"It was hard upon high noon; and Ahab, seated in the bows of his high-hoisted boat, was about taking his wonted daily observation of the sun [the noon sight] to determine his latitude [if he had a chronometer, he could have also determined his longitude]. Well that Ahab's quadrant [a device used to sight the sun to measure its elevation] was furnished with colored glasses, through which to take sight of that solar fire -- to catch the precise instant when the sun should gain its precise meridian [the sun is said to be 'on the meridian' at local noon -- the latin A.M., ante meridiem, and P.M., post meridiem, follow from this]. At length the desired observation was taken; and with his pencil upon his ivory leg, Ahab soon calculated what his latitude must be at that precise instant [this gives him his distance north of the equator; but he needs longitude to plot his position as a point on a chart]."
"Then falling into a moment's reverie, he again looked upwards towards the sun and murmured to himself: 'High and mighty Pilot! thou tellest me truly where I am -- but canst thou the least hint where I shall be? Where is Moby Dick? This instant thou must be eyeing him.'"
"Then gazing at his quadrant, he pondered again, and muttered: 'Foolish toy! babies' plaything of haughty Admirals, and Commodores, and Captains; but what after all canst thou do? Thou canst not tell where one drop of water or one grain of sand will be to-morrow noon; and yet with thy impotence thou insultest the sun! Science! Curse thee, thou vain toy! Curse thee, thou quadrant!' dashing it to the deck, 'no longer will I guide my earthly way by thee!' [This is quite a tantrum, and proof to the crew -- or ought to be -- that their Captain is unfit to command.] 'The level ship's compass, and the level dead-reckoning, by log and by line; these shall conduct me, and show me my place on the sea.' [By deciding to navigate by 'dead-reckoning', Ahab has taken on quite a handicap] 'Aye, thus I trample on thee, thou paltry thing that feebly pointest on high; thus I split and destroy thee!' [Bravely spoken like a spoiled brat who can't have his way. Ahab displays a colossal selfishness that puts the men under his command in dire jeopardy.]
Fedallah, who watched all this unseen by Ahab, is described as displaying "a sneering triumph" on his face meant for Ahab, and "a fatalistic despair" meant for himself. Ahab has just heard fantastic prophecies aplenty out of the mouth of Fedallah. Looking to his 'scientific' instrument, he despairs of getting any predictions at all out of the quadrant, and in a fit of temper stomps it to death. Ahab has already renounced smoking his pipe (Chapter 30) and his razors (Chapter 113) -- now he renounces the quadrant. Deepening depression.
Ahab gives the command to head for the equator: "To the braces! Up helm! -- Square in!" As the Pequod heads south, Starbuck predicts that Ahab's fiery life will amount to nothing but ashes; jolly Stubb says, "Ahab, but thou actest right; live in the game, and die in it!"