277] 



TIDAL FRICTION. 



501 



Since in these expressions n't + x/a 4- e measures the hour-angle 

 of the moon past the meridian of any point (x) on the canal, it 

 appears that high-water will follow the moon's transit at an in- 

 terval ti given by n't^ = %. 



If c 2 < rc/ 2 a 2 , or h/a < n' 2 a/g, we should in the case of infinitesimal 

 friction have ^ = 90, i.e. the tides would be inverted (cf. Art. 178). 

 With sensible friction, % will lie between 90 and 45, and the 

 time of high-water is accelerated by the time-equivalent of the 

 angle 90 - %. 



On the other hand, when h/a > n' 2 a/g, so that in the absence of 

 friction the tides would be direct, the value of ^ lies between 

 and 45, and the time of high-water is retarded by the time- 

 equivalent of this angle. 



The figures shew the two cases. The letters M t M' indicate the positions 

 of the moon and ' anti-moon ' (see p. 365) supposed situate in the plane of the 

 equator, and the curved arrows shew the direction of the earth's rotation. 



It is evident that in each case the attraction of the disturbing 



