On the Knights Moves over the Chess-board. 237 
The path of the Knight over the board is of two kinds, ter- 
minable and interminable. It is interminable , whenever the last 
or concluding move of a series is made in a square which lies 
within the Knight's reach of that from which he originally set 
out ; and terminable in every other instance. 
The celebrated Euler published a paper on this subject in the 
Memoirs of the Academy of Berlin for 1759, and has there 
given a method of filling up all the squares, setting out from 
one of the corners. He has likewise given an endless or inter- 
minable route, and he explains a principle by which the routes 
may be varied so as to end upon any square. Solutions of the 
same problem have also been given by Montmort, Demoivre, 
and Mairan, which are given in Plate VI. in the following order : 
Terminable Routes over the whole Board. 
No. 1. By Euler. 
No. 6. By Demoivre. 
2. 
Ditto. 
7. 
Mairan. 
a 
Ditto. 
8. 
Montmort. 
4 
Ditto. 
9. 
the Author. 
5. 
Demoivre. 
10. 
the Author. 
Interminable Routes over the whole Board. 
No. 11. By Euler. 
No. 16. 
The Author. 
12. 
Monsieur W- 
17. 
Ditto. 
13. 
the Author. 
18. 
Ditto. 
14 
Ditto. 
19. 
Ditto. 
15. 
Ditto. 
20. 
Ditto. 
Art. VI. — Remarks on the Phenomena of the Fall of the Leaf 
and the Physiology of the painted Corolla of the Flower . 
By John Murray, F. L. S. M. W. S. he. 
The phenomenon of the fall of the leaf in autumn has been 
variously accounted for. The learned and eloquent President 
of the Linnean Society has presumed it dependent on the ma- 
turation and expansion or swell of the bud, and this opinion 
has been adopted by others. M. Vaucher ingeniously compro- 
mises the question by considering the leaf soldered or cemented 
to the twig. This latter hypothesis is soon discussed. The 
most careless observer can discover die continuity of the vessels. 
