That's a difficult question allright <img src="/forum/images/icons/wink.gif" alt="" />
Normally. The thing worn under Chainmail in the 13th. Century is called Aketon, a three-layered, Linen or Leather, cotton, and linen. (
http://www.matuls.pl/grafika/ikony/pikowaniec1_2.jpg )
Outside, it's a Jack, fabric armour that can be worn independently or in conjunction with chain mail. (
http://www.matuls.pl/grafika/ikony/jackchains1.jpg ). It's also made up of 3 layers, but in the middle it's 15 to 40 layers of raw linen!
If I can take a guess, the Jack was invented to actually protect the mail itself, espetially if it's poor quality. I also believe, that if a Jack was worn, then the Aketon was not so thick, or, not even used, and only a simple linen clothing was taken. Or, this rather warm armour of aketon-mail- and jack was worn in the northern regions. In winter, you could still freeze to death... But in Jerusalem, whoever took a jack was probably cooked alive....
What you mean, with plate on the arms and leg and no plate on the chest but a brigandine, is rather 14th. century, and a bit of the 15th. Why this happened I do not know for sure. Wither big plates for chest were to expensive, or not yet invented, or the Brigandine is a better wear for horsemanship... I own a gothic plate armour and I also had a Brigandine on, and the brigandine was a much better wear. It was not so heavy, and allowed for more movement, while protecting from sword attacks just as well. But, and this is my guess, a plate chest protects better from projectiles, while a brigandine was not, and that's why they abandonet it.
Szab