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, arid is ever liable to be judged by 

 its accordance with facts. But a false or grossly erroneous I 

 assertion of a fact often stands in the way of science for a I 

 long time, because it maybe 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 i 

 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 I 

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

 cause no other cause of it had ever been suggested or was I 

 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 I 

 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 I 

 equation to which there could be no corresponding plain 

 geometrical solution*. This is a case of reductio ad I 

 alsurdum, a form of argument of a totally different I 



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



z 'Thdorie Physiologique de la Musique', Paris, 1868, p. 113. 



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



