382 Prof. J. Thomson on Flux and Reflux of Water 



infinite result is not easily understood, as regards its deve- 

 lopment. 



But the development of infinitely great magnetic force by 

 a plane sheet of/ is very easily followed in full detail, not 

 merely with sinusoidal/, but with/ constant. Considering 

 the latter case, the emission of H is continuous, as before 

 described, from the surface of/. Now place a plane infinitely 

 conducting barrier parallel to/, say on the left side. We at 

 once stop the disturbances going to the left and send them 

 back again, unchanged as regards H, reversed as regards E. 

 The H disturbance on the left side of / therefore commences 

 to be doubled after the time a/v has elapsed, a being the dis- 

 tance of the reflecting barrier from the plane of/, and on the 

 right side after the interval 2a/v. Next, put a second infi- 

 nitely conducting barrier on the right side of /. It also 

 doubles the H disturbances as they arrive ; so that, by the 

 inclusion of the plane of / between impermeable barriers, 

 combined with the continuous emission of H, the magnetic 

 disturbance mounts up infinitely, in a manner which may be 

 graphically followed with ease. Similarly, with / alternating, 

 at particular frequencies depending upon the distances of the 

 two barriers from/. 



Returning to the spherical case, an infinitely conducting 

 internal screen, with no external, produces 



R (u a w '-w a u <)(u-w a ) 



Hv(w '—u r ) J v ' 



We cannot produce infinite H in this case, because the 

 absence of an external barrier will not let it accumulate. 

 Shifting the surface of / right up to the screen, or vice versa, 

 simplifies matters greatly, reducing to the case of § 42. 



May 8th, 1888. 



XL. On Flux and Reflux of Water in Open Channels or in 

 Pipes or other Ducts. By Professor James Thomson, 

 LL.D., F.R.S* 



IN the autumn of 1872 I was staying at a place named 

 Castlerock, on the north coast of Ireland, between the 

 mouth of the Bann River and the entrance to Lough Foyle. 



* Communicated by the Author, having been read in the British 

 Association Meeting at Bath, 1888, Section A. 



