358 THE PRINCIPLES OF SCIENCE. [CHAP. 



results agree too closely. Such coincidences should raise 

 our suspicion that the apparatus in use is in some way 

 restricted in its operation, so as not really to give the true 

 result at all, or that the actual results have not been faith- 

 fully recorded by the assistant in charge of the apparatus. 



If then we cannot get twice over exactly the same 

 result, the question arises, How can we ever attain the 

 truth or select the result which may be supposed to 

 approach most nearly to it ? The quantity of a certain 

 phenomenon is expressed in several numbers which differ 

 from each other ; no more than one of them at the most 

 can be true, and it is more probable that they are all 

 false. It may be suggested, perhaps, that the observer 

 should select the one observation which he judged to be 

 the best made, and there will often doubtless be a feeling 

 that one or more results were satisfactory, and the others 

 less trustworthy. This seems to have been the course 

 adopted by the early astronomers. Flamsteed, when he 

 had made several observations of a star, probably chose in 

 an arbitrary manner that which seemed to him nearest to 

 the truth. 1 



When Horrocks selected for his estimate of the sun's 

 semi-diameter a mean between the results of Kepler and 

 Tycho, he professed not to do it from any regard to the 

 idle adage, " Medio tutissimus ibis," but because he 

 thought it from his own observations to be correct. 2 But 

 this method will not apply at all when the observer has 

 made a number of measurements which are equally good 

 in his opinion, and it is quite apparent that in using an 

 instrument or apparatus of considerable complication the 

 observer will not necessarily be able to judge whether 

 slight causes have affected its operation or not. 



In this question, as indeed throughout inductive logic, 

 we deal only with probabilities. There is no infallible 

 mode of arriving at the absolute truth, which lies beyond 

 the reach of human intellect, and can only be the distant 

 object of our long-continued and painful approximations. 

 Nevertheless there is a mode pointed out alike by common 

 sense and the highest mathematical reasoning, which is 



1 Baily's Account of Flamsteed, p. 376. 



2 The Transit of Venus ac 



Venus across the Sun, by Horrock-'-i, London, 1859, 

 p. 146. 



