2 - Mr. G. H. Darwin on Fallible Measures 



plete certainty that we cannot have affected the principal 

 event in any way by the method of observing. In experiments, 

 however, it is impossible to imitate exactly the proposed con- 

 ditions ; so that, even when corrections have been applied, and 

 when we can estimate the degree of uncertainty in the method 

 of observing, there remains another sort of uncertainty, viz. 

 as to the closeness with which the proposed conditions were 

 imitated ; that is to say, the principal event is rendered un- 

 certain and complex. 



The case of experiments graduates into that of observations 

 of natural phenomena, where we have no control over the dis- 

 turbing causes, and have no opportunity of slightly altering 

 the conditions. 



The line of demarcation between the principal event, whose 

 laws are to be determined, and the disturbances, here becomes 

 still more undefined. And where we are still groping after a 

 law of the phenomena (as in the case of meteorology) it is 

 unknown what is to be classed as the principal event and what 

 as disturbances. It is like looking at a series of irregular 

 waves with ripples of various sizes on their surface ; until 

 some law in the formation of the waves is discovered, it is 

 unknown how large a ripple may be neglected in the discovery 

 of that law. Nevertheless the only chance of discovery seems 

 to be to neglect the ripples by some arbitrary rule, and to ex- 

 amine the main features of the series of waves. 



The problem of how best to combine a number of discon- 

 tinuous observations into a continuous law, so as to give a 

 general representation of them after disturbances due to falli- 

 bility of measures, runs of chance (as in statistics), &c. have 

 been set aside, is one that constantly presents itself for solution ; 

 and a rational and methodical treatment can hardly fail to be 

 of value. 



The most frequent occasion for the solution of the problem 

 arises from the necessity of drawing a curve passing close to 

 the extremities of a number of ordinates ; and the usual way 

 of solving it is to draw a curve without abrupt changes of 

 curvature as close to the points as possible. If the changes of 

 curvature are abrupt enough, the curve may be made to pass 

 exactly through the points ; but then each observation is treated 

 as exact, and we have exactly the case of the series of waves 

 with ripples on them. But, by what precedes, it appears that 

 we had better omit the ripples ; and the question remains as to 

 how far we are justified in smoothing down the curve. This 

 process of smoothing is often done by the free hand ; but it 

 will probably be done better by a system ; and it will be an 

 additional advantage if the system admits of arithmetical as 

 well as graphical application. 



