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of a bucket of a turbine wheel, constructed by Mr. U. A. Boyden, experiments upon which, conducted with the most scrupulous care, had shown it to produce an effect equal to eighty-eight per cent. of the power expended ; and stated that some of Mr. Boyden's wheels had given the astonishing result of ninety-two per cent. of the power.

Professor Peirce made some remarks in regard to the fraction which expresses the law of vegetable growth, which he compared with the ratio of the mean motions of the planets, and found to express more nearly the arrangement of these bodies than Bode's law. For this purpose, Neptune's period of revolution must be multiplied by i x i to obtain that of Uranus. The period of Uranus must be multiplied by } x { to obtain that of Saturn. Saturn's period must be multiplied by i x to obtain that of Jupiter, and so on. If this law is true, there can be only one planet within the orbit of Mercury, and no planet beyond Neptune. This law or harmony seems to be that to which successive development in general tends to conform, and is manifested when other forces opposed to it are not too powerful. The atomic laws are opposed to it, in crystallizing and other chemical processes; and also the higher laws of organization, such as those of bilateral division in the higher animals.

Professor Peirce remarked that the perturbative function of planetary motion had been developed by Hansen, according to the eccentric anomaly of one of the planets, in a numerical form; and exhibited the first terms of a literal development of this function, which is more simple than the usual form of development according to the mean anomaly. He thought there were reasons for believing that some other form of development will be discovered better adapted to cases of great inclinations and eccentricities; inasmuch as, in case the two orbits do not approach each other within a small distance, the development of this function should not contain any term capable of becoming infinite.

Dr. C. T. Jackson laid before the Academy a number of VOL. II.

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specimens of native phosphate of lime, or apatite, from a large vein discovered by Mr. Alger and himself in Hurdstown, New Jersey, during the month of June last, and offered the following remarks : —

“ These specimens exhibit, in a striking manner, the various col. ors and forms of this interesting mineral, justifying the name given to it by mineralogists, in allusion to its deceptive appearance. Specimens of the crystallized mineral from Bolton, Massachusetts, St. Law. rence Co., New York, Murcia in Spain, and Hungary, were also shown, in illustration of its variable external appearance. The New Jersey specimens were crystallized, massive, and granular, and possessed various colors, such as olive-green, rosin-yellow, brown, and dingy white, and some of them were covered with iridescent films of oxide of iron. The peculiar resinous lustre of the broken surface may be pointed out as most generally characteristic of the mineral. By chemical tests its nature is readily proved, it being at once dissolved in nitric acid, and giving, when neutralized by ammonia, the characteristic yellow precipitate of phosphate of silver when tested with nitrate of silver. The presence of fluorine may also be demonstrated by decomposing the pulverized mineral by sulphuric acid, and allowing the fluohydric acid to act upon glass,

“ Chlorine may be proved to be present by adding nitrate of silver to the nitric solution of the mineral. From these experiments, it appears that this mineral has the usual composition of apatite. Although crystals of this mineral have before been observed in the magnetic pyrites of this locality, the nature of the great vein of massive phosphate of lime had not been detected; its dead white appearance on the surface, and its structural changes into rhombic prisms of 80° and 120°, giving no idea of its true nature."

Dr. Jackson stated that he had advised Mr. Alger to obtain a lease of this locality, and to work the phosphate of lime for agricultural use, and that mining operations had since been begun, and thirteen tons of the mineral were now on their way to Boston, and would be converted into prepared phosphates.

He then spoke of the importance of augmenting the proportions of phosphates in our soils, and showed that they are essential to the healthy growth of both plants and animals. In

reply to a remark of Dr. Holland of London, Dr. Jackson gave some account of the researches of Professor Daubeny of Oxford, England, who had been employed by the British government to investigate the economical value of the phosphate of lime of Estremadura, Spain. Prof. Daubeny found that the mineral phosphate of lime answered as well as bones in prepared phosphates for agriculture, but that the supply in Spain was too limited to be of much importance.

Three hundred and thirty-eighth meeting.

November 5, 1850. - MONTHLY MEETING. The PRESIDENT in the chair.

Professor Guyot, in behalf of the committee appointed to consider the expediency of recommending the adoption of the centigrade thermometrical scale, and the metrical barometrical scale, made a report, to which was appended a series of resolutions. A discussion of considerable length ensued, in which Messrs. Horsford, Lovering, B. A. Gould, Jr., Paine, Guyot, W. F. Channing, Peirce, Agassiz, Everett, and Treadwell took part; and the resolutions were amended and passed as follows:

"1. Resolved, That the American Academy earnestly recommend the adoption of the metrical scale for the barometer destined for the observations made in behalf of the State of Massachusetts and of the Smithsonian Institution, not only for the sake of convenience, but also as a first step leading to a general adoption of the metrical system of weights and measures in scientific matters.

“2. As regards the thermometer, that the scale of Fahrenheit, in actual use in this country, be retained for the present.

“3. That a committee be appointed to consider the propriety and the practicability of introducing the modified Fahrenheit's scale mentioned in the report, or some other possessing similar advantages, as a universal scale, and to correspond with eminent meteorologists and scientific societies.

“4. That notice be given to the Smithsonian Institution of the opinion of the Academy on the subject of this report.”

The Academy then

Voted, That the committee to be appointed in pursuance of the foregoing resolutions consist of the gentlemen who reported them ; viz. Messrs. Guyot, Agassiz, Peirce, Lovering, and B. A. Gould, Jr.”

Professor Agassiz made an oral communication of considerable length upon the classification and homologies of radiated animals.

Professor Lovering read a part of a letter from Captain Lefroy, of the Toronto Observatory, to Mr. W. C. Bond, representing that there is danger that the magnetic observations at that place may be discontinued after next March, and expressing a desire that the Academy would use its influence in promoting their continuance for a further period of three years. He then offered the following resolutions, which, after some remarks by Mr. Guyot in their support, were adopted:

“1. That, in the opinion of this Academy, it is highly desirable that the magnetical and meteorological observatory at Toronto should be sustained for another period of three years.

“2. That a committee be appointed to correspond with the American Minister at London, or with the Royal Society, as they may think best, with the view of urging upon the British government the scientific importance of prolonging their magnetical and meteorological operations in British America, and thus coöperating with similar observations to be made more or less extensively at different stations in the United States.”

Hon. Edward Everett, Mr. W. C. Bond, Mr. Guyot, Professor Lovering, and Mr. J. P. Hall, were appointed a committee to carry the foregoing resolutions into effect.

Professor Lovering made some remarks upon the advantages of the French system of weights and measures over all others, and offered the following resolutions, which were adopted :

“1. That the decimal system of weights and measures, based upon the French metre, possesses advantages which belong to no other system that has been adopted or proposed ; that it is the only existing system which is symmetrical in its parts, simple in its reductions, and which maintains in its various denominations that invariable and recoverable value which adapts the observations and experiments recorded in it for ready and permanent use over all the world.

“ 2. That the Academy authorize the use of the system in their own publications, and recommend its adoption for scientific purposes wherever it is practicable.”

On motion of Professor Agassiz, it was

Voted, That these resolutions be communicated to other scientific bodies of a similar character to that of the Academy."

On motion of Professor Agassiz, it was “ Voted, That the Recording Secretary be authorized, with the concurrence of the President, to call a semi-monthly meeting of the Academy at their hall, whenever any Fellows shall have such an amount of scientific matter prepared for communication, as to render a special meeting expedient.”

Three hundred and thirty-ninth meeting. November 13, 1850. — QUARTERLY MEETING. The PRESIDENT in the chair.

The President laid before the Academy two letters, written in the year 1796, by Count Rumford, to the late John Adams, then President of the Academy; among whose papers they were recently found by Hon. C. F. Adams, and by him transmitted to the President.

The following gentlemen were elected Members of the Academy :

Professor Alexis Caswell, of Brown University.

Professor William Chauvenet, of the U. S. Naval Academy, Annapolis.

Professor Lovering stated that Part II. of Vol. IV. of the Memoirs of the Academy would be printed in a week or two, and that two papers of the fifth volume were already printed.

In accordance with an arrangement made by Dr. Bowditch, the children represented to be Aztecs, from Central America, were exhibited to the Academy. They excited much interest. The boy presented, in the form of his head and the expres

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