 | 1816 - 764 σελίδες
...fmall arc of a circle, the time of one vibration is to the time of a body's falling perpendicularly through half the length of the pendulum as the circumference of a circle is to its diameter. Let PE (fg. 5.) be the pendulum which defcribes the arch ANC in the time of one vibration ; let PN be perpendicular... | |
 | Charles Hutton - 1818 - 652 σελίδες
...tangent CF is parallel to the chord AD. PROPOSITION XXX. 1 48. When a Pendulum vibrate» in n cycloid ; the Time of one Vibration, is to the Time in which...the Length of the Pendulum, as the Circumference of o Oír de is to its Diameter. LET Ава be the cycloid ; BB its axis, or the diameter of the generating... | |
 | William Nicholson - 1821 - 402 σελίδες
...roots of the times of their vibrations. 4. The time of one vibration is to the time of the deserist, through half the length of the pendulum, as the circumference of a circle to its diameter. 5. Whence the length of a pendulum, vibrating seconds, will be found 39.2 inches nearly;... | |
 | William Nicholson - 1821 - 406 σελίδες
...roots of the times of their vibrations. 4. The time of one' vibration is to the time of the descent, through half the length of the pendulum, as the circumference of a circle to its diameter. 5. Whence the length of a pendulum, vibrating seconds, will be found 39.2 inches nearly... | |
 | James Renwick - 1822 - 476 σελίδες
...square roots of their lengths. The time of an oscillation is to the time of the fall of a heavy body through half the length of the pendulum as the circumference of a circle is to its diameter. The lengths of pendulums are inversely as the squares of the number of their respective vibrations... | |
 | Charles Hutton - 1822 - 680 σελίδες
...parallel to the chord AD. i ~, , ' * PROPOSITrON XXX. 148. When a Pendulum vibrates in a cycloid ; the Time of one Vibration, is to the Time in which a Body falls through half the ,£tength of the Pendulum, as the Circumference of a ' ' cle w to its Diameter. LET ABB be the cycloid... | |
 | 1822 - 520 σελίδες
...square roots of their lengths. The time of an oscillation is to the time of the fall of a heavy body through half the length of the pendulum as the circumference of a circle is to its diameter. The lengths of pendulums are inversely as the squares of the number of their respective vibrations... | |
 | James Mitchell - 1823 - 666 σελίδες
...time of vibration in any arc, is to the time in which a heavy body would fall by the force of gravity through half the length of the pendulum; as the circumference of a circle is to its diame ter. Now by the laws of falling bodies J -- = the time of a 2ff liody falling through i I, or... | |
 | 1823 - 872 σελίδες
...cii cle, the time of ene vibration U lo tbe time of a body's falling perpendicularly through half tbe length of the pendulum, as the circumference of a circle is to its diameter. Let PE (fig. 5.) be the pendulum which describes Fig. -• the arch ANC in the time of one vibration }•... | |
 | William Emerson - 1825 - 506 σελίδες
...VIBRATES IN A CYCLOID, THE TIME OF OSE VIBRATION IS TO THE TIME OF A BODY'S FALLING PERPENDICULARLY THROUGH HALF THE LENGTH OF THE PENDULUM, AS THE CIRCUMFERENCE OF A CIRCLE TO THE DIAMETER. Let ADa be the cycloid, FD its axis, FGD the generating circle. Let the body descend... | |
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Half the Length of the Pendulum, as the Circumference of a Circle is to its Diameter... 
