1863.] 561 



of the oesophagus and the pylorus ligatured, without including the 

 vessels, so that the circulation through the organ was left free. In 

 one hour and forty minutes death took place, and on the parts being 

 examined immediately, perforation, with extensive digestion of the 

 interior of the stomach throughout, was found. The author con- 

 sidered that the question of result was clearly shown to resolve itself 

 into one dependent on degree of power possessed by the acid contents 

 of the stomach on the one hand, as against the alkaline circulation 

 on the other. With a certain amount of acid only in the stomach, 

 the circulation can aiford the required protection; whilst with a 

 larger amount the influence of the acid prevails, and digestive solu- 

 tion of the organ is the result. Allow, now, the contents of the 

 stomach to remain the same, and vary the degree of vascularity in 

 the parts submitted to the digestive influence. We have simply here 

 a converse arrangement of the circumstances ; and the position is 

 represented by the situation of the stomach as compared with that 

 of the frog's legs and rabbit's ear. 



III. " On a Question of Compound Arrangement." By J. J. 

 SYLVESTER, M.A., F.R.S., Professor of Mathematics in 

 the Royal Military Academy, Woolwich. Received April 

 27, 1863. 



My successful but as yet unpublished researches into the Theory of 

 Double Determinants have involved the consideration of the follow- 

 ing curious case of arrangements. 



There are given m+n l counters of n distinct colours just capable 

 of being packed into m urns. The question refers to the distribution 

 of the counters among the urns, subject to the condition that it shall 

 not be possible to form a closed circuit of double colours between 

 any number of the urns chosen arbitrarily, ex. gr. we must allow no 

 distribution of counters in which one urn contains blue and yellow, 

 a second yellow and red, a third red and green, and a fourth green 

 and blue, because here blue, yellow, red, and green would form a 

 closed circuit. This condition, it is evident, excludes the same com- 

 bination of colours from existing in any two of the urns, and also the 

 repetition of any one colour in the same urn. Any distribution of 

 counters obeying this condition may be called an excyclic distribution. 



