Sept. 2 2, 1887] 



NATURE 



503 



This question was very skilfully treated by Magnus in 1852. 

 He showed by experiment that, when a rotating sphere is ex- 

 posed to a current of air whose direction is perpendicular to the 

 axis of rotation, the side of the sphere which is advancing to 

 meet the current is subject to greater pressure than is that which 

 is moving in the direction of the current. This difference of 

 pressures tends to make the sphere move in a direction perpen- 

 dicular at once to the current and to the axis of rotation— the 

 direction, in fact, in which the part of the sphere facing the 

 current is being displaced. But it is a matter of no consequence 

 whether the current of air comes against the sphere, or the 

 sphere moves in the opposite direction (and with the same speed) 

 through still air. Hence Magnus's experimental result amounts 

 toihis : — If a spherical ball be rotating, and at the same time 

 advancing in still air, it will deviate from a straight path in the 

 same direction as that in which its front side is being carried by 

 the rotation. 



The physical explanation of the difference of pressures in 

 question requires analysis which would be altogether out of 

 place in an article like this. But, even without it, we feel our- 

 selves to be on perfectly safe ground when we recollect that 

 Magnus's result was obtained by direct experiment, and there- 

 fore expresses a physical truth. 



Bearing in mind the statement italicized above, let us now 

 consider the anomalous behaviour of a golf ball. The key of the 

 position is "slicing." He who understands this will, without 

 much further trouble, master the rest of the difficulties above 

 referred to. Slicing is effected by the player's drawing the club 

 towards his body while it is in the act of striking the ball. The 

 ball is thus treated almost precisely as is a whipping-top — i.e. 

 it is not merely driven forwards, but is made to spin about a 

 nearly vertical axis. The side of the ball to which the club was 

 applied was drawn in towards the player. Hence, as the ball 

 advances, its front is moving towards the player's right, and the 

 deviation takes place to that side accordingly. 



A "topped" ball "dooks"(?.^. plunges, as it were, head- 

 long downwards). We can see at once that it should be so, in 

 accordance with the general statement. For, in topping, the 

 upper part of the ball is made to move forward faster than does 

 the centre, consequently the front of the ball descends, in virtue 

 of the rotation, and the ball itself skews in that direction. 



When a ball is "under-cut " it gets the opposite spin to the 

 last, and, in consequence, it tends to deviate upwards instead of 

 downwards. The upward tendency often makes the path of a 

 ball (for a part of its course) concave upwards in spite of the 

 effects of gravity. This is usually regarded as a very strange 

 phenomenon, even by men to whom ' ' dooking " seems natural 

 enough. As will be seen later, a "jerked" ball must, from the 

 way in which the face of the club is moving at impact, have 

 this spin, and consequently must skew upwards. 



Since a " heeled " ball deviates to the right as a " sliced " ball 

 does, it must be rotating in a similar manner. But a "toed" 

 ball deviates to the left, and must, therefore, have the opposite 

 spin. The way in w'hich the spin is produced in these cases is 

 not so easy to explain as it was in the case of topping. W^e may 

 begin, however, by saying that the terms "heeling " and " toe- 

 ing " are entirely misleading, if they be taken to imply neces- 

 sarily the hitting of the ball with the heel or the toe of the club 

 as the case may be. For, as will soon appear, a ball may be 

 heeled off the toe of a club, or toed off the heel, at pleanire ! 

 And when a man holds his club properly, so that in the act of 

 striking the ball the club-hecui is moving in a direction exactly 

 perpendicular to the face, there will be neither heeling nor toe- 

 ing whatever part of the face strikes the ball, provided it be 

 struck by the face proper, and not by an edge. It will not be 

 driven so far by the heel, or by the toe, as by the proper centre 

 of percussion ; but there will be no spin, and therefore no 

 skewing. 



The true explanation, therefore, of heeling and toeing is to be 

 found in the fact that the club-head, when it strikes the ball, is 

 not moving perpendicularly to the face ; or, what comes practic- 

 ally to the same thing, the face of the club is not perpendicular 

 to the direction in which the club is moving {i.e. it is to be pre- 

 sumed the direction which it is desired that the ball should 

 take). In this case we may regard the motion of the head as 

 resolved into two parts — one perpendicular to the face, the other 

 parallel to it. The former gives translation only to the ball. 

 The latter gives it not only translation, but rotation also. When 

 the toe of the club is too much thrown back — 2.(?.'when the heel 

 is too much forward — the motion parallel to the face is from toe 



to heel, exactly as in "slicing." "Heeling" and "slicing" 

 are thus practically the same thing, so far at least as the ball is 

 concerned. But, so far as the player is concerned, they are 

 quite different ; and (what is of far more importance) the modes 

 of cure are entirely dissimilar. To cure slicing, cease to pull in 

 your arms ; to cure heeling, place your club beside the ball as 

 in addressing, and note the lie of the head. If that be incorrect, 

 put it right ; if it be correct, the fault lies in "gripping" (instead 

 of holding loosely) with your right hand. Many a man's play 

 has been spoiled for the day by his having applied (too often by 

 his caddie's advice) the cure for " heeling " when the disease 

 was " slicing," or vice versd. 



When the toe of the club is turned inwards, the face is pushed 

 tangentially outwards behind the ball, so that the spin and its 

 consequences are exactly the reverse of those just described. 



From what has been said above, it is obvious that the flight 

 of a ball, if it be nearly spherical and have its centre of gravity at 

 its centre, depends solely upon the imp\dse originally given to 

 it. [If the centre of gravity be not in the centre of the ball, it 

 is only by mere chance (in teeing) that the ball escapes having a 

 rapid rotation given to it, even by the most accurate of drivers. 

 Should it fortunately escape initial rotation, still its flight cannot 

 be regular. A simple and exceedingly expeditious test of this 

 defect CDnsists in placing the ballon mercury in a small vessel. 

 If, in that position, it oscillates rapidly about the vertical, it should 

 be at once rejected as absolutely worthless.] This is a point on 

 which opinions of the wildest extravagance are often expressed. 

 Some balls, it is said, " will not fly," &c. How if they were fired 

 from a blunderbuss ? Nobody seems to have made the trial in the 

 only reasonable way — viz. by using a cross-bow or a catapult to 

 give the initial speed. With such an instrument two homo- 

 geneous spherical balls of equal size and weight, whatever their 

 other peculiarities, would be despatched under exactly the same 

 conditions, and their behaviour could be compared — it would not 

 require to be contrasted. 



But he is correct (in meaning, though not in his English) who 

 says that some balls " won't drive." It is easy to recognize a 

 good ball by trial, but difficult to define one, at least without 

 periphrasis. A good ball is one which acquires, under given 

 conditions of good driving, as great an initial speed as possible, 

 coupled with the minimum of rotation. 



So far as we are aware, all direct scientific experiments on 

 elastic resilience have been made at low speeds, and consequently 

 with but slight distortion of the impinging bodies. But the cir- 

 cumstances of a "drive "in golf are of a totally different 

 character ; so that the results of the drive must be themselves 

 regarded as the only data of the requisite kind which we possess. 

 In this matter very valuable data (not for golf alone) might easily 

 be obtained by measuring the height to which a ball rebounds 

 when fired from a powerful catapult against a wooden or stone 

 floor ; recording on each occasion the extent to which the springs 

 of the weapon were extended, and the appended weight which 

 would produce the same extension. Some keen golfer may thus 

 find thoroughly useful as well as congenial occupation, when his 

 happy hunting-grounds are inches deep in snow. P. G. T. 



SCIENTIFIC SERIALS. 



Bulletin de V Acadimie Royale de Belgiqiie, June. — On the 

 problematic satellite of Venus, by Paul Stroobant. After a 

 complete survey of the various appearances of this object be- 

 tween the years 1645 and 1768, the author discusses the different 

 conjectures advanced by astronomers to explain the phenomenon. 

 The theory of a true satellite is rejected on the ground that no 

 orbit could be made to correspond with all the recorded observa- 

 tions, while the elements calculated by Lambert from some of 

 them would make the planet ten times larger than its actual size. 

 In the same way are disposed of the other suggestions that it 

 might be the reflection of Venus on certain frozen particles in 

 the atmosphere, or an inter- Mercurial planet, or a planet with a 

 revolution slightly differing from that of Venus, or an asteroid, 

 and the like. Several reasons are then advanced in support of 

 the view that the pretended satellite is to be referred to certain 

 small fixed stars near which Venus was passing when the various 

 observations were taken. This explanation is specially obvious 

 in one instance, where the movement attributed to the supposed 

 satellite is precisely the proper motion, but in the opposite direc- 

 tion, of Venus at that moment in relation to the fixed stars. — 

 On a specimen of crystalline iron-glance formed on some old iron 



