## Huygens’ Use of Pendulums

 Last time we learned that Henry Cavendish determined a value for G, the universal gravitational constant, fast on his way to determining a quantity he was determined to find, the Earth’s mass.   Today we’ll see how the previous work of Christiaan Huygens, a contemporary of Isaac Newton’s, helped him get there.       First Cavendish used algebra to rearrange terms in Newton’s gravitational formula so as to solve for M, Earth’s mass.   Rearranged, Newton’s formula becomes, M = (g × R2) ÷  G       But in order to solve for M, Cavendish first needed to know Earth’s acceleration of gravity, g.   To aid him in this calculation he referred back to the work of Christiaan Huygens, a Dutch mathematician from Newton’s time. Huygens was eager to devise a formula capable of predicting clock pendulums’ motions on ships, his goal being to invent a timepiece accurate enough to make navigating ships easier.   He hypothesized that a key factor in predicting a pendulum’s movement was an unknown constant, the acceleration of gravity factor, g, which Newton had previously posited existed.   Through meticulous observation, Huygens came to realize that the time it took for pendulums to complete one swing back and forth was dependent not only on the length of the pendulum, but also this unknown quantity.       In order for Huygens’ computations to work, the value of g had to be a constant, meaning, its value could not vary between computations; g‘s value was in fact a fudge factor, a phantom he would assign a specific numerical value.   Huygens’ needed it in order to make his hypothesis work, a practice commonly use by scientists, even today.   Determining a value for g would allow Huygens to successfully relate the length of the pendulum to the timing of its swing and to create a mathematical relationship between them.       Huygens ultimately determined g’s value to be a whopping 32.2 feet per second per second, or 32.2 ft/sec2.    We’ll see how he did it next time. _______________________________________
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