342 Sir W. Thomson on the Propagation of Laminar 



power of) error, abstraction faite du signe, is 



twice (Mean~square-of-error — (Mean-Error) 2 ) 

 Number of Observations 

 that is, here, 



2(6-4-4)-^-25878 = -00019. 



Whence the Modulus is about *014, while the observed ecart 

 is '4 — some thirty times larger. This gives odds of nonillions 

 to one against the First Exponential. The corresponding 

 odds against the Probability-curve are some hundreds to one. 



It should be observed that the sums of powers may be 

 taken for integral portions of the curve's extent, rather than 

 for the whole. This plan seems theoretically more correct, 

 since the fulfilment of the law of error is to be looked for 

 rather in the body of the curve than at the extremities. 

 There arise, however, practical difficulties about the compu- 

 tation in the case of some curves; in the absence of tables for 

 the values of \x*$(x)da:. The Probability-curve itself affords 

 an instance. 



Different modes of verification will be appropriate to 

 different cases. Bat it is not the purpose of this paper 

 to provide a complete Manual of empirical evidence; but 

 rather to show in what sort of way the examination of 

 experience may be assisted by the Mathematical Theory of 

 Errors and Method of Statistics. 



XLY. On the Propagation of Laminar Motion through a tur- 

 bulently moving Lnviscid Liquid. By Sir William Thomson, 

 LL.D., F.R.S* 



1. TN endeavouring to investigate turbulent motion of water 

 -«- between two fixed planes, for a promised communication 

 to Section A of the British Association at its coming Meeting 

 in Manchester, I have found something seemingly towards a 

 solution (many times tried for within the last twenty years) 

 of the problem to construct, by giving vortex motion to an 

 incompressible inviscid fluid, a medium which shall transmit 

 waves of laminar motion as the luminiferous aether transmits 

 waves of light. 



2. Let the fluid be unbounded on all sides, and let u, v, w 

 be the velocity-components, andp the pressure at (x, y, z, t). 

 We have 



du dv dw _ n , . 



dx + dy + Tz~^ (i) ' 



* Communicated by the Author, having been read before Section A of 

 the British Association at its recent Meeting in Manchester. 



