Mr. W. J. M. Rankine on Plane Water-lines, 303 



black or white ground than white lines on a black ground, or 

 black on white. 



The faculty of perceiving what we see is one which depends so 

 much upon practice, that any observer, however critical he may 

 be in other observations, is not unlikely to fail in his first attempts 

 to ascertain what are the peculiarities of his own vision in respect 

 to some of the particulars indicated in the above experiments. 

 The habit of careful scrutiny of objects in focus does not facili- 

 tate our perception of the impressions produced by focal and 

 chromatic aberrations in objects under abnormal circumstances. 

 In all experiments upon vision, it is necessary for us to remember 

 that the impression produced upon the retinas differs from the 

 impression produced upon the mind in many important particu- 

 lars, though in how many it is difficult to say. 



11 Grey Street, Newcastle-upon-Tyne, 

 August 1863. 



XLIII. Abstract of an Investigation on Plane Water-lines. By 

 W. J. Macquorn Rankine, C.E., LL.D., F.R.SS.L. § E.$c* 



[With a Plate.] 

 1. PT^HIS paper contains an abstract of a mathematical inves- 

 -■- tigation which has been communicated in detail to the 

 Royal Society. By the term " plane water-line " is meant one 

 of those curves which a particle of a liquid describes in flowing 

 past a solid body, when such flow takes place in plane layers. 

 Such curves are suitable for the water-lines of a ship ; for during 

 the motion of a well-formed ship, the vertical displacements of 

 the particles of water are small compared with the dimensions 

 of the ship ; so that the assumption that the flow takes place in 

 plane layers, though not absolutely true, is sufficiently near the 

 truth for practical purposes f. 



2. The author refers to the researches of Professor Stokes 

 (Camb. Trans. 1842) "On the Steady Motion of an Incom- 

 pressible Fluid/' and of Professor William Thomson (made in 

 1858, but not yet published), as containing the demonstration 

 of the general principles of the flow of a liquid past a solid body J. 



3. Every figure of a solid, past which a liquid is capable of 

 flowing smoothly, generates an endless series of water-lines, 



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

 ciation at Newcastle-upon-Tyne in August 1863. 



•j* As water-line curves have at present no single word to designate them 

 in mathematical language, it is proposed to call them Neoids, from vtjos, 

 the Ionic genitive of vavs. 



t See also a paper by Dr. Hoppe, in the * Quarterly Journal of Mathe- 

 tics' for March 1856. 



