346 PHILOSOPHICAL TRANSACTIONS. [aNNO 1718. 



Nor have I been very solicitous about making nice numeral calculations, having 

 only proposed to exhibit a method of estimating, with greater certainty than 

 seems to have been hitherto done, the forces with which the air in expiration 

 acts on the blood-vessels that creep along the internal superficies of the lungs. 

 Whence it may be known, whether these forces be equal for producing these 

 effects, which are ascribed to them by some of the most learned medical authors. 



Prob. 3. — ^To determine the impetus of the blood in the cava near the right 

 auricle of the heart ; or the motions of the blood through all the veins and 

 arteries, besides the pulmonary. 



Let g he = the quantity of blood thrown into the aorta in one systole of 

 the heart ; / = the mean length of the whole arterio- venous duct, having a 

 regard to the longer and shorter branches; t = the time between two pulsations. 

 Hence, by theor. 3, case 4, the impetus sought is = j; that is, the impetus 

 of the blood in the cava, is equal to the motion of the mass of blood, thrown 

 out at one systole into the aorta, whose velocity is such, as with it the whole 

 length of the veins and arteries may be run over, in the time between two pul- 

 sations, a. E. I. 



If in the human body we suppose q = 2 ounces avoirdupois; 1=6 feet; 

 t = ^". Then the impetus of the blood in the vena cava will be equal to the 

 motion of a weight of 1 2 lb. that runs over the length of an inch in each 

 second of time ; or to the motion of a weight of 1 lb. that runs over -l a foot 

 in the same time, which is nearly the velocity of the blood in the cava; for, 

 from Dr. Keill, we suppose the section of the cava to be ^ of a square inch. 



Cor, — From this problem arise, mutatis mutandis, all the corollaries of the 

 first problem. 



Prob. 4. — To determine tlie absolute motion of the blood in the cava, or the 

 motion of the blood through all the veins and arteries, besides the pulmonary, 

 omitting the resistance of the vessels. 



Let the natural velocity of the blood, be to that velocity with which the 

 blood would flow, after removing all resistance, as 1 to x. Then since by the 

 cor. of the preceding prob. and cor. 1 of prob. 1, the motion of the blood is in 

 the ratio of the velocity, hence the motion sought will be = — . q. e. i. 



If the proportion found by experiment, by Dr. Keill, be admitted as near the 

 truth, jc will be = 2.5. 



Whence, supposing the same things as in the preceding prob. the absolute 

 motion of the blood in the cava, is equal to the motion of a weight of 30 lb. 

 that runs over the length of an inch in a second of time; or to the motion of a 

 weight of 2 lb. that runs over i^ foot in the same time; with which velocity 



