133 



cessive additions reach the third or some higher term, and also if 

 the sum added to l6n-^Sn be equal to the term with which the 

 operation commenced, it is contended the following term may be 

 attained, and so on, and every number of the form 8?i-\-4 will be 

 composed of 4 odd squares. The pdper concludes by a suggestion 

 that the method is applicable to several other similar problems. 



2. " On the Valves of the Heart." By W. Savory, Esq. Com- 

 municated by Edward Stanlev, Esq., F.R.S. Received September 

 30, 185-2. 



The paper contains observations upon the structure and connections 

 of the auriculo-ventricular and arterial valves of thehuraan heart, which 

 the author thinks will assist in explaining their nature and functions. 



The relation of the " four orifices " in the base of the heart is ex- 

 amined, and it is shown that the aortic and left auriculo-ventricular 

 apertures are not separated as the others are ; that no muscular 

 tissue of the ventricle intervenes between them, but that when the 

 auricles and great vessels are separated from the ventricles (which 

 may be accomplished with facility after prolonged boiling), the aortic 

 aperture is separated from the left auriculo-ventricular only by the 

 anterior mitral valve ; and when this is removed (or even while it re- 

 mains), it is plainly seen that onl)'- one a])erture exists whose borders 

 are formed by the muscular tissue of the ventricle, and in shape 

 somewhat resembling the figure 8. This is divided into two por- 

 tions, an anterior (aortic) and posterior (auriculo-ventricular) by the 

 anterior mitral valve, and above it, by the posterior wall of the aorta, 

 into which is inserted a large portion of the anterior wall of the left 

 auricle, but no muscular tissue of the ventricle intervenes. 



When the auricles and vessels are removed, it is seen that the 

 three orifices are bounded by thick and convex borders formed by 

 the bases of the ventricles. Those on the left side are broadest ; 

 the difference between the two sides corresponding with the differ- 

 ence in thickness between the walls of the ventricles. The forma- 

 tion of these muscular borders, and the general arrangement and 

 direction of the muscular fibres at these parts, is examined. The 

 fibres forming the walls of the ventricles converge around these 

 apertures. The most superficial fibres may be traced up from the 

 walls of the ventricles, curving obliquely over the convex border, 

 and having their extremities, for the most part, fixed around the 

 orifices. We may remove these fibres layer after layer, and still 

 find the same arrangement to obtain, the deeper fibres lying more 

 transversely and obliquely intersecting those above and below. 



If now the auricles and great vessels which have been detached are 

 replaced in their natural situation, it is observed that the auricles 

 are connected with the inner surface of these convex borders, while 

 the walls of the vessels pass down on to the outer surface. This 

 fact is an important one when viewed in connection with the valves, 

 and will be presently considered. In the mean time it may be re- 

 marked, that the formation of the auriculo-ventricular grooves in 

 which the coronary vessels lie, is explained. These vessels are 

 Proceedings of the Royal Society. Vol. VI. No. 85. lo 



