G. (George) Greenhill.

A treatise on hydrostatics online

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conditions is the (limiting) ratio of the small increment
of pressure to the cubical compression produced.

Thus if the pressure rises from MP to M'P', or from p
to p — Ap, then the elasticity is

,. —Ap dp

Av/v av

a positive quantity because p increases as v diminishes.

On the diagram,

PIi = Av,BP'=-A2J,
and the elasticity is

lb p|^ = NP tan NP V= NV,

if the tangent at P meets ON in V.

Thus along an isothermal hyperbola (§ 198)
NV= ON, so that the elasticity is p.
Along an adiabatic

nfyip = constant,
NV^y . ON, and the elasticity is yp (§ 233).



/ 'pdv — -



516 THE FIRST AND SECOND LAWS

The work done in expanding to the volume v or OM
is represented by the area EMPF; and if FP is the
adiabatic curve of a perfect gas, this work is (§ 233)
'P^Va-pv _-r fia-0

- = — JX IT,

y-1 y-1

I'O

reducing for an isothermal curve along which y = 1 to
pv log vjv^ = RQ log pjp.

423. As the piston moves from E to M, and the point
F follows along the curve FP, a certain quantity H units
of heat is absorbed (or given out) by the gas, which
depends upon the shape of the curve FP, upon the
characteristic equation of the gas (§ 198), and upon the
change of the internal energy of the gas.

As the piston moves from M' to M, suppose that dH
units of heat are absorbed, and that the change of inter-
nal energy is dE heat units ; then, according to the First
Law of Thermodynamics,

dH=dE+AdW, (1)

where dW denotes the number of units of work performed
in the motion from M' to M\ in this case dW^fdv.

It is beyond the scope of the present treatise to discuss
the Second Law of Thermodynamics and Thomson's
Absolute Scale of Temperature ; it will be sufficient
for our purposes to assume that the absolute scale of
temperature is given practically by the indications of
an Air or Hydrogen Thermometer (§ 221) obeying the
Characteristic Equation (§ 198),
pv = RQ.

Thus in the experiments on the Absolute Dilatation of
Mercury (§ 164) an air thermometer must be employed,
as the mercury thermometer could not detect variations
in the coefficient of expansion.



OF THERMODYNAMICS. 517

It is assumed also that the Second Law of Thermo-
dynamics is embodied in the equation

dH=ed4>, (2)

where is a certain function, called the entropy ; then

dE=dH—A'pdv = 9d(p-A2Jdv, (3)

embodying the First and Second Laws.

The internal energy E depends only on the state of
the gas as given by p, v, 6, its pressure, volume, and
temperature, connected by the Characteristic Equation,

F{p,v,e)= - 0;
so that a change in E is independent of the intermediate
states; or, in other words, dE is a perfect differential,
and so also is d(f), according to the Second Law.

The First and Second Laws of Thermodynamics are
thus expressed by the relations

/dH=AW, /dH/e = 0,
W denoting the work done, and the integrals being
taken round a closed cycle in which there is no escape
of heat by conduction ; the quantity dH/6 is sometimes
called the heat-weight of the heat dH.

If H units of heat pass from a body at a temperature
02 to another body at a lower temperature 6^, the entropy
of the first body falls HjO^ and of the second rises H/G^ ;
so that the entropy of the system rises

1 1^



\0^ 02-

The entropy is thus unchanged if no heat passes
except between bodies at the same temperature; but
conduction of heat between bodies of different temper-
ature raises the entropy, and the entropy thus tends
to a maximum.



518 THERMODYNAMICAL RELATIONS.

424. Of the four quantities f, v, 6, <{>, two only are
independent ; and any pair may be taken as independent
variables.

Prof Willard Gibbs selects v and as variables, so
that from (3), with Clausius's notation for partial differ-
ential coefficients,

But denoting by x, y any pair of independent variables

^, , 'dE „dy<p . 'dyV 'dE 3^^ ^3'*^.

so that ^^ = ^ - ^V^' ^5— = ^^T, — ^P-^, >

dx ?« ^dx dy dy ^ ay



3^
dxdy ~'dy'dx~^ ^dxdy ^ ""dy dx ^^^'dx'dy



and ;^^^ =.5— ^ + 0:^"^""^^ 5 ^P-



^30 3^ 3V_^9E3-_^



dxdy dxdy dx dy -^dx^y'
30 3^_39 30_ ./3p 3u_^ 'dv\
dx dy dy dx \dx dy dy dxJ'

|M = ^?iE^) (4)

d{x, y) 3(33, y)

This proves that if the plane of the {p, v) diagram is
covered by isothermal lines, for which Q is constant, and
isentropic or adiabatio lines, for which ^ is constant,
then integrating round any closed cycle,

ffdQd(^ = AffdfdbV = A times the area of the cycle ;
or the area of the cycle is JffdQdf.

425. A cycle a^y^ which is bounded by two iso-

thermals 0j and Q^, and two adiabatics 0j and 02' ^^

called a Oarnbt cycle, fig. 107 ; and it thus encloses an area

J(02-0i)(0,-0i) (5)



THE GARNOT CYCLE. 519

With Q and ^ as variables, the Carnot cycle on the
(0, <f) diagram is a rectangle.

Starting from the point a{Qy 0^) and moving along the
side a/3, the entropy ^^ is constant, and no heat is
absorbed or given out in this compression.

In expanding from ,8 {Q^, (j>i) along ^y, the tempera-
ture 02 is constant, and the heat absorbed is thus

^2 = ^2(<p2 — 'Pi)-

In expanding from y (O^, (j)^ to 8 along y8, the en-
tropy 02 is constant, and no heat is gained or lost.

From § (0j, 02) back to a along Sa, the temperature 0^
is constant, and the entropy changes from 02 to 0^, so
that the heat given out is

iri=0i(02-0i).

The heat which has disappeared in completing the
Carnot cycle is

^2-^l=(02-0l)(^2-0l)

= A times the area of the cycle, or the work done,
in accordance with the First Law of Thermodynamics;
also the heat-weights,

The efficiency of the cycle, defined as the ratio of the
heat converted into work to the heat absorbed, is thus,
H^ — H^ 6o — 9-i ,n\

-^ET^^ ('^>

Carnot assumed that the efficiency of an engine working
in this cycle between the temperatures 0^ and 02, was

0(02-01);
and he supposed that G was constant ; but we see now
that 0, called Carnot's function, is the reciprocal of the
absolute temperature of the source of heat.



520 REVERSIBILITY OF THE CARA^OT CYCLE.

The Carnot cycle a/3yJ is reversible ; that is, if described
in the reverse direction aSy^, as in a refrigerating
machine, the heat H^ absorbed at temperature 0j is
given out as heat H^ at a higher temperature Q^, at the.
expense of the work represented by the area of the cycle.

Carnot's principle asserts that the efficiency of a
reversible cycle is a maximum ; for if it were possible
to obtain a greater efficiency by another arrangement,
this could be made to drive the Carnot cycle backwards
and thus create energy, and realise " Perpetual Motion."

Thus a thermodynamic engine, for instance a low
pressure engine, working between the extreme tempera-
tures of the freezing and boiling points, 0°C and 100° C,
gives away at least 273 out of 373 units of heat to the
condenser ; so that its efficiency falls short of 0'27.

426. By taking x, y to represent any pair of the
variables p, v, 6, (jt, we obtain various thermodynamical
relations ; thus with independent variables



(i.) p, v;


3(0, ^)_

3(^3, v) '


= A-








(ii.) e, <t> ;


d{p, v)

3(0, 4>y


= J;








(iii.) d,f;


dp


dpv

'^30'


or


dpV

dd"


jde<p
dp


(iv.) p, <j> ;


300

dp


^t-


or


dpV_
d<t>


•^ dp '


(V.) e, V ■


dm


^dd'


or


d,p

dd~


jdei>,
dv '


(vi.) V, (j> ;


300

dv


d(j>


or


d^p _
d(p


jd^e

dv '



THERMODYNAMICAL RELATIONS.



521



These relations are proved geometrically in Maxwell's
Theory of Heat, by taking the Carnot cycle a^yS so
small that it may be considered a parallelogram ABGD ■
and now an inspection of fig. 108 shows that the area
of the parallelogram, or

JA6A,p = AK.Ak = AL.Al^AM.A')n = AN.A'n.




Fig. 107.



Fig. 108.



Then the relation (iii.) is equivalent to



(iii.)



AK
A0'






for AK is the dilation of v at constant pressure, while
Ak is — A„p, is the diminution of pressure corresponding
to the increment A<p along the isothermal AD.

Similarly the relations (iv.), (v.), (vi.) are equivalent to

(iv.) ^ = J^i. with AL=A^v, Al = A^p;



(v.) 4?=J-^, with AM=A.p, Am:
A9 Am



Aev;



(vi.) 4^=j4^, with AN=Am, An=-A,pv.



An'



522 THERMOD YN AMIGA L RELA TIONS.

427. The specific heat c for any given change of state
is given by

_ dH _ „ d(ji _ ^d(p dx ^ d(f> dy
^^W~ de~ "d^ de^^dy Te'

and if the change of state is given by the relation

f{x,y) = 0,

then ?/^+§/^ = 0,

dx de dy dd '

and W^ Wd^

dx dd^dy dd '

so that = 0^-^ I ^-^^d) .. (7)

Taking Q and v as variables, and denoting the S.H. at
constant volume by c^, then

. ^ _(fiB<t> dv_ . 3„p dv

Thus if Cp denotes the S.H. at constant pressure, when

'd^ dep dv_
dO "^ dv de '

..-.=-<f)/^ w

Now the elasticity at constant temperature is (§ 422)

dep
dv
so that, denoting it by Eg,

Ee{cp-c;)r=Ave(^^)\ (9)



THERMODTNAMIOAL RELATIONS. 523

The elasticity wlieii no heat is allowed to escape is
given by



V



and



3^ M^ AN
E^_ dv An AL
'Eg~ ?)^p~ Alc~ AM

'dv Am AK



Again referring to fig. 107, AM is the increase of
pressure at constant volume due to a rise of temperature
A0 or a quantity of heat c„A0, and AN is the increase
due to a quantity of heat 0A^ ; so that
c^_AM
6A(P~AN
Also at constant pressure, AK is the increase of volume
due to the heat CpAO and AL to the heat 9A(f> ; so that
CpA6_AK
dA(p~AL'
Therefore, for all substances,

Cp_AK AN _E^ ,-.„.

^,~zz ■ AJi~Eg ^ '

Maxwell proves equations (8) and (9) geometrically
from fig. 107, as follows: —

E -E -v(^^ Ak\ _ &r&ei ABGD _^AN
^ ^~ \An Am/ Am,. An Am,'
_ ^AM A(p
''"'^ANAe'

o.{E^-Ee)=vB^^ aI = ^^JMA^ A?

= Ave{^y=Ave(^)" = Ee{Cp-c^),

since c^ £'0 = CpE^.



524 THERMODYNAMIC AL RELATIONS

428. Applying these formulas to air, for which

pv = R6,

then M = ^=P, M=_^=_£;

and Cp — Cy=:AR= R/J.

Also Cp = yc„, where y is 1'4, about (§ 228); so that
_ yAR _ AR

''p-y-V ''"-y-r

With British units, J =119, R=5SS (§ 200); so that
^i? = 0-068, c^ = 0-238, c„= 0-170;
and the numbers are the same with metric units and the
Centigrade scale; these numbers were obtained in this
manner by Rankine in 1850, before they had been de-
termined experimentally.

If we divide the S.H. Cv by the s.v. v of the gas, we
obtain the thermal capacity per unit volume; this is
found to be very nearly the same number for all gases
at the same temperature.

The numerical value of y is determined most accurately
from the observed velocity of sound (§ 228) ; another
mode of determination, due to Clement and Desormes,
is to compress air into a closed vessel, and to observe
the pressure p, when the temperature 6 is the same as
that of the atmosphere.

A stopcock is then opened, and suddenly closed when
the air ceases to rush out; and it is assumed that the
enclosed air has expanded adiabatically to atmospheric
pressure p.

After a time the air inside will regain the surrounding
temperature 6, and its pressure p^ is again observed;
so that 02> the temperature at the instant of closing the
stopcock, is given by 0^ = Oplp^-



OF A PERFECT GAS. 525

If V denotes the volume of the vessel, then the air left
inside, at pressure p^ and temperature 6, originally
occupied a volume Vpjp^ at pressure p^^; and in ex-
panding adiabatieally to volume V it assumed the atmo-
spheric pressure p ; so that

py^=Pi{ypiiPiV> or pjp-=(pjp^)-y,

iogPi-logp

log Pi- log K
429. Taking 6 and v as variables with a perfect gas,

dH= edd> = c„de + e^'^dv
av

= c^dd + A6 -Za^v = c^dd + Apdv,

so that we may put

E = c„e = ABe/{y-l).

Thus the internal energy of the gas, in heat units S, in
the state represented by the point a in the diagram of
fig. 107, is A times the area of the indefinitely extended
adiabatic curve aaSv, cut ofi" by the ordinate aa.

The increase in internal energy E in passing from the
state a to the state j8 by any path a^ is thus A times
the area vaah^v ; and this area is made up of aa6/3, repre-
senting the work done in compressing the gas from a to
/3, and of va^v, representing the mechanical equivalent
of the heat supplied in going from a to /3.

, dd , , r,dv

Also dtp = c„-^- +AIi — ;

and, integrating,

^ = c„ log -t- {Cp — c„)log v + a constant
= c„ log0i;'>''^-fa constant,

^-9^o=«viog|Qy"=c.iog^^(jj.



526 EXAMPLES.

"With Q and <p as variables,

(c^ - c„)log ^ = ^ - 00 - Cp log 5- ;

so that the isometrics and isobars of a perfect gas are
logarithmic curves on the (6, 0) diagram.

In the Carnot cycle a^yS for a perfect gas, for instance
in an ideal gas engine, the work done in compressing the
gas adiabatically from a to /3 is

R{02-O^)l(y-n

and this work is therefore given out again in the adia-
batic expansion from" y to S, so that the areas aah^ and
ycdS are equal (fig. 107) ; and the above equations also
show that

1 Y

Oa_qd_/e^y-'- bi3^cy_fe.2y-\

Ob Og \dj ' aa cW
Ocl aa_0c_bl3



Oa dS Ob cy ^'^ '"'
The work done, per lb or g of the gas, by the isothermal
expansion from /3 to y is •

while the work consumed by the isothermal compression
from (5 to a is ^^i(02~^i) .■

the difference, as before, being

Examples.
(1) Prove that the orthogonal curves of the adiabatics on
the (y>, v) diagram are the similar hyperbolas
p^ — yv^ = constaii t.



EXAMPLES. 527

Prove that the isothermals and adiabatics cut
at a maximum angle cot"^ 2^y on the line

p^y — v = Q.
Discuss the same problem for the isometrics
and isobars on the (6, <f>) diagram.

(2) Prove that, if a perfect gas expands along the curve

yu*^ = constant, the work done by expansion is
(y — l)/(y — /c) of the mechanical equivalent of the
heat absorbed.

(3) Prove that the specific heat of a perfect gas, expanding

along the curve f{p, v) = 0, is

(4) Prove that, iipv = Rd";

Cp-Cy=nm6''-\

(5) Determine the heat equivalent of the kinetic energy

of rotation of the Earth, supposed homogeneous
and of S.H. c ; and determine the number of degrees
which this heat would raise the temperature of the
Earth, taking c = 0-2.

(6) Find what fraction of the coal raised from a mine

500 fathoms deep is used in the engine raising the
coal, and 30 times its weight of water, supposing
the heat of combustion of 1 lb of coal is 14,000
RT.U., and the efiiciency of the engine is j-.

(7) Compare the work done and the work given out

when V ft^ of atmospheric air is compressed adia-
batically to n atmospheres, cooled down to the
original temperature, and expanded adiabatically
to atmospheric pressure ; for instance, in a White-
head torpedo.



528 TABLES.

TABLE I.— DENSITY OF WATER (MENDELEEF).



c.


s(g/cm3).


i)(lb/i"ts).


j;(oni'/g).


C.


s(g/cm'*).


i)(lb/ft3).


v{cm^lg).





0-999873


62-4162


1-000127


40°


0-992334


61 -9456


1 -007725





0-999992


62-4237


1-000008


50°


0-988174


61 -6860


1-011967


10°


0-999738


62-4078


1 000262


60°


0-983356


61-3852


1-016926


15°


0-999152


62-3712


1-000849


70°


0-977948


61 -0476


1-022549


20°


998272


62-3163


1-001731


80°


0-971996


60-6760


1-028811


■25°


0-997128


62-2449


1 -002881


90°


0-965537


60-2729


1-035693


30°


0-995743


62-1584


1-004275


100°


0-958595


59-8395


1-043193



TABLE II


—SPECIFIC GRAVITY.




Platinum,


22


Aluminium,


2-6


Pure Gold,


19-4


Stone, Brickwork, or Earth


2


Standard Gold,


17-5


Glycerine,


1-26


Mercury,


13-6


Sea Water,


1-026


Lead,


11-4


Pure Distilled Water,


1


Silver,


10-5


Ice,


0-92


Copper,


8-8


Oak,


0-93


Brass,


8


Petroleum,


0-88


Wrought Iron or Steel, -


7-8


Pure Alcohol,


0-79


Cast Iron,


7-2


Cork,


0-24





TABLE lU.-


-ROOMAGE.




Salt Water,


35 Wjton.


Cast Iron,


4-6 ft-Vton.


Fresh Water,


36 „


Wheat or Grain,


45


Coal,


40 to 46


Timber,


66


Pig Iron,


9


Tea,


90

1



INDEX.



Absolute dilation of mercury 243
Absolute temperature . . 242
Accumulator . . . .22
Adiabatic expansion . . 266

^lian 52

Aggregation of cylindrical

particles . . . .48
Airlock . . . .355

Air pumps .... 366
Air pump and condensing

pump combined . . . 378
Air thermometer . . . 307
Alexander .... 391
Alloys and mixtures, . . 120

Amagat 287

Amagat gauge . . .25
Andrews . . . 242, 306
Aneroid barometer . 15, 265
Angle of contact . . . 403
Angle of repose . . .45
Angle of the centre . . 460
Angular oscillations of a float-
ing body . . . 228
Anticlastic . . .160
Aral Sea . . 79
Archimedes . . 1, 93, 484
Archimedes' principle . 77, 93
Ar^omfetre . . . .127
Aristotle . . . . 105
Ascending and descending

buckets .... 424
Ascensional force . . . 331
Atmosphere . . . .11
Atmospheric air . . .128



PAGE

Atwood 152

Average density . . .98
Average pressure over a surface 81
Axis of spontaneous rotation 66

Babinet's. barometric formula 310
Barads .... 489

Barker's mill ... 462

Barlow curve . . 395

Barometer . . . 251

Baroscope .... 105
Bear Valley dam . . .55
Bending moment . . . 414
Bernoulli's lintearia . 409

Bernoulli's theorem . . 467
Berthelot » . .95, 354

Biquadratic feet . . .64
Bixio and Barral . . . 337
Blackwall Tunnel . . .77
Block coefficient . . . 213
Body plan . . . .210
Bourdon's pressure gauge 14, 265
Boyle ... 3, 21, 366

Boyle's law . . 280, 286, 294
Boyle's statical baroscope . 105

Boys 412

Bramah ... .18

British thermal unit . . 505
Bubble electrified . . . 416
Budenberg . . . .18
Buoyancy . . . 94

Buoyancy, centre of . .149
Buoyancy, curve (or surface) of 149
Buoyancy, simple . . . 149

2l 529



530



INDEX.



PAGE

Cailletet .... 5
Caissons .... 356
Caissons of the Forth Bridge . 182
Calorie ... . 505

Camels ... . 139

Capillary attraction . . 398
Capillary curve . . . 407
Captive balloon . . .331
Cardioids . . .163

Carnot cycle . . 518

Camot's function . . . 519
Cartesian diver . . 301

Caspian Sea . . .79

Catenoid . . .418

Cathetoraeter . . . 243
Celsius . ... 246

Centigrade . . . 246

Centimetre . . .10

Centre of buoyancy ■ . . 149
Centre of oscillation . . 65
Centre of percussion . . 65
Centre of pressure . 43, 60

Centrifugal pump . . 473

Centrobario .... 457
Change of level in a loco-
motive boiler . . . 430
Change of trim . . .151
Channel Tunne . . 356, 484
Characteristic equation of a
perfect gas .... 281

Charles 3

Charles II. . . 100, 289, 398
Charles or Gay Lussac's law . 280
Chicago. . . . 139
Chimney draught
Chisholm
Circle of inflexions
Circular inch .
Clark and StansSeld
Clearance
Clemens Herschel .
CoeflScient of contraction 462, 470
CoeflScient of cubical compres-
sion 318

Coefficient of discharge . . 463
Coefficient of expansion . 241

Coefficient of fineness . 140, 213
Coefficient of velocity . . 463
Common surface of two
liquids . . . .36



321
103
177
13
139
370
469



Component horizontal thrust

of a liquid . . . .80
Component vertical thrust . 73
Compound vortex . . . 473
Compressibility of mercury . 318
Compressibility of water . 317
Condensing pump . . . 374
Conditions of stability of a

ship 148

Cone .... 189, 194
Conemaugh Dam . . 45

Coney Island stand pipe 76, 387
Conical pendulum . . . 224
Conjugate stresses . . 391

Conservatoire des Arts et

Mi^tiers . . . .104
Conveotive currents . . 38
Conveolive equilibrium of the

atmosphere . . .313
Cornish pumping engine . 34
Corrections for weighing in

air 304

Cosmos . . . 337
Cotes . . .100
Coxwell. . . . 332
Coxwell's balloon . . . 338
Cream separator . . 445
Critical temperature . 242, 306
Cross curves of stability 152, 167
Crown of Hiero . . .99
Ctesibius . . 2, 360
Cubical compression . . 515
Cup of Tantalus . . .277
Curve (or surface) of buoy-
ancy 149

Curve of dynamical stability . 161
Curves of pressure and density 319
Curves et surfaces analytiques 210
Curves et surfaces topographi-

ques 210

Carve of statical stability . 161
Cylinder .... 189
Cylinder floating upright . 191
Cylinder or prism floating
horizontally . . ,193

D'Alembert's principle . . 429
Dalton's law .... 285
Daniell .... 262

D'Arlandes . . . 327



INDEX.



531



Daymard
Dead Sea



PAGE

. 190
79, 98, 123, 125, 234
Ueep-sea sounding machine . 289
Delestage . . . 335

De Morgan .... 220
Density . . 30, 96

Dewar . . . . 6, 266
Differential air thermometer . 308
Dilation by heat . . . 241
Diving bell and diving dress . 347

Draft 138

Draught of a chimney . . 321
Druitt Halpin . . .435
Duokham . . 24

Dulong and Petit . . 243

Dupin . . . . 160

Dupin's theorems . . .159
Dynamical stability . . 230
Dynamics of the Siphon . 273



515,



Earth' pressure

Earthwork dam

Ebullition

Effective force

Eiffel Tower .

Elastica

Elasticity

Elastic limit .

Electrified bubble .

Elgar .

Ellipsoid

Elliptic functions .

EUipticity

Ellis

Energy of compression

Energy of immersion

Energy of liquid .

Entropy

Equality of fluid pressure

Equation of the three cubes

Equilibrium of bubbles .

Equilibrium of liquids in

' bent tube .

Equilibrium of rotating liquid 499

Equilibrium of the atmosphere 489

Espaoe nuisible . . . 370

Evelyn 347

Exeter Canal .... 389
Experimental verification of
Boyle's law



392
43
302
429
287
409
522
. 445
. 416
. 180
189, 202
. 230
. 459
. 265
. 320
. 143
. 20
. 517
16
336
300

233



286



PAGE

Fahrenheit ... 247

Fahrenheit or Nicholson

hydrometer . . 110, 115
Fire engine .... 360
First law of dynamics . . 505

Fleuss 355

Fleuss and Jackson air pump 381
Flexaral rigidity . . . 410
Floating body partly sup-
ported .... 214
Flottaison . . . .140
Flow with variable head . 464

Fluid 4, 7

Fluid friction . . 480

Force pump . . 360

Forced vortex . . . 473
Forth Bridge . . . 77

Freeboard . . .138

Free circular vortex . 472

Free spiral vortex . . . 472
Free surface of a liquid . . 28
Free surface of the ocean . 457
Friction brake . . . 435
Frontinns . . 2, 470

Froude . . 468, 481



Galileo .

Garnett .

Gas

Gaseous laws .

Gasholder

Gauge glass .

Gaussian measure of curvature 411

Gay Lussac . . 3, 259, 280

General equations of

equilibrium
Geocentric latitude
Giffard's injector .
Gorman ....
Governor of a gasholder
Gradient of the barometer
Gramme
Graphical construction of the

working of a condenser
Graphical representations of

Boyle's law
Gravimetric density of gun

powder ....
Gravitating spheres
Gravitation measure of force



. 3
. 126
4, 279
. 280
. 341
. 429



484
460
466
356
344
267
10

377

294



130
497

282



532



INDEX.



Greathead

Great Salt Lake .

Green

Green's transformation

Griffiths

Guillaume

Guillaume de Moerbek

Gulf Stream .

Guthrie .



PAGE

. 356
79, 98
. 334
. 487
. 508
. 258
. 1
38, 489
. 118



220,



Half-breadth plan . . .210
Hare's hydrometer . . 237

Hauksbee . . . .366
Hauksbee air pump . . 367
Head of water . .33

Heat equivalent of work . 508
Heat weight .... 517
Heaviness . . .30

Heeling effect of the screw

propeller .... 178
Height of the homogeneous

atmosphere
Heinke .....
Helicoid ....
Hermite
Hero

Herresschoflf .
Hiero of Syracuse .
H.M.S. "Achilles"
Hooke .
Horace .

Hudson River Tunnel
Huygen's barometer
Hydraulics .
Hydraulic gradient
Hydraulic Power Company
Hydraulic press . . .17
Hydraulic ram . . . 428
Hydrodynamics . . 8

Hydrogen or gas balloon . 330
Hydrometer 110,114,115,125,237
Hydrostatic balance . 98, 99
Hydrostatic bellows . 18

Hydrostatic paradox . . 21
Hydrostatic thrust . .41
Hydrostatic thrust in a mould 74
Hyperboloid . . . 189, 202

Imperial measures of capacity 106
Impulse turbine . . . 479



252

. 556

. 420

337

2, 277, 360

. 388

. 95

150

366

2

77

263

461

276, 481

21



Impulsive pressure

Inclining couple

Indicatrix . . . .

Indicator diagram .

Injector on thermodynamical

principles . . . .
Interchange of buoyancy and

reserve of buoyancy .
Intermittent siphon
Internal energy
Inverted siphons
Involute
Isobars .
Isobath inkstand
Isooar&nes
Isometrics
Isothermals .
Isothermal equilibrium of the

atmosphere



PAOE

426
158
159
510

508



180
. 277
. 516
. 276
163, 432
. 282
219
. 156
. 282
. 282



309



Jacobi's rotating ellipsoid ' . 502
Jamin . . . 103, 245, 287
Jenkins .... 163, 438
Jordan's glycerine barometer 263



Online LibraryG. (George) GreenhillA treatise on hydrostatics → online text (page 30 of 31)