XV] OF BLOOD VESSELS 669 



Then, if we make the distance DE very small, the angles iCo and 

 iCg are nearly equal, and may be so treated. And again, if DE 

 be very small, then DE'E becomes a right angle, and L (or 

 DE') =- 1 cos x^. 



But if L be the loss of energy per unit distance in the wide 

 tube AB, and L' be the corresponding loss of energy in the narrow 

 tube DP, etc., then IL = LL' , because, as we have assumed, the 

 loss of e;aergy on the route DP is equal to that on the whole 

 route DEP. Therefore IL = IL' cos iCg, and cos x^ ^ LjU . That 

 is to say, the most favourable angle of branching will be such 

 that the cosine of the angle is equal to the ratio of the loss of 

 energy which the blood undergoes, per unit of length, in the main 

 vessel, as compared with that which it undergoes in the branch. 



While these statements are so far true, and while they 

 undoubtedly cover a great number of observed facts, yet it is 

 plain that, as in all such cases, we must regard them not as a 

 complete explanation, but a& factors in a complicated phenomenon : 

 not forgetting that (as the most learned of all students of the 

 heart and arteries, Dr Thomas Young, said in his Croonian 

 lecture*) all such questions as these, and all matters connected 

 with the muscular and elastic powers of the blood-vessels, 

 "belong to the most refined departments of hydraulics." Some 

 other explanation must be sought in order to account for a 

 phenomenon which particularly impressed John Hunter's mind, 

 namely the gradually altering angle at which the successive inter- 

 costal arteries are given off from the thoracic aorta : the special 

 interest of this case arising from the regularity and symmetry of 

 the series, for "there is not another set of arteries in the body 

 whose origins are so much the same, whose offices are so much 

 the same, whose distances from their origin to the place of use, 

 and whose uses [? sizes] | are so much the same." 



* On the Functions of the Heart and Arteries. Phil. Trans. 1809^ pp. 1-31, 

 of. 1808, pp. 164-186; Collected Works, i, pp. 511-534, 1855. The same lesson is 

 conveyed by aU such work as that of Volkmann, E H. Weber and PoiseuiUe. 

 Cf. Stephen Hales' Statical Essay.", n, Introduction: "Especially considering 

 that they [i.e. animal Bodies] are in a manner framed of one continued Maze of 

 innumerable Canals, in which Fiuid^'are incessantly circulating, some with great 

 Force and Rapidity, others with very different Degrees of rebated Velocity: 

 Hence, etc." 



■j- "Sizes" is Owen's editorial emendation, which seems amply justified. 



