%% 
%%  A DANTE-Edition example
%% 
%%  Example 04-01-11 on page 135.
%% 
%%  Copyright (C) 2010 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1,2
%% 
\documentclass[]{article}
\pagestyle{empty}
\setlength\textwidth{183.78818pt}
\usepackage[utf8]{inputenc}% adapt maybe
\usepackage[paper=70mm:85mm,pagesize]{typearea}
\setlength\parindent{0pt}
\usepackage[english]{babel}
\usepackage{fancyhdr}
\lhead{\small\texttt{\textbackslash caption} demo}
\pagestyle{fancy}
\setcounter{page}{1}
\renewcommand\thepage{page \arabic{page}}

\usepackage{longtable} \setlength\LTcapwidth{1in}% <-- change length

\begin{document}
Text without sense before the now inserted \texttt{longtable}.
\begin{longtable}{@{}l c r p{1.5cm}@{}}
L & C & R & box\\\hline
\endfirsthead
\multicolumn{4}{@{}l}{\small\ldots\emph{continued}}\\\hline
L & C & R & box\\\hline
\endhead
\hline
\multicolumn{4}{r@{}}{\small\emph{continued on the next page} \ldots}
\endfoot
\endlastfoot% empty last footer, no line after caption
l & c & r &1st row\\l & c & r & 2nd row\\l & c & r & 3rd row\\l & c & r & 4th row\\
l & c & r &5th row\\l & c & r & 6th row\\l & c & r & 7th row\\l & c & r & 8th row\\
l & c & r &9th row\\l & c & r &10th row\\l & c & r &11th row\\l & c & r &12th row\\\hline
\caption{Table caption with 1\,inch width}\label{tab:l4}
\end{longtable}
\end{document}