1863.] 



Dr. Rankine on Plane Water-Lines, 



15 



John Hall Gladstone, Esq., Ph.D. ; Joseph Dalton Hooker, M.D. ; Henry 

 Bence Jones, M.A., M.D. ; Prof. James Clerk Maxwell, M.A. ; Prof. Wil- 

 liam Pole, C.E. ; Archibald Smith, Esq., M.A. ; Prof. Henry J. Stephen 

 «mith, M.A. ; The Earl Stanhope, P.S.A., D.C.L. ; Prof. James Joseph 

 Sylvester, M.A. ; Thomas Watson, M.D., D.C.L. ; Prof. Charles Wheat- 

 stone, D.C.L. ; Rev. Prof. Robert Willis, M.A. 



The question of Captain Ibbetson's readmission into the Society was put 

 to the ballot, and, the ballot having been taken. Captain Ibbetson was 

 declared to be readmitted. 



The following communications were read : — 



L "Account of Magnetic Observations made between the years 1858 

 and 1861 inclusive_, in British Columbia, Washington Territory, 

 and Vancouver Island." By Captain R. W. Haig, R.A. Com- 

 municated by the President. Received November 4, 1863. 



(Abstract.) 



This paper contains the results of magnetic observations made between 

 the years 1858 and 1861 inclusive, in British Columbia, Washington 

 Territory, and Vancouver Island. The results are tabulated ; and from 

 them the direction and position of the lines of equal dip, total force, and 

 declination or variation are determined. 



Three maps at the end show the position of these lines, the stations of 

 observation, and the observed values of the three magnetic elements at 

 each station. 



II. " On Plane Water-Lin es.'' By W. J. Macquorn Rankine, C.E., 

 LL.D., E.R.SS.L. & E., Assoc. Inst. N.A., &c. Received July 28, 

 1863. 



(Abstract.) 



1. 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 displace- 

 ments 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 pur- 

 poses*. 



2. The author refers to the researches of Professor Stokes (Camb. Trans. 

 1842), "On the Steady Motion of an Incompressible Fluid," and of Pro- 



* As water-line curves have at present no single word to designate them in mathe- 

 matical language, it is proposed to call them Neoids, from vijbs, the Ionic genitive of 

 vavs. 



