104' Mr. A. W. Hobson oti the Equation 



chemical action of an acid solution on a metal gives signs of 

 electrical disturbance on the condenser; the physical force of 

 magnetism produces by induction an instantaneous disturb- 

 ance in the natural electrical fluid of a metallic wire, without 

 setting it in a continuous current. But when two forces are in 

 action, one of which is capable of disturbing the natural elec- 

 tricity of the ponderable matter, and the other of evolving it 

 from the integrant molecules of the same, that fluid may be 

 set into a continuous current in a complete circuit. Notwith- 

 standing the appearance of truth in this mode of explaining 

 the phfenomenon of the continuous electric current, there are 

 some facts which merit a deeper investigation, aided by expe- 

 riment, before assigning it as the just cause of this phaeno- 

 menon. A voltaic pair composed of two different metals, for 

 example, gives an electric current in a given direction when 

 it is immersed in one liquid, and the direction may be inverted 

 when another different liquid is substituted for the first. The 

 examination of facts of this kind will probably furnish ma- 

 terials for a second note. 



XXII. On the Equation of Cojitinuity in Fluid Motion, By 

 Alfred William Hobson, B.A. St. John's College, Cam- 

 bridge*. 

 ''■"'HE proof of this equation given by the various authors 

 -■- of treatises on hydrodynamics is the same in all; in fact 

 nearly evei'y writer since Poisson has contented himself with 

 a mere translation of his words in art. 648 of his Traile de 

 Mecanique. As however 1 do not remember to have seen 

 anywhere a statement of the reasons for the assumption from 

 which the equation is obtained, the following investigation may 

 be interesting to some, especially as the equation itself is found 

 by a much shorter process than the usual one, and unencum- 

 bered with several steps which are perhaps not quite satisfac- 

 tory to those reading the common method for the first time. 



The fluid is supposed to be divided into small portions or 

 ' elements,' each of which is acted upon by accelerating forces 

 X, Y, Z parallel to the coordinate axes. The first thing to be 

 remarked is that X, Y, Z must be the same yb?- the whole ex- 

 ic7it of the element on which they are su]iposed to act, i. e. 

 we must take the element so small that there is no variation 

 in either X, Y or Z in passing from any one of its parts to 

 another. Now since these forces are considered as functions 

 of (.r, y, z) varying for any, the sliglitest variation in either .r, 

 y or ;;, it is plain that if we consider the forces mathematically 

 * Communicated by the Author. 



