THE CIRCULATION OF THE BLOOD. 325 



it would ascend an equal distance. If now this height is represented by F, and a 

 line be drawn from it, parallel to the line of pressure until it meets the reservoir at 

 x, it will be seen what percentage, x y, or h' of the primary propelling power is con- 

 sumed in imparting the observed velocity. 



Of the total pressure a small portion is left over which is utilized in forcing into, 

 and overcoming the resistance offered by, the orifice of the horizontal tube. The 

 initial pressure in P therefore divides itself mainly into two portions; one, the larger 

 by far, h, is utilized in overcoming the resistance to the flow of the water; the other, 

 the smaller, h' in imparting velocity. 



Thus the two phenomena presented by the flow of a liquid through a tube with 

 rigid walls and of uniform diameter are velocity and pressure, of which the former 

 is the same for each cross-section, and the latter at any point directly proportional 

 to the resistance to be overcome. 



If, instead of a horizontal tube of uniform diameter, there be substituted a 

 tube the middle third of which is enlarged, the conditions will be similar to 

 the previous case until the fluid flows into the enlarged portion, when the velocity 

 will diminish, being inversely proportional to the area of the cross-section. The 

 resistance will be also diminished and therefore less of the pressure force or 

 driving power will be consumed than in the first section of the tube, and as a result, 

 the lateral pressure will fall less rapidly than in the first section. When the liquid 

 flows into the narrow or third section, the primary velocity returns. Though the 

 resistance again increases the amount to be overcome is small, and hence there is 

 a rapid and steady fall of pressure. 



On the contrary, if a tube be substituted the middle third of which is narrowed, 

 the conditions will be similar to the previous cases until the liquid flows into 

 the narrowed section, when at once the velocity increases and becomes inversely 

 proportional to the area of the cross-section; the resistance being increased at the 

 same time, there will be a rapid consumption of the pressure force and a steep fall 

 of lateral pressure. On flowing into the third section, the velocity again diminishes 

 and the pressure falls though more slowly to the end of the tube. 



THE FLOW OF A LIQUID THROUGH A SERIES OF BRANCHING AND 

 AGAIN UNITING TUBES WITH RIGID WALLS. 



In a system of this character, such as represented in Fig. 151, there must follow 

 as a result of the repeated branchings, a progressive increase in the total sectional 

 area of the collective tubes coincident with a progressive decrease in the sectional 

 area of individual tubes in the section B c, while in the section c D, there must 

 follow a progressive decrease in the total sectional area of the collective tubes coin- 

 cident with a progressive increase in the sectional area of individual tubes, conse- 

 quently there will be a combination of the two conditions alluded to in the two 

 preceding paragraphs, namely, an enlargement of the stream bed coincident with 

 a diminution in size of the individual tubes composing it, in the middle section. 

 Moreover, for the purpose here intended it may be assumed that the tubes com- 

 posing the middle section c are microscopic in size and that their total sectional 

 area bears to the sectional area of tube A the ratio of 600 to i . 



If the system is connected with a pressure vessel, as in the preceding instance, 

 and the stop cock is suddenly opened, the column of water will exert a downward 

 pressure, and in consequence the water will be driven into and through the system 

 with a definite velocity and pressure. 



The velocity of the fluid will gradually decrease from B to c in a ratio inversely 

 proportional to the total area of each cross-section until at c, it will attain its mini- 

 mal value; the velocity will again increase from c to D in a ratio inversely pro- 



