Section 51. If such increase does not exceed four per cent of the existing capital stock of the company, the directors, without first offering the same to the stockholders, may sell the shares by auction to the highest bidder, at not less than the par value thereof, to be actually paid in cash. They may also so sell at public auction any shares, which, after the expiration of the time limited in the notice required by the preceding section, remain unsubscribed for by the stockholders entitled to take them. Such shares shall be offered for sale in Boston, or in such other town as may be prescribed by the department; and notice of the time and place of such sale shall be published at least five times during the ten days immediately preceding the sale in each of at least three of such daily newspapers as may be prescribed by the department.