M A C H I N E. 



^ tVe mbving force the mod commodious diredion, and 

 whc; it can be done of caufing its aclion to be applied im.'ne- 

 dia;ely to the body to be rtiovcd. Thefe, it is true, can 

 rarelv be united, but the former may, in moll inllances, be ac- 

 complifiied ; of which the ufe of the fintple lever, pulley 

 and wheel and axle, furnifh many examples. The fecond 

 objeft gained by the ufe of machines, is an accommodation 

 of the velocity of the work to be performed, to the velocity 

 with which alone a natural power can a<S. Thus, whenever 

 the working pov/er acls with a certain velocity, which cannot 

 be changed, and the work mull be performed with a greater 

 velocity, a machine is interpofid round a fixed fupport, and 

 the diliance of the impelled and working points are taken 

 ia the proportion of the two given velocities. But the ef- 

 fen'^ial advantage of machines, and that in faft which proper- 

 ly ^pertains to the theory of mechanics, confiifs in augment- 

 iog, or rather modifying the energy of the moving power, 

 in fuch a manner that it may produce effeds, of which it 

 would otherwife have been ir.capable. Thus a man might 

 carry up a flight of ileps twenty pieces of ftone, each weigh- 

 ing fay 3olbs. one by one, i.. as fmall a time as he could, with 

 the fame labour, raife them all together with a piece of ma- 

 chinery, that would have tlit! velocities of the impelled and 

 working points as twenty to one, and in this cafe the inftru- 

 ment would furnifli no real advantage except in laving his 

 fteps. B !t if a large block of 20 times 30, or 6colbs , were 

 to be raifed to the fame height, it would far exceed his ut- 

 raolt eiForts to accompli{h it, without the intervention of 

 feme machine. Or the fame purpofe mav be illwflrated 

 fomewhat differently, confining the attention ItiU to thofe ma- 

 chines whofe motion ia uniform. The produciy-u reprefen's, 

 during the unit of time, the effeil which refults from the 

 motion of therefiftance ; this motion being produced in any 

 manner whatever. If it be produced by applying the moving 

 force immediately to the rcfiilance, ic is neceffary, not only 

 that the produft F V :=■ f'd,hut alfo at the fame time F =f 

 and V = ^> ;' if, therefore, as mod frequently happens, f be 

 greater than F, it will be abfo'.utely impoffible to put the re- 

 finance in motion, by applying the ra''vjng power mmiediate- 

 Jy to it. Now, machines furnifh the means of difpofing of the 

 product F V in fuch a manner, that it may always be equal to 

 jf-v, however m.uch the faclorsf F V rr.ay differ from the analo- 

 gous factors iny * ; and confequently of putting the fyltem in 

 motion, whatever may be the excefs ofy" above F. Or, gene- 

 rally, as Prony remarks, (Arch. Hydiaul. art. 501.) ma- 

 chines enable us to difpofe of the factors F V / in fuch a 

 manner, that while that .product conti^iues the fame, its fac- 

 tors may have to each other any ratio at pleafure. Thus, to 

 give another example : fuppofe that a man, exerting his 

 llrenglh immediately upon a mafs of 25lbs. can raife it ver- 

 tically, with the velocity of four feet^cr fecond ; the fame 

 man afting upon a mafs of iooo!i>s. cannot give it any ver- 

 tical motion, though he exerts his utmoll ftrength, unlefs he 

 has rt'courfe to lome machine. Now he is capable of producing 

 an efFett equal to 3, x 4 x / ; the letter t being introduced, 

 becaufe, if the labour be continued, the vaiue of t will not 

 be indefinite, but comprifed wilhm aifignable limits. Thus 

 we have 25 X 4 x / ^ 1000 x ^< x / ; and, confequently, 

 1) := -r'cth of a foot. This man may, therefore, with a machine 

 as a lever, or axis in peritrichlo, caufea mafs oT icoolbs. 

 to rife ,'j,th of a foot m the fame timS that he could raife 

 iclbs. 4 feet without a machine ; or he may raife the 

 crreater weight as far as the lefs, by employing forty times 

 as much time. From what has now been fajd on the extent 

 of the effefts which may be attained by machines, it will be 

 fetn, that fo long as a moving force «xercifes a detertninate 



effort with a velocity hkewife determinate, or fo long as the 

 produft of thcfe is conftant, the effects of the machine will 

 remain the fame : fo that under this point of view, fuppofing 

 the preponderance of the effort of the moving power, and ab- 

 llrafting from inertia and friction of materials, the conve- 

 nience of application, &c., all machir.es are equally perfect. 

 But from what has been (hewn in the preceding part of this 

 article, a moving force may, by diminifhing its velocity, aug- 

 ment its effort, and reciprocally. There is, therefore, a cer- 

 tain effort of the moving force, fuch that its product bv the 

 velocity, which comports to that effort, is the greateft polfi- 

 ble. Now admitting of the truth of the refults in the pre- 

 ceding propofitions V = ^ W, or F = 5 ^, and thefe two ■ 

 values obtaining together their produdl, -^\ i W expreffes 

 the value of the greatelt effect with refpeft to the unit of 

 tm;e ; and in prattice it will always be advifable to approach 

 as nearly to thefe values as circumftances will admit, for it 

 cannot be expected that it can al.va) s be exactly attained. - 

 But a fmall variation will not be of much confequence ; for 

 by a well known property of thofe quantities, which admit;' 

 ot a proper maximum or minimum, a value affumed at a mo- 

 derate diliance from either of thefe e.\tremes, will produce- 

 no fenfible change in the etfeft. 



If the relation of F to V followed any other law than that' 

 which we have affumed, we Hioiild find from • the expreffion 

 of that law, values of Fand V,,&c. different from the pre- 

 ceding, but the general method would be Hill nearly the 

 famv. 



Wi*h refpeft to praftice, the grand ohjeft- in all cafes^- 

 Ihould be to procure an uniform motion, becaufe it is fronv- 

 that which, ceteris paribus, the greatelt eftett, always refults. 

 Every irregularity in the motion wattes fome of the impelling;^ 

 power, and it is the greatelt only of the varying velocities 

 which is equal to that, which it would acquire if it moved ■ 

 uniformly tliroughout ; for while the motion accelerates, the 

 impelling power is greater than what balances the refiftance- 

 at that timeoppofed to it, and the velocity is lefs than what 

 the machine would acquire, if moving uniformlv ] and when • 

 the machine attains its greateft velocity, it attains it becaufe 

 the power is not then acting againit tiie whole reCftance. In 

 both thefe cafes, tlierefore, the performance of the machine 

 is lefs than if the power and the refiftance were exactly ba-- 

 lanced, ia which cafe it would move uniformly. Befides - 

 this, when the motion of a machine, and particularly a- 

 vc-ry ponderous one, is irregtilar, there are, as we have al- 

 ready remarked in the preceding part of this article, conti- 

 nual repetition'; of fti-ains and joits", which foon derange, ands 

 ultid'.afely dellroy the whole liructure. 



In the preceding remarks and propofitions, relative to the ■ 

 maximum eff-i5t of machines, we have availed ourfelves of an ' 

 interefting chapter on this iubject in Gregory's Mechanics, . 

 in which the theory is purfued to a much greater length than • 

 our limits will admit of, botli with regard to machines whofe 

 motions are uniform and accelerated ; and to which we would ; 

 refer the reader for further information. See al.'o Prony'g - 

 " Architedture Hydraulique," from art. 487 to 507 ; and 

 the lall cd tion of Fcrgufon's Mechanics by Brewller, in ■ 

 which an interefting paper on this fubjedt is given by pro- 

 feffor Lcflie. 



Machine for taking down extemporaneous pieces of mu- 

 fic, commonly called •uolunlaries. Such a contrivance h^s ■ 

 been long among mufical defidir:i\i ai the moil important 

 kind. To fix fuch floating founds as are generated in 

 the extatic moments of enthufiafm, while " bnght-eyed . 

 fancy 



«• Scatters ■ 



