Brown. — Phenomena of Variation. 521 



information which may be given also by a table. * This refers 

 to the information which is directly derived from experiment ; 

 but, this usually being insufficient for the practical applica- 

 tions, we have to perform interpolation in order to get what 

 we want. This may be done graphically or by application of 

 the calculus, but in either case the result is a guess. It will 

 be here asserted that, a priori, we have nothing to show that 

 the judgment of an engineer or physicist will lead to error 

 more readily than will the corresponding assumptions of a 

 computer. We shall refer to the judgment as the arbiter in 

 this indeterminate question of interpolation. 



■i. So far we have accepted the results of experiment, but 

 it is evident that such knowledge must (in continuous varia- 

 tion) be inaccurate to some extent ; data we get by measuring- 

 must be subject to fortuitous error, and may be subject to 

 svstematic error due to the system of measurement — instru- 

 ments may be wrongly calibrated, and so on. Fortuitous 

 error may be made definite by the application of the theory 

 of probability, provided, of course, that the necessary work 

 is done in the experiments ; and we may take from this 

 application the information that the true values (but still 

 affected by systematic causes) of the quantities lie within 

 limits of probable error— more probably so than not — the 

 probability of a value being the true one decreasing 

 very rapidly outside these limits, as indicated by the well- 

 known frequency curve. It is much to be regretted that in 

 many researches, even of the classical kind, no attempt is 

 made to assign limits of probable error. In an example 

 which has come under the writer's notice this was not done, 

 although repeated measurements at each datum point were 

 made, with the result that a very laborious research is ren- 

 dered very much less valuable than it would have otherwise 

 been. The effects of this lack of system are usually not very 

 apparent at the time trie research is made ; it is only when 

 the matter comes to be looked at from a new standpoint, 

 or examined for residual phenomena, that the absurdity of 

 giving such figures as accurate without a statement of pro- 

 bable error becomes apparent. This, of course, applies to 

 those measurements which form the connecting-link between 

 theory and the things that happen ; many practical experi- 

 ments are made under a well-understood convention as to 

 negligible error. 



5. In a graph such information as to probable error could 

 be conveyed by giving a band (twice the probable error in 

 vertical width) instead of a line for a curve, or a row of ver- 

 tical lines instead of a series of dots for datum values (that 



* See sections 10 to 15. 



