792 REPOBT— 1898. 



4. Stream Line Motion with Viscous Fluids in tioo Dimensions, and in 

 three Dimensions. By Professor H. S. Hele-Siiaw, LL.D. See 

 Reports, p. 136. 



5. Mathematical Proof of the Identity of the Stream Lines obtained by 

 means of a Viscous Film witlb those of a Perfect Fluid moving in tivo 

 Dimensions. By Sir G. G. Stokes, F.R.S. See Reports, p. 143. 



6. On Graphic Rejjresentations of the tivo simplest cases of a Single Wave : 

 (a) Condensational-raref actional, (b) Distortional. By Lord Kelvin, 

 G.C.V.O. 



For the simplest possible elementary wave of condensation and rarefaction, 

 begin with an infinitely thin spherical shell containing air 1 per cent, denser than 

 the air around it, and let the resistance of the shell be suddenly annulled, i'or 

 the simplest possible elementary distortional wave, begin with a globular portion 

 in the interior of a large homogeneous elastic solid, with proper application of 

 tangential force to keep it turned round any diameter through half a degree of 

 angle from its position of undisturbed equilibrium, and let the disturbing force be 

 suddenly annulled. 



Diagrams weie exhibited to the Section by aid nf which all the details of the 

 two kinds of discontinuous wave thus produced were fully explained. 



7. A JS'eiv Method of Describing Cycloidal and other Curves. 

 By Professor H. S. Hele-Shaw, LL.D. 



A brief description of the instrument by which the curves are obtained was given. 

 The instrument is described at length, together with certain of its practical appli- 

 cations, in a paper read before Section G, an earlier form having been shown in 

 May of the present year at the Royal Society Soiree, although no printed description 

 of it has hitherto appeared. 



The essential points are : — 



(1) The employment of auxiliary circles instead of the actual pitch circles of 

 two sheets of cardboard which turn in connection with each other. 



(2) A method by which the actual axis of rotation for each sheet is dispensed 

 with, virtual axes only being employed. 



By means of this instrument the describing pen or pencil used to mark out 

 the cycloidal or involute curve can be made to draw the complete curve instead of 

 only a portion of it as obtained by the ordinary methods, while the use of the 

 virtual centres enables circles of any diameter to be employed, since it is no longer 

 necessary to have a ti.xed centre lor the cardboard within the limited range of a 

 drawing-board or drawing-table. Hence, in the hmit, the cycloid itself in which 

 the circle rolls along a straight line, or an involute curve when the straight line 

 rolls on a circle can be obtained, as well as ordinary epicycloidal and hypocycloidal 

 curves, and the methods in which these curves are obtained are illustrated, as well 

 as the rules for the adjustment of the instrument for any required conditions. 



Since one well-known method of describing an ellipse is by means of a point 

 attached to a circle rolling within another of twice its diameter, it is obvious that 

 this instrument, the essential principle of which is the rolling of two imaginary 

 pitch circles upon each other, can be applied to draw ellipses of any required 

 eccentricity or magnitude. 



Finally, the second feature of the new instrument above referred to, and which 

 the author believes to be new, enables centres of curvature of two surfaces 

 revolving on each other to be continuously varied. 



The instrument was brought before the Section because it appears to offer to 



