I've got the answer for the tube with three compartments, it's a plumber's container for holding rosin, grease, and flour. One of my friends found it in a book entitled "Encyclopedia of Antique Tools and Machinery" by C.H. Wendel (page 171), the three substances were all necessary for the soldering process of assembling the joints of lead pipe. A similar grease and rosin box can be seen on this page:
http://chestofbooks.com/home-improv...ard-Practical/The-Plumber-s-Tools-Part-2.html
The web site states "When rosin, grease, etc., are not kept in some such receptacle they become scattered among the tools, and are not only hard to find when needed, but adhere to the tools and get them into dirty condition."
The tool book said they were made in three different sizes.
Someone here had sent me a link to this thread, I posted the item on my web site a few months ago but didn't get an answer until today. My "What is it?" web site can be seen here:
http://55tools.blogspot.com/
And my post with the rosin box is on this page:
http://55tools.blogspot.com/2010/12/set-369.html