which at the equator is the part of gravity, from whence it decreases continually, till at the poles it quite vanishes. Much has been faid of the advantages of making a pendulum VIBRATE IN THE ARC OF A CYCLOID, in which it would defcribe the greatest and leaft entire vibrations in the fame time; but this property is only demonftrated on a fuppofition that the whole mafs of the pendulum is concentrated in a point, but this cannot take place in any really vibrating body. And when the pendulum is of finite magnitude, there is no point given which determines the length of the pendulum; but on the contrary, the center of ofcillation will not occupy the fame place in the given body, when describing different parts of the track it moves through, but will continually be moved in refpect of the pendulum itfelf during it's vibration. This prevents the determination of the time of the vibration in a cycloid, except in the above-mentioned imaginary cafes. There are many other obftacles which concur in rendering the application of this curve to the vibration of pendulums, a fource of errors far greater than thofe which it's peculiar property is intended to obviate. It is therefore wholly dif ufed in practice, and it would be only lofing time to dwell on it's peculiar properties. To find the length of a pendulum, that shall make any number of vibrations in a given time. Reduce the given time into feconds, then fay, as the fquare of the number of vibrations given: to the iquare of this number of feconds:: fo is 39.13 to the length of the pendulum fought, in inches. Ex. Suppofe it makes 50 vibrations in a minute; here a minute is = 60 feconds; then, As 2500 (the fquare of 50): 3600 (the fquare of 3600 × 39:13 2500 bf60):: 39.13: to the length 146868 2500 56.34 inches, the length required. If it be required to find a pendulum that shall vibrate fuch a number of times in a minute; you need only divide 140868, by the fquare of the number of vibrations given, and the quotient will be the length of the pendulum. If the pendulum is a thread with a little ball at it, then the distance between the point of sufpenfion and the center of the ball is efteemed the length of the pendulum. But if the ball be large, fay, as the distance between the point of fufpenfion, and the center of the ball, is to the radius of the ball; fo is the radius of the ball to a third proportional. Set of this from the center of the ball downward, gives the center of ofcillation. Then the whole diftance from the point of fufpenfion to this center of ofcillation, is the true length of the pendulum. If the bob of thé pendulum be not a whole fphere, but a thin fegment of a fphere, as in moft clocks; then to find the center of ofcillation, fay, as the distance between the point of fufpenfion and the middle of the bob, is to half the breadth of the bob; fo is half the breadth of the bob to a third proportional. Set one third of this length from the middle of the bob downwards, gives the center of ofcillation. Then the distance between the centers of fufpenfion and ofcillation, is the exact length of the pendulum. Having the length of a pendulum given, to find how many vibrations it shall make in any given time. Reduce the time given into feconds, and the pendulum's length into inches; then fay, as the given length of the pendulum: to 39.13 fo is the fquare of the time given to the fquare of the P3 number number of vibrations, whose square root is the number fought. Example. Suppose the length of the pendulum is 56.34 inches, to find how often it will vibrate in a minute. 1 minute 60 feconds. Then 56.34 (the length of the pendulum): 39.13:: 3600 (the fquare of 60) to the fquare of the number of vibrations 3600 + 39.13 140868 =2500, and ✓ 2500 50 56.34 56.34 the number of vibrations fought. If the time given be a minute, you need only divide 140868 by the length, and extract the root of the quotient for the number of vibrations. OF TIME. As time in itself does not fall under the notice of our fenfes, and as the parts thereof go on in a continued fucceffion one after another, no two exifting together, it is impoffible to difcover the equality or inequality of any two portions of time, by an immediate comparifon of one with the other. It is therefore neceffary, in order to diftinguish the parts of time, to have recourfe to fomething fenfible, and of a different nature from time, as a measure thereof. In the firft ages of the world, men obferving the frequent rifing and fettings of the fun, took the one or the other for their firft measure of time; calling that portion of time which paffed between the two rifings or fettings, which immediately fucceeded each other, by the name of a day, In like manner, it is rational to fuppofe, that obferving the frequent returns of the new and full moons, they made the one or the other their fecond measure of time, calling that space which paffed between two fucceffive 2 fucceffive new or full moons, by the name of a moon or month. For fome time they contented themfelves with those measures, without knowing or confidering whether they were accurate or in accurate. In proportion as fcience dawned upon the human mind, men became better acquainted with the motion of the heavenly bodies; they then difcovered irregularities in the apparent motion of the fun, and of confequence an inequality in the natural days which depend on that motion. By confidering the caufes of this inequality, they were led to make fuch alterations in the natural days, by adding to fome and taking from others, as reduced them all to a mean equal length, each day being made to confift of 24 equal hours, each of which is fubdivided into 60 equal parts called minutes, and these into 60 other equal parts called feconds, and fo on in a fexagefimal progreffion and thefe parts of time thus reduced to an equality, conftitute the mean or equal time, as it ftands diftinguished by aftronomers from the unequal or apparent time, as measured by the apparent motion of the fun. In order to have a conftant measure of equal time, HUYGENS, a man who added the acuteft penetration to the moft indefatigable induftry, contrived a method of adapting pendulums to clocks, whereby their motions are fo exactly regulated, that in one whofe movements are rightly adjusted, the seconds, minutes, and hours, are for fome time pointed out with the greatest exactness. The principle of motion in a clock is derived from the power either of a weight or fpring; either of these forces is fufficient to actuate or put in motion the fyftem of wheels and pinions which compofe the intermediate parts of the clock; the indexes fixed on the axis point out the proper fubdivifions P 4 divifions of time on appropriate circles upon the face of the clock; and a pendulum or ballance is added, to regulate or render uniform the motion communicated to the machine. The force of the weight is derived from the power of gravity, and this being always the fame in a given quantity of matter, the force of the weight may be confidered as a conftant quantity, or always remains the fame in the fame medium, and is therefore a uniform power or principle of motion. If the pendulum be put in motion by a pufh of the hand, it will continue to move backward and forward till the refiftance of the air or the friction at the point of fufpenfion deftroys the original impreffed force. But at every vibration of the pendulum, the teeth of the crown wheel acts upon the pallets, fo that after one tooth has commanicated motion to one pallet, it efcapes, and the oppofite tooth acts upon the oppofite pallet, and efcapes in the fame manner; and thus each tooth efcapes after having communicated it's motion to the pallets in fuch manner that the pendulum, inftead of being flopped, continues to move. Let EGF, fig. 15, pl. 2, represent the swingwheel of a clock, that is to revolve in the direction EGF; let C and D reprefent the pallets moveable on an axis at A, and fo connected with the pendulum as to be made to vibrate along with it. Suppofe the ball to vibrate from R to B, one of the teeth of the wheel refting against the pallet C, whofe figure is feen enlarged at IK L; when the pendulum returns towards Q, the pallet c is drawn out, the wheel preffing firft along the plane IK, and afterwards on the inclined plane KL; the preffure of the wheel on K L pufhes the pallet,. or aflifts it's motion, till at length the tooth flips off the point L. During this time the pallet D, whofe |