20 THE PRINCIPLES OF SCIENCE. 



it, we have a conclusive negative proofs. On this account, 

 as it has been well said, false facts in science 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. Thus it was long believed that the character 

 or quality of a musical sound, as distinguished from its 

 pitch must depend upon the form of the undulation, be- 

 cause 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 lu- 

 minous points attached to the strings of various instru- 

 ments, and thus actually observed the different modes of 

 undulation 2 . 



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 

 equation to which there could be no corresponding plain 

 geometrical solution a . This is a case of reductio ad 

 absurdum, a form of argument of a totally different 



y Chambers's ' Astronomy/ ist ed. p. 31. 



z "Th^orie Physiologique de la Musique', Paris, 1868, p. 113. 



a Peacock, 'Algebra/ vol. ii. p. 344. 



