MACHHTS. 



MACHINERY. 



to be a 



UM vembU, UM! making the result aero, we 



Jr'-fc'-O; whence / -|' 



and. by eubftitutkm, T - Iv'. 



Hence, if UM rneistinns oppoaed to the machine i* tuceptible of 

 bete* varied, it should be rendered roch that the velocity v of the 

 point of application of the equivalent force ie one-third of the greatest 

 VWodt/ 7 which the power 0*0 produce if tinmbted. Substituting 



Urfavalueof v in the above equation far r we get r-.ir'; therefore 

 r v, the momentum of iiupulw, or the effect of the machine, become* 

 rV when that effect U maximum, the resistance remaining 



n 



If two bodie* are connected together by a flexible line (iuppoeed to 

 be without weight) paeing over a pulley at the common summit of a 

 doubly inclined plane, the parts of the line being parallel to the sur- 

 face* of the two planes; the relation between the weighU may be 

 determined eo that the momentum of that which ia to be raised by the 

 descent of UM other may be a maximum. Let p and be the weighU 

 of the bodie*, or the force* of gravity acting on them vertically, and let 

 and r be the respective inclinations of t lie planes on which they are 

 placed, to the horizon ; then p sin. 8 and w sin. f are the foroe* of 



gravity on the planes, and consequently-?--?: *" "" * 1* the ac- 



ealerative force by which p descends. 



Now, by dynamic*, the velocity of a body varies with the force and 

 time ; therefore, v representing the velocity of p or v, and ( the time 



: 



sin " tf ain f 

 .___-.,, 



and consequently the momentum if r varies with 



nvsin w**in 



I : 



this expression is to be a maximum ; therefore, differentiating it, ic 

 being the variable, and making the result equal to zero, the value of tr 

 may "be found in term* of /> by a quadratic equation : thus, the required 

 relation may be obtained. 



If it were required to find, in any machine which when reduced to 

 iU moat simple state may be considered as a lever or a wheel and 

 axle, the ratio of the velocity of the moving power to that of the 

 rnslrtsnf to be overcome when the latter is a maximum, the following 

 pruceai may be used. 



Let the arm* of the luppoeed lever, or the semi-diameters of the 

 upposed wheel and axle, be represented by r and r', the power ji being 

 applied at the extremity of r, and the resistance to at that of r 1 . By 



the nature of the lever, p= in the case of equilibrium ; therefore, 



when the power is such as to produce motion, the motive force may bo 



erf* 

 expressed by / if applied at the extremity of r. Now, in order 



that the momentum of the inertia of tr at a distance i j from the 

 fulcrum may be made equivalent to the momentum of inertia of a 

 body at a distance r, on representing such body by p", we have 



p'i*i*r /> ; whence j>"= -j;-: the whole inertia to be overcome, if 



* 



applied at a distance r from the fulcrum, will therefore be p + -jj-, 



and the acccUrativ* foroe at the extremity of r will be 



But, by dynamic*, UM velocity of a body varies with the force and 

 time ; therefore, rennnMilIng the velocity at the e 



velocity at the end of the arm r by r, 



in order to obtain the velocity at UM end of the arm r, the expression 

 for r must be reduced hi the ratio of r to r*; therefore the velocity at 

 UM latter extremity varies with 



TUe expreeaion U to be a maximum ; therefore, on differentiating it, 

 f being the variable and making the remit equal to cero, there will 

 be obtained the ratio of r to /(which i* the nine as that of the 

 velocities of P and v) oonafaUntiv with the condition that the velocity 

 of > is a maximum. 

 In UM theory of machine*, the modification of motion and the 



modification of foroe take plaoe together, and are connected by certain 

 laws ; but id the study of the subject there is an advantage in first 

 considering the principles of the modification of motion, which are 

 based upon a branch of geometry called cinrmatirt, and afterward* 

 considering the principles of the combined modificati n and 



foroe, which are founded both on geometry and on the laws of 

 dynamics. The separation of cinematics from dynamics is due mainly 

 to Honge, Ampere, and Willis. The modern view of the subject of 

 applied mechanic* may be beat studied in the following v 

 Poncelet, 'Mecanique ImlnotriflK- :' M..iin, 'Notion* KondamenUlee 

 de Mecanique;' Willis, On the Principles of Mechanism;' Moseley, 

 ' Mechanic* of Engineering and Architecture;' Wbewell, ' Mechanics 

 of Engineering ;' Rankinc, ' On Applied Mechanic*; and on ' Prime 



M . . : - ' 



MACHINERY. It i* proposed to consider hi this article the 

 influence which U exercised by machinery u|x>n the general interest* of 

 mankind, and especially upon the well-being of different clauses of 

 society. There is no subject in the present age which is more 

 deserving of attention ; and none perhaps in which all classes are so 

 much concerned. Whatever theoretical opinions may be entertained 

 by speculative men, the use of machinery in aid of human labour, or, 

 a* some contend, instead of it, i* rapidly increasing and cannot be 

 restrained ; it is right therefore for all men to endeavour to judge for 

 themselves in what manner it U valuable to society, and whether the 

 injuries attributed to it be real or imaginary. By some, every new 

 machine ia viewed as an addition to the wealth and resources of a 

 country ; by others it ia regarded a* a hateful rival of human industry 

 as iron contending with straining sinews** steam struggling against 

 the life and blood of man. The one view is full of hope and promise ; 

 the other is fraught with gloom and sadness. One would present 

 society advancing in wealth and comfort ; the other would show it 

 descending faster and faster into wretchedness. But even those who 

 believe that the inventive faculties of men have been engaged in 

 devising for themselves a curse, would gladly be convinced that 

 cheerful anticipations of good are consistent with sound philosophy. 



The influence of machinery is of two kinds ; 1st, as it affects the 

 production and consumption of commodities ; and 2udly, as it affect* 

 the employment of labour. 



As regards production, the effects of machinery have been well 

 described to be the same " as if every man among us had become 

 suddenly much ptrontrer and more industrious." (' Results of Ma- 

 chinery,' 7th edit. p. o. < uid oi macliiiii-ry, ten men can 

 perform the work of twenty, anil perform it better and more quickly, 

 the products of their labour are as much increased as if they had really 

 " become suddenly much stronger and more industrious," and, it may 

 be added, more skilful. Thus production, which is the object of all 

 labour, U more abundant, and society enjoys the results of industry at 

 a lea* cost. Who can doubt that this is a great benefit, unless it be 

 attendm! with evils which are not at first perceptible f No man labours 

 more than is necessary to effect his object, and his constant desire i* 

 to contrive modes of saving his own physical exertions. A rich soil 

 and a fine climate are universally esteemed as blessings because the 

 people enjoy abundance with comparatively little labour. A poor soil 

 and bad climate are evils, because the husbandman must labour much, 

 though the produce of his industry be small. 



Labour without adequate result* ia always regarded as a curse, and 

 almost every human invention, from the earliest, times, has had for its 

 objects the saving of labour and the increase of production. Horses 

 and other beasts of burden were made to work for man ; to bear loads 

 which otherwise they must have borne themselves ; to draw the plough 

 which otherwise their own strength must have forced through the 

 (mil. To the same object all nature has been made subservient The 

 stream turns the mill, and does the work of man ; the wind performs 

 the same office. A boat is built to save men the labour of cm 

 their goods to a distance, and it is less labour to row the boat than to 

 carry its cargo : but rowing is laborious, and sails were invented that 

 the wind should do the work of man. In all other matters it has been 

 the same. Man is weak in body, and ill endowed by nature with the 

 mean* of aelf -preservation and subsistence. Many animals are stronger 

 and most animals are more active than himself : they can pursue their 

 prey with more certainty, they are armed with weapons of offence and 

 defence, and they need no shelter from the weather but that which 

 nature has provided ; their own powers and their own instinct suffice 

 for their preservation. But man was created naked and defenceless. 

 To live he must invent, and reason was given to him that he might 

 force all nature into his service. His teeth and nails were powerless 

 against the fang* and claws of the wild beast ; but his hands were 

 formed with wondrous aptitude for executing the tasks which reason 

 eet them. He invented tools and implements and weapons, and all 

 nature became hi* slave. He wa* now able to make hi* own strength 

 effect as much as if he had become stronger and more industrious. 

 He produced more for his own comfort and subsistence, with littlu 

 labour, than the greatest exertions could otherwise have obtained for 

 him. Every successive invention has made him more powerful, has 

 increased his strength, and multiplied the productions of his industry ; 

 and at length the giant power of steam has peopled the world with 

 inanimate slaves, who do his work faster and better than he did it him- 

 self with the greatost labour and the most ingenious tools. 



