Grenier, a French flag officer, had produced his L’Art de la Guerre sur Mer, in which he boldly attacked the law laid down by De Grasse, that so long as men-of-war carried their main armament in broadside batteries there could never be any battle order but the single line ahead.  In Grenier’s view the English had already begun to discard it, and he insists that, in all the actions he had seen in the last two wars, the English, knowing the weakness of the single line, had almost always concentrated on part of it without regular order.  The radical defects of the line he points out are:  that it is easily thrown into disorder and easily broken, that it is inflexible, and too extended a formation to be readily controlled by signals.  He then proceeds to lay down the principle on which a sound battle order should be framed, and the fundamental objects at which it should aim[6].  His postulates are thus stated: 

’1.  De rendre nulle une partie des forces de l’ennemi afin de reunir toutes les siennes contre celles qui l’on attaque, ou qui attaquent; et de vaincre ensuite le reste avec plus de facilite et de certitude.

’2.  De ne presenter a l’ennemi aucune partie de son armee qui ne soit flanquee et ou il ne put combattre et vaincre s’il vouloit se porter sur les parties de cette armee reconnues faibles jusqu’a present.’

Never had the fundamental intention of naval tactics been stated with so much penetration, simplicity, and completeness.  The order, however, which Grenier worked out—­that of three lines of bearing disposed on three sides of a lozenge—­was somewhat fantastic and cumbrous, and it seems to have been enough to secure for his clever treatise complete neglect.  It had even less effect on French tactics than had Nelson’s memorandum on our own.  This is all the more curious, for so thoroughly was the change that was coming over English tactics understood in France that Villeneuve knew quite well the kind of attack Nelson would be likely to make.  In his General Instructions, issued in anticipation of the battle, he says:  ’The enemy will not confine themselves to forming a line parallel to ours....  They will try to envelope our rear, to break our line, and to throw upon those of our ships that they cut off, groups of their own to surround and crush them.’  Yet he could not get away from the dictum of De Grasse, and was able to think of no better way of meeting such an attack than awaiting it ‘in a single line of battle well closed up.’

In England things were little better.  In spite of the fact that at Camperdown Duncan had actually found a sudden advantage by attacking in two divisions, no one had been found equal to the task of working out a tactical system to meet the inarticulate demands of the tendency which Grenier had noticed.  The possibilities even of Rodney’s manoeuvre had not been followed up, and Howe had contented himself with his brilliant invention for increasing the impact and decision of the single line.  It was reserved for Nelson’s genius to bring a sufficiently powerful solvent to bear on the crystallised opinion of the service, and to find a formula which would shed all that was bad and combine all that was good in previous systems.[7]