His Bill an Augur is — Pastor

His Bill an Augur is
His Head, a Cap and Frill
He laboreth at every Tree
A Worm, His utmost Goal.
(F.990/J.1034)
[1] Bill:: a poster, notice, about the augur's job. Augur:: a religious official who foretold events by the singing, chattering, or signs derived from various events. Some editions change the word to Auger to fit the answer woodpecker.
[2] Cap and Frill:: a pastor (or priest) hat with tassel.
[3] laboreth, every Tree:: to post the church notice at every tree.
[4] Worm:: a despised, contemptible person. Dickinson in her letter (L.193) wrote: Our Pastor says we are a "Worm." How is that reconciled? "Vain-sinful Worm" is possibly of another species.

MORE ABOUT HATS. "the priest's hat is an object of our uncompromising opposition. Its original is the noble sombrero, . . . it now resembles nothing but a triangle of spouting set round a black jelly mould — taking up a great deal of room, but casting no breadth of shade — wide as the pretensions of the Church of Rome, but shallow as her foundations in this Island. ─ Punch, Volume 19 (1850)