Royal Society. 51 



short paper iu the last Number of the Philosophical Magazine, 

 on the extension of Lagrange's Rule of Interpolation, where I 

 used to denote that such a choice of signs was to be made, the 

 awkward and un suggestive symbol " ? " There exists, however, 

 a very simple algebraical mode of denoting the presence of the 

 factor +1 or —1, according to the order of the natural num- 

 bers in the scale 6^, 6^, 9^, . . . d„- 



f has been always consecrated by me to the purpose of signifying 

 that the product of the squared diiferences is to be taken of the 

 elements with which it is in regimen ; and iu the paper adverted to 

 I introduced the highly convenient new symbol ^* to denote that 

 the product is to be taken of the simple differences obtained by 

 subtracting from each element in regimen therewith every sub- 

 sequent element in the arrangement of the elements as set down. 

 By aid of this new symbol f*, the positive or negative character 

 of any permutation, as 0^, 6^, . . . 6^, can be completely expressed; 

 for ?4(^p 00, 0s, ... d„)-^^Hh 2, 3, . . . n) will be +1 or -1 

 according as 1, 2, 3, . . . n and 6^, 0^, 0q,.. . 0„ belong to the 

 same group, or to opposite groups in the natural dichotomous 

 separation of the permutations of the n symbols in question, and 

 thereby the desired object of giving a functional representation 

 of the ambiguous sign is perfectly attained. 



X. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from vol. vi. p. 306.] 



Nov. 17. 1853.— Dr. Wallich, V.P., in the Chair. 



THE following papers were read : 

 1. " Oil the Nerves which supply the Muscular Structure of 

 the Heart." By Robert Lee, M.D., F.R.S. 



The author remarks that, in a paper entitled " On the GangHa 

 and Nerves of the Heart," published in the Philosophical Trans- 

 actions, Part L 1839, it is asserted, that " it can be clearly demon- 

 strated that every artery distributed throughout the walls of the 

 uterus and heart, and every muscular fasciculus of these organs, is 

 supplied with nerves upon which ganglia are formed." 



He then states that " recent dissections which I have made of 

 the heart of the race-horse, in which both the muscular and ner- 

 vous structures are largely developed, demonstrate, that from the 

 outer surface to the lining membrane the walls are universally per- 

 vaded with nerves, on which ganglia are formed, or enlargements 

 invested with neurilemma, into which nerves enter and from which 

 they issue, as in all the other ganglia of the great sympathetic 

 nerve. 



" From these dissections it is seen that the ganglionic nerves 

 E2 



