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" ... the increase in length ; the velocities being in a ratio somewhat less than that of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the two. "
Tracts on Mathematical and Philosophical Subjects: Comprising Among Numerous ... - Page 79
by Charles Hutton - 1812 - 485 pages
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 404 pages
...always increases as the gun is longer ; though the increase in velocity is but very small in comparison to the increase in length ; the velocities being in...of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - Mathematics - 1812 - 624 pages
...always increases as the gun is longer ; though the increase in velocity is but very small in comparison to the increase in length , the velocities being in...the ' square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the...
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The Eclectic review. vol. 1-New [8th], Volume 10

1813 - 662 pages
...other circumstances are as in this tablet. Table of Charges producing the Greatest Velocity. ' « 3d]y. It appears that the velocity continually increases...indeed nearly in the middle ratio between the two. 4thly. Jt appears from the table of ranges in Art. 121, p. 76, that the range increases in a much less...
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The Quarterly Review, Volume 9

William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray (IV), Rowland Edmund Prothero (Baron Ernle) - English literature - 1813 - 556 pages
...increases as the gun is longer ; though the increase in velocity is but very small in comparison with the increase in length ; the velocities being in a...of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the...
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The Quarterly Review, Volumes 9-10

English literature - 1813 - 1102 pages
...increases as the gun is longer; though the increase in velocity is but very small in comparison with the increase in length ; the velocities being in a...of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...continually increases as the gun is longer, though the increase in velocity is but very small in respect of the increase in length, the velocities being in a ratio' somewhat less than that of the square roob of the length of the bore, but somewhat greater tl an that of the cube roots of the k-njth, and...
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The Quarterly Review, Volume 9

William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray (IV), Rowland Edmund Prothero (Baron Ernle) - English literature - 1813 - 540 pages
...increase in velocity is but very small in comparison with the increase in length ; the velocities bemg in a ratio somewhat less than that of the square roots of the length oi the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle...
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A Course of Mathematics: For the Use of Academies, as Well as ..., Volume 2

Charles Hutton - Arithmetic - 1818 - 652 pages
...longer ; though the increase in velocity is but very small in comparison to the increase in leng'.h ; the velocities being in a ratio somewhat less than...of the square roots of the length of the bore, but greater than thai of the cube roots of the same, and is indeed nearly in the middle ratio between the...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...continually increases as the gun is longer, though the ¡ncrenic in velocity is but very small in respect of the increase in length, the velocities being in a ratio somewhat less than that nf the square root* of the length of the bore, but somewhat greater than that of the cube roots of...
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A Course of Mathematics for the Use of Academies, as Well as Private Tuition

Charles Hutton - Mathematics - 1822 - 680 pages
...but very small in comparison to the increase in length ; the velocities being in a ratio someWhaUess than that of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the...
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