X] ON GEODESICS 745 



become bent upon itself, or if at some point its walls bulge outwards 

 in a diverticulum or pouch, then the old system of geodesies will 

 only mark the shortest distance between two points more or less 

 approximate to one another, and new systems of geodesies, 

 peculiar to the new surface, will tend to appear, and link 

 up points more remote from one another. This is evidently the 

 case in the human stomach. We still have the systems, or their 

 unobhterated remains, of circular and longitudinal muscles; but 

 we also see two new systems of fibres, both obviously geodesic 

 (or rather, when we look more closely, both parts of one and the 

 same geodesic system), in the form of annuh encircling the pouch 

 or diverticulum at the cardiac end of the stomach, and of obhque 

 fibres taking a spiral course from the neighbourhood of the 

 oesophagus over the sides of the organ. 



In the heart we have a similar, but more complicated pheno- 

 menon. Its musculature consists, in great part, of the original 

 simple system of circular and longitudinal muscles which enveloped 

 the original arterial tubes, which tubes, after a process of local 

 thickening, expansion, and especially tuisting, came together to 

 constitute the composite, or double, mammalian heart; and these 

 systems of muscular fibres, geodesic to begin with, remain geodesic 

 (in the sense in which we are using the word) after all the twisting 

 which the primitive cylindrical tube or tubes have undergone. 

 That is to say, these fibres still run their shortest possible course, 

 from start to finish, over the complicated curved surface of the 

 organ; and, as Borelli well understood, it is only because they do 

 so that their contraction, or longitudinal shortening, is able to 

 produce its direct eifect in the contraction or systole of the heart*. 



As a parenthetic corollary to the case o-f the spiral pattern upon 

 the wall of a cyhndrical cell, we may consider for a moment the 

 spiral fine which many small organisms tend to follow in their path 



* The spiral fibres, or a large portion of them, constitute what Searle called 

 "the rope of the heart" (Todd's Cyclopaedia, ii, p. 621, 1836). The "twisted 

 sinews of the heart" were known to early anatomists, and have been frequently 

 and elaborately studied: for instance, by Gerdy {Bull. Fac. Med. Paris, 1820, 

 pp. 40-148), and by Pettigrew (Phil. Trans. 1864), and again by J. B. Macallum 

 {Johns Hopkins Hospital Report, ix, 1900) and by Franklin P. Mall {Amer. Journ. 

 Anat. XI, 1911). 



