Pocketbook of Useful Formulæ and Memoranda
for Civil and Mechanical Engineers

631 OF ENGINEERING FOBMULÆ. Differential and Integral Calculus—continued. Example of the application op the Calculus to Curves. Let A — Major axis of an ellipse .............. = say 40. a — Minor axis of ditto .......... — say 20. y = Any ordinate .................... . • — 7'1414, x — Any abscissa corresponding with y = 6. Then the equation of an ellipse being y2 = —% (A x — æ2) ; «^^-^-^ = 0=10.-^-^, A2 A- * x 20 — x — iy the differential of which is 10 — - - 2 y =--- dv so — x , dx iy and — = -—- = • 491; also — = —--------- dæ iy dV 20 ~g / / d as \ » Length of tangent T = 3/ V 1 + ( „ subtangent t — y normal N = y 1 + /dyy \dx) = 2-04. — 16-225 = 14’568 = 1-955 , , dy „ subnormal n — y ” dx Tan. of angle of T with t = “ = • 491 = tan. 26° 10' N<.te.-<Zx, d y, &c.,in this and in the preceding diagrams are shown aa having considerable magnitude, but properly they should be mdejimtdy small 3-506