Chapter X: The Flight of the Golf Ball (2)

It is equally obvious that on the upper portion of the ball the progression through the air is at the same rate, but in so far as regards its frictional-producing result on the air, it is lessened by the fact that the upper portion of the ball is revolving or spinning backwardly towards the player. The result of this is that the ball is getting much more friction on the lower portion than it is on the top, but as speed can always dominate spin, this is not very apparent until about two-thirds of the carry.

As the speed of the ball begins to decrease, the friction of the spin gets a better grip on the air, and the result is that with the continual rubbing of the air on the lower portion of the ball, it is forced upward and so it continues until the lifting power of the combined propulsion and revolution is exhausted. By this time the ball has arrived at the highest point of its trajectory and it then begins in the natural order of things to fall towards the earth.

It is obvious that by this time much of the back-spin will have been exhausted, but there still remains a considerable amount of rotation, and as the ball begins to fall towards the earth this back-spin which has hitherto been used for forcing the ball upwards into the air, still exerts its influence, and as it is travelling towards the earth the remnant of the back-spin exerts its influence to extend the carry of the ball, because the main frictional portion of the ball has, to a certain extent, on account of the dropping of the ball, been altered and shifted probably a little more towards the lower side of the ball.

The result of all this is that by the time this ball, in a well played drive, comes to earth, most of the beneficial back-spin which obtained for it its long flight, will have been exhausted, and that portion which remains and has not been exhausted will, in all probability, be killed on impact, for the ball pitches on one point, and naturally the top portion tends to throw forward so that the ball will run along the course. It stands to reason that it would require an enormous amount of back-spin to stay with the ball during the period of its low flight, to lift the ball then to the highest point in its trajectory near the end of its carry, to stay with it still in its descent, and then to be strong enough to resist the shock of landing so as to check the run of the ball. The result is that on account of the low trajectory of this ball and of the phenomena explained by me, it is frequently, when well played, and particularly in dry weather, a good runner, so that we see that in this ball we have practically the ideal golf drive; a drive with which no other can compare; a drive which is as good, although it is called the wind-cheater, for a still day as in a gale.

From this explanation it will be seen what a poor chance anyone would have who follows Professor Thomson's ideas of obtaining the beneficial back-spin of golf from the loft of the club and a horizontal blow.

Professor Thomson gives some illustrations of the pull and the slice. In two of his figures he shows horizontal blows being produced in a straight line with the line of flight. Both of these, I may say, are absolutely impossible in golf. He shows a slice in Fig. 29 which would be much more likely to result in a pull, and he shows a pull in Fig. 31 which would almost certainly result in a slice even if the shots were possible, which, as he shows them, they are not.

Professor Thomson shows by diagram an ordinary slice which he says is produced by "such a motion as would be produced if the arms were pulled in at the end of the stroke." This in itself is an utterly loose definition. What Professor Thomson evidently means is if the arms were pulled in during the stroke or at the moment of impact, but as I have shown the slice is not produced by the arms being pulled in at the moment of impact. It is produced by the club head travelling across the ball at an angle to the intended line of flight of the ball. Professor Thomson shows the slice in this case by diagram, and correctly, but he says that if the club were fixed rigidly and the ball were fired at the club down the same line as the club made in its previous stroke, the ball would come off the club in exactly the same manner as when it was hit by the club, but in this he is making a very grave error, as I think I shall be able to show.

I shall quote Professor Thomson with regard to this matter. His proposition is so simple that although I give his indicating letters it will not be necessary for me to reproduce his diagram. He says:

Suppose, now, the face of the club is not square to its
direction of motion, but that looking down on the club its
line of motion when it strikes the ball is along P Q (Fig.
28), such a motion as would be produced if the arms were
pulled in at the end of the stroke, the effect of the impact
now will be the same as if the club were at rest and the ball
projected along R S, the ball will endeavour to roll along
the face away from the striker; it will spin in the direction
shown in the figure about a vertical axis. This, as we have
seen, is the spin which produces a slice.

This, as we have already seen, is not the spin which produces a slice, but we need not waste any further time going into that matter. We can, however, deal with what Professor Thomson meant to say when he wrote

... 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.

For the purpose of analysing what Professor Thomson evidently meant when he wrote this, let us take the ordinary case of a slice. We all know now quite well that a slice is produced by a glancing blow coming inwardly across the intended line of flight, and Professor Thomson tells us it is exactly the same thing whether we hit the ball with the club or fire the ball against the club. Let us see how this works out in the slice.

We will consider, for the sake of argument, that the slice has been produced by a stroke which has come across the intended line of flight at an angle of 30 degrees. We shall now fasten our club rigidly and fire the golf ball out of a catapult against its face so that it hits it dead in the centre, and so that it travels down a line at an angle of 30 degrees to the face. Now most of us know enough elementary mechanics to know that in hitting a still object such as the face of the golf club, the ball will come off it at the same angle at which it hit it--in other words that the angle of reflection is the same as the angle of incidence, allowing always, of course, for the slight alteration which will be made by the loft of the club. In this case, of course, we have one object which is absolutely still, and all the motion during impact is confined to the ball.

Now let us consider the impact in the slice. In this case the club strikes the ball a violent blow. The ball, to a very great extent, flattens on the face of the club, and both the ball and the club travel together for a certain distance across the direct line of flight to the hole, and during the time that they are thus travelling together the club is imparting spin to the ball and influencing its direction, so that instead of the ball doing anything whatever in the nature of spinning off the face of the club at a natural angle, it is driving, during its initial stages, very straightly for a long distance before the spin begins to take effect.

It seems to me that the slice may be taken as a very good illustration showing that what Professor Thomson meant to explain is quite incorrect from a golfing point of view. It is quite evident that before we could accept as authoritative the explanations which have been given by Professor Thomson of these somewhat abstruse problems, it would be necessary for us to have, as he puts it, "a new dynamics."

I have already dealt very fully both in England and America with this remarkable lecture by Professor Thomson. I have criticised it in the leading reviews and magazines of the world, and the authoritative golfing paper of England--_Golf Illustrated_--in a leader, invited Professor Thomson to make good his assertions, but he has not been able to do so. One can understand fallacious matter being published under the names of professional golfers when one knows quite well that the majority of the work is done by journalists hired for the purpose, but it is almost impossible to understand how such utterly false doctrine could be put out by so eminent a man, and under the auspices of the Royal Institution of Great Britain.

The flight of the ball has always been a fascinating and for most people a very mysterious subject, but except in one or two matters there is no mystery whatever about the flight of the golf ball, but even amongst practical golfers there is an amazing lack of accurate information. For instance, we find Mr. Walter J. Travis, in _Practical Golf_ at page 139, saying:

With a very rapid swing, the force or energy stored up in the
gutta ball is greater than in the Haskell. The latter, by
reason of its greater comparative resiliency does not remain
in contact with the club head quite so long, and therefore
does not receive the full benefit of the greater velocity of
the stroke in the same proportion as the less resilient
gutta. It flies off the face too quickly to get the full
measure of energy imparted by a very swift stroke. This
responsiveness or resiliency, however, asserts itself in a
greater and more compensating degree in the case of the
shorter driver. It makes up, in his case, for the lack of
speed, and he finds his distance very sensibly increased.

This is a remarkable error for a golfer like Mr. Travis to make. It is abundantly plain that the rubber-cored ball stays on the face of the club much longer than the old gutta-percha ball did. Provided that there were such things in the world as incompressible balls, the impact in the drive would be of the least possible duration with them, but the more compressible the ball becomes the longer it will dwell on the face of the golf club.

That the rubber-cored ball does dwell for a greater period on the face of the club is responsible, to a great extent, for the fact that the modern ball swerves much more when sliced or pulled than did the old guttie in similar circumstances, and the reason seems to be that on account of the fact that the ball stays longer on the face of the club during the time that the club is going across the intended line of flight, it is able to impart to the ball a much greater spin. This spin, as we know, exerts its influence principally towards the end of the ball's flight, and in all probability it gets to work now approximately at the same place where the spin in the old gutta-percha ball began to assert itself, but probably a little further in the carry.

We all know that once the spin has begun to assert itself so as to make the ball swerve, its deflection from the line, particularly with a suitable wind, is extremely rapid, and we all know equally well that the carry of the rubber-cored ball is much longer than that of the old gutta-percha. It stands to reason that the ball having a much greater distance wherein to swerve will execute a correspondingly larger swerve than it would if its carry were shorter.

We find some amazing statements made by authors who profess to deal with golf. For instance at page 167 of _The Mystery of Golf_, we are informed that

... another important thing about the follow-through, surely,
is this. As Mr. Travis has pointed out, such is the
resiliency of the rubber ball that club and ball are in
contact for an appreciable period of time--the impact, that
is, is not instantaneous. It is highly probable that the
trajectory of the ball is largely influenced by this period
of contact. If you follow through your club head travels in
precisely the same line as the ball, and the flight of the
ball is by this rendered straighter, steadier, and longer.

This, truly, is a wonderful instance of analytical thought by one who is attempting to explain the mystery of golf. He has come to the conclusion that "it is highly probable that the trajectory of the ball is largely influenced by this period of contact."

I have seen many goals kicked at Rugby football, and have kicked a few myself, and I am almost sure that in every case when a goal was scored the boot had a good deal to do with the direction. Marvellous _analysis_ this!

We may, however, discard these wonderful efforts of analysis and deal with the remark made by the author that "if you follow through, your club head travels in precisely the same line as the ball," for this is absolutely incorrect in the case of many strokes wherein one desires to influence the flight of the ball by applying spin. For instance, at practically no time of its travel, no matter how good the stroke is and how perfect one's follow-through, is the club head in the slice or the pull "in precisely the same line as the ball." This is merely one of hundreds of instances of confused thought for which the poor golfer has to suffer.

I have before referred to the idea of pulling and slicing to counteract wind. It is astonishing how deeply rooted this idea is. At page 53 of _Concerning Golf_ Mr. John L. Low says: "There is no shot which produces such straight results as the sliced shot against a right hand breeze," to which I reply that there is no shot which gives such straight results as the straight shot in itself without slice or pull of any description whatever, and that as a matter of fact it is practically impossible to calculate within twenty yards, and that means double the distance, where one will land if one starts pulling and slicing in a cross wind.

A characteristic stroke, showing Duncan's perfect finish in
the drive.]

This is a matter of such importance that I must quote Harry Vardon in support of my statement. He says at page 92 of _The Complete Golfer_:

Now, however, that this question is raised, I feel it
desirable to say, without any hesitation, that the majority
of golfers possess vastly exaggerated notions of the effect
of strong cross winds on the flight of their ball. They
greatly over-estimate the capabilities of a breeze. To judge
by their observations on the tee, one concludes that a wind
from the left is often sufficient to carry the ball away at
an angle of 45 degrees, and indeed sometimes when it does
take such an exasperating course and finishes on the journey
some fifty yards away from the point from which it was
desired to despatch it, there is an impatient exclamation
from the disappointed golfer, "Confound this wind! Who on
earth can play in a hurricane!" or words to that effect. Now
I have quite satisfied myself that only a very strong wind
indeed will carry a properly driven ball more than a very few
yards out of its course, and in proof of this I may say that
it is very seldom when I have to deal with a cross wind that
I do anything but play straight at the hole without any
pulling or slicing or making allowances in any way.

If golfers will only bring themselves to ignore the wind,
then it, in turn, will almost entirely ignore their straight
ball. When you find your ball at rest the afore-mentioned
forty or fifty yards from the point which you desired to send
it, make up your mind, however unpleasant it may be to do so,
that the trouble is due to an unintentional pull or slice,
and you may get what consolation you can from the fact that
the slightest of these variations from the ordinary drive is
seized upon with delight by any wind, and its features
exaggerated to an enormous extent. It is quite possible
therefore that a slice which would have taken the ball only
twenty yards from the line when there was no wind, will take
it forty yards away with the kind assistance of its friend
and ally.

These are, unquestionably, words of wisdom. There can be no doubt whatever that the straight ball is the ball all the time in golf, and it is absolutely certain that what Vardon says about the effect of the wind on the golf ball is true. Wind has remarkably little effect on the golf ball which is driven without spin. I have had no doubt on this subject for at least seventeen years. I had my lesson in one ball during the course of a match played over my home links in New Zealand. One of the holes was on top of a volcanic mountain at a place where New Zealand is only a few miles wide, and there was a howling gale raging from ocean to ocean right across the island. I can remember as if it were yesterday, the champion of New Zealand, as he was then, playing this hole. He drove a very high and perfectly straight ball from tee to green, and the ball travelled to all appearances as directly as if there had been no wind whatever, whereas had there been the least slice on the ball it would have been picked up by the wind and carried away into the crater which lay sixty or a hundred yards off the course.

Speaking of Mr. Low reminds me that he makes some extraordinary statements with regard to spin. At page 35 of _Concerning Golf_ he says: "I have said that a ball with left to right spin swings in the air towards the left in exactly the opposite direction from a sliced ball and from contrary causes." It is obvious that this is wrong, for the spin of the slice is from left to right, and of course, as every one knows, that spin makes the ball swerve towards the right, which is the swerve of the slice.

At page 32 Mr. Low makes the same error. He says there: "Now a pulled ball comes round to the left because the sphere is rotating from left to right, or in the direction contrary to the hands of a watch." This, of course, is a contradiction, for the hands of a watch as we look at them do rotate from left to right, but in any case Mr. Low's explanation is quite incorrect, because the spin of the ball is not in a direction contrary to the hands of a watch laid face upwards on the ground, as Mr. Low affirms.

Mr. Low says at page 31:

Every child nowadays seems to know how to slice a ball; you
have only to ask the question and the answer will come
quickly enough, "Oh, draw the hands in when you are hitting,"
or, in other words, spin the ball in the direction of the
hands of a watch laid face upwards on the ground. The ball
advancing with this spin finds it is resisted most strongly
by the atmosphere on its left side, and therefore goes
towards the right in the direction of least resistance. The
converse is the case with a pulled ball in the sense of a
ball which curves in the air from right to left.

We have already shown in dealing with Professor Thomson's article that this statement is quite incorrect. In passing I may also refer to the fact that Mr. Low's idea of the production of the slice, viz. by drawing the hands in when one is hitting, is also wrong. There is no drawing in of the hands at the moment of impact in the properly played slice. It is the drawing in, if we may use the term, of the head of the club in its travel across the intended line of flight, but not anything which is done intentionally during impact. However, that is by the way.

Mr. Low is evidently under the impression, as was Professor Thomson, that the spin of the ball in the slice is about a vertical axis. This is an error in itself, as we have shown, but it is not nearly so bad an error as it is to say that the pull is the converse of the slice in this respect, for, as we have seen, if the ball were merely spinning about a vertical axis it could not possibly have the running powers which it possesses, to say nothing of its low flight. Although Mr. Low has got somewhat mixed in describing his rotation, it is evident from his reference to the hands of the clock that his ideas are correct in so far as regards the general direction of spin, but where he is at fault is in stating the axis of rotation of his ball.

If we accept Mr. Low's statement about the axis of rotation we shall have the pulled ball, when it lands, striking the earth with a spin equivalent to a sleeping top, but that is not what we want in the pulled ball, for neither would it give us the low trajectory which we desire so much, nor would it give us, on landing, the running which we desire, if anything, still more. The spin which we desire to produce and which we must have in our minds to produce when we are playing the stroke, is such a spin as will give us, when the ball lands, approximately the spin of a disc top as it falls to earth when its spin is nearly exhausted. I am speaking now, of course, not of the question of degree, but of the plane of spin. We must have our ball spinning in such a plane that when it touches the earth it will behave in the same manner as the disc top does when its side comes into contact with the floor.

In dealing with "The Science of the Stroke," James Braid in _Advanced Golf_ goes into an analysis of the effect of spin on flight. He says early in the chapter:

At the present time most players know how they ought to be
standing, and what the exact movements of their arms, wrists,
and body should be in order to swing the club in the right
way and make the ball travel as far as possible, but they do
not all know, and in few cases one suspects have ever
troubled to think, what is the process by which these
movements, when properly executed, bring about the desired
effect.

I do not know how Braid can truthfully say that at the present time most players know how they ought to be standing, when we are confronted with the fact that his own book, _Advanced Golf_, and practically every book which has been published on the game, tells the unfortunate golfer to stand as he ought not to be standing instead of giving him the simple truth and sound golf, and it is incomprehensible to me how Braid can say that they know "what the exact movements of their arms, wrists, and body should be in order to swing the club in the right way," when he himself has confessed in _Advanced Golf_ that, particularly with regard to the wrists, which unquestionably have a most important function to fulfil in the golf drive, he absolutely does not know where they come in. It is useless in a work on _Advanced Golf_ to assume on the part of one's readers a knowledge superior to that which the author of the book himself has given as his own limitations. Braid says:

They have the cause and also the effect, but they do not
often see the connection between the two. Of course, the ball
in a ball game moves always according to scientific laws, but
it has seemed to those who have studied these matters that
the scientific problems involved in the flight of the golf
ball are more intricate, but at the same time more
interesting, than in many other cases.

Of course this is quite stupid, because, as I have frequently explained, there is no special set of mechanical laws for golf--or the golf ball.

The golf ball follows in all respects exactly the same laws as those which govern the flight and run of any other ball. The only difference in connection with the golf ball is that it is probably the most unscientifically constructed ball in the world of sport. Braid continues:

The chief matter of this kind that it is desirable the golfer
should understand is that concerning the character and effect
of the spin that is given to the golf ball when it leaves the
club. This spin is at the root of all the difficulties and
all the delights of the game, and yet there are some
players--one might even say many--who do not even know that
their ball spins at all as they hit it from the tee.

I may pause here to note that James Braid says that spin is at the root of all the difficulties and all the delights of golf. This is in many respects quite an exaggeration, but I am giving it exactly as he says it, for the simple reason that it emphasises the fact which I have always insisted on, that a proper knowledge of the application of spin to the golf ball is essential for one who would attain to the greatest success or who would obtain the greatest enjoyment from the game.

Braid quotes the work of the late Professor Tait very extensively. Referring to the most important subject of back-spin, he says:

It appears to be the proper regulation of the under-spin
given to the ball when applying it from the tee and through
the green, at all events when length is what is most
required, that makes success, and it is in this way that
players of inferior physical power must make up for their
deficiency and drive long balls.

I may say at once that any idea whatever of the proper regulation of back-spin in the drive is, from the point of view of practical golf, merely nonsense. In so far as regards obtaining extra distance by driving a low ball with back-spin, whose properties I have already fully described, there is nothing whatever to be done but to get back-spin and as much of it as one possibly can. The golfer has yet to be born who in driving can obtain too much back-spin. Braid says:

It is in the long drive that the principles of spin are most
interesting and important, but it must be remembered also
that they are very prominent in their action upon the flight
of the ball in the case of many other shots, and the
peculiarities of different trajectories can generally be
traced to this cause after a very little thought by one who
has a knowledge of the scientific side of the matter, as
explained by Professor Tait. This is particularly the case
with high lofted approach shots.

One may remark here, perhaps, that there is no more unsuitable stroke in which to study the peculiarity of the application of back-spin to the trajectory of the ball than in the high lofted approach shots, for it is in such shots as these practically an impossibility, if one may so express it, to locate the influence of the spin on the flight of the ball. It is quite a different thing in the wind-cheater class of stroke where one sees the ball travelling low across the turf and can absolutely mark the place where the back-spin begins to get to work and give the ball its upward tendency towards the end of the drive, and, when the velocity of the ball has become sufficiently reduced, to allow the back-spin to exert its lifting power.

I now come to a matter which is of very great importance in the application of back-spin to the ball. It is quite evident to me that Braid is falling into the same error as that which was originally made by Professor Tait, and followed fifteen years later by Professor Sir J. J. Thomson. On page 226 he says:

Therefore the great authority concluded that good driving
lies not merely in powerful hitting, but "in the proper
apportionment of quite good hitting with such a knack as
gives the right amount of under-spin to the ball"; and one of
his calculations was to the effect that, in certain
circumstances, a man who imparted under-spin to his ball when
driving it might get a carry of about thirty yards more than
that obtained by another man who hit as hard but made no
under-spin. There would, of course, be a great difference in
the comparative trajectories of the two balls. In the case of
the short one there is no resistance to gravity, and
consequently, in order to get any sort of flight at all, the
ball must be directed upwards when it is hit from the tee,
or, to use a scientific term, there must be "initial
elevation." This may be only very slight, but it is quite
distinguishable, and in fact a player, who is only at the
beginning of his practice, and has little knowledge of the
principles of the game, will generally be found trying to hit
his ball in an upward direction, and by that means will make
it travel farther than it would have done otherwise. On the
other hand, the ball that is properly driven by a good player
is not only not consciously aimed upwards, but, according to
Professor Tait, is not hit upwards. For some distance after
it has left the tee it follows a line nearly parallel with
the ground, and eventually rises as the result of the
under-spin which is forcing it upwards all the time.

We may pause here to consider a few of the statements in this remarkable passage. I may say again that the idea of driving a ball with the "proper apportionment of quite good hitting with such a knack as gives the right amount of under-spin to the ball" is simply a wild guess at what takes place during the execution of a correct drive with back-spin. The proper playing of this stroke is a matter of very considerable difficulty, and it is practically a certainty that no golfer has ever lived or ever will live who could regulate his back-spin in the drive to any appreciable extent; all that he ever thinks of doing--all that he is ever likely to do--is to obtain his back-spin, _and as much of it as he can_.

It is, of course, quite wrong to say that in the ball hit without back-spin there is "no resistance to gravity," for if there were no resistance to gravity the ball would be on the earth. However, we know quite well what is meant, although, when we are dealing with a matter which is absolutely a matter of science, we do not expect such loose statements as these. I should probably have passed this remark, but for the fact that it is emphasised by the statement that in order to get any sort of flight at all the ball must be directed upwards when it is hit from the tee, which again, as a matter of practical golf, is what nine of ten golfers do, although we are told that "a player who is only at the beginning of his practice, and has little knowledge of the principles of the game, will generally be found trying to hit his ball in an upward direction."

It is astonishing how few players, even of quite a good class, are content to leave the question of elevation entirely to the club. It probably would be no exaggeration to say that quite ninety per cent of the players make an attempt, however extremely slight it may be, to assist the club in lifting the ball from the earth. According to the best theory in golf, this is quite wrong, for the blow should be at least in a horizontal direction, which practically it never is, and preferably in the line of the arc formed by the club head in its travel through the air on its downward path. The latter case, of course, would produce back-spin, and a considerable amount of it. The former would probably produce slight back-spin, but a very slight amount. However, the very great majority of golfing hits are at the moment of impact proceeding upwardly, and it is this fact which puts any idea whatever of the unconscious application of back-spin by the ordinary golfer quite beyond serious consideration. The amount of back-spin which is unconsciously applied to the golf ball is practically negligible.

We see that, according to Professor Tait, the ball which is properly driven by a good player is not only not consciously aimed upwards, but that it is actually not hit upwards. Indeed we are told that for some distance after it has left the tee it follows a line nearly parallel with the ground and eventually rises as the result of the under-spin that is forcing it upwards all the time. This statement is not in accordance with the experience of practical golfers. It is evident that Professor Tait was under the impression, in which, as I have stated before and now emphasise, he has been followed by Professor Sir J. J. Thomson, that the beneficial back-spin in golf is obtained by the loft of the club. There can be no doubt whatever that if a golf ball were struck a blow by a golf club having any considerable degree of loft and proceeding at the moment of impact in a straight line, the result would be to impart some degree of back-spin, but this is not what happens in practical golf. At no portion of the travel of the head of the club in the golf drive is it proceeding in a horizontal direction, and in the vast majority of cases, at the moment of impact, even with the very best of stroke players, the club is going upward. If this were not so it would be impossible for many of our greatest drivers to get the trajectories they do with the comparatively straight-faced clubs which they use.

Braid quotes an experiment which was made by Professor Tait in the course of his investigations with regard to the qualities of under-spin. It appears that the Professor laid a ball to the string of a crossbow, the string being just below the middle of the ball, so that when it was let go it would impart a certain amount of under-spin to it. When he shot the ball in this way he made it fly straight to a mark that was thirty yards distant; but when he shot it a second time, pulling the string to the same extent and laying it to the middle of the ball so that no under-spin would be given to it, the ball fell eight feet short of the same mark.

It is impossible to accept such a rough and crude experiment as this as evidence in any way whatever of the influence of back-spin in the drive; rather it would seem to show beyond a shadow of doubt that the extra carry was obtained because the power of propulsion was applied to the ball at a lower portion, and therefore tended to give it a greater trajectory. It should be obvious that this result would be obtained even disregarding the question of back-spin, which in such an extremely short flight as thirty yards would certainly not have any opportunity whatever to make such a difference in the length of carry as that suggested.

It is, however, when we come to deal with questions of practical golf that we find that the ideas of the late Professor Tait will not bear looking into.

Braid says:

However, it is well to bear in mind one thing that the
Professor said, "The pace which the player can give the club
head at the moment of impact depends to a very considerable
extent on the relative motion of his two hands (to which is
due the 'nip') during the immediately preceding two-hundredth
of a second, while the amount of beneficial spin is seriously
diminished by even a trifling upward concavity of the path of
the head during the ten-thousandth of a second occupied by
the blow."

Here we have plain evidence of the fact that Professor Tait is under the impression that there is some particular snap which he calls "nip" imported into the stroke immediately before impact. We have already dealt fully with this matter. We remember what Vardon has said in condemning the idea, and we know that Braid himself has confessed that he knows nothing about the matter, so it will not seem disrespectful if we come to the conclusion that we can disregard this vague statement about the "nip" in the blow. We can then proceed to notice the really important remark made that "the amount of beneficial spin is seriously diminished by even a trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow." It seems to me that this last statement is absolutely accurate, and it is the thing which I have always contended for in dealing with the practical side of golf driving, as contradistinguished from the purely theoretical, which has been put before us by Professor Tait, and following him, by Professor Sir J. J. Thomson. It will be observed that Professor Tait said that the amount of beneficial spin is "seriously diminished by even a trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow."

Some of my readers may remember that when I was dealing with Professor Sir J. J. Thomson's lecture before the Royal Society in an article which appeared in _The English Review_ in February 1911, I stated that what actually did happen was that there took place in practically every drive at golf exactly this "trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow," and that therefore the amount of beneficial back-spin obtained from the loft of the club was practically negligible.

It is quite clear that Professor Tait was under the impression that back-spin was got from the loft of the club proceeding in a horizontal direction, but it is well known now to golfers who give the science of the game any attention whatever, that back-spin is not obtained in this manner, and that back-spin so obtained would be practically ineffectual as an aid to distance, for the loft of the driver and the brassy is not sufficient, even if the golf drive were played in the manner suggested, to produce any considerable amount of back-spin. As we have already seen, the beneficial back-spin in the golf drive is obtained by the club striking the ball _long before the beginning_ of the "upward concavity of the path of the head," that is to say, in its arc _as it is proceeding downwards_ to the lowest point in the swing from which it then starts that "upward concavity."

I have emphasised and re-emphasised this matter, for it is evident that when famous men like Professors Tait and Thomson start out with an absolutely erroneous idea, an idea which is _fundamentally_ wrong, it is quite natural for less gifted men to be led astray. Braid says, and it must be remembered that this is in _Advanced Golf_ (page 229): "So far as I know, it cannot be stated in accurate scientific terms and figures, and by lines drawn on paper, what is the proper scientific swing in order to get the best drive." This seems to me, especially in a book like this, to be a wonderful statement, particularly when we are dealing with the scientific results arrived at by men of the greatest eminence, results which I may say have been known for more than two hundred and fifty years.

There is no doubt whatever which is the best way to swing in order to get the best drive, and it can be explained in scientific language and shown by diagram and by figures, and in fact it has been so shown again and again.

Braid says:

What golfers have done, therefore, in the past has been to
find out gradually which is the best way in which to hit the
ball in order to make it travel far, and thus they have
groped their way to the stances and swings which, if the
truth were known, would probably be set out by science as the
best possible ones for the purpose.

This very well expresses what has taken place. The golfers have "groped their way" to what they have found out, without a glimmering of the scientific reasons for doing it, and the consequence is that, as they got their practice first, and were not informed of what they were doing by that theory which is the best of all theory, the concentrated essence of the practice of experts, they have signally failed to impart their science to those who have come after them.

At page 229 Braid says:

However, there are certain things that the player should know
about his drive when it is right, and which he should aim at
producing, and they have been very well set forth by
Professor Tait as the result of his investigations into the
trajectories of golf balls hit under varying conditions of
club-force, wind, and so forth. One of the first things to
say, and this is really important in estimating their chances
of making certain carries that are constantly set to them in
the course of their play, is that some golfers have a
delusion to the effect that the ball is at its highest point
in the middle of its flight--that is to say, they think that
just about half-way between the point from which it was hit
and the point at which it will touch the ground again, the
ball is at its highest, and after that commences to fall
again. In this belief when they have, say, a 140 yards' carry
to make, they will reckon that their ball must then be coming
down very fast towards the turf, having been at its highest,
some 50 or 60 yards before. They may think in such
circumstances that they ought to hit up a little more and try
to hit harder to make up for doing so. They would be wrong
entirely, and that because they did not know what the
under-spin was that they gave to the ball, or what effect it
had on its flight. Thus in the case just quoted, assuming
that the ball had a total carry of from 150 to 160 yards, it
would be at its highest point when it had travelled about 130
yards, and there would be no occasion to hit up, unless the
object to be carried were very high.

It is obvious that in such a case as that given no practical golfer would in any way whatever consider the question of the _amount_ of back-spin on his ball, for he would know that he has no possibility whatever of gauging its effect in the air in such a shot, and he will leave that to regulate itself and to act when the ball strikes the earth.

It is unquestionable that theoretically this may be done, and it is well known that I am a strong advocate of the use of back-spin, but in the case quoted by Braid there is nothing whatever to show that the ball has been played in such a manner as to produce an appreciable quantity of serviceable back-spin, or that such a method of play is necessary or advisable.

Braid continues:

The fact is that a well-driven ball that has a total
carry--that is, from the tee to the point where it touches
the turf again, and not the distance of the obstacle that it
clears--of about 165 yards, under normal conditions of wind
and weather, is at its highest about 135 yards from the point
where it was struck, and after that it begins to fall
rapidly. This is chiefly the result of the under-spin which
is given to it when it is struck by the driver in the proper
way, and it shows the importance of under-spin to the golfer,
for if there were none, then all our courses would have to be
shortened, hazards brought closer to the tee, and the
principles upon which the game is played would have to be
altered in many respects. If there were no under-spin, then
the ball would have no help against the force of gravity, and
the result would be that the highest point of its flight
would be half-way between the point from which it was driven
and that at which it alighted.

We see here again strong evidence of the fact that Braid is under the same impression as Professor Tait, and that is that the back-spin of golf is obtained from the loft of the club, whereas the loft of the club has one function, and that is to raise the ball from the earth, and there will be no particular necessity to alter our courses, for in ordinary every-day golf, back-spin is practically not used, except when it is intentionally applied by the golfer by means of the stroke suitable for its production.

Braid gives a series of diagrams taken from Professor Tait's lecture which illustrate various trajectories of golf balls driven in varying circumstances. Many of these are so entirely theoretical that I need not consider them, but in referring to one of them Braid says:

The ball which has travelled farthest, or rather the one that
has been given most carry, is that which has been hit in the
right way, and to which has therefore been imparted the right
amount of under-spin. This is, in fact, the ideal trajectory
of a well-driven ball. It starts low, rises very slowly and
gradually, the line of flight bending upwards slightly, and
does not come down too quickly after the vertex has been
reached.

This is, on the whole, a sound but very general description of an accurately played wind-cheater, but the remarkable thing is that although Braid expresses himself in such terms of admiration for this particular ball he does not anywhere in _Advanced Golf_ show us how to produce the stroke which gives this beneficial back-spin. This surely is a very great oversight. Nor so far as I have been able to see does he explain clearly how the beneficial back-spin of golf is obtained.

Braid shows clearly by his quotation from Professor Tait's article that in the Professor's mind was the deep-rooted idea that it was possible to drive golf balls by a stroke delivered at the moment of impact in the same manner as is a blow from a billiard cue, but, needless to say, this is in the golf drive utterly impracticable. Professor Tait, in his paper, used a considerable number of diagrams to show that too much back-spin is bad in the drive, but as I have already pointed out, although this is very well in mere theory, it does not work out in the slightest degree in golf. It is easy to take light balloons and give them back-spin and show that it influences their trajectories to such an extent that they will go behind the point where they were struck, but a golf ball is a very small, hard, and heavy thing, and by the time that its back-spin begins to exert its influence in a marked manner on its flight it has travelled a considerable distance and the rate of spin will have materially diminished, so that no golfer need ever be afraid of applying too much back-spin to his drive.

Braid proceeds:

Of course, as already indicated, the golfer does not know,
and in one sense does not care exactly how much under-spin he
gives to his ball when he drives it, only being aware that he
has given too much or too little according to results, and
knowing also that in either case excess or otherwise was due
to faulty stance or swing--most frequently this--or both. In
the present case of this high trajectory, the exact amount of
under-spin given to the ball is half as much again as that
given to the properly driven ball, and under the same normal
conditions these would be the relative flights of the two
balls.

Now it is obvious that if Professor Tait was under the impression that the beneficial back-spin of golf was obtained merely from the horizontal blow delivered through the centre of the ball's mass, so that the ball took some slight spin by its roll up the face of the club, he had no very accurate idea of the rate of spin of that ball at the moment it left the face of the club, so that any attempt whatever on his part to measure the respective rates of spin of the different flight of these balls must be received with very great caution. As a matter of fact the rate of spin of the golf ball at the moment it leaves the club in a well-played drive with back-spin would be immeasurably faster than anything supposed by Professor Tait, who based his calculations on the ball obtaining this back-spin _from the loft of the club_, which is undoubtedly a grave error, and Braid wholly subscribes to this error, which is not to be wondered at, for Professor Sir J. J. Thomson, one of the most eminent scientists, has fallen into the same trap.

Professors Tait and Thomson and James Braid talk much about the possibility of obtaining too much back-spin in the drive. This is scarcely theoretically possible in golf, and it is practically impossible. I will give an example taken from practical golf which will, I believe, quite convince any golfer that the possibility of obtaining too much back-spin in the drive need never be considered.

Let us imagine a very badly sliced ball. By a badly sliced ball I do not necessarily mean an extremely quick slice where the ball leaves the line of flight to the hole quite suddenly, nor do I mean a ball pushed away to the right of the line to the hole; what I do mean is a ball which has been so sliced that it takes a tremendous curve from left to right, beginning to develop that slice in a pronounced manner at, say, half to two-thirds of its carry, which is quite bad enough for a slice. We frequently see in such a case, particularly on a windy day, and even on a still one, the great power which the spin has to deflect the ball from the line to the hole. It must be remembered that in this curve the spin is assisted by gravity--the ball is falling much of the time as it is being edged away--and even then it will be apparent that it is easy to get much greater spin in the slice than it is in the wind-cheater, for the simple reason that in the slice one has an unrestricted cut across the ball, whereas one has not this opportunity with the wind-cheater, for one hits the ground immediately one passes the ball.