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 C 

 a fi C 



AB C 

 A b 

 a B C 



ABC 

 A 6 C 

 a B C 

 a B c 



ABCD 

 A be D 



ABCD 

 A BCd 

 A B c d 



A bCD 

 A l> c D 

 aBC D 

 o B c D 

 a B c d 

 a 6 C d 



PROBLEM vi 



ABODE 

 A B C de 

 ABc D E 

 A B c d e 

 AbCDE 

 aBCDE 

 o B C d e 

 ab C D E 

 abode 



A b c D e 

 aBC d E 

 a b C d E 



ABCDE 

 ABC De 

 AB C d e 

 A B c d e 

 AbC DE 

 A b c d E 

 Abode 

 aB C D e 

 a B C! d e 

 a B c D e 



a b C D e 



o b C dE 



a b e D e 



o b c d E 



PROBLEM u. 



ABcDEF 



ABc D F 



A b C D / 



Ab c D E / 



A b c D / 



A b cd E F 



A b c d e F 



Be DE F 



Be D e F 



Be d E F 



bCDE F 



bC D e F 



b C D e/ 



be De f 



b c D E / 



b c d e F 



PROBLEM i. 



ABC DeF 



ABc D E/ 



AbCDEF 



A bC De F 



A b c D F 



BC DE; 



B c D B/ 



bC D e F 



b C d e F 



b c D e f 



bode/ 



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 



