After finishing her son's letter, the mother's tears trickled down.
Tips
history
Recorded in Song scholar Ma Tingluan's 《题汪水云诗》: '余展读甲子初作,微有汗出,读至丙子诸作,潸然泪下。' — he sweated while reading the earlier poems, then wept silently at the later ones.
register
Literary register. Often paired with 不禁 / 不由得 (can't help but). For everyday 'cry' use 哭 or 流泪; 潸然泪下 is for quiet, dignified weeping in moving scenes.