The Representation of Oceanic Movements and Kinematics 353 



in the present case that the remaining current was indeed very regular but still included 

 a weak periodic disturbance of about 1 7 h. Since it was not improbable that a wave 

 of this type could occur in such current measurements (inertia oscillation) this wave 

 was also eliminated by taking means again over a 17 h period.* Finally, the basic 

 current remains. It has been plotted in Fig. 146 for both components. It changes only 

 slightly with time; the A^-component gradually decreases from 10 to about —4 cm/sec 

 and then remains almost constant, the ^'-component changes from —12 to —17 

 cm/sec. 



A more detailed analysis of the periodic components can be made by ordinary 

 harmonic analysis and gives the following equations {t in hours) : 



7.TT Iv 



TV-component: +6-6 cos .- (/ — 17-6 h) + 4-6 cos j^{t — 2-3 h) 



277 , 



+ 6-0 cos yj(t - 12-6h). 

 S'-component: +2-7 cos i^{t - 20-4 h) + 3-8 cos -r^ (^ - 5-2h) 



l-rr 



+ 5-3 cos ynit - 0-Oh). 



The time ? = corresponds thereby rather accurately to 3 moon hours before the 

 moon passes the meridian at Greenwich (17 June, 1938). The ampUtudes are given in 

 cm/sec. All three waves show almost the same amplitude; the inertia wave also is 

 quite pronounced and, as can be expected from this, can become quite visible in the 

 current. Calculations of the current from both components obtained by the harmonic 

 analysis, and in addition the basic current of the curves presented in Fig. 146, follow 

 the observed values very satisfactorily. However, the differences between the smoothed 

 curves and the observations show that the current measurement is subject to manifold 

 disturbances which are very largely random (or observational errors). 



From the smoothed mean values for a full period of the single waves current 

 diagrams can be constructed and can be compared with the current ellipses which 

 were calculated from the harmonic values. The left-hand side of Fig. 147 shows this 

 comparison for the semidiurnal tide and on the right-hand side for the 17 h inertia 

 wave. The smoothing of the subsequent values by harmonic analysis is rather obvious 



* For a curve y formed by the superposition of two harmonic waves of different periods T^ and 

 T2 which has the form 



y = acos"^ U - ej) + 6 cos -^ (/ - eg) 

 ^1 -'2 



if a continuous mean is taken over the period T^ the Tg-wave will disappear completely and there will 

 be left 



y = ^\ y dt = a —^ sm -;^^ cos ~ (/ - ^i). 



The amplitude is changed, but not the period and the phase of the T^ wave. If Tj is 17 h and T^ is 

 24 h then the amplitude of the 17 h wave which was previously a will now be —Q-lla, that is, the 

 Tj-wave is now inverse to the original wave and its amplitude is almost five times less than before. 



2A 



