Philosophical MagazineTaylor & Francis, 1836 - Physics |
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Page 9
... equations ( 2. ) are similar to the first , consequently if we transform them in the same man- d & d2 n ner , and ( by the principles of dynamics ) put ddt ' d ? dt2 d2 & d t den d t d for X , Y , Z , we shall have = mΣ . { $ ( r ) ...
... equations ( 2. ) are similar to the first , consequently if we transform them in the same man- d & d2 n ner , and ( by the principles of dynamics ) put ddt ' d ? dt2 d2 & d t den d t d for X , Y , Z , we shall have = mΣ . { $ ( r ) ...
Page 10
... equation ( 4. ) , and sup- pose the particles to be so arranged in their state of equili- brium that for every ... equation ( 4. ) will become d ° ફ્ d to = mΣ . { ♢ ( r ) + & ( r ) △ x2 } Az2 ( ' d d * ફ્ + · dz d4 A z2 3.4 the ...
... equation ( 4. ) , and sup- pose the particles to be so arranged in their state of equili- brium that for every ... equation ( 4. ) will become d ° ફ્ d to = mΣ . { ♢ ( r ) + & ( r ) △ x2 } Az2 ( ' d d * ફ્ + · dz d4 A z2 3.4 the ...
Page 11
... equation ( 6. ) , and it will become n2 — s9 k2 + = √ ( · - 52- S / 2 $ 2 3.4 k n k = 0 ; hence 4 ) = $ ( 1 – - 3.4 . k2 ) ka 2.3.4 512 ) , nearly . As the equations ( 6. ) and ( 7. ) are similar , and as we have put a sin k≈ + b cos ...
... equation ( 6. ) , and it will become n2 — s9 k2 + = √ ( · - 52- S / 2 $ 2 3.4 k n k = 0 ; hence 4 ) = $ ( 1 – - 3.4 . k2 ) ka 2.3.4 512 ) , nearly . As the equations ( 6. ) and ( 7. ) are similar , and as we have put a sin k≈ + b cos ...
Page 25
... equations obtained with the omission of the sign of summation . This will be understood on a comparison of those ... equation ( 20. ) , ) we shall readily per- ceive that the values of these coefficients in their exact form ( that is ...
... equations obtained with the omission of the sign of summation . This will be understood on a comparison of those ... equation ( 20. ) , ) we shall readily per- ceive that the values of these coefficients in their exact form ( that is ...
Page 43
By X. On the Theory of Congeneric Surd Equations . W.G. HORNER , Esq . ( In a Letter addressed to T. S. Davies , Esq . , F.R.S. L. & E . ) * [ If those mathematicians who have met with a quadratic equation + whose " roots " either under ...
By X. On the Theory of Congeneric Surd Equations . W.G. HORNER , Esq . ( In a Letter addressed to T. S. Davies , Esq . , F.R.S. L. & E . ) * [ If those mathematicians who have met with a quadratic equation + whose " roots " either under ...
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