Intelligence and Miscellaneous Articles. 73 



It is also shown that if instead of the weight on the piston being 

 suddenly increased it were to be suddenly diminished, exactly analo- 

 gous results, mutatis mutandis^ would occur, — the effect of the sudden 

 removal of part of the weight being instantaneously to diminish the 

 pressure to a finite distance below the piston — such diminution having 

 its maximum immediately beneath the piston, and thence gradually 

 diminishing till, at a certain distance below the piston, the whole 

 pressure will be exactly the same as it was before any part of the 

 weight was removed. 



If the piston were wholly removed, the pressure of the air originally 

 in contact with it at the instant of removal would be zero. 



It is then shown that the addition to or diminution from the weight 

 on the piston in the case last considered will produce no immediate 

 change in the horizontal pressure in the air below the piston. 



It is next shown that in cases where there is no impressed velocity, 

 as in the case first considered in this paper, the instantaneous pres- 

 sure pi may be expressed in terms of its partial differential coefficients, 

 and of the density at the point where the pressure is being considered. 



It is also shown that, in the general case, where the whole or a 

 portion of the fluid is endued with velocity, the instantaneous pressure 

 may be ascertained by adding to the expression of the last paragraph 

 a term involving the density and the partial differential coefficients 

 of the velocity at the point where the pressure is being considered. 



It is finally shown that, in the case of the transmission of a pulse 

 through a cylindrical tube where the motions are small, the equation 

 of motion will be of this form, 



d 2 y _a 2 d 2 y _b 2 d 2 y , 

 dt 2 ' dx 2 dxdt 

 where x denotes the distance from the origin measured parallel to 

 the axis of a given stratum in the state of rest, y the same distance 

 at the time t, and a 2 and b 2 are constants, the value of a 2 being the 

 same as in the ordinary theory. 



As this equation leads to the conclusion that there are two veloci- 

 ties, it results that, except perhaps in very rare instances, in which a 

 duplication has been observed in sounds heard at very great distances, 

 the proposed correction of the theory of the motion of elastic fluids 

 will not practically affect the theory of sound. 



By the method adopted in the case of elastic fluids, the author 

 conceives himself to have established that, in what are commonly 

 termed inelastic fluids, the pressure during motion will not be equal 

 in all directions. 



XI. Intelligence and Miscellaneous Articles. 



BIOGRAPHICAL NOTICE OF THE LATE JOHN TAYLOR, ESQ., 

 F.R.S., F.G.S., ETC. 



MR. JOHN TAYLOR was the eldest of five sons of 

 Mr. John Taylor of Norwich, whose name is still held 

 in traditional respect in his native city, and in affectionate 



