414 THE PRINCIPLES OF SCIENCE. [CHAP. 



In order that a negative argument founded on the non- 

 observation of an object shall have any considerable force, 

 it must be shown to be probable that the object if existent 

 would have been observed, and it is this probability which 

 defines the value of the negative conclusion. The failure 

 of astronomers to see the planet Vulcan, supposed by some 

 to exist within Mercury's orbit, is no sufficient disproof of 

 its existence. Similarly it would be very difficult, or even 

 impossible, to disprove the existence of a second satellite of 

 small size revolving round the earth. But if any person 

 make a particular assertion, assigning place and time, then 

 ooservation will either prove or disprove the alleged fact. 

 If it is true that when a French observer professed to 

 have seen a planet on the sun's face, an observer in Brazil 

 was carefully scrutinising the sun and failed to see it, we 

 have a negative proof. False facts in science, it has been 

 well said, are more mischievous than false theories. A 

 false theory is open to every person's criticism, and is ever 

 liable to be judged by its accordance with facts. But a 

 false or grossly erroneous assertion of a fact often stands 

 in the way of science for a long time, because it may be 

 extremely difficult or even impossible to prove the falsity 

 of what has been once recorded. 



In other sciences the force of a negative argument will 

 often depend upon the number of possible alternatives 

 which may exist. It was long believed that the quality 

 of a musical sound as distinguished from its pitch, must 

 depend upon the form of the undulation, because no other 

 cause of it had ever been suggested or was apparently 

 possible. The truth of the conclusion was proved by 

 Helmholtz, who applied a microscope to luminous points 

 attached to the strings of various instruments, and 

 thus actually observed the different modes of undulation. 

 In mathematics negative inductive arguments have 

 seldom much force, because the possible forms of expres- 

 sion, or the possible combinations of lines and circles in 

 geometry, are quite unlimited in number. An enormous 

 number of attempts were made to trisect the angle by the 

 ordinary methods of Euclid's geometry, but their in- 

 variable failure did not establish the impossibility of the 

 task. This was shown in a totally different manner, by 

 proving that the problem involves an irreducible cubic 



