288 Proceedings of the Royal Irish Academy. 



jST.B. — The units of mass, space, and time are assumed : 

 Unit of mass = atomic weight of hydrogen ; 

 Unit of space = radius of hydrogen molecule ; 

 Unit of time is found hy making the angular velocity of the 

 hydrogen molecule equal to unity. 

 The equations (A) and (C) contain six unknown quantities, viz. : 

 r' I Til <^' / wij a^l ei, 



and cannot be made use of, without some hypotheses. 

 Let us suppose 



n = 1 / a^ = / £1=0, 



or, that the chlorine molecule has the same radius as the hydrogen 

 molecule, and that the combination takes place in the cheapest way, 

 without additional area, and without loss of energy by the collision of 

 'the atoms. 



These hypotheses reduce equations (A) and (C) to the following : 



(3+ 1 ,, , vi, + /3 



y8 



r-(x) — 



(A) 



^,V.!!^; (C) 



where vii = — , and is proportional to the periodic time of chlorine, &c. 



Wl 



If we eliminate co' , we find 



(3 + 1 m,^ + (3 ' 

 and, if we eliminate r', we find 



/3 ., K + ^)^ (^^ 



(i) 



"We have already shown that the combination (catastrophe) is 

 greatly aided by chlorine, &c., having an opposite rotation to hy- 

 di'ogen, and their periodic times having a small common multiple. 

 "We shall therefore assume vh to be an integer and negative. 



"We are able to assign a probable limit to the value of mi by 

 the consideration that the stability of the hydrochloric, &c., molecule 

 must be greater than that of the hydrogen molecule. 



