Mr. J. Walsh on Parallel Straight Lines. 271 



The lower end of this screw rests in the hole in the top of 

 the magnet; and by turning the milled head to the right or 

 left, the points s s of the silver wires may be heightened or 

 lowered at pleasure ; and consequently their contact with the 

 mercury in the cell F E may be regulated to the greatest 

 nicety ; the attainment of which was the only embarrassment 

 I had to encounter with the original apparatus. However, by 

 means of this improvement my anticipations were soon agree- 

 ably realized by witnessing the first thermo rotation ever pro- 

 duced by the influence of a central magnet. 



I must here beg leave to observe, that the only attempt I 

 ever heard of (and the only one perhaps on record) was with 

 the apparatus of Professor Cumming, and a similar attempt 

 by Professor Barlow with a combination upon the same prin- 

 ciples. 



The latter gentleman, however, has candidly confessed the 

 failure of the experiment, and sufficiently accounted for the in- 

 efficacy of the apparatus upon the principle of its construction. 



I am, gentlemen, yours respectfully, 

 Artillery Place, Woolwich Wm. STURGEON. 



P.S. — April 13. I have since succeeded in forming a sphere 

 of galvanized wires, to rotate by the influence of both poles of 

 an internal magnet. 



This experiment was suggested on reading the late Dr. 

 Halley on the theory of the earth ; and although it may not 

 be considered as a proof of that philosopher's notion of ter- 

 restrial magnetic variation, yet perhaps it may tend in some 

 measure to strengthen the hypothesis. A description of the 

 apparatus shall be the subject of another paper. 



W. S. 



XLVI. On Parallel Straight Lines. By John Walsh, Esq.* 



T X this paper my object is not to terminate a controversy, 

 ■*■ but to render service to science, to banish from it, as far 

 as this is in my power, all fallacious reasoning about an ele- 

 mentary principle which is the basis of all mathematical 

 science. I must observe again, that the difficulty encoun- 

 tered in the theory of parallels, arises out of the nature of 

 things. It arises From this, that space has no limit. Can the 

 geometer imagine space beyond which there is no space ? Can 



* Communicated by the Author. 



