733 



SPRING. 



SPRING CARRIAGE. 



731 



length. Ite ordinary consequence is, after the first pain is gone by, to 

 produce some degree of swelling, and a considerable dull aching pain 

 of the injured part, which is greatly increased by any movement of it. 

 These signs are due to an inflammation of the sprained tissues, which 

 partakes of the slowness and obstinacy that characterise all the diseases 

 of the tendons and ligaments, and which, if not early and duly 

 attended to, frequently terminates in thickening, rigidity, and even 

 more serious disorganisation of them and the adjacent parts. 



The treatment to be adopted for sprains is the immediate application 

 of leeches, in number proportionate to the severity of the injury and 

 the importance of the part. They should be repeated till the pain and 

 swelling are distinctly decreased : the part should be kept perfectly at 

 rest and cool, and the patient's general health should be kept or made 

 good. When the pain has nearly ceased, and there remains little more 

 than stiffness of the injured part, stimulating liniments (the common 

 soap liniment, or a mixture of hartshorn and oil, for example) may 

 be used. 



sl'RING. [SKASONS, CHANGE OF.] 



SPRING, in Mechanics, is an elastic plate or rod, which is cm- 

 ployed as a moving-power, or a regulator of the motions of wheel- 

 work ; also to ascertain the weights of bodies, or to diminish the effects 

 of concussion. 



The elder Bernoulli was the first whose attention was directed to 

 the curvature assumed by elastic bodies, and he succeeded in resolving 

 the problem in the case of a rectilinear plate being fixed at one end and 

 Lent by a weight applied at the other : it being assumed as a principle 

 that, at any point in an elastic body, the force by which the body when 

 bent by any power endeavours to recover its previous position is pro- 

 portional to the angle of contact at that point ; that is, to the angle 

 which a tangent to the curve surface of the body makes, at the point, 

 with that surface. 



In order to give some idea of the manner in which the effects of 

 elasticity are to be determined mathematically, let A B be a thin elastic 

 plate immovably fixed at A, and bent into the form AB' by a power p 

 applied at B, and let n, a, a a' be two consecutive elementary portions 

 of thfi bent plate : let also r, represent the unknown force of elasticity 

 acting perpendicularly to a a' by which that element tends to recover 

 the direction a, a, from which it has been made to deviate by the 

 power at B ; and for simplicity let it be supposed that this power acts 

 in the direction B' c parallel to A B. Let fall ap perpendicularly on 

 B'c; also represent B'/> by :e and a p by y. Then, by mechanics r.y 

 expresses the momentum of the power at B* to bend the plate at a, 

 and in the case of equilibrium we have P . y E. But E varies with the 



angle of contact, or the angle between the element aaf and a, a pro- 

 duced, and that angle in any part of A B' varies inversely with the 

 radius of curvature at that part ; therefore let r be the known radius 

 of curvature at a point where the force of elasticity is given, and let 

 this force be represented by : also let n be the radius of cur- 

 vature at a point, as a, where the force is represented by K. Then 

 1 1 tr E" 



: t : : : E, or = E, and putting E' for er, we have f.y = . 



f R K B 



Substituting in place of B the differential expression for the radius of 

 curvature, the elastic force might be obtained by the processes of 

 integration. The integral, however, can only be obtained approxi- 

 li. 't. ]y. 



If the elastic plate were in a vertical position with its lower end A 

 resting on an immovable object, and a weight p, applied at the upper 

 extremity B', were to act in a direction towards A, the equations of the 

 curve, approximately determined, are (the deflection being small) 



(P \i r. 



jpj'.andL = (1 + -J 



where :r is any abscissa from B' on the line B' A, y is the corresponding 

 ordinate, A is the greatest deflection, or the ordinate at the middle 

 point in B'A, k = B A, and L is the length of the curve line A as' : also 

 the greatest weight which the plate or spring will bear without beiid- 



E'*"- 

 ing when pressed in that direction is expressed by j . ( = 3'1416). 



E'T 1 

 Ifp exceed by a small quantity the value of TO* , where m a 



any whole number whatever, the spring will make several bends 

 crowing the straight line A B' in m I points between the two ex- 

 tremitiw. 



When the elastic plate, hi a horizontal position, is fixed at one end, 

 a* A, and the weight P, applied at the extremity B', acts always 

 vertically, the equation becomes (the deflection being small) 



V 



where c is the tangent of the angle of contact at n'. If, on account of 

 the sraallness of this angle, c be neglected, it will follow, when x is 

 made equal to B' c, that the whole deflection AC or B B' will vary 

 nearly with the weight p, and with the cube of the length of the 

 spring. 



The use of a spring as a moving-power may be best exemplified in 

 its application to watch-work. The main-spring of a watch is a thin 

 and narrow plate of well-tempered steel, which is coiled in a spiral 

 form : one of its extremities is attached to a pivot or axle, and the 

 other to the interior circumference of the cylindrical box in which it is 

 contained. In being wound, the spring closes round the axle, and 

 afterwards, in the effort by its elasticity to recover its former position, 

 it turns the cylinder in a contrary direction : thus the chain which is 

 attached to the exterior circumference of the cylinder and to the fusee 

 causes the latter to revolve. 



A slender and highly elastic spring of a like form is employed to 

 produce a vibratory motion in the balance ring of a watch : one ex- 

 tremity of the spring is attached to the axle of the balance, and the 

 other to some part of its circumference. If a movement of small 

 extent about the axle be given in one direction to the balance, the 

 spring will be compressed near the axle, and, in the effort to recover 

 its previous state, the balance-ring will be moved round in a contrary 

 direction ; but the force of elasticity carries any point in the ring 

 beyond the place which it occupies when the ring is in a state of rest ; 

 and when that force is destroyed by the compression again produced 

 in the spring, near the axle, the balance is made to return in the 

 direction in which it was first moved. Thus an alternate motion in 

 the balance-ring is continued ; the time of the vibrations, and con- 

 sequently the velocities with which the wheels revolve, depending 

 upon the force of elasticity in the spring. The elastic power of the 

 spring varies with the tension, and is directly proportional to the 

 angle through which the spring is wound about the axle; and thus the 

 vibrations of a spring, like those of a pendulum in a cycloidal arc, 

 are isochronous. [ELASTICITY.] The length of the spring and the 

 diameter of the balance are increased by heat and diminished by cold ; 

 consequently, without some compensating power, the times of vibra- 

 tion will vary according to the changes of temperature. 



When a carriage moving along a level road passes suddenly over an 

 obstacle, so that a point in the circumference of the wheel is in contact 

 with the obstacle, the centre of the wheel describes a circular arc 

 about the point of contact as a centre ; and then, if the carriage is 

 perfectly rigid, a portion of its velocity will be lost. In order to 

 maintain that velocity, aiuulditional force of draught would be necessary ; 

 and an expression for this additional force is investigated in WhewelTs 

 'Mechanics' (art. 261, and the following). Part of this additional 

 force is employed in counteracting the motion of ascent, and the re- 

 mainder, which is generally much the greater quantity, in diminishing 

 the effect of the sudden change which takes place in the direction of 

 the motion of the carriage. This latter part may be in a considerable 

 degree removed by the use of springs ; for then, on the wheel meeting 

 the obstacle, the suspended body of the carriage bending the springs 

 by its weight, the centre of gravity of that body is made to describe a 

 curve line, to which its previous rectilinear direction is a tangent ; and 

 thus the jerks which arise from movements in directions making finite 

 angles with one another are avoided. 



The force of draught required -in addition to that which is due to 

 friction, when a stiff carriage passes over a roughly paved road, varies 

 as the square of the velocity and the height of the stones directly, and 

 as the radius of the wheel inversely. 



SPRING -BALANCE. [BALANCE; DYNAMICS; WEIGHING - JI.v.- 

 cniNi:s.] 



SPRING CARRIAGE. The progress of a wheel-carriage, even 

 upon the best of roads, is impeded by the wheels coming in contact 

 with, and being compelled to rise over, undulations of surface which 

 check their rolling motion. In many old rough pavements, owing to 

 the openness of the joints, and the wear of the stones, the road 

 consists of a series of blunt ridges, in passing over which the motion of 

 t ! ; v, heel can be no other than a succession of jolts. The surface of a 

 well-made road of broken stone, when in perfect order, presents few 

 important asperities ; but when metal or broken stone has been 

 recently laid on, it is exceedingly rough. If a rigid carriage be drawn 

 over any of these surfaces, the irregularities which affect the path of 

 the wheels will be communicated through them to the body, to which 

 they will impart a jolting or vibratory motion. In a four-wheeled 

 carriage the movement of the body will be influenced by the discor- 

 dant motions of .the fore and hind wheels; and it will be continually 

 liable, owing to the imperfections of the road, to have the whole of its 

 weight thrown upon three wheels, whereby the framework will he 

 exposed to injurious strains. To enable it to sustain such strains, the 

 framework must be made very strong and heavy ; and the destructive 

 and painful effect of increasing the velocity of inelastic carnages would 

 alone have been sufficient to limit the speed of vehicles. 



One of the simplest means of alleviating concussion is that often 

 adopted in light carts, of suspending the seat from the sides of the 

 body by leather straps. Next to this is the use of straps to suspend 

 the body itself, an expedient which seems to have been occasionally 

 resorted to from an early period. With very few exceptions, it 

 appears that slung or suspended carriages were not used until the 1 7th 



