Here is a class of burners that utilize brass tabs to hold the burner from the inside. Springs were also used. There are a couple similarly styled with prongs, but I list them here for they are similar in appearance.

The COMET was made by the firm of Holmes, Booth & Haydens.

A COMET variant. A brass spring to grasp the chimney.

The WILMOT Burner, patented October 4, 1870.

An 1874 variant of the WILMOT. Wilmot Mfg. Co., Bridgeport, Conn.

Here's a Holmes, Booth and Haydens burner, the CLIMAX.

Russel patent burner, 1872, by Scovill Mfg. Co.

The RADIANT by Benedict and Burnham. Weeden's patent, 1872.

NEW CALCIUM LIGHT burner, circa 1870.

The TOOFS burner, August 11, 1868.

The MAGIC SUN burner, patented March 16, 1869.

The KEYSTONE burner, by Powell & Bros., Camden, NJ, patented 1868.

This is the Collins Burner. Invented by Michael Henry Collins, pat'd 1865.