So far as we can judge, the current view at this time was that where fleets were equal, every known form of concentration was unadvisable upon an unshaken enemy. The methods of the Duke of York's school were regarded as having failed, and the result appears to have been to convince tacticians that with the means at their disposal a strict preservation of the line gave a sure advantage against an enemy who attempted an attack by concentration. Tactics, in fact, in accordance with a sound and inevitable law, having tended to become too recklessly offensive, were exhibiting a reaction to the defensive. If the enemy had succeeded in forming his line, it had come to be regarded as too hazardous to attempt to divide his fleet unless you had first forced a gap by driving ships out of the line. This idea we see reflected in the 6th paragraph of the Duke of York's twenty-second article (1673) and in Russell's new twenty-third article, enjoining ships to close up any gap that may have been caused by the next ahead or astern having been forced out of the line. Briefly stated, it may be said that the preoccupation of naval tactics was now not so much to break the enemy's line, as to prevent your own being broken.

But the matter did not end here. It was seen that when your own fleet was superior, concentration was still practicable in various ways, and particularly by doubling. Tacticians were now mainly absorbed in working out this form of attack and the methods of meeting it, and Russell's elaborate articles for handling squadrons and subdivisions independently may well have had this intention.

The new phase of tactical opinion is that which we find expounded in Père Hoste's famous work, L' Art des armées navales, ou Traité des évolutions navales, published in 1697 at the instigation of the Comte de Tourville. The author was a Jesuit, but claims that he is merely giving the result of his experience while serving with the great French admirals of that time, who had learned all they knew either as allies or enemies of the English. 'For twelve years,' he says in his apology for touching naval subjects, 'I have had the honour of serving with Monsieur le Maréchal d'Estrées, Monsieur le Duc de Mortemart, and Monsieur le Maréchal de Tourville in all the expeditions they made in command of naval fleets; and Monsieur le Maréchal de Tourville has been kind enough to communicate to me his lights, bidding me write on a matter which I think has never before been the subject of a treatise.'

The whole system of tactics that he develops is based, like Russell's, on the single line ahead and the independent action of squadrons. The passages in which he elaborates the central battle idea of concentration by doubling are as follows: 'The fleet which is the more numerous will try to extend on the enemy in such a manner as to leave its rearmost ships astern, which will immediately turn [se repliera] upon the enemy to double him, and put him between two fires. Remark I.—If the more numerous fleet has the wind it will be able more easily to turn its rear upon that of the enemy, and put him between two fires. But if the more numerous fleet is to leeward it ought none the less to leave its rear astern, because the wind may shift in the fight. Besides, the fleet that is to leeward can edge away insensibly in fighting to give its rearmost ships a chance of doubling on the enemy by hugging the wind. Remark II.—I know that many skilful people are persuaded that you ought to double the enemy ahead; because, if the van of the enemy is once in disorder it falls on the rest of the fleet and throws it infallibly into confusion.' And by the aid of diagrams he proceeds to show that this view is unsound, because the van can easily avoid the danger while the rear cannot. To support his view he instances the entire success with which at the battle of La Hogue, Russell, having the superior fleet, doubled on Tourville's rear.

'To prevent being doubled,' he proceeds, 'you must absolutely prevent the enemy from leaving ships astern of you, and to that end you may adopt several devices when you are much inferior in number.

'I. If we have the wind we may leave some of the enemy's leading ships alone, and cause our van to fall on their second division. In this manner their first division will be practically useless, and if it forces sail to tack upon us it will lose much time, and will put itself in danger of being isolated by the calm which generally befalls in this sort of action by reason of the great noise of the guns. We may also leave a great gap in the centre of our fleet, provided the necessary precautions be taken to prevent our van being cut off. By these means, however inferior we be in numbers, we may prevent the enemy leaving ships astern of us. Example.—Everyone did not disapprove the manner in which Admiral Herbert disposed his fleet when he engaged the French in the action of Bevesier [i.e. Beachy Head] in the year 1690. He had some ships fewer than ours, and he had determined to make his chief effort against our rear. That is why he ordered the Dutch leading division to fall on our second division. Then he opened his fleet in the centre, leaving a great gap opposite our centre. After which, having closed up the English to very short intervals, he opposed them to our rear, and held off somewhat with his own division so as to prevent the French profiting by the gap which he had left in his fleet to double the Dutch. This order rendered our first division nearly useless, because it had to make a very long board to tack on the enemy's van, and the wind having fallen, it was put to it to be in time to share the glory of the action.[3]

'II. If the less numerous fleet is to leeward, the gap may be left more in the centre and less in the van, but it is necessary to have a small detachment of men-of-war and fireships so as to prevent the enemy profiting by the gaps in the fleet to divide it.

'III. Others prefer to give as a general rule, that the flag officers of the less numerous fleet attack the flag officers of the enemy's fleet;[4] for by this means several of the enemy's ships remain useless in the intervals, and the enemy cannot double you.

'IV. Others prefer that the three squadrons of the less numerous fleet each attack a squadron of the more numerous fleet, taking care that each squadron ranges up to the enemy in such a manner as not to leave any of his ships astern, but rather leaving several vessels ahead.

'V. Finally, there are those who would have the less numerous fleet put so great an interval between the ships as to equalise their line with that of the enemy. But this last method is, without doubt, the least good, because it permits the enemy to employ the whole of its strength against the less numerous fleet. I agree, however, that this method might be preferred to others in certain circumstances; as when the enemy's ships are considerably less powerful than those of the less numerous fleet.'