rso 
M E C II A N I C S. 
vary their preflure according to any law he finds moi’t con¬ 
venient. If is in this manner that the watchmaker, by the 
form of the fufee, produces an equal preflure on the 
wheel-work by means of a very unequal action of the 
main-fpring. In like manner, by making the outer arch- 
lieads. portions of a proper fpiral inftead of a circle, we 
can regulate the force of the beam at pleafure. Thus we 
fee how much more manageable an engine is in this form 
than Newcomen’s was, and aifo more eafily inveftigated 
in refpeft of its power in its various portions. The 
knowledge of this lad circumftance was of mighty con- 
i'equence, and without it no notion could be formed 'of 
what it could perform. This fuggefted to Mr. Watt the 
tife of a gauge (very improperly called a barometer), to 
indicate the degree of vacuum in his engines; and we 
deem it of important confequence to the well-going of the 
engine, the profit of the proprietor, and the credit of the 
engineer; yet in many engines in London we fee this 
important inftrument either out of repair, or wholly laid 
afid.e. The form is given at fig. 117. They have been 
made of glafs ; but, if the quickfilver is not very pure, 
the alloy with w hich the venders of this article adulterate 
it is by conftant ailion brought to the furface, and that 
and the vapour together make the tube fo fouFthat no 
precifion can be obtained. Iron therefore is the belt ma¬ 
terial; both parts of the tube fiiould be correftly of one 
diameter, or elle the refult will be erroneous. This tube 
mult communicate with the condenfer by a fmall cppper 
pine, and a (top-cock be placed between the gauge and 
condenfer. The index in this inftrument is a light deal 
rod, which is put into the (horter tube; and, quickfilver 
being poured into it within three inches of the end, the 
rod is put into the tube, and it floats on the quickfilver. 
It is almoft needlefs to remark, that the graduations on 
this inftrument muft be inverted with regard to thole of 
a Angle tube. 
We muft not omit in this place one deduction made by 
Mr. Watt from his obfervations, which may be called a 
dilcovery of great importance in the theory of the engine. 
Let ABCD (fig. 118.) reprefent a feffion of the cylinder 
of a fleam-engine, and EF the furface of its pifton. Let 
us fuppofe that the fleam was admitted while EF was in 
contaft w ith A B, and that, as foon as it had preffed it 
down to the fituation EF, the fteam-cock is flint. The 
fleam writ continue to prefs it down ; and, as the fleam 
expands, its preflure diminifhes. We may exprefs its 
preflure (exerted all the while the pifton.moves from the 
fituation A B to the fituation E F) by the line EF. If 
we fuppofe the elasticity of the fleam proportional to its 
denlity, as is nearly the cafe with air, we may exprefs the 
preflure on the pilion in any other pofifion, fuch as K L 
or DC, by K l and Dc, the ordinates of a rectangular 
hyperbola F/c, of which A E, AB, are the afiymptotes, 
and A the centre. The accumulated preflure during the 
motion of the pilton from EF to D C will beexprefled by 
the area EFcDE, and the preflure during the whole mo¬ 
tion by the area ABFcDA. Now it is well known 
that the area E F c D E is equal to ABFE multiplied by 
the hyperbolic logarithm of — L. and the 
a A E A E 
whole area ABFcDAiserABFEx^i-i-L • 
Thus, let the diameter of the pifton be 24 inches, and the 
preflure of the atmofphere on a fquare inch be 14 pounds ; 
the preflure on the pifton is'6533 pounds. Let the whole 
iiroke be 6 feet, and let the fleam be flopped when the 
pifton has defcended 18 inches, or 1 • 5 feet. The hyper¬ 
bolic logarithm of — is 1-3862943. Therefore the accu- 
1 '5 
mulated preflure ABFcDA is =6333X2'3862943, =15114 
pounds. 
As few profeflional engineers are poflefled of a table of 
-hyperbolic logarithms, while tables of common logarithms 
are or (hotild be in the hands of every perfon who is much 
engaged in mechanical calculations, let the following me¬ 
thod be praclifed. Take the common logarithm of AP, 
A 
and multiply it by 2-3026 ; the product is the hyperbolic 
logarithm of The accumulated preflure, while the 
pifton moves from A B to E F, is 6333 X t> or Amply 6333 
pounds : therefore the fleam, while it expands into the 
whole cylinder, adds a preflure of 8781 pounds. Suppofe 
that the fleam had got free admiflion during the whole 
defcent of the pi Ton ; the accumulated preflure would 
have been 6333X4,01-25332 pounds. 
Here Mr. Waft obferved a remarkable refult. 'The 
fleam expended in this cafe would have been four times 
greater than when it was flopped at one-fourth ; and ye-t 
the accumulated preflure is not twice as great, being nearly 
five-thirds. One-fourth of the fleam performs nearly 
three-fifths of the work, and an equal quantity performs 
more.than twice as much work when thus admitted dur¬ 
ing One-fourth of the motion. This is a curious and an 
important information, and the advantage of this method 
of working a fleam-engine increafes in proportion as the 
fleam is fooner flopped ; but the increafe is not great after 
the fleam is rarefied four times. The curve approaches 
near to the axis, and fmall additions are made to the area. 
The expenfe of fuch great cylinders is confiderable, and 
may not always be compenfated by this advantage. 
It is very pleafing to obferve fo many unlooked-for ad¬ 
vantages refulting from an improvement made with the 
foie view of leffening the wafte of fleam by condenfation. 
While this purpofe is gained, we learn how to hufbaml 
the fleam which is not thus, wafted. The engine becomes 
more manageable, and is more eafily adapted to every 
variation in its talk; and all its powers are more eafily 
computed. 
The aftive mind of its ingenious inventor did not flop 
here. It had always been matter of regret that one-half 
of the motion was unaccompanied by any work. It was 
a very obvious thing to Mr. Watt, that, as the fleam ad¬ 
mitted above the pilton preffed it down, fo fleam admitted / 
below the pifton prefled it up with the fame force, pro¬ 
vided that a vacuum were made on its upper fide. This 
was eafily done, by connecting the lower end of the cylin¬ 
der with the boiler, and the upper end with the condenfer. 
Fig. 119. Plate XXX. is a reprefentation of the fleam- 
engine in its molt improved ftate, exactly copied from Mr, 
Watt’s figure accompanying his fpeeification. Here BB 
is a fection of the cylinder, furrounded at a fmall diftance 
by the cafe 1111 . The feCtion of the pifton A, and the 
collar of leathers which embraces the pifton-rod, gives a 
diftinfl notion of its conftruClion, of the manner in which 
it is connected with the pifton-rod, and how the packing 
of the pilton and collar contributes to make ail tight. 
From the top of the cylinder proceeds the horizontal pipe. 
Above the letter D is obferved the feat of the fleam-valve, 
communicating with the box above it. In the middle of 
this may be obferved a dark (haded circle. This is the 
mouth of the upper branch of the (team-pipe coming from 
the boiler. Beyond D, below the letter N, is the leat of 
the upper condenfing-valve. The bottom of the cylinder 
is made fpherical, fitting the pifton, fo that they may 
come into entire contafi. Another horizontal pipe pro¬ 
ceeds from this bottom. Above the letter E is the feat of 
the lower fleam-valve, opening into the valve-box. This 
box is at the extremity of another fleam-pipe marked C, 
which branches off from the upper horizontal part, and 
defcends obliquely, coming forward to the eye. The 
lower part is reprefented as cut open, to (how its interior 
conformation. Beyond this fleam-valve, and below the 
letter F, may be obferved the feat of the lower condenf- 
ing-valve. A pipe defcends from hence, and at a fmall 
diftance below unites with another pipe G G, which comes 
down 
