The correct answer is B) magnetism from the earth's magnetic field. Compass variation is caused by the difference between true north (the geographic north pole) and magnetic north (the magnetic north pole). This difference is due to the earth's magnetic field, which can cause a compass needle to point in a slightly different direction from true north. The variation depends on the vessel's location and can change over time as the earth's magnetic field shifts. The other answer choices are incorrect because they do not accurately describe the primary cause of compass variation. Worn gears, lack of oil, and onboard magnetism can affect compass accuracy, but they do not cause the fundamental variation between true and magnetic north.