100 Mr. J. Walsh on parallel straight Lines.. 



purpose, with the names of the metals on their respective 

 leaves. 



The whole apparatus packs up in a neat mahogany box. 



This instrument differs from the galvanometers I have seen 

 described. I use a powerful magnet for detecting and de- 

 termining a slight galvanic influence ; whereas in the galva- 

 nometer a feeble needle is used for that purpose. Many other 

 differences might easily be pointed out, whether advantages 

 or not is not for me to determine. 

 ] am, gentlemen, 



lours, &c. 

 Artillery Place, Woolwich. Wm. STURGEON. 



XIX. On Parallel Straight Lines. By Mr. John Walsh. 



A SOLID is that which resists the touch. Surfaces are the 

 J -*- boundaries of solids. Lines are the boundaries of sur- 

 faces. Points are boundaries of lines. When the surfaces of 

 two solids are such, as that any one surface of the one being 

 placed any where on any one surface of the other, there shall 

 be no space between them, — these are called plane surfaces, 

 and their boundaries are called straight lines. If such sur- 

 face is placed any where on any other surface any how 

 bounded, and that there is no space between them, — this other 

 also is a plane surface. Two straight lines cannot inclose space. 

 Two straight lines that intersect each other are in the same 

 plane ; and three straight lines that meet each other are in 

 the same plane. 



Let x and y be two straight lines intersecting each other, 

 and let the plane of the triangle ABC be so placed on the 

 plane of x and y as that A B shall always fall on x; and let 

 A' B' C', A" B" C" be any two positions of the triangle ABC; 

 then shall A' C be parallel to A" C". This follows from the 

 invariability of the angles of the triangle ABC. 



Axiom. When a straight line intersects any one of two 

 parallel straight lines, it cannot be parallel to the other. 



This is the same as Euclid's axiom. It appears to me to 

 be more evident in this form. It is not however so logical as 

 that of the Greek geometer, as it is intended to elucidate a 

 property of angles. 



When a straight line falls on two parallel straight lines, it 

 makes equal angles with them both. (Preceding prop, and 

 axiom.) 



Professor Leslie, in a note to his Elements of Geometry, se- 

 cond edition, shows that M. Legendre has failed in his attempt 



to 



