work to be performed is a load raifed with a certain ve¬ 
locity by means of a rope winding round a hollow drum, 
and if the (impleft combination of mechanical powers for 
producing this velocity (liould give a firiall diameter to the 
drum, then this combination mult give way to another 
which correfponds with a larger fize of the drum ; for, on 
account of the inflexibility of the ropes, a great portion 
of the impelling power would be wafted in winding them 
about the circumference of a fmall drum. 
The ad vantages of Amplifying machinery, are well exem¬ 
plified in the'following capllan, which unites great ftrength 
and fimplicity. It is reprefented at fig. 90. Plate VI. where 
A D is a compound barrel compofed of two cylinders of 
different radii. The rope DEC is fixed at the extremity of 
the cylinder D ; and, after palling over the pulley E, w hich 
is attached to the load by means of the hook F, it is coiled 
round the other cylinder C, and fixed at its upper end. 
The capftan-bar A B urges the compound barrel C D 
about its axis, fo that, while the rope coils round the cy¬ 
linder D, it unwinds itfelf from the cylinder C. Let us 
fuppofe that the diameter of the part D of the barrel is 21 
inches, while the diameter of the part C is only 20 inches ; 
and let the pulley E be 20 inches in diameter. When the 
barrel A D, therefore, has performed one complete revo¬ 
lution by the preffure exerted at B, 63 inches of rope, 
equal to the circumference of the cylinder, will be ga¬ 
thered upon the cylinder D, and 60 inches will be un¬ 
wound from the cylinder C. The quantity of wound 
rope, therefore, exceeds the quantity that is unwound by 
63—60=3 inches, the difference of their refpedlive peri¬ 
meters ; and the half of this quantity, or inches, will 
be the (pace through which the load or pulley E moves by 
one turn of the bar. If a fimple capftan of the fame di- 
menfions had been employed, the length of rope coiled 
round the barrel would have been 60 inches,; and the 
/pace described' by the pulley, or load to be overcome, 
would have been 30 inches. Now, as the power is to the 
weight as the velocity of the weight is to the velocity of 
the power, and as the velocity of the power is the fame in 
both capftans, the weights which they wili raife will be 
as to 30. If it is vyifhed to double the power of the 
machine, we have only to cover the cylinder C with 
lathes a quarter of an inch thick, fo that the •difference 
between the radii of each' cylinder may be half as little as 
before ; for it is obvious that the power of the capftan in¬ 
creases as the difference between the radii of the cylinders 
is diminifhed. As we increafe the power, therefore, we 
increafe the ftrength of our machine, while all other en¬ 
gines are proportionally enfeebled by an augmentation of 
power. Were we, for example, to increafe the power of 
the common capftan, we mu ft diminifh the barrel in the 
fame proportion, fuppoling the bar A B not to admit of 
being lengthened, which will not only diminifh its ftrength, 
but deftroy much oi its power by the additional flexure of 
the rope. 
.This capftan may be eafily converted into a crane by 
giving the compound barrel a horizontal pofition, and 
finbftituting a winch inftead of the bar A B.' The fiupe- 
riority of loch a crane above the common ones does not 
require to be pointed out; but it has this additional ad¬ 
vantage, that it allows the weight to flop at any part of 
its progrefs, without the aid of a ratchet-wheel and catch, 
becaufe the two parts of the rope pull on the contrary fides 
of the barrel. The rope indeed which coils round the 
larger part of the barrel adts with a larger lever, and con- 
fequently with greater force, than the other; but, as this 
excefs of force is not fufficient to overcome the frifticn of 
the machine, the weight will remain ftationary in any 
part of its path. Appendix to Fergnfon's LcElures, vol. ii. 
'l lie principle on which the preceding capftan is con- 
ftrudted, might be applied with great advantage when two 
fi pauate axles, A'C, B D, fig. 91. are driven by means of 
the winch H and the wheels B and A. It is evident that, 
hen the winch is turned round in one direction, the rope 
is unwound from the axle B D ; the wheel B drives the 
Vol. XIV. No. 3003. 
6G 1 
wheel A, fo that the axle A C moves in a direflion oppo- 
fite to that of B D, and the rope is coiled round the 
axle AC, If the wheels A, B, are ofthe fame diameter 
and the fame number of teeth, the weight W will be .fta¬ 
tionary, as the rope wound about one axle will be al¬ 
ways equal to what is unwound from the other. If the 
wheels' have different diameters, or different numbers of 
teeth, the quantity of rope wound round the one axle will 
exceed what is unwound from the other, and the weight 
will be raifed. 
Of the Teeth of Wheels. 
In the machinery for modifying and adapting a rota¬ 
tory motion, the firft which prefents itfelf is the commu¬ 
nication by means of toothed wheels acting on each other. 
This is the molt general method in machinery, becaufe it 
tranfmits the motion with certainty and accuracy; and, if 
the teeth are properly formed, wheels perhaps confume 
lefs force in friition than any other method ; but this is a 
fiubject underltood by few mechanics. In the treadles on 
the conftrudtion of mills, and other w'orks of this kind, 
are many inltruffions for the formation of the teeth of 
wheels, and almofl every noted millwright has his own 
noftrums ; but they are molt of them defective in princi¬ 
ple, or at lea ft they are only correct in certain cafes, which 
have by experiment or theory been determined, and are 
extremely fallacious when applied indifferently to all 
cafes, as is the millwright’s cuftom. An inveltigation of 
this fulijeiSt, as applied to delicate mechanilin, where ac¬ 
curacy rather than ftrength is the objedt, will be found in 
our article Horology, vol, x. p. 326 & fieq. and we nowr 
propofe to give fome further applications of thofe princi¬ 
ples to w heels of larger dimenfions. 
In the formation of the teeth of wheels, a fmall devia¬ 
tion from the perfedt form is not, perhaps, of very great 
importance, except in cafes where a very large wheel 
drives a very fmall one, a cafe the judicious engineer 
fhould always avoid. The grand point to be attended to, is 
to adopt fuch aconftructior. as will infure all the teeth of 
a wheel being precifely equal, and to make as great a num¬ 
ber of them as the ftrength will admit. This will caufe 
feveral teeth to be in adtion at once, and make the commu¬ 
nication of the motion extremely fmootli and uniform. 
To obtain ftrength in the cogs when they are made fine, 
the width or-thicknefs of the wheel muft be increafed j 
and this is one of the greateft practical improvements 
which has been made in machinery for thefe laft twenty 
years. Formerly the belt engineers, fuch as S.neaton, di- 
redted the teeth of large cog-wheels to be four and five 
inches diftabt from each other, or pitch, as the millwrights 
term it. Such wheels always act unequally upon each 
other in confequence of the point of contact of the large 
cogs conftantly altering its pofition, becoming alternately 
nearer or farther from the centre of one or other of the 
wheels ; and this, tending to increafe the acting radius of 
one, whilft it diminifhes the other, caufes their velocity 
and powers to vary at every cog that paffts by, and the ma¬ 
chine works by ftartsand jerks. The wheel-work of mo¬ 
dern machinery is confirudted with fine cogs, feldommcre 
than one and a half or two inches pitch, and as much 
length of cog, or breadth ofthe wheel, as will make them 
fufficiently ftrong. We have feen fome wheels in a large 
cotton-mill, which bore a ftrain equal to thirty horfesV 
power, in which they were nine and twelve inches broad 
upon the face. Cog-wheels are found to work molt 
fmoothly when the teeth of the large wheel are made of 
hard wood, and the teeth of the fmall one of call iron, the 
adfing furfaccs being drelfed or filed fmooth and to the 
true figure. A mechanic, in contriving any machinery, 
fhould always bear in mind, that, where he introduces cog¬ 
wheels, they fhould be as large in their diameters as is con¬ 
fident with'other circumltances, becaule this allows the 
teeth to be made finer, in proportion to the power they are 
to bear, than if they were of fmafler radii; and the teeth, 
therefore, nearer the centre : it alfio occafions lefs preffure 
BE or 
