492 PROFESSOR TAIT ON 



Though the present communication is thus specially devoted to some curio us 

 phenomena observed in the game of golf, it contains a great deal which has more 

 extended application : — to which its results can easily be adapted by mere numerical 

 alterations in the data. Therefore I venture to consider its subject as one suitable for 

 discussion before a scientific Society. 



In my short sketch of the history of the problem I failed to notice either of two 

 comparatively recent papers whose contents are at least somewhat closely connected 

 with it. These I will now very briefly consider. 



The first is by Clerk-Maxwell* " On a particular Case of the Descent of a Heavy 

 Body in a Resisting Medium." The body is a flat rectangular slip of paper, falling with 

 its longer edges horizontal. It is observed to rotate about an axis parallel to these 

 edges, and to fall in an oblique direction. The motion soon becomes approximately 

 regular ; and the deflection of the path from the vertical is to the side towards which 

 the (temporarily) lower edge of the paper slip is being transferred by the rotation. 

 [When the rectangle is not very exact, or the longer edges not quite horizontal, or the 

 slip slightly curved, the appearance, especially when there is bright sunlight, is often 

 like a spiral stair-case.] Maxwell examines experimentally the distribution of currents, 

 and consequently of pressure, about a non-rotating plane upon which a fluid plays 

 obliquely ; and shows that when the paper is rotating the consequent modification of 

 this distribution of pressure tends to maintain the rotation. The reasoning throughout 

 is somewhat difficult to follow, and the circumstances of the slip are very different from 

 those of a ball : — but the direction of the deflection from the unresisted path is always 

 in agreement with the statement made by Newton. 



Much more intimately connected with our work is a paper by Lord RAYLEiGHt 

 " On the Irregular Flight of a Tennis Ball," in which the " true explanation " of the 

 curved path is attributed to Prof. Magnus. The author points out that, in general, the 

 statement that the pressure is least where the speed is greatest, is true only of perfect 

 fluids unacted on by external forces ; whereas in the present case the whirlpool motion 

 is directly due to friction. But he suggests the idea of short blades projecting from the 

 ball, the pressure on each of which is shared by the contiguous portion of the spherical 

 surface. Here we have practically Newton's explanation — i.e. the " pressing and beating 

 of the contiguous air." Lord Rayleigh's paper contains an investigation of the form of 

 the stream-lines when a perfect fluid circulates (without molecular rotation) round a 

 cylinder, its motion at an infinite distance having uniform velocity in a direction per- 

 pendicular to the axis of the cylinder. And it is shown that the resultant pressure. 

 perpendicular to the general velocity of the stream, has its magnitude proportional alike 

 to that velocity and to the velocity of circulation. [There are some comments on this 

 paper, by Prof. Greenhill, in the ninth volume of the journal referred to.] 



* Cambridge and Dublin Mathematical Journal, ix. 145 (1854). 

 t Messenger of Mathematics, vii. 14 (1878). 



