115 



FORCE. 



FORCING. 



140 



to be 16 and 8 ounces, the pressures are in both cases the same, 

 namely the weight of one ounce; but the masses of matter moved 

 are 17 and 9 ounces (for in both cases the moving ounce is part of 

 the whole quantity moved). The velocities at the end of any given 

 time are found to be inversely as 17 and 9 : so that by the time a 

 velocity of 9 feet per second is created in the mass of 17 ounces, 17 

 feet per second is created in that of 9 ounces. The connection of 

 pressure, velocity created by pressure, and time which pressure takes 

 to create velocity, as deduced from experiment, is contained in the 

 following results : 



1. The same pressure continually acting upon a given mass for 

 different times produces velocities which are proportional to the times, 

 and augments velocity by equal portions in equal times. 



2. The same pressure applied to different masses of matter (that is, 

 to different weights of matter) during the same time, produces velocities 

 which are inversely proportional to those masses. 



3. The velocity of falling bodies is accelerated by 32'19 feet in every 

 second : and in that proportion for all other times. 



If then a pressure which is the same as that of a weight V produces 

 motion in a mass of matter whose weight is w, during t seconds, then 

 because the weight of v acting upon the mass of v for that time would 

 produce 32'19 x t feet of velocity, we have 



Velocity produced by v acting on v (or 32'19 x t), 



is to velocity produced by v acting on w (which is to be found), 



inversely as v to w, or as w to v : whence 

 v 



Telocity acquired is T. * 32'19 1 feet per second. 



If it were required to reduce the weight w, having a velocity v, to a 

 state of rest in a given time, say ( seconds, and if p were the pressure 

 requisite to be applied to w during the t seconds to produce this effect, 

 we must remember that the velocity destroyed by a pressure in any 

 direction is the same as would have been created in the same time in 

 the opposite direction, if the mass in question had been already at rest. 

 Thus, 



x 32'19 x t must be = v or P = 

 w 



w f 

 32-19 t 



Hence, in different masses, the pressures necessary to destroy the 

 motions in the same given time are as the products of the masses and 

 velocities. Thus, 



The pressure which will in one-hundredth of a second reduce to rest 

 a mass of 10 ounces moving 100 feet per second, is to the pressure 

 which will (also in one-hundredth of a second) reduce to rest 20 ounces 

 moving 85 feet per second, as 10 x 100 to 20 x 85, or as 1000 to 1700. 

 It is customary to call this product of mass and velocity the momentum 

 or moving force of the body. [MOMENTUM.] 



When bodies are in motion, and with a continually varying velocity, 

 it becomes desirable to consider their motion, not at all with reference 

 to the masses which are moved, and solely with reference to the altera- 

 tions of velocity which are produced. Thus if a feather and a cannon- 

 ball move together in the same way, the force that is exerted upon the 

 feather is the same in motive effect (upon the feather) as that which 

 acts on the ball (upon the ball). It is customary to ascertain the 

 amount of velocity which would be produced in one second if the 

 acceleration, such as it is at the point in question, continued uniformly. 

 [ACCELERATION.] And this result is called the accelerating force : for 

 which the simple term acceleration might be advantageously substituted. 

 It is found by the rules of the differential calculus in the following 

 manner (for the demonstration, see VELOCITY). If a point move in a 

 line in such a manner that x feet is its distance from a given point in 

 the line at the end of the time t seconds, and if x be a function of t, 



then the velocity of the body (r) at the end of the tune t is feet 



d t 



per second, and the acceleration which that velocity is then undergoing 

 is such as, if allowed to continue uniformly for one second, would 



increase the velocity by _f or - feet. Thus, if x=t* + t 3 , or if a 



at dC 



point move through t' + < 3 feet in t seconds, the velocity at the end of 

 that time is 2 1 + 3 ( 2 feet per second, and iU acceleration is 2 + 6 t ; or 

 (for instance) at the end of 10 seconds the velocity (320 feet per 

 second) is undergoing acceleration at a rate which would, if continued 

 undisturbed for one second, add 62 feet in that second : or at the end 

 of the eleventh second, the velocity would be 382 feet per second. 

 If / be this accelerating force, we have then 



d x dv d'x 



v = Tr f = rfl = ~d?' "* = /** 



Thes? are called the equations of motion. 



Any unit of time might be chosen instead of one second, but not 

 without the following caution. Let g be the velocity generated by a force 

 acting uniformly for one second ; then 60 g is the velocity produced in 

 60 seconds or in one minute. If then we measure the acceleration by 

 </, when the unit is one second, it might seem that we should use 60 g 

 "I of y, when the unit is one minute. But it must be remem- 

 bered that when we use the r. unute as a unit of time, we must measure 

 velocities by the space* wlu'ch would be described in one minute. 

 Now, in the preceding, 60 ;/ means that the body, at uu end of one 



ARTS A!0> 801. DIV. VOL. I\ . 



minute, is moving at the rate of 60 g per second ; that is at the rate of 

 60 x 60 x g per minute. Hence 3600 rj is the measure of the accelera- 

 tion, when both velocity and acceleration are referred to the minute 

 instead of the second. 



Referring to what precedes, we see that accelerating forces (or 

 accelerations) are proportional inversely to the masses in which they 

 are produced, and directly to the pressures which produced them. 



v 

 Thus the pressure v acting on the weight w, produces - x 3219 feet 



of velocity in every second. 



The greatest difficulty in the way of the beginner is his liability to 

 confound an increase of velocity with an increase of length described. 

 He should carefully attend to the article ACCELERATION, by which he 

 will see that a velocity uniformly increasing causes unequal spaces to be 

 described in equal successive portions of time ; while a uniformly 

 increasing length described means a uniform velocity, or a velocity 

 which does not change at all. 



FORCES, IMPRESSED AND EFFECTIVE. When various pres- 

 sures act at different points of a system, the forces which act upon any 

 one point are not those which would, by themselves, produce the motion 

 which that point really has, in consequence of the motion of the system. 

 Thus, suppose a pendulum with two balls, one above and the other 

 (which we suppose to be much the heavier) below the point of suspen- 

 sion. The forces which act on the upper ball would, if it were free of 

 the larger one, cause it to descend ; while, in consequence of the 

 connection of the two balls, the smaller actually does vibrate like a 

 pendulum turned upside down, or as if its gravitating tendency were 

 upwards instead of downwards. Here is an instance in which the 

 impressed force acts downwards and the effective force vipwards ; that 

 is, the motion which actually ensues is such as would require a force 

 acting upwards to cause it. 



One of the most important principles in dynamics is that known by 

 the name of D'Alembert, and is enunciated thus : the impressed forces 

 are altogether equivalent to the effective forces, or if the directions of 

 the latter were all changed, the former would equilibrate them. 

 Suppose an infinitely small portion of time to elapse, during which the 

 different small masses into which the system may be divided receive 

 certain infinitely small accelerations or retardations. From these the 

 effective forces may be deduced, for they are the forces which would 

 severally produce the actual changes of velocity which take place. If 

 then, forces equal and contrary to the effective forces thus deduced 

 were applied at each point, all the motion created by the impressed 

 forces would be destroyed ; that is, the effective forces are such as 

 would (applied in contrary directions) prevent the impressed forces 

 from producing any motion. This proof might be put into more 

 accurate language, but it is in substance the one which is us lally 

 given. [VIRTUAL VELOCITIES.] 



FORCES, PARALLELOGRAM OF. Any two forces acting a the 

 same point, and represented hi magnitude and direction by two straight 

 lines, are equivalent to a third force which is represented in magnitude 

 and direction by the diagonal of the parallelogram constructed with the 

 two lines as its sides. [COMPOSITION.] This theorem is frequently 

 called that of the parallelogram of forces. 



FORCES, PHYSICAL CORRELATION OF. [PHYSICAL FORCES.] 



FORCING, in horticulture, is the art of hastening the growth and 

 maturity of flowers, fruits, and vegetables by artificial means. 



Many of our finest exotic fruits are indigenous to warmer countries, 

 and would scarcely ripen even in our warmest seasons ; but by this 

 art they are brought to great perfection in cold climates, and by 

 advancing or retarding artificially the growing season of hardy kinds 

 they also can be had in regular succession throughout the greater part 

 of the year. 



Although forcing to any extent is but of recent date in England, 

 yet it appears to have been practised in other countries at a very early 

 period of time. Sir Joseph Banks, in the ' Hort. Trans.,' cites some 

 epigrams from Martial, to show that hothouses were not unknown to 

 the Romans, and arrives at the conclusion that in all probability they 

 had both vineries and peach-houses, formed of talc instead of glass, 

 which is now commonly used. Pliny tells us that Tiberius, who was 

 fond of cucumbers, had them in his garden throughout the year by 

 means of (specularia) stoves, where they were grown in boxes, wheeled 

 out in fine weather, and replaced in the night or in cold weather (Plin. 

 ' Hist. Nat.,' xix. 23) ; whence it may be inferred that forcing houses 

 were not unknown to the Romans, though they do not appear to have 

 been in general use. This branch of horticulture was almost unknown 

 in Britain until the end of the 17th or beginning of the 18th century, 

 and Lady Mary Wortley Montagu, on her journey to Constantinople in 

 the year 1716, remarks the circumstance of pineapples being served up 

 in the dessert at the electoral table at Hanover, as a thing she had 

 never before seen or heard of. Sir Joseph Banks justly remarks, had 

 pines been then grown in England, her ladyship, who moved in the 

 highest circles, could not have been ignorant of the fact. They were 

 however certainly grown at Hampton Court in the reign of Charles II. 

 It is said that the discovery of peach-forcing in Holland arose from an 

 old Dutch gardener having, in a bad season when his peaches would 

 not ripen, accidentally placed the sashes of a hotbed over them, which 

 had the effect of ripening them. Even after forcing was practised to 

 a considerable extent, its principles were so little understood, that 



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