220 Prof. Stevelly on the Doctrine of Parallel Lines 



The formula C^* H^^ 0^, to which these analyses lead, differs 

 from the one formerly given, C^* H** 0®, by 1 equivalent of 

 water. I prefer the former, since the substance employed in the 

 last analyses was evidently purer than that used in any previous 

 one. It will be seen also, that the formula just given is con- 

 firmed by an examination of the products of decomposition of 

 rubian with chlorine. 



[To be continued.] 



XXIX. The Doctrine of Parallel Lines considered in a new 

 Method. By John Stevelly, LL.D.y Professor of Natural 

 Philosophy in Queen's University , Ireland. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, Belfast, July 3, 1856. 



HAVING been lately engaged teaching my youngest son 

 the elements of Euclid, 1 was again induced to waste 

 some hours on a subject on which in my schoolboy and college 

 days I, in common I suppose with every schoolboy and collegian 

 since the days of Euclid, had over and over again wearied myself 

 in vain. On this occasion, however, the matter presented itself 

 to my mind in a form which, to me at least, was quite new, and 

 which seems to afford a solid foundation for the doctrine of 

 parallel lines, and to place the subject in a form not perhaps un- 

 suited to elementary instruction. 



If you agree with me, and think it worth a place in your 

 valuable Magazine, it is at your service. 



I am. Gentlemen, with much respect. 



Your obedient Servant, 



John Stevelly. 



.JZ. 



Definition, 



Let two straight lines in ^ 



the same plane [wxditiA yz) be ~ 



said to be parallel when both 



stand at right angles to the 



same straight line (A, B). }/ IB 2: 



Cor, I. Hence two parallel lines, if produced indefinitely on 

 either side, can never meet. (Otherwise a triangle would be 

 formed with an external angle equal to an internal remote angle, 

 as both are right. This would contradict the 16th of Euclid's first 

 book.) 



Cor, II. Hence equally distant points from A and B, taken 

 along wx and yz on each side of AB, are equally distant from 



