TBANSACTIONS OP SECTION A. 583 



tlie normals to the surfaces of junction of the media are parallel to the impulses in 

 the first polygon or to the applied forces in the second. 



The angles of the three polygons are thus similarly divided by the lines which 

 are drawn one at each angle. Call the two parts into which one of the angles is 

 divided a and a', one being acute and the other obtuse. 



In the first polygon, since the component velocity perpendicular to the impulse 

 remains unchanged, we have 



t) sin a = v' sin a', 



V and v' denoting the velocities before and after an impulse. 



In the second polygon, since the applied force at any corner is balanced by tha 

 two tensions T, T' of the two portions of string which meet there, we have 



T sin a = T' sin a'. 



In the third polygon the law of sines in refraction gives 



/i sin a = jx' sin a'. 



Hence we have 



V _ T _ fi. _ sin a' 



v' " T ~ / ""sin"^' 



The changes in v, T, and /x are therefore proportional when we pass from any side 

 to the next. 



4. On the Stretcliing of Liquids. 

 By Professor A. M. Worthington, M.A., F.B.A.S. 



The author described the three methods that have been employed by previous 

 observers to subject a liquid to tension. These are : — ■ 



(1) The barometer tube method, by which Professor Osborne Eeynolds had 



succeeded in subjecting mercury to a tension of five or six atmospheres 

 due to its own weight. 



(2) The centrifugal method, devised by the same observer, and by means of 



which he had subjected water to a pull of about five atmospheres 

 (72'5 lbs. per square inch) ; while the author had succeeded in reach- 

 ing with alcohol a tension of 7-9 atmospheres, or 116 lbs. per square 

 inch, and with strong sulphuric acid a tension of ll'S atmospheres, or 

 173'4 lbs. per square inch. 



(3) The method of cooling, discovered by Berthelot, and described by him, 



' Ann. de Chimie ' xxx. (1850) : Sur la dilatation forcee des liquides. 



In this method a liquid deprived of air by boiling nearly fills a very strong 

 closed glass tube. On slight heating it expands and fills the whole tube, com- 

 pressing the residual air, which dissolves under the increasing pressure and finally 

 disappears. The liquid may now be greatly cooled, but remains extended, filhng 

 the whole tube, of which at last it lets go its hold with a violent ' click,' and the 

 bubble of residual air and vapour reappears. , 



By this means Berthelot succeeded in stretching water by about y-J^ of its 

 whole volume, alcohol by about ^^, and ether by about ^ ; and the author learns 

 that Berthelot's experiments were repeated with even higher results by Mr. Creel- 

 man in Professor Tait's laboratory in Edinburgh. . 



Reasons were given for believing that the rupture is in no case due to the hmit 

 of the cohesion having been reached, but rather to the imperfect adhesion of the 

 liquid to the walls of the vessel, owing to the presence of air, either in a film or in 

 microscopic cavities. The effect of long boiling is to get rid of this adherent air, 

 and the apparent increase in the cohesion is to be attributed rather to this cause 

 than the liberation of air from solution. 



The author then described the form of apparatus arrived at after many trials, 

 by which the tension of the liquid and the extension produced by it could be 

 simultaneously measured. 



