MECHANICS. 
6'20 
Among the various inventions which we have received 
from antiquity, that of water-mills is entitled to the higbeft 
place, whether we confider the ingenuity which they di(- 
play, or the ufeful purpofes to which they are fubfervient. 
In the infancy of the Roman republic, the corn was ground 
by hand-mills confining of two niill-ftones, one of which 
was moveable, and the other at reft. The upper mill-ftone 
was made to revolve either by the hand applied direCHy 
to a winch, -or by means of a rope winding round a cap- 
Itan. The precife time when the impulfe or the weight 
of water was fubftituted in the place of animal labour, is 
not exaClly known. From an epigram in the Arithologia 
Graeca, there is reafon to believe that water-mills were in¬ 
vented during the reign of Auguftus; but it is ftrange 
that in the defcription given of them by Vitruvius, who 
lived under that emperor, they are not mentioned as of re¬ 
cent origin. The invention of wind-mills is of a later 
date. According to fotne authors, they were firft ufed in 
France in the fixth century; while others maintain that 
they were brought to Europe in the time of the crufades, 
and that they had long been employed in the eaft, where 
the fcarcity of water precluded the application of that agent 
to machinery. 
The fcience of mechanics feems to have been ftationary 
till the end of the 16th century. In 1577 a treatife on 
mechanics was publiftied by Guidus Ubaldus, but it con¬ 
tained merely the difcoveries of Archimedes. Simon 
Stevinus, however, a Dutch mathematician, contributed 
greatly to the progrefs of the fcience. He difcovered the 
parallelogram of forces; and has demonftrated in his 
Statics, publiftied in 1586, that, if a body is urged by two 
forces in the direction of the fides of a parallelogram, and 
proportional to thefe fides, the combined aCtion of thefe 
two forces is equivalent to a third force aCiing in the di¬ 
rection of the diagonal of the parallelogram, and having 
its intenfity proportional to that diagonal. This im¬ 
portant difcovery, which has been of fuch fervice in the 
different departments of phyfics, ftiould have conferred 
upon its author a greater degree of celebrity than he 
has actually enjoyed. His name has fcarcely been en¬ 
rolled in the temple of fame ; but juftice may yet be done 
to the memory of fuch an ingenious man. He had like- 
wile the merit of illuftrating other parts of ftatics ; and he 
appears to have been the firft who, without the aid of the 
properties of the lever, difcovered the laws of equilibrium 
in bodies placed on an inclined plane. His works were 
reprinted in the Dutch language in 1605. They were 
tranflated into Latin in 1608, and into French in 1634; 
and in thefe editions of his works his Statics were en¬ 
larged by an appendix, in which he treats of the rope- 
machine, and on pulleys aCting obliquely. 
The doCtrine of the centre of gravity, which had been 
applied by Archemides only to plane furfaces, was now 
extended by Lucas Valerius to folid bodies. In his work 
entitled De Centro Gravitatis SoU&prum Liber, publiftied at 
Bologna in 1661, he has difcuffed this fubjeCt with fuch 
ability, as to receive from Galileo the honourable appel¬ 
lation of the “ Novus noftrae tetatis Archimedes.” 
I11 the hands of Galileo the fcience of mechanics af¬ 
firmed a new form. In 157a he wrote a fmall treatife on 
ftatics, which he reduced to this principle, that it requires 
an equal power to raife two different bodies to altitudes 
in the inverfe ratio of their weights, or that the fame 
power is requifite to raife ten pounds to the height of one 
hundred feet, and twenty pounds to the height of fifty 
feet. This fertile principle was not purfued by Galileo 
to its different confequences. It was left to Defcartes to 
apply it to the determination of the equilibrium of ma¬ 
chines, which he did in his explanation of machines and 
engines, without acknowledging his obligations to the 
Tufcan philofopher. In addition to this new principle, 
Galileo enriched mechanics with his theory of local mo¬ 
tion. This great difcovery has immortalized its author; 
and whether v\e confider its intrinfic value, or the change 
which it produced on the phyficall'ciences, we are led to 
regard it as nearly of equal importance with the theory* 
of univerfal gravitation, to which it paved the way. The 
firft hints of this new theory were given in W\sSyJiema Cof- 
micurn . The fubjeCV was afterwards fully difcuffed in ano¬ 
ther entitled “ Difcurfus et Demonftrationes Mathematic® 
circa duas novas Scientias pertinentes ad Mechanicam et 
Motum Localem,” publiftied in 1638. This work is di¬ 
vided into four dialogues : the firft of which treats of 
the refiftance of folid bodies before they are broken ; the 
fecond points out the caufe of the cohefion of folids 5 in 
the third he difeuffes his theory of local motions, compre¬ 
hending thofe which are equable, and thofe which are uni¬ 
formly accelerated. In the fourth he treats of violent 
motion, or the motion of projectiles ; and in an appendix 
to the work he demonftrates feveral propofitions relative 
to the centre of gravity of folid bodies. In the firft of 
thefe dialogues he has founded his reafoning on principles 
which are far from being correCt, but he has been more 
fuccefsful in the other three. In the third dialogue, which 
contains his celebrated theory, he difeuffes the doCtrine 
of equable motions in fix theorems, containing the dif¬ 
ferent relations between the velocity of the moving body, 
the fpace which it deferibes, and the time employed in 
its defcription. In the fecond part of the dialogue, which 
treats of accelerated motion, he confiders all bodies as 
heavy, and compofed of a number of parts which are all® 
heavy. Hence he concludes that the total weight of the 
body is proportional to the number of the material parti¬ 
cles of which it is compofed ; and then reafons in the fol¬ 
lowing manner: As the weight of a body is a power al¬ 
ways the fame in quantity, and as it conltantly aCts with¬ 
out interruption, the body mult be continually receiving 
from it equal impulfes in equal and fuccefiive inftar.ts of 
time. When the body is prevented from falling by being 
placed on a table, its weight is inceffantly impelling it 
downwards; but thefe impulfes are inceffantly deftroyed 
by the refiftance of the table, which prevents it from 
yielding to them. But, where the body falls freely, the 
impulfes which it perpetually receives are perpetually ac¬ 
cumulating, and remain in the body unchanged in every 
refpeCl excepting the diminution which they experience 
from the refiftance of air. It therefore follows, that a. 
body falling freely is uniformly accelerated, or receives 
equal increments of velocity in equal times. Having efta. 
bliftied this as a definition, he then demonftrates, that the 
time in which any fpace is del’cribed by a motion uniformly 
accelerated from reft, is equal to the time in which the 
fame fpace would be deferibed by an uniform equable mo¬ 
tion with half the final velocity of the accelerated motion 5 
and that, in every motion uniformly accelerated from reft, 
the ipaces deferibed are in the duplicate ratio of the times 
of defcription. After having proved thefe theorems, he 
applies the doCtrine with great luccefs to the afeent and 
deicent of bodies on inclined planes. 
The theory of Galileo was embraced by his pupil Tori- 
celli, who illullrated and extended it in his excellent work 
entitled De Motu graviuvi naturaliter accellerato, publiftied 
in 1644. In his treatife De Motu projeBorum, publiftied in 
the Florentine edition of his works in 1664, he has added 
feveral new and important propofitions to thofe which 
were given by his rnafter on the motion of projectiles. 
The fuccefs of Galileo in inveftigating the doCtrine of 
reCtilineal motion, induced the illuftrious Huygens to turn 
his attention to curvilineal motion. In his celebrated 
work De Horologio Ojcillatorio, publiftied in 1673, he has 
ftiown that the velocity of a heavy body defeending along 
any curve, is the fame at every inftant, in the direction 
of the tangent, as it would have been if it had fallen 
through a height equal to the correfponding vertical ab- 
feifs; and, from the application of this principle to the 
reverie cycloid with its axis vertical, he difcovered the 
ifochronifm of the cycloid ; or that a heavy body, from 
whatever part of the cycloid it begins to fall, always ar¬ 
rives at the lower point of the curve in the fame fpace of 
time. By thefe dilcuftions, Huygens was gradually led 
te 
