282 Dr. Rankine on the Properties 



pended in this manner, a portion of them pass into the mole- 

 cular atmospheres and elevate the temperature of the liquid. If 

 the pressure upon the free surface of the liquid exceeds the 

 pressure of the atmosphere, the molecular atmospheres are more 



71 



compressed, the value of m becomes greater, and the ratio — 



diminishes in consequence ; from this cause the limit of the re- 

 cess of the particles (Od, fig. 1) diminishes, and the maximum 

 repulsion dn increases (see Table I.). The resulting vapour has, 

 therefore, at the same time a higher tension and a greater 

 density. 



According to the theoretical views now advanced, the " inte- 

 rior work " which Tyndall maintains is expended in the act of 

 liquefaction, and also in that of vaporization, in " moving the 

 atoms into new positions," or in conferring " potential energy " 

 upon them, is consumed in each instance in pressing up the 

 electric atmospheres that surround the atoms of the substance ; 

 and heat disappears in the process in proportion to the effect 

 thus produced. 



[To be continued.] 



XXXIII. Summary of the Properties of certain Stream-Lines. 

 By W. J. Macquorn Rankine, C.E., LL.D., F.R.SS.L.fyE* 



1. PTHHE investigation, of which the present paper is a sum- 

 -■- mary, consists of three parts. It is a sequel to one of 

 which an abstract was read at the Meeting of the British Asso- 

 ciation in 1863, and which has since been printed in full in the 

 Philosophical Transactions f. It relates to the paths in which 

 the particles of a liquid move past a solid body. In the previous 

 paper (which was confined to motion in two dimensions) those 

 paths were called " Water-Lines," and were treated of with a view 

 mainly to their use as figures for the horizontal or nearly hori- 

 zontal water-lines of ships. In the present paper they are called 

 " Stream-Lines," as being a more general term, and one less liable 

 to be misunderstood when motion in three dimensions is con- 

 sidered. 



The term " Neoid " (vrjoecSr]?, ship-like) proposed in the pre- 

 vious paper as a general name for water-line curves in two di- 

 mensions, may be extended to all the stream-lines discussed in 

 the present paper ; for they are all applicable to certain lines on 

 the surface of a ship. 



* Communicated by the Author, having been read at the British Asso- 

 ciation Meeting, Bath, September 19, 1864. 



t An abstract of that previous investigation appeared in the Philoso- 

 phical Magazine for October 1863. 



