 Eaton took orders and was beneficed, but being unable to conform to the regulations of the church as interpreted by Archbishop Laud, he accompanied his eldest brother Theophilus Eaton to New England in 1637, and became the colleague of John Davenport at New Haven.A difference of opinion afterwards arose between him and Davenport.At the convention of 4 June 1639 (O. S.) Eaton took exception to the fifth article of the constitution, which limited the right of voting and of holding public office to church members only on the ground that ‘the free planters ought not to surrender this power out of their hands.’ After his brother and Davenport had replied, he found so little support that he withdrew his dissent.