254, 



PvEPORT 1876. 



Fig. 8: 



No. 1. 



No. 2. 



Let the pressure at B, the beginning of the tube, on the initial interface, 

 outside of which the water may be regarded as statical, or as having no 

 important energy of motion, be denoted by hi, ; or, what comes to the same 

 thing, let the depth from the stUl-water surface-level down to the beginning 

 of the tube at B be denoted by hb, as is marked in the figure. It is thus to 

 be noticed that the fall of free level incurred by a particle in flowing along 

 the guide-tube from B to U is the vertical distance from the stiU-water sur- 

 face-level, W L, down to T, the top of the pressure-column for the flowing 

 water at U. This fall of free level may be denoted (in conformity with the 

 notation in Theorem I.) by C- 



Let the vertical descent from B to U bo denoted by/; so that /is the fall 

 of a particle in passing from B to U. In case of an ascent in any guide- 

 tube, from its beginning to any point U in its course, we shall have the fall 

 / negative. 



Let the abatement of pressure-height from B to U be denoted by h, or let 

 hi) — h=k. Thus in case of an increase of pressure-height in any guide-tube, 

 from its beginning to any point U in its course, Jc will be negative. 



Por No. 2, let the same letters of reference to the diagram, and the same 

 notation, be used as for No. 1, with the modification for No. 2 merely of the 

 attachment of an accent to each letter. 



Now as a part of the data on which the present investigation under Pro- 

 position A is founded, it is to be assumed that a unital pressure is somehow 

 maintained at E', the end of the guide-tube in No. 2, n times that which is 

 anyhow maintained at the corresponding point E in No. 1. Thus, if we 

 denote these two pressures expressed as pressure-heights, at E and E' respec- 

 tively, by he and (he)', we have (Jie)' ^nhe ; and hence the fall of free level 

 from beginning to end in No. 2 is n times the fall of free level from beginning 

 to end in No. 1. 



