NATURAL PHILOSOPHY MATTER, MOTION, AND HEAT. 



trial. The experimental proof is better suited to 

 our present purpose, and any one may make it 

 for himself. Over two pulleys, A and B, let a 

 string be passed, having two weights, w, it/, 

 attached, one at each end, with a small ring in 



\JU" 



Fig. 10. 



the middle, and to this ring let another weight, 

 less than the sum of the other two, be suspended. 

 This third weight will pull down the ring R a 

 certain way, and at last take up a position of rest ; 

 the three forces will be in equilibrium. If the 

 weights TV and it/ are equal, it is evident that it/' 

 will hang midway between the pulleys. But we 

 suppose them unequal ; and then every one's 

 experience will tell him that the ring will be 

 drawn nearer to the greater. Suppose w = 4 

 pounds, a/ = 6, and it/' = 8 ; draw on paper the 

 exact figure made by the strings ; take any small 

 unit of length, and set off 4 such units from R to 

 m, and 6 from R to n ; through m and n draw 

 mo and no parallel to Rn and Rm, and join R0. 

 It will be found that R0 is in the same straight 

 line with Rn/', and also that it contains 8 units 

 of length. 



As ba in fig. 9 is equal to Re, and in the same 

 direction, the two component forces and their 

 resultant are represented by the three sides of the 

 triangle R&a ; and the resolution of forces is thus 

 often represented by the half of the parallelogram 

 of forces, to save drawing the whole. 



The following is an example of the resolution 

 of forces : 



Let TP be a ship, SL its sail, WA the direction 

 of the wind, and let the length of WA represent 

 the force of the wind. WA can be resolved into 

 AB perpendicular to the sail, and BW parallel to 



Fig. ii. 



it, the latter of which has no effect in pressing on 

 the sail ; therefore AB is the effective pressure on 

 the sail. Were the vessel round, it would move 

 in the direction BA. Let BA be resolved into CA 

 and BC, the former, CA, acting in the direction of 

 the keel or length of the vessel, or in the direction 



CA, and the latter perpendicular to it, or in the 

 direction of the breadth. The former pressure, 

 CA, is the only "pressure that moves the vessel 

 forward, the other, BC, makes it move sideways. 

 From the form of the vessel, however, this latter 

 force, BC, produces comparatively little lateral 

 motion ; any that it does occasion is called lee-way. 

 By a similar double resolution, we may represent 

 how much of the actual force of the wind is effective 

 in turning round the arms of a wind-mill. 



THIRD LAW. 



If a man standing in a boat attempt to push 

 off another boat of the same size that is along- 

 side, both boats will recede equally from each 

 other ; if he pull the other boat towards him, 

 his own boat advances half-way to meet it A 

 magnet draws a piece of iron towards it ; but the 

 magnet is also drawn towards the iron, as is seen 

 when they are both suspended so as to move 

 freely. In all these cases, we see that the body 

 that we consider as acting upon the other, is itself 

 acted upon in turn, and in the opposite direction : 

 this is what is meant by reaction. 



In saying that the action and reaction are equal, 

 it is meant that the momentum produced or de- 

 stroyed on both sides is the same. If the magnet 

 and the piece of iron above spoken of are of the 

 same weight, they move to meet each other with 

 equal velocities, for thus only can the momentum 

 be the same in both cases. If the magnet is three 

 times the weight of the piece of iron, the iron must 

 move with three times the velocity of the magnet 

 in order to have equal moving force ; and so it is 

 found to do. 



In the last instance, both motions would still be 

 visible. But let a boat of a ton weight be pushed 

 away from the side of a ship of a thousand tons' 

 weight, and then only one seems to move ; for 

 while the boat moves off a yard, the ship recedes 

 only the thousandth part of a yard, which it would 

 require minute observation and measurement to 

 render apparent. From this we can pass to the 

 extreme case of a boat pushed off from shore. 

 Where is the evidence of reaction here ? We see 

 none, it is true ; still, the consideration of the cases 

 already adduced, and of a thousand similar, lead 

 us irresistibly to believe that the shore, if it is free 

 to move, must recede from the boat. We cannot 

 help believing, then, that when a stone falls in 

 other words, when the earth draws a stone towards 

 it the earth is itself drawn, or falls, towards the 

 stone. 



COMMON MOTION. 



When a system of bodies has, from any cause, 

 received a common motion, their positions, with 

 regard to one another, remain unaffected by it, 

 and in considering their relative motions, we may 

 leave their common motion out of account ; every- 

 thing is as if the system were at rest. This arises 

 from the property of inertia, as already expounded. 

 When a ship is going steadily, all things go on in 

 the cabin as in a room. On deck, a ball thrown 

 upwards comes down in the same spot ; the deck 

 has not slipped away from under it The motal 

 inertia of the ball carried it on while in the air 

 with the motion it had acquired from the ship. 



The feats of equestrians depend upon this law 

 of common motion. Riding at full speed, they 

 throw up balls, which return into the hand. The 



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