342 Mr. G. H. Knibbs : Mathematical Analysis oj 



It is obvious we can make no secure deductions from 

 single observations. The fact that there are no observations 

 at high temperatures when the dryness was small, greatly 

 limits the possibility of accurately analysing the data, and 

 shows the need of further observations. Results can probably 

 be best obtained by suitably grouping results, for example, 

 to show the progressive increase of dryness as the temperature 

 is raised. The results it will be found lend themselves 

 fairly well to such a determination, but are less satisfactory 

 in any attempt to ascertain lor the same temperature the 

 effect of increasing dryness. 



10. Principle of deducing a Formula. 



When observations disclose considerable intrinsic inconsist- 

 encies, grouping will often assist in disclosing their general 

 trend. The principle of reduction may be thus stated : — 



In reducing observations showing discrepancies, the mag- 

 nitudes of which are relatively large, it is to be remembered 

 that the probability of values found for relatively small 

 terms is also very small. Thus it follows that their inclusion 

 is often unmeaning, unless they are indicated by theoretical 

 considerations (<?. g. that they are necessary terms in any 

 rationally deduced formula). It is thus evident that " group 

 means " will often more clearly indicate the trend of the evi- 

 dence than will individual results, a fact of which advantage has 

 often to be taken in the analysis of statistical data. The legi- 

 timacy of any term derived from group means may be roughly 

 deduced by considering whether it lies within or without the 

 range of the probable errors of the data on which it depends. 

 If it be without, its significance is very questionable. 



11. Desirable to use Saturation Deficit as argument. 



With regard to the choice of the element by means of which 

 the dryness of the air is to be quantitatively expressed in a 

 formula, it is, for example, obvious that we could employ T — t 

 or 77, together with J£, or else we could employ ?. We reject, 

 however, T — t since the complexity of the resulting function 

 would be objectionable. We also may reject 77 because its 

 absolute significance varies with T or jj^ and we shall show 

 by an appropriate tabulation that this rejection is justifiable. 



12. Deduction of the Formula for Total Loss. 

 In applying the method of means it will be necessary first 

 to reject observations that would appear to be decidedly 

 anomalous owing to wind velocity, and to arrange the 

 balance (either individually or in group means) with like 

 conditions of " relative dryness/'' In this way we obtain 

 the following results from the data from W. A. 0. 



