But if L be the loss of energy per unit distance in the wide tube AB, and Lÿ£¢ãý be the corôÙreôÙsponôÙding loss of energy in the narrow tube DP, etc., then lL
=ã₤lÿ£¢2ãLÿ£¢ãý, because, as we have assumed, the loss of energy on the route DP is equal to that on the whole route DEP. Therefore lL =ã₤lLÿ£¢ãýã₤cosã₤xÿ£¢2ã₤, and cosã₤xÿ£¢2 =ã₤Lã₤ãã₤Lÿ£¢ãý. 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 as 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 lecture19) all such questions as these, and all matters connected with the muscular and elastic powers of the blood-vessels, ãbelong to the most refined departments of hydraulics.ã Some other explanation must be sought in order to account for a phenomenon which particularly impressed John Hunterãs mind, namely the gradually altering angle at which the successive intercostal arteries are given off from the thoracic aorta: the special interest of this case arising from the regularity and symmetry of the series, for ãthere 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]20 are so much the same.ã