Mr Taylor, Tides in the Bristol Channel 



321 



Let Jiq be the mean depth and Bq the breadth of a section at 

 distance Xq from the head of the channel. Then 



h = hQx/xQ, b = bQx[xQ. 

 Inserting these values in (1) the equation becomes 



where A; = a%/% (^)- 



Putting z^ = kx,^ = -qz, this equation becomes 



The solution of this is ^ =^ AJ^ {2z), where J^ represents a Bessel's 

 Function of the first order. Replacing the origmal variables the 



solution becomes ,,,-,. /a\ 



r^ = KJj_{2V{kx)}IVikx) (4), 



where Z is a constant. 



Comparison with tidal observations in the Bristol Channel. 



For this purpose a chart of the Bristol Channel was taken and 

 a curved line was drawn down the middle of the channel (see fig. 1). 



Sections A, B, C, D, E, F, G were taken at convenient points 

 and roughly at right angles to the centre line. These sections are 

 shown on the sketch chart (fig. 1). The breadth b, and mean depth 

 h of the channel at low water at each of these sections was found 

 The distance x of its mid-point from the head of the channel 

 down the curved line was also measured. The figures so obtained 

 are given in Table I. The head of the channel was taken as being 

 at Portishead, near Bristol. 



Table I. 



Dimensions of Bristol Channel at various sections. 



Section 



A 

 B 

 C 

 D 

 E 

 F 

 G 



Distance 



from Portishead, 



miles 



61-7 



49-7 



42 



25 



15-5 



8 







Two diagrams were then drawn showing the relationship 

 between 6 and x, and between h and x. These are shown m figs. 2 



