Time and its Measurement

Excerpts

• Time and its Measurement

  Thus to measure a length we may take a foot-rule, and by applying it to the given length as often as is necessary, we shall find how many feet the length contains.

• Time and its Measurement

  The true solar day is not however always of the same duration.

• Time and its Measurement

  I believe it is not generally known that a sun-dial can be so constructed that the shadow will, for a short time near sunrise and sunset, move backwards on the dial

• Time and its Measurement

  The Julian calendar made the year, on an average, contain 365.25 days. The actual value is, very approximately, 365.242216 days.

• Time and its Measurement

  The French were the last civilized nation to abandon the use of true time: this was in 1816.

• Time and its Measurement

  Our experiences are consistent with this statement, and that is as high an authority as a mathematician hopes to get.

• Time and its Measurement

  The time occupied by a given amount of some liquid or sand in running through a given orifice under the same conditions is always the same, and by noting the level of the liquid which has run through the orifice, or which remains to run through it, a measure of time can be obtained.

• Time and its Measurement

  Most of these early clocks were regulated by horizontal balances: pendulums being then unknown.

• Time and its Measurement

  so arranged that the cylinder descended with uniform velocity between two vertical pillars on which the hours were marked at equidistant intervals.

• Time and its Measurement

  Both move round in the same direction, but the angular velocity of the hour-hand is twice as great as that of the sun. Hence the rule.

• Time and its Measurement

  To do this it is sufficient to point the hour-hand to the sun, and then the direction which bisects the angle between the hour and the figure xii will point due south.

Equations

• Time and its Measurement

  a = N - 4 \{N/4\}

  The remainder a, when the year N is divided by 4, equals N minus 4 times the integral part of N/4.

• Time and its Measurement

  b = N - 7 \{N/7\}

  The remainder b, when the year N is divided by 7, equals N minus 7 times the integral part of N/7.

• Time and its Measurement

  c = N - 19 \{N/19\}

  The remainder c, when the year N is divided by 19, equals N minus 19 times the integral part of N/19.

• Time and its Measurement

  \xi = \{N/100\}\allowbreak - \{N/400\} - \{N/300\}

  In the Gregorian calendar the correction xi for the year N is the integral part of N/100 minus the integral part of N/400 minus the integral part of N/300.

• Time and its Measurement

  \eta = \{N/100\}\allowbreak - \{N/400\} - 2

  In the Gregorian calendar the correction eta for the year N is the integral part of N/100 minus the integral part of N/400 minus 2.

• Time and its Measurement

  \xi = 0

  In the Julian calendar the correction xi is zero.

• Time and its Measurement

  \eta = 0

  In the Julian calendar the correction eta is zero.

• Time and its Measurement

  m=15

  In the Julian calendar the Easter constant m equals 15.

• Time and its Measurement

  n = 6

  In the Julian calendar the Easter constant n equals 6.

• Time and its Measurement

  m = 22

  For the years 1582 to 1699 inclusive in the Gregorian calendar, the Easter constant m equals 22.

• Time and its Measurement

  n = 2

  For the years 1582 to 1699 inclusive in the Gregorian calendar, the Easter constant n equals 2.

• Time and its Measurement

  m = 23

  For the years 1700 to 1799 in the Gregorian calendar, the Easter constant m equals 23.

• Time and its Measurement

  n = 3

  For the years 1700 to 1799 in the Gregorian calendar, the Easter constant n equals 3.

• Time and its Measurement

  c > 10

  The exceptional Easter case that moves Easter-day one week earlier applies only when c is greater than 10.

• Time and its Measurement

  \sin^{-1} (\cos \omega \sec \tfrac{1}{2} \omega) - \cot^{-1} \{ \sin \omega \cos(l - \tfrac{1}{2} \omega) (\cos^2 l - \sin^2 \omega)^{-\frac{1}{2}} \}

  The angle through which the shadow of a normal style moves backwards between sunrise and noon on the longest day, for a dial placed to cut the meridian midway between the equator and the tropic.

Problems

No exercises in this chapter.