54 The Division oj Angles and Arcs of Circles. 



ordinary than those instruments on the table. I confess I am 

 not able to judge as to what practical application could be made 

 of them, and I think if they are intended to do away with the 

 reasoning properties in the use of the compass and rule it would 

 perhaps be a mistake to have Mr. Murphy's apparatus made 

 applicable for scholastic purposes. From a mechanical point of 

 view, I may mention one matter referred to, viz., the screws 

 being considered extremely fine 35 to the inch. It may be 

 interesting to know that I myself have cut in the lathe screws 

 of 100 to the inch on steel bars 7 inches long by | inch 

 diameter. The first screw required 28 hours of close application. 

 It was necessary to use a microscope to examine the thread ; 

 and when the tool was at all blunt, it has taken me as long as 

 an hour and a half to insert the point of a re-sharpened tool 

 into the thread already cut. I believe that threads of 250 

 to the inch have been cut at Mr. Edison's laboratory. I 

 cannot at all profess to criticise the diagrams shown ; but I 

 am perfectly certain that I convey the mind of the Council of 

 this Society in expressing to Mr. Murphy our sincere thanks 

 for his very valuable gift. 



Profkssor Everett having seconded the vote of thanks, 

 mentioned that a Belfast schoolboy, A. A. Robb, a pupil of Mr. 

 Nixon, had discovered a way of dividing a circle into seven 

 equal parts. (See vol. 55 of the reprint of the Educational 

 Times.) Prof. Everett then exhibited a linkwork of his own 

 invention (a kind of lazy-tongs), which solved the problem of 

 dividing an angle into any number of equal parts ; and showed 

 a drawing of another linkwork for the same purpose, invented 

 by Professor Sylvester. 



Professor Purser. — Mr. Murphy has touched upon the 

 question of the possibility of the solution of certain problems 

 in Geometry, and the impossibility of the solution of others. 

 It is of interest to examine exactly what we mean by this. 

 When the ancient mathematicians produced a problem in- 

 soluble by Plane Geometry they meant that the construction 

 for solving it could not be effected by drawing right lines and 



