MEN

199

MEE

height

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

3193-0

321

322

323

324

325

326

327

328

329

330

331

332330

334

335

336

337

338

339

340

341

342

343

344

345

346

347

Table of Areas, Sfc., — Continued.

Area Seg.

•195422•195337197252•198168•199085200003200922201841202761203863204605205527206451207376208301209227210154•211082212011•212940•213871•214802•215733•216666•217599•218533•219468• 220404•22134022227722321522415422509322603322697422791522885822980123074523168923268423358023452623547323642123736923831823926824021824116924212]

Heigh

Area Seg.

Heigh

Area Seg*

Heigh

Area Seg.

.348

.243074

.399

.292390

.450

.342782

.349

.244026

•400

. 293396

. 451

343777

.350

.244980

.401

. 294349

.452

. 344772

.351

.245934

.402

. 295330

. 453

. 345768

.352

. 246889

.403

. 296311

. 454

. 346764

.353

. 247845

.404

. 297292

. 455

. 347759

.354

. 248801

. 405

. 298273

.456

. 348755

. 335

. 249757

. 406

. 299255

. 457

. 349752

.356

.250715

.407

.300238

.458

• 350748

.357

.251673

.408

. 301220

.459

.351745

.358

.252631

.409

. 302203

.460

• 35274*1

359

. 253590

.410

. 303187

.461

• 353789

.360

.254550

.411

.304171

. 462

• 354736

.361

.255510

.412

. 305155

.463

■ 355732

362

. 256471

.413

. 306140

.464

• 356730

.363

257433

.414

. 307125

. 465

• 357727

.364

. 258395

.415

.308110

.466

■ 358725

.365

. 259357

.416

. 309096

. 467

■ 359723

.366

. 260320

.417

.310081

.468

• 360721

.367

. 261284

.418

.311068

.469

• 361719

.368

.262248

.419

. 312054

.470

• 362717

.369

.263213

.420

.313041

.471

• 363715

.370

.264178

.421

.314029

.472

• 364713

.371

.265144

422

.315016

.473

• 365712

.372

.266111

423

.316004

.474

• 366710

.373

.267078

.424

.316992

.475

• 367709

.374

. 268048

. 425

•317981

.476

• 368708

.375

.269013

.426

.318970

.477

• 369707

.376

. 269982

427

•319959

.478

• 370706

.377

.270951

.428

.320948

.479

• 371705

.378

.271920

429

.321938

.480

• 372704

.379

. 272890

.430

. 322928

.431

• 373703

.380

.273816

.431

.323918

.482

• 374702

.381

. 274832

.432

• 324909

.483

• 375702

.382

.275803

.433

• 325900

.484

• 376702

.383

.276775

. 434

. 326892

.485

• 377701

.384

. 277748

.435

. 327882

.486

• 378701

.385

. 278721

.436

. 328874

.487

• 379700

.386

.279694

.437

• 329866

. 488

• 380700

.387

.280668

.438

. 330858

.489

. 381699

388

.281642

.439

•331850

.490

■ 382699

389

.282617

. 440

•332843

.491

• 383699

.390

. 283592

.441

• 333836

.492

. 384699

391

.284568

.442

. 334829

.493

• 385699

.392

.285544

.443

• 335822

.494

. 386699

393

. 286521

.444

336816

.495

387699

.394

.287498

.445

•337310

.496

388699

.395

.288476

.446

338804

.497

389699

396

. 289453

.447

•339798

. 498

390699

397

. 290430

.448

340793

• 499

.391699

398

.291411

.449

•341787

. 500

392699

JlHd 17 lp a

e Area of the Segment of a circle by the preced-ing Table.

so tf' e hei S ht the segment by the diameter of tlie; loo -the quotient may contain three places of deci-

hi ° r ' 1 '

col Um ; lur , the corresponding number to the quotient intt! r ' 2oilt al U; '8ht, then take out the number in the sametl 6 *°P > ' n the vertical column intitled Area Seg. atllls taken U “'P^y the square of the diameter by the number

ettt.

out.

and the product will be the area of the«lrY' e '{4ht ( ? e< l u 'red the area of the segment of a circle,

of

which is two, and the diameter of the

52)2.000(.038156

440

416

re “>ain s 24, which

24

24

X?

13

= A-

The area of the segment corresponding to .038, is .009763,but since there is a fraction over and above .038 of findthe next greater area .010148 ; take the difference betweenthese two areas, which is .000385, multiply this differenceby the fraction f 3 , and it gives, .000177, which being addedto .009763, gives .009940 for the area of the segment,answering to .038

The Table is founded upon the following principle : Letthe diameter of a circle be 1, which suppose divided into1,000 equal parts, through every one of which imagine per-pendiculars drawn and continued both ways to the cir-cumference.

Then, since the versed sine is .001, we have v =r .001 and

v .001 .1 _ 4v - 4

v = '999 = 999

therefore A

4t> ,-

~ T ^ v v ~ 3000

\/

.000999 =r .00004214, and b =

A V

5 v

.00004215999 X 5

.00000001, whence the first number of the table is .00004215.

The second versed sine is .002 = v, therefore v = .998

v 2 1 8

— — — — — whence a = ——v 998 199 3000

.00011914

and

V .001996 =

A V

.00011914, and b == -— =

-= .00000005 ; there-

5v _ 499 X 5

fore the second number is .00011919.

The third versed sine is .003 = v, therefore v = 1 —.003 —

12 --

f 0002991 = .00021876:

v 4 ,

.997, whence — = , and A =

v 997

, A»

also b = -— =5 v

3000

.00021876 X 3

= .00000013 ; thence the

5 X 997

third number of the Table is .00021889.

And by this method the whole might be computed ; butafter a sufficient number of terms are found at the beginningof the table, the rest may be had (to seven or eight places ofdecimals) by this rule : let a, (3, y, S, denote any four termssucceeding in the order of the letters, then S = a -(3

X y—(3.

And if any term of this Table be divided by 78539816, ormultiplied by its reciprocal, it will produce the common tableof segments, when the area is unity.

MERIDIAN, in astronomy, a great circle of the sphere,passing through the zenith, nadir, and poles of the world,crossing the equinoctial at right angles, and dividing thesphere into two hemispheres, the one eastern, and the otherwestern.

It is called meridian, from the Latin meridies, noon, ormid-day, because when the sun is in this circle, it is noon inall places situated under it.

Meridian, in geography, a great circle, as paqd, passingthrough the poles of the earth p and Q, and any given placeat z. So that the plane of the terrestial meridian is in theplane of the celestial one.

Hence, 1. As the meridian invests the whole earth, thereare several places situated under the same meridian. And,2. As it is noon-tide whenever the centre of the sun is inthe meridian of the heavens, and as the meridian of theearth is in tlie plane of the former, it follows, that it is noonat the same time, in all places situate under the samemeridian. 3. There are as many meridians on the earth asthere are points conceived in the equator. In effect, themeridians always change, as the longitude of the place isvaried; and may be said to be infinite; each respectiveplace, from east to west, having its respective meridian.