Equation 4 · The Machine Before Electronics
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
constituents determined by fitting the expression to a record of observed water levels at that specific place. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol phi_n
constituents determined by fitting the expression to a record of observed water levels at that specific place.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Here is a known astronomical angular frequency, while and are constituents determined by fitting the expression to a record of observed water levels at that specific place. The division of labour is the whole trick. The frequencies are universal and can be built into gearing once. The amplitudes and phases are local and must be adjustable.
Sources cited in the article section
- [3] William Thomson's Tide Predicting Machine, 1872 ↗
- [2] Tide Predicting Machines ↗
- [1] Lord Kelvin and His Analog Computer ↗
These citations give research context. Read each source to check which claims it supports.