Let the angle YCB, to which the yard is braced up, be called the trim of the sails, and expressed by the symbol b. This is the complement of the angle DCI. Now Cl:ID rad.:tan. DCI = I:tan. DCI = I: cotan. b. Therefore we have finally I: cotan. b = A':B':tan.2x, and A' cotan. b B 'angent, and tan. 'x = cot. This equation evidently ascertarns the mutual relation between the trim of the sails and the leeway.
'It is quite evident, is it not, Jacky darling?' said a hopeful voice, and a rather large young woman bent kindly over him (for at this stage in his memory he was only twelve, a stocky little boy, and tall, nubile Queeney sailed high above).
'Why, no, Queeney,' said the infant Jack. 'To tell you the truth, it ain't.'
'Well,' said she, with untiring patience. 'Try to remember what a cotangent is, and let us begin again. Let us consider the ship as an oblong box'
For a while he considered the Sophie as an oblong box. He had not seen a great deal of her, but there were two or three fundamentals that he knew with absolute certainty: one was that she was under-rigged she might be well enough close to the wind, but she would be a slug before it; another was that his predecessor had been a man of a temper
entirely unlike his own; and another was that the Sophie's people had come to resemble their captain, a good sound quiet careful unaggressive commander who never set his royals, as brave as could be when set upon, but the very opposite of a Sallee rover. 'Was discipline to be combined with the spirit of a Sallee rover,' said Jack, 'it would sweep the ocean clean.' And his mind descending fast to the commonplace dwelt on the prize-money that would result from sweeping the ocean even moderately clean.
'That despicable main-yard,' he said. 'And surely to God I can get a couple of twelve-pounders as chasers. Would her timbers stand it, though? But whether they can or not, the box can be made a little more like a fighting vessel more like a real man-of-war.'
As his thoughts ranged on so the low cabin brightened steadily. A fishing-boat passed under the Sophie's stern, laden with tunny and uttering the harsh roar of a conch; at almost the same time the sun popped up from behind St Philip's fort it did, in fact, pop up, flattened like a sideways lemon in the morning haze and drawing its bottom free of the land with a distinct jerk. In little more than a minute the greyness of the cabin had utterly vanished: the deck-head Was alive with light glancing from the rippling sea; and a single ray, reflected from some unmoving surface on the distant quay, darted through the cabin windows to light up Jack's coat and its blazing epaulette. The sun rose within his mind, obliging his dogged look to broaden into a smile, and he swung out of his cot.
The sun had reached Dr Maturin ten minutes earlier, for he was a good deal higher up: he, too, stirred and turned away, for he too had slept uneasily. But the brilliance prevailed. He opened his eyes and stared about very stupidly: a moment before he had been so solidly, so warmly and happily in Ireland, with a girl's hand under his arm, that his waking mind could not take in the world he saw. Her touch was still firm upon his arm and even her scent was there: vaguely he picked at the crushed leaves under him -dianthus perfragrans. The scent was reclassified a flower, and nothing more and the ghostly contact, the firm print of fingers, vanished. His face reflected the most piercing unhappiness, and his eyes misted over. He had been exceedingly attached; and she was so bound up with that time.
He had been quite unprepared for this particular blow, striking under every conceivable kind of armour, and for some minutes he could hardly bear the pain, but sat there blinking in the sun.
'Christ,' he said at last. 'Another day.' With this his face grew more composed. He stood up, beat the white dust from his breeches and took off his coat to shake it. With intense mortification he saw that the piece of meat he had hidden at yesterday's dinner had oozed grease through his handkerchief and his pocket. 'How wonderfully strange,' he thought, 'to be upset by this trifle; yet I am upset.' He sat down and ate the piece of meat (the eye of a mutton chop); and for a moment his mind dwelt on the theory of counter-irritants, Paracelsus, Cardan, Rhazes. He was sitting in the ruined apse of St Damian's chapel high above Port Mahon on the north side, looking down upon the great winding inlet of the harbour and far out beyond it over a vast expanse of sea, a variegated blue with wandering lanes; the flawless sun, a hand's breadth high, rising from the side of Africa. He had taken refuge there some days before, as soon as his landlord began to grow a shade uncivil; he had not waited for a scene, for he was too emotionally worn to put up with any such thing.
Presently, he took notice of the ants that were taking away his crumbs. Tapinoma erraticum. They were walking in a steady two-way stream across the hollow, or of his inverted wig, as it lay there looking very like an abandoned bird's nest, though once it had been as neat a physical bob as had ever been seen in Stephen's Green. They hurried along with their abdomens high, jostling, running into one another: his gaze followed the wearisome little creatures, and while he was watching them a toad was watching him: their eyes met, and he smiled. A splendid toad: a two-pound toad with brilliant tawny eyes. How did he manage to make a living in the sparse thin grass of that stony, sun-beaten landscape, so severe and parched, with no more cover than a few tumbles of pale stone, a few low creeping hook-thorned caper-bushes and a cistus whose name Stephen did not know? Most remarkably severe and parched, for the winter of 1799-1800 had been uncommonly dry, the March rains had failed and now the heat had come very early in the year.