Chapter X: The Flight of the Golf Ball (1)

The flight of the ball, and particularly of the golf ball, exercises a strange fascination for many people to whom the phenomena of flight exhibited by a spinning ball travelling through the air, are not of the slightest practical importance. That is to say, there is an immense number of people who take merely a scientific, and one might almost say an artistic interest in the effects produced by the combined influence of spin and propulsion. Scientific men have been for many years well aware of the causes which produce the swerve of a ball in the air. By swerve I mean, of course, a curve in the flight of the ball which is due to other causes than gravitation, and in the word swerve I do not include the drift of a ball which has been perfectly cleanly hit, but which, in the course of its carry, has been influenced by a cross wind. This does not legitimately come under the heading of swerve. It is more correctly described as drift, and will be dealt with in due course.

In the _Badminton Magazine_ of March 1896, the late Professor Tait published an article on "Long Driving." Professor Tait was a practical golfer and a very learned and scientific man. He proved most clearly that a golf ball could not be driven beyond a certain distance. He proved this absolutely and conclusively by mathematics, but, so the story runs, his son, the famous Freddie Tait, proved next day with his driver, that his father's calculations were entirely wrong, for he is alleged to have driven a golf ball over thirty yards farther than the limit which his learned parent had shown to be obtainable. Naturally, Professor Tait had to reconsider his statements, and he then arrived at the conclusion that there must have been in the drive of his son, which had upset his calculations, some force which he had not taken into consideration. He soon came to the conclusion that this was back-spin, and he dealt with this matter of back-spin, which is a matter of extreme importance to golf, in a most erudite article, which is much too advanced for the ordinary golfer, so I shall content myself here with referring to just a few of the most important points in connection with it. It is necessary that I should, in dealing with the flight of the ball, give those of my readers who are not already acquainted with the simple principles of swerve, some idea of what it is which causes the spinning ball to leave the line of flight that it would have taken if it had been driven practically without spin.

The explanation is very simple. If a ball is proceeding through the air, and spinning, the side which is spinning _towards the hole_ gets more friction than the other side which is spinning _away from the hole_. It is well known that a projectile seeks the line of least resistance in its passage through the air. It follows that the greater friction on the _forward spinning_ half causes the ball to edge over towards the side which is spinning away from the hole. This, in a very few words, is the whole secret of swerve.

Professor Tait stated in his article that Newton was well aware of this fact some 230 years before the publication of the professor's article, and that he remarked when speaking of a spinning tennis ball with a circular as well as a progressive motion communicated to it by the stroke, "that the parts on that side where the motions conspire must press and beat the contiguous air more violently, and there excite a reluctancy and reaction of the air proportionately greater."

This really is an extremely simple matter and a very simple explanation. I have taken care to explain it so simply, for swerve is, by a very great number of people, looked upon as an abstruse problem--in fact, my book on _Swerve, or the Flight of the Ball_, is catalogued as a treatise on applied mathematics, instead of, as I intended it to be, simply a practical application of the ascertained facts to the behaviour of the ball in the air.

Professor Tait's article has enjoyed a wonderful vogue. Although it was published nearly twenty years ago it is quite frequently quoted at the present time. There are, however, in it some errors which one would not have expected to have found in such a scientific article. Speaking of the golf ball shortly after it has left the club, Professor Tait said:

It has a definite speed, in a definite direction, and it
_may_ have also a definite amount of rotation about some
definite axis. The existence of rotation is manifested at
once by the strange effects it produces on the curvature of
the path so that the ball may skew to right or left; soar
upwards as if in defiance of gravity, or plunge headlong
downwards instead of slowly and reluctantly yielding to that
steady and persistent pull.

There is, in this statement of Professor Tait's, a fundamental error in so far as regards the flight of the ball. He said: "The existence of rotation is manifested at once by the strange effects it produces on the curvature of the path." This is incorrect from a scientific point of view, and it is also badly stated. The existence of rotation is not manifested "at once"; in very many cases, practically in all, the ball proceeds for quite a long distance before the effect of rotation is seen. This is more particularly so when it is a matter of back-spin, but it is equally true of the pulled ball or the sliced ball. Both of these proceed for a considerable distance before the effect of spin is noticeable. In fact it is well known to all golfers that the spin begins to get to work as the velocity of the ball decreases. Also it seems as though it is incorrect to refer to the strange effects it (rotation) produces on the curvature of the path, for it is the rotation itself which produces the curvature.

Professor Tait then said:

The most cursory observation shows that a ball is hardly ever
sent on its course without some spin, so that we may take the
fact for granted, even if we cannot fully explain the mode of
its production. And the main object of this article is to
show that long carry essentially involves under-spin.

I shall deal with these two statements later on.

Professor Tait said:

To find that his magnificent carry was due merely to what is
virtually a toeing operation--performed no doubt in a
vertical and not in a horizontal plane, is too much for the
self-exalting golfer!

The fact, however, is indisputable. When we fasten one end of
a long untwisted tape to the ball and the other to the ground
and then induce a good player to drive the ball
(perpendicularly to the tape) into a stiff clay face a yard
or two off, we find that the tape is _always_ twisted in such
a way as to show under-spin; no doubt to different amounts by
different players, but proving that the ball makes usually
from about one to three turns in six feet, say from forty to
a hundred and twenty turns per second, this is clearly a
circumstance not to be overlooked.

It is wonderful how easily a scientific man, as Professor Tait was, can be led astray when he sets out to find the thing he has imagined. Professor Tait, by a footnote to his article in the _Badminton Magazine_, to my mind entirely discounts the value of his experiments. His footnote is so important that I must quote it fully. He says:

In my laboratory experiments, players could not be expected
to do _full_ justice to their powers. They had to strike as
nearly as possible in the centre, a ten-inch disc of clay,
the ball being teed about six feet in front of it. Besides
this pre-occupation, there was always more or less concern
about the possible consequence of rebound, should the small
target be altogether missed.

It will be apparent even to anyone who is not possessed of a scientific or analytical mind that Professor Tait _compelled_ his players to endeavour to play their strokes in such a manner that the ball had to travel down a line decided on by Professor Tait. I do not know at what height Professor Tait placed his clay disc from the earth, but it is evident that if he put it very low down it would involve the playing by the golfer of a stroke which would naturally produce back-spin, and in any case the trajectory was arbitrarily fixed. In experimenting with such a stroke as this, and in such a manner as this, it should be evident that there should have been no restriction whatever as to the player's trajectory. If it was decided that it was necessary to catch the ball in a clay disc, that disc should have been so large that it was impossible for the golfer's ball to escape it. It should not have been necessary for the golfer _to aim_ at the disc. The mere fact of his aiming at the disc and the ball being teed so near as six feet to the disc, all tended to produce the shot which would give the results which Professor Tait was looking for, but that does not prove that the ordinary stroke at golf is produced in a similar manner, and I do not for one moment believe that it is.

In speaking of _the stroke proper_ Professor Tait said:

The club and the ball practically share this scene between
them; but the player's right hand, and the resistance of the
air, take _some_ little part in it. It is a very brief one,
lasting for an instant only, in the sense of something like
one ten-thousandth of a second.

We may note here that Professor Tait said: "_The right hand and the resistance of the air_ take _some_ little part in it." One would be inclined to think from this that Professor Tait was, as indeed was probably the case, an adherent of the fetich of the left, for there can be no doubt that in "the stroke proper" the right hand does much more than take "_some_" little part in it.

I think that Professor Tait is wrong in his idea that under-spin, or, as I prefer to call it, back-spin, is essential to a long carry. I firmly believe that a ball which is hit with practically no spin whatever, can have a very long carry. However, as the paper which I am now about to consider follows in many ways very closely on the lines of Professor Tait's article, I shall leave this matter for consideration when I am dealing with that paper.

The paper which I am now referring to is one which was read at the weekly evening meeting of the Royal Institution of Great Britain on Friday, 18th March 1910, by Professor Sir J. J. Thomson, M.A., LL.D., D.S.C., F.R.S., M.R.I., O.M.; Cavendish Professor of Experimental Physics, Cambridge; Professor of Physics, Royal Institution, London; Professor of Natural Philosophy, Royal Institution, and winner of the Nobel Prize for Physics, 1906. The title of this paper was "The Dynamics of a Golf Ball." It will be observed that neither the Institution under the auspices of which this lecture was delivered, nor the lecturer, is inconsiderable. Professor Thomson is, without doubt, a very distinguished physicist, and we must therefore receive anything he writes with a certain amount of respect. There are, however, in this paper, so many remarkable statements that it is necessary for me to deal with it quite fully.

Professor Thomson tells us very early in the lecture that Newton was well aware of the cause of swerve which I have already set out, some 250 years ago, and that he remarked that in a spinning tennis ball the "parts on that side where the motions conspire, must press and beat the contiguous air more violently, and there excite a reluctancy and reaction of the air proportionately greater."

Professor Thomson says at the beginning of his lecture:

There are so many dynamical problems connected with golf that
a discussion of the whole of them would occupy far more time
than is at my disposal this evening. I shall not attempt to
deal with the many important questions which arise when we
consider the impact of the club with the ball, but shall
confine myself to the consideration of the flight of the ball
after it has left the club.

I may say here that Professor Thomson, although he announces his intention of doing this, is later on in his paper, as we shall see, tempted into considering the questions of impact, and, in my opinion, making several grave errors therein. We may, however, in the meantime, pass this by.

Professor Thomson continues:

This problem is in any case a very interesting one, which
would be even more interesting if we could accept the
explanations of the behaviour of the ball given by some
contributors to the very voluminous literature which has
collected around the game. If this were correct, I should
have to bring before you this evening a new dynamics and
announce that matter when made up into golf balls obeys laws
of an entirely different character from those governing its
action when in any other condition.

This, at the outset, is an extremely remarkable statement to come from so eminent a physicist, for I may say that Professor Thomson, after making a remark of this nature, proceeds to explain the phenomena of swerve on exactly the same links which I have set out fully and explicitly in my book _Swerve, or the Flight of the Ball_. That, however, is a matter of small importance. It may be that Professor Thomson has not had the opportunity of perusing this book. It may indeed be that Professor Thomson has been unfortunate enough only to have read articles wherein an erroneous explanation of the well-known phenomena of the flight of the ball is given. Be that as it may, there can be no doubt that the explanation which has been given of the causes of swerve has been adequate and accurate, and there would not have been any necessity whatever for Professor Thomson to bring before the learned Institution whose fellows listened to his address "a new dynamics." It would have been sufficient if he had correctly explained the phenomena of the flight and run of a golf ball according to the well-recognised laws which govern the flight and run of all balls. This, however, he quite failed to do.

Professor Thomson says: "If we could send off the ball from the club as we might from a catapult, without spin, its behaviour would be regular, but uninteresting." It is quite possible to send a golf ball off a club without spin. It is just as possible, from a practical point of view, to send a golf ball away without spin from the face of a driver as it is from the pouch of a catapult. The catapult is a machine, and it is a certainty that it can be made to propel a golf ball without any initial spin whatever. A machine can be made to drive a golf ball with just as little spin, and as a matter of practical golf, by far the greater number of golf balls are driven without appreciable spin--that is to say, without spin which has any definite action on the flight of the ball.

The learned lecturer says: "A golf ball when it leaves a club is only in rare cases devoid of spin." It is impossible to prove or disprove this statement, for practically no ball goes through the air with the same point always in front. We may see this quite clearly if we care to mark a lawn-tennis ball, and to hit it perfectly truly, and slowly, so that it goes almost as a lob across the net. We shall see even then that the marked part of the ball moves from one place to another. In fact, even if a golf ball were driven by a machine which did not impart to it any initial spin, it is almost a certainty that that ball would not have proceeded far before it had acquired sufficient motion to justify one in technically calling it spin. Spin, however, is a delightfully indefinite word, but this much one may at least say, and it is, in effect, a contradiction of Sir J. J. Thomson's assertion, namely that in the vast majority of balls hit with golf clubs, especially by skilled players, the effect of spin on the stroke _unless designedly applied_, which is comparatively rare, is practically negligible.

Professor Thomson says that

... a golf ball, when it leaves the club, is only in rare
cases devoid of spin, and it is spin which gives the
interest, variety, and vivacity to the flight of the ball;
it is spin which accounts for the behaviour of a sliced or
pulled ball; it is spin which makes the ball soar or "douk,"
or execute those wild flourishes which give the impression
that the ball is endowed with an artistic temperament and
performs these eccentricities, as an acrobat might throw in
an extra somersault or two for the fun of the thing. This
view, however, gives an entirely wrong impression of the
temperament of a golf ball, which is, in reality, the most
prosaic of things, knowing while in the air only one rule of
conduct which it obeys with an intelligent conscientiousness,
that of always following its nose. This rule is the key to
the behaviour of all balls when in the air, whether they are
golf balls, base-balls, cricket balls, or tennis balls.

The idea of a spherical object having a nose is so unscientific and so inexact that it is not necessary for me to dwell very strongly on it here, and I should not do so were it not that this looseness of description is of considerable importance in dealing with Professor Thomson's ideas. He continues:

Let us, before entering into the reasons for this rule, trace
out some of its consequences. By the nose on the ball we mean
the point on the ball furthest in front.

It will be obvious to my readers that this description is scientifically extremely inaccurate, for if we take a line through the ball from the point of contact with the club to the point on the ball farthest in front, which Professor Thomson calls its nose, we shall find that the flight of that ball will always be in that same line produced, whereas in the spinning ball it is nothing of the sort. The whole trouble here is that Professor Thomson wants to have the "nose," as he calls it, of the ball, both a fixed and a moving point. This, obviously, is most unscientific. If the nose of the ball is the point that is farthest in front, I cannot say too emphatically that it stands to reason that the ball in flight will go straight out after that point, but the fact is that the point in front is continually changing; moreover, the fact that the ball goes the way it is spinning is not explained by any tendency of the ball to wander that way on account of the spin irrespective of the friction of the air.

It will thus be seen that Professor Thomson's explanation in this matter is incorrect and misleading. This is about the most unscientific explanation which could be given of this matter, and it is one which is calculated to mislead people who would otherwise understand the matter quite clearly, so we shall drop Professor Thomson's idea of giving the ball a "nose" which is always in the front of it, but which is also supposed to be continually travelling sideways. It is obvious that Professor Thomson cannot have it both ways.

It is very clear indeed that Professor Thomson is not well acquainted with the method of applying spin to balls which are used in playing games. He says:

A lawn-tennis player avails himself of the effect of spin
when he puts "top-spin" on his drives, _i.e._ hits the ball
on the top so as to make it spin about a horizontal axis, the
nose of the ball travelling downwards as in figure 4; this
makes the ball fall more quickly than it otherwise would, and
thus tends to prevent it going out of the court.

I have played lawn-tennis for more than twenty years, and I am the author of three books on the game, one of which is supposed to be the standard work on the subject, and I can assure Professor Thomson that no lawn-tennis player would dream of doing anything so silly as to hit a lawn-tennis ball "on the top" in an attempt to obtain "top-spin."

The scientific method of obtaining top-spin is to hit the lawn-tennis ball on what Professor Thomson, if he were driving the ball over the net to me, would call its nose--that is to say, I should hit the ball on the spot which was farthest from Professor Thomson. I should hit it there with a racket whose face was practically vertical, but I should hit it an upward, forwardly glancing blow which would impart, as Professor Thomson expresses it, "spin about a horizontal axis to the ball."

Professor Thomson goes so far as to show by diagram the travel of a ball which has been hit so as to impart top-spin to it, but even in this diagram he is absolutely wrong, for he shows that immediately the ball has been hit with top-spin it begins to fall, but this is not so. In lawn-tennis the ball travels for a long distance before the spin begins to assert itself, and to overcome the force of the blow which set up the spin.

Professor Tait makes this same error in his article on "Long Driving," and it is quite evident to me that Professor Thomson is following, in many respects, the errors of his eminent predecessor.

Professor Thomson also says:

Excellent examples of the effect of spin on the flight of a
ball in the air are afforded in the game of base-ball. An
expert pitcher, by putting on the proper spin, can make the
ball curve either to the right or the left, upwards or
downwards; for the side-way curves the spin must be about a
vertical axis; for the upward or downward ones, about a
horizontal axis.

There are no particular laws with regard to the curves of a base-ball. The same laws regulate the curves in the air of every ball from a ping-pong ball to a cricket ball, and Professor Thomson, in saying that "for the side-way curves the spin must be about a vertical axis," is absolutely wrong. Every lawn-tennis player who knows anything whatever about the American service, will know that Professor Thomson is utterly wrong in this respect, for the whole essence of the swerve and break of the American service, which has a large amount of side-swerve, is that the axis of rotation shall be approximately at an angle of fifty degrees, and any expert base-ball pitcher will know quite well that he can get his side-curve much better if he will, instead of keeping his axis of rotation perfectly vertical, tilt it a little so that it will have the assistance of gravitation at the end of its flight instead of fighting gravitation, as it must do if he trusts entirely to horizontal spin about a vertical axis for his swerve.

Professor Thomson says:

If the ball were spinning about an axis along the line of
flight, the axis of spin would pass through the nose of the
ball, and the spin would not affect the motion of the nose;
the ball, following its nose, would thus move on without
deviation.

The spin which Professor Thomson is describing here is that which a rifle bullet has during its flight, for it is obvious that the rifle bullet is spinning "about an axis along the line of flight," and that the axis of spin does pass through the nose of the bullet, but we know quite well that in the flight of a rifle bullet there is a very considerable amount of what is called drift. It is, of course, an impossibility to impart to a golf ball during the drive any such spin as that of the rifle bullet, although in cut mashie strokes, and in cutting round a stymie, we do produce a spin which is, in effect, the same spin, but this is the question which Professor Thomson should set himself to answer. He states distinctly that a ball with this spin would not swerve. If this is so, can Professor Thomson explain to us why the rifle bullet drifts? As a matter of fact, a ball with this spin _would_ swerve, but not to anything like the same extent as would a ball with one of the well-recognised spins which are used for the purpose of obtaining swerve.

Finish of drive, showing clearly how Braid's weight goes on to
the left leg.]

Professor Thomson proceeded to prove by the most elaborate experiments the truth of those matters stated by Newton centuries ago, but it will not be necessary for me to follow him in these, because these principles have been recognised for ages past.

It is curious to note that in the reference to Newton, who was aware of this principle of swerve so long ago, we are shown that Newton himself did not quite grasp the method of production of the stroke, although he analysed the result in a perfectly sound manner. Writing to Oldenburg in 1671 about the Dispersion of Light, he said in the course of his letter: "I remembered that I had often seen a tennis ball struck with an oblique racket describe such a curved line." The effect of striking a tennis ball with an oblique racket is, generally speaking, to push it away to one side. The curve, to be of a sufficiently pronounced nature to be visible, must be produced by the passage of the racket across the intended line of flight of the ball.

This matter of the different pressure on one side of the ball from that on the other is very simple when one thoroughly grasps it. Professor Thomson gives in his paper an illustration which may perhaps make the matter clearer to some people than the explanation which is generally given. He says:

It may perhaps make the explanation of this difference of
pressure easier if we take a somewhat commonplace example of
a similar fact. Instead of a golf ball let us consider the
case of an Atlantic liner, and, to imitate the rotation of
the ball, let us suppose that the passengers are taking their
morning walk on the promenade deck, all circulating round the
same way. When they are on one side of the boat they have to
face the wind, on the other side they have the wind at their
backs. Now, when they face the wind, the pressure of the wind
against them is greater than if they were at rest, and this
increased pressure is exerted in all directions and so acts
against the part of the ship adjacent to the deck; when they
are moving with their backs to the wind, the pressure against
their backs is not so great as when they were still, so the
pressure acting against this side of the ship will not be so
great. Thus the rotation of the passengers will increase the
pressure on the side of the ship when they are facing the
wind, and diminish it on the other side. This case is quite
analogous to that of the golf ball.

Even in this simple illustration it seems to me that Professor Thomson is wrong, for he is pre-supposing that which he does not state--a head wind. It is quite obvious that these passengers might have to face a wind coming from the stern of the ship, and in this case the analogy between the passengers circulating round the deck of a ship, and his golf ball would receive a serious blow. In stating a matter which is of sufficient importance to be dealt with before such a learned body as the Royal Institution of Great Britain, it is well to be accurate. If Professor Thomson had stated that his Atlantic liner was going into a head wind, or, for the matter of that, even proceeding in a dead calm, his analogy might have been correct, but it is obvious that he has left out of consideration a following wind of greater speed than that at which the liner is travelling.

Professor Thomson has not added anything to the information which we already possessed with regard to the effect of back-spin on a ball; rather has he, as I shall show when dealing with the question of impact with the ball, clouded the issue. At page 12 of his remarkable lecture he says: "So far I have been considering under-spin. Let us now illustrate slicing and pulling; in these cases the ball is spinning about a vertical axis." We here have a very definite statement that in slicing and pulling the ball is spinning about a vertical axis, but it is not doing so.

Professor Thomson has "an electromagnet and a red hot piece of platinum with a spot of barium oxide upon it. The platinum is connected with an electric battery which causes negatively electrified particles to fly off the barium and travel down the glass tube in which the platinum strip is contained; nearly all the air has been exhausted from this tube. These particles are luminous, so that the path they take is very easily observed."

These particles, I may explain, take, in Professor Thomson's mind, the place of golf balls, and by an electromagnet he shows us exactly what golf balls do, but it seems to me that if Professor Thomson is not absolutely clear what is happening to the sliced ball and the pulled ball, there is a very great chance that, like Professor Tait, he may induce his particles to do the thing that he wishes them to do, and not the thing that a real golf ball with a real pull or a real slice would do. This, as a matter of fact, is exactly what Professor Thomson does, for, as I shall show quite simply and in such a manner as absolutely to convince the merest tyro at golf, Professor Thomson is utterly wrong when he states that in the slice and the pull the ball is spinning about a vertical axis.

I shall not need any diagrams or figures to bring this home to anyone who is possessed of the most rudimentary knowledge of mechanics. It should be quite evident to anyone that to produce spin about a vertical axis it would be necessary to have a club with a vertical face, or to strike a blow with the face of the club so held that at the moment of impact the face of the club was vertical. Now this does not happen with the slice at golf, for the very good reason that if one so applied one's club, the ball would not rise from the earth. The club which produces the slice is always lofted in a greater or less degree, and quite often the natural loft is increased by the player designedly laying the face back during the stroke. It is evident that in the impact with the driver or brassy, the ball, especially the modern rubber-cored ball, flattens on to the face of the club and remains there whilst the club is travelling across the line of flight. This naturally imparts to the ball a roll--in other words, as the club cuts across the ball it rolls it for a short distance on its face.

It is obvious that this rolling process will, to a greater or less extent, give to the ball a spin about an axis which is approximately the same as that of the loft on the face of the club. Therefore, it is clear that in all sliced balls the axis of spin will be inclined backward. It seems likely, also, that as the axis of spin is inclined backward and the ball is rising, there will be some additional friction at the bottom of it which would not be there in the case of a ball without spin. This probably helps to produce the sudden rise of the slice. In all good cut shots with lofted clubs, the angle of the axis of spin is to a very great extent regulated by the amount of loft on the face of the club.

Professor Thomson's error with regard to the slice being about a vertical axis is beyond question, but his error in saying that the axis of rotation of the pull and the slice is identical, is, from a golfing point of view, simply irretrievable. Print is a very awkward thing--_it stays_. The merest tyro at golf knows quite well that the pulled ball and the sliced ball behave during flight and after landing on the ground in a totally different manner from each other. If Professor Thomson knows so much, it should unquestionably be evident to so distinguished a scientist that there must be a very considerable difference in the rotation of these balls. The slice, as is well known, rises quickly from the ground, flies high, and is not, generally speaking, a good runner. The pull, on the other hand, flies low and runs well on landing.

It is not merely sufficient to contradict Professor Sir J. J. Thomson in these matters, so I shall explain fully the reason for the difference in the flight and run of the slice and the pull. The slice is played as the club head is returning across the line of flight, and therefore is more in the nature of a chop than is the pull. Frequently the spin that is imparted to the ball is the resultant of the downward and inwardly glancing blow. This not only leaves the axis of rotation inclined backward, but sometimes inclined also slightly away from the player, but it is obvious that even if the ball had, as Professor Thomson thinks it has, rotation about a vertical axis, which is the rotation of a top, such rotation would, on landing, tend to prevent the ball running, for, as is well known, every spinning thing strives hard to remain in the plane of its rotation, but the slice is more obstinate still than this, for the axis of rotation being inclined backward, frequently at the end of the flight, coincides with the line of flight of the ball, so that the ball is spinning about an axis which, to adopt Professor Thomson's term, runs through its "nose." This means that the slice frequently pitches in the same manner as might a rifle bullet if falling on its "nose," and the effect is, to a very great extent, the same. The ball tries to stay where it lands.

Let us now consider the flight and run of the pull. The pull is played by an upward, outward, glancing blow. The ball is hit by the club as it is going across the line of flight away from the player and this imparts to the ball a spin around an axis which lies inward towards the player. This means that the pull goes away to the right, and then swerves back again towards the middle of the course if properly played, and upon landing runs very freely. The reason for this run has not been clearly understood by many, and it is quite evident that Professor Thomson does not know of it, so I shall give an extremely plain illustration.

Nearly every boy has at some time played with a chameleon top, or some other top of the same species, that is to say, a disc top. Every boy who has played with such a top will be familiar with the fact that when the spin is dying away from the top, it rolls about until one edge of it touches the earth or whatever it is spinning on. Immediately this happens the top runs away as carried by the spin.

That is about the simplest illustration which it is possible to give of the plane of spin of the pulled ball during its flight and of its run after it has touched the earth, but from this very simple explanation it will be perfectly obvious to anyone who gives the matter the least consideration that not only is the axis of rotation of the pull and the slice dissimilar, but as a matter of fact the rotation of the pull and the slice is almost diametrically opposed the one to the other.

Professor Thomson says:

Let us now consider the effect of a cross wind. Suppose the
wind is blowing from left to right, then, if the ball is
pulled, it will be rotating in the direction shown in figure
26 (from right to left); the rules we found for the effect of
rotation on the difference of pressure on the two sides of a
ball in a blast of air show that in this case the pressure on
the front half of the ball will be greater than that on the
rear half, and thus tend to stop the flight of the ball. If,
however, the spin was that for a slice, the pressure on the
rear half would be greater than the pressure in front, so
that the difference in pressure would tend to push on the
ball and make it travel further than it otherwise would.

I have not given this aspect of the question a great amount of thought, but it seems obvious that in playing for a slice in the circumstances mentioned by Professor Thomson, it is extremely unlikely that the greater pressure would be, as he says, on the rear half. If, indeed, this were so the slice would, in my opinion, not take effect; also on account of the tremendous speed of the golf ball it seems to me utterly improbable that in any ordinary wind which one encounters on a golf links it would be possible to obtain on the rear half of a golf ball a greater pressure than that on the forward spinning half, or, to be more accurate, quarter of the ball. I cannot help thinking that Professor Thomson in saying that in such a case as this the greater pressure would be on the rear half of the ball is falling into an error, for it seems to me that he is overlooking the tendency of the ball to set up for itself something in the nature of a vacuum which will undoubtedly tend to protect the rear portion of the ball from the force which must assail it in front during its passage through the air.

Professor Thomson says that "the moral of this is that if the wind is coming from the left we should play up into the wind and slice the ball, while if it is coming from the right we should play up into it and pull the ball."

That is Professor Thomson's theory. I shall give my readers the benefit of my practice, which is that whenever there is a cross wind of any description whatever, hit the ball as straight as it is possible for you to do it, right down the middle of the course from the tee to the hole, and forget all about pulls or slices. On a windy day avoid anything whatever in the nature of side-spin because once you have applied it to a ball you never know where that ball is going to end, and if you want any confirmation for this practice you may get it from Harry Vardon in _The Complete Golfer_, for there can be very little doubt that a side wind has nothing like the effect on the ball that golfers seem to imagine, provided always, of course, that the ball be hit cleanly and without appreciable spin. It is not given to one golfer in a thousand to know how to use the pull and slice to obtain assistance from the wind and also to be capable of executing the strokes. As a matter of practical golf these strokes should, for at least ninety-five per cent of golfers, be rigidly eschewed.

At the beginning of Professor Thomson's article he said:

I shall not attempt to deal with the many important questions
which arise when we consider the impact of the club with the
ball, but confine myself to the consideration of the flight
of the ball after it has left the club.

It would, indeed, have been well if Professor Thomson had carried out his expressed intention of leaving this matter alone, for in dealing with it he has shown most conclusively that he has no practical grip of the question which he has attempted to deal with. At page 15 of his article he says:

I have not time for more than a few words as to how the ball
acquires the spin from the club, but if you grasp the
principle that the action between the club and the ball
depends only on their _relative_ motion, and that it is the
same whether we have the ball fixed and move the club, or
have the club fixed and project the ball against it, the main
features are very easily understood.

I can readily believe that this statement of Professor Thomson's is absolutely accurate. The only thing which troubles me about it is that I think the person of ordinary intellect will find it absolutely impossible to "grasp the principle" which Professor Thomson lays down. If we have the club fixed and project the ball against it, we know quite well that the ball will rebound from the club, but if we are to have the ball fixed and move the club against it, nothing will happen unless we move the club fast enough, in which case we should simply smash the club.

This is a most amazing illustration of looseness of thought--such an astonishing illustration that I should not have believed Professor Thomson capable of it if it had not been published broadcast to the world with his authority. Of course, I know perfectly well what Professor Thomson means to say, but I have not to deal with that, and as a matter of fact what he means to say is quite wrong, but it will be sufficient for me to show that what he _does_ say is wrong.

Professor Thomson then goes on to say:

Suppose Fig. 27 represents the section of the head of a
lofted club moving horizontally forward from right to left,
the effect of the impact will be the same as if the club were
at rest and the ball were shot against it horizontally from
left to right.

Here Professor Thomson shows that he is quite under a misapprehension as to the production of the golf stroke. He pre-supposes that the club is moving in a horizontal direction at the moment it hits the ball. In a vast majority of instances, probably in about ninety per cent of cases, the club is not moving in a horizontal direction--in fact, it would be hardly too much to say that it never moves in a horizontal direction. It is nearly always moving either upwards or downwards in a curve at the moment it strikes the ball, so that it stands to reason, especially when the club face is travelling upwards, which is what it does in the great majority of cases, that the blow is never delivered horizontally, but is always struck more or less upward through the ball's centre of mass.

Practical teachers of golf know how extremely hard it is to induce the beginner, and for the matter of that many people who are far beyond beginners, to trust the loft of the club to raise the ball from the earth; so many players never get out of the habit of attempting to hit upwards.

It stands to reason that if the blow in golf were delivered as with a billiard cue, any blow struck in that manner, provided the face of the club had sufficient loft, would tend to produce back-spin, but practically no blow in golf is struck in the manner described by Professor Thomson; nor is the beneficial back-spin of golf obtained in this manner, in fact the loft of the club has comparatively little to do with producing the back-spin which so materially assists the length of the carry. There can, of course, be no doubt that loft does assist a person in producing this back-spin, or, as Professor Thomson calls it, under-spin, but to nothing like the extent which is imagined by the worthy Professor. The beneficial back-spin of golf is obtained by striking the golf ball before the head of the club has reached the lowest point in its swing; in other words, the back-spin is put on a golf ball by downward cut--by the very reverse to that cut which is put on a ball when a man tops it badly. In the one case it is up cut, or, as it is called in lawn-tennis, top, which is a misleading term which has led many people, besides Sir J. J. Thomson, astray, and in the other case it is downward cut, which is exactly similar in its effect to the chop at lawn-tennis.

Professor Thomson, for the purpose of illustrating the fact that the golf ball obtains the beneficial spin, which influences its carry so materially, from the loft of the club, shows us a club face with a loft much greater than that of a niblick, and proceeds to demonstrate from this loft, which it is unnecessary to tell a golfer does not exist on any club which is used for driving, that the ball acquires its back-spin from the loft of the face of the club.

I have already referred to the Professor's fundamental fallacy that the golf stroke is delivered in a horizontal line--in effect that the force of the blow proceeds horizontally, but he is guilty of another very great error from the point of view of practical golf when he shows a club such as he has done, in order to explain how the beneficial back-spin of golf is obtained. Such a club as he shows might be useful for getting out of a bunker, but it certainly would be of no use whatever in practical golf for driving. As every golfer knows, the face of the driver is, comparatively speaking, very upright, and firing a ball at a wall built at the same angle as the loft of a driver would certainly not produce on that ball much in the way of back-spin. The idea of a modern golf ball which flattens very considerably on the face of the club, rolling up the face of a driver on account of its loft, is too ridiculous to be considered seriously by a practical golfer.

The trouble is that Professor Thomson always takes for his hypothesis something which does not exist in golf, so that in the great majority of cases it does not really matter to us what he proves. As a matter of fact, there is in golf only one horizontal stroke, and that is the stymie stroke introduced into the game by me, and which I have hereinbefore fully described. This stroke shows us conclusively how the power goes mostly into elevation instead of into propulsion. It is an absolute answer, if one were required, to Professor Thomson's theories. Professor Thomson's error is of such a fundamental nature that I must quote his sentence again in giving my readers the full paragraph wherein he exposes the delusion under which he is suffering. He says:

Suppose Fig. 27 represents the section of the head of a
lofted club moving horizontally forward from right to left,
the effect of the impact will be the same as if the club were
at rest and the ball were shot against it horizontally from
left to right. Evidently, however, in this case the ball
would tend to roll up the face, and would thus get spin about
a horizontal axis in the direction shown in the figure; this
is under-spin and produces the upward force which tends to
increase the carry of the ball.

This is the rock upon which Professor Thomson has split. He is under the impression that the beneficial back-spin of golf is obtained by loft, whereas it is perfectly possible to obtain the beneficial back-spin of golf with a club having a vertical face, and being at the moment of impact in a vertical plane, but in order to do this it would be necessary that the ball should be teed very high, as indeed one of the most famous professionals in the world is in the habit of doing when he is playing for a low ball against the wind.

When in _Modern Golf_ I stated that a high tee for a low ball was practical golf, it was considered revolutionary, if not incorrect, doctrine, but players now understand that by using the high tee for a low ball they are enabled to cut down beyond the ball more than they could do if the ball were lying on the earth, and that they are, in this manner, enabled to obtain much more of the back-spin which gives the ball its extra carry, and also to play it with less loft.

This is a very serious error for a man of Professor Thomson's attainments to make, and indeed it is to me a wonder how he could possibly make the mistake of thinking that the force in the blow at golf is administered horizontally. This is one of the worst errors which he has made, but the idea that the back-spin of golf is obtained mainly by the loft of the club is utterly unsound and pernicious. It is so unsound, and the correct understanding of the method of producing this stroke is so important to golf, especially to the golf of the future, that I must explain fully how this stroke is obtained.

I have already shown that it is played by a downward glancing blow which hits the ball before the club reaches the lowest point in its swing, and I have already shown the delusion under which many players labour, even including so eminent a player as Harry Vardon, that the ball is struck down on to the earth. Although the ball is struck a descending blow, there is in the blow much more of the forward motion than the downward, so that all the ordinary principles with regard to getting the ball up into the air, apply with equal force to this stroke as to any other, and it is a matter of prime importance that the ball must be struck below the centre of its mass--that the loft of the club must get in underneath what is popularly called the middle of the ball. If this does not take place the ball will not rise from the earth, and to show as Harry Vardon does, at page 170 of _The Complete Golfer_, that the ball must be struck at or above the centre of its mass, and with, as he indicates at page 106, a vertical face, is utterly unsound golf.

I cannot emphasise too strongly that in this miscalled push shot, which is answerable for all back-spin, the loft must be allowed to do its work in the ordinary manner, otherwise the stroke will be a failure.

Having now made it perfectly clear how this stroke is obtained, I must explain a little more clearly the wonderful character of this ball which is without any doubt whatever, in my mind, the king of golf strokes in so far as regards obtaining distance and accuracy and direction. On account of the downward glancing blow the ball has been struck, it leaves the club with a very great amount of back-spin. The hands are always forward of the ball at the moment of impact in this stroke when it is properly played. It stands to reason that this, to a certain extent, decreases the loft of the club with which the stroke is played. The result is that the ball goes away on the first portion of its journey with a very low flight, keeping very close indeed to the earth. All the time it is doing this, however, the ball, as we know, is spinning backwards, which means that the lower portion of the ball is spinning towards the hole, and that it is on the lower portion of the ball that the motions of progression and revolution conspire.