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Equation 10 · Part 4 · The Machine Before Electronics

Symbol τ

z(t)=∫0ty(τ) dxdτ dτz(t) = \int_{0}^{t} y(\tau) \, \frac{dx}{d\tau} \, d\tau
τ\tau

What this part means

τ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

τ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Summation is the easy operation to build. Integration is the one that opens up a whole class of problems, and the mechanism that made it practical was the wheel-and-disc integrator: a wheel riding on a rotating disc at a radius that can be varied, so that the wheel’s rotation accumulates the product of the disc’s rotation and the instantaneous radius. If the disc rotation represents the independent variable and the radial position represents the dependent one, the wheel angle represents z(t)=∫0ty(τ) dxdτ dτz(t) = \int_{0}^{t} y(\tau) \, \frac{dx}{d\tau} \, d\tau. which is to say, the integral of y with respect to x , produced continuously and without arithmetic.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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