Theory of the Method of False Position, G65 



consideration on quantities whose real values may be con- 

 sidered absolutely known by past experience, the values of the 

 physical conditions being varied for the four trials. The 

 method of false position will then give us very closely the 

 most suitable physical conditions for undertaking investiga- 

 tions of the proposed kind. 



A very simple extension of these ideas ought to make the 

 method of considerable service to experimental psychology. 

 What are the psycho-physkal conditions best suited to mental 

 judgment or to clearness of sense-perception ? Interval after 

 food or exercise, external temperature, pulse, &c, &c, are all 

 " constants " whose best values can be found by the " method 

 of false position/' and a novel field for research seems to 

 suggest itself here. 



Lastly, turning to more mathematical conceptions, the 

 method appears to offer a definite systematical treatment for 

 the combination of the results of different series of observa- 

 tions on the same physical substance. For example, two 

 observers give a pressure-volume formula of the same form 

 for a gas, but with different values of the constants. It is 

 required to modify the constants, so that the formula may fit 

 most closely a new set of data, or the combined data of the 

 previous observations. In such cases the formulae may be 

 used as trial solutions, and additional trial solutions be made, 

 if required, by very slightly varying the constants. 



Another such application will occur to the astronomer, 

 namely, the modification of the constants on which planetary 

 and cometary orbits depend. Here as many observed 

 positions of the body may be used as the calculator can be 

 taxed with, and the six constants of the orbit found by trial 

 solutions differing slightly in their constants from the approxi- 

 mate or hitherto current values. I am not aware that the 

 method of false position has ever been used by astronomers, 

 but I think it possibly might be of assistance to them. 



Having indicated some possible uses of the present method, 

 I give an illustration of its application. I limit myself to 

 one case in order that this paper may not be unduly extended. 

 I hope in some experiments about to be undertaken to give 

 later an example of more practical utility. 



Illustration. — Let us fit a good circle to the following Hy^ 

 points : 



0=0, 



//o = 0, 



0=3, 



y.-% 



0=1, 



y =i'5, 



0=4, 



#0=1 



0=2, 



y„=i-8, 







By simply plotting the points on a piece of decimal paper 



