CHAPTER XV 



HELMHOLTZ IN BERLIN PHYSICAL RESEARCHES 

 CONTINUED 



IN 1868, Helmholtz pressed farther the analogy 

 between the equations of fluid motion and those 

 of electricity and heat in a paper on movements in 

 discontinuous fluids. He also endeavoured to account 

 for certain discrepancies that exist between theory 

 and experiment. He found that such discrepancies 

 are greatest in cases where the current enters a wide 

 space through an opening having sharp edges. In 

 such circumstances, discontinuity of the fluid occurs ; 

 it is, as it were, torn asunder, and a surface of separa- 

 tion is formed with rounded edges ; rupture will only 

 occur with increased velocity of the fluid. These 

 investigations have also a practical bearing on the 

 theory of the flow of water through cylindrical pipes, 

 and on the origin of rotational movements. In this 

 memoir, also, he showed the applications of several 

 formulae to electricity, in which the co-ordinates are 

 expressed as functions of the potential and its con- 

 jugate functions. For example, he discussed the case 



201 



