260 THE PRINCIPLES OF SCIENCE. [CHAP. 



cedent events, disconnected from the general body of 

 physical science. 



Events, again, may often exhibit a regularity of suc- 

 cession or preponderance of character, which the simple 

 formula will not take into account. For instance, the 

 majority of the elements recently discovered are metals, 

 so that the probability of the next discovery being that of 

 a metal, is doubtless greater than we calculated (p. 258). 

 At the more distant parts of the planetary system, there 

 are symptoms of disturbance which would prevent our 

 placing much reliance on any inference from the prevailing 

 order of the known planets to those undiscovered ones 

 which may possibly exist at great distances. These and 

 all like complications in no way invalidate the theoretic 

 truth of the formulas, but render their sound application 

 much more difficult. 



Erroneous objections have been raised to the theory of 

 probability, on the ground that we ought not to trust to 

 our a priori conceptions of what is likely to happen, but 

 should always endeavour to obtain precise experimental 

 data to guide us. 1 . This course, however, is perfectly in 

 accordance with the theory, which is our best and only 

 guide, whatever data we possess. We ought to be always 

 applying the inverse method of probabilities so as to take 

 into account all additional information. When we throw 

 up a coin for the first time, we are probably quite ignorant 

 whether it tends more to fall head or tail upwards, and 

 we must therefore assume the probability of each event 

 as \. But if it shows head in the first throw, we now 

 have very slight experimental evidence in favour of a 

 tendency to show head. The chance of two heads is 

 now slightly greater than J, which it appeared to be at 

 first, 2 and as we go on throwing the coin time after time, 

 the probability of head appearing next time constantly 

 varies in a slight degree according to the character of our 

 previous experience. As Laplace remarks, we ought 

 always to have regard to such considerations in common 

 life. Events when closely scrutinized will hardly ever 

 prove to be quite independent, and the slightest pre- 



1 J. S. Mill, System of Logic, 5th edition, bk. iii. chap, xviii. 3. 



2 Todhunter's History, pp. 472, 598. 



