Let it be tried whether any middle ground can be taken which will at once support a due supremacy of the national authority. what does it mean?

This means that let the suggestion/method be tried in order to come to a point of agreement that will be adopted to support and provide the expected superiority to the national authority.

Explanation:

The statement was made by James Madison to Edmund Randolph in 1787. Madison wanted a strong central government to provide order and stability. He wanted the "middle ground" that will help provide a due supremacy to the national authority. He was right to have supposed that it will not be well suited for the national government to oversee the entire task of a vast country.  

James Madison was an American statesman and Founding Father. He served as the fourth president of the United States from 1809 to 1817.  

answer; /// (c) i believe that the correct answer is; ///full faith and credit.

answer

the speaker of ,’i want politician to make more of an effort for lgbt rights’, will be served well by joining an interest group.

explanation

an interest group is one that aims at influencing public policy on reasons derived by a common interest .in this case, lgbt rights are rights for the gay society which is a special group of individuals with specific interest concerning their relationship with other individuals. hope this !