376 Dr. Dorothy Wrinch and Dr. H. Jeffreys on Certain 



this result is, it is curious that uo attempt has yet been made 

 to evaluate even the order o£ magnitude o£ the probability in 

 such inferences. We shall return to this point later. At 

 present we shall only note that some criterion must be 

 introduced that deterniines the probabilities of the values 

 of the dependent variable according to different physical 

 laws, any one of which satisfies the purely empirical data. 



In experimental work, however, it usually happens that a 

 seiies of observations made at different times are connected 

 with the time by no simple law. Two cases naturally arise. 

 First, it may be possible to find a simple law that nearly fits 

 the observations : that is to say, the divergences of the 

 observed values from those predicted by the law may be 

 small compared with their total variation in the whole range 

 considered. In the above case, for instance, the observed 

 values of x at times 5, 10, 15, 20 seconds might have been 

 5, 21, 44, 81 cms. ; but the difference between any of these 

 and the value predicted for the same value of t by the law 

 5x = t 2 never exceeds 1 cm., which is only § \ of the whole 

 range of .variation of x. In such a case it is a mere master 

 of description to say that the observed values are satisfied 

 by the law within a certain margin, ^hich we call " error. " 

 The inferences to be drawn in this case will be of the form 

 " the probability that the observed quantity at a certain 

 time will lie between certain values is so much." 



The other case is where no simple law is known that fits 

 the observations even approximately. There is now no 

 better procedure than some conventional method of inter- 

 polation, based on the use of a formula containing a 

 number of undetermined constants equal to the number 

 of observations. That this fits the observations is again 

 mere description ; but the difference between the methods 

 by which the laws are obtained in the two cases may 

 be expected to correspond to a difference between the 

 results inferred. It evidently rests en the existence of a 

 simple relation with certain relations to the observed quan- 

 tities ; and it is important to notice that whenever one exists 

 it is always adopted in practice, in spite of the fact ihat 

 the method of interpolation will in eveiy case give a relation 

 which has the advantage over the simple cne that it fits the 

 observations exactly instead of approximately. Evidently 

 in scientific practice simplicity is considered to outweigh 

 accuracy of description ; the question is, whether this is 

 due to practical convenience alone, or to some unexpressed 

 assumption that the results inferred by its means are in 

 some way more probable or accurate on the whole than 



