A. A. sombre caverns rose to their feet and stood to attention: 'Eyes front!' 'Sit down/ he said. They were very cheerful, the troglodytes. Under the dank earth they sung, wrote letters innumerable, and waited for soup and the night. Outside, beneath an awning of plaited straw> the spotters, who are replaced every half-hour, watched at the four points of the compass. The Lieutenant put on a show for us. The spotter signalled an imaginary aeroplane and with remarkable speed the guns were ready to fire. 'Target on V Tire!' The shooting is directed by the trembling needle of the predictor, that astounding apparatus with the brain of a dazzling arithmetician. To reach an aeroplane that is moving at a vaguely determined height at a speed of three to four hundred miles an hour presents a problem worthy of an Einstein, a problem only to be solved in four dimensions. The guns of the A. A. fire upon an aeroplane in the future. To the predictor, a metal box larded with frames, the officer submits the elements of the problem: the direction and speed of the wind, the height of the machine as determined by the telemeter, the speed of the aeroplane, et cetera. An equation has to be established between these data and the direction of 49