WHIRLING-TABLE. 



bearers, the round plates S and T will be drawn up to the 

 top of their refpeftire towers O and P. 



There are feveral brafs weights, fome of two, fome of 

 three, and others of four ounces, to be occafionally put 

 within the towers O and P, upon the round plates S and T ; 

 each weight having a round hole in the middle of it, for 

 going upon the fockets or axes of the plates, and being flit 

 from the edge to the hole, that it may flip over the line 

 which comes from each ball to its refpeftive plate. 



For a fpecimen of the experiments which may be made 

 with this machine, we fliall fubjoin the following. 



1. Removing the bearer M X, put the loop of the line b, 

 to which the ivory ball a is faftened, over a pin in the centre 

 of the board d, and turn the winch B ; and the ball will 

 not immediately begin to move with the board, but, on ac- 

 count of its inaftivity, endeavour to remain in its ftate of 

 reft. But when the ball has acquired the fame velocity 

 with the board, it will remain upon the fame part of the 

 board, having no relative motion upon it. However, if the 

 board be fuddenly ftopped, the ball will continue to revolve 

 upon it, until the friftion thereof ftops its motion ; fo that 

 matter refills every change of ftate, from that of reft to that 

 of motion, and "vice •vcrjd. 



2. Put a longer cord to this ball ; let it down through 

 the hollow axis of the bearer M X and wheel G, and fix a 

 weight to the end of the cord below the machine ; and this 

 weight, if left at liberty, will draw the ball from the edge 

 of the whirling-board to its centre. Draw off' the ball a 

 little from its centre, and turn the winch ; then the ball will 

 go round and round with the board, and gradually fly far- 

 ther from the centre, raifing up the weight below the ma- 

 chine ; and thus it appears that all bodies revolving in circles, 

 have a tendency to fly off^ from thefe circles, and muft be 

 retained in them by fome power proceeding from or tending 

 to the centre of motion. Stop the machine, and the ball 

 will continue to revolve for fome time upon the board ; but 

 as the friftion gradually ftops its motion, the weight afting 

 upon it will bring it nearer and nearer to the centre in 

 every revolution, till it brings it quite thither. Hence 

 it appears, that if the planets met with any refiftance in 

 going round the fun, its attraftive power would bring them 

 nearer and nearer to it in every revolution, till they fell 

 into it. 



3. Take hold of the cord below the machine with one hand, 

 and with the other throw the ball upon the round board as 

 it were at right angles to the cord, and it will revolve upon 

 the board. Then, obferving the velocity of its motion, 

 pull the cord below the machine, and thus bring the ball 

 nearer the centre of the board, and the ball will be feen to 

 revolve with an increafing velocity, as it approaches the 

 centre : and thus the planets which are neareft the fun per- 

 form quicker revolutions than tb'jfe which are more remote, 

 and move with greater velocity in every part of their re- 

 fpeftive circles. 



4. Remove the ball a, and apply the bearer M X, whofe 

 centre of motion is in its middle at iv, direftly over the 

 centre of the whirling-board d. Then put two balls (V and 

 U) of equal weights upon their bearing wires, and having 

 fixed them at equal diftances from their lefpeftive centres 

 of motion txi and x upon their filk cords, by the fcrew-nuts, 

 put equal weights in the towers O and P. Laftly, put the 

 catgut-ftrings E and F upon the grooves G and H of the 

 fmall wheels, which, being of equal diameters, will give 

 equal velocities to the bearers above, when the winch B is 

 turned ; and the balls U and V will fly off toward M and 

 N, and raife the weights in the towers at the fame inftant. 

 This fhews, that when bodies of equal quantities of matter 



revolve in equal circles with equal velocities, their centrifu- 

 gal forces are equal. 



5. Take away thefe equal balls, and put a ball of fix 

 ounces into the bearer M X, at a fixth part of the diftance 

 w 2 from the centre, and put a ball of one ounce into the 

 oppofite bearer, at the whole diftance xy ■= w^; and fix 

 the balls at thefe diftances on their cords, by the fcrew-nuts 

 at the top : then the ball U, which is fix times as heavy as 

 the ball V, will be at only a fixtKp;it of the diftance from 

 its centre of motion ; and confequently will revolve in a 

 circle of only a fixth part of the circumference of the circle 

 in which V revolves. Let equal weights be put into the 

 towers, and the winch be turned; which (as tie catgut- 

 ftring is on equal wheels below) will caufe the balls to re- 

 volve in equal times : but V will move fix times as faft as 

 U, becaufe it revolves in a circle of fix tim-^s its radius, and 

 both the weights in the towers will rife r>t unce. Hence it 

 appears, that the centrifugal forces of revolving bodies are 

 in direft proportion to their quantities of matter multiplied 

 into their refpeftive velocities, or into their diftances from 

 the centres of their refpeftive circles. 



If thefe two balls be fixed at equal diftances frorn their 

 refpeftive centres of motion, they will move with equal 

 velocities; and if the tower O has fix times as much weight 

 put into it as the tower P has, the balls will raife their 

 weights exaftly at the fame moment : /, e. the ball U, 

 being fix times as heavy as the ball V, has fix times as much 

 centrifugal force in defcribing an equal circle with an equal 

 velocity. 



6. Let two balls, U and V, of equal weights be fixed on 

 their cords at equal diftances from their refpeftive centres 

 of motion lu and x ; and let the catgut-firing E be put 

 round the wheel K (whofe circumference is only half that 

 of the wheel H or G) and over the pulley j to keep it 

 tight, and let four times as much weight be put into the 

 tower P, as in the tower O. Then turn the winch B, and 

 the ball V will revolve twice as faft as the ball U in a circle 

 of the fame diameter, becaufe they are equi-diftant from the 

 centres of the circles in which they revolve ; and the weights 

 in the towers will both rife at the fame inftant, which fliews 

 that a double velocity in the fame circle will exaftly balance 

 a quadruple power of attraftion in the centre of the circle : 

 for the weights in the towers may be confidered as the 

 attraftive forces in the centres, afting upon the revolving 

 balls ; which, moving in equal circles, are as if they both 

 moved in the fame circle. Whence it appears, that if 

 bodies of equal weights revolve in equal circles with unequal 

 velocities, their centrifugal forces are as the fquares of the 

 velocities. 



7. The catgut-ftring remaining as before, let the diftance 

 of the ball V from the centre x be equal to 2 of the divi- 

 fions on its bearer ; and the diftance of the ball U from the 

 centre w be 3 and a fixth part ; the balls themfelves being 

 equally heavy, and V making two revolutions by turning 

 the winch, whilft U makes one ; fo that if we fuppofe the 

 ball V to revolve in one moment, the ball U will revolve in 

 two moments, the fquares of which are i and 4 : therefore, 

 the fquare of the period of V is contained 4 times in the 

 fquare of the period of U. But the diftance of V is 2, the 

 cube of which is 8, and the diftance of U is 3c', the cube 

 of which is 32 very nearly, in which 8 is contained 4 times : 

 and therefore the fquares of the periods of V and U are to 

 one another as the cubes of their diftances from x and lu, the 

 centres of their refpeftive circles. And if the weight in 

 the tower O be 4 ounces, equal to the fquare of 2, the 

 diftance of V from the centre x ; and the weight in the 

 tower P be 10 ounces, nearly equal to the fquare of 3,;, the 



3 B 2 diftance 



