Til.] 



INDUCTION. 



127 



tions deductively from four laws of correction, but my 

 correspondents found that three simpler laws, equivalent 

 to the four more complex ones, were the best answer ; these 

 laws are as follows : a = ac, b = cd, d = E/. 



In case other readers should like to test their skill in the 

 inductive or inverse problem, I give below several series 

 of combinations forming problems of graduated difficulty. 



A B e 

 A b C 

 a B C 



ABC 

 A 6 C 

 a B C 

 a B c 



ABC 

 A b C 

 a B C 



ABCD 

 A b c D 

 a B c d 

 a b C d 



ABCD 

 A B Cd 

 A B c d 



AbCD 

 A b c D 

 aBC D 

 aB c t> 

 a B c d 

 a b C d 



PROBLEM vi. 



ABODE 

 A B C d t 

 ABcD E 

 A B c d e 

 A b C D E 

 a B C D E 

 a B C d 

 ab C D E 

 abode 



A 6 c D e 

 oBC d E 

 a 6 C d E 



ABCDE 

 A BC De 

 AB C d e 

 A. B c d e 

 AbC D E 

 A & c d E 

 A & c d e 

 a B C D e 

 a B C d e 

 a B c D 



a 6 C D e 



a b C d E 



a b c D 



a b c d E 



PROBLEM n. 



ABcDEF 

 A B c 1) e P 

 A b C D e/ 

 A b c D E / 

 A b c D e / 

 A b c d E F 

 A b c d e V 

 oBc DE F 

 a Be D e F 

 a Be d E F 

 a bCDE F 

 a bC D e F 

 a 6 C D e f 

 a b c D / 

 a b c D E / 

 a b c d e F 



PROBLEM x. 



ABC DeF 

 ABc D E/ 

 AbCD E F 

 A bC De F 

 A b c D e F 

 a B C D By 

 aB c D E/ 

 a bC D e F 

 a b C d F 

 a b c D e / 

 a b c d e / 



Induction of Simple Identities. 



Many important laws of nature are expressible in the 

 form of simple identities, and I can at once adduce them 

 as examples to illustrate what I have said of the difficulty 

 of the inverse process of induction. Two phenomena are 

 conjoined. Thus all gravitating matter is exactly co- 

 incident with all matter possessing inertia ; where one 



