What does "in proportion as" mean in these sentences? I've seen the expression "in proportion as" in different passages, but I don't understand what it means in the context, though I know what "in proportion" means. For example, in Common Sense by Thomas Paine: but as nothing but heaven is impregnable to vice, it will unavoidably happen, that 【in proportion as】 they surmount the first difficulties of emigration, which bound them together in a common cause, they will begin to relax in their duty and attachment to each other... in Report on Manufactures by Alexander Hamilton: 【In proportion as】 the mind is accustomed to trace the intimate connexion of interest, which subsists between all the parts of a Society united under the same government--the infinite variety of channels which serve to Circulate the prosperity of each to and through the rest--in that proportion will it be little apt to be disturbed by solicitudes and Apprehensions which originate in local discriminations. These two sentences are extremely long. Could anyone please clarify the meaning of "in proportion as" in the context? Thank you sooooooooo much.