Professor Peirce presented a communication upon the Solution of Equations by the Means of Geometric Diagrams. Professor Peirce also presented a communication upon the form assumed by an elastic sac containing a fluid. The positions of unstable equilibrium he found to divide themselves into four special forms, the annular, cylindrical, that of the cylinder with a bilateral character, and the double or multiple cylinder. The ultimate form of the first case is a sphere.
He also alluded to the interest of this fact to those who were not themselves mathematicians. For the primitive forms which Professor Agassiz had found to be the four types of the animal kingdom were the same, the Radiata being represented by the sphere, the Mollusca by the cylinder, the Articulata by the bilateral, and the Vertebrata by the double cylinder. Now, as all animal forms begin as elastic sacs, containing fluids, these forms seem the necessary ones for the condition of equi librium. This led to a discussion, in which Messrs. Eustis and Peirce took part.
Professor Wyman exhibited to the Academy some fossil bones from New Zealand, evidently the thigh-bone, tibia, and tarsus of some one of the largest birds, probably either the Dinornis or Palapteryx. The tarsus was especially interesting, as exhibiting the rudiments of two bones besides the de veloped one, bones of which no traces exist in other birds ex cept in the embryonic state ; a phenomenon analogous to that occurring in the metatarsal bones of Ruminants.
Professor Peirce communicated some observations of Messrs. Southworth and Hawes, daguerreotypists, in relation to photo graphic images taken for the stereoscope. They had found in practice, that, when two points of view were in a horizontal line, the image as seen in the stereoscope appeared distorted, in consequence of the horizontal lines not being represented in relief, like the vertical ones. They had, however, observed that the best images were produced when the position of the two points of view was such that the vertical component was equal to the horizontal one.
Professor Peirce stated that he had seen a number of photo types taken in each way, and that he was able to confirm the statements of Messrs. Southworth and Hawes, that portraits taken with two points of view on the same level had a pecu liarly unpleasant effect. Professor Lovering reminded the Academy that Leonardo da Vinci had pointed out the impossibility of representing ob jects correctly in pictures when their distance from the eyes was within a certain limit. Dr. B. A. Gould said that the circumstance of objects appear ing in relief when observed in ordinary binocular vision might be explained like the outness recognized in monocular vision, by means of the imaginative and suggestive faculties acting unconsciously on reflection. It seemed but natural that a dif ference of level in the points of view should be necessary to make relief manifest in systems of horizontal lines.
The discussion was continued by Messrs. Peirce, Gould, and C. T. Jackson. Professor Eustis gave a new demonstration of the property of the ellipse, that the subtangent is independent of the con jugate axis. He showed that this led to a more simple con struction than any other given.
Three hundred and sixty-sixth meeting
July 26, 1852. – Adjourned Monthly Meeting.
The President in the chair.
The Corresponding Secretary presented a paper from Dr. Leidy of Philadelphia, upon the Osteology of the Hippopota mid . Professor Peirce continued his remarks upon the forms as sumed by an elastic sac containing fluid, and stated that he had succeeded in reproducing them artificially by the use of gum, the force of gravity being eliminated, as in Plateau’s ex periments, by immersing the gum in a mixture of alcohol and water of the same specific gravity.
Three hundred and sixty-seventh meeting.
August 10, 1852. – Quarterly Meeting.
The President in the chair.
Dr. Pierson offered a tribute to the memory of the late Thomas Cole, Esq., a Fellow of the Academy ; after a sketch of Mr. Cole’s life and labors, he offered the following resolutions, which were unanimously adopted : ?
” Resolved, That the Academy deplores, in the death of its late Fellow, Thomas Cole, Esq., of Salem, the loss of a valuable and active associate, whose simplicity of mind, sincerity of heart, and in tellectual acquirements, the result of years of persevering industry, peculiarly fitted him for scientific pursuits, and acquired for him a cordial regard from all who knew him.” Resolved, That the Academy sincerely condole with his bereaved family in the affliction occasioned by his sudden decease. ” Resolved, That a copy of these resolutions be transmitted to the family of the deceased.”