An elementary treatise on mechanics, embracing the theory of statics and dynamics, and its applications to solids and fluids (1849)
Smith, Augustus William, 1802-1866 · New York, Harper · leaf 279
of a rectangular CENTER OF PRESSURE. 255 surface vertically immersed, and having one side in the surfaceof the fluid. Let YYj be the line of intersectionof the immersed surface ABCD with Ti-the surface of the fluid, and conceiveABCD divided into n rectangles by-horizontal lines, n being a very… … , bhn The distances of these rectangles from the surface are their squares,Hence nbh h 2h 3h e -, —, —, &c.;n n n If 2Vf 37i2 s n n n bh3 bh3.22 bh\& e =—(l + 29+39+ n*). n But when n is very large, the sum of the mth powers of thenatural numbers 1,2, 3, &c, to n is wi+1 Also, „ bh3 n3\…
Mechanics, Analytic
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