144 



292. Further minor current components are to be anticipated be- 

 cause of the variation of the friction term, with the square of the 

 velocity; for, if the primary current components are: 



5 sin (m2^+|S), Bi sin (s2/+/3i), and so on, the friction term becomes: 



F=±[B sin (m2^+^)+5isin (s,/+/3i)+ . . . ?/C'r 



=^±{B'/C'r) sin^ {m2t+^)±{B,'IC'r) sin-^ (so^+jSO . . . (180) 



±{2BB,ICh) sin (m.^+Z?) sin (soZ+ft) . . . 



The terms in this expression for F which contain the squares of the 

 sines of functions of the speeds m2, S2, etc., afford components of the 

 friction term with speeds of the corresponding harmonic components, 

 and their over tides. The terms which contain the products 01 the 

 sines of functions of these speeds may be rephiced b}?- the algebraic 

 sum of the proper trigonom,etric functions of the sums and difference 

 of the angles, and hence of the speeds. Components of the friction 

 term,, and corresponding components of the current, with speeds which 

 are the sums and differences of the speeds of the principal tidal com.- 

 ponents, may therefore be anticipated. These may be term.ed 

 compound current components. 



293. The currents set up by tides of the mixed or of the diurnal 

 types should equally well be resolvable into components wdth the 

 speeds of the harmonic tidal components, together with overcurrents 

 and compound current components. Furthermore, in the propagation 

 of the tide through a long channel, the overcurrents and compound 

 currents may create corresponding overtides and compound tides. 



294. The mathematical relation between the com.ponents of the tide 

 and the componenets of the current, when frictional resistance must 

 be taken into consideration, does not appear to offer a profitable field 

 for investigation; but, as explained in chapter X, the component cur- 

 rents may be determined by an harmonic analysis of the observed 

 currents in a channel. 



