These magazine links will take you to a landing page in one of the library databases. With a couple of clicks you can get to the more familiar version of the magazine. You still need to make two choices- what year you want to look at and the article you want to read.
Choose a Year and Issue
If you click the magazine title "Time" in the Reading list, it takes you to this landing page:
Choose a year.
A dropdown will list the magazine issues for that year. Pick one.
Pick an Article
Pick an article and click the "PDF Full Text" option.
Once you are here you can browse within that issue of the magazine.