The inertia and drag coeffi cien ts o f cylinders and plates in simple sinusoidal c urrents are investigated. The midsection of a rectangu lar basin wi t h standing wa ves s urg ing ill it is selected as t he locale of curren ts. The cyl inde rs and plates are fi xed hori zontally a nd below t h e water surface. The average values of t he inertia and d rag coefficients over a wave cycle sh ow variations wh e n the intensity of t he current and t he s ize of th e cylinders or plates a re ch anged. These variation s, h owever, can be correlated wi t h t h e p eriod parameter Um TI D, where U m is th e maximum intensity of t he sinusoidal c urrent, T is the p eriod of t he wave a nd D is t he di am eter of t he cylinder or t he width of the plate. For t he cylinders UmTI D eq ua ling 15 is a c ri tical rond ition y ielding t he lowest va lu e of t he inertia coefficient a nd th e largest valu e of t he drag coe ffic ie11t. For t he plates t he higher values of t he drag coefficie nt are assoc iated with t he small er va. lu es of Um TI D a nd t he higher valu es of t he mass coe ffici e nt wi t h t he larger valu es of Um TI D . The variatio n of th e coefficients with t he phase of t h e wa ve is examin ed a nd the bearing of t hi s o n t he formul a for the fo rces is disc ussed. The flow patterns aro und t he cylinde rs a nd plates a re examined photographically, a nd a s uggestion is advan ced as to t he physical m eaning of the parameter Um TI D.

The comp lex p ote ntial of t wo cylinders mo ving in an infi n it e li q uid is determ in ed b y the m et hod of image do uble ts, a nd t he solution is exp ressed as an infin ite series in rectangular coordin ates. App roxima te solutions in fi n ite form are g iven for vari ous cases. A met hod for generali zing t h e solution for t he ease of more than two cylind er s is indicated . Applications to t he fl ow i ndn ced b y a cylinder movi n~ in t he p rese nce of p]n,ne bound aries are given a nd t he st ream lines are illustrated in certai n cases.

Thc di s tur?ance .created at the inte~'face o~ a two-lay~r liquid system by the horizontal motIOn of a cy l~nd~r In th~ upper lay~r IS studIed for vanous sizes a nd shapes of cylinders, depths of the hqlllds, cyllllder velO CItIes, and d ensity ratios. The disturbances fall into thrce categori es. First, when the layers are of equal thickness in most cases a train of progressi ve o.scillatory waves is produced at the interface. Seco;ld, when the d epth of the d e nscr layer IS much less than the d epth of the fres h-water layer, the profile of th e interface us ua lly resembles that corresponding to positive internal solitary waves. Third, when the d e pt h of the denser layer IS much greater than the d epth of the fr esh-water layer in most cases an internal hydra ulic jump is produced. The characteristics of the di sturbances in ea~h category a!'e related to t he size of the cylinder, the d epths of the liquids, the cylinder velOCIty, the denSIty ratIO, a nd the total distance of travel of the cylinder. A t heoretical a nalysis is gi ven for disturbances of the first category.

Recent development of the global plate motion indicates that changes in the products of inertia of the earth due to tectonic plate movement may provide a secular shift of the mean pole. In this paper we present a mathematical procedure for calculating this shift based on the plate theory. Explicit expressions are obtained for the dependence of the secular polar shift on the dimensions and locations of the plate boundaries. Numerical results show that the secular motion of the mean pole is 0.0002″ yr−1 in the direction of 67°W. Hence it is deduced that the influence of the plate motion on the secular polar shift may account for 10% of the observed value.

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