Please find a patch attached.

I took some before-and-after screenshots depicting the impact of each
"hunk" of the diff.  (An earlier attempt to submit this patch with this
illustrative support was thwarted by the attachment size limit.)

You can find the screenshots here:

https://www.dropbox.com/s/glbb7uhyu3fi1dm/groff-backslash-c-corrections.tar.gz?dl=0

Regards,
Branden
diff --git a/contrib/mm/groff_mm.7.man b/contrib/mm/groff_mm.7.man
index 3aa0d827..9f03b5a3 100644
--- a/contrib/mm/groff_mm.7.man
+++ b/contrib/mm/groff_mm.7.man
@@ -124,13 +124,13 @@ command:
 .LP
 .I XXX
 is the name of the register,
-.I n\c
-\~is the value to be assigned, and
-.I i\c
-\~is the increment value for auto-increment.
+.IR n \~is
+the value to be assigned, and
+.IR i \~is
+the increment value for auto-increment.
 .
-.I n\c
-\~can have a plus or minus sign as a prefix if an increment
+.IR n \~can
+have a plus or minus sign as a prefix if an increment
 or decrement of the current value is wanted.
 .
 (Auto-increment or auto-decrement occurs if the number register is
@@ -179,10 +179,10 @@ Set the format with
 .
 .
 .LP
-.I R\c
-\~is the name of the register,
-.I c\c
-\~is the format.
+.IR R \~is
+the name of the register,
+.IR c \~is
+the format.
 .
 .RS
 .LP
@@ -208,12 +208,11 @@ A@0, A, B, C, .\|.\|., Z, AA, AB, .\|.\|.
 In
 .BR m@TMAC_M_PREFIX@m ,
 the fonts (or rather, font styles)
-.B R\c
-\~(normal),
-.B I\c
-\~(italic), and
-.B B\c
-\~(bold) are hardwired to font positions
+.BR R \~(normal),
+.BR I \~(italic),
+and
+.BR B \~(bold)
+are hardwired to font positions
 .BR 1 ,
 .BR 2 ,
 and\~\c
@@ -1221,8 +1220,8 @@ directly after\~\c
 .B H
 is ignored.
 .
-.B H\c
-\~takes care of spacing and indentation.
+.BR H \~takes
+care of spacing and indentation.
 .
 .IP
 .B Page ejection before heading
@@ -2305,8 +2304,8 @@ Does not output an empty page if currently at the top of an odd page.
 .BI P\  \fR[\fPtype\fR]\fP
 Begin new paragraph.
 .
-.B P\c
-\~without argument produces left\-justified text,
+.BR P \~without
+argument produces left\-justified text,
 even the first line of the paragraph.
 .
 This is the same as setting
@@ -3907,8 +3906,8 @@ and
 are specified through
 .BR .WA / .WB .
 .
-.I n\c
-\~is the counter, 1-max, and
+.IR n \~is
+the counter, 1-max, and
 .I flag
 is true for the last name.
 .
diff --git a/src/devices/grodvi/grodvi.1.man b/src/devices/grodvi/grodvi.1.man
index fd093bff..50adbf0e 100644
--- a/src/devices/grodvi/grodvi.1.man
+++ b/src/devices/grodvi/grodvi.1.man
@@ -275,7 +275,7 @@ mounted at font positions 1 to\ 4.
 The fonts are grouped into families
 .B T
 and
-.B H\ \c
+.B H
 having members in each of these styles:
 .
 .RS
diff --git a/src/preproc/eqn/eqn.1.man b/src/preproc/eqn/eqn.1.man
index 5901dbe3..2d42b64b 100644
--- a/src/preproc/eqn/eqn.1.man
+++ b/src/preproc/eqn/eqn.1.man
@@ -231,8 +231,8 @@ is when the equation is encountered.
 .TP
 .BI \-p n
 This says that subscripts and superscripts should be
-.I n\~\c
-points smaller than the surrounding text.
+.IR n \~points
+smaller than the surrounding text.
 .
 This option is deprecated.
 .
@@ -313,7 +313,9 @@ Possible types are:
 .
 .RS
 .TP \w'punctuation'u+2n
-an ordinary character such as \[oq]1\[cq] or \[oq]\fIx\fP\[cq];
+ordinary
+an ordinary character such as \[oq]1\[cq] or
+.RI \[oq] x \[cq];
 .
 .TP
 operator
@@ -805,8 +807,8 @@ This sets parameter\~\c
 .I p
 to value\~\c
 .IR n ;
-.I n\~\c
-is an integer.
+.IR n \~is
+an integer.
 .
 For example,
 .
@@ -1133,8 +1135,8 @@ is between 1 and\~9, is replaced by the
 .IR n-th
 argument if the macro is called with arguments;
 if there are fewer than
-.I n\~\c
-arguments, it is replaced by nothing.
+.IR n \~arguments,
+it is replaced by nothing.
 .
 A word containing a left parenthesis where the part of the word
 before the left parenthesis has been defined using the
diff --git a/tmac/groff_ms.7.man b/tmac/groff_ms.7.man
index 53d868a7..cdc96940 100644
--- a/tmac/groff_ms.7.man
+++ b/tmac/groff_ms.7.man
@@ -517,8 +517,8 @@ The argument
 .I xx
 is either a numeric argument to indicate the
 level of the heading, or
-.I S\ xx\ xx\ \c
-".\|.\|."
+.B S\~\c
+.IR "xx\~xx\~" .\|.\|.\&
 to set the section number explicitly.
 .
 If you specify heading levels out of sequence,

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