This will sound like a strange question, but I need the answer for an
opinion essay I am writing.  Here it is: in 18th century England,
would a gentleman wear his wig (a.k.a. periwig) while alone and at
ease in his home, say while reading a book or writing a letter?  Or,
would he likely only wear this hair adornment in public and in formal
attire?  In addition to the answer, I will need a reference I can
cite.  Thanks!  David

A wig was usually removed and replaced by a cap when an 18th Century
gentleman was relaxing at home.

"At home, among friends, 'Monsieur' would wear a nice silk dressing
gown over a vest or a waistcoat and a cap instead of his wig."

The Art of Dress in 18th century New France: a glimpse into everyday living
http://www3.sympatico.ca/gousse-matte/fdl/Clothing.html

"Men's dress in the 18th century was also subject to the vagaries of
fashion. A typical example of male 'undress' wear, similar to the
female wrapping gown, was the 'banyan' or 'Indian nightgown'. This can
be seen in Jonathan Richardson the Elder's 1732 'Portrait of the
Artist's Son'. The sitter wears a red silk banyan, arranged in folds
over his fine white linen shirt. He also wears a matching nightcap,
which despite its name could be worn at any time of the day but never
in bed. This form of headgear was put on at home, in informal
surroundings when one removed one's wig."

Did U Know: 'Mrs Frances Hesketh', by Joseph Wright of Derby (1734-97)
http://www.diduknow.info/aotm/furtherReading.asp?id=21&venue=2

"Banyan:
An undress robe worn by men. The banyan was cut in two basic
variations: an unfitted version somewhat like a kimono or modern
bathrobe, and a fitted version which somewhat resembled a man's coat
only with full length, loose skirts. The banyan was typically worn by
gentlemen relaxing at home and was worn over shirt, waistcoat, and
breeches, usually with a cap to cover the head in lieu of a wig."

Glossary of 18th Century Costume Terminology
http://www.ai.mit.edu/people/sfelshin/revwar/glossary.html

"A banyan cap was worn informally at home when a fashionable man
removed his wig. Sometimes he would even entertain visitors at home
and this is why some of these caps are beautifully embroidered to
convey a gentleman's weath and status to his friends."

Trousseau: c. 1690-1720 Gentleman's Banyan Cap 
http://www.trousseau.net/trousseau2.asp?P=2&I=101 

Google search strategy:

Google Web Search: "18th century" "instead of" OR "in lieu of" wig
://www.google.com/search?hl=en&q=%2218th+century%22+%22instead+of+%22+OR+%22in+lieu+of%22+wig

Google Web Search: "18th century"  wig informal
://www.google.com/search?hl=en&q=%2218th+century%22++wig+informal

Google Web Search: "18th century" wig cap
://www.google.com/search?hl=en&q=%2218th+century%22+wig+cap

I hope this is precisely the information you need. If it is not, or if
a link doesn't work for you, please request clarification; I'll be
glad to offer further assistance before you rate my answer.

Best regards,
pinkfreud