What exactly is a "veil"? Is it a scarf that you put on your head? Why is this done? Why don't they say "Amen" at Communion? Does everyone kneel at the Communion rail?
Well here's the scoop, I'm surprised no one more qualified to answer these questions is doing so (i.e. a women), but I'll try my best.
A veil is a mantilla. Its a head covering that Catholic women traditionally wear. Here is a web page showing the 2 most common types of veils. The one on the left is more modern 1950s/1960s style while the one on the right is more traditional. You'll usually see a mix of the two styles at traditional chapels.
http://www.ocdsrose.com/chapel_caps.htm
Women can also just wear a hat instead of the veil, but many just prefer the veil I guess.
Why isn't Amen said? Its because the Priest when he distributes communion says the Amen for you. "Corpus Domini nostri Jesu Christi custodiat animam tuam in vitam aeternam. Amen" "May the Body of our Lord Jesus Christ preserve thy soul unto life everlasting. Amen." So there is no need for you to say Amen. All of the Eastern Rite masses I've ever attendend (Ukranian, Armenian, Melkite, Syro-Malankar) similarly don't require you to say Amen either. Its only Novus Ordo where people say Amen for commmunion.
Everyone kneels for communion and receives on the tongue. Every once in a while you'll see somebody standing for commmunion and thats because they have bad knees. So unless you have a medical problem which prevents you from kneeling you have to kneel at the altar rail to receive communion.
"What exactly is a "veil"? Is it a scarf that you put on your head? Why is this done?"
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This is a good source for chapel veils, mantillas, etc. Those things including hats qualify as head coverings for Church. http://www.halo-works.com/shopping/veils.html You can browse through the site and get a sense for what we're talking about.
The Apologia site is an excellent resource on all things traditional. http://www.kensmen.com/catholic/index.html
On this page she gives a very good explanation as to why we wear veils. I'll excerpt some of it below.
http://www.kensmen.com/catholic/theveil.html
A couple of people have posted links to mantillas; IIRC, the mantilla came in during the 60s. In the 50s, women typically wore hats to be "dressy" -- check out some old I Love Lucy reruns! Some women and girls used to wear a silk scarf -- a square one folded into a triangle and tied under the chin; this was discouraged by the nuns. (Jackie Kennedy was shown going into church like that one Sunday, and there was an uproar!)
The reason for head covering was attributed to St. Paul -- I don't have the reference handy, but he said a woman's head should be covered, because "a woman's hair is her glory" (and would be a distraction to men).
There were abuses in the old days too -- for a "visit" (churches used to be unlocked during the day, and you could stop in and light a candle, say a prayer), some -- esp. high school girls -- would bobby pin a kleenex to their heads!
I wear various kinds of head covering, depending on where I am.
When I go to my regular parish for Mass, I usually wear a chapel cap, which looks a whole lot like a black doilie. (On Easter Sunday, I wear the one and only hat that ever looked nice on me.)
If I am at an FSSP chapel, I switch over to the longer chapel veil.
As for WHY I do it...well, I do it to show that I really believe in Jesus' presence at Mass. I do it to remind myself to be reverent. I even do it because my mother did it before me, my grandmother before her, and her mother before that.
For a period of time (during college), I did not wear a head covering to church because I felt funny about being the only one. As I got older, I realized that wasn't a good enough reason and I started wearing it again.
I get some ladies asking where I got the veils, I get some people laughing at me, and I even get some truly scathing sarcasm directed at me (yes, even from some of the clergy).
But I'm doing what I think is right, and I'm teaching my kids that even if some people make fun of you, you should ALWAYS try to do what's right.
Regards,