Wellington Philosophical Society. 545 



the whole series of odd numbers, a right-angled triangle would be the 

 result. From which he deduced the curious fact that, if the length 

 of one side of a triangle be an odd number, and the square of this 

 number be equal to the sum of tbe lengths of the other two sides, of 

 which one is greater than the other by 1, the triangle is a right-angled 

 triangle. The paper was illustrated by diagrams of several triangles 

 of various proportions, and by a graphic solution of the geometrical 

 problem involved. 



Major-General Schaw said that the fact was curious and interesting, 

 and, though it might not be new, was certainly not generally known. 

 He did not think that it would have any practical value in triangles the 

 perpendicular of which exceeded 7. Even in the case of the latter 

 number the triangle became very " ill-conditioned," the angle opposite 

 to the perpendicular being very acute, and therefore difficult to fix 

 accurately. 



3. " The Moas'and the Moa-hunters," by M. A. cle Quatre- 

 fages; translated by Laura Buller. Communicated by Sir 

 W. Buller. (Transactions, p. 17.) 



4. " On the Nature of Stinkstone (Anthraconite)," by W. 

 Skey. (Transactions, p. 379.) 



5. "Further Eesults obtained in support of my Theory as 

 to the Oxidation of Gold in presence of Air and Water," by 

 W. Skey. (Transactions, p. 381.) 



35 



