What did James Madison say about interest groups in Federalist Paper #10?

What did James Madison say about interest groups in Federalist Paper #10? In particular, discuss how he suggested that the new U.S. Constitution solved the potential problems with interest groups. Do you think the points made in Federalist Paper #51 are valid?
Briefly compare the three reasons that people join interest groups. What is different between the motives of people joining groups? Do you think any of the reasons are better than the others?
What is the difference between a special interest group and a public interest group? Find an example of each type of interest group on the internet. Briefly describe the groups you've found and explain how it's activities make it a good example of that type of group.