You just need to use it as:
Form1 m_frm = new Form1();
private void button_add_Click(object sender, EventArgs e)
{
m_frm.Show();
}
and in Form 1 you need to handle the closing event:
private void Form1_FormClosing(object sender, FormClosingEventArgs e)
{
e.Cancel = true;
this.Hide();
}