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Committee of Publication.
Joseph LOVERING,

JEFFRIES WYMAN,
CHARLES W. ELIOT.

Committee on the Library.
John B. HENCK, CHARLES PICKERING,

John Bacon.

Committee to audit the Treasurer's Accounts.
CHARLES E. WARE,

CHARLES J. SPRAGUE.

The following gentlemen were elected members of the Academy :

Nathaniel Thayer of Boston, to be Resident Fellow in Class III. Section 3.

Professor William P. Atkinson of Cambridge, to be Resident Fellow in Class III. Section 2.

Hon. Horace Gray, Jr. of Boston, to be Resident Fellow in Class III. Section 1.

Stephen P. Ruggles of Boston, to be Resident Fellow in Class I. Section 4.

Professor Noah Porter of Yale College, to be Associate Fellow in Class III. Section 1.

Chief Justice Ira Perley of New Hampshire, to be Associate Fellow in Class III. Section I.

Dr. A. W. Chapman of Appalachicola, to be Associate Fellow in Class II. Section 2.

George Bentham of London, to be Foreign Honorary Member in Class II. Section 2, in place of the late Professor Lindley.

Herve Auguste Etienne Alban Faye of Paris, to be Foreign Honorary Member in Class I. Section 2, in place of the late M. Encke.

William John Macquorn Rankine to be Foreign Honorary Member, in Class I. Section 4, in place of the late Admiral Smyth.

Five hundred and seventieth Meeting.
June 12, 1866. — ADJOURNED ANNUAL MEETING.
The PRESIDENT in the chair.

Professor Lovering communicated an unanimous recommendation from the Rumford Committee that the following vote be passed, viz. :— That the Rumford Premium be awarded to Alvan Clark of Cambridge, for his improvements in the manyfacture of refracting telescopes, as exhibited in his method of local correction.

Professor Lovering described Mr. Clark's methods of testing and polishing lenses, and recounted the grounds of the Committee's recommendation.

The report was accepted, and on motion of Dr. Jacob Bigelow the vote was unanimously passed.

Five hundred and seventy-first Meeting. : September 11, 1866. — MONTHLY MEETING. The PRESIDENT in the chair.

The President read letters relative to exchanges ; also letters from Professor Rankine and M. Faye in acknowledgment of their election into the Academy.

The President called the attention of the Academy to the recent decease of Professor Henry D. Rogers of Glasgow, of the Associate Fellows, formerly a Resident Fellow; also of

r. Reuben D. Mussey and Mr. James Hayward of the Resident Fellows..

Professor Winlock read the following communication from Professor Daniel Treadwell:

The force of every moving body, or that attribute by which a moving dy overcomes any resistance opposed to it, is the product of two ctors, namely, mass and velocity. There is an old dispute as to the ve value of one of these factors, the velocity; but it may, I think, be " the present time confidently assumed that the value assigned to it oy Leibnitz, namely, its square, is the true value in this case. Taking this then to be established, we have a very simple, easy, and direct method of comparing, one with another, the forces of cannon-balls of every possible weight, or rather inertia, as measured by their weight, moving with any velocity that may be impressed upon them. In making this comparison between the forces of the balls used, especially in the most powerful of the vaunted American and English cannon of modern construction, it will be necessary first to establish some standard which may be used as the unit of measure, with which the others are severally compared and tried. To do this I shall take the ball of the old 32-pounder under a velocity of 1,600 feet a second, this being a mass and velocity with which all artillerists are familiar, being that produced by eight pounds of powder, the full charge of this gun; and I shall use the force possessed by this ball under these conditions as the standard, or unit of the standard, by which the force of any others may be compared or measured.

It is very desirable that the unit of every standard of measure should be taken from some simple and familiar object, of the quantity of which we can not only form a conception, but with which we have a familiar sensible acquaintance. Our common standards of weight and measure have been thus derived, the grain of wheat forming the unit of one, and the human arm and foot that of the other. In the more complex instance of the power of the steam-engine, the strength of the horse furnishes the basis of the standard of measure, and this again is defined in a certain number of pounds raised one foot high against the opposing force of gravitation. It will be at once perceived that, although a 32-pound shot moving with a velocity of 1,600 feet a second may form some image capable of being grasped by the conception, yet we must utterly fail to form a distinct idea of the quantity represented by 32 multiplied by the square of 1,600, or of the algebraic symbols m vä, representing the product of a mass by the square of a velocity. It will be seen, however, that we may bring the proposed standard of comparison out of this dark envelope, by changing the factor of the velocily into a physical equivalent taken in a vertical line a certain number of feet high. Thus, instead of saying that the force of a 32pound shot under a velocity of 1,600 feet a second is numerically represented by 32 X 2,560,000, we may substitute for this last factor the height to which the shot would rise if it were pointed directly upwards in vacuo, so that it should be freed from every atmospheric and other resistance except that cf gravitation alone. To do this we have only to calculate the height to which a body will rise under the given conditions, and for which we have a very simple formula, —

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=h, in which v is the velocity of the shot, g the velocity acquired by

a body falling one second, and h the height sought; and we then have our standard unit in pounds raised to a known height. In the case before us we shall find the height to be 40,000 feet; and if we multiply this by the weight of the ball or shot, 32 pounds, we have a product of 1,280,000, or 1,280,000 pounds raised one foot high, as the equivalent of the force of a 32-pound shot moving with a velocity of 1,600 feet a second. We can have no difficulty in forming a conception of this amount of force, or power, and applying it as a measure of the force of shot of other weights moving with other velocities. We may, in fact, compare it with the force of a steam engine, reducing both to a common measure in the horse power. Thus, the horse power being 33,000 pounds one foot high in one minute, we have 1338889 = 39; or the 32-pound shot, when it leaves the mouth of its cannon, equal to the work of 39 horses during one minute of time.

Although we may, by this method ascertain, with great exactness, the comparative forces and, consequently, value, of different shot, it requires yet another step of computation to enable us to compare together the value of different guns; to ascertain their relative strength, whether it be derived from the different materials of which they are made, or the peculiar mode or form of their construction. Thus, suppose it to be determined by accurate experiment that a certain ball from a cast-iron Rodman gun has the same force that is possessed by a ball from a wrought-iron coil gun. This fact can give no warrant to the inference that the cast iron is equal in strength to wrought iron, or that a certain method of casting produces a gun of equal value and efficiency to guns made of forged coils. It may be, and must be in this case, that a much greater weight of the inferior metal is required to produce the strength supplied by a smaller amount of the better metal.

To supply the deficiency of the computation thus pointed out, and extend the proposed standard so as to become a measure of the strength of the gun as well as of the force of the shot, we shall find to require but a moment's attention. Having already seen that our standard 32-pound shot has a force of 1,280,000 pounds one

VOL. VII.

18

foot high (32 X 40,000), if we divide this product, representing the strength of the whole gun, by the weight of the metal of which the gun is made up in pounds, we shall obtain the strength, or work which may be done by each pound of which the gun is constituted. We shall find the result of this computation (the weight of our standard 32-pounder being 7,500 pounds) to be (129520020 =171) 171 pounds, in shot, raised one foot high by every pound of metal which forms the body of our standard gun.

By this form of computation we may compare, numerically, the strength of one gun with another, and assign to each the true value derived from its peculiar metal, or the method employed in its construction, free from all adventitious strength that may be supplied by a mere increase of mass or quantity of material. The accuracy of the result will of course depend upon the experimental determination of the weight of the shot and the velocity which the gun may be relied upon to enable us actually to produce and practise, without exceeding the limits of the strength of the gun.

Dahlgren. I now proceed to the application of these forms of computation to the guns now most relied upon in the American and English service. First the cast-iron ten-inch gun known in this country as the ten-inch Columbiad, and described as follows:Diameter of bore,

10 inches. Weight of gun,

15,059 pounds. Weight of shot,

128 " Charge of powder,

18 " Initial velocity of shot,

1,044 feet. From these several elements the following results are obtained by the mode of computation before pointed out. Height to which the shot will rise if pointed directly upward, in vacuo, 17,030

feet. Force in pounds raised one foot high, 2,179,840. Force compared with the 32-pound shot under a velocity of 1,600 feet a

second, this being taken as 1, 1.7. Force in number of horses working one minute of time, 66.2. Number of pounds (in shot) raised one foot high, by each pound in the weight of the gun, 144.7.

Rodman. Passing from this to the giant of the service, the Rodman fifteeninch gun, which gives the following elements to be subjected to computation :

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