On the Difference of Longitude Between the Observatories of Brussels And Greeenwich, As Determined By Galvanic Signals
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If the two clocks had no relative rate, the four numbers E t , E 2 , E J5 E 4 , Royal Astron. Soc. Vol. XXIV. c io Mr. Airy on the Difference of Longitude of Brussels and Greenwich, would be equal. As it is certain, however, that there was a relative rate, the only supposition that we can venture to make is, that the rate was uniform during the hour. We may also, in most cases, assume, that the mean of the signals in each quarter of hour corresponded (with sufficient approxi- mation) to the mid...dle of the quarter of hour. Let the relative rate for one quarter of hour be r : then the equations become E r +t =e, E, + r-t =e a E, +2 r + t = e, E , +3 r — t = e 4 The easiest way of treating these equations is the following : Subtract the double of the second equation from the sum of the first and third : 4 t = e t -(- e, — 2 e„ or t = 4 Subtract the sum of the second and fourth equations froni the double of the third : 2 e, — e, — e A 4 t = 2 e, — e z — e,, or t = 4 The mean of these two determinations may probably be adopted as preferable to either of them alone.
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To quickly assess the difficulty of the text, read a short excerpt:
If the two clocks had no relative rate, the four numbers E t , E 2 , E J5 E 4 , Royal Astron. Soc. Vol. XXIV. c io Mr. Airy on the Difference of Longitude of Brussels and Greenwich, would be equal. As it is certain, however, that there was a relative rate, the only supposition that we can venture to make is, that the rate was uniform during the hour. We may also, in most cases, assume, that the mean of the signals in each quarter of hour corresponded (with sufficient approxi- mation) to the mid...dle of the quarter of hour. Let the relative rate for one quarter of hour be r : then the equations become E r +t =e, E, + r-t =e a E, +2 r + t = e, E , +3 r — t = e 4 The easiest way of treating these equations is the following : Subtract the double of the second equation from the sum of the first and third : 4 t = e t -(- e, — 2 e„ or t = 4 Subtract the sum of the second and fourth equations froni the double of the third : 2 e, — e, — e A 4 t = 2 e, — e z — e,, or t = 4 The mean of these two determinations may probably be adopted as preferable to either of them alone.
What to read after On the Difference of Longitude Between the Observatories of Brussels And Greeenwich, As Determined By Galvanic Signals?
You can find similar books in the "Read Also" column, or choose other free books by Sir George Biddell Airy to read onlineMoreLess
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