A valediction is a goodbye. In this goodbye to his beloved, the speaker forbids mourning. His reasons are as follows:
In the second stanza, he states that is would be a "profanation" or soiling of their love to air their grief in front of ordinary people ("the laity"). By keeping their feelings to themselves, the lovers keep them pure.
He goes on to contrast the love he and his beloved share to that of "sublunary lovers'." Sublunary means worldly, or in this context, fleshy. Most lovers can't stand to be apart because their love is based on the flesh. However, as the speaker reminds his beloved, their love is based on the "mind" and soul. Since their "two souls are one" or united, distance can't really separate them, only stretch them out.
And if their souls are, in fact, two, they are still alway connected. The speaker compares this connectedness to a drawing compass: they have each a separate leg but are always linked by a center. The speaker likens his beloved to the leg of the compass planted in the center of the paper as the speaker revolves out around it in a wide circle: they are apart but the beloved is still following and leaning towards the circle her lover is making.
The speaker also affirms that the physical separation is only temporary, using the erotic image of erection to describe the homecoming after the journey.
These reasons seem believable to me. People who are genuinely in love, which is what the poem describes, think about each other all the time and therefore still feel connected when they are apart. They can also anticipate the joy of being reunited.
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