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If you take a compass to a field and line it up with the Pole Star, the two usually disagree by a few degrees. Navigators, surveyors and phone apps all have to correct for this. An 11th-century note of the effect comes from Shen Kuo, a Chinese official who wrote about magnetised needles in the 11th century. This post covers who he was, what he actually wrote, the physics behind it, and a worked example of correcting a compass bearing.
Who was Shen Kuo?
The MacTutor biography (which spells him Shen Kua) gives his dates as 1031 to 1095. He was born in Hangzhou and rose through the Song civil service, working on water control, land reclamation and map-making. In 1072 he became Director of the Astronomy Bureau, where he planned to measure the positions of the Moon and planets three times a night for five years, and dismissed six staff he found falsifying data.
His career collapsed after a military defeat he was blamed for. In 1086 he was pardoned and allowed to live at an estate he named Dream Brook, where he spent his last years. There he wrote his most famous book, Brush Talks from Dream Brook (Mengxi Bitan), covering mathematics, astronomy, geology, optics, medicine and much more. MacTutor notes that it mentions the magnetic compass and its use in map-making, and that he read sea shells in a mountain cliff as evidence that the land had once been a shore.
What did Shen Kuo write about the compass?
The passage is in chapter 24 of the Brush Talks, which you can read in the original Chinese on Wikisource. In summary, he wrote:
Practitioners of the technical arts rub the point of a needle with a lodestone, and it can then point south, "but it always deviates slightly to the east and does not point due south."
Floated on water, the needle wobbles. Balanced on a fingernail or the rim of a bowl, it turns easily but slips off.
It works better hung from a single silk fibre, fixed to the middle of the needle with a speck of wax the size of a mustard seed, in a place with no wind.
Some needles, after rubbing, point north instead. His household had both kinds.
He admitted that nobody could explain why a lodestone makes a needle point south.
Why does a compass needle not point to true north?
Rubbing a steel needle with a lodestone magnetises it, making it a small bar magnet. A freely hung magnet lines up with the horizontal part of the Earth's magnetic field. But the Earth's magnetic poles are not at the geographic poles, and the field has local irregularities, so magnetic north and true north differ.
NOAA's National Centers for Environmental Information define magnetic declination as "the angle between magnetic north and true north", positive when magnetic north is east of true north and negative when it is west. They add that declination changes over time and with location, which is why their calculator uses up-to-date models of the Earth's field.
Shen Kuo's other puzzle, some needles pointing north and some south, also has a simple explanation. Which end of the needle becomes a north-seeking pole depends on which pole of the lodestone you rub with and in which direction you stroke. Our post on the magnetic dipole and the bar magnet covers the field of a small magnet like this one.
Worked example: how do you correct a compass bearing?
Suppose your compass says a temple lies on a magnetic bearing of 30°, measured clockwise from magnetic north. The local declination is 2° West. What is the true bearing? (These are example numbers; look up the real value for your town with NOAA's calculator.)
Write declination with its sign. West is negative, so D = −2°.
Use the rule true bearing = magnetic bearing + D.
Calculate. True bearing = 30° + (−2°) = 28°.
Check it with a sketch. If magnetic north is 2° west of true north, a bearing measured from magnetic north starts 2° further anticlockwise. The true bearing is 2° smaller. That matches.
Now try the reverse. A map gives a true bearing of 100° and the declination is 1.5° East (D = +1.5°). The compass bearing you should follow is 100° − 1.5° = 98.5°.
The most common mistake is getting the sign wrong. Draw true north and magnetic north on a sketch every time, and the rule stops being something to memorise.
What can a student learn from Shen Kuo?
Shen Kuo combined careful practical detail (silk fibre, mustard-seed of wax, no wind) with honesty about what he did not understand. When you write up an experiment, copy both habits: describe your set-up precisely enough that someone else could repeat it, and say clearly which results you cannot yet explain. For how European scientists later explained the Earth as a giant magnet, see our post on William Gilbert and magnetism.
When the link between a bar magnet, field lines and a compass feels fuzzy, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can go back to the idea you are missing.
Try it today: look up the declination for your town on NOAA's calculator and correct one compass bearing by hand.
