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Zab (j), ». a war spear.

zauber, n. a wave, breakers.

zazer, zarazer, zager, a. white.

zerem (m), n. a cross.

zewar, n. a land crab.

zi (j), n. the mangrove.

ziai, n. the south west; ziai pek, S.S.W.

ziau, n. the dura-mater. Paper is called ziau-wali or jiauwali, "jauali" of service book, etc. (wali = calico, cloth), as it is the wali which resembles the dura-mater. Owing to their familiarity with corpses (making mummies, etc.), the natives were well acquainted with the parchment-like character of the outer membranous covering of the brain.

zigerziger, a. thorny, prickly.

ziru, a. cold.

ziz, n. a wound.

zogo, n. a fetish, charm, an oracle (possibly also a totem, cf. agud);

hence, sacred, holy; zogo jiauali, Bible; zogo meta, a church, zogoem, v. to sanctify.

zogole, n. the temporary sacred men who divine with any particular zogo, or the three chief men of the initiation ceremonies (used in the Gospels for " priest").

zogozogo, a. tabu, sacred, hence holy.

zole, w. a fire-charm in the shape of a roughly fashioned, crouching,

pregnant woman in stone, zor (j), dead coral.

zorom, a. bright, shining, like reflection of sun on water; hence, glory.

zoromzorom, a. shining.

zup, n. a bamboo tobacco pipe.

zug.

zurkagem (m), a. round.

Part II. of this ' Study' will be published in the next Volume of the Pretetdiusi, and will contain: vin. Sketch of Saibui Grammar: Ix. Specimens of the Saibai Language: x Saibai-English Vocabulary: xi. Sketch of the Daudai Grammar: xu. Specimens of the Daudai Language: xm. Daudai-Engliih Vocabulary: Xit. Native Names of people and places in Torres Straits: xv. A List of Intro•duced and Adapted Words: xvi. Concluding Remarks.

XXXII.

ON A PROBLEM IN VORTEX MOTION. Br "FRANCIS ALEXANDER TARLETON, Sc.D., LL.D., F.T.C.D.

[Read Dbcembbr 12, 1892.]

If a perfect liquid, extending in all directions to infinity, be in motion under the influence of two parallel rectilinear vortices of small section and infinite length whose strengths are equal and opposite, the motion will take place in planes perpendicular to the axes of the vortices ; and the lines of flow in one of these planes will (as is well known) he a system of coaxal circles having as their limiting points the intersections of the plane with the vortex axes. From hence it has been concluded that, if a single rectilinear vortex of small section exist in a liquid bounded by a parallel circular cylinder, the motion of the liquid will be that due to the given vortex A, together with another parallel vortex of equal and opposite strength, passing through the point which is the inverse with respect to the circular section of the cylinder of the intersection of A with the plane of this section.

When the liquid whose motion is under consideration is contained within the rigid cylinder, the inference above is correct; but it seems to have hitherto escaped the attention of mathematicians that, in the case of a liquid extending to infinity, and bounded internally by a rigid cylinder, the conditions of the problem are not satisfied by a motion such as has been described. In order to see this, let us suppose that, at first, a single rectilinear vortex exists in an infinite liquid unbounded in every direction. The current function due to the vortex will then be given by the equation i]/ = -m log r, where 7i7» is the strength of the vortex, and r the distance of any point in the plane of motion from the point A in which it is met by the vortex axis. Let us now suppose that a circular cylinder of liquid parallel to the vortex becomes rigidified, and let us inquire how the motion of the remaining liquid is thereby affected. In the first place, the current function in the new state of motion must be constant at all points of the circle 8 bounding the section of the cylinder in the plane of motion. This. condition is fulfilled by supposing the motion to be the same as that due to the effect of the given vortex along with another of strength - rrm situated at the point B, which is the inverse or electrical image of A in the circle S. The current function at any point P is then

i BP

and this is constant when P is on the circle.

Up to the present time it seems to have been supposed that the condition above is sufficient. This, however, is not the case; for we have no warrant for asserting that there can be only one function of the co-ordinates which differs by a constant from m log AP at each point of S, is constant at infinity, and satisfies Laplace's equation throughout the field of motion. On the other hand, there is another condition which the motion must satisfy, which apparently has been hitherto overlooked.

"When a cylinder of liquid is rigidified, the only immediate effect on the surrounding liquid is an impulsive pressure at each point of the cylindrical boundary. Such a pressure will produce an additional velocity potential in the moving liquid; and the essential character of a velocity potential so produced is that it should have only one value at each point of the field—in other words, be acyclic throughout the field, though not necessarily a single valued function. Hence it follows that the circulation in every circuit throughout the field outside the cylinder must remain unaltered by its rigidification.

BP

The function m log —=, when taken as the current function, does

not satisfy the condition now mentioned, and hence cannot be the current function. In fact, in order to get the motion of the liquid outside the cylinder, we must suppose this motion to be that due to the original vortex at A, along with a vortex of equal and opposite strength at B, and a third vortex, of the same strength as that of the original one, placed at the centre C of the circle 8.

The current function is then given by the equation

BP
<l/ = mlog -j-p- m log CP,

and all the conditions of the question are satisfied.

It is easy to see now that we have obtained the only possible correct solution of the problem.

In fact, we know by Green's theorem that, disregarding a constant, there can be only one function of the co-ordinates which satisfies the equation ^<j> = 0 and is acyclic throughout the field, and whose differential coefficient along the normal is given at each point of the circle S, and also at infinity. Now the velocity potential correspond

HP

ing to the current function m log -^= satisfies all the specified condi

tions, and is therefore the only function which does. Hence the state of motion supposed is the only possible state of motion satisfying the conditions of the problem.

The case of a circular cylinder has been considered at length; but it is obvious that whatever be the form of the curve bounding the section of the cylinder in the plane of motion, the current function roust be constant along this curve, and such that the corresponding circulation in every circuit throughout the field of motion is the same as that due to the actually existing vortex which causes the motion.

By these two conditions the motion of the liquid is determined in all cases in which it is due to a rectilinear vortex of infinite length and small section, situated in a liquid extending to infinity, and containing a fixed rigid cylinder of infinite length parallel to the vortex

XXXIII.

NOTES ON THE CORRELATION OF THE LATER AND POST-
PLIOCENE TERTIA.RIES ON EITHER SIDE OF THE
IRISH SEA, WITH A REFERENCE TO THE FAUNA
OF THE ST. ERTH VALLEY, CORNWALL. Br ALFRED
BELL.

[communicated BY DB. Scharff.]
[Read Noyembek 14, 1892.]

With the exception of the country bordering the western end of the Caledonian canal crossing Scotland, there is very little possibility of the discovery of fresh deposits of later Tertiary age in the United Kingdom. So many specialists having taken part in the investigation of the faunas of the different members of this group, a fairly comprehensive view of the whole is now available for study; and a comparison and correlation of the various organic assemblages may suggest some lines of research as to the course of events that have led to the delimitation and configuration of this portion of the earth's surface.

The fauna of the Post-Pliocenes is larger than is generally supposed, a brief summary of a catalogue compiled during some yearspast from all available sources presenting the following results:—

[table][merged small][merged small]
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