October i8, 1894J 



NA TURE 



597 



ON THE DOCTRINE OF VISCONTINUITY OF 

 FLUID MOTION, IN CONNECTION WITH 

 THE RESISTANCE AGAINST A SOLID 

 MOVING THROUGH A FLUID} 



IV. 



§ 25. A NOTHER decisive demonstration that the 

 ^^ doctrine of discontinuity is very far from 

 an approximation to the truth, is afforded, in an exceed- 

 ingly interesting and instructive manner, by Dines' obser- 

 vations of the pressures on the two sides of a disk held at 



dead 



""ff^ 



dead i<J 



a^-^' 



+ ni 

 "t'urVu'unt ,„ 



,t ' 



ot ; 



V\^. 2. 



right angles to a relative wind of 60 statute miles per hour 

 (88 ft. per sec), produced by carrying it round at the end 

 of the revolving arm of his machine. The observations 

 were described in a communication to the Royal Meteoro- 

 logical Society in May 1890. In his paper of June of 

 the same year, in the Royal Society Proceedings already 

 referred to, he states the results, which are, that at the 

 middle of the front side an augmentation of pressure, 

 and at the middle of the rear side a diminution of pres- 



it at the rate of 88 feet per second. The latter shows 

 that there is a " suction " at the centre of the rear side 

 very nearly equil to half the augmentation of pressure on 

 the front ; instead of there being neither suction nor 

 augmented pressure as taught in the doctrine of dis- 

 continuity ! 



§ 26. The accompanying diagrams (2, 3,4, 5) represent 

 several illustrations of the doctrine of discontinuity in the 

 motion of an inviscid fluid, less attractive to writers on 

 mathematical hydrokineiicsthanihat represented in Fig. :, 

 (whether as it stands, or varied to suit oblique incidence;, 

 because each is instantly soluble without 

 mathematical analysis, and they do not, 

 like it in the two-dimensional case, con- 

 stitute illustrations of the beautiful mathe- 

 matical method for finding surfaces of 

 constant fluid velocity in prolongation of 

 given surfaces along which the velocity 

 is not constant, originated by Helm- 

 holtz,' developed in a mathematically 

 most interesting manner by Kirchotf,- 

 and validly applied to the theory of the 

 "vena contracta" by Rayleigh.- 



§ 27. A cylindric jet (not necessarily 

 of circular cross-section; issuing from a 

 tube with sharp edge, into a -ery large 

 volume of fluid of the same density as 

 that of the jet, is represented in Fig. 2. 

 This case was carefully considered by 

 Helmhollz,^ both for the ideal inviscid 

 incompressible fluid and for real water 

 or real air. He gave good reason for 

 believing that, with real water or real 

 air, and at distances from the mouth as 

 great as several times the diameter of 

 the tube (or the least diameter, if it 

 is not of circular cross section) the surrounding fluid is 

 nearly at rest, and the jet is but little disturbed from 

 the kind of motion it had in passing out of the tube ; and 

 therefore that the eftlu.x is nearly the same as, other 

 circumstances the same, it would be if the atmosphere 

 into which the jet is discharged were inertia-less. This 

 conclusion, which is of great importance in practical 

 hydraulics, has been confirmed by careful experiments 

 made eight years ago in the physical laboratory of the 



'V, 



Fig. 3- 



B ^ — -— ,/./ ,E,,^,. 

 ////////y/////y//////2> 



FlC. 4. 



w wfmwM . 



M 



dead water 



dpad water 



B 



M 



Fig. 5- 



sure, measured respectively by f82 /and •89 /of water, 

 were found. These correspond to heads of air, of density 

 1, 800 of that of water, equal respectively to 121 .\ and 

 59J feet. The former is in almost e.xact accordance with 

 rigorous mathematical theory for an inviscid incompres- 

 sible fluid; which gives 88 644, or 122/, feet for the 

 depth corresponding to the pressure at the water-shed 

 point or points, of a solid of any shape moving through 



' Coiuinued from p.lge 575. 



NO. 1303, VOL. 50I 



University of Glasgow by two young officers of the 

 .\inerican Navy, Mr. Capps and the late Mr. Hewes. 

 I believe it has been tested and confirmed by other 

 experimenters. 



§ 28. The very simplest application of the doctrine of 

 discontinuity to the theory of the resistance of fluids to 



1 " Wis5«nsch.iflliche .\bhandlungen,'* vol. i. pp. 153-156. 



- " Vorlesungen uber Mathematischc Physik, ' vol. xxi. 



■• " Notes on Hydrotyn-^tnics," /'/;//. .\tat:- i3;6, second half-year. 



* " Wiss. Abh.," vol. i. pp. 153-153. 



