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Five months had been employed in the march from New Carthage to the plains of Italy, of which the actual passage of the Alps had occupied fifteen days. Hannibal's first care was now to recruit the strength of his troops, exhausted by the hardships and fatigues they had undergone. After a short interval of repose, he turned his arms against the Taurinians (a tribe bordering on, and hostile to, the Insubrians), whom he quickly reduced, and took their principal city (Turin). The news of the approach of P. Scipio next obliged him to turn his attention toward a more formidable enemy. In the first action, which took place in the plains westward of the Ticinus, the cavalry and light-armed troops of the two armies were alone engaged, and the superiority of Hannibal's Numidian horse at once decided the combat in his favor. The Romans were completely routed, and Scipio himself severely wounded; in consequence of which he hastened to retreat beyond the Ticinus and the Po, under the walls of Placentia. Hannibal crossed the Po higher up, and, advancing to Placentia, offered battle to Scipio; but the latter declined the combat, and withdrew to the hills on the left bank of the Trebia.

It is impossible to conceive how the taking of Liege prevented the English from landing and invading Belgium. That statement is hardly a compliment to the intelligence or the geographical knowledge of the American people. The fact is that Liege was taken a long time before the British troops landed at Calais, and it is still today in the hands of the Germans without in the least interfering with the arrival of British reinforcements in France and in the territory still left in the possession of Belgium. The fact is that Liege was not taken to prevent the British from entering Belgium, but because it was part of the plan of the German General Staff to invade Belgium at once, to march across her territory, to crush the army of France as soon as possible, and then to turn and attack the Russians on the east.

In some cases, where the density of the solution differs greatly from that of water, the percentage by weight may be given; and in others, mixtures of two or more liquids, the percentages may be given by volume or by weight; as so many c.c. in 100 c.c., or as so many grams in 100 grams, or even as so many grams in 100 c.c. In such cases it must be distinctly shown which method of statement is adopted. One grain per gallon means 1 grain in 70,000 grain-measures, or one part in 70,000. Dividing by 7 and multiplying by 10 will convert grains per gallon into parts per 100,000. Inversely, dividing by 10 and multiplying by 7, will convert parts per 100,000 into grains per gallon. Grams per litre are parts per 1000; multiplying by 100 will give parts per 100,000, and multiplying by 70 will give grains per gallon. Among foreign systems of weights, the French is by far the best. Kilograms (2.205 lbs.) per quintal (220.5 lbs.) are parts per cent.; and grams (15.43 grs.) per quintal are parts per 100,000. From the rule already given, grams per quintal may be converted into ounces to the ton by multiplying by 0.327. The German loths per centner (1/2 oz. (avoirdupois) to 100 lbs.) equal parts per 3200; they are converted into parts per cent. by dividing by 32, or into ounces (troy) per ton by multiplying by 10.208.

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