The motif of an eagle standing on one leg, with sun and pine tree imparts several symbolic meanings. An eagle (ying) perched on one leg (duli) is a rebus for the phrase yingxiong duli (A great man towers over his peers). The imagery evokes ideals of courage, loyalty and the ability to achieve great things. The combination of an eagle and a pine tree conveys a wish that such a great man will live a long life.
For a similar silhouette agate bottle with an eagle, see R. Holden, Rivers and Mountains Far From the World. The Rachelle R. Holden Collection, no. 35. For a discussion on the Official School of hardstone carving, see Moss, Graham and Tsang, A Treasury of Chinese Snuff Bottles, Vol. 2, Quartz, no. 258, with numerous examples.