This evening, at 7 o’clock, a magnificent rainbow was observed, the colors of which were unusually vivid. REGULAR MEETING, JULY 17TH, 1865. President in the chair. Ten members present. REGULAR MEETING, AUGUST 7TH, 1865. President in the chair. Nine members present: Dr. C. T. Jackson, visitor. Donations to the Cabinet: Three boxes of shells; Duplicate fossils of the U. S. Exploring Expedition; Types of Dana’s Geology; Fossils from the Upper Missouri; Miscellaneous fossils of the United States, received from the Smithsonian Institution; Trachytic porphyry from the “Basalt” Cliff, three miles from the Big Tree Grove, Calaveras, presented by Dr. Jackson. Donations to the Library: Annual Report of the Museum of Comparative Zoology of Cambridge, 1864; Proceedings of the Academy of Natural Sciences of Philadelphia, for January, February and March, 1865; Proceedings of the American Academy of Arts and Sciences, June-September, 1864; Review of American Birds, by Prof. S. F. Baird; Proceedings of Albany Institute; The Law of Increase and the Structure of Man, by F. A. Liharyik; Oration and Poem delivered at the Commencement of the College of California; Proceedings of the Royal Horticultural Society of London; Meteorological Results, Toronto, 1860-2; Magnetical Abstracts, Toronto, 1854-60, 1856-62. Dr. Ayres remarked the appearance of a species of Barracouta, (_Sphyrena Argentea_,) on the coast of California, off Point Conception. Dr. C. T. Jackson read the following paper, relative to the Big Trees of Calaveras County. MEASUREMENTS OF THE HEIGHT AND CIRCUMFERENCE OF TWENTY-FIVE OF THE “BIG TREES,” (_SEQUOIA GIGANTEA_,) IN CALAVERAS COUNTY, BY DR. CHARLES T. JACKSON AND MR. JOSEPH B. MEADER, AUGUST 2D AND 3D, 1865. Instruments made use of:— 1. Sir H. Douglass’ Reflecting Semicircle; (Cary). 2. A Reflecting Level; made by J. H. Temple, of Boston. 3. A common Measuring Tape. The horizontal point was fixed upon each tree, and the angle measured by the Reflecting Semicircle, and protracted by it. The circumference of the trees was measured above the swell of the roots, about six feet, where the stem takes its proper form. Several measurements, originally made with too high an angle, were taken over again with a longer base, so as to avoid the error of refraction in the glasses of the mirrors. We trust, therefore, that the following measurements will be found to be correct.