系 xì is a hand holding silk threads. The oracle-bone and bronze forms show a hand grasping one or more strands of silk, the bundled threads hanging below the fingers. The modern shape preserves both halves: the short stroke at the top is the remnant of the gripping hand (爪, a clawing hand from above), and below it sits 糸 (mì), the radical that pictures a skein of twisted silk. As a structure the character reads 系 = 丿 (the hand) over 糸 (silk), one hand keeping many threads gathered as one.

To hold threads together is to connect them, and from that single image the character fans out into the connecting vocabulary of modern Chinese:

1. Connection, relation between things. The tie itself: 关系 guānxi (relationship; connection), 联系 liánxì (to link; to contact), 系列 xìliè (a series, things strung in a row).
2. System, an ordered whole. Many parts bound into one structure: 系统 xìtǒng (system), 体系 tǐxì (a structured system; framework), 太阳系 tàiyángxì (the solar system).
3. Department, a faculty of a university. A branch of study held together as a unit: 中文系 zhōngwénxì (the Chinese department), 系主任 xìzhǔrèn (department head).
4. To tie, to fasten (read jì). In its everyday verb sense the character is read jì: 系鞋带 jì xiédài (to tie one's shoelaces), 系扣子 jì kòuzi (to do up a button), 系安全带 jì ānquándài (to fasten a seatbelt).

The thread that runs through every sense is the original thread itself: the hand that holds strands together. Bound abstractly, it is a relationship or a system; bound by a branch of learning, it is a department; bound literally with a cord, it is the knot you tie. The two readings split the labor: xì carries the abstract senses of connecting and system, while jì carries the concrete, physical act of tying.

When 系 names not a single tie but a whole structure of ties, it becomes the word for a system. 系统 xìtǒng (系 connection + 统 tǒng, to unify or govern) is the modern catch-all for any ordered whole whose parts work together: a computer 系统, a transit 系统, the digestive 系统, an economic 系统. The same 系 gives 体系 tǐxì (a structured framework, as in 教育体系, the education system) and the astronomer's 太阳系 tàiyángxì, the solar system, the sun and its planets bound by gravity into one family.

From "a bound whole" the character also took on the meaning of a university department. A 系 is the unit that holds a single field of study together: 中文系 zhōngwénxì (the Chinese department), 历史系 lìshǐxì (the history department), 物理系 wùlǐxì (the physics department). The person who heads it is the 系主任 xìzhǔrèn. Here 系 stands alone as a noun, the smallest academic home where everyone shares one subject.

系 is a polyphone, and the two readings divide cleanly along the abstract-versus-physical line. Read xì, it carries every connecting and system sense covered above: 关系, 系统, 中文系, and the bookish verb "to link" in 联系. Read jì, it shrinks to one concrete job: to tie or fasten something with a cord, strap, or knot. 系鞋带 jì xiédài is to tie your shoelaces, 系扣子 jì kòuzi is to do up a button, 系安全带 jì ānquándài is to buckle a seatbelt.

A useful rule of thumb: if you could mime the action with your hands, knotting, buckling, fastening, it is jì. If the connection is invisible, a relationship, a system, a department, it is xì. The single glyph keeps the silk-holding hand for both, but only the jì reading still ties an actual knot.

See a hand at the top of 系 gathering a hank of silk, 糸, into its fingers: one hand, many threads, all held as one. That gesture of holding strands together is the whole character. Every meaning is something bound.

Bind people and you get a relationship (关系). Bind parts into an ordered whole and you get a system (系统). Bind a field of study into one academic home and you get a department (中文系). And bind a cord into an actual knot, and the reading shifts to jì: you 系鞋带, tie your shoelaces. When you meet 系, ask what is being held together, and then ask whether you could tie it with your hands. If yes, it is jì; if the tie is invisible, it is xì.