This section is from the book "The Soul Of Golf", by P. A. Vaile. Also available from Amazon: The soul of golf.
I am quite in accord with what James Braid says about this method of putting, and I do not for one moment think that the short grip should be used for approach puts, but I am sure the nearer one gets to the hole the closer one should get down to the ball. Braid deals further on with the question of shortening one's putter. He says:
As to the length of the shaft, many players, because they find that they always grip their putters a foot or so from the end of it, proceed in due course to have the best part of that foot cut off, or in purchasing a new putter they have the shaft cut very short. Are they quite satisfied that it is not better to have a fair amount of shaft projecting up above the place where they grip when that place is very low down?
The answer to this is that in many cases the wood which projects above the grip is very much in the way of true putting. Any golfer who is foolish enough to cut anything like a foot off any club without any compensation to the head in the way of balance must be expected to pay the penalty for his ignorance, and anyone having a club constructed for him on such a principle, or, rather, want of principle, will inevitably pay for it. Braid goes on to say:
Often enough no consideration is given to this point; it is not imagined that the shaft above the grip can serve any useful purpose. Yet it is constantly found that a putter cut down is not the same putter as it was before, not so good, and has not the same balance; and, again, many players must have been surprised sometimes, when doing some half-serious putting practice with a cleek, iron, or driving mashie, each club with its long shaft, to find out what wonderfully accurate work could be done in this way. The inference from all experience, having theoretical principle to back it, is that the top or spare part of the shaft acts as a kind of balance when the putter is gripped low down, and tends materially to a more delicate touch and to true hitting of the ball. A very little reflection will lead the reader to believe that this is so, and in some cases it may lead him towards a revision of his present methods.
Personally, I should not think that even "a very little reflection" would be necessary to induce anyone to believe that the top part of the shaft acts "as a kind of balance" when the putter is gripped low down, but it is quite obvious that it is possible to build a putter, let us say, for the sake of example, two-thirds of the length of an ordinary putter, which is just as perfectly balanced as the long club. This is not any question of theory - it is a matter of absolutely proved and tried practice in golf. One may have a perfect putter which will be ruined by taking a few inches off the shaft. The balance of that putter is probably irrevocably destroyed, unless, perchance, the owner is lucky in adding weight to the head in some way, but dealing with a putter like this is tricky work for one who does not understand it. The main point in connection with this matter of Braid's, which I have quoted, is that he gives a kind of qualified approval to the idea of the short putter for short puts. Personally, I think it is the soundest of sound golf, and I am inclined to think that before many years we shall see the shorter clubs used in their proper place when their value is more clearly understood.
Vardon has some very interesting things to say in his book, The Complete Golfer, on "Complicated Putts," while dealing with what he calls "one of the most difficult of all putts - that in which there is a more or less pronounced slope from one side or the other, or a mixture of the two." As he truly says, "In this case it would obviously be fatal to putt straight at the hole." He continues: "I have found that most beginners err in being afraid of allowing sufficiently for the slope "; and I have found that nine champions of ten make exactly the same error. It is as bad a fault at golf as it is at bowls to be "narrow," by which, in golf, is meant not to allow enough for the slope of the green, for it is obvious that if one is narrow one does not give the hole a chance any more than one does when one is short; so we may add to the stock maxim in putting "Never up, never in," another one, which is just as sound, "Never be narrow."
Vardon goes fully into the general principles underlying these complicated puts, but as I have already indicated, this is unquestionably a matter which can only be settled by practice on the green; but he also goes into the question of the manner in which the stroke should be played, and here we have a subject which legitimately comes within the scope of this work. He continues:
But there are times when a little artifice may be resorted to, particularly in the matter of applying a little cut to the ball. There is a good deal of billiards in putting, and the cut stroke on the green is essentially one which the billiard player will delight to practise, but I warn all those who are not already expert at cutting with the putter to make themselves masters of the stroke in private practice before they attempt it in a match, because it is by no means easy to acquire. The chief difficulty which the golf student will encounter in attempting it will be to put the cut on as he desires, and at the same time to play the ball with the proper strength and keep on the proper line. It is easy enough to cut the ball, but it is most difficult, at first at all events, to cut it and putt it properly at the same time. For the application of cut, turn the toe of the putter slightly outwards and away from the hole, and see that the face of the club is kept to this angle all the way through the stroke. Swing just a trifle away from the straight line outwards, and the moment you come back on to the ball draw the club sharply across it. It is evident that this movement, when properly executed, will give to the ball a rotary motion, which on a perfectly level green would tend to make it run slightly off to the right of the straight line along which it was aimed.
 
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