Ok, I think I see what you are trying to do. Here is one way of many to code this sort of thing:

#!usr/bin/perl
use strict;
use warnings;

my $nHeaderLines = 2;
my $nDataLinesPerFile = 4;

my @header;

# the "Big File" is the DATA segment below,
# maybe millions of lines...

for (1..$nHeaderLines) # read header lines from big file
{
   my $header_line = <DATA>;
   push @header, $header_line;
}

# divide the big file data into smaller files,
# each with the initial header...

my $nFile = 0;
my $fileNameBase = "SmallerFile";
my $nDataLine = 99999;

my $line;
while ($nDataLine++, defined ($line = <DATA>))
{
   if ($nDataLine > $nDataLinesPerFile) # start new file
   {
       $nFile++;
       my $name = "$fileNameBase$nFile.txt";
       open (OUT, '>', "./$name") or die "$!";
       print OUT @header;
       $nDataLine=1;
   }
   print OUT $line;
}

print "Program Done!\n";

__DATA__
Header 1
Header 2
data 1
data 2
data 3
data 4
data 5
data 6
data 7
data 8
data 9
[download]

PS: This code has no advance knowledge of how many smaller files will be created. Nothing like "34 files" is hard coded.
The code creates "as many files as are needed". In the case above, there are 3 files. data lines 1,2,3,4 in one file, data lines 5,6,7,8 in another and the last 9th data line in a third file.