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. PROBLEM I. A B *c* A *b* C *a* B C PROBLEM II. A B C A *b* C *a* B C *a* B *c* PROBLEM III. A B C A *b* C *a* B C *a* B *c* *a* *b* *c* PROBLEM IV. A B C D A *b* *c* D *a* B *c* *d* *a* *b* C *d* PROBLEM V. A B C D A B C *d* A B *c* *d* A *b* C D A *b* *c* D *a* B C D *a* B *c* D *a* B *c* *d* *a* *b* C *d* PROBLEM VI. A B C D E A B C *d* *e* A B *c* D E A B *c* *d* *e* A *b* C D E *a* B C D E *a* B C *d* *e* *a* *b* C D E *a* *b* *c* *d* *e* PROBLEM VII. A *b* *c* D *e* *a* B C *d* E *a* *b* C *d* E PROBLEM VIII. A B C D E A B C D *e* A B C *d* *e* A B *c* *d* *e* A *b* C D E A *b* *c* *d* E A *b* *c* *d* *e* *a* B C D *e* *a* B C *d* *e* *a* B *c* D *e* *a* *b* C D *e* *a* *b* C *d* E *a* *b* *c* D *e* *a* *b* *c* *d* E PROBLEM IX. A B *c* D E F A B *c* D *e* F A *b* C D *e* *f* A *b* *c* D E *f* A *b* *c* D *e* *f* A *b* *c* *d* E F A *b* *c* *d* *e* F *a* B *c* D E F *a* B *c* D *e* F *a* B *c* *d* E F *a* *b* C D E F *a* *b* C D *e* F *a* *b* C D *e* *f* *a* *b* *c* D *e* *f* *a* *b* *c* D E *f* *a* *b* *c* *d* *e* F PROBLEM X. A B C D *e* F A B *c* D E *f* A *b* C D E F A *b* C D *e* F A *b* *c* D *e* F *a* B C D E *f* *a* B *c* D E *f* *a* *b* C D *e* F *a* *b* C *d* *e* F *a* *b* *c* D *e* *f* *a* *b* *c* *d* *e* *f* *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 coincident with all matter possessing inertia; where one property appears, the other likewise appears. All crystals of the cubical system, are all the crystals which do not doubly refract light. All exogenous plants are, with some exceptions, those which have two cotyledons or seed-leaves.