THE THEORY OF PROBABILITY. 229 



in one direction. But as we do not previously know in 

 which way a preponderance will exist, we have no more 

 reason for expecting head than tail. Our state of know- 

 ledge will be changed, indeed, should we throw up the 

 coin many times in succession and register the result. 

 Every throw gives us some slight information as to the 

 probable tendency of the coin, and in subsequent calcula- 

 tions we must take this into account. In other cases 

 experience might show that we had been entirely mis- 

 taken ; we might expect that a die would fall as often 

 on each of the six sides as on each other one in the long 

 run ; trial might show that the die was a loaded one, 

 and fell much the most often on a particular face. The 

 theory would not have misled us : it treated correctly 

 the information we had, which is all that any theory 

 can do. 



It may be asked, Why spend so much trouble in calcu- 

 lating from imperfect data, when a very little trouble 

 would enable us to render a conclusion certain by actual 

 trial \ Why calculate the probability of a measurement 

 being correct, when we can try whether it is correct ? 

 But I shall fully point out in later parts of this work 

 that in measurement we never can attain perfect coin- 

 cidence. Two measurements of the same base line in a 

 survey may show a difference of some inches, and there 

 may be no means of knowing which is the better result. 

 A third measurement would probably agree with neither. 

 To select any one of the measurements, would imply that 

 we knew it to be the most nearly correct one, which we 

 do not. In this state of ignorance, the only guide is the 

 theory of probability, which proves that in the long run 

 the mean of different quantities will come most nearly to 

 the truth. In all other scientific operations whatsoever, per- 

 fect knowledge is impossible, and when we have exhausted 

 all our instrumental means in the attainment of truth,- 



