“slight air, and purging fire”
In Elizabethan natural philosophy, all matter was composed of four elements: earth, water, fire, and air. Fire and air were the 'lighter' (less dense) elements that rose upward, while earth and water were heavy and sank. 'Slight' here means thin or insubstantial; 'purging' describes fire's power to refine and cleanse, burning off impurities.
“My life, being made of four, with two alone Sinks down to death, oppress'd with melancholy”
Elizabethan medicine taught that a healthy person required a balanced mixture of all four elements. When the two light elements (air and fire) depart from the speaker, only the heavy pair (earth and water) remain. Earth and water together produced black bile, which caused melancholy — the humor associated with heaviness, sadness, and physical decline. The speaker is literally dying of an elemental imbalance.
historical Melancholy and the malcontent“This told, I joy; but then no longer glad, I send them back again, and straight grow sad”
The closing couplet is the sonnet's volta (turn): instead of resolving the grief of absence, it traps the speaker in a perpetual loop. Joy at the news of the beloved's health immediately re-dispatches thought and desire back to him, which instantly recreates the emptiness and sadness. The poem offers no consolation, only the endless turning of the cycle.
historical The sonnet form