Elements of analysis as applied to the mechanics of engineering and machinery . ts c and p. If, in the above formulae, we put u = t^ v = P^ 0 = 0,/?=^, and y ^ s, there result the following formulae for the calculation of c and p-. _ !• (t*) I (St) - Z (f) I (st^- J (P) X («) - 2- (f) 1 («») p y (f) s (sc) - z (t^) I (s() 2 X (t-) X (<•) — X (f) 2 («») whence, the following: t f f t s St sf 1 1 1 1 5 5 5 3 9 2t 81 20 60 180 5 25 125 625 38 190 950 1 49 343 2401 58,5 409,5 2866,5 10 100 1000 10000 101 1010 10100 Amounts 184 1496 13108 222,5 1674,5 14101,5 = ^ (n = ^ (n = ^ (^0 = I(s) = I{st)
Elements of analysis as applied to the mechanics of engineering and machinery . ts c and p. If, in the above formulae, we put u = t^ v = P^ 0 = 0,/?=^, and y ^ s, there result the following formulae for the calculation of c and p-. _ !• (t*) I (St) - Z (f) I (st^- J (P) X («) - 2- (f) 1 («») p y (f) s (sc) - z (t^) I (s() 2 X (t-) X (<•) — X (f) 2 («») whence, the following: t f f t s St sf 1 1 1 1 5 5 5 3 9 2t 81 20 60 180 5 25 125 625 38 190 950 1 49 343 2401 58,5 409,5 2866,5 10 100 1000 10000 101 1010 10100 Amounts 184 1496 13108 222,5 1674,5 14101,5 = ^ (n = ^ (n = ^ (^0 = I(s) = I{st) = Z(sO. 60 ELEMENTS OF AJ^ALYSIS. [AuT 3t. From the above there results13108 . 1674,5 — 1496 c = iP = 14101,5 184 . 13108 — 1496184 . 14101,5 — 1496 1496J 6 74^ l496 85340 1738689624 184 . 13108 —1496 . 1496 173860 and hence, the following formula for the observed motion: s = 4,908 t + 0,5155 . t\According to this formula, we have = 4,908 ft. and= 0,5155 ft., for the times . 0 1 3 5 7 10 sec. the spaces . . 0 5,43 19,36 37,43 59,62 100,63 ft. Fig. If the times (t) be taken asabscissas, and the observed, aswell as the estimated, spaces(s) as ordinates, a curve AB,, may be drawn throughthe ends of the estimated co-ordinates, which will pass be-tween the points M^N^O^P^Qdetermined by the observedco-ordinates, in such a mannerthat the sum of the squaresof the deviation of the same from these points will be as Fig. 49. t = 0 1 small as possible on both sides. Art. 37. If, in default of a formula for the constant progressionof a magnitude y, or its dependence upon another magnitude ^, itbe necessary to determine a value of the magnitude y which cor-responds to a given value of ^, bymeans of the values of x and y asknown by experience or taken froma table, we must make use of the pro-cess of interpolation^ of which onlythe most important part is to be com-municated here. If the abscissas A jr = x. =: ,a?j, and A 31., = ^.,, Fig. 49, andthe corresponding
Size: 1715px × 1457px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1860, bookpublisherphiladelphiakingba
