we may infer that, if the records were 

 based on averages of eleven or more individuals for each entry, the agreement of the 

 observed and calculated values would be well within 1 per cent. 



Another method of testing these results is by determining the relation of the per- 

 centage differences calculated for the individual cases. On enumerating the cases in 

 which the calculated values are in excess, it is found that they are just seventeen, or 

 one-half the total number of records, thus leaving seventeen cases where the calculated 

 values are below those observed. Table I shows that the average value of the per- 

 centage deviations exhibiting deficiency is 3.8 per cent., while for those in excess it 

 is 3.0 per cent. The plus and minus percentage deviations, therefore, nearly balance, 

 as they should do if they depended on accidental causes. 



We see, therefore, that the formula gives results very close to those observed. On 



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