L1SH-G ■ Entered according to Act of Congress in the year 1896. by E. G. MOEHL, in the office of the Librarian of Congress at Washington. D. C. READ Y RECKONER . ■ ■ « ■■i n ■ !— — —— ■— i ll ll ——a — — ^— — MATHEMATICAL Universal Manual WITH Directions, Examples and Complete Computation Tables T • * • FOR THE PRACTICAL USE OF Technologists, Engineers, Builders and Merchants PREPARED BY E. G. MOEHL Chicago: E. G. MOEHL PUBLISHING CO. 1897 Edw. Bfeh, Jr , Book and Job Printer. UTatfyematifcfyes Üntt>erf&{ ^&nbbnd} — mit — Meilung, JSei|piefen unb ooffflünbigeii fcedjnuiigs4a6e(Teii • • ■ • 3um praftifd^en (^ebraucr) für Öedjniker, Ingenieure, iau=lanö«ierHer unD Bauleute 33eatbeitet unb herausgegeben von €. (5. moety. V^W Cbicaöo: |T^Iä0 tum <£♦ ©♦ jptoshl & ©0 1897 (?bn>. Seel) St., öudj« unb ^Icctberij^Xrucfctci. preface/ With this work the author has made it his task to remedy a long-felt want in all territories of mathematics, by putting together as many tables as possible, from the lowest unit to the highest number. The work shall be an authoritative reckoner for each technologist, buil- der, etc., in all branches of his trade. Thorough and practical knowledge as well as many years' experience in all branches of mathematics and al- gebra made it easy for the author to furnish an entirely correct work, and he answers for the correctness of his work, especially his tables, to its full extent. Should the work answer the ex- pectations entertained, the author will issue further additions resp. computation tables (sphere, cylinder, etc.). The work is divided into three parts, which will appear in rapid succession. P o t w t t ©er SBevfaffer fyat eS fid) mit biefem SBer'fe juv Aufgabe geftettt, einem iängft auf allen ©ebieten ber 'JJlat.^ematif em= pfuubeuen33ebürfnif? babuvcl) abhelfen, bafc er möglicrjft v t e 1 e X a b e 11 e n üou ber niebevften ©inljett bis jut pafften 3ap gufammengefteEt fjat. ®a§ ffßeif foil jebem Xedftuifev, 93au=£aitbroerfer it. f. id. ein maftgebeuber 33ered)uer für a(le-3wetge feines Berufes fein. ©rüiiblidje unb praftifdje ftenutniffe, foioie langjährige Erfahrungen auf allen ©ebieten 'be? üftatljematif unb Algebra, matten eS bem SBcrfaffer leidet, eine burdjauS forrefte Arbeit ju liefern, unb fte.fjt berfelbe für bie s Jtic^ttgf'ett feines SerfeS, befonberS feiner Tabellen, in oolleiu Umfange ein. ©otlte baS ißerf beu gehegten ($imar= tiiugeu eiit)pred)eu, fo rotib ber $erfa[jev -weitere 3lnt)änge, refp. 33eied)uung§= Tabellen (ftugef, Eijltnber u. f. m.), fot= gen laffen. £)aS Söeif ift in biet 2l'btf)eilungeu ein- geteilt, meld)e in rafdjer golge erjdjetueu roerben. Explanatory preface* By the calculation of the tables the metric measure is the foundation, and to compute bases, the ratio of the diameter to the circumference (periph- ery) 1 to 3,14 (pi) is used. If the foot is divided into 10 parts — 1 foot = 10 inches @ 10 lines— the table is used as by the metric system. In the metric measure the diameters a^e expressed in centimeters. In each table from 1 — 165, one centimeter, to 280, etc., five centimeters are added, consequently the smallest diameter is one centimeter, and the largest diam- eter is 1000 centimeters = 10 meters. For feet — 1 inch to 1000 inches = 100 feet. For lines — 1 line to 1000 lines = 10 feet. The diameters are expressed in whole numbers, which may be given any name. If the circumference of a circle, or the perimeter of a surface or solid, is to be computed in the metric measure, the diameter and height are called centimeters, for feet, inches, or lines. From this it is evident that all num- bers in the tables are factors, which may be given any of the above names. The diameters, as already men- tioned, are expressed in whole num- bers; the height in decimals of the length = 1 meter = 10 decimeters = 100 centimeterf = 1000 millimeters, consequently 3 decimal places = trlöuternöea Pormori 93et Berechnung bet* ' Tabellen ift ba§ metrifdje^ftafj bie ©runbfage, nnb rourbe gur Berechnung ber ©runbflädjen bte SBerljaltuifjjaljl be§ T)urd)meffer§ jitm £ret§itmfang (^enprjerte) 1 311 3,14 (pi) genommen. 3ft ber gitfjin 10 Triette eingeteilt: 1 gufj = 10 3o(t @ 10 Stuten, jo finb bte Tabellen tote bet bent metrtfdjeu 2Rafje nt gebrauchen. gilt ba% metrifdje 9Jtaf$ finb bte ©urdj* meffer (T)tameter) in (Centimeter au§= gebrückt; in jebet Tabelle oon 1—165 mit 1 Centimeter, bi§ 280 mit CeutU meter 3 u f a £ berechnet; mithin tfi ber fletnfte ©urdjmeffer == 1 Centimeter, ber größte ©urdnneffer == 1000 Centimeter = 10 2Keter. $ür Mr- 1 Bolt big 1000 30a = 100 ftufc. %m Stuten: 1 Stute bi§ 1000 Stuten = 10 gufc. T)te T)urcr)meffer finb in gangen 3 a ^6ii auSgebrücft, melden mau eine jebe 33e= uennung beilegen t'auu. 3ft ein Körper-, glädjeus ober &rei§= umfang im ^eterntaft 311 berechnen, fo legt man beut SDurdjmeffer, fonne ^>öt;eu= 3af)fen, bie Benennung Centimeter für guj3, 3oö ober Stute, bei. $terau§ ift ei[id)t(td), baft fäntmtttdje QafyUn ber Tabellen gaftoren finb, metdjeu mau jebe ber üorfterjeuben Benennungen beilegen faun. T)te T)nrd)ineffer, rote bereits t)or= ermähnt, ftub tu gangen SafyUn auäge; —6— 0.1 = 1/10 = 1 dm.; 0.01 = 1/100 = 1 cm.; 0001 = 1/1000 = 1 mm. 1 foot = 2 decimal places = 0.1 = 1/10 = 1 inch: 0.01 = 1/100 = 1 line. Square measure: 1 sq. m. = 100 sq. dm. == 10,000 sq. cm. = 1,000000 sq. mm., consequently 6 decimal places of which the 1st and 2nd places to the right of the whole number are sq. decimeters, the 3rd and 4th places are sq. centimeters, and the 5th and 6th places are sq. millimeter. 1 sq.ft.= 100 sq.in.=10,000 sq.lines, consequently 4 decimal places of which the 1st and 2nd places to the right of the whole number are sq. in., and the 3rd and 4th places are sq. lines. The other places are fraction of lines. Example: 1.876534 sq. m. is read as follows: 1 sq. m. 87 sq. dm. 65 sq. cm- 34 sq. mm.; or 1.876534 sq. ft. = 1 sq. ft. 87 sq. in. 65 sq. lines (34 is frac- tion of lines). Cubic measure: 1 cu. m. = 1000 cu. dm. = 1,000000 cu. cm. = 1,000000000 cu. mm., consequently 9 decimal places, of which the 1st, 2nd and 3rd places to the right of the whole num- ber are cu. decimeters, the 4th, 5th and 6th places are cu. centimeters, and the 7th, 8th and 9th places are cu. millimeters. 1 cu. ft. = 1000 cu. in. = 1,000000 cu. lines, consequently 6 decimal places, of which the 1st, 2nd and 3rd places to the right of the whole number are cu.in., and the 4th, 5th and 6th places are cu. lines. The 7th, 8th and 9th places are a fraction of lines. Example: 3.765401015 cu. m. is read as follows: 3 cu. m. 765 cu. dm. 401 bviicfr, bte §of)tn:&af)U\\ in fecund* ©ntdjfieHen be§ fiangeiimctfjeS, 1 3Mev = 10 decimeter == 100 Centimeter = 1000 2fttttimetev, mithin 3 ©ecimaU 23rutf)fteUen = 0,1 = 1/10 = 1 dm., 0,01 — 1/100 == 1 cm., 0,001 == 1/1000 = 1 mm., 1 ftitfj = 2 Decimals 93rucl) [teilen = 0,1 = 1/10 = 1 §1., 0,01 = 1/100 = 1 I. ^lädjenmaft 1 qm. — 100 qdm. = 10000 qcm. = 1,000000 qmm., mithin 6 $5ecimal=28rud) [teilen; Ijteroon i[t bte 1. unb 2. ©telle, retf)t§ t)om ©anjen, Quabrat=2)ecimeter, bie 3. nnb 4. ©telle Qttabrat=(5entimeter, bte 5. nnb 6. ©telle Qnabratmilltmeter. 1 qtffj. = 100 qjl. = 10000 ql. ; mithin 4 £>ectnialbru$>= [teilen, ipteroon tft bie 1. nnb 2. ©telle, redjt§ üom ©aujeii, Quabratjott, bte 3. unb 4.©telle, Quabratttnien, bteroeiteren 33 ntdp [teilen [tnb 33rnd)t^eite ber Sinie. 93eifpiel: 1,876534 Qnabratmeter tft abliefen rt)te : 1 qm. 87 qdm. 65 qcm. 34 qmm. ; tit $ufe 1 qf jj. 87 qjl. 65,34 ql. jtörpermafj : 1 Äubif meter = 1000 kbdm. = 1,000000 kbcm. =1,000000000 kbmm. ; mithin 9 ©ectmctlsSBrudjfietten, t)iernad6) tfi bte 1., 2., 3. $)ecimat=33ntcl)= [telle, red)t§ oom ©angen, föubifbecimeter, bte 4., 5., 6. ©telle ßubifcentimeter, bte 7., 8., 9. ©telle tfubifmitttmeter ; 1 ^ubtf= fufj = 1000 fbjl. = 1,000000 tbl. ; mit* Ijtn 6 $)ecimat=93riicl)[telteit, fyternadj i[t biel., 2., 3. £)ectmat=23rud)[telle, red)t§ com @anjen, ^ubtfyolt, bie 4., 5., 6. ©telle Äubminten, bte 7., 8., 9. ©telle [tnb SBrud&t^eile ber Stute. SBeifpief : 3,765401015 ßubifmeter i[t abliefen roie 3 kbm. 765 kdm. 401 kcm. 015 kmm. ; in ftufe = 3 fbffe. 765 fbjl. 401,015 Fbl. _ ■( _ cu.cm. 015 cu. mm.; or 3.765401015 cu. ft. = 3 cu. ft. 765 cu. in. 401 cu.l. (015 being fraction of lines). Forms of cylinders, rollers, cones, frustums of cones, spheres, ellipses, are computed in volume, basis, outer and inner surfaces, as well as circum- ference (periphery) and sectors. For the computation of basis of re- gular sectors, the measure of which is given in degrees, a small table will be quoted among the examples. In the section for computation of ring-shaped walling of hollow bodies, according to tables, they are also computed from the diameter, 1 cm. to 10 m , resp. 10 to 100 ft. To these belong cisterns, arches of bridges, and tunnels in regular ellip- tical form, etc. The direction for the use of the above is very exact, and will be shown by special illustrations and explanations. Before the III. section of the area, plane of circle, and basis as well as cube table, a table under the heading "£ Radius Table" is adjoined, in which, according to the diameters resp. radii (for each table) i of the radius is computed. This number is multiplied by the entire spherical surface, and the cube of the sphere is obtained. After the main tables' tables of comparison are quoted in the appendix, in the contents of which the relation of the line, inch, foot and yard, in measures of length, sur- face and volume, to the metric meas- ure, and the gallon to the liter as well as the liter to the gallon, are given. The division of the entire work, through its simple and practical ar- rangement, replaces the index. formen t>ou Gr/Onbern, 2öalgen, Re- geln, abgewürgten Regeln, ber Äugeln, (Slltpfen, [tub berechnet in Änbiftnfjalt, @ruubfläd)e, äußere unb innere $täd)en, foroie be§ ÄreiSumfang§ (^eriprjerie) unb Jh'etSaitSfdjnitteit (©eftoren). $ür ©runbflädjen in regelmäßigen 2tuS« [crjnitten (©ectoren), beven ^ftafce nadj) ©reiben angegeben, ift gu bereu SBeredj« nung eine Heine Nabelte unter ben 53ei= [pieleu angeführt. Unter bem Slbfdjnitt ber ^tugbered^ nung ber ^ofjlforper nadj ben Tabellen (tub btefetben ebeitforoof;! com £)urd)= meffer, lern. bi§ 10m., refp. 10 Bis 100 §uß, berechnet, £>terju gepren : (5t)fter= mn, 23rücfenbogen unb 'Juuueie in regel= mäßiger (Sttipfenfovm. §)ie ©ebrauepanroeijung für ba§ 33or= ftepube ift eine feljr genaue unb roirb bmd) '3eid)nuitgen unD [pecielle (?däu= terung bavgelegt. 53or ber III 2(btrjeiiung, ber Quabrats Ärei§s unb @runbftäd)e, foroie Äubif; tah^Ut, ift eine Tabelle unter ber Ueber= fcfjrift „i 3ftabiu§ Tabelle" eingefügt, in roeidjer, nacr) beuDurcrjmeffern begro. dia- bteu (für |ebe ber Tabellen), ber £ D^abiuS aufgerechnet fid) befinbet ; mit biefer,3ar)l ift bie gange ftugelftädje gu muttipiigtren, rooourdjman ben Äubifin^att beringet erhält. yiaty ben ^aupttabeUen ftub, im %\\- puge, 23ergieidrjung§tabeUen angeführt, in bereu Sinljalt bie 3Serr)ältniff e ber Sinie, 3oli, §uf unb 2)arb§ im Sangen*, ^Iä= <$en- unb Äubifinpft gum metrifc^en Wa$e, eben fo roobt bie ©atlon gum Siter, roie Siter gur ©allou augegeben finb. Die (Sintljeilung be§ gangen 2ßerfe§ er= fefet, burdj feine einfache unb praftifdje Slrangirung, ba§ 3nl}att§--$ergeicr)nij3. Hbbrexnations, ft foot, feet in inches 1 line hi meter dm decimeter cm centimeter mm millimeter sq square sq. ft square foot sq. in square inch sq. 1 square line sq. m square meter sq. dc square decimeter sq. cm square centimeter sq. mm square millimeter cu .cubic cu. ft cubic foot cu. in cubic inch cu. *. cubic line cu. m cubic meter cu. dm cubic decimeter cu. cm cubic centimeter cu. mm cubic millimeter C Centrigrade (Celsius) Fahr Fahrenheit Dm Dekameter Hm Hektometer Km Kilometer mi mile It liter T ton cwt hundred-weight kg kilogram lb pound S gram . mg milligram S S spherical surface r radius -f- plus X times — minus = equal, are -;- divide. fffc&m^uncrim. f fe W }i. i$oii i fitnte m . ..«fleeter dm decimeter cm (Zentimeter mm SttiUimeter q Quctbrctt . qff* Quabratfufj q$I Ouabratjoa qf Duabratlinie qm Ouabratmeter qdm Ouabratbectmeter qcm Duabratcentimeter qmm Quabratmidinieter ft» Äubtf fbffc , Jhtbtffuß fbjl ßubifjoU fbt ...ftubifliuie kbm Äubifmeter kbdm Äubifbecimeter kbcm Änbif centimeter kbmm Äubifmittimeter (5 (ZetftuS fta^r ga^ren^eit 35m SMameter £m £>eftometer Am kilometer It fitter ctr (Zentner pfb «jSJunb kgr Kilogramm gr @ramm dgr £)ecigramm cgr (Zentigramm mgr SÖcilügramm r SftabiuS Zb\ Tabelle + plus X mot — minus = gletd), ftub -*- geseilt EXAMPLES. SPHERE. The sphere deserves our special notice. It is a body with a curved surface, each point of which is equal- ly distant from its center. A straight line from any point in the surface to the center of the sphere is called radius, and the prolongation of the same until it reaches the sur- face again is called diameter. -In the sphere, as in the circle, all radii are of the same length, and the diameters also. Imagine a sphere be- ing cut through the center into two rarts, the plane surfaces of these two parts represent the greal circles of the sphere, the radii of which are equal to the radii of the sphere. The area of the surface of a sphere, also called spherical surface, is found if the area of one of its largest circles is multiplied by four. The cube of a sphere is found by multiplying one-third of its radius by its spherical surface. It seems suitable to the purpose to explain the above statements about the circle and the sphere by a few examples, and assuming for both a diameter of 36 cm. Diameter: 36 cm. Radius: 18 cm. Circumference (Periphery ) : 36 X 3. 14 = 1.1304 = 1 m. 13 cm. 0.4 mm. Plane of circle: r.Xr.X3.14 = 18 X18X3.14 = 0,101736 = 10 sq. dm. 17 sq. cm. 36 sq. mm. Spherical surface: 4Xr.Xr. X3.14 (18X18X3.14) = 4x0.101736 = 0.4060440 = 40 sq. dm. 69 sq. cm, 44 sq. mm. Volume of a sphere: (|Xr.)x4 3 eifptele. (Sine gents beioubere 53eadjtung non unterer ©ehe nevbtent bie Äugel. ©ie ift ein föörper mit gekrümmter Oberfläche, bereu fämmtlidje fünfte gleid) raeit von bem im 3 uuent ^ev ^ügel liegenben ÜJhttelpithfte entfernt fiub. ©tue gerabe finite r>on trgenb einem fünfte bei Oberfläche bi% nun 9Jtittel= puufte ber föugel tyetfjt $albmefjer linb bie Verlängerung berfelben, bis fte bie Oberfläche abermals trifft, tft berSHirdj* meffer. 2ßie beim Greife fiub audj bei jeberföu= gel alle £albmeffer unb 2)urd)meffer ber= fetben einanber gleid). Renten mir uns eine föugel uon (Sbeuen burdjfdjnitteu, raeldje burd) ben 3Jnttelpunft bevfelben gefyeu, fo [teilen btefe bie fogeuannten größten Greife ber Jhtgel nor, bereu ^alb= meffer gleich bem ^atbmeffer ber föugel fiub. 2)en Ouabratinljalt ber Oberfläche einer Jatgel, für$er bielatgelflädje genannt, er= tjält man, menu ber 3>nf)a(t eines iljrer größten Greife »termal genommen wirb. ©er iatbifinrjait einer Angel wirb ge= fnnben, inbem ein drittel it)re§ |>alb= mefferS mit iljrer föugelflädje mulnpltjirt mirb. @S erfct)eiitt jraecimäfeig, bteoor[te^en = ben Angaben Überpreis unb jhigel burd) einige s £eifpiele &tt erläutern unb neunten mir für beibe einen £>urdjmeffev uou 36 cm. an. ©urdjmeffer : 36 cm. £albmefjer (?ftabiu§): 18 cm. Kreislinie ( v £eripJ)erie): 36 X 3,14 = 1,1304 = 1 m. 13 cm. 0,4 mm. Äreisfladje: r. X r. X 3,14= 18x18 X 3,14 = 0,101736 = 10 qdm. 17 qcm. 36 qmm. Äugelftädje : 4x(r. Xr. X3,14) = (18x 18x3,14) = 4X0,101736 = 0,406944 = 40 qdm. 69 qcm. 44 qmm. JhtgelinljaU: (£Xr.) X 4(r.Xi'.X3,14) -10- (r.Xr.X3.14) = 0.406944x0.06 = 0.024398640 cu.m.= 24cu.dm. 398 cu. cm. 640 cu. mm. Product if diameter is taken in cm. Now we will turn to the tables, and, as in the above example, assume the diameter of the sphere to be 36 cm. To alleviate the explanation, a table, as far as it is needed for the various relative numbers of the spherical surface and the volume of a sphere, is herewith added. Largest plane of intersection % spherical surface f spherical surface. Whole spherical surface. From the above account it is evi- dent that the area of the spherical surface lies between 1 and 4 (in meas- ure of height) in every table. A diameter that is perpendicular to the two great circles of a sphere is called the axis, and its ends are called poles. All circles which have a common axis, and the planes of which are parallel, are. called parallel circles, and the largest of them the equator circle. Those circles, however, which have a diameter coinciding with the axis, are called meridian circles. = 0,406944x0,06 = 0,024398640 kbm. = 24 kbdm. 398 kbcm. 640 kbmm. ^vobuft, wen it bev £)uvd)meffev in Mentis meter genommen. 9cunmel)v geljen roiv ju ben Tabellen über nub nehmen, inie in üorfterjenbem 23eifptele, ben £)urd)ineffer bev Jtugel mit 36 cm. 3 UV Orvleichtevuug bes> gii @r= lautevubeu füge id) bie betveffenbe Za- bette, foroeit biefelbe jn ben üevfdjtebeneu ^evrjäUiiifcjaljlen ber Äugelflädje nub bem ^ufyalte gebraucht roivb, tjiev an. ©vöfete ®uvd)fd)uitt§fläd>e. I ftugelfläcfye. f Äugelflädje. @anje 5tugelfläd)e. 9(u§ yovfteljeubev 3Cu3fü^rung tft er= ftcr)tlid), baft ber Quabratiuljalt bev Sin- gelflädje jiuifdjen 1 uub 4 (be§ ^o^eu^ maBe§) tu einer jebeu Tabelle liegt. (Sin ju einem föugelfreife feufredjt fteljenber ©urdjineffer rjetftt bie 3fre be§ ÄugelfretfeS uub bie (Snbpunfte feine 2llle ftreife, welche eine gemetufd)aft= Iid)e 2lve Ijaben uub bereu (Ibeueu bafyer parallel fiub, ljei|en ^avattett'veife, ber größte üou tf)neu ber 2(equatovfvet§. Äveife bagegeu, roeld)e bie 2lre jjitm £)uvd)meffev |aben, alfo buvd) bie beiben ^3ole gehen uub bie ^ßavallelfveife fenf- redjt burd)fd)neibeu, Reifen s Jftevtbiaii; fveife. High •pod) Diameter 36 cm. 'Enirdjmeffe 36 cm. 1 9 3 4 0,101736 0,203472 0,305208 0,406944 THE SPHERE, Diameter: 900 cm. Circumference (Periph- ery): Table, Sec. I. 900 cm. : 28 m. 2dm. 6 cm.; lines*: 28 ft. 2 in. 6 1.; inches**: 282 ft. 6 in. Spherical surface: Table, Sec. III. 900 cm. 4: 254 * Lines means: diameter taken in lines. * Inches means: diameter taken in inches. £)t e Angel. SDuvdjmeffev: 900 cm. ÄretSumf a n g $$ert= pbevie) — $bl. 2ibth. I. 1). 900 cm.: 28 m. 2 dm. 6cm ; in Siiiien*: 28 ffe. 2 $t. 6 I.; in 3oa**: 282 f jj. 6 jl. ft it g e I f t ä d) e — Tbl. 5lbt§. III. 900 cm. 4 : 254 * ©oil fyeifeen : benTmrdjmeffer in Linien genommen. ** Sott tyeifeen: ben S5unf)meffer in ^oll genommen. —11- sq. m, 34 sq dm.; lines: 254 sq.ft. 34 sq. in.; inches: 25434 sq. ft. Cube: £ r. = 1.50 m.X 254.34 = 38 L.510 cu.m. = 381 cu.m. 510 cu dm. ; lines: 381 cu. ft. 510 cu. in.; inches: 38151.0 cu. ft. The great circle divides the sphere into two equal parts (hemispheres), which have a common circumference and basis. THE HEMISPHERE. Circumference (Periph- ery ) -Table, Sec.I. 900 cm. : 28 m. 2 dm. 6 cm.; lines: 28 ft. 2 in. 6 1.; inches: 282 ft. 6 in. Basis: Table, Sec. III. 900 cm. 1: 63 sq. m. 58 sq. dm. 50 sq. cm.; lines: 63 sq. ft. 58 sq. in 50 sq. 1.; inches: 6358 sq. ft. 50 sq. in. Spherical surface: Table, Sec. III. 900 cm. 4: 254.34 -f- 2 = 127 sq. m. 17 sq. dm.; lines: 127 sq ft. 17 sq. in. ; inches: 12717 sq. ft. Cube: k r. = 1.50x254.34 = 381.510 cu. m.-7-2 == 190 cu. m. 755 cu. dm.; lines: 190 cu. ft. 755 cu. in.; inches: 19075 cu. ft. 500 cu. in. SECTORS from the poles whose divergence equals 1 20 deg. divide the sphere into 3 parts 90 u u a a a 4 a 72 " 60 " 51.42-' 45 " 40 " 30 « 20 15 " SECTOR. Sector of 120 degrees of a sphere with a diameter of 900 cm., and its circumference divided into 360 de- grees, beginning at the poles and qm. 34 qdm. ; in Sinien: 254 qffj. 34 qjl.; in 30a: 25434 qfjj. »Alibi findet It: J r. = 1,50 m. X 254,34 = 381,510 kbm. = 381 kbm. 510 kbdm. ; in Sinien: 381 fbffe. 510 fbj(.; in Sou": 38151,0 fbffc. £}erÄugetfvet3 (^eriptjerte) jevlegt bie Äuget in 2 X^eife (.palbfugetn), roeldje einanber gletd) uub gemeiufdmftttdjeit Umfang nnb ©runbflädSe babeu. 3) i e £> a 1 b f it g e I. Stx e t§um fang ($eri= pt)evie)-1bl. 2lbU).i. 900 cm. m. dm. tn 2t= in 5 t( 60 6 •« 51.42 7 . i 45 8 1 < 40 9 " 30 12 a 20 18 a 15 24 it 6 cm. men: 28 ffj. 2 j(. 6 Sou: 282 ft. 6 &I. ©runbflad&e — £bl. 2tbt§. III. 900 cm. 1: 63 qm. 58 qdm. 50qcm. ; in filmen: 63 qffe. 58 qjl. 50 q(. ; in 30U = 6358 qfp. 50 qjl. Ä it g e I f I a d) e-Xbt. 3tbtti. III. 900 cm. 4: 254,34 + 2 = 127 qm. 17 qdm. ; in Sinien : 127 qffi. 17 q$L ; in $oU: 12717 qffs. Ä it b i H n t) a f t — £ r.=l, 50x251, 34 = 381,510 kbm.-j-2 = 190 kbm. 755 kbdm.; in Stnien: 190 fbffe. 755 fb}l. ; in 3olI: 19075 fbff . 500 «13. Ä x e i § a it 3 f d) n 1 1 1 e non ben Stolen tin (Seutrirotnfel can 120 @rab sevlegt bie Äuget in 3X()eite. QO 4 u w a 11 a n * r/ 12 „ 1 8 04 Ä it g e I a it § f d) it i 1 1 au3 ber Äuget tin Tmvdjmeffev uon 900 cm. uub ber in 360 ©vabe eingeteilte Umfang, lueldjer uon ben 9 43oten auSgetjt uub bie ^avattelfveife feufvedjt buvd)= fd)iteibet, uon 120 ©mb. Tiutfor 3. —12- cutting the parallel circles at right angles. Divisor 3. Circumference: Table, Sec. I, 900 cm. = 28 m. 2 dm. 6 cm. h- 3 = 9 m. 4 dm. 2 cm. mm. = circumference of sector; lines: 9 ft. 4 in. 2 1.; inches: 94 ft. 2 in. Spherical surface: Table, Sec. III. 900 cm. 4: 254.34 sq. m. ■*- 3 == 84 sq. m. 78 sq. dm. = shperical surface of the sector; lines: 84 sq.ft. 78 sq.in.; inches: 8478 sq. ft. Cube: £ r. = 1.50x254 34 = 381.51 cu. m.-s- 3 = 127 cu m. 170 cu.dm. = cube of the sector; lines: 127 cu. ft. 170 cu. in.; inches: 12717 cu. ft. Sector of 90 degrees . Divisor 4. Circumference: Table, Sec. I. 900 cm.: 28 m. 2 dm. 6 cm. -4- 4 = 7 m. dm. 6 cm. 5 mm. = circumference of the sector; lines: 7 ft. in. 6.5 1 ; inches: 70 ft, 6 in. 5 1. Spherical stuf ace: Table, Sec. III. 900 cm. 1: 63.5850 sq. m. = 63 sq. m. 58 sq. dm. 50 sq. cm. = spherical surface of the sector; lines: 63 sq. ft. 58 sq. in. 50 sq. 1.; inches: 6358 sq. ft. 50 sq. in. Cube: * r. = 1.50X254 34 = 381.51 cu. m.-i-4 = 95 cu. m. 377 cu. dm. 500 cu. cm. = cube of the sector; lines: 95 cu. ft. 377 cu. in. 500 cu. 1.; inches: 9537 cu. ft. 750 cu. in. Sector of 45 degrees of the hemis- phere, diameter 900 cm. Divisor 8. Circumference: Table, Sec. I. 900 cm.: 28 m. 2dm. 6 cm. -f- 8 = 3 m. 5 dm. 3 cm. 2 5 mm. = circumference of the sector; lines: 3 ft. 5 in. 3.25 1.; inches: 35 ft. 3 in. 2.5 1. Basis: Table, Sec. Ill 900 cm. 1: 63.5850 sq. m. H- 8 = 7 sq. m 94 sq. dm. 81 sq. cm. 25 sq. mm. = basis of the sector; lines: 7 sq. ft. 94 sq. in. 81.25 sq. 1 ; inches: 794 sq.ft. 81 sq.in. 25 sq. 1. Spherical surface: Table, Sec. III. 900 cm. 2: 127.17 sq. m. -4- 8 '= 15 St v e i § it m f a 11 g : £bl. Wbty. I. 900 cm.: 28 m. 2 dm. 6 cm. -4- 3 = 9 m. 4 dm. 2 cm. mm. = Umfang be§ 2tii§[d&nitt§ ; in Sinten: 9 ffj. 4 §1. 2 I.; in 3oH:94f|j. 2 si. 1. £ it g e I f I a dj e : Zhl 2lbt§. III. 900 cm. 4: 251,34 qm. -j- 3 = 84 qm. 78 qdm. £ngelftäcl)e be§ 2ht§fc§mtt§ in Stnten: 84 qfjj. 78 q$l. ; in 3oU: 8478 qrfe. Ä it b 1 f t n fj a 1 1 : ir.=l,50x251,34= 381.51 kbm. -5- 3=127 kbm. 170 kbdm. ftiibifiugatt be§ 2lu§fd)iütt§ in Stnten: 127 fbf&. 170 fbjl. ; tn,3ott: 12717 fbffc. Äug elauSf djjuitf, rote oor, aber im SBiuFel Don 90 ©rab. jjtmfor 4. £r et § umfang: Zbl. 2lbt§. I. 900 cm. : 28 m. 2 dm. 6 cm. -f- 4 = 7 m. dm. 6 cm. 5 mm. Umfang be§ f?iigelans|djnittin£inien: 7ff}.- 0jL6.5 I. ; in 3oa: 70ff3. 6jl. 51. K it g e I f 1 ä d) e : ZU. 2lbt$. III. 900 cm. 1 : 63,5850 qm . = 63 qm. 58 qdm. 50 qcm. Äugelflädje be§ 2(ii§fdjmtt§: in Siiiicn-: 63 qffj. 58 qjl. 50 ql. ; in^oU: 6358 qffc. 50 qjl. Ä u b i f t n f) a 1 1 : i r. = 1,50X254,34 = 381,51 kbm. -*- 4 = 95 kbm. 377 kbdm. 500 kbcm. £nbifin^alt be§ 21u§[d)uitt§ in Shtieit: 95 fbffe. 377 fbjl. 500 fbl. ; in 3oE: 9537 fbffj. 750fb$t. 2tu§fd)ititt anö bei £ alb fit gel, im $)itrdjmeffer üoit 900cm. im (äentrirotnfel oon 45 ©tab. SDioifov 8. Ä r e i § u m f a it g : 2bt. m§. I. 900 cm.: 28 m. 2 dm. 6 cm. -5- 8 = 3 m. 5 dm. 3 cm. 2,5 mm. ÄieiSnmfang in Stnien: 3 ffe. 5 3I. 3,25 1.; in 3ott: 35 f|. 3 jr. 2,5 I. @ r it n b f I ä d) e : Xbl. 2tbt§. III. 900 cm. 1: 63,5850' qm. -j- 8 = 7 qm. 94 qdm. 81 qcm. 25 qmm. @runbf(äd)e be§ 2Iu§fdjmtt§ in Stnten : 7qff3. 94qjt. 81,25 qt, in £oU: 794 qfjj. 81 qjl. 25 qt Äugelf Xftd^c: %U. 2lbt§. III. 900 cm. 2: 127,17 qm. + 8 = 15 qm. 89 qdm. 25 qcm. Äugelflädje be§ 2(u3= — vs— sq. m. 89 sq. dm. 25 sq. cm. == spher- ical surface of the sector; lines: 15 sq. ft. 89 sq. in. 25 sq. I. ; inches: 1589 sq. ft. 25 sq. in. Cube: 190.755 -i- 8 — 23 cu. m. 844 cu. dm. 375 cu. cm. = cube of the sector; lines: 23 cu. ft. 844 cu. in. 375 cu. 1.; inches: 2384 cu. ft. 437 cu. in. 500 cu. 1. Sector (as above) but 60 degrees. Divisor 6. Circumference: Table, Sec. I. 900 cm. : 28 m. 2 dm. 6 cm. -h 6 = 4 m. 7 dm. 1 cm. = circumference of the sector; lines: 4 ft. 7 in. 11.; inches: 47 ft. 1 in. Basis: Table, Sec III 900 cm. 1': 63.5850 sq. m. -4- 6= 10 sq. m. 59 sq. dm. 75 sq. cm. = basis of the sec- tor; lines: 10 sq. ft. 59 sq. in. 75 sq. 1.; inches: 1059 sq. ft. 75 sq. in. Spherical surface: Table, Sec. III. 900 cm. 2: 127.17 sq.m. h- 6 = 21 sq. m 19 sq. dm. 05 sq, cm. = spherical surface of the sector; lines: 21 sq. ft. 19 sq. in. 05 sq, 1.; inches; 2119 sq. ft. 05 sq. in. Cube: 190,755 cu. m.-s-6 = 31 cu. m. 792 cu. dm. 500 cu. cm. = cube of the sector; lines: 31 cu. ft. 792 cu. in. 500 cu. 1.; inches: 3179 cu. ft. 250 cu. in. The hollow sphere has an inner and outercircu mfere nee, which are parallel circles. The figure which lies between the two circumferences is called a circular ring. The diameter of the large circle is 900 cm. depth of the jacket (walling, etc.) is 50 cm. = 50 -(- 50 = 100 cm. = lm., consequent^ the diameter of the inner circle is 800 cm. Cube of larger sphere: Table, Sec. III. 900 cm. 4: S. S. = 254.34 sq.m. X £ r. = 1.50 m. = 381,510 cu. m. Cube of smaller sphere: Table, Sec. III. 800 cm. 4: S. S. = 200.96 sq. m. X i r. == 1.333 m. = 267.87968 cu.m. 113,630320 cu. m. subtracted = cube of jacket(walling etc.); lines ;113cu. ft. fcr)uitt§ in Sinten: 15qffj. 89qsf. 25 q(., in^oU: 1589 qf^. 25 qjt. 'tfnbiHn^alt: 190,755 -f- 8 == 23 kbm. 844 kbdm. 375 kbem. äubif? in§altbe§2tu§[d&mtt§ in gtmeu: 23fbfe. 844fbjl. 375 fbl. ; tit £0(1: 2384 f'bff. 437 fb]l. 500 tbl 21 it § f d) n 1 1 t, röte oor, aber tut (Sentit; rotufel »on 60 @rab. ©iotfor 6. ftrei§ umfang: XU. 5(btl). I. 900 cm. : 28 m. 2 dm. 6 cm. -T-6 = 4m. 7 dm. 1 cm. Umfang be§ Stuäfdjutttä in Stuten : 4 ff . 7 jl. 1 1 ; in 3ott : 47 ff . m ©rnnbflädje: XU. Hbtrj. III. 900 cm. 1 : 63,5850 qm. -*- 6 = 10 qm. 59 qdm. 75qcm. ©runbftadjeb. 2(u3jd)itttt§ tu Stuten: 10 qffj. 59 qjl. 75 qt. ; in 3oll: 1059 qff . 75 qjl. ßugelftäd&e: XU. 2lbr§. III. 900 cm. 2: 127,17 qm. -j- 6 = 21 qm. 19 qdm. 05 qcm. föugelfTödje tu Stuten: 21 qf jj. 19 qjl. 05 q(. ; tit 3otf: 2119 qf jj. 05 q$I. Ä u B i f i it l) a 1 1 : 190,755 kbm. -f- 6 =31 kbm. 792 kbdm. öOOkbcm. ßubif= tnljalt be§ 5iu§[d)ititt§ in Stuten: 31 fbffe. 792 t%\. 500 tU. ; in ßolt: 3179 fofß. 250 fbgl. 2) i e .Iporj I fug el t)at einen inneren nub äußeren Umfang (^ertp^erie), [tub ^Parattetfreife, bte ^roifdjen beibeit ^eri= prjerieu Uegenbe $tgur nennt mau einen Ä'retSrtug. ©er Snrdjmeffer be§ großen ftretfeS tft 900 cm., bte ©tärfe be§ Daniels (üttanerroerf'S itfro.) tft 50 cm. = 50-f-50 cm. = 1 m., folglid) ber $>urd)meff er be§ inneren Äretf e§=800 cm. Ä u b t ft it r) a 1 1 b. gr. ftgl. XU. 21bt§. Ill: 900cm. 4: j?glfld»e=254,34 qm.X \ r. = 1,50 m.= 381,510 kbm. ff u b t f t it | a It b. ft. Ägl. £bl. 2(btf). Ill: 800 cm. 4: ftgtfldje = 200,96 qm. X i r. = 1,333 m. = 267,87968 kbm. ßubiruttjalt be§ s D?autet§ (fitbtrabtrt) = 113,630320 kbm. ; in Sinien: 113 fbf fe. 630 &#. 320 tU. ; in 3ott: 11363 fbffe. 032 fbjf. 14- 630 cu. in. 320 cu. 1.; inches: 11363 cu. ft. 032 cu. in. The inner sherical surface of the jacket of the larger sphere is equal to the spherical surface of the smaller sphere: Table, Sec. III. 800 cm. 4 = 200 sq. m. 96 sq. dm.; lines: 200 sq. ft. 96 sq. in.; inches: 20096 sq. ft. The hemisphere (hollow) is fre- quently used for domes on large buildings and churches, etc., and in smaller proportions for boilers, etc. THE DOME. The dome, diameter: 900 cm., depth of jacket (walling, etc.): 50 cm., inner vacant space, diameter 800 cm. Circumference (outer): Table, Sec. I. 900 cm.: 28 m. 2 dm. 6 cm.; lines: 28 ft. 2 in. 6 ]. ; inches: 282 ft. 6 in. Circumference (inner): Table, Sec. I. 800 cm.: 25 m. 1dm. 2 cm.; lines: 25 ft. 1 in. 2 1.; inches: 251 ft. 2 in. Basis of the larger hemisphere less the basis of the smaller hemisphere equals basis of jacket* Basis of larger hemishere: Table, Sec. III. 900 cm. 1: 63.5850. Basis of smaller hemisphere: Table, Sec. III. 800 cm. 1 = 50.24. Basis of jacket (walling, etc.) of the dome: 13.3450 sq. m. = 13 sq. m. 34 sq. dm. 50 sq. cm.; lines: 13 sq. ft. 34 sq. in. 50 sq. 1. ; inches: 1334 sq. ft. 50 sq. in. Cube of jacket of whole hollow sphere: 113.63032 cu. m. -^2=56.81516 cu. m. = 56 cu. m. 815 cu. dm. 160 cu. cm.; lines: 56 cu. ft. 815 cu. in. 160 cu.L; inches: 5681 cu. ft. 516cu.in. = cube of jacket (walling) of dome. Outer hemispherical surface: Table, Sec. III. 900 cm. 2: 127 sq.m. 17 sq. dm.; lines: 127 sq. ft. 17 sq. in.; inches: 12717 sq. ft. Inner hemispherical surface: Table, Sec. III. 800 cm. 2: 100 sq. m. 48 sq. dm.; lines: 100 sq. ft. 48 sq. in.; inches: 10048 sq. ft. D i e fö u g e t f I ä er) e be§ inneren Wanted bei größeren föugel ift = b e v föugelflädje bei Heineren föuget: Xhl 2lbttj. III. 800 cm. 4 = 200 qm. 96 qdm. ; in Linien: 200 qffj. 96 qjl. ; in Soil: 20096 qf^. Die -£>albfugel (r)ofy() finbet r»iet üßerroeubung ju föuppetn auf großen ©ebäuben uiib ftirdjeu itfro., im f feinerem aftafjfiabe ju föeffetn nfro. Die Ä ü p p e f. Die ft up pel, Dmdjmeffei 900 cm. 9Jlanretftctif"e (üftaueiroerf u[ro.) 50 cm., innerer Itdjte dtaum Duid)= meffer 800 cm. St r e i § u m f a n g anderer (^eitpfyeiie) 1hl 2lbtt). I. 900 cm. : 28 m. 2 dm. 6 cm.; tu Linien: 28 fjj. 2 jl. 6 1.; in 3oU:282fB. 6 jt. Ä v e t § u m f a n g innerer. ZU. 21btl). I. 800 cm. : 25 m. 1 dm. 2 cm. ; in hinten: 25 ffj. 1 jl. 2 l ; tu Botf: 251 ffr. @ i n u b f t ä dj e bei größeren ipatb- t'uget, weniger ber ©innbflädje ber fTeine- len ^albfiigef, tft bte ©runbftädje be§ 2RänteI§. ©innbffädje bei gv. ipalbfnget. Xhi. 3lbt£). III. 900 cm. 1 : 63,5850 qm. ©ruubflädje ber ft. .Ipatbfttget. Db(. %btf). III. 800 cm. 1 : 50,24 qm. @ r u n b f I ä d) e b e § s 3ft a n t e 1 § (üttauernjerfS) bei Düppel = 13,3450 qm. = 13 qm. 34 qdm. 50 qcm. ; tu hinten: 13 qffe. 34 qjl. 50 q(. ; in 3oü: 1334 qfjj. 50 qjl. föubtfinfjatt be§ Mantels bei ganzen £ofjlfugel = 113,63032 kbm. -*- 2=56,81516 kbm.=56 kbm. 815kbdm. 160 kbcm. ; in Stuten: 56 fbfjj. 815 fbjl. 160 fbt. ; in „Bot!: 5681 fbffe. 516 fb$t. föubtruitjatt be3 Mantels (SJtauerroerfS) bei Jhtppet. 9t e u | e r e $ a I b f u g e t f t ä d) e : £bl. Slbtf). III. 900 cm. 2: 127 qm.- 17 qdm. ; in Stuten : 127 qfjj. 17 q$[. ; in 3oü: 12717 qfjj. —15- Cube of vacant space: 267 cu. m. 879 cu. dm. 800 cu. cm.; lines: 267 cu. ft. 879 cu. in. 800 cu. 1.; inches; 26787 cu. ft. 980 cu. in. Should a hemisphere be divided into sectors, the same proceeding as given for the sphere may apply. Sector of 72 degrees of sphere. Divisor 5. the hemi- Circumference: 28 m. 2 dm. 6 cm.-f 5 = 5 m. 6 dm. 5 cm. 2 mm.= circum- ference of the sector; lines: 5 ft. 6 in. 5.2 1.; inches: 56 ft. 5 in. 2 1. Spherical surface (outer): 127.17 sq. m. -7- 5 = 25 sq. m. 43 sq. dm. 40 sq. cm. = spherical surface (outer) ot the sector; lines: 25 sq. ft. 43 sq. in. 40 sq. 1.; inches: 2543 sq. ft. 40 sq. in. Spherical surface (inner): 100.048 sq. m. -s- 5 — 20 sq. m. 00 sq. dm. 96 sq. cm. = spherical surface (inner) of the sector; lines: 20 sq. ft. OOsq.in. 96 sq. 1.; inches: 2000 sq. ft, 96 sq. in. 00 sq. 1. Cube of jacket: 56.81516 cu. m. -f- 5=11 cu. m. 363 cu. dm. 032 cu.cm. ; lines: 11 cu. ft. 363 cu. in. 032 cu. 1.; inches: 1136 cu. ft. 303 cu.in. 200cu.l. Basis: 13.345 sq. m. -f- 5 = 2 sq. m. 66 sq. dm. 90 sq. cm.; lines: 2 sq. ft. 66 sq. in. 90 sq. 1. ; inches: 266 sq. ft. 90 sq. in. 3 n n e v e -p a L b f it g e I f t ä d) e : Ibl 2lbtt). III. 800 cm. 2: 100 qm. 48*qdm. ; in ginien: 100 qfjj. 48 qU. ; in 3oU: 10048 qffe. £ u b t f i n § a 1 1 b e § It d) t e n 31 a n= m e§ : 267 kbm. 879 kbdm. 800 kbcm. ; in Einten: 267 fbftf. 879 fbjl. 800 fbt. ; in 3oU : 26787 fbfj. 980 fbjl. ©oU bte ipalbt'ttgel in Sutsfdjnitten (©ectoren) jevlegt roerben, fo ift ba§ 9Ser= fahren jit oenüenben, roeldjeg bet ber 33olIfnge( angegeben. % it § [ dj it i 1 1 an§ bei ^albfnget (Jtnppel ufto.), ©ector im SCBinfel won 72 @rab. ©ioifor 5. & r e i § it m f a n g (^ettpfyerie) 28 m. 2 dm. 6 cm. -f- 5 = 5 m. 6 dm. 5 cm. 2 mm. Umfang be§ ©ector§ in ginien : 5f|. 6§l. 5,2I.;in3ött:56f|.-58l. 2 (. tngelf tädje, ändere, 127,17 qm. -=- 5 = 25 qm. 43 qdm. 40 qcm. Ängelfläd&e, änjjere, in ginien: 25 qrp. 43 qjl. 40 ql. ; in 3o(( : 2543 qffj. 40 q\l Äitgelf 1 ä dh e, innere, 100,048 qm. -r- 5 = 20 qm. 00 qdm. 96 qcm. ; in glitten : 20 qf &. 00 q$f. 96 q(. ; in 3oU : 2000 qffc. 96 qji. 00 ql. £ it b i f t it Ij a 1 1 b e s 1 a n t e ( § 56,81516 kbm. ■*- 5 = 11 kbm. 363 kbdm. 032 kbcm. ; in ginien: 11 fbfB- 363fbai. 032 fbl. ; in 3otl: 1136 fbffe. 303 fbjl. 200 fbl. © r it n b f I ä d) e 13,345 qm. -r- 5 = 2 qm. 66 qdm. 90 qcm. ; in ginien: 2qffc. 66qjl. 90 ql. ; tit 30U: 266 qffj. 90 q${. THE ROLLER OR CYLINDER Roller (lying), Pillar or Cylinder (standing). $te 2B. III. 38 cm.=5 =0,566770 0,6 =0,0680124 0,04=0,00453416 5,64=0,63931656 kbm. = 639kbdm. 316 kbcm. 560 kbmm. £ubiftn§alt in Siuten: 639 1^1.316,56 tU.; tit 3oH: 63 tbfft. 931 fbjl. 656 fbl. (Sine it 21 u § f cf; it t 1 1 («Sector) genommen im (Sentriroinfel ber @runb= fiddle oon 90 ®rab. ©totfor 4. £ it b i t t it f) a r t : 0,63931656 kbm. h-4=159 kbdm. 829 kbcm. 140 kbmm. ßubifin^alt in Stiiien: 159 fbjt. 829,14 tU. ; tu 3oli: 15 fbf£. 9821% 914 fbl. @ r u it b f t ä er; e : 0,113354 qm. -- 4=28 qdm. 33 qcm. 85 qmm. Quabrat= tnljalt in Stuten: 28 qjl. 33,85 ql. ; in 3oE: 28qffe. 33 q$I. 85 ql. Wl a it t e I f l ä er, e : 6,741580 qui.-s- 4=1 qm. 68 qdm. 53 qcm. 95 qmm. Quabrattn^alt be§ Mantels in Siuten : 1 qf&. 68 qjl. 53,95 ql. ; in 3oll : 16 qf fe. 85 q^l. 39,5 ql. ÄreiS umfang (^ertpljerte) : 1,1932 m. -r- 4 = 2 dm. 9 cm. 8,3 mm. ^rei§= umfang tu Sinteu : 2 jl. 9,83 I. ; tit $oU : 2ffe. 93I. 8,3 1. £)te Tabellen, bet 33ered)ituug oon einzelnen SBertftetneit jit großen @e= -17— A Stone for building with diameter of 1.48 m., height 44 cm, Circumference: Table, Sec.1. 4.48 m. = 4 m. 6 dm. 4 cm. 7.2 mm.; lines: 4 ft. 6 in. 4.72 L; inches: 46 ft. 4 in. 7.2 1. Surface of jacket: Table, Sec. II. 1.48m.: 0.4 =1.85888 0.04 =0.185888 0.44 cm. =2. 044768 sq.m. = 2 sq. m. 04 sq. dm. 47 sq. cm. 68 sq. mm.; lines: 2 sq. ft. 0.4 sq. in. 47.68 sq. 1.; inches: 20 sq. ft. 44 sq. in. 76.8 sq. 1. Basis: Table, Sec. III. 148 cm. 1: 1.719464 sq. m. =1 sq. m. 71 sq. dm. 94 sq. cm. 64 sq. mm.; lines: 1 sq. ft. 71 sq. in. 94.64 sq. 1. ; inches: 171 sq. ft. 94 sq. in. 64 sq. 1. Cube: Table, Sec. III. 148 cm.: 0.4 =0.6877856 0.04=0.06877856 0.44=0.756564160 cu.m. = 756cu.dm. 564cu.cm. 160cu.mm. ; lines: 756 cu. in. 564.16 cu. 1. ; inches: 75 cu. ft. 656 cu. in. 416 cu. 1. From a stone for building which has a diameter of 148 cm. and a height of 44 cm., take a sector of 120 degrees. Divisor 3. Circumference of stone: 4.6472 m. -v-3=l m. 5 dm. 5 cm. — circumference of the sector; lines: 1ft. 5 in. 5 1.; inches: 15 ft. 5 in. Surface of jacket of stone: 2.044768 sq. m. -f- 3 = 68 sq. dm. 12 sq. cm. 96 sq. mm. = surface of jacket of sector; lines: 68 sq. in. 12.96 sq. 1.; inches: 6 sq. ft. 81 sq. in. 20.6 sq. 1. Basis: 1.719464 sq. m. ~- 3 = 57 sq. dm. 31 sq. cm. 55 sq. mm. = basis of the sector; lines: 57 sq. in. 31.55 sq. 1. ; inches: 57 sq. ft. 31 sq. in. 55 sq. 1. Cube: 0.756564160 cu. m. -=- 3 = 252 cu. dm. 188 cu. cm. 053 cu. mm. = cube of the sector; lines: 252 cu. in. 188.053 cu. 1.; inches: 25 cu. ft. 218 cu. in. 805.3 cu. 1, böubeit, 23rüdenbogen, 23rittf en topfen je. angeroanbt, bewähren fid) gut nub ev= fpareit Diet 3eit. (§ t it SEB c r f ft e i it im SD u r d)= m e f f e r oo« 1,4.8 m. fyod) = 44 cm. ÄretSumfang: £M. 2tf>t§. I. 148 cm. : 4 m. 6 dm. 4 cm. 7,2 mm. ÄreiSumfaug in Sinien: 4 fjj. 6 jl. 4,72 I.; in BoU : 46 ffe. 4 gl. 7,2 t. «Diautelf Iä<$ e: ™- ^- H- 148 cm. : 0,4 =1,85888 0,04 =0,185888 0,44cm.=2,044768 qm. = 2 qm. 04 qdm. 47 qcm. 68 qmm. $ftautelfläd)e in Staten: 2 qfjj. 04qjl. 47,68 qi. ; in ^ott : 20 qftf . 44 qji. 76,8 q(. ® x it it b f I ä dt) e : £bl. 9lbt§. III. 148 cm. 1: 1,719464 qm. = 1 qm. 71 qdm. 94 qcm. 64 qmm. ; ©niiibftäcfye in Staten : 1 qftf. 71 qgl. 94,64 qi. ; in £oU : 171 qfjj. 94qjl. 64 qi. ßubifin^ait: Xbl. 2lbt§. III. . 148 : 0,4 =0,6877856 0,04=0,06877856 0,44=0,756564160 kbm. = 756 kbdm. 564 kbcm. 160 kbmm. jtubtrmtjatt tit Sime« : 756 fbjl. 564,16 fbl.; tn^oil: 75 fbffe. 656 fb*l. 416 fbl. 23on bet« SBerffteiue i«t 3)urd)meffev r»o« 148 cm. «lib 44 cm. r)od) ne^me einen 2htSfd)itttt ((Sector) im (Sentrtanufel oon 120 @rab. 2)taifor 3. j? t e i S u m f a n g be§ ®teine§ : 4,6472 m. -f- 3 = 1 m. 5 dm. 5 cm. ÄretSumfang in Staten: 1 ffj. 5 j(. 5 I. ; in Sott :10 ft. 5 jl. W a « t e I f l ä d) e: 2,044768 qm.-*- 3 = 68 qdm. 12 qcm. 96 qmm. 3ftantel= fläche beS ©teineS in Stuten : 68 q$(. 12,96 qi. ; in 3oü : 6 qffe. 81 qjl. 29,6 qi. ©runbf tad) e: 1,719464 qm. -f- 3 = 57 qdm. 31 qcm. 55 qmm. @vuub= $äü)z tit Stuten: 57 qjl. 31,55 ql. ; in 3ott: 57 qffe. 31 qjL 55 qt. ßubtftn^alt: 0,756564160 kbm. +- 3 = 252 kbdm. 188 kbcm. 0,53 kbmm. ; Äubifiutyalt in Siuieu : 252 Ibjl. 188,053 fbt. ; in ^ott: 25 fbffe. 218 fbgl. 805,3 fbl. —18- To test wire cords, ropes, etc. , as to their absolute strength, or to manu- facture them, I point to the respective table in the appendix of the book, which table is also for computation of cylinders, according to square surface of transverse section. A wire cord has a diameter of 2 centimeters. How much weight in kilograms will it lift without tearing? Table, Sec. III. 2 cm. 1: 314 sq. mm. 1 sq. mm. cord tears with a weight of 80 kilogram = 314 X 80 = 25120 kg. For practical use, however, for the sake of safety only one-third of the above given weight is taken, consequently 25120 -*- 3 = 8373 kilo- gram. Now we come to the computation of a circular ring formed by two con- centric circles. To this belong hollow cylinders, tanks, barrels, etc., also large reservoirs for water, oil and gas, as well as wells and tunnels. The cylinder ring divided into two parts, etc. , forms bridge, door and window arches, etc. The system for this computation is like the one used for the hollow sphere. The hollow cylinder has an inner and outer circumference, and that which lies between the two circum- ferences is the jacket, also called walling, etc. A STONE FOR BUILDING. A window arch in the whole circle. Large diameter: 148 cm., depth of walling: 22 cm. =22 + 22 cm. = 44 cm. substracted from 148 cm. = 104 cm.=small diameter. Heigbt=35cm. Cube: Table, Sec. III. 148 cm.: 0.3 =0.515839200 0.05 = 0.085973200 0.35 = 0.601812400 cu. m. Um 2)rat)tf eile ober %am ufto. auf ifyre abfohlte gefjigfeit gu prüfen ober anju= fertigen, roetfe id) auf bie barauf beutg= neljmenbe £aoeüe im 2Inr)ang biefeS 33ud)e§ Jjtn. 3ft aucrj (Sr)ttnber=23ereä> uuug, nacf) Quabratfladje be§ Oner; burcfjf dntitt3. (Sin 3) r a Ij t f e U fyat einen £)itrd)= meffer con 2 (Zentimeter, roteoiel ©eroic^t in Kilogramm fyebt baffelbe, ofyne ju reiften? fabelte 2lbt tj. III. 2 cm. , 1 : 314 qmm. 1 qmm. ©ratjt jerreiftt bei einem ange= gehängten ©eraidjte oon 80 Kilogramm = 314 x 80 = 25120 ftlgr. ; beim praf= tifdjen @ebraud)e foil, ber (Sidjerfyett Toegen, bod) nur ber brttte £r)eü ber an- gegebenen Xragfraft angenommen Toer= ben. ^otglid) : 25120 + 3 = 8373 £iio= gramm. 9cunmefyr gefyt e§ jur 9ftingbered)nung über; fjtequ gehören ipofytcnliuber, 93ier= fü^tbütten, gaffer ufro., fotoie größere 33el)älter für 28affer, Del itnb @a§, Brunnen nnb Tunnel. £)er (Solinber: ring gui ufro. geseilt, bilbet Brüden;, ^ürs'unb $eufterbogen ufro. £)a§ SerecfjnungSfoftem ift gleich bem bei ber £or;ltugeI angerceubeten. £)er £>or;(cr)imber fyat einen inneren uub äußeren 5tret§riug, ba§ ^rotfdjen be'i- ben &ret§rtugen tiegenbe ift ber Kautel, and) Reibung ober 2öaub genannt. (Sin 28 e r f ft e t u. (Sin g e n ft e r b o g e n im ganjen Greife, @rofter £)urd)meffer : 148 cm. ©tärfe be§ 2ftautei§ : 22 cm. = 22 + 22 cm. = 44 cm., ah oon 148 cm. = 104cm. fleU ner ©ur^meffer, £öf)e: 35 cm. i ff üb if tub. a It: £61. 3lbt$. HI. 148 cm. : 0,3 =0,515839200 0,0 5=0,085973200 ~~Öj5=0, 601812400 kbm. —19- Cube according to large diameter. Cube: Table. Sec. III. 104 cm. : 0.3 =0.254716800 - 0.05 = 0.0424328 00 0.35 = 0.297149600 cu. m. Cube according to small diameter. Cube according to large diameter: 0.601812400, less cube according to small diameter, 0.297149600: Cube of window arch, 0.304662800 cu. m. = 304 cu. dm. 662 cu. cm. 800 cu. mm. : lines: 0.304 cu. in. 662.8 cu.J.; inches: 30 cu. ft, 466 cu. in. 280 cu. lines. Circumference (outer): Table, Sec. I.-, 148 cm. : 4 m. 6 dm. 4 cm. 7.2 mm. : lines: 4 ft. 6 in. 4.72 1.; inches: 46 ft. 4 in. 7.2 1. Circumference (inner): Table, Sec. I., 104 cm. : 3 m. 2 dm. 6 cm. 5.6 mm.: lines: 3 ft. 2 in. 6.56 1.; inches, 32 ft. 6 in. 5.6 1. Outer surface Sec. II., 148: of jacket : Table, 0.3 = 1.394160 0.05 = 0,232360 0.35 = 1.626520 == 1 sq. m. 62 sq. dm. 65 sq. cm. 20 sq. mm.; lines: 1 sq. ft. 62 sq. in. 65.2 sq. I.; inches: 16 sq. ft. 26 sq. in., 52 sq. 1. Inner surface Sec. II, 104: of jacket : Table. 0.3 =0.979680 0.05 = 0.163280 0.35 = 1,142960 = 1 sq. m. 14 sq. dm. 29 sq. cm. 60 sq. mm.; lines: 1 sq. ft. 14 sq. in. 29.6 sq. 1.; inches: 11 sq. ft. 42 sq. in. 96 sq. 1. Basis: Table, Sec. III. 148, 1: 1.719464 sq. m., less. Basis: Table, Sec. III. 104, 1: 0,849056 sq. m.; Basis of the jacket 0.870408 sq. m. = 87 sq. dm. 04 sq. cm. 08 sq. mm.; lines: 87 sq. in. 04.08 sq. 1.; inches: 87 sq. ft. 04 sq. in. 08 sq. 1. The circular ring divided into two equal parts gives arches for doors jhtbtfinlialt nad; bem großen £nrd)tnefjer. M : ub t t* t n$ alt: Zbi. 2lbt§. 104 cm. : 0,3 =0,254716800 0,05=0,042432800 III. 0,35=0,297149600 kbm. Äubif in§alt nad) bem flehten £urd)meffer. Änbifinfjalt be§ großen $)urd(jmeffer§ : 0,601812400 kbm., roeniger be§ Änbif= infyaltS be§ flehten £urdjmeffev§; Jtnbif= Inhalt be§ U. ©urd)tneffer§ : 0,297149600 kbm. , gibt beuÄubtfinljctlt b e § ft e n ft e v b o g e n § : 0,304662800 kbm. = 304 kbdm. 662 kbcm. 800 kbmm. ; Änbifinljalt in Suiten: 0,304 fbjl. 662,8 fbl. ; in 3oll : 30 fbffe. 466 fbjl. 280 fbl. Ibl. mm. 561.; Ä r e i § it m f a n g , äußerer : Zb\. %bty. I. 148: 4 m. 6dm. 4cm. 7,2 mm. fciSumfang in Sinten : 4 f jj. 6 jl. 4,72 1. ; tn3oH:46f^4 S L 7,2 1. St r e t 3 it m f a it g , innerer: 21b tlj. I. 104 : 3 m. 2 dm. 6 cm. 5,6 ] ÄreiSuinfang in Sinten : 3 f jj. 2 jl. 6,5 in ,3otl : 32 ftf. 6 $1. 5,6 1. Mantelfläche, ändere: Zbi. 2fbt§. II: 148 cm. : 0,3 =1,394160 qm. 0,05=0,23236 qm. 0,35=1,626520 qm. = 1 qm. 62 qdm. 65 qcm. 20 qmm. ÜJiantelflädje, ändere, in Sinteit: 1 qffi. 62 qjl. 65,2 ql. ; in 3oll : 16 qfjj. 26 q$l. 52 ql. Mantelfläche, innere: Zbi. 2lbt&. II. 104: 0,3 =0,979680 qm. 0,05=0,163280 qm. 0,35=1,142960= 1 qm. 14 qdm. 29 qcm. 60 qmm. ; Mantel- fläche in Sinten: 1 qffj. 14qjt. 29,6 ql.; tn^oll: 11 qf£. 42q$l. 96 fl 1 - ©runbpdje: Zbl 2lbt§. III. 148, 1: 1,719464 qm. ©rnnbftädje : ZU. Slbtr,. III. 104, 1: 0,849056 qm., roeniger bel- obigen @ r n it b f l ä d) e enthält bie beg 2Rantel3 mit : 0,870408 qm. = 87 qdm. 04 qcm. 08 qmm. ©rnnbflädje be§ Mantels in Sinten : 87 qjl. 04,08 ql. ; in Boa: 87qfB- 04 q$l. 08 ql. Ten 9fcmgförpei(£rei§bogen) in 2 gleite Steile geseilt, bilbet Söogen für Spüren —20- and windows. The products of the above computed, of circumfer- ence, basis (here face), etc., divided by 2, give the con- tents of the half circular rings, doors, and windows, etc. For sectors of the circular ring, the fre- quently mentioned pro- ceeding applies. STEAM BOILER. Larger diameter 1.48 m., jacket 1 cm. 1 -- 1 = 2 cm., consequently the small diameter: 1.46 m. High (long): 85 cm. Cube of large diameter: Table, Sec. Ill, 148: 8 = 13.755712 cu. m. 0,5 = 0.859732 cu, m. 8.5 m. = 14.615444 cu. m. Cube of small diameter: Table, Sec. 111,146: 8 = 13.386448 cu. m. 0.5 = 0.836653 cu. m . 8 5 = 14.223101 cu. m. Cube of vacant space=14 cu. m. 223 cu. dm. 101 cu. cm. ; lines: 14 cu. ft. 223 cu. in. 101 cu. 1.; inches: 1422 cu. ft. 310 cu. in. 100 cu. 1. The cube of the vacant space sub- tracted from the cube of the large diameter equals the cube of the jacket = 392 cu. dm. 343 cu. cm.; lines: 392 cu. in. 343 cu. 1.; inches: 39 cu. ft. 234 cu. in. 300 cu. 1. Circumference (outer): Table. Sec. I, 148: 4 m. 6 dm. 4 cm. 7.2 mm.; lines: 4 ft. 6 in. 4.72 1.; inches: 46 ft. 4 in. 7.2 1. Circumference (inner): Table, Sec. I, 146: 4 m. 5 dm. 8 cm. 4.4. mm.; lines: 4 ft. 5 in. 8 44 1.; inches: 45 ft. 8 in. 4.41, Surface of jacket (outer): Table, Sec. II, 148: 8 = 37.1776 0.5= 2.3236 8.5 = 39.5012 sq. m. unb $en[ter. SMe ^robttfte, be§ 23ovbeied)= ueten, oom Umfang, bev ©runbfladje (fyter (Stirnfläche) ufro., buret) 2ge^ irjettt, werben ben Sntyalt für bte falben £vet§bogen, ber £ljüreu unb $enfter ttfro. er; geben. %iix 2lu§fcfyuttte ( III. ' 148 : 8 =13,755712 kbm. 0,5 = 0,859732 kbm. 8,5 m.=14,615444 kbm. £ u b t f i u $ a I t be§ flehten £)uia> meffevS: £bt. 2lbt§. III. 146: 8 =13,386448 kbm. 0,5= 0,836653 kbm . 8,5=14,223101 kbm. == 14 kbm. 223 kbdm. 101 kbcm. ft u b i f i u I) a 1 t b e § listen Raumes in Stuten: 14 fbffj. 223 fbjl. 101 !bl. ; tu 30Ü: 1422 fbffe. 310 fM. 100 m. ®en jhibifin^alt be§ listen Canutes, fubtrarjtrt »out Äubiftn^alt be§ großen ©urd&mefferS, tft ber Äubtfuttyalt b e § yjl a n t e I § : 392 kbdm. 343 kbcm. ; in gtuien: 392 tbgl. 343 fbl. ; in ^ott: 39 fbffe. 234 fbgl. 300 fbl. St x e t § u nt f a it g, äußerer : £bl.2n>tr). I, 148: 4 m. 6 dm. 4 cm. 7,2 mm. ^ret§tunfang tu Stuten : 4 ffj. 6 jt. 4,72 1. ; in BoU: 46 ft. 4 jl. 7,2 I. SC v e t § u m f a it g, innerer : Tbl. Sibtlj. I, 146: 4 m. 5 dm. 8 cm. 4,4 mm. tetSumfang tit Sinten : 4 ffj. 5ji. 8,44 I. ; in Soil: 45 ffc. 8 ji. 4,4 I. 2tt a it t e I f l ä <$ e, ändere : W. 2lbt$. 11,148: 8 =37,1776 0,5= 2,3236 8,5 = 39,5012 qm. = 39 qm. -21- = 39 sq. m. 50 sq. dm. 12 sq mm.; lines: 39 sq. ft. 50 sq. in. 12 sq. 1. ; inches: 395 sq. ft. 01 sq. in. 20 sq. 1. Surface of jacket (inner): Table, Sec. II, 146: 8 = 36.6752 0.5 = 2.2922 8.5 = 38.9674 sq. m. = 38 sq. m. 96 sq. dm. 74 sq. cm.; lines: 38 sq. ft. 96 sq. in.; 74 sq. 1.; inches: 389 sq. ft.; 67 sq. in.; 40 sq. 1. Basis and face: Table, See. III, 1: 1.719464 sq. cm.; each 1 sq. m. 71 sq. dm. 94 sq. cm. 64 sq. mm.; lines: 1 sq. ft. 71 sq. in. 94.64 sq. 1. ; inches: 17i sq. ft. 94 sq. in. 64 sq. 1. The cone is equivalent to one-third of a cylinder, which has an equal basis and height respectively. There- fore the cube of a cone is found by multiplying the area of the basis by one-third of the height. A CONE (TOWER). Basis: 1.85 m. in diameter; high: 6.25 m. = 6.25 -r- 3 = 2.09 m. Cube: Table, Sec. Ill, 185: 2 =5.373325 0.09 =0.241799625 2.09m.=5.6L5124625 cu.m. = 5 cu. m. 615 cu. dm. 124 cu. cm. 625 cu. mm.; lines: 5 cu. ft. 615 cu. in. 124.625 cu. I.;* inches: 561 cu. ft. 512 cu. in. 462.5 cu. 1. Basis: Table, Sec. Ill, 185: 2 sq. m. 68 sq. dm. 66 sq. cm, 62.5 sq. mm.; lines: 2sq. ft. 68 sq. in. 66.625 sq. 1.; inches: 268 sq. ft. 66 sq. in. 62.5 sq. 1. Circumference at basis: Table, Sec. I: 5 in. 8 dm. cm. 9 mm. ; lines: 5 ft. 8 in. 09 1.; inches: 58 ft. in. 9 1. Surface of jacket: Table, Sec. II, 185: 2 =11.618 0. 09 = 0.52281 "2.09 m. = 12.14081 sq. m. = 12 sq. m. ]4sq. dm. 08 sq. cm. 10 50 qdm. 12 qcm. ; in gtnten : 39 qf jj. 50qjl. 12 ql; tit £oil: 395 qffj. 01 q$(. 20 ql. m a it t e t f I ä tf) e , innere : £b(.21btr,. II, 146: 8 =36,6752 0,5= 2,2922 8,5 = 38,9674 qm. = 38 qm. 96 qdm. 74 qcm. ; in gtmeu: 38 qffj. 96qjl. 74 ql.; tn^oU: 389 qf|. 67 qjf. 40 ql. (Sruitb uub Oberfläche: Tbl. 2H>t§. Ill, 1 : 1,719464 qm. j e = 1 qm. 71 qdm. 94 qcm. 64 qmm. ; in Sinteii : 1 qf|. 71 qgt. 94,64 I. ; in^od: 171 qffc. 94 q^i. 64 ql. £)er Äegel ift ein £ com (Snlinber, roeI= eher mit irjtn gleichen ©runb uub gleiche £>örje Ijat, bafyer finbet man ben StnbiU inljalt eine§ Kegels, roenn man ben Qna= brattnrjalr ber @runbptf)e mit £ £ör;e multipltctrt. (Sin ^eg el (£f)urm k.). (55 r it n b f I ä dt) e : 1,85 m. im ©uvdjmeffer; £od): 6,25 m. = 6.25 -f- 3 = 2.09 m. An biting alt: Xbl 2lbtb. Ill, 185: 2 0,09 = 5,373325 = 0,241799625 2,09 m. =5,615124625 kbm. = 5 kbm. 615 kbdm. 124 kbem. '* 625 kbmm. tfubtfinfjalt be§ fc gel§ in Stuten : 5 fbffe.. 615 fbji. 124.625 fbf. ; in Boo : 561 fbfjj. 512 fbjt. 462.5 fbl. © r n it b f 1 ä d) e : £bt. Stbtr,. Ill, 185 : 2 qm. 68 qdm. 66 qcm. 62,5 qmm; ©rmibfläd&e in Stuten: 2 qffj. 68 qti. 66,625 ql. ; iu^ott: 268 qf jj. 66 qjt. 62,5 ql. £ r e i § u m f a it g an ber ©runbpebe : £bf. mtf). 1 : 5 m. 8 dm. cm. 9 mm ; Äretsumfang in Stuten : 5 ffc. 8 gl. 0,9 I. : in SoU : 58 f fe. gl. 9 I. SO^antelfXädhe: £bt. Slbtb. II, 185 : 2 = 11,618 0,09 = 0,52281 == 12 qm. 2,09 m. = 14 qdm. 08 : 12,14081 qm. qcm. 10 mm. -22- sq. mm. ; lines: 12 sq. ft. 14 sq. in. 08.1 sq. L; inches: 121 sq. ft. 40 sq. in. 81 sq. 1. 9Kanteipc§e tu Linien: 12 qffj. 14 qit, 08.1- ql. ; in 3oö: 121 qffe. 40 qjl. 81 qf. JACKET, ROLLED UP. If the jacket of the cone has a depth of 24 cm. = 24 -f 24 = 48 cm. sub- tracted from the diameter 185 cm. = 137 cm. equals the diameter of the vacant space, also the height, exclus- ive 34 cm. (= 1£ of depth of jacket) subtracted from £ of height = 2.09 — 34 = 1.75 m. Cube: Table, Sec. Ill, 137: 1 = 1.473366500 0.7 = 1.031356550 0.05 = 0.073668325 1.75 = 2.578391375 cu. m. = 2 cu. m. 578 cu. dm. 391 cu. cm. 375 cu. mm. = cube of vacant space; lines: 2 cu. ft. 578 cu. in. 391.375 cu. 1.; inches: 257 cu. ft. 839 cu. in. 137.5 cu. 1. Cube of whole cone: 5.615124625, less cube of vacant space: 2.578391375, = 3.036733250 cu. m. Cube of jacket: 3 cu. m. 036 cu. dm. 733 cu. cm. 250 cu. mm.; lines: 3 cu. ft. 036 cu. in. 733.25 cu. 1.; inches: 303 cu.. ft. 673 cu. in. 325 cu. 1. The surface of the jacket is equal to the surface of the jacket of the cube of the vacant space, conse- quently the inner surface of the jacket. Table, Sec. II, 137: 1 = 4.3018 0.7 =3.01126 0.05 = 0.215090 1.75 = 7.528150 sq. m. = 7 sq. m. 52 sq. dm. 81 sq. cm. 50 sq. mm. = inner surface of the jacket; lines: 7 sq. ft. 52 sq. in. 81.5 sq. 1. : inches: 75 sq. ft. 28 sq. in. 15 sq. 1. 9Ri f g e r o I R e r ü)c a n t e I. 3ft ber Mantel be§ £egel§ 24 cm. ftarf = 24 -f 24 = 48 cm. fnbtrarjirt »om ©urdjmeffev 185 cm. = 137 cm. ift ber ©urd&meffer be§ lichten Raumes, forme bei feofyz erc *- ü011 34 cm. (= 1£ ber ©tchle be§ 9ftantel§)fubtra§irt oou £ ber £ör,e = 2.09 — 34 = 1,75 m. Ä it b i f i it f) a It. %bl 2lbt$. Ill, 137 : 1 = 1,473366500 0,7 = 1,031356550 0,05= 0,073668325 1,75= 2,578391375 kbm. = 2 kbm. 578 kbdm. 391 kbcm. 375 kbmm. : Mnfinrjalt be§ Itcrjteit ^attnteg; Utgittteri: 2 fbffe. 578 fbgl. 391,375 fM; tit £01!: 257 fbffc. 839 fbjl. 137,5 fbl. Jfttbtfin^ait b. g. £egel§ : 5,615124625 ; Jhtbtfutr;alt be§ listen Raumes: 2,578= 391375, fubtra^tr 1=3,036733250 kbm. Ätt b if tit r, alt be§ SDianteiS: 3 kbm. 036 kbdm. 733 kbcm. 250 kbmm. ; tit glitten: 3 fbfjj. 036 fbjl. 733,25 fbl.; in 3oU : 303 fbffc. 673 fbjl. 325 fbl. ®ie 9ftantelfläcr;e ift gletdj ber 9ftan= tetflädje be§ listen Raumes ; alfo bie in- nere gtäcfje be§ Mantels. ZM. 5ibtf,. II, 137: 1 = 4,3018 0,7 =3,01126 0,05 = 0,215090 1,75 = 7,528150 qm. 7 qm. = 52 qdm. 81 qcm. 50 qmm. ^nnere 2ft ant elf I ää) e in Stuten : 7qf£. 52 qjl. 81,5 ql. ; tit Bolt: 75 qfjj. 28q^t. 15 ql. Ar c i Sum f an g: Stbl. 2Ibtr,. I, 175; lifter torn: 4 m. 3 dm. cm. 1,8 mm.; in hinten: 4 ffj. 3 jl. 0,18 1.; in Boll: 43 fft. gl. 1,8 1. -23- Oircumference: Table, Sec. I, 175, vacant space: 4 in. 3 dm. cm. 1.8 mm.; lines: 4 ft. 3 in. 0.18 1.; inches: 43 ft. in. 1.8 1. Basis: Table, Sec. Ill, 137, 1: 1.4733665 sq. m. subtracted from the basis of the whole cone equals the area of the basis of the jacket: 2.6866625 — 1.4733665 sq. cm. = 1 sq. m. 21 sq. dm. 32 sq. cm. 96 sq. mm. = basis of the jacket; lines: 1 sq. ft. 21 sq. in. 32.96 sq. 1.; inches: 121 sq. ft. 32 sq. in. 96 sq. 1. Sectors given in degrees are to be computed according to the examples already given. The frustum of a cone, figure 9 : We add the diameter of the larger and smaller bases, and divide the sum by 2, thus mak- ing the frustum of a cone equi- valent to a cylinder of the same height, and a basis that would be a mean basis. £ i e © r u n b f t ä d) e: £bt. Hbtr,. Ill, 137, 1: 1,4733665 qm., fubtral)irt con bet ©ruubfläcfje be§ ganzen Äegel§, tft ber Quabratuiljaltber ©ntnbflädje be§2ftan= tet§ =2,6866625 qm. — 1,4733665 qm. = 1 qm. 21 qdm. 32 qcm. 96 qmm. Q u a b r a t i it r) a 1 1 ber © r it it b = f lädje tit Sinieu: 1 qffe. 21 qjl. 32,96 ql. ; in Both 121 qffj. 32 qjt. 96 ql. ÄegelauSfdjnitte (©ecroren) nacf) ben ©raben ber (Seiitrtroiiir'el ber @runbfläd)e gegeben, fiub nad) ben bereits angefült)r= ten Setfptelen ju berechnen. ©er a b g e ft u m p f t e £ e = gel, $tgur 9. Wan abirt ben ©urdjmeffer ber größeren nnb tin- neren (55viutbfläcr)e nnb tljeilt bag ^robuf't burd) 2 ; babuvdt) f efct man ben abgeftunipften föegel etilem (Snttnber qleid), raetcfier mit irjm gleiche £)örje nnb eine ©runbflädje bat, meiere eine mittlere ©runb; fläche fein roürbe. Fig 9. A PILLAR. m. Diameter of base: 1.64 top: 84 cm; 164 -4- 84 cm. == 1.24 m. = mean diameter, of pillar: 25.6 m. Cube: Table, Sec. Ill, 124: 20. =24.140320 5. = 6.035080 0.6= 0.724209600 , at the 248 -*- 2 Height 25.6 = 30.899609600 cu. m. = 30 cu. m. 899 cu. dm. 609 cu. cm. 600 cu. mm.; lines: 30 cu. ft. 899 cu. in. 609.6 cu. 1.; inches: 3089 cu. ft. 960 cu. in. 960 cu. 1. Sectors of the pillar are computed according to the rules quoted several times. A CHIMNEY (FORGE). At base 1.64 m., at top 84 cm., high 25.6 m. (This is the measure of the (Sine @ ft u I e. ©urdjmeffer unten: 1,64 m; oben: 84 cm. ; 164 + 84 cm. = 248-5- 2 = 1,24 m. mittlerer SMircfjmeffev, bte ©cutte ift Ijod) : 25,6 m. ftubifinrjatt: Xbl. 2tbt§. 111,124: 20 = 24,140320 5 = 6,035080 0,6 = 0,724209600 25,6 m. = 30,899609600 kbm. = 30 kbm. 899 kdm. 609 kbem. 600 kbmm. .ftnbtftnbaft ber (Säule in Siuteii: 30 fbffe. 899f&$I. 609.6 fM.; in Boll: 3089 fbff. 960 fl&jl, 960 fbl. 2tu§fd)nitte (©ectorett) au$ ber ©aitle, roerbeu nadj ben mefnfatf) angeführten Ocegetn berechnet. (Sin eif ftavf im Swinge, unten : 132 cm. ; oben : 52 cm. ; um ben Äufeifinfjalt be§ diuiQ- manerroerfg be§ ©djornfteiuS ju finbeu beregnet uad) ben Nabelten, einen Ghjltu= ber = bem ©itrcbmeffer be§ listen dtan- me§ be§ ©d)0tnftein§. #ubtfht§alt: ZU. %bt% 111,32: 20 = 1,607680 5 = 0,401920 0,6 = 0,0482304 25,6 m. = 2,057830400 kbm. £)iefe§ rßvöbuft, »on bem $robufte ber oorbereduteteu (Säule fubtra^iri, gibt ba% ^robuft be§ ^rf)ornfteiu§ = £tiug= mauerroerfeS. Äitbiftnfyatt ber ©ante 30,8996096; jhibtfinljalt be§. listen jRattme§ be§ ©tf)ornftein§ 2,0758304 = 28,841779200 kbm. = 28 kbm. 841 kdm. 779 kbcm. 200 kbmm. Ä u b t ft n f) a 1 1 b e § 9ft i n g m a u e r* ro e r f e § be§ ©djoriifiemS in Stuten : 28 fbffe. 841 fbjt. 779,2 fbl. ; in Soli: 2884 fbff. 177 fbgl. 920 fbl. St r e i § u m f a it g (^ertpl^erie) nuten : XM. 2lbrlj. I: 1,64 m. = 5 m. 1 dm. 4 cm. 9,6mm. ; in Stuten: 5 f ft. 1 gl. 4,96 (.; tu Bott : ölffe. 4 gl. 9,6 1. ÄreiSumfaug (^eriptyerie) oben : %bl 2lbt§. I, 84: 2 m. 6 dm. 3 cm. 7,6 mm. ; ßteiSumfang in Linien : 2 f jj. 6 jl. 3,76 1.; iu^oE: 26 fft. 3 jl. 7,6 t. Stetigere Mantelfläche, uadj bem mittleren $}urdjmeffer oon 1,24 in. Quabrattn^alt ; Sbt. 2tbt$. II. , 124 : 20 • = 77,872 5 — 19,468 0,6 = 2,33616 25,6 m. = 99,67616 qm. = 99 qm. 67 qdm. 61 qcm. 60 qmm. ift bie Mantelflädje für bie ©ante unb bem ©d)otnftein; in Sinten: 99 qffj. 67 qgl. 61,6 ql. ; in 3otl : 996 qf ft. 76 q$l. 16 ql. © r u u b f l ä d) e ber © ä u l e : Xhl. 2(btf). III, 164, 1: 2,111336 qm. Oberfläche ber ©ante: £bl. 2lbt&. III, 84, 1 : 0,553896 qm. ; ® r u n b - f l ä d) e b e § l i d) t e u ÄauineS: Xbl. -25- Sec. Ill, 32, 1 : 0.080384 sq. m. sub- tracted from the basis of the pillar, 2.111326 sq. m. = basis of round wall- ing beloiv, 2.030952 sq. m. = % sq. m. 03 sq. dm. 09 sq. cm. 52 sq. mm.; lines: 2 sq. ft. 03 sq. in. 09.52 sq. 1.; inches: 203 sq. ft 09 sq. in. 52 sq. 1. Upper surface -of pillar: 0.553896 less : 0.080384 0.473512 sq. m. = upper surface of the round walling of the chimney. 47 sq. dm. 35 sq. cm, 12 sq. mm. ; lines : 47 sq. in. 35. 12 sq. 1. ; inches: 47 sq. ft. 35 sq. in. 12 sq, 1. THE PAIL. Diameter, at base, 30 cm.; at top, 38 cm. ; high, 42 cm. ; contents : = 30 + 38 = 68 ■+- 2 = 34 cm. = mean diam- eter Cube (capacity.): Table, Sec. Ill, 34: 0.4 = 0.0362984 .02 = 0.00181492 0.42 = 0.038113320 cu. m- 38 cu. dm. 113 cu. cm. 320 cu. mm. = capacity of pail. Capacity in liters: 38.114 round; lines: 38 cu. in. 113.32 cu. 1.; inches: 3 cu. ft. 811 cu. in. 332 cu. 1. BUTTER VAT. Bottom, 34 cm.; top, 46 cm. in diameter: high: 52 cm.; contents? = 34 -f 46 = 80 -f- 2 = 40 cm. mean diameter. Cube (capacity): Table, Sec. 111,40: 0.5 = 0.0628 0.02 = 0.002512 capacity: 0.52 = 0.065312 cu. m. = 65 cu. dm. 312 cu. cm. In Liters: 65312. Given in weight, the ratio of the measure of contents would be 2(6 1^. Ill, 32, 1: 0,080384 qm., fitD= trafjirt dou ber unteren ©runbflädje bev ©ante: 2,111336 qm. = 2,030952 qm.: @runbf t ädj e bes> dt tu a, man cr= tr> e r f § u it t e n = 2 qm. 03 qdm. 09 qcm. 52 qmm. ; in Sinten : 2 qffj. 03 qjl. 09,52 ql. ; in^ott: 203qfft. 09 q^l. 52 q(. O b e r f t ä d) e b e r © ä u"l e : 0,553896 0,080384 (Subtract: 0,473512qm. Oberfläche b e § dt t n g m a u e x- to e r t § b e § © dj o r u ft e i u § : 47 qdm. 35 qcm. 12 qmm; in Stnien: 47 q$l. 35,12 I; tuBoU: 47 qffj. 35 q$t. 12 (. (Sin (5 i m e r. ©urdjmeffer, unten 30cm. ; oben 38 cm. ; \)o&) 42 cm. 3nr,alt ? = 30 -f 38 = 68 -*- 2 = 34 cm. mittlerer £>urd) = meffer. »Rauminhalt: £M. 2tbt$. Ill, 0,4 =0,0362984 0,02 = 0,00181492 34 0,42 = 0,038113320 kbm. dt a u m i n f) a 1 1 b e § @ t m e r § : 38 kbdm. 113kbcm. 320kbmm. 3? annuity alt it a ä) -ßi t er: 38114 rond. ; itad) Stuten : 38 fbjl. 113.32 fbl. ; uad)3olt:3fbffc. 811 fbjl. 332 fbl. 95 u 1 1 e r f a % 23oben 34 cm., oben 46 cm. •Dnrd); meffer; Ijod) 52 cm. ; 3n$alt? 34 + 46 = 80 -r- 2 = 40 cm. im mittleren $)urd)= meffer. Sn^alt: Xbl 2tbt§. 111,40: 0,5 = 0,0628 0,02 = 0,002512 tominljalt: 0,52 = 0,065312 kbm. = 65 kbdm. 312 kbcm. ; in Stter : 65312. Waü) bent ©erotd)te angegeben roüibe ba§ Sftafjüevljältnijj beS ^lttjalteS -26- very different. (See table of specific weights. ) Cube in lines: 65 cu. in. 312 cu. 1. ; in inches: 6 cu. ft. 531 cu. in. 200 cu. 1. VESSEL FOR WATER, OIL OR GAS. Diameter 75 feet; depth of walling 2.5; deep (high) 65 feet; 2.5 + 2. 5 ft. = 5 ft. subtracted from 75 ft. .= 70 ft. = diameter of the vacant space. Cube: Table, Sec. Ill, 750: 60 = 2649.3750 5= 220 78125 65 = 287015.625 Cube: Table, Sec. Ill, 700: 60 = 2307.90 5= 192 325 65 = 250022.5 = cube of small diameter subtracted from cube of large diameter: 287015,625 less: 250022.500 36993.125 cu. ft. = Cube of round walling = 36993 cu. ft. 125 cu. in.; lines: 369 cu. ft. 931 cu. in. 250 cu. 1. ; centimeter: 369 cu. m. 931 cu. dm. 250 cu. cm. Circumference (outer): Table, Sec. I, 750: 235 ft. 5 in.; lines: 23 ft. 5 in. 5 1.; centimeter: 23 m., 5 dm. 5 cm. Circumference (inner): Table, Sec. I, 700: 219 ft. 8 in.; lines: 21 ft. 9 in. 8 1 ; centimeter: 21 m. 9 dm. 8 cm. Basis of large diameter: Table, Sec. Ill, 750: 4415 sq. ft. 62 sq. in. 50 sq. 1. Basis of small diameter: Table, Sec. Ill, 700: 3846 sq.ft. 50 sq. in. Loiver and upper surface of the round ivalling, each: 569 sq. ft. 12 sq. in. 50 sq. 1.; lines: 5 sq. ft. 69 sq. in. 1.52 sq. 1. ; centimeter: 5 sq. m. 69 sq. dm. 12 sq. cm. 50 sq. mm. Outer surface of jacket: Table, itec. II, 750: 60= 1413.0 5 = 117.75 65 = 15307.50 sq. ft. jefyr uerfdjiebeu fein, (fierce jpecififcfye @e= roidjtätabelle.) jlnbifinfyalt in giitieit : 65 fb*(. 312 fbl. ; in Sou: 6 fbft. 531 fbjl. 200 fbl. S33a Her =, Del-- ober @ a 3= behaltet. ©urdjmeffer : 75 ft. 3ftauerftärfe 2,5 ; tief ($od&) 65 ft. 2,5 + 2,5 ft. = 5 ft. fnbtrabjrt dou 75 ft. = 70 ft. = ©itid)= meffer ini lidjten Canine. £ u b i I i it r, a 1 1 : %b\. mtl). Ill, 750 : 60 = 2649,3750 5= 220,78125 65 = 287015,625 ß u b i f i ii r, a 1 1 : £bl. Äf. Ill, 700: 60 = 2307,90 5= 192,325 65 = 250022,5 Äitbtfinljalt be§ Hetnen ©urdjmefferS ; Utbtra^irt r>om Äubifinfjalt be§ großen ©itrcrjmeffer : 287015,625—250022,500 = fö it b i f t n t) a It b e § $K i ii g m a u e r= ro e r f § : 36993,125 fbft. = 36993 fbft. 125 fbjl. ; in Stnten: 369 fbft. 931 fbjl. 250fM.; in cm.: 369 kbm. 931kbdm. 250 kbcm. Ä r e t § n nt f a n g 0$ertpr)erie) äußerer.: £bl. Stbtr,. I, 750: 235 ft. 5 gl.; in Stitien: 23 ft. 5 jl. 5 I. ; in cm.: 23 m. 5 dm. 5 cm. Äretsumfang (^ertpfyerie) innerer: £bl. Slbtl). I, 700: 219 ft. 8 jl. ; in ginien: 21 f^. 9 jl. 8 I ; in cm.: 21 m. 9 dm. 8 cm. ©runbflädje be§ großen ©urd&meffer§ : £bl. 2lbtr,. Ill, 750: 4415 qft. 62 qjl. 50 ql. @miibfläcf)e be§ Heineit $Diird&meffer§:XbI. 2lbt§. Ill, 700: 3846 qft. 50 qjl. $Iäd)e be§ nn t er en it n b oberen 9^ i it g m a it e r ro e r f § : je 569 qft. 12 qjl. 50 ql. ; in ginien: 5 qft. 69 q^l. 12,5 ql. ; tit cm.: 5 qm. 69 qdm. 12 qcm. 50 qmm. Mantelfläche, äufjere: £b(. Wbtf). II, 750. 60 = 1413,0 5 = 11 7,75 65 = 15307750 qft". -27— = 1530? sq. ft. 50 sq. in.; lines: 1530 sq ft. 75 sq. in.; centimeter: 1530 sq. m. 75 sq. dm. Inner surface of jacket: TaTrie, Sec. II. 700: 60 = 1318.8 5 = 109.9 gallons 65 = 14287.0 = 14287 sq. ft. ; lines: 1428 sq ft. 70 sq. in.; centi- meter: 1428 sq. m. 70 sq. dm. The capacity of the above vessel» etc., is 250022.5 cu. f t = *7079.653 cu- m. and, therefore, contain **7,079,653 liters of water = 1,870, 11 1.505 gallons. According to the table of specific weights, a hollow body with a capac- ity of 1 cu. m. = 1000 cu. dm. con- tains 1000 liters of water by a tem- perature of 4 degrees Centigrade, con- sequently the vacant space of the vessel contains 250022.5 cu. ft. = 7079.653 cu. m. multiplied by 1000 = 7,079,653 liters = 1,870,111.505 of water. If the round wall is cut in its vert- ical position, in the largest diameter, down to the basis into two equal parts, we get a bridge arch in a hemi- circle with a span of 70 feet, depth of wall 2.5 ft., and length of 65 ft. If we divide the various computa- tions of the round wall by 2, we get the computations of the bridge arch. Cube of the wall: 36993.125 cu. ft. -r- 2 = 18496 cu. ft, 562 cu. in. 500 cu. 1.; lines: 184 cu. ft. 965 cu. in. 625 cu. 1.; centimeter: 184 cu. m. 964 cu. dm. 625 cu. cm. Area of basis: 569.1250 sq. ft. -=- 2 = 284 sq. ft. 56 in. 25 sq. 1.; lines: 2 sq. ft. 84 sq. in. 56.25 sq. L; centi- meter: 2 sq. m. 84 sq. dm. 56 sq. cm. 25 sq. mm. Circumference (outer): 235.5 ft. -*- 2 == 115 ft. 7 in. 5 1.; lines: 11 ft. 5 in. 7.5 1.; centimeter: 11 m. 5 dm. 7 cm. 3 mm. Circumference (inner): 219.8 ft. +- 2 * See table of comparison : 1 cu. ft. to 1 cu. m. ** See table of comparison: 1 liter to 1 gallon. = 15307 qftj. 50 qjf. ; in fitnteu : 1530 qfft. 75 qjl. ; in cm. : 1530 qm. 75 qdm. W a it t e I f I ä d) e , innere : Xbl. WKtf). II, 700: 60= 1318,8 05 = 109,9 65= 14287,0 = 14287 qftf. ; in fitnteu : 1428 qfft. 70 qjl. ; in cm. : 1428 qm. 70 qdm. 2)er ltd)te Dtemiurjalt be§ üorftefjen= ben 2ßafferber;älter3 n. f. ro. beträgt 250022,5 ff &. = * 7079,653 kbm. , nimmt [omit eine Sßaffermaffe »on **7,079,653 fiiter = 1,870,111,505 (Motten auf. 9?ad) ber Labette über fpectftfd)e§ @e= rotdjt nimmt ein -Iporjiförper oon 1 kbm. = 1000 kbdm. Dictum, 2Baffer bet einer Temperatur non 4 @rab be§ lOOtfjeiltgeu Xfjermometer oon (Selfiuä 1000 fitter auf. 9ftttr;tn nimmt ber lichte Staunt be§ 2Bafferber,älter§ 250022,5 fbfp\ = 7079,653 kbm., multtplicirt mit 1000 = 7,079,653 fitter = 1,870,111,505 ©alt auf. ©urd)fdmeibet man ba§ 3fttugmauer= roerf tu feiner feufrecfjten ©teltung, im größten SDuvdjmeffer bi§ §ur ©ruubftadje, in gleiche Xfjeüe, fo erhält mau einen SSrürJfeitbogeu im ^albfrerä mit lichtem $)urd)ineffer («Spannung) oon 70 fjj., eine s Iftauerftärfe oon 2,5 fjj. uub eine fiäuge oon 65 fjj. ZfyeiU mau bie oerfdnebeneu s $robucte be§ 9fttngmauerroerf§ burdj 2, fo errjätt mau bie ^ßrobucte be§ 93rücfen= bogen§: Wattenoerf, ftubttiurjatt: 36993,125 f bf §. -s- 2 = 18496 föffe. 562tb$l. 500 fbl.; in fitnteu: 184 fbffe. 965 fb$l. 625 fbl. ; in cm. : 184 kbm. 965 kbdm. 625 kbcm. ©ruubflädje, Ouabvatinfcalt: 569,1250 qfjj. -4- 2 = 284 qffj. 56 qjr. 25 qt.; in glitten: 2 qffc. 84 q$I. 56,25 ql. ; tu cm.: 2 qm. 84 qdm. 56 qcm. 25 qmm. £rei§uutfang (^ertpljerie), äußerer: 235,5 f^. -- 2 = 115 ff?. 1]l 5 1.; in fitnteu : 11 ff;. 5 j{. 7,5 l. ; in cm. : 11 m. 5 dm. 7 cm. 5 mm. ßretSumfang, innerer: 219,8 fjj. -f- 2 * 5ielje ^Sergfcicftuug§ta6eUen : 1 fbfjj. ju 1 kbm. ** ^Sielje ^ergleidningStabellen: 1 Viter jur i3att. = 109 ft. 9 in. ; lines: 10 ft. 9 in. 9 1. ; centimeter: 10 m. 9 dm. 9 cm. Outer surface of jacket : 15307.5 sq. ft. -T- 2 = 7653 sq. ft. 75 sq. in. ; lines : 765 sq. ft. 37 sq. in. 50 sq. 1. ; centi- meter: 765 sq. m. 37 sq. dm. 50 sq. cm. Inner surface of jacket: 14287.0 sq. ft. -f- 2 = 7143 sq. ft. 50 sq. in. ; lines : 714 sq. ft. 35 sq. in.; centimeter: 714 sq. m. 35 sq. dm. By sectors of the entire walling we proceed as already given for door and window arches. THE BARREL to be computed as a hollow cylinder. If the base of the barrel is 0.50 m., at bung hole 0.60 m. high, then the mean diam- eter = 0.50 + 0.60 = 110 -4- 2 = 0.55 m., and 0.85 m. long. Cube: Table, Sec. Ill, 55 : 0.8 =0.189970 0.05 = 0.011873125 0.85 = 0.201843125 = 201 cu. dm. 843 cu. cm. 125 cu. mm. Capacity 202 liters; lines: 201 cu. in. 843.125 cu. 1.; inches: 20 cu. ft. 184 cu. in. 312.5 cu. 1. THE ELLIPSE. Such forms are frequently used for piers, etc., arch walls of drainage canals, tunnels, mashing tubs, wash- coops, etc. In computation of bodies with elliptical forms, the circle is com- monly used, but it is more exact to compute the area according to the mean diameter = 109 ffj. 9 gl. ; tii ßintcn : 10 f |j. 9 jl. 9 I. ; ijt cm.: 10 m. 9 dm. 9 cm. Sttantelfläd&e, auf ere: 15307,5 qffj. -*- 2 = 7653 qffe. 75 qjl. ; in Stuten : 765 qffe. 37qjl. 50 ql. ; in cm.: 765 qm. 37 qdm. 50 qcm. 2Raiitelp<$e, innere: 14287,0 qffj. -*- 2==7143qffe. 50qjl.; in gtnteit: 714 qffc. 35 q$l. ; in cm. : 714 qm. 35 qdm. S3ei £ret§au§fdjmtten (©ectoren) au§ bem gefammten 9ttauerraerfe rairb oer= fahren, rate bereits für£l)ür= nub geufter= bogen angegeben. 2) t e St o n it e (ftafe) al§ iporjlcoltnber ju berechnen. 3ft eine Sonne ant SPoben 0,50 m., beim ©punblod) 0,60 v)od), bann ift ber mittlere ©urrfjmeffer 0,50 + 0,60 = 110 -f- 2 = 0,55 m. nnb 0,85 lang. 2) er ÄuB if i it ^ alt: $bl. 111,55: 0,8 =0,189970 0,05 = 0,011873125 2lbtr,. 0,85 = 0,201843125 kbm. = 201 kbdm. 843 kbcm. 125 kbmm. = 9? a it m t it t) a It für 202 Stter. Äubif- tn^alt in Stnieu: 201 fbjl. 843,125 fbt. ; in 3o(t: 20fbffj. 184 fbjt. 312,5 fbl. 5D i c ie ©rnnbfläcbe ift 7,30 m. lang, 2,20 m. breit, ber mittlere £urd)meffer 7,30 -\- 2.20 = 9,50m.H-2= 4,75 m., bie £öt)e 22,5 m. Äubif in £) a 1 1 : ZU. 2(btfj.III, 475: 20 = 354,231250 2 = 35,4231250 0,5 = 8,855781250 22,5 = 398,510156250 kbm. = 398 kbm. 510 kbdm. 156 kbcni. 250 kbmm. ; in ginten : 398 fbf jj. 510 fbjl. 156,25 fbl. ; in Boa : 39851 fbffc. 015 fbjt. 625 qt. 5)t e @nt nb f I ä dt) e: ZU. Slbtrj. Ill, 475, 1 : 17 qm. 71 qdm. 15 qcm. 62,5 qmm. ; in glitten: 17 qfjj. 71 qjl. 15,625 qt. ; in ^oll: 1771 qffj. 15 qjt. 62,5 qt. ßreiSumfang (^erip^erie): ZU. $tWt). I, 475 : 14 m. 9 dm. 1 cm. 5 mm. ; in ginien: 14 ffj. 9 jl. 1,5 t. ; in Bolt: 149 ft. 1 St. 5 I. SDie 90ft an t e tf I a ä) e: ZU. 2lbt§. 11,475: 20 =298,30 2 = 29,830 0,5 = 7,4575 22,5 = 335,5875 qm. = 335 qm. 58 qdm. 75 qcm. ; in ginien : 335q|f3. 58qVl. 75 qt. ; in Soli: 3355 qffc. 87 q 3 (. 50 qt. — 30— TUNNEL OR DRAINAGE CANAL. High 8.50 m., wide 7 m. = 15.50 -s- 2 = 7.75 = mean diameter; depth of walling: 62.5 cm., 62.5 + 62.5 = 125 cm., subtracted from 7.75 m. = 6.50 = small diameter; entire length of the tunnel: 115 m. Large diameter: Table, Sec. Ill» 7.75: * 60 = 2828.943750 50 = 2357.453125 5= 2.35.7453125 115 = 5422.142187500 cu. m. Small diameter: Table, Sec. Ill, 6.50: 60 = 1939.975 50 = 1658.3125 5= 165.83125 115 = 3764.11875 cu. m. Large diameter: 5422.142187500 cu.m. Small diamet er: 3764.11875 1658.0234375 cu. m. = 1658 cu. m. 023 cu. dm. 437 cu. cm. 500 cu. mm. Cube of wall of the tunnel. Lines: 1658 cu. ft. 023 cu. in. 437.5 cu. 1.; inches: 165802 cu. ft. 343 cu. in. 750 en. 1. Circumference (outer): Table, Sec. I, 775 : 24 m. 3 dm. 3 cm. 5 mm. ; lines : 24 ft. 3 in. 3.5 1 ; inches: 243 ft. 3 in 5 1. Circumference (inner): Table, Sec. I, 650: 20 m. 4 dm. 1 cm.; lines: 20 ft. 4 in. 1 1.; inches: 204 ft. 1 in. Surface of jacket: Table, Sec. II, 650: 60 = 1224.6 50 — 1020.5 5 = 102.05 115 m. = 2347.15 sqm. = 2347 sq. m. 15 sq. dm.; lines: 2347 sq. ft. 15 sq. in.; inches: 23471 sq. ft... 50 sq. in. Basis of large diameter: Table, Sec. Ill, 1: 47.1490625, less basis of small diameter: Table, Sec. Ill, 1: 33.16625 = 13.9828125 sq.m. = 13 sq. m. 98 sq. dm. 28 sq. cm. 12.5 sq. mm. = Area of the basis (here face) of the wall of £ it it it e l ober 31 b j it g § f a n a I. |)odJ) : 8,50 m., breit 7 m. = 15,50 ■*■ 2 = 7,75 mittlerer £)urcr)meffer ; Waiter ift ftarf 62,5 cm. = 62,5 + 62,5 = 125 cm., ab oon 7,75 m. = 6,50 m. rTeiuer ©urdmteff er ; gauge gauge be§£unnel§: 115 m. ® r o ft e r $) u r c§ m e f f e r. ZU. 3lbt$. Ill, 7 / 75: 60 = 2828,943750 50 = 2357,453125 5 = 235,7453125 115 m. = 5422,142187500 kbm. kleiner © it r $ m e f f e r. £&*• 2lbtMII, 6/50: 60 = 1939,975 50 = 1658,3125 5 == 165,83125 115 m. = 3764,11875 kbm. @r. £)urdjmeffer 5422,142187500 kbm. m. gm rdntteffer 3764,11875 1658,0234375 kbm.= 1658 kbm. 023 kbdm. 437 kbem. 500 kmm. ^ it b i ft it Ij a 1 1 b e § 2Ji a u e r= to e r f S t) o m X u it it e I , in Stuieit : 1658 fbffc. 023 fbjl. 437,5 tU. ; in 3oU : 165802 f&f j$. 343 jfbjl. 75Ö fbl. ÄreiSutnfang (?j3 erip^eri e),' äußerer: ZU. 2lbtl) I, 775:24m. 3 dm. 5 mm.; tit Stnien : 24 ffe. 3 gl. 3,5 1. ; tu Bott: 243 ffe. 3 ji. 5 L ÄretS umfang (Sß e r t p § e r i e), innerer: ZU. 2lbr§. I, 650: 20m. 4 dm. 1cm.; tu Stuten: 20 fjj. 4 $1. 11.; tu Bolt: 204 ff;, 1 3t. Want elf ladder ZU. 2(btlj. II, 650: 60 =1224,6 50 = 1020,5 5 = 102,05 115 m. = 2347,15 qm. = 2347 qm. 15 qdm. ; in Stuten : 2347 qf|.15qal.; ill Boll: 23471 qfjj. 50 qjL (Sruubflädje, grower Tmrdnueff er: ZU. 3lbtl). Ill, 1: 47,1490625; ©runbftädje, »einer S5utd&meffer: ZU. Slbtl). Ill, 1: 33,16625; [nbtra^irt: 13,9828125 qm. = 13 qm. 98 qdm. 28 qcm. 12,5 qmm. -31- the tunnel ; lines: 13 sq. ft. 98 sq. in. 28.125 sq. 1.; inches: 1398 sq. ft. 28 sq. in. 12.5 sq. 1. COOLING- VAT. . 2.10 m. at the base, 1.90 m. at the top = 400 -f- 2 = 2.00 m. mean dia- meter, high 6.4 m. Contents? Cube: Table, Sec. Ill, 200: 6 = 18.84 0.4 = 1.256 6.4 m. — 20.096 cu. m* = 20096 liters capacity: lines: 20 cu. ft. 096 cu. in.: inches: 2009 cu. ft. 600 cu. in. TRUNK OF A TREE. (The diameter taken in lines 210 1. "= 2.1ft.) Measures: at base 2.8 ft., at top 1.4 ft. = 2.8 + 1.4 = 4.2 ft. -5- 2 = 2 ft. 1 in. mean diameter, high 45 ft. Cube: Table, Sec. Ill, 210: 40 = 138.4740 ft. 5 = 17.309250 ft. 45 ft. = 155.783250 cu. ft. = 155 cu. ft. 783 cu. in. 250 cu. 1.; -inches: 15578 cu. ft. 325 cu. in. In the metric measure: 155 cu. m. 783 cu. dm. 250 cu. cm. Trunk of a tree: measures as above. Diameter taken in lines. Table, Sec. 111,21: 40 ft. = 1.38474 5 ft. =0.173092 5 45 ft, = 1.5578325 cu. ft. Place the decimal point 2 places from the left to the right, then the result, the diameter taken in inches, is correct: 155 cu. ft. 783 cu. in. 250 cu. I.; in lines: 1 cu. ft. 557 cu. in. 832.5 cu. 1.; in cm. : leu. m. 557 cu. dm. 832 cu. cm. 500 cu. mm. Proof: The diameter Table, Sec. Ill, 21 : 21 cm, or 21 1. (2.1 in.), r. 0.105 X 0.105 = 0.011025 X 3.14 = 0.03461850 = square * The table 210 (the diameter taken in inches), then the meau diameter is equal to 31 ft. Qua b rat i nlja 1 1 bev ®nntb-, |j i e r © t i r it f i ä dj e , be§ £uunel= tnauerroerfS tit Stuten : 13 qft. 98 q$t. 28,125 ql. ; in 3oU: 1398 qft. 28 qjl. 12,5 q(. £ it b ( f a jj. 2,10 m. am 93oben, 1,90 m. oben = 400 -r- 2 = 2,00 m. mittlerer ©urd)= meffer, l)od) 6,4 m. ^nfjait'? £M. 2(btb. Ill, 200 : 6 = 18,84 0,4 = 1,256 6,4 m. = 20,096 kbm. = 20096 gtter dt a it m i it f) a It ; in gtmeu: 20 fbft. 096fb$(.; in 3ott: 2009 fbft. 600 fb^(. 93 a it m (t a m nt. (ftaä) bem £)urd)meffer ber fit nie ge= nommen: 210 glitten = 2,1 ft.) Sftafje, unten 2,8 ft., oben 1,4 ft. = 2,8 + 1,4 = 4,2 ft. + 2 = 2 ft. 1 hi. mittlerer £)urd»meffer ; Ijod): 45 ft. Äitbiftu^alt: Zbl. 2tbt§. Ill, 210 : 40 = 138,4740 ft. 5 = 17,309250 45 ft. = 155,783250 fbft. = 155 fbft. 783 fbjl. 250 fM.*; in 3ott: 15578 fbft. 325 fb\L ; im metrifd&en ma% : 155 kbm. 783 kbdm. 250 kbem. 93 a it m ft a m m : 9ttcfte, rate oben, hen ©urdjmeffer tit 3°ß genommen. Xbl 2lbtb. Ill, 21 : 40 ft. = 1,38474 5 ft. = 0,1730925 45 ft. = 1,5578325 fbft. Wlan fe^e bag Äomma = 2 2>ectma(= brudntetteu rjou ttnf§ uacb red)t§, al§= baun tft bag ^probnft, ben £)urd)meffer al§ 3°ü genommen, richtig, bemnad) : 155 fbft. 783fb$i. 250 fbl. ; in giuten : 1 fbft. 557 fb$l. 832,5 fbl. ; in cm. : 1 kbm. 557 kbdm. 832 kbem. 500 kbmm. 33eroet§: ben ©urduneffer £bt. Kbit). Ill, 21: 21cm. ober 21 1. (= 2,1 ill.) genommen, r. 0,105 X 0,105 = 0,011025 X 3,14 = 0,03461850 = Qiiabrab@ritnbftädje = 8£ectmalbrnd)= * $5ie Zabeüt 210 (ben £urdjincffev in ^oll pe- nommen), bann tft ber mittlere ©urdimefter 21 if;. -32— basis = 8 decimal places. The diam- eter in inches: Table, Sec. Ill, 21: 2 ft. 1 in. = r. = 1.05 X 1.05 == 1.1025 X 3.14 = 3.461850 square basis = 6 decimal places. The metric measure is the foun- dation of the tables (cm. as diameter). The centimeter, is like the line, the second decimal place next to the whole number. If I place the decimal point 2 places from the left to the right, the relation, the diameter taken in inches, is established. The above is authoritative for all the cube tables. In the measures of length and height there is no variation, whether the figures be named meter, feet or inches. To compute larger dimen- sions, the diameter is taken in inches, while by dimensions to 10 feet in diameter, the results agree exactly with the metric measure as the tables prove. The planes of circles are sub- ject to the same conditions as those prescribed for bases. The rules quoted in the above examples serve for com- putations in constructing machines and wagons, as well as cog-wheels, etc. In conclusion I will say that for the examples I have used figures that are indeed to show how the tables are used in computing planes of circles and bases, but irrespective of tech- nical rules, ftetteu. £)en ©urdjmeffer in goß'- $bi. Slbtf). HI, 21 : 2 ffc. 1 gi. = r. = 1,05 x 1,05 = 1,1025 X 3,14 = 3,461850 Quabrat=@runbfläcf;e = 6 ©ectmalftellen. ©en Tabellen liegt ba§ tnetvifdje Wa$ (cm; im ©urdmteffer) git ©ritubc. £)ev cm. tft, gtetd) ber Stute, bte jroeite ©ectmalbrudjfietk nacrj bent ©etilen; fefce id) ba§ Äomma um 2 £)ecimalbrud)= ftetten con Ituf§ nadj red)t§, jo tft ba§ ^erfyättnifj, ben £oU at» £)urd)meffer genommen, Kjergeftettt. 93orfteIjenbe§ ift für fämmtltdje töubiftabeüen maftgebenb. ^m Sängen^, bejm. ^öljeimtajj, tritt eine $eräuberung ntdjt ein, ob man bte garjleu mit Steter, ftnfj ober £oU u. f. to. benennt. 93et ber 33eredjuung oon größeren SHitienfumen tft ber ©urdjmeffer im 3oü= ma|e 31t oerroenbeu, raäfyrenb bei ©tmen= fionen bt§ 51t 10 §11 fj be§ $)urd)meffer§ bte ^ßrobufte genau mit bem metrifdjen yjlafy, rate bte Nabelten aitäroeifett, über; etnfttmmen. £)ie ^ret§fläd)en unterliegen beufefben ©ebingnngen, raelcfje bei ben Beifpielen bev @runbp$e oorge[d)vteben [tub. 3ur 93erecf)nuug beim Wa[d)tnen= ttnb 2öagenbau, forate Äamm= ttnb 3arnt; ^ftäber, btenen bie in ben oorfterjeriben SBeifpielen angeführten Regeln. 3um ©djhttj ratff idj nodj bemerken, baft td) jtt ben 33etfpteten ^a^Un genom= men t)abe, raetdje raofyt nadjraeifeu fofleu, rate bte Tabellen nur SBeredjmuta. oon tot§; uiib ©runbflädjeu, foraie Körpern ju gebrauchen finb. j[ebocr) ofyue D^ücfftdjt auf bautedt)nifct)e Regeln. SECTION I. Circumference ©JaßfeA. (PERIPHERY.) Ikrcieumfange - Tabellen* -Ro- table I. — CIRCUMFERENCE. ZabtUe I. — &ret0ttmfatt0» Circumference. Circumference. Circumference. Diam- Diam- eter. Diam- eter. 5)urd); nieffer. ft. in. St. lines f. SDnrd); tnefier. ft. ffe- in. if- lines 1, eter. urd) meffer — g&, I, cm. £o.cf). 57 58 59 60 61 62 63 0*01 0.017898 0.018212 0.018526 0.018840 0.019154 0.019468 0.019782 9.02 0.035796 0.036424 0.037052 0.037680 0.038308 0.038936 0.039564 0*03 0.053694 0.054636 0.055578 0.056520 0.057462 0.058404 0.059346 3.04 0.071592 0.072848 0.074104 0.075360 0.076616 0.077872 0.079128 3.05 0.089490 0.091060 0.092630 0.0942 0.095770 0.097340 0.098910 0,06 0.197388 0.109272 0.111156 0.113040 0.114924 0.116808 0.118692 0.07 0.125286 0.127484 0.129682 0.131880 0.134078 0.136276 0.138474 0.08 0.143184 0.145696 0.148208 0.150720 0.153232 0.155744 0.158256 0.09 0.161082 0.163908 0.166734 0.169560 0.172386 0.175212 0.178038 0.1 0.178980 0.182120 0.185260 0.1884 0.191540 0.194680 0.197820 0.2 0=357960 0.364240 0.370520 0.3768 0.383080 0.389360 0.395640 0*3 0.536940 0.546360 0.555780 0.5652 0.574620 0.584040 0.593460 0.4 0.715920 0.728480 0.7-1040 0.7536 0.766160 0.778720 0.791280 0.5 0.8949 0.9106 0.9263 0.9420 0.9577 0.9734 0.9891 0.6 1.073880 1.092720 1.111560 1.1304 1.149240 1.168080 1.186920 0.7 1.252860 1.274840 1.296820 1.3188 1.340780 1.362760 1.384740 0.8 1.431840 1.456960 1.482080 1.5072 1.532320 1.557440 1.582560 0.9 1.610820 1.639080 1.667340 1.6956 1.723860 1.752120 1.780380 1 1.7898 1.8212 1.8526 1.8840 1.9154 1.9468 1.9782 2 3.5796 3.6424 3.7052 3.7680 3.8308 3.8936 3.9564 3 5.3694 5.4636 5.5578 5.6520 6.7462 5.8404 5.9346 4 7.1592 7.2848 7.4104 7.5360 7.6616 7.7872 7.9128 '5 8.9490 9.1060 9.2630 9.42 9.5770 9.7340 9.8910 6 10.7388 10.9272 11.1156 11.3040 11.4924 11.6808 11.8692 7 12.5286 12.7484 12.9682 13.1880 13.4078 13.6276 13.8474 8 14.3184 14.5696 14.8208 15.0720 15.3232 15.5744 15.8256 9 16.1082 16.3905 16.6734 16.9560 17.2386 17.5212 17.8038 10 17.8980 18.2120 18.5260 18.84 19.1540 19.4680 19.7820 11 19.6878 20.0332 20.3786 20.7240 21.0694 21.4148 21.7602 12 21.4776 21.8544 22.2312 22.6080 22.9848 23.3616 23.7384 13 23.2674 23.6756 24.0838 24.4920 24.9002 25.3084 25.7166 14 25.0572 25.4968 25.9364 26.3760 26.8156 27.2552 27.6948 15 26.8470 27.3180 27.7890 28.26 28.7310 29.2020 29.6730 16 28.6368 29.1392 29.6416 30.1440 30.6464 31.1488 31.6512 17 30.4266 30.9604 31.4942 32.0280 32.5618 33.0956 33.6294 18 31.2161 32.7816 33.3468 33.9120 34.4772 35.0424 35.6076 19 34.0062 34.6028 35.1994 35.7960 36.3926 37.9892 37.5858 20 35.7960 36.4240 37.0520 37.68 38.3080 38.9360 39.5640 30 53.6940 54.6360 55.5780 56.52 57.4620 58.4040 59.3460 40 71.5920 72.8480 74.1040 75.36 76.6160 77.8720 79.1280 50 89.49 91.06 92.63 94.20 95.77 97.34 98 91 60 109.3880 109.2720 111.1560 113.04 114.9240 116.8080 1 118.6920 — 48 — Area of the surface of the jacket. — Quabrcttiiifyalt ber ITCantelfläcfye. High. Diameter— in., 1., cm. ©nid) meffer — jl , I., cm. £otf>. 64 65 66 67 68 69 70 0*01 0.020096 0.020410 0.020724 0.021038 0.021352 0.021666 0.021980 0*02 0.040192 0.040820 0.041448 0.042076 0.042704 0.043332 0.048960 0*03 0.060288 0.061230 0.062172 0.063114 0.064056 0.064998 0.065940 0.04 0.080384 0.081640 0.082896 0.084152 0.085408 0.086664 0.087920 0.05 0.100480 0.102050 0.103620 0.105190 0.106760 0.108330 0.1099 0.06 0.120576 0.122460 0.124344 0.126228 0.128112 129996 131880 0*07 0.140672 0.142870 0.145168 0.147266 0.149464 0.151662 0.153860 0.08 0.160768 0.163280 0.165892 0.168304 0.170816 0.173228 0.175840 0.09 0.180864 0. 183690 0.186516 0.189342 0.192168 0. 194994 0.197820 0.1 0.200960 0.2041 0.207240 0.210380 0.213520 0.216660 0.2198 0.2 0.401920 0.4082 0.414480 0.420760 0.427040 0.433320 0.4396 0.3 0.602880 0.6123 0.621720 0.631140 0.640560 0.649980 0.6594 0.4 0.803840 0.8164 0.828960 0.841520 0.854080 0.866640 0.8792 0.5 1.0048 1.0205 1.0362 1.0519 1.0676 1.0833 1.0990 0*0 1.205760 1.2246 1.243440 1.262280 1.281120 1.299960 1.3188 0.7 1.406720 1.4287 1.450680 1.472660 1.494640 1.516620 1.5386 0.8 1.607680 1.6328 1.657920 1.683040 1.708160 1.733280 1.7584 0.9 1.808640 1.8369 1.865160 1.89342 1.921680 1.949940 1.9782 1 2.0096 2.0410 2.0724 2.1038 1.1352 2.1666 2.1980 2 4.0192 4.0820 4.1448 4.2076 4.2704 4.3332 4.3960 3 6.0288 6.1230 6.2172 6.3114 6.4056 6.4998 6.5940 4 8.0384 8.1640 8.2896 8.4152 8.5408 8.6664 8.7920 5 10.0480 10.2050 10.3620 10.5190 10.6760 10.8330 10.99 ' 6 12.0576 12.2460 12.4344 12.6228 12.8112 12.9996 13.1880 7 14.0672 14.2870 14.5068 14.7266 14.9464 15.1662 15.3860 8 16.0768 16.3280 16.5792 16.8304 17.0816 17.3328 17.5840 9 18.0864 18.3690 18.6516 19.9342 19.2168 19.4994 19.7820 to 20.0960 20.41 20.7240 21.0380 21.3520 21.6660 21.98 11 22.1056 22.4510 22.7964 23.1418 23.4872 23.8326 24.1780 12 24.1152 24.4920 24.8688 25.2456 25.6224 25.9992 26.3760 13 26.1248 26.5330 26.9412 27.3494 27.7576 28.1658 28 5740 14 28.1344 28.5740 29.0136 29.4532 29.8928 30.3324 30 7720 15 30.1440 30.6150 31.0860 31.5570 32.0280 32.5990 32.97 16 32.1536 32 6560 33.1584 33.6608 34.1632 34.7656 35.1680 17 34.1632 34.6970 35.2308 35 7646 36.2984 36.8322 37.3660 18 36.1728 36.7380 37.3032 37.8684 38.4336 38.9988 39.5640 19 38.1824 38.7790 39.3756 39.9722 40.5688 41.1654 41.7620 20 40.1920 40.82 41.4480 42.0760 42.7040 43.3320 43.96 30 60.2880 61.23 62.1720 63.1140 64.0560 64.9980 65.94 40 80.3840 81.64 82.8960 84.1520 85.4080 86.6640 87.92 50 100.48 102.05 103.62 105.19 106.76 108.33 109.90 60 120.5760 122.46 124.3440 126.2280 128.1120 129.9960 131.88 49 — Area of the surface of the jacket. — (Quabrattrtfjalt ber tHantelflacfye. nigh. Diameter — in., L, cm. 2)ur$ meffer — j) '., 1., cm. $0&). 71 72 73 74 75 76 77 0.01 0.022294 0.022608 0.022922 0.023236 0.023550 0.023864 0.024178 0*02 0.044588 0.045216 0.045844 0.046472 0.0471 0.047728 0.048356 0*03 0.066882 0.067824 0.068766 0.069708 0.070650 0.071592 0.072534 0*04 0.089176 0.090432 0.091688 0.092944 0.0942 0.095456 0.096712 0*05 0.111470 0.113040 0.114610 0.116180 0.117750 0.119320 0.120890 0*06 0.133764 0.135648 0.137532 0.139416 0.1413 0.143184 0.145068 0*07 0.156058 0.158256 0.160454 0.162652 0.164850 0.167048 0.169246 0*08 0.178352 0.180864 0.183376 0.185888 0.1884 0.190912 0.193424 0*09 0.200646 0.203472 0.206298 0.209124 0.211959 0.214776 0.217602 0*1 0.222940 0.226080 0.229220 0.232360 0.2355 0.238640 0.241780 0.2 0.445880 0.452160 0.458440 0.464720 0.4710 0.477280 0.483560 0*3 0.668820 0.678240 0.687660 0.697080 0.7065 0.715920 0.725340 0.4 0.891760 0.904320 0.916880 0.929440 0.9420 0.954560 0.967120 0.5 1.1147 1.1304 1.1461 1.1618 1.1775 1.1932 1.2089 0.6 1.337640 1.356480 1.375320 1.394160 1.4130 1.431840 1.450680 0.7 1.560580 1.582560 1.604540 1.626520 1.6485 1.670480 1.692460 0.8 1.783520 1.808640 1.833760 1.858880 1.8840 1.909120 1.934240 0.9 2.006460 2.034720 2.062980 2.091240 2.1195 2.147760 2.176020 1 2.2294 2.2608 2.2922 2.3236 2.3550 2.3864 2.4178 2 4.4588 4.5216 4.5844 4.6472 4.71 4.7728 4.8356 3 6.6882 6.7824 6.8766 6.9708 7.0650 7.1592 7.2534 4 8.9176 9.0432 9.1688 9.2944 9.42 9.5456 9.6712 5 11.1470 11.3040 11.4610 11.6180 11.7750 11.9320 12.0890 6 13.3764 13.5648 13.7532 13.9416 14.13 14.3184 14.5068 7 15.6058 15.8256 16.0454 16.2652 16.4850 16.7048 16.9246 8 17.8352 18.0864 18.3376 18.5888 18.84 19.0912 19.3424 9 20.0646 20.3472 20.6228 20.9124 21.1950 21.4776 21.7602 10 22.2940 22.6080 22.9220 23.2360 23.55 23.8640 24. 1780 11 24.5234 24.8688 25.2142 25.5596 25.9050 26.2504 26.5958 12 26.7528 27.1296 27.5064 27.8832 28.26 28.6368 29.0136 13 29.9822 29.3904 29.7986 30.2068 30.6150 31.0232 31.4314 14 31.2116 31.6512 32.0908 32.5304 32.97 33.4096 33.8492 15 33.4410 33.9120 34.3830 34.8540 35.3250 35.7960 36 2670 16 35.6704 36.1728 36.6752 37.1776 37.68 38.1824 38.6848 17 37.8998 38.3336 38.9674 39.5012 40.0350 40.5688 41.1026 18 40.1292 40.5946 41.2596 41.8248 42.39 42.9552 43.5204 19 42.3586 42.8552 43.5518 44.1484 44.7450 45.3416 45.9382 20 44.5880 45.2160 45.8440 46.4720 47.10 47.7280 48.3560 30 66.8820 67.8240 68.7660 69.7080 70.65 71.5920 72.5340 40 89.1760 90.4320 91.6880 92.9440 94.20 95.4560 96.7120 50 111.47 113.04 114.61 116.18 117.75 119.32 120.89 60 133.7640 135.6480 137.5320 139.4160 141.30 143.1840 145.0680 — 50 Areaof the surface of the jacket. — Quabratmfyalt bev tHantelflacfye. High. Diameter- -in., 1., cm. £)uvd)Tne[fer — $t., I., cm. £od). 78 79 80 81 82 83 84 0.01 0.024492 0.024806 0.025120 0.025434 0.025748 0.026062 0.026376 0*02 0.048984 0.049612 0.050240 0.050868 0.051496 0.052124 0.052752 0<03 0.073476 0.074418 0.075360 0.076302 0.077244 0.078186 0.079128 0*04 0.097968 0.099224 0.100480 0.101736 0.102992 0.104248 0.105504 0.05 122480 0.124030 0.1256 0.127170 0.128740 0.130310 0.131880 0.06 0.146952 0.148836 0.150720 0.152604 0.154488 0.156372 0.158256 0.07 0.171444 0.173642 0.175840 0.178038 0.180236 0.182434 0.184632 0.08 0.195936 0.198448 0.200960 0.203472 0.205984 0.208496 0.211008 0.09 0.220428 0.223254 0.226080 0.228906 0.231732 0.234558 0.237384 0.1 0.244920 0.248060 0.2512 0.254340 0.257480 0.260620 0.263760 0.2 0.489840 0.496120 0.5024 0.508680 0.514960 0.521240 0.527520 0.3 0.734760 0.744180 0.7536 0.763020 0.772440 0.781860 0.791280 0.4 0.979680 0.992240 1.0048 1.017360 1.039920 1,042480 1.055040 0.5 1.2246 1.2403 1.2560 1.2717 1.2874 1.3031 1.3188 0.6 1.469520 1.488360 1.5072 1.526040 1.54488 1.563720 1.582560 0.7 1.714440 1.736420 1.7584 1.780380 1.802360 1.824340 1.846320 0*8 1.959360 1.984480 2.0096 2.034720 2.059840 2.084960 2.110080 0.9 2.204280 2.232540 2.2608 2.289060 2.317320 2.345580 2.373840 1 2.4492 2.4806 2.5120 2.5434 2.5748 2.6062 2.6376 2 4.8984 4.9612 5.0240 5.0868 5.1496 5.2124 5.2752 3 7.3476 7.4418 7.5360 7.6302 7.7244 7.8186 7.9128 ■ 4 9.7968 9 9224 10.0480 10.1736 10.2992 10.4248 10.5504 5 12.2460 12.4030 12.56 12.7170 12.8740 13.0310 13.1880 6 14.6952 14.8836 15.0720 15.2604 15.4488 15.6372 15.8256 7 17.1444 17.3642 17.5840 17.8038 18.0236 18.2434 18.4632 8 19.5936 19 8448 20.0960 20.3472 20.5984 20.8496 21.1008 9 22.0428 22.3254 22.6080 22.8906 23.1732 23.4558 23.7384 10 24.4920 24.8060 25.12 25.4340 25.7480 26.0620 26.3760 11 26.9412 27.2866 27.6320 27.9774 28.3228 28.6682 29.0136 12 29.3904 29.7672 30.1440 30.5208 30.8976 31.2744 31.6512 13 31.8396 32.2478 32.6560 33.0642 33.4724 33.7806 34.2888 14 33.2888 34.7284 35.1680 35.6076 36.0472 36.3868 36.9264 15 35.7380 37.2090 37.68 38.1510 38.6220 38.9930 39.5640 16 38.1872 39.6896 40.1920 40.6944 41.1968 41.5992 42.2016 17 40.6364 42.1702 42.7040 43.2378 43.7716 44.2054 44.8392 18 43.0856 44.6508 45.2160 45.7812 46.2464 46.8116 47.4768 19 45.5348 47.1314 47.7280 48.3246 48.8212 49.4178 50.1144 20 48.9840 49.6120 50.24 50.8680 51.4960 52.1240 52.7520 30 73.4760 74.4180 75.36 76.3020 77.2440 78.1860 79.1280 40 97.9680 99.2240 100.48 101.7360 102.9920 104.2480 105.5040 50 122.46 124.03 12.560 127.17 128.74 130.31 131.88 60 146.9520 148.8360 150.72 152.6040 154.4880 156.3720 [158.2560 51 Area of the surface of the jacket. — (Puafcrattnfyalt ber ITTantelfläcfye. High. Diameter— in., 1., cm. £urd)mef|er — jl., I., cm. 85 86 87 88 89 90 91 0*01 0.02 0*03 0*04 0.05 0.06 0.0? 0.08 0.09 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 40 50 60 0.026690 0.053380 0.080070 0.106760 0.133450 0.160140 0.186830 0.213520 0.240210 0.2669 0.5338 0.8007 1.0676 1.3345 1.6014 1.8683 2.1352 2.4021 2.6690 5.3380 8.0070 10.6760 13.3450 16.0140 18.6830 21.3520 24.0210 26.69 29.3590 32.0280 34.6970 37.3660 40.0350 42.7040 45.3730 48.0420 50.7110 53.38 80.07 106.76 133.45 160.14 0.027004 0.054008 0.081012 0.108016 0.135020 0.162024 0.189028 0.216032 0.243036 0.270040 0.540080 0.810120 1.080160 1.3502 1.620240 1.890280 2.160320 2.430360 2.7004 5.4008 8.1012 10.8016 13.5020 16.2024 18.9028 21.6032 24.3036 27.0040 29.7044 32.4048 35.1052 37.8056 40.5060 43.2064 45.9068 48.6072 51.3076 54.0080 81.0120 108.0160 135.02 162.0240 0.027318 0.054636 0.081954 0.109272 0.136590 0.163908 0.191226 0.218544 0.245862 0.273180 0.546360 0.819540 1.092720 1.3659 1.639080 1.912260 2.185440 2.458620 2.7317 5.4636 8.1954 10.9272 13.6590 16.3908 19.1226 21.8544 24.5862 27.3180 30.0498 32.7816 35.5134 38.2452 40.9770 43.7088 46.4406 49.1724 51.9042 54.6360 81.9540 109.2720 136.59 163.9080 0.027632 0.055264 0.082896 0.110528 0.138160 0.165792 0.193424 0.221056 0.248688 0.276320 0.552640 0.828960 1.105280 1.3816 1.657920 1.934240 2.210560 2.486880 2.7632 5.5264 8.2896 11.0528 13.8160 16.5792 19.3424 22.1056 24.8688 27.6320 30.3952 33.1684 35.9316 38.6948 41.4580 44.2512 46.9744 49.7376 52.5008 55.2640 82.8960 110.5280 138.16 165.7920 0.027946 0.055892 0.083838 0.111784 0.139730 0.167676 0.195622 0.223568 0.251514 0.279460 0.558920 0.838380 1.117840 1.3973 1.676760 1.956220 2.235680 2.515140 2.7946 5.5892 8.3838 11.1784 13.9730 16.7676 19.5622 22.3568 25.1514 27.9460 30.7406 33.5352 36.3298 39.1244 41.9190 44.7136 47.5082 50.3028 53.0974 55.8920 83.8380 111.7840 139.73 167.6760 0.028260 0.056520 0.084780 0.113040 0.1413 0.169560 0.197820 0.226080 0.254340 0.2826 0.5652 0.8478 1.1304 1.4130 1.6956 1.9782 2.2608 2.5434 2.8260 5.6520 8.4780 11.3040 14.13 16.9560 19.7820 22.6080 25.4340 28.26 31.0860 33.9120 36.7380 39.5640 42.39 45.2160 48.0420 50.8680 53.6940 56.52 84.78 113.04 141.30 169.56 0.028574 0.057148 0.085722 0.114296 0.142870 0.171444 0.200018 0.228592 0.257166 0.285740 0.571480 0.857220 1.142960 1.4287 1.714440 2.000180 2.285920 2.571660 2.8574 5.7148 8.5722 11.4296 14.2870 17.1444 20.0018 22.8592 25.7166 28.5740 31.4314 34.2888 37.1462 40.0036 42.8610 45.7184 48.5758 51.4332 54.2906 57.1480 85.7220 114.2960 142.87 1171.4440 — 52- Areaof the surface of the jacket. — ^uabrattnt|alt bet 2TtanteIft5d?c. High. Diameter — in., L, cm. £)urdjnief]er — §) ., 1., cm. £odj. 92 93 94 95 96 97 98 0.01 0.028888 0.029202 0.029516 0.029830 0.030144 0.030458 0.030772 0*02 0.057776 0.058404 0.059032 0.059660 0.060288 0.060916 0.061544 0.03 0.086664 0.087606 0.088548 0.089490 0.090432 0.091374 0.092316 0*04 0.115552 0.116808 0.118064 0.119320 0.120576 0.121832 0.123088 0*05 0.144440 0.146010 0.147580 0.149150 0.150720 0.152290 0.153860 0*06 0.173328 0.175212 0.177096 0.178980 0.180864 0.182748 0.184632 0*07 0.202216 0.204414 0.206612 0.208810 0.211008 0.213206 0.215404 0*08 0.231104 0.233616 0.236128 0.238640 0.241152 0.243664 0.246176 0*09 0.259992 0.262818 0.265644 0.268470 0.271296 0.274122 0.276948 0.1 0.288880 0.292020 295160 2983 0.301440 0.304580 307720 0,2 0.577760 0.584040 0.590320 0.5966 0.602880 0.609160 0.615440 0.3 0.866640 0.876060 0.885480 0.8949 0.904320 0.913740 0.923160 0.4 1.155520 1.168080 1.180640 1.1932 1.205760 1.218320 1.230880 0.5 1.4444 1.4601 - 1.4758 1.4915 1.5072 1.5229 15386 0.6 1.733280 1.752120 1.770960 1.7898 1.808640 1.827480 1.846320 0.7 2.022160 2.044140 2.066120 2.0881 2.110080 2.132060 2.154040 0.8 2.311040 2.336160 2.361280 2.3864 2.411520 2.436640 2.461760 0.9 2.599920 2.620180 2.656440 2.6847 2.712960 2.741220 2.769480 1 2.8888 2.9202 2.9516 2.9830 3.0144 3.0458 3.0772 2 5.7776 5.8404 5.9032 5.9660 6.0288 6 0916 6.1544 3 8.6664 8.7606 8.8548 8.9490 9.0432 9.1374 9.2316 • 4 11.5552 11.6808 11.8064 11.9320 12.0576 12.1832 12.3088 5 14.4440 14.6010 14.7580 14.9150 15.0720 15.2290 15.3860 6 17.3328 17 5212 17.7096 17.8980 18.0864 18.2748 18.4632 7 20.2216 20.4414 20.6612 20.8810 21.1008 21.3206 21.5404 8 23.1104 23.3616 23.6128 23.8640 24.1152 24.3664 24.6176 9 25.9992 26.2818 26.5644 26.8470 27.1296 27.4122 27.6948 10 28.8880 29.2020 29.5160 29.83 30.1440 30.4580 30.7720 11 31.7768 32.1222 32.4676 32.8130 33.1584 33.5038 33.8492 12 34.6656 35.0424 35.4192 35.7960 36.1728 36.5496 36.9264 13 37.5544 37.9626 38.3708 38.7790 39.1872 30.5954 40.0036 14 40.4432 40.8828 41.3224 41 7620 42.2016 42.6412 43.0808 15 43.3320 43.8030 44.2740 44.7450 45.2160 45.6870 46.1580 16 46.2208 46.7232 47.2256 47.7280 48.2304 48.7328 49.2352 17 49.1096 49 6434 50.1772 50.7110 51.2448 51.7786 52.3124 18 51.9984 52.5636 53.1288 53.6940 54 2592 54.8244 55.3896 19 54.8872 55.4838 56.0804 56.6770 57.2736 57.8702 58.4668 20 57.7660 58 4040 59.0320 59.66 60.2880 60.9160 61.5440 30 86.664 87.6060 88.5480 89.49 90.4320 91.3740 92.3160 40 115.5520 116.8080 118.0640 119.32 120.5760 121.8320 123.0880 50 144.440 146.01 147.58 149.15 150.72 152.29 153.86 60 173.3280 175.2120 177.0960 178.98 180.8640 182.7480 184.6320 — 53 — Area of the surface of the jacket. -*- (Quctbrattnfyalt ber IHantelflädje. High. Diainetei — in., 1., cm. £)uvd) mefjer — $1 , I., cm. £od). 99 100 101 102 103 104 105 0*01 0.031086 0.0314 0.031714 0.032028 0.032342 0.032656 0.032970 0*02 0062172 0.0628 0.063428 0.064056 0.064684 0.065312 0.065940 0*03 0.093258 0.0942 0.095142 0.096084 097026 0.097968 0.098910 0*04 0.124344 0.1256 0.126856 0.128112 0.129368 0.130624 0.131880 0*05 0.155430 0.1570 0.158570 0.160140 0.161710 0.163280 0.164850 0,06 0.186516 . 0.1884 0.190284 0.192168 0.194052 0.195936 0-197820 0*07 0.217602 0.2198 0.221998 0.224196 0.226394 0.228592 0.230790 0*08 0.248688 0.2512 0.253712 0.256224 0.258736 0.261248 0.263760 0*09 0.279774 0.2826 0.285426 288252 0.291078 0.293904 0.296730 0*1 0.310860 0.3140 0.317140 0.320280 0.323420 0.326560 0.3297 0*2 0.621720 0.6280 0.634280 0.640560 0.646840 0.653120 0.6594 0.3 0.932580 0.9420 0.951420 0.960840 0.970260 0.979680 0.9891 0*4 1.243440 0.2560 1 268560 1.281120 1.293680 1.306240 1.3188 0*5 1.5543 1.57 1.5857 1.6014 1.6171 1.6328 1.6485 0*6 1.865160 1.8840 1.902840 1.921680 1.940520 1.959360 1.9782 0*7 2.176020 2.1980 2.219980 2.241960 2 263940 2.285920 3.3079 0*8 2.486880 2.5120 2 537120 2.562240 2.587360 2.612480 2.6376 0,9 2.797740 2.8260 2.854260 2.882520 2.910780 2.939040 2.9673 1 3.1086 3.14 3.1714 3.2028 3 2342 3.2656 3.2970 2 6.2172 6.28 6.3428 6.4056 6.4684 6.5312 6.5940 3 9.3258 9.42 9.5142 9.6084 9.7026 9.7968 9.8910 4 12.4344 12.56 12.6856 12.8112 12.9368 13.0624 13.1880 5 15.5430 15.70 15.8570 16.0140 16.1710 16 3280 16.4850 6 18.6516 18.84 19.0284 19.2168 19.4052 19.5936 19.7820 7 21.7602 21.98 22.1998 22.4196 22.6394 22 8592 23.0790 8 24.8688 25.12 25.3712 25 6224 25.8736 26.1248 26.3760 9 27.9774 28.26 28.5426 28.8252 29.1078 29.3904 29.6730 10 31.0860 31.40 31.7140 32 0280 32.3420 32.6560 32.97 11 34.1946 34 54 34.8854 35.2308 35.5762 35.9216 36.2670 12 37.3032 37.68 38.0568 38.4336 38.8104 39.1872 39.5640 13 40.4118 40.80 41.2282 41.6364 42,0446 42.4528 42.8610 14 43.5204 43.96 44.3996 44.8392 45.2788 45.7184 46.1580 15 46.6290 47.10 47.5710 48.0420 48.5130 48.9840 49.4550 16 49.7376 50.24 50.7424 51.2448 51.7472 52.2496 52.7520 17 52.8462 53.38 53.9138 54 4476 54.9814 55.5152 56.0490 18 55.9548 56.52 57.0852 57.6504 58.2156 58.7808 59.3460 19 59.0634 59.66 60.2566 60.8532 61.4498 62.0464 62.6430 20 62 1720 62.80 63.4280 64.0560 64.6840 65.3120 65.94 30 93.2580 94.20 95.1420 96.0840 97.0260 97.9630 98.91 40 124.3440 125.60 126.8560 128.1120 129.3680 130.6240 131.88 50 155.43 • 157.0 158.57 160 14 161.71 163.28 164.85 60, 1 186.5160 188.40 190.2840 192.1680 194.0520 195.9360 197.82 54- Area of the surface of the jacket. — Qiia&rattnfyalt ber IHantelfifäcfye. High. Diameter- —in., 1., cm. ©uvdjmeffer — it i. , cm. £od). 106 107 108 109 110 Ill 112 0.01 0.033284 0.033598 0.033912 0.034226 0.034540 0.034854 0.035168 0*02 0.066568 0.067196 0.067824 0.068452 0.069080 0.069708 0.070336 0*03 0.099852 0.100794 0.101736 0.102678 0.10360 0.104562 0.105504 0*04 0.133136 0.134392 0.135648 0.136904 0.138160 0.139416 0.140672 0*05 0.166420 0.167990 0.169560 0.171130 0.1727 0.174270 0.175840 0,06 0.199704 0.201588 0.203472 0.205356 0.207240 0.209124 0.211008 0*07 0.232988 0.235186 0.237384 0.239582 0.241780 0.243978 0.246176 0*08 0.266272 0.268784 0.271296 0.273808 0.276320 0.278832 0.281344 0.09 0.299556 0.302382 0.305208 0.308034 0.310860 0.313686 0.316512 0*1 0.332840 0.335980 0.339120 0.342260 0.3454 0.348540 0.351680 0*2 0.665680 0.671960 0.678240 0.684520 0.6908 0.697080 0.703360 0.3 0.998520 1.007940 1.017360 1.026780 1.0362 1.045620 1.055040 0.4 1.331360 1.343920 1.356480 1.369040 1.3816 1.394169 1.406720 0.5 1.6642 1.6799 1.6956 1.7113 1.7270 1.7427 1.7584 0.6 1.997040 2.015880 2.034720 2.053560 2.0724 2.091240 2.110080 0.7 2.329880 2.351860 2.373840 2.395820 2.4178 2.439780 2.461760 0.8 2.662720 2.687840 2.712960 2.738080 2.7632 2.788320 2.813440 0.9 2.995560 3.023820 3.052080 2.080340 3.1086 3.136860 3.165120 1 3.3284 3.3598 3.3912 3.4226 3.4540 3.4854 2.5168 2 6.6568 6.7196 6.7824 6.8452 6.9080 6.9708 7.0336 3 9.9852 10.0794 10.1736 10.2678 10.3620 10.4562 10.5504 4 13.3136 13.4392 13.5648 13.6904 13.8160 13.9416 14.0672 ■ 5 16.6420 16.7990 16.9560 17.1130 17.27 17.4270 17.5840 6 19.9704 20.1588 20.3472 20.5356 20.7240 20.9124 21.1008 7 23.2988 23.5186 23.7384 23.9582 24.1780 24.3978 24.6176 8 26.6272 26.8784 27.1296 27.3808 27.6320 27.8832 28.1344 9 29.9556 30.2382 30.5208 30.8034 31.0860 31.3686 31.6512 10 33.2840 33.5980 33.9120 34.2260 34.54 34.8540 35.1680 11 36.6124 36.9578 37.3032 37.6486 37.9940 38.3394 38.6848 12 39.9408 40.3176 40.6944 41.0712 41.4480 41.8248 42.2016 13 43.2692 43.6774 44.0856 44.4938 44.9020 45.3102 45.7184 14 46.5976 47.0372 47.4768 47.9164 48.3560 48.7956 49.2352 15 49.9260 50.3970 50.8680 51.3390 51.81 52.2810 52.7520 16 53.2544 53.7568 54.2592 54.7616 55.2640 55.7664 56.2688 17 56.5828 57.1166 57.6504 58.1842 58.7180 59.2518 59.7856 18 59.9112 60.4764 61.0416 61.6068 62.1720 62.7372 63.3024 19 63.2396 63.8362 64.4328 65.0294 65.6260 66.2226 66.8192 20 66.5680 67.1960 67.8240 68.4520 69.08 69.7080 70.3360 30 99.8520 100.7940 101.7360 102.6780 103.62 104.5620 105.5040 40 133.1360 134.3920 135.6480 136.9040 138.16 139.4160 140.6720 50 166.42 167.99 169.56 171.13 172.70 174.27 175.84 60 199.7040 201.5880 203.4720 205,3560 207.24 209.1240 211.0080 -55- Area of the surface of the jacket. -*- CQuabratinfyalt ber IHatttelftädje. High. Diameter — in., 1., cm. £>urdjme|fer — 5 ., 1., cm. .pod). 113 114 115 116 117 118 119 0.01 0.035482 0.035796 0.036110 0.036424 0.036738 0.037052 1 0.037366 0.02 0.070964 0.071592 0-072220 0.072848 0.073476 0.074104 0.074732 0.03 0.106446 0.107388 0.108330 0.109272 0.110214 0.111156 0.112098 0.04 0.141928 0.143148 0.144440 0.145696' 0.146952 0.148208 0.149464 0.05 0.177410 0.178980 0.180550 0.182120 0.183690 0.185260 0.186830 0.06 0.212892 0.214776 0.216660 0.218544! 0.220428 0.222312 0.224196 0.07 0.248374 0.250572 0.252770 0.254968 0257166 0.259364 0.261562 0.08 0.283856 0.286368 0.288880 0.291392 0.293904 0.296416 0.298928 0.09 0.319338 0.322164 0.324990 0.327816 0.330642 0.333468 0.336294 0.1 0.354820 0.357960 0.3611 0.364240 0.367380 0.370520 0.373660 0.2 0.709640 0.715920 0.7222 0.728480 0.734760 0.741040 0.747320 0.3 1.064460 1.073880 1.0833 1.092720 1.102140 1.111560 1.120980 0.4 1.419280 1.431840 1.4444 1.456960 1.469520 1.482080 1.494640 0.5 1.7741 1.7898 1.8055 1.8212 1.8369 1.8526 1.8683 0.6 2.128920 2.147760 2.1666 2.185440 2.204280 2.223120 2.241960 0.7 2.483740 2.505720 2.5277 2.549680 2.571660 2.593640 2.615620 0.8 2.838560 2.863680 2.8888 2.913920 2.939040 2.964160 2.989280 0.9 3.193380 3.221640 3.2499 2.378160 3.306420 3.334680 3.362940 1 3.5482 3.5796 3.6110 3.6424 3.6738 3.7052 3.7366 2 7.0964 7.1592 7.2220 7.2848 7.3476 7.4104 7.4732 3 10.6446 10.7388 10.8330 10.9272 11.0214 11.1156 11.2098 4 14.1928 14.3184 14.4440 14.5696 14.6952 14.8208 14.9464 5 17.7410 17.8980 18.0550 18.2120 18 3690 18.5260 18.6830 6 21.2892 21.4776 21.6660 21.8544 22.0428 22.2312 22.4196 7 24.8374 25.0572 25.2770 25.4968 25.7166 25.9364 26.1562 8 28.3856 28.6368 28.8880 29.1392 29.3904 29.6416 29.8928 9 31.9338 32.2164 32.4990 32.7816 33.9642 33.3468 33.6294 10 35.4820 35.7960 36.11 36.4240 36.7385 37.0520 37.3660 11 39.0302 39.3756 39.7210 40.0664 40.4118 40.7572 41.1026 12 42.5784 42.9552 43.3320 43.7088 44.0856 44.4624 44.8392 13 46.1266 46.5348 46.9430 47.3512 47.7594 48.1676 48.5758 14 49.6748 50.1144 50.5540 50.99g6 51.4332 51.8728 52.3124 15 53.2230 53.6940 54.1650 54.6360 55.1070 55.5780 56.0490 16 56.7712 57.2736 57.7760 58.2784 58.7808 59.2832 59.7856 17 60.3194 60.8532 61.3870 61.9208 62.4546 62.9884 63.5222 18 63.8676 64.4328 64.9980 65.5632 66.1284 66.6936 67.2588 19 67.4158 68.0124 68.6090 69.2056 69.8022 70.3988 70.9954 20 70.9640 71.5920 72.22 72.8480 73.4760 74.1040 74.7320 80 106.4460 107.3880 108.33 109.2720 110.2140 111.1560 112.0980 40 141.9280 143.1840 144.44 145.6960 146.9520 148.2080 149.4640 50 177.41 178.98 180.55 182.12 183.69 185.26 186.83 60 J 212.8920 214.7760 216.66 1 218.5440 220.4280 222.3120 224.1960 — 56 — Area of the surface of the jacket. — (Quabratin^alt ber tftantelftäcfye. High. Diameter -in., 1., cm. £)uvcf)meffei — §t., L, cm. £od). 120 121 122 123 124 125 126 0.01 0.037680 0.037994 0.038308 0.038622 0.038936 0.039250 0.039564 0*02 0.075360 0.075988 0.076616 0.077244 0.077872 0.0785 0.079128 0.03 0.113040 0.113982 0.114924 0.115866 0.116808 0.117750 0.118692 0.04 0.150720 0.151976 0.153232 0.154488 0.155744 0.1570 0.158256 0.05 0.1884 0.189970 0.191540 0.193110 0.194680 0.196250 0.197820 0.06 0.226080 0.227964 0.229848 0.231732 0.233616 0.2355 0.237384 0.07 0.263760 0.265958 0.268156 0.270354 0.272552 0.274750 0.276948 0.08 0.301440 0.303952 0.306464 0.308976 0.311488 0.3140 0.316512 0.09 0.339120 0.341946 0.344772 0.347598 0.350424 0.353250 0.356076 0.1 0.3768 0.379940 0.383080 0.386220 0.389360 0.3925 0.395640 0.2 0.7536 0.759880 0.766160 0.772440 0.778720 0.7850 0.791280 0.3 1.1304 1.139820 1.149240 1.158660 1.168080 1.1775 1.186920 0.4 1.5072 1.519760 1.532320 1.544880 1.557440 1.57 1.582560 0.5 1.8840 1.8997 1.9154 19311 1.9468 1.9625 1.9782 0.6 2.2608 2.279640 2.298480 2.317320 2.336160 2.3550 2.373840 0.7 2.6376 2.659580 2.681560 2.703540 2.725520 2.7475 2.769480 0*8 3.0144 3.039520 3.064640 3.089760 3.114880 3.14 3.165120 0.9 3.3912 3.419460 3.447720 3.475980 3.504240 3.5325 3.560760 1 3.7680 3.7994 3 8308 3.8622 3.8936 3.9250 3.9564 2 7.5360 7.5988 7.6616 7.7244 7.7872 7.85 7.9128 3 11.3040 11.3982 11.4924 11.5866 11.6808 11.7750 11.8692 4 15.0720 15.1976 15.3232 15.4488 15.5744 15.70 15.8256 5 18.84 18.9970 19.1540 19.3110 19.4680 19.6250 19.7820 6 22.6080 22.7964 22.9848 23.1732 23.3616 23.55 23.7384 7 26.3760 26.5958 26.8156 27.0354 27.2552 27.4750 27.6948 8 30 1440 30.3952 30.6464 30.8976 31.1488 31.40 31.6512 9 33.9120 34.1946 34.4772 34.7598 35.0424 35.3250 35.6076 10 37.68 37.9940 38.3080 38.6220 38.9360 39.25 39.5640 11 41.4480 41.7934 42.1388 42.4842 42.8296 43.1750 43.5204 12 45.2160 45.5928 45.9696 46.3464 46.7232 47.10 47.4768 13 48.9840 49.3922 49.8004 50.2086 50.6168 50.0250 51.4332 14 52 7520 53.1916 53.6312 54.0708 54.5104 54.95 55.3896 15 56.52 56.9910 57.4620 57.9330 58.4040 58.8750 59.3460 16 60.2880 60.7904 61.2928 61.7952 62.2976 62.80 63.3024 17 64.0560 64.5898 65.1236 65.6574 66.1912 66.7250 67.2588 18 67.8240 68.3892 68.9544 69.5196 70.0848 70.65 71.2152 19 71.5920 72.1886 72.7852 73.3818 73.9784 74.5750 75.1716 20 75.36 75.9880 76.6160 77.2440 77.8720 78.50 79.1280 30 113.04 113.9820 114.9240 115.8660 116.8080 117.75 118.6920 40 150.72 151.9760 153.2320 154.4880 155.7440 157.0 158.2560 50 188.40 189.97 191.54 193.11 194.68 196.25 197.82 60 226.08 227.9640 229.8480 231.7320 233.6160 235.50 237.384 -57- Area of the surface of the jacket. — jC^uabrattnfyalt ber JTtantelffacfye. High. Diameter— in., I., cm. £>urcf)meffer — j (., (., cm. $od). 127 128 129 130 131 132 133 0.01 0.039878 0.040192 0.040506 0.04082C »| 0.041134 0.041448 0.041762 0.02 0.079756 0.080384 0.081012 0.08164C 0.082268 0.082896 0.083524 0*03 0.11963 A 0.120576 0.121518 0.122460 0.123402 0.124344 0.125286 0,04 0.159512 0.160768 0.162024 0.163280! 0.164536 0.165792 0.167048 0,05 0. 199390 0.200960 0. 202530 0.20 U 0.205670 0.207240 0.208810 0.06 0.239268 0.241152 0.243036 0.244920 0.246804 0.248688 0.250572 0*011 0.279146 0.281344 0.283542 0.285740 0.287938 0.290136 0.292334 0,08 0.319024 0.321536 0.324048 0.326560 0.329072 0.331584 0.334096 0,09 0.358902 0.361728 0.364554 0.367380 0.370306 0.373032 0.375858 0*1 0.398780 0-401920 0.405060 0.4082 0.411340 0.414480 0.417620 0*2 0.797560 0.803840 0.810120 0.8164 0.822680 0.828960 0.835240 0,3 1.196340 1.205760 1.215180 1.2246 1.234020 1.243440 1.252860 0.4 1.595120 1.607680 1.620240 1.6328 1.645360 1.657920 1.670480 0.5 1.9939 2.0096 2.0253 2.0410 3.0567 2.0724 2.0881 0*6 2.392680 2.411520 2.430360 2.4492 2.468040 2.486880 2.205720 0*7 2.791460 2.813440 2.835420 2.8574 2.879380 2.901360 2.923340 0.8 3.190240 3.215360 3.240480 3.2656 3.290720 3.315840 3.340960 0.9 3.589020 3.617280 3.645540 3.6738 3.702060 3.730320 3.758580 1 3.9878 4.0192 4.0506 4 0820 4.1134 4.1448 4.1762 2 7.9756 8.0384 8.1012 8.1640 8.2268 8.2896 8.3524 3 11.9634 12.0576 12.1518 12.2460 12.3402 12.4344 12.5286 4 15.9512 16.0768 16.2024 16.3280 16.4536 16.5792 16.7048 5 19.9390 20.0960 20.2530 20.41 20 5670 20.7240 20.8810 6 23.9268 24.1152 24.3036 24.4920 24.6804 24.8688 25.0572 1 27.9146 28.1344 28.3542 28.5740 28.7938 29.0136 29.2334 8 31.9024 32.1536 32.4048 32.6560 32.9072 33.1584 33.4096 9 35.8902 36.1728 36.4554 36.7380 37.0206 37.3032 37.5858 10 39.8780 40.1920 40.5060 40.82 41.1340 41.4480 41.7620 11 43.8658 44.2112 44.5566 44.9020 45.2474 45.5928 45.9382 12 47.8536 48.2304 48.6072 48.9840 49.3608 49.7376 50.1144 13 51.8414 52.2496 52.6578 53.0660 53.4742 53.8824 54.2906 14 55.8292 56.2688 56.7084 57.1480 57.5876 58.0272 58.4668 15 59.8170 60.2880 60.7590 61.23 61.7010 62.1720 62.6430 16 63.8048 64.3072 64.8096 65.3120 65.8144 66.3168 66.8192 17 67.7926 68.3264 68.8602 69.3940 69.9278 70.4616 70.9954 18 71.7804 72.3456 72.9108 73.4760 74,0412 74.6064 75.1716 19 75.7683 76.3648 76.9614 77.5580 78.1546 78.7512 79.3478 20 79.7560 80.3840 81 0120 81.64 82.2680 82.8960 83.5240 30 119.6340 120.5760 121.5180 122.46 123.4020 124.3440 125.2860 40 159.5120 160.7680 162.0240 163.28 164.5360 165.7920 167.0480 50 199.39 200.96 202.53 204.10 205.67 207.24 208.81 60 239.2680 1 241.1520 243.0360 244.92 1 246.8040 248.6880 250.5720 58 — Area of the surface of the jacket. — (Quabrattttfyatt ber Ittantelftctcfye. High. f Diameter- -in., 1., ein. ©urdjmeffer — jl. I., cm. £od). 134 135 136 137 138 139 140 0.01 0.042076 0.042390 0.042704 0.043018 0.043332 0.043646 0.043960 0*02 0.084152 0.084780 0.085408 0.086036 0.086664 0.087292 0.087920 0.03 0.126228 0.127170 0-128112 0.129054 0.129996 0.130938 0.131880 0.04 0.168304 0.169560 0.170816 0.172072 0.173328 0.174584 0.175840 0.05 0.210380 0.211950 0.213520 0.215090 0. 216660 0.218230 0.2198 0.06 0.252456 0.254340 0.256224 0.258108 0.259992 0.261876 0.263760 0.07 0.294532 0.296730 0.298928 0.301126 0.303324 0.305522 0.307720 0.08 0.336608 0.339120 0.341632 0.344144 0.346656 0.349168 0.351680 0.09 0.378684 0.381510 0.384336 0.387162 0.389988 0.392814 0.395640 0.1 0.420760 0.4239 0.427040 0.430180 0.433320 0.436460 0.4396 0.2 0.841520 0.8478 0.854080 0.860360 0.866640 0.872920 0.8792 0.3 1.262280 1.2717 1.281120 1.290540 1.299960 1.309380 1.3188 0.4 1.683040 1.6956 1.708160 1.720720 1.733280 1.745840 1.7584 0.5 2.1038 2.1195 2.1352 2.1509 2.1666 2.1823 2.1980 0.6 2.524560 2.5434 2.562240 2.581080 2.599920 2.618760 2.6376 0.7 2 945320 2.9673 2.989280 3.011260 3.033240 3.055220 3.0772 0.8 3.366080 3.3912 3.416320 3.441440 3.466560 3.491680 3.5168 0.9 8.786840 3.8151 3.843360 3.871620 3.899880 3.928140 3.9564 1 4.2076 4.2390 4.2704 4.3018 4.3332 4.3646 4.3960 2 8.4152 8.4780 8.5408 8.6036 8.6664 8.7292 8.7920 3 12.6228 12.7170 12.8112 12.9054 12.9996 13.0938 13.1880 4 16.8304 16.9560 17.0816 17.2072 17.3328 17.4584 17.5840 5 21.0380 21.1950 21.3520 21.5090 21.6660 21.8230 21.98 6 25.2456 25.4340 25.6224 25.8108 25.9992 26.1876 26.3760 7 29.4532 29.6730 29.8928 30.1126 30.3324 30.5522 30.7720 8 33.6608 33.9120 34.1632 34.4144 34.6656 34.9168 35.1680 9 37.8684 38.1510 38.4336 38.7162 38.9988 39.2814 89.5640 10 42.0760 42.39 42.7040 43.0180 43.3320 43.6460 43.96 11 46.2836 46.6290 46.9744 47.3198 47.6652 48.0106 48.3560 12 50.4912 50.8680 51.2448 51.6216 51.9984 52.3752 52.7520 13 54.6988 55.1070 55.5152 55.9234 56.3316 56.7398 57.1480 14 58.9064 59.3460 59.7856 60.2252 60.6648 61.1044 61.5440 15 63.1140 63.5850 64.0560 64.5270 64.9980 65.4690 65.94 16 67.3216 67.8240 68.3264 68.8288 69.3312 69.8336 70.3360 17 71.5292 72.0630 72.5968 73.1306 73.6644 74.1982 74.7320 18 75.7368 76.3020 76.8672 77.4324 77.9976 78.5628 89.1280 19 79.9444 80.5410 81.1376 81.7342 82.3308 82.9274 83.5240 20 84.1520 84.78 85.4080 86.0360 86.6640 87.2920 87.92 30 126.2280 127.17 128.1120 129.0540 129.9960 130.9380 131.88 40 168.3040 169.56 170.8160 172.0720 173.3280 174.5840 175.84 50 210.38 211.95 213.52 215.09 216.66 218.23 219.80 60 252.4560 254.34 256.2240 258.1080 259.9920 261.8760 263.76 — 59 — Areaof the surface of the jacket. — jQuabratmfyalt bet HTantelfläc^e. High. Diarnetei — in., 1., cm. £)uvdjme(|ei' — 3! ., 1., cm. $0$. 141 142 143 144 145 146 147 0.01 0.044274 0.044588 0.044902 0.045216 0.045530 0.045844 0.046158 0*02 0.088548 0.089176 0.089804 0.090432 0.091060 0.091688 0.092316 0,03 0.132822 0.133764 0.134706 0.135648 0.136590 0.137532 0.138474 0*04 0.177096 0.178352 0.179608 0.180864 0.182120 0.183376 0.184632 0.05 0.221370 0.222940 224510 0.226080 0.227650 0.229220 0.230790 0,06 0.265644 0.267528 0.269412 0.271296 0.273180 0.275064 0.276948 0*07 0.309918 0.312116 0.314314 0.316512 0.318710 0.320908 0.323106 0.08 0.354192 0.356704 0.359216 0.361728 0.364240 0.366752 0.369264 0.09 0.398466 0.401292 0.404118 0.406944 0.409770 0.412596 0.415422 0.1 0.442740 0.445880 0.449020 0.452160 0.4553 0.458440 0.461580 0.2 0.885480 0.891760 0.898040 0.904320 0.9106 0.916880 0.923160 0.3 1.328220 1.337640 1.347060 1.356480 1.3659 1.375320 1.384740 0.4 1.770960 1.78352 1.796080 1.808640 1.8212 1.833760 1.846320 0.5 2.2137 2.2294 2.2451 2.2608 2.2765 2.2922 2.3079 0.6 2.656440 2.675280 2.694120 2.712960 2.7318 2.750640 2.769480 0.7 3.099180 3.121160 3.143140 3.165120 3.1871 3.209080 3.231060 0*8 3.541920 3.567040 3.592160 3.617280 3.6424 3.667520 3.692640 0.9 3.984660 4.012920 4.041180 4.069440 4.0977 4.125960 4.154220 1 4.4274 4.4588 4.4902 4.5216 4.5530 4.5844 4.6158 2 8.8548 8.9176 8.9804 9.0432 9. 1060 9.1688 9.2316 3 13.2822 13.3764 13.4706 13.5648 13.6590 13.7532 13.8474 4 17.7096 17.8352 17.9608 18.0864 18.2120 18.3376 18.4632 5 22.1370 22.2940 22.4510 22.6080 22.7650 22.9220 23.0790 6 26.5644 26.7528 26.9412 27.1296 27.3180 27.5064 27.6948 7 30.9918 31.2116 31.4314 31.6512 31.8710 32.0908 32.8196 8 35.4192 35.6704 35.9216 36.1728 36.4240 36.6752 36.9264 9 39.8466 40.1292 40.4118 40.6944 40.9770 41.2596 41.5422 10 44.2740 44.5880 44.9020 45.2160 45.53 45.8440 46.1580 11 48.7014 49.0468 49.3922 49.7376 50.0830 50.4284 50.7738 12 53.1288 53.5056 53.8824 54.2592 54.6360 55.0128 55.3896 13 57.5562 57.9644 58.3726 58.7808 59.1890 59.5972 60.0054 14 61.9836 62.4232 62.8628 63.3024 63.7420 64.1816 64.6212 15 66.4110 66.8820 67.3530 67.8240 68.2950 68.7660 69.2370 16 70.8384 71.3408 71.8432 72.3456 72.8480 73.3504 73.8528 17 75.2658 75.7996 76.3334 76.8672 77.4010 77.9348 78.4686 18 79.6932 80.2584 80.8236 81.3888 81.9540 82.5192 83.0844 19 84.1206 84.7172 85.3138 85.9104 86.4070 87.1036 87.7002 20 88.5480 89.1760 89.8040 90.4320 91.06 91.6880 92.3160 30 132.8220 133.7640 134.7060 135.6480 136.59 137.5320 138.4740 40 177.0960 178.3520 179.6080 180.8640 182.12 183.3760 184.6320 50 221.37 222.94 224.51 226.08 227.65 229.22 230.79 60 265.6440 267.5280 269.4120 271.2960 [ 273.18 275.0640 276.9480 — 60 — Area of the surface of the jacket. — (Quctbratinfyalt bet* tTTarttelfläcfye. High. Diametei •—in., 1., cm Sard) meffer — gl.",.t., cm. §odj. 148 149 150 151 152 153 154 0.01 0.046472 0.046786 0.0471 0.047414 0.047728 0.048042 0.048356 0*02 0.092944 0.093572 0.0942 0.094828 0.095456 0.096084 0.096712 0*03 0.139316 0.140358 0.1413 0.142242 0.143181 0.144126 0.145068 0.04 0.185888 0.187144 0.1884 0.189656 0.190912 0.192168 0.193424 0.05 0.232360 0.233930 0.2355 0.237070 0.238640 0.240210 0.241780 0,06 0.278832 0.280716 0.2826 0.284484 0.286368 0-288252 0.290136 0.07 0.325304 0.327502 0.3297 0.331898 0.334096 0.336294 0.338492 0.08 0.371776 0.374288 0.3768 0.379312 0.381824 0.384336 0.386848 0.09 0.418248 0.421074 0.4239 0.426726 0.429552 0.432378 0.435204 0.1 0.464720 0.467860 0.4710 0.474140 0.477280 0.480420 0.483560 0.2 0.929440 0.935720 0.9420 0.948280 0.954560 0.960840 0.967120 0.3 1.394160 1.403580 1.4130 1.422420 1.431840 1.441260 1.450680 0.4 1.858880 1.871440 1.8840 0.896560 1.909120 1.921680 1.934240 0.5 2.3236 2.3392 2.3550 2.3707 2.3864 2.4021 2.4178 0.6 2.788320 2.807160 1.8260 2.844840 2.863680 2.882520 2.901360 0.7 3.253040 3.275020 3.2970 3.318980 3.340960 3.362940 3.384920 0.8 3.717760 3.742880 3.7680 3.793120 3.818240 3.843360 3.868480 0.9 4.182480 3.210740 4.2390 4.267260 4.295520 4.323780 4.352040 1 4.6472 4.6786 4.71 4.7414 4.7728 4.8042 4.8356 2 9.2944 9.3572 9.42 9.4828 9.5456 9,6084 9.6712 3 13.9416 14.0358 14.13 14.2242 14.3184 14.4126 14.5068 4 18.5888 18.7144 18.84 18.9656 19.0912 19.2168 19.3424 5 23.2360 23.3930 23.55 23.7070 23.8640 24.0210 24.1780 6 27.8832 28.0716 28.26 28.4484 28.6368 28.8252 29.0136 7 32.5304 32.7502 32.97 33.1898 33.4096 33.6294 33.8492 8 37.1776 37.4288 37.68 37.9312 38.1824 38.4336 38.6848 9 41.8248 42.1074 42.39 42.6726 42.9552 43.2378 43.5204 10 46.4720 46.7860 47.10 47.4140 47.7280 48.0420 48.3560 11 51.1192 51.4646 51.81 52.1554 52.5008 52.8462 53.1916 12 55.7664 56.1432 56.52 56.8968 57.2736 57.6504 58.0272 13 60.4136 60.8218 61.23 61.6382 62.0464 62.4546 62.8628 14 65.0608 65.5004 65.94 66.3796 66.8192 67.2588 67.6984 15 69.7080 70.1790 70.65 71.1210 71.5920 72.0630 72.5340 16 74.3552 74.8576 75.36 75.8624 76.3648 76.8672 77.3696 17 79.0024 79.5362 80.07 80.6038 81.1376 81.6714 82.2052 18 83.6496 84.2148 84.78 85.3452 85.9104 86.4756 87.0408 19 88.2968 88.8934 89.49 90.0866 90.6832 91.2798 91.8764 20 92.9440 93.5720 94.20 94.8280 95.4560 96.0840 96.7120 30 139.4160 140.3580 141.30 142.2420 143.1840 144.1260 145.0680 40 185.8880 187.1440 188.40 189.6560 190.9120 192.1680 193.4240 50 3232.36 233.93 235.50 237.07 238.64 240.21 241.78 60 '278.8320 280.7160 282.60 284.4840 286.3680 288.2520 290.1360 61- Area of the surface of the jacket. — (Quabratint^alt ber HTantelftäcfye. Uigh. Diametei p — in., 1., cm. £itrtf meffer — 3 [.; I., cm. &od). loo 156 157 158 159 160 161 O.Ol 0.048670 0.048984 0.049298 0.049612 0.049926 0.050240 0.050554 0*02 0.097340 0.097968 0.098596 0.099224 0.099852 0.100480 0.101108 0.03 0.146010 0.146952 0.147894 0.148836 0.149778 0.150720 0.151662 0*04 0.194680 0.195936 0.197192 0.198448 0.199704 0.200960 0.202216 0*05 0.243350 0.244920 0.246490 0.248060 0.249630 0.2512 0.252770 0*06 0.292020 0.293904 0.295788 0.297672 0.299556 0.301440 0.303324 0.07 0.340690 0.342888 0.345086 0.347284 0.349482 0.351680 0.353878 0.08 0.389360 0.391872 0.394384 0.396896 0.399408 0.401920 0.404432 0.09 0.437030 0.440856 0.443682 0.446503 0.449334 0.452160 0.454986 0.1 0.4867 0.489840 0.492980 0.496120 0.499260 0.5024 0.505540 0.2 0.9734 0.979680 0.985960 0.992240 0.998520 1.0045 1.011080 0.3 1.4601 1.469520 1.478940 1.488360 1.497780 1.5072 1.516620 0.4 1.9468 1.959360 1.971920 1.984480 1.997040 2.0096 2.022160 0.5 2.4335 2.4492 1.4649 2.4806 2.4963 2.5120 2.5277 0.6 2.9202 2.939040 2.957880 2.976720 2.995560 3.0144 3.033240 0.7 3.4069 3.428880 3.450860 3.472840 3.494820 3.5168 3.538780 0.8 3.8936 3.918720 3.943840 3.968960 3.994080 4.0192 4.044320 0.9 4.3803 4.408560 4.436820 4.465080 4.493340 4.5216 4.549860 1 4.8670 4.8984 4.9298 4.9612 4.9926 5.0240 5.0554 2 9.7340 9.7968 9.8596 9.9224 9.9852 10.0480 10.1108 3 14.6010 14.6952 14.7894 14.8836 14.9778 15.0720 15.1662 4 19.4680 19.5936 19.7192 19.8448 19.9704 20.0960 20.2216 5 24.3350 24.4920 24.6490 24.8060 24.9630 25.12 25.2770 6 29.2020 29 3904 29.5788 29.7672 29.9556 30.1440 30.3324 7 24.0690 34.2888 34.5086 34.7284 34.9482 35.1680 35.3878 8 38.9360 39.1872 39.4384 39.6896 39.9408 40.1920 40.4432 9 43.8030 44.0856 44.3682 44.6508 44.9334 45.2160 46.4986 10 48.67 48.9840 49.2980 49.6120 49.9260 50.24 50.5540 11 53.5370 53.8824 54.2278 54.5732 54.9186 55.2640 55.6094 12 58.4040 58.7818 59.1576 59.5344 59.9112 60.2880 60.6648 13 63.2710 63.6802 64.0874 64.4956 64.9038 65.3120 65.7202 14 68.1380 68.5786 69.0172 69.4568 69.8964 70.3360 70.7756 15 73.0050 73.4760 73.9470 74.4180 74.8890 75.36 75.8310 16 77.8720 78.3744 78.8768 79.3792 79.8816 80.3840 80.8864 17 82.7390 83.2728 83.8066 84.3404 84.8742 85.4080 85.9428 18 87.6060 88.1712 88.7364 89.3016 89.8668 90.4320 90.9982 19 92.4730 93.0696 93.6662 94.2628 94.8594 95.4560 96.0536 20 97.34 97.9680 98.5960 99.2240 99.8520 100.48 101.1080 30 146.01 146.9520 147.8940 148.8360 149.7780 150.72 151.6620 40 194.68 195.9360 197.1920 198.4480 199.7040 200.96 202.2160 50 243.35 244.92 246.49 248.06 249.63 251.20 252.77 60 292.02 293.9040 295.780 297.6720 299.5560 301.44 303.3240 62 — Area of the surface of the jacket. — Quabratinfyalt ber Hlantelflädje. High. Diameter — in., 1., cm. £)urd) nteffer — jl .,!., cm £ocf). 162 163 164 165 170 175 180 0.01 0.050868 0.051182 0.051496 0.051810 0.053380 0.054950 0.056520 0*02 0.101736 0.102364 0.102992 0.103620 0.106760 0.1099 0.113040 0*03 0.152604 0.153546 0.154488 0.155430 0.160140 0.164850 0.169560 0.04 0.203472 204728 0.205984 0.207240 0.213520 0.2198 0.226080 0*05 0.254340 0.255910 0.257480 0.259050 0.2669 0.274750 0.2826 0*06 0.305208 0.307092 0.308976 0.310860 0.320280 0.3297 0.339120 0.07 0.356076 0.358274 0.360472 0.362670 0.373660 0.384650 0.395640 0*08 0.407944 0.409456 0.411968 0.414480 0.427040 0.4396 0.452160 0*09 0.457812 0.460638 0.463464 0.466290 0.480420 0.494550 0.508680 0*1 0.508680 0.511820 0.514960 0.5181 0.5338 0.5495 0.5652 0.2 1.017360 1.023640 1.029920 1.0362 1.0676 1.0990 1.1304 0*3 1.526040 1.535460 1.544880 1.5543 1.6014 1.6485 1.6956 0*4 2.034720 2.047280 2.059840 2.0724 2.1352 2.1980 2.2608 0.5 2.5434 2.5591 2.5748 2.5905 2.6690 2.7475 2.8260 0.6 3.052080 3.070920 3.089760 3.1086 3.2028 3.2970 3.3912 0.7 3.560760 3.582740 3.604720 3.6267 3.7366 3.8465 3.9564 0.8 4.069440 4.094560 4.119680 4.1448 4.2704 4.3960 4.5216 0.9 4.578120 4.606380 4.634640 4.6629 4.8042 4.9455 5.0868 1 5.0868 5.1182 5.1496 5.1810 5.3380 5.4950 5.6520 2 10.1736 10.2364 10.2992 10.3620 10.6760 10.99 11.3040 3 15.2604 15.3546 15.4488 15.5430 16.0140 16.4850 16.9560 4 20.3472 20.4728 20.5984 20.7240 21.3520 21.98 22.6080 5 25.4340 25.5910 25.7480 25.9050 26.69 27.4750 28.26 6 30.5208 30.7092 30.8976 31.0860 32.0280 32.97 33.9120 7 35.6076 35.8274 36.0472 36.2670 37.3660 38.4650 39.5640 8 40.6944 40.9456 41.1968 41 4480 42.7040 43.96 45.2160 9 45.7812 46.0638 46.3464 46.6290 48.0420 49.4550 50.8680 10 50.8680 51.1820 51.4960 51.81 53.38 54.95 56.52 11 55.9548 56.3002 56.6456 56.9910 58.7180 60.4450 62.1720 12 61.0416 61.4184 61.7952 62.1720 64.0560 65.94 67.8240 13 66.1284 66.5366 66.9448 67.3530 69.3940 71.4350 73.4760 14 71.2152 71.6548 72.0944 72.5340 74.7320 76.93 79.1280 15 76.3020 76.7730 77.2440 77.7150 80.07 82.4250 84.78 16 81.3888 81.8912 82.3936 82.8960 85.4080 87.92 90.4320 17 86.4756 87.0094 87.5432 88.0770 90.7460 93.4150 96.0840 18 91.5624 92.1276 92.6928 93.2580 96.0840 98.91 101.7360 19 96.6492 97.2458 97.8424 98.4390 101.4220 104.4050 107.3880 20 101.7360 102.3640 102.9920 103.62 106.76 109.90 113.04 30 152.6040 153.5460 154.4880 155.43 160.14 164.85 169.56 40 203.4720 204.7280 205.9840 207.24 213.52 219.80 226.08 50 254.34 255.91 257.48 259.05 266.90 274.75 282.60 60 305.2080 307.0920 308.9760 310.86 320.28 329.70 339.12 63 — Area of the surface of the-jacRet. — (Quabmrmrjait bcr JTtanteljtäcfye. High. Diameter —in., 1., cm. SDurdj meffer — jt . , I. , cm. £od). 185 190 195 200 205 210 220 0.01 0.058090 0.059660 0.061230 0.0628 0.064370 0.065940 0.069080 0*02 0.116180 0.119320 0. 122460 0.1256 0.128740 0.131880 0.138160 0.03 0.174270 0.178980 0.183690 0.1884 0.193110 0.197820 0.207240 0.04 0.232360 0.238640 0.244920 0.2512 0.257480 0.263760 0.276320 0.05 0.290450 0.2983 0.306150 0.3140 0.321850 0.3297 0.3454 0.06 0.348540 0.357960 0.367380 0.3768 0.386220 0.395640 0.414480 0.07 0-406630 0.417620 0.428610 0.4396 0.450590 0.461580 0.483560 0.08 0.464720 0.477280 0.489840 0.5024 0.514960 0.527520 0.552640 0.09 0.522810 0.536940 •0.551070 0.5652 0.579330 0.593460 0.621720 0.1 0.5809 0.5966 0.6123 0.6280 0.6437 0.6594 0.6908 0.2 1.1618 1.1932 1.2246 1.2560 1.2874 1.3188 1.3816 0.3 1.7427 1.7898 1.8369 1.8840 1.9311 1.9782 2.0724 0.4 2.3236 2.3864 2.4492 2.5120 2.5748 2.6376 2.7632 0.5 2.9045 2.9830 3.0615 3.14 3.2185 3.2970 3.4540 0.6 3.4854 3.5796 3.6738 3.7680 3.8622 3.9564 4.1448 0.7 4.0663 4.1762 4.2861 4.3960 4.5059 4.6158 4.8356 0.8 4.6472 4.7728 4.8984 5.0240 5.1496 5.2752 5.5264 0.9 5.2281 5.3694 5.5107 5.6520 5.7933 5.9346 6.2172 1 5.8090 5.9660 6.1230 6.28 6.4370 6.5940 5.9080 2 11.6180 11.9320 12.2460 12.56 12.8740 13.1880 13.8160 3 17.4270 17.8980 18.3690 18.84 19.3110 19.7820 20.7240 4 23.2360 23.8640 24.4920 25.12 25.7480 26.3760 27.6320 5 29.0450 29.83 30.6150 31.40 32.1850 32.97 34.54 6 34.8540 35.7960 36.7380 37.68 38.6220 39.5640 41.4480 1 40.6630 41.7620 42.8610 43.96 45.0590 46.1580 48.3560 8 46.4720 47.7280 48.9840 50.24 51.4960 52.7520 55.2640 9 52.2810 53.6940 55.1070 56.52 57.9330 59.3460 62.1720 10 58.09 59.66 61.23 62.80 64.37 65.94 69.08 11 63.8990 65.6260 67.3530 69.08 70.8070 72.5340 75.9880 12 69.7080 71.5920 73.4760 75.36 77.2440 79.1280 82.8960 13 75.5170 77.5580 79.5990 81.64 83.6810 85.7220 89.8040 14 81.3260 83.5240 85.7220 87.92 90.1180 92.3160 96.7120 15 87.1350 89.49 91.8450 94.20 96.5550 98.91 103.62 16 92.9440 95.4560 97.9680 100.48 102.9920 105.5040 110.5280 17 98.7530 101.4220 104.0960 106.76 109.4290 112.0980 117.4360 18 104.5620 107.3880 110.2140 113.04 115.8660 118.6920 124.3440 19 110.3710 113.3540 116.3370 119.32 122.3030 125.2860 130.2520 20 116.18 119.32 122.46 125.60 128.74 131.88 138.16 30 174.27 178.98 183.69 188.40 193.11 197.82 207.24 40 232.36 238.64 244.92 251.20 257.48 263.76 276.32 50 290.45 298.30 306.15 314.00 321.85 329.70 345.40 60 348.54 357.96 367.38 376.80 J86.22 395.64 414.48 — 64 Area of the surface of the jacket. — Quabrattnt|alt ber tnantelfläcf/e. High. Diameter- - in. , 1. , cm. £)urd)meff er — 3I , I., cm. £odj. 225 230 j 240 250 260 270 275 0.01 0.070650 0.072220 0.075360 0.0785 0.081640 0.084780 0.086350 0*02 0.1413 0.144440 0.150720 0.1570 0.163280 0.169560 0.1727 0.03 0.211950 0.216660 0.226080 0.2355 0.244920 0.254340 0.259050 0.04 0.2826 0.288880 0.301440 3140 0.326560 0.339120 0.3454 0*05 0.353250 0.3611 0.3768 0.3925 0.4082 0.4239 0.431750 0.06 0.4239 0.433320 0.452160 0.4710 0.489840 0.508680 0.5181 0.07 0.494550 0.505540 0.527520 0.5495 0.571480 0.593460 0.604450 0*08 0.5652 0.577760 0.602880 0.6280 0.653120 0.678240 0.6908 0*09 0.635850 0.649980 0.678240 0.7065 0.734760 0.763020 0.777150 0.1 0.7065 0.7222 0.7536 0.7850 0.8164 0.8478 0.8635 0.2 1.4130 1.4444 1.5072 1.57 1.6328 1.6956 1.7270 0*3 2.1195 2.1666 2.2608 2.3550 2.4492 2.5434 2.5905 0.4 2.8260 2.8888 3.0144 3.14 3.2656 3.3912 3.4540 0.5 3.5325 3.6110 3.7680 3.9250 4.0820 3.2390 4.3175 0.6 4.2390 4.3332 4.5216 4.71 4.8984 5.0868 5.1810 0*7 4.9455 5.0554 5.2752 5.4950 5.7148 5.9346 6.0445 0.8 5.6520 5.7776 6.0288 6.28 6.5312 6.7824 6.9080 0*9 6.3585 6.4998 6.7824 7.0650 7.3476 7.6302 7.7715 1 7.0650 7.2220 7.5360 7.85 8.1640 8.4780 8.6350 2 14.13 14.4440 15.0720 15.70 16 3280 16.9560 17.27 3 21.1950 21.6660 22.6080 23.55 24.4920 25.4340 25.9050 4 28.26 28.8880 30. 1440 31.40 32.6560 33.9120 34.54 5 35.3250 36.11 37.68 39.25 40.82 42.39 43.1750 6 42.39 43.3320 45.2160 47.10 48.9840 50.8680 51.81 7 49.4550 50.5540 52.7520 54.95 57.1480 59.3460 60.4450 8 56.52 57.7760 60.2880 62.80 65.3120 67.8240 69.08 9 63.5850 64.9980 67.8240 70.65 73.4760 76.3020 77.7150 10 70.65 72.22 75.36 78.50 . 81.64 84.78 86.35 11 77.7150 79.4420 82.8960 86.35 89.8040 93.2580 94.9850 12 84.78 86.6640 90.4320 94.20 97.9680 101.7360 103.62 13 91.8450 93.8860 97.9680 102.05 106.1320 110.2140 112.2550 14 98.91 101.1080 105.5040 109.90 114.2960 118.6920 120.89 15 105.9750 108.33 113.04 117.75 122.46 127.17 129.5250 16 113.04 115.5520 120.5760 125.60 130.6240 135.6480 138.16 17 120.1050 122.7740 128.1120 133.45 138.7880 144.1260 146.7950 18 127.17 129.9960 135.6480 141.30 146.9520 152.6040 155.43 19 134.2350 137.2180 143.1840 149.15 155.1160 161.0820 164.0650 20 141.30 144.44 150.72 157.00 163.28 169.56 172.70 30 211.95 216.66 226.08 235.50 244.92 254.34 259.05 40 282.60 288.88 301.44 314.00 326.56 339.12 345.40 50 353.25 361.10 376.80 392.50 408.20 423.90 431.75 60 423.90 433.32 452.16 471.00 489.84 508.68 518.10 — 65 — Area of the surface of the jacket. — QJuabratmtjalt ber lUantclfiacbc. High. Diameter- -in., 1., cm. $Duvd>ttieffer — jl., 1. , cm. $od). 280 290 300 310 320 325 350 0*0i 0.087920 0.091060 0.0942 0.097340 0.100480 0.102050 0.1099 0*02 0.175840 0.182120 0.1884 0.194680 0.200960 0.2041 0.2198 0*03 0.263760 0.273180 0.2826 0.292020 0.301440 0.306150 0.3297 0*04 0.351680 0.364240 0.3768 0.389360 0.401920 0.4082 0.4396 0*05 0.4396 0.4553 0.4710 0.4867 0.5024 0.510250 0.5495 0.06 0.527520 0.546360 0.5652 0.584040 •0.602880 0.6123 0.6594 0*0? 0.615440 0.637420 0.6594 0.681380 0.703360 0.714350 0.7693 0*08 0.7 03360 0.728480 0.7536 0.778720 0.803840 0.8164 8792 0*09 0.791280 0.819540 0.8478 0. 876060 0.904320 0.918450 0.985)1 0*1 0.8792 0.9106 0.9420 0.9734 1.0048 1.0205 1.0990 0*2 1.7584 1.8212 1.8840 1.9468 2,0096 2.0410 2.1980 0*3 2.6376 2.7318 2,8260 2.9202 3.0144 3.0615 3.2970 0*4 2.5168 3.6424 3.7680 3.8936 4.0192 4.0820 4.3960 0*5 4.3960 4.5530 4.71 4.8670 5.0240 5.1025 5.4950 0*« 5.2752 5.4636 5.6520 5.8404 6.0288 6.1230 6.5940 0*7 6.1544 6.3742 6.5940 6.8138 7.0336 7.1435 7.6930 0*8 7.0336 7.2848 7.5360 7.7872 8.0384 8.1640 8.7920 0*9 7.9128 8.1954 8.4780 8.7606 9.0432 9.1845 9.8910 1 8.7920 9.1060 9.42 9.7340 10.0480 10.2050 10.99 2 17.5840 18.2120 18.84 19.4680 20.0960 20.41 21.08 3 26-3760 27.3180 28.26 29.2020 30.1440 30.6150 32.97 4 35.1680 36.4240 37.68 38.9360 40 1920 40.82 43.96 5 43.96 45.53 47.10 48.67 50.24 51.0250 54.95 6 52.7520 54.6360 56.52 58.4040 60.2880 61.23 65.94 7 61.5440 63.7420 65.94 68.1380 70.3360 71.4350 76.93 8 70 3360 72.8480 75.36 77.8720 80.3840 81.64 87 92 9 79.1280 81.9540 84,78 87.6060 90.4320 91.8450 98.91 10 87.92 91.06 94.20 97. «34 100.48 102.05 109.90 11 96.7120 100.1660 103.62 107.0740 110.5280 112.2550 120.89 12 105.5040 109.2720 113.04 116.8080 120.5760 122.46 131.88 13 114.2960 118.3780 122.46 126.5420 130.6240 132.6650 142.87 14 123.0880 127.4840 131.88 136.2760 140.6720 142,87 153.86 15 131.88 136.59 141.30 146.01 150.72 153.0750 164.85 16 140.6720 145.6960 150.72 155.7440 160.7680 163.28 175.84 17 149.4640 154.8020 160.14 165.4780 170.8160 173.4850 186.83 18 158.2560 163.9080 169.56 175.2120 180.8640 183.69 197.82 19 167.0480 173.0140 178.98 184.9460 190.9120 193.8950 208.81 20 175.84 182.12 188.40 194.68 200.96 204.10 219.80 30 263.76 273.18 282.60 292.02 301.44 306.15 329.70 40 351.68 364.24 376.80 389.36 401.92 408.20 439 60 50 439.60 455.30 471.00 486.70 502.40 510.25 549.50 60 527.25 546.36 565.20 584.04 602.88 612.30 659.40 66 Area of the surface of the jacket. — (Quabrattnfyalt btv tftantelflacfye. High. Diameter —in., I., cm. ©uvdji neffcr — 3L , i. , cm. $od). 375 400 425 450 475 500 525 0.01 0.117750 0.1256 0.133450 0.1413 0.149150 0.1570 0.164850 0.02 0.2355 0.2512 0.2669 0.2826 0.g983 0.3140 0.3297 0*03 0.353250 0.3768 0.400350 0.4239 0.447450 0.4710 0.494550 0*04 0.4710 0.5024 0.5338 0.5652 0.^966 0.6280 0.6594 0*05 0.588750 0.6280 0.667250 0.7065 0.745750 0-7850 0.824250 0,06 0.7065 0.7536 0.8007 0.8478 0.8949 0.9420 0.9891 0*07 0.824250 0.8792 0.934150 0.9891 1.044050 1.0990 1.153950 0*08 0.9420 1.0048 1.0676 1.1304 1.1932 1.2560 1.3188 0*09 1.059750 1.1304 1-201050 1.2717 1.342350 1.4130 1.483650 0*1 1.1775 1.2560 1.3345 1.4130 1.4915 1.57 1.6485 0.2 2.3550 2.5120 2.6690 2.8260 2.9830 3.14 3.2970 0.3 3.5325 3.7680 4.0035 4.2390 4.4745 4.71 4.9455 0.4 4.71 5.0240 5.3380 5.6520 5.9660 6.28 6.5940 0.5 5.8875 6.28 6.6725 7.0650 7.4575 7.85 8.2425 0.6 7.0650 7.5360 8.0070 8.4780 8.9490 9.42 9.8910 0.7 8.2425 8.7920 9.3415 8.8910 10.4405 10.99 11.5395 0.8 9.42 10.0480 10.6760 11.3040 11.9320 12.56 13.1880 0.9 10.5975 11.3040 12.0105 12.7170 13.4235 14.13 14.8365 1 11.7750 12.56 13.3450 14.13 14.9150 15.70 16.4850 2 23.55 25.12 26.69 28.26 29.83 31.40 32.97 3 35.3250 37.68 40.0350 42.39 44.7450 47.10 49.4550 4 47.10 50.24 53.38 56.52 59.66 62.80 65.94 5 58.8750 62.80 66.7250 70.65 74.5750 78.50 82.4250 6 70.65 75.36 80.07 84.78 89.49 94.20 98.91 7 82.4250 87.92 93.4150 98.91 104.4050 109.90 115.3950 8 94.80 100.48 106.76 113.04 119.32 ' 125.60 131.88 9 105 9750 113.04 120.1050 127.17 134.2350 141.30 148.3650 10 117.75 125.60 133.45 141.30 149.15 157.00 164.85 11 129.5250 138.16 146.7950 155.43 164.0650 172.70 181.3350 12 141.30 150.72 160.14 169.56 178.98 188.40 197.82 13 153.0750 163.28 173.4850 183.69 193.8950 204.10 214.3050 14 164.85 175.84 186.83 197.82 208.81 219.80 230.79 15 176.6250 188.40 200.1750 211.95 223.7250 235.50 247.2750 16 188.40 200.96 213.52 226.08 238.64 251.20 263.76 IT 200.1750 213.52 226.8650 240.21 253.5550 266.90 280.2450 18 211.95 226.08 240.21 254.34 268.47 282.60 298.73 19 223.7250 238.64 253.5550 268.47 283.3850 298.30 313.2150 20 235.50 251.20 266.90 282.60 298.30 314.00 329.70 30 353.25 376.80 400.35 423.90 447.45 471.00 494.55 40 471.00 502.40 533.80 565.20 596.60 1 628.00 659.40 50 588.75 628.00 667.25 706.50 745.75 : 785.00 824.25 60 , 706.50 753.60 800.70 847.80 894.90 ' 942.00 989.10 — 67 — Area of the surface of the jacket'. — Quabrattnfyalt ber ITTantelfiäcbc. High. Diameter — in., I., cm. ^urcfymefjei — $1. {., cm. |>odj. 550 575 600 625 650 675 700 0.01 0.1727 6.180550 0.1884 0.196250 0.2041 0.211950 0.2198 0*02 0.3454 0.3611 0.3768 0.3925 0.4082 0.4239 0.4396 0*03 0.5181 0.541650 0.5652 0.588750 0.6123 0.635850 0.6594 0*04 0.6908 0.7222 0.7536 0.7850 0.8164 0.8478 0.8792 0*05 0.8635 0.902750 0.9420 0.981250 1.0205 1.059750 1.0990 0,06 1.0352 1.0833 1.1304 1.1775 1.2246 1.2717 1.3188 0*07 1.2089 1.263850 1.3188 1.373750 1.4287 1.483750 1.5386 0*08 1.3816 1.4444 1.5072 1.57 1.6328 1.6956 1.7584 0*09 1.5543 1.624950 1.6956 1.766250 1.8369 1.907550 1.9782 0*1 1.7270 1.8055 1.8840 1.9625 2.0410 2.1195 2.1980 0.2 3.4540 3.6110 3.7680 3.9250 4.0820 4.2390 4.3960 0,3 5.1810 5.4165 5.6520 5.8875 6.1230 6.3585 6.5940 0.4 6.9080 7.2220 7.5360 7.85 8.1640 8.4780 8.7920 0.5 8.6350 9.0275 9.42 9.8125 10.2050 10.5975 10.99 0.6 10.3620 10.8330 11.3040 11.7750 12.2460 12.7170 13.1880 0*7 12.0890 12.6385 13.1880 13.7375 14.2870 14.8365 15.3860 0*8 13.8160 14.4440 15.0720 15.70 16.4280 16.9560 17.5840 0>9 15.5430 16.2495 16.9560 17.6625 18.4690 19.0755 19.782 1 17.27 18.0550 18.84 19.6250 20.41 21.1950 21.98 2 34.54 36.11 37.68 39.25 40.82 42.39 43.96 3 51.81 54.1650 56.52 58.8750 61.23 63.5850 65.94 4 69.08 72.22 75.36 78.50 81.64 84.78 87.92 5 86.35 90.2750 94.20 98.1250 102.05 105.9750 109.90 6 103.62 108.33 113.04 117.75 122.46 127.17 131.88 7 120.89 126.3850 131.88 137.3750 142.87 148.3650 153.86 8 138.16 144.44 150.72 157.00 163.28 169.56 175.84 9 155.43 162.495 169.56 176.6250 183.69 190.7550 197.82 10 172.70 180.55 188.40 196.25 204.10 211.95 219.80 11 189.97 198.6050 207.24 215.8750 224.51 233.1450 241.78 12 207.24 216.66 226.08 235.50 244.92 254.34 263.76 13 224.51 234.7150 244.92 255.1250 265.33 275.5350 285.74 14 241.78 252.77 263.76 274.75 285.74 296.73 307.72 15 259.05 270.8250 282.60 294.3750 306.15 317.8250 329.70 16 276.32 288.88 301.44 314.00 326.56 339.02 351.68 IT 293.59 306.9350 320.28 333.6250 346.97 360.2150 373.66 18 310.86 324.99 339.12 353.25 367.38 381.41 395.64 19 328.13 343.0450 357.96 372.8750 387.79 402.6050 417.62 20 345.40 361.10 876.80 392.50 408.20 423.90 439.60 30 518.10 541.65 565.20 588.75 612.30 635.85 659.40 40 690.80 722.20 753.60 785.00 816.40 847.80 879.20 50 863.50 902.75 942.00 981.25 1020.50 1059.75 1099.00 60 1036.20 1083.30 1130.40 1177.50 1224.60 1271.70 1318.80 Area of the surface of the jacket. — Quabratmfyalt ber tTtantelfläcfye. High. Diameter— in. , 1., cm. 2)urdjmeffer — g(., L,cm. $od). 725 750 775 800 825 850 0.01 0.227650 0.2355 0.243350 0.2512 0.259050 0.2669 0*02 0.4553 0.4710 0.4867 0.5024 0.5181 0.5338 0.03 0.682950 0.7065 0.730050 0.7536 0.777150 0.8007 0.04 0.9106 0.9420 0.9734 1.0048 1.0362 1.0676 0.05 1.138250 1.1775 1.216750 1.2560 1.295250 1.3345 0.06 1.3659 1.4130 1.4601 1.5072 1.5543 1.6014 0.07 1.593550 1.6485 1.703450 1.7584 1.813350 1.8683 0.08 1.8212 1.8840 1.9468 2.0096 2.0724 2.1352 0.09 2.048850 2,1195 2.190150 2.2608 2.331450 2.4021 0.1 2.2765 2.3550 2.4335 2.5120 2.5905 2.6690 0.2 4.5530 4.71 4.8670 5.0240 5.1810 5.3380 0.3 6.8295 7.0650 7.3005 7.5360 7.7715 8.0070 0.4 9.1060 9.42 9.7340 10.0480 10.3620 10.6760 0.5 11.3825 11.7750 12.1675 12.56 12.9525 . 13.3450 0.6 13.6590 14.13 14.6010 15.0720 15.5430 16.0140 0.7 15.9355 16.4850 17.0345 : 17.5840 18.1335 18.6830 0.8 18.2120 18.84 19.4680 ' 20.0960 20.7240 21.3520 0.9 20.4885 21.1950 21.9015 22.6080 23.3145 24.0210 1 22.7650 23.55 24.3350 25.12 25.9050 26.69 2 45.53 47.10 48.67 50.24 51.81 53.38 3 68.2960 70.65 73.0050 75.36 77.7150 80.07 4 91.06 94.20 97.34 100.48 103.62 106.76 5 113.8250 117.75 121.6750 125.60 129.5250 133.45 6 136.59 141.80 146.01 150.72 155.43 160.14 7 159.3550 164.85 170.3450 175.84 181.3350 186.83 8 182.12 188.40 194.68 200.96 207.24 213.52 9 204.8850 211.95 219.0150 226.08 233.1450 240.21 10 227.65 235.50 243.35 251.20 259.05 266.90 11 250.4150 259.05 267.6850 276.32 284.9550 293.59 12 273.18 282.60 292.02 301.44 310.86 320.28 13 295.9450 306.15 316.3550 326.56 336.7650 346.97 14 318.71 329.70 340.69 351.68 362.67 373.66 15 341.4750 353.25 365.0250 376.80 388.5750 400.35 16 364.24 376.80 389.36 401.92 414.48 427.04 17 387.0050 400.35 413.6950 427.04 440.3850 453.73 18 409.77 423.90 438.03 452.16 466.29 480.72. 19 432.5350 447.45 462.3650 477.28 492.1950 507.11 20 455.30 471.00 486.70 502.40 518.10 533.80 30 682.95 706.50 730.05 753.60 777.15 800.70 40 910.60 942.00 973.40 1004.80 1036.20 1067.60 50 1138.25 1 1177.50 1216.75 1256.00 1295.25 1334.50 60 1365.90 | 1413.00 1460. 10 1507.20 1554.30 1601.40 Area of the surface of [the jacnst. — Quaöratmfyalt ber tllanteljlacfye. High. Diameter — in., I., cm. £uvcf)mefjer - -${., [-., cm. £>otf). 875 900 925 950 975 1000 0.01 0.274750 0.2826 0.290450 0.2983 0.306150 0.3140 0.02 0.5495 0.5652 0.5809 0.5966 0.6123 0.6280 0.03 0.824250 0.8478 0.871350 0.8949 0.918450 0.9420 0*04 1.0990 1.1804 1.1618 1.1932 1.2246 1.2560 0*05 1.373750 1.4130 1.452250 1.4915 1.530750 1.57 0*06 1.6485 1.6956 1.7427 1.7898 1.8369 1.8840 0*07 1.923250 1.9782 2.033150 2.0881 2.143050 2.1980 0.08 2.1980 2.2608 2.3236 2.3864 2.4492 2.5120 0.09 2.472750 2.5434 2.614050 2.6847 2.755350 2.8260 0.1 2.7475 2.8260 2.9045 2.9830 3.0615 3.14 0.2 5.4950 5.6520 5.8090 5.9660 6.1230 6.28 0.3 8.2425 8.4780 8.7135 8.9490 9.1845 9.42 0.4 10.99 11.3040 11.6180 11.9320 12.2460 12.56 0.5 13.7375 14.13 14.5225 14.9150 15.3075 15.70 0.6 16.4850 16.9560 17.4270 17.8980 18.3690 18.84 0.7 19.2325 19.7820 20.3315 20.8810 21.4305 21.98 0.8 21.98 22.6080 23.2360 23.8640 24.4920 25.12 0.9 24.7275 25.4340 26.1405 26.8470 27.5535 28.26 1 27.4750 28.26 29.0450 29.88 30.6150 31.40 2 54.95 56.52 58.09 59.66 61.23 62.80 3 82.4250 84.78 87.1350 89.49 91.8450 94.20 4 109.90 113.04 116.18 119.32 122,46 125.60 5 137.3750 141.30 145.2250 149.15 153.0750 157.00 6 164.85 169.56 174.27 178.98 183.69 188.40 7 192.3250 197.82 203.3150 208.81 214.3050 219.80 8 219.80 226.08 232.36 238.64 244.92 251.20 9 247.2750 254.34 261.4050 268.47 275.5350 282.60 10 274.75 282.60 290.45 298.30 306.15 314.00 11 302.2250 310.86 319.4950 328.13 336.7650 345.40 12 329.70 339.12 348.54 357.96 367 38 376.80 13 357.1750 367.38 377.5850 387.79 397.2950 408.20 14 384.65 395.64 406.63 417.62 428.61 439.60 15 412.1250 423.90 435.6750 447.45 459.2250 471.00 16 439.60 452.16 464.72 477.28 489.84 502.40 17 467.0750 480.42 493.7650 507.11 520.4550 533.80 18 494.55 508.68 522.81 536.94 551.07 565 20 19 522.0250 536.94 551.8550 566.77 581.6850 596.60 20 549.50 565.20 580.90 596.60 612.30 628.00 30 824.25 847.80 871.35 894.90 918.45 942.00 40 1099.00 1130.40 1161.80 1193.20 1224.60 1256.00 50 1373.75 1413.00 1452.25 1491.50 1530.75 1570.00 60 1648.50 1695.60 1742.70 1789.80 1836.90 1884.00 SECTION Hi. CUBE TABLES $ «HMlKtlttttfl III. wt»ik'®attjellcn 72 _ i«3 RAMUS TABLE-%af>tUt* Diam- Diam- Diam- eter. Radius \-t Radius eter. Radius }:i Radius eter. Radius Ya. Radius mefl*r. £alb= mcficv % |>aibmefier $ur<$; tnefjer. ftatb* me [ja 1 -j .vmlbmeffer £iird)= mefler. #Qlbs niefjtT % .palbmeffev cm. m. m. cm. mm. cm. m. m. cm. mm. cm. m. m. cm. mm. 1 0.005 1.67 43 0.215 7 1.67 85 0.425 14 1.67 2 0.01 3.3 44 0.22 3.3 86 0.43 14 3.3 3 0.015 5.0 45 0.225 7 5.0 87 0.435 14 5.0 4 0.02 6.7 46 0.23 7 6.7 88 0.44 14 6.7 5 0.025 8.33 47 0.235 7 8.33 89 0.445 14 8.33 6 0.0B 1 0. 48 0.24 8 0. 90 0.45 15 0. 7 0.035 1 1.67 49 0.245 8 1.67 91 0.455 15 1.67 8 0.04 1 3.3 50 0.25 8 3.3 92 0.46 15 3.3 9 0.0-45 1 5.0 51 0.255 8 5.0 93 0.465 15 5.0 10 0.05 1 6.7 52 0.26 8 6.7 94 0.47 15 6.7 11 0.055 1 8.33 53 0.265 8 8.33 95 0.475 15 8.33 12 0.06 2 0. 54 0.27 9 0. 96 0.48 16 0.0 13 0.065 2 1.67 55 0.275 9 1.67 97 0.485 16 1.67 14 0.07 2 3.3 56 0.28 9 3.3 98 0.49 16 3.3 15 0.075 2 5. 57 0.285 9 5.0 99 0.495 16 5.0 16 0.08 2 6.7 58 0.29 9 6.7 100 0.50 16 6.7 17 0.085 2 8.33 59 0.295 9 8.33 101 0.505 16 8.33 18 0.09 3 0. 60 0.30 10 0. 102 0.51 17 0. 19 0.095 3 1.67 61 0.305 10 1.67 103 0.515 17 1.67 20 0.10 3 3.3 62 0.31 10 3.3 104 0.52 17 3.3- 21 0.105 3 5.0 63 0.315 10 5.0 105 0.525 17 5.0 22 0.11 3 6.7 64 0.32 10 6.7 106 0.53 17 6.7 23 0.115 3 8.33 65 0.325 10 8.33 107 0.535 • 17 8.33 24 0.12 4 0. 66 0.33 11 0. 108 0.54 18 0. 25 0.125 4 1.67 67 0.335 11 1.67 109 0.545 18 1.67 26 0.13 4 3.3 68 0.34 11 3.3 110 0.55 18 3.3 27 0.135 4 5.0 69 0.345 11 5.0 111 0.555 18 5.0 28 0.14 4 6.7 70 0.35 11 6.7 112 0.56 18 6.7 29 0.145 4 8.33 71 0.355 11 8.3 113 565 18 8.33 30 0.15 5 0. 72 0.36 12 0. 114 0.57 19 0. 31 0.155 5 1.67 73 0.365 12 1.67 115 0.575 19 1.67 32 0.16 5 3.3 74 0.37 12 3.3 116 0.58 19 3.3 33 0.165 5 5.0 75 0.375 12 5.0 117 0.585 19 5.0 34 0.17 5 6.7 76 0.38 12 6.7 118 0.59 19 6.7 35 0.175 5 8.33 77 0.385 12 8.33 119 0.595 19 8.33 36 0.18 6 0. 78 0.39 13 0. 120 0.60 20 0. 37 0.185 6 1.67 79 0.395 13 1.67 121 0.605 20 1.67 38 19 6 3.3 80 0.40 13 3.3 122 0.61 20 3.3 39 0. 195 6 5.0 81 0.405 13 5.0 123 0.615 20 5.0 40 0.20 6 6.7 82 0.41 13 6.7 124 0.62 20 6.7 41 0.205 6 8.33 83 0.415 13 8 33 125 0.625 20 8.33 42 0.21 7 0. 84 0.42 14 0. 126 0.63 21 0. — •73 113 RAMUS TABLE— ZabeUt. (Continued — '^ort'eUung. ) Diam- Diam- Diam- eter. Radius Ya Radius eter. Radius }j Radius eter. Radius 1.3 Radius 5Durdj:= mefiev. m cuei- % .^iiiömefier S)uvd); meffev. meffev }-i .f>a (bmeffer SMtvd): niefjcv. £alb- meffev Y& \> erb mefiev cm. ng i n. cm. mm. cm. m. j n. cm. mm. cm. m. m. cm. mm. 127 , 0.(535 . . 21 1.67 157 0.785 . . 26 1 67 320 1.60 . . 53 3.3 128 0.64 . 21 3.3 158 0.79 . . 26 3.3 325 1.625 . . ! 54 1.67 129 0.645 . . 21 5.0 159 0.795 . . 26 5. 350 1.75 . . 58 3.3 130 0.65 . . 21 6 7 100 0.80 . . 26 6.7 375 1.875 . . 62 5.0 131 0.655 . . 21 8.83 101 0.805 . . 26 8.33 400 2.00 . . 66 6.7 132 0.66 . . 22 0. 102 0.81 . . 27 0. 425 2.125 . . 70 8.33 133 0.665 . . 22 1.67 103 0.8J5 . . 27 1.67 450 2.25 . . 75 0. 134 0.67 . . 22 3.3 104 0.82 . 27 3.3 475 2.375 . . 79 1.67 135 0.675 . . 22 5.0 105 0.825 . . 27 5.0 500 2.50 . . 83 3.3 136 0.68 . . 22 6.7 170 0.85 . 28 3.3 525 2.625 . . 87 5.0 137 0.685 . 22 8.33 175 0.875 . . 29 1.67 550 2.75 . . 91 6.7 138 0.69 . '. 23 0. 180 0.90 . . 30 0. 575 2.875 . . 95 8.33 139 0.695 . . 23 1.67 185 0.925 . . 30 8.33 000 3.00 1 0. 140 0.70 . . 23 3.33 190 0.95 . . 31 6.7 025 3.125 1 04 1.67 141 0.705 . . 23 5.0 195 0.975 . . 32 5.0 050 3.25 1 08 3.3 142 0.71 . . 23 6.7 200 1.00 . 33 3.3 075 3.375 1 12 5.0 143 0.715 . . 23 8.33 205 1 . 025 . . 34 1.67 700 3.50 1 16 6.7 144 0.72 . . 24 0. 210 1.05 . . 35 0. 725 3.625 1 20 8.33 145 0.725 . . 24 1.67 220 1.10 . . 36 6.7 750 3.75 1 25 0. 140 0.73 . . 24 3.3 225 1.125 . . 37 5.0 775 3.875 1 29 1.67 147 0.735 . 24 5.0 230 1.15 . . 38 3.3 800 4.00 1 33 3.3 148 0.74 24 6.7 240 1.20 . . 40 0. 825 4.125 1 37 5.0 149 0.745 . . 24 8.33 250 1.25 . . 41 6.7 850 4.25 1 41 6.7 150 0.75 . 25 0. 200 1.30 . . 43 3.3 875 4.375 1 15 8.33 151 0.755 . . 25 1.67 270 1.35 . . 45 0. 900 4.50 1 50 0. 152 0.76 . 25 3.3 275 1 . 375 . . 45 8.33 925 4.625 1 54 6.7 153 0.765 . 25 5.0 280 1.10 . 46 6.7 950 4.75 1 58 3.3 154 0.77 . 25 6.7 290 1.45 . . 48 3.3 975 4.875 1 62 5.0 155 0.775 . . 25 8.33 300 1 . 50 . 50 0. 1000 5.00 1 66 6.7 150 0.78 . 26 0. 310 1.55 . . 51 6.7 -75 Diameter— in., lines, cm. £)urdj meffev— jl., 1., cm. High 1 2 3 4 5 Etc. Square o f Basis. — Quabrotinljalt ber jfreis* uub ©runbflädje. 0.0000735 0.000314 0.0007065 0.001256 0.0019625 Cube. ÄiibuS. 0*01 0.000000785 0.000003140 0.000007065 0.000012560 0.000019625 0,02 000001570 0.000006280 0.000014130 0.000025120 0.000039250 0,03 000002355 0.000009420 0000021195 000037680 0.000058875 0,04 0.000003140 000012560 0.000028260 0.000050240 0.000078500 0,05 0-000003925 0.000015700 0.000035325 0.000062800 0.000098125 0.06 0-000004710 0.000018840 0.000042390 0.000075360 0.000117750 0,07 0.000005495 0.000021980 000049455 0.000087920 0.000137375 0,08 0.000006280 0.000025120 0,000056520 0.000100480 0.000157 0,09 0.000007065 0.000028260 0.000083585 0.000113040 0.000176625 0,1 0.000007850 000031400 0.000070650 0.000125600 0.000196250 0,2 0-000015700 0.000062800 0.000141300 0.000251200 0.000392500 0,3 0.000023550 0.000094200 0.000211950 0.000376800 0.000588750 0,4 0.000031400 0.000125600 0.000282600 0.000502400 0.000785 0,5 0-009039250 0.000157 0.000353250 0.000628 0.000981250 0,0 0.000047100 0.000188400 0.000423900 0.000753600 0.001177500 0,7 0.000054950 0.000219800 0.000494550 0.000879200 0.001373750 0,8 0.000062800 0.000251200 0.000565200 0.001004800 8.001570 0,9 0.000070650 0.000282600 0.000635850 0.001130400 001766250 1 0.000078500 0.000314 0.000706500 0.001256 001962500 2 0.000157 0.000628 0.001413 0.002512 0.003925 3 0.000235500 0.000942 0.002119500 0.003768 0.005887500 4 0.000314 0.001256 0.002826 0.005024 0.007850 5 000392500 0.001570 0.003532500 006280 0.009812500 6 0.000471 001884 0.004239 0.007536 0.011775 7 0.000549500 0.002198 0.004945500 0.008792 0.013737500 8 0.000628 0.002512 0.005652 0.010048 0.015700 9 0.000706500 0.002826 006358500 0.011304 0.017662500 10 0.000785 003140 0.007085 0.012560 0.019625 11 0.000863500 0.003454 0.007771500 0.013816 021587500 12 0.000942 0.003768 0.008478 0.015072 0.023550 13 0.001020500 0.004082 0.009184500 0.016328 025512500 14 0.001099 0.004396 0.009891 0.017584 0.027475 15 0.001177500 0.004710 0.010597500 0.018840 0.029437500 16 0.001256 0.005024 0.011304 0.020096 0.031400 17 0.001334500 0.005338 0.012010500 0.021352 0.033362500 18 0.001413 0.005652 0.012717 0.022608 0.035325 19 0.001491500 0.005966 0.013423500 0.023864 037287500 20 0.001570 0.006280 0.014130 0.025120 0.039250 30 0.002355 0.009420 0.021195 0.037680 0.058875 40 0.003140 0.012560 0.028260 0.050240 078500 50 0.003925 0.015700 035325 0.062800 0.098125 60 0.004710 0.018840 0.042390 0.075360 0.117750 -76 Diameter — in., lines, cm. ©urdjmeffer — §1., 1. , cm. High. 6 7 8 9 10 Etc. Square c >f Basis. — QuabrctthtljaU ber ftret§= mtb @nnibpd)e. £ocf), 2C. 0.002826 0.0038465 0.005024 0.006385 0.00785 Cube. §tübuä. 0.01 0.000028260 0.000038465 0.000050240 0.000063585 0.000078500 0*02 0.000056520 0.000076930 0.000100480 . 0,000127170 0.000157 0*03 0.000084780 0.000115395 0.000150720 000190755 0.000235500 0*04 0.000113040 0.000153860 0.000200960 0.000254340 0.000314 0*05 000141300 0.000192325 0.000251200 0.000317925 0.000392500 0*06 0.000169560 0.000230790 0.000301440 0.000381510 0.000471 0*07 0.000197820 0.000269255 0.000351680 0.000445095 0.000549500 0.08 0.000226080 0.000307720 0.000401920 0.000508680 0.000628 0*09 0.000254340 000346185 0.000452160 0.000572265 0.000706500 0*1 0.000282600 0.000384650 0.000502400 0.000635850 0.000785 0.2 0.000565200 0.000769300 0.001004800 0.001271^00 0.001570 0.3 0.000847800 0.001153950 0.001507200 0.001907550 0.002355 0.4 0.001130400 0.001538600 0.002009600 0.002543400 0.003140 0.5 0.001413 0.001923250 0.002512 0.003179250 0.003925 0.6 0.001695600 0.002307900 0.003014400 0.003815100 0.004710 0*7 0.001978200 0.002692550 0.003516800 0.004450950 0.005495 0.8 0.002260800 0,003077200 0.004019200 0.005086800 0.006280 0*9 0.002543400 0.003461850 0.004521600 0.005722650 0.007065 1 0.002826 0.003846500 0.005024 0.006358500 0.007850 2 0.005652 0.007693 0.010048 0.012717 0.015700 • 3 008478 0.011539500 0.015072 0.019075500 0.023550 4 0.011304 0.015386 . 0.020096 0.025434 0. 03 1400 5 0.014130 0.019232500 0-025120 0.031792500 0.039250 6 0.016956 0.023079 0.030144 0.038151 0.047100 !» 0.019782 0.026925500 0.035168 0.044509500 0.054950 8 0.022608 0.030772 0.040192 0.050868 0.062800 9 0.025434 0.034618500 0.045216 0.057226500 0.070650 10 0.028260 0.038465 0.050240 0.063585 0.078500 11 0.031086 0.042311500 0.055264 0.069943500 0.086350 12 0.033912 0.046158 0.060288 0.076302 0.094200 13 0.036738 0.050004500 0.065312 0.082660500 0.102050 14 0.039564 0.053851 0.070336 0.089019 0.109900 15 0.042390 0.057697500 0.075360 0.095377500 0.117750 16 045216 0.061544 0.080384 0.101736 0.125600 17 0.048042 0.065390500 085408 0.108094500 0.133450 18 0.050868 0.069237 0.090432 0.114453 0.141300 19 0.053694 0,073083500 0.095456 0.120811500 0.149150 20 0.056520 0.076930 0.100480 0.127170 0.157 . 30 0.084780 0.115395 150720 0.190755 0.235500 40 0.113040 0.153860 0.200960 0.254340 0.314 50 0.141300 0.192325 0.251200 0.317925 0.392500 60 0.169560 0.230790 j 0.301440 1 0.381510 0.471 — 77 — Diameter— in. , lines, cm. ©urcfymeffev — jl., I., cm. High, Etc. £>odj, 11 is 13 14 15 Square of Basis. — Ouctbrattnljcttt bei jfretsh itnb ©nuibflMjc. 0.0000735 0.000314 0.0007065 0.001256 0.0019625 Cube. jhtbus. 0*01 0.000094985 0.000113040 0.000132665 0.000153860 0.000176625 0*02 0.000189970 0.000226080 0.000265330 0.000307720 0.000353250 0*03 0.000284955 0.000339120 0.000397995 0.000461580 0.000529875 0.04 0.000379940 0.000452160 0.000530660 0.000615440 0.000706500 0*05 0. 000474925 0.000565200 0.000663325 0.000769300 0.000883125 0,06 0.000569910 0.000678240 0.000795990 0.000923160 0.001059750 0^07 0.000664895 0.000791280 0.000928755 0.001077020 0.001236375 0.08 0,000759880 0.000904320 0.001061320 0.001230880 0.001413 0.09 0.000854865 0.001017360 0.001193985 0.001384740 0.001589625 0.1 0.000949850 0.001130400 0.001326650 0.001538600 0.001766250 0.2 0.001899700 0.002260800 0.002653300 0.003077200 0.003532500 0.3 0.002849550 003391200 0.003979950 0.004615800 0.005298750 0.4 0.003799400 0.004521600 0.005306600. 0.006154400 0.007065 0.5 0.004749250 0.005652 0.006633250 0.007693 0.008831250 0.6 0.005699100 0.006782400 0.007959900 0.009231600 0.010597500 0.7 0.006648950 0.007912800 0.009286550 0.010770200 0.012363750 0.8 0.007598800 0.009043200 8.010613200 0.012308800 0.014130 0.9 0,008548650 0.010173600 0.011939850 0.013847400 0.015896250 1 0.009498500 0.011304 0.013266500 0.015386 0.017662500 2 0.018997 0.022608 0.026533 0.030772 0.035325 3 0.028495500 0.033912 0.039799500 0.046158 0.052987500 4 0.037994 0.045216 0.053066 0.061544 0.070650 5 0.047492500 0.056520 0.066332500 0-076930 0.088312500 6 0,056991 0.067824 0.079599 0.092316 0.105975 7 0.066489500 0.079128 0.092865500 0.107702 0.123637500 8 0.075988 090432 0.106132 0.123088 0.141300 9 0.085486500 0.101736 0.119398500 0.138474 0.158962500 10 0.094985 0.1*13040 0.132665 0.153860 0.176625 11 0.104483500 0.124344 145931500 0.169246 0.194287500 12 0.113982 0.135648 0.159198 0.184632 0.211950 13 0.123480500 0.146952 0.172464500 0.200018 0.229612500 14 0.132979 0.158256 0.185731 0.215404 0.247275 15 0.142477500 0.169560 0.198997500 0.230790 0.264937500 16 0.151976 0.180864 0.212264 0.246176 0.282600 17 0.161474500 0.192168 0.225530500 0.261562 0.300262500 18 0.170973 0.203472 0.238797 0.276948 0.317925 19 0.180471500 0.214776 0.252063500 0.292334 0.335587500 20 0.189970 0.226080 0.265330 0.307720 0.353250 30 284955 0.339120 0.397995 0.461580 0.529875 40 0.379940 0.452160 530660 0.615440 0.706500 50 0.474925 0.565200 0.663325 0.769300 0.883125 60 0.569910 0.678240 0.795990 0.923160 1.059750 78-- Diameter — in., lines, cm. ©urdjmeffev — jl., 1. cm. High, 16 17 18 19 20 Etc. Square of Basis. — Ouabvatinfyatt ber jtreigs nub ©runbflädje. £od), cc. 0.020096 0.0226865 0.025434 0.0283385 0.0314 Cube. ßuBuft; 0*01 0.000200960 0.000226865 0.000254340 0.000283385 0.000314 0.02 0.000401920 0.000453730 0.000508680 0.000566770 0.000628 0*03 0.000602880 0.000680595 0.000763020 0.000850155 0.000942 0,04 0.000803840 0.000907460 0.001017360 0.001133540 0.001256 0*05 0.001004800 0.001134325 0.001271700 0.001416925 0.001570 0.06 0.001205760 0.001361190 0.001526040 0.001700310 0.001884 0*07 0.001406720 0.001588055 0.001780380 0.001983695 0.002198 0.08 0.001607680 0.001814920 0.002034720 0.002267080 0.002512 0*09 0.001808640 0.002041785 0.002289060 0.002550465 0.002826 0.1 0. 002009600 0.002268650 0.002543400 0.002833850 0.003140 0*2 0.004019200 0.004537300 0.005086800 0.005667700 0.006280 0*3 0.006028800 0.006805950 007630200 0.008501550 0.009420 0.4 0.008038400 0.009074600 0.010173600 0.011335400 0.012560 0.5 0.010048 0.011343250 0.012717 0.014169250 0.015700 0.6 0.012057600 0.013611900 0.015260400 0.017003100 0.018840 0.1 0.014067200 0.015880550 0.017803800 0.019836950 0.021980 0.8 0.016076800 0.018149200 0.020347200 0.022670800 0.025120 0.9 0.018086400 0.020417850 0.022890600 0.025504650 0.028260 1 0.020096 022686500 0.025434 0.028338500 0.031400 2 0.040192 045373 0.050868 0.056677 0.062800 3 0.060288 0.068059500 0.076302 085015500 0.094200 4 0.080384 0.090746 0.101736 0.113354 0.125600 5 0.100480 0.113432500 0.127170 0.141692500 0.157 6 0.120576 0.136119 0.152604 0.170031 0.188400 7 0. 140672 158805500 0.178038 0.198369500 0.219800 8 0.160768 0.181492 0.203472 0.226708 0.251200 9 0.180864 0.204178500 0.228906 0.255046500 0.282600 10 0. 200960 0.226865 0.254340 0.283385 0.314 11 O.221056 0.249551500 0.279774 0.311723500 0.345400 12 0.241152 0.272238 0.305208 0.340062 0.376800 13 0.261248 0.294924500 0.330642 0.368400500 0.408200 14 0.281344 0.317611 0.356076 0.396739 0.439600 15 O.301440 0.340297500 0.381510 0.425077500 0.471 16 0.321536 0.362984 0.406944 453416 0.502400 17 0.341632 0.385670500 0.432378 0.481754500 0.533800 18 0.361728 0.408357 0.457812 0.510093 0.565200 19 0.381824 0.431043500 0. 48324(5 0.538431500 0.596600 20 0.401920 0.453730 508680 0.566770 0.628 30 0. 602880 0.680595 0.763020 0.850155 0.942 40 0. 803840 907460 1.017360 1.133540 1.256 50 1.004800 1.134325 1.271700 1.416925 1.570 60 1.205760 1.361190 1.526040 1.700310 1.884 — 79-- High, Etc. £odj. :c. Diameter — in., lines, 'cm. 5Durdjmeffer— $U, I. cm. 21 22 23 24 25 Square of Basis. — Ouabratiufjctlt ber Äret§= nub ©ruubflädjie. 0.0346185 | 0.037994 0.0415265 0.045216 0.0490625 Cube. Äu bug. 0*01 0.000346185 0.000379940 0.000415265 0.000452160 0.000490625 0.02 0.000692370 0.000759880 0.000830530 0.000904320 0.000981250 0*03 0.001038555 0.001139820 0.001245795 0.001356480 0.001471875 0*04 0.001384740 0.001519760 0.001661060 0.001808640 0.001962500 0.05 0.001730925 0.001899700 0.002076325 0.002260800 0.002453125 0,06 0.002077110 0.002279640 0.002491590 0.002712960 0.002943750 0*07 0.002423295 0.002659580 0.002906855 0.003165120 0.003434375 0.08 0.002769480 0.003039520 0.003322120 0.003617280 0.003925 0.09 0.003115665 0.003419460 0.003737385 0.004069440 0.004415625 0*1 0.003461850 0.003799400 0.004152650 0.004521600 0.004906250 0*2 0.006923700 0.007598800 0.008305300 0. 009043200 0.009812500 0.3 0.010385550 0.011398200 0.012457950 0.013564800 0.014718750 0.4 0.013847400 0.015197600 0.016610600 0.018086400 0.019625 0.5 0.017309250 0.018997 0.020763250 0.022608 0.024531250 0.6 0.020771100 0.022796400 0.024915900 0.027129600 0.029437500 0.7 0.024232950 0.026595800 0.029068550 0.031651200 0.034343750 0.8 0.027694800 0.030395200 0.033221200 0.036172800 0.039250 0.9 0.031156650 0.034194600 0.037373850 0.040694400 0.044156250 1 0.034618500 0.037994 0.041526500 0.045216 0.049062500 2 0.069237 0.075988 0.083053 0.090432 0.098125 3 0.103855500 0.113982 0.124579500 0.135648 0.147187500 4 0.138474 0.151976 0.166106 0. 180864 0.196250 5 0.173092500 0.189970 0.207632500 0.226080 0.245312500 6 0.207711 0.227964 0.249159 0.271296 0.294375 1 0.242329500 0.265958 0.290685500 0.316512 0.343437500 8 0.276948 0.303952 0.332212 0.361728 0.392500 9 0.311566500 0.341946 0.373738500 0.406944 0.441562500 10 0.346185 0.379940 0.415265 0.452160 0.490625 11 0.380803500 0.417934 0.456791500 0.497376 0.539687500 12 0.415422 0.455928 0.498318 0.542592 0.588750 13 0.450040500 0.493922 0.539844500 0.587808 0.637812500 14 0.484659 0.531916 0.581371 0.633024 0.686875 15 0.519277500 0.569910 0.622897500 0.678240 0.735937500 16 0.553896 0.607904 0.664424 0.723456 785 17 0.588514500 0.645898 0.705950500 0.768672 0.834062500 18 0.623133 0.683892 0.747477 0.813888 0.883125 19 0.657751500 0.721886 0.789003500 0.859104 0.932187500 20 0.692370 0.759880 0.830530 0.904320 0.981250 30 1.038555 1.139820 1.245795 1.356480 1.471875 40 1.384740 1.519760 1.661060 1.808640 1.962500 50 1.730925 1.899700 2.076325 2.260800 2.453125 60 2.077110 2.279640 2.491590 2.712960 2.943750 — 80 — Diameter — in., lines, cm, SDitrd^meffev — $1., I., cm. High. Etc. §0%, 20 27 28 | 20 30 Square of Basis. — Quctbratinljalt ber ^vei§- unb ®runbflädje. 0.053066 0.0572265 0.061544 0.0660185 0.07065 Cube. ÄubiiS. 0.01 0.000530660 000572265 0.000615440 0.000660185 0.000706500 0*02 0.001061320 0.001144530 0.001230880 0.001320370 0.001413 0*03 0.001591980 0.001716795 001846320 0.001980555 0.002119500 0*04 0.002122640 0.002289060 002461760 0.002640740 0.002826 0*05 0.002653300 0.002861325 0.003077200 0.003300925 0.003532500 0*06 0.003183960 0.003433590 0.003692640 0.003961110 0.004239 0,07 0.003714620 0.004005855 0.004308080 0.004621295 0.004945500 0*08 0.004245280 0. 004578120 0.004923520 0.005281480 0.005652 0*09 004775940 0. 005150385 0.005538960 0.005941665 0.006358500 0,1 0.005306600 0. 005722650 0.006154400 0.006601850 007065 0.2 0.010613200 O.O1144530O 0.012308800 0.013203700 0.014130 0.3 0.015919800 0.017167950 0-018463200 0.019805550 0.021195 0.4 0.021226400 0.022890600 0.024617600 0.026407400 0.028260 0.5 0.026533 O.02861325O 0.030772 0.033009250 0.035325 0.6 0.031839600 0.034335900 0.036926400 0.039611100 0-042390 0,7 0.037146200 0.040058550 0.043080800 0.046212950 0.049455 0.8 1 0,042452800 0.045781200 0.049235200 0.052814800 0.056520 0.9 0.047759400 0.051503850 0.055389600 0.059416650 0.063585 1 0.053066 0.057226500 0.061544 0.066018500 0.070650 2 0.106132 0.114453 0.123088 0.132037 0.141300 3 0.159198 0.171679500 0.184632 0.198055500 0.211950 4 0.212264 0.228906 0.246176 0.264074 0.282600 5 0.265330 0.286132500 0.307720 0.330092500 0.353250 6 0.318396 0.343359 0.369264 0.396111 0.423900 7 0.371462 0.400585500 0.430808 0.462129500 0.494550 8 0.424528 0.457812 0.492352 0.528148 0.565200 9 0.477594 0.515038500 0.553896 0.594166500 0.635850 10 0.530660 0.572265 0.615440 0.660185 0.706500 11 0.583726 0.629491500 0.676984 0.726203500 0.777150 12 0.636792 0.686718 0.738528 0.792222 0.847800 13 0.689858 0.743944500 0.800072 0.858240500 0.918450 14 0.742924 0.801171 0.861616 0.924259 0.989100 15 0.795990 0.858397500 0.923160 0.990277500 1.059750 16 0.849056 0.915624 0.984704 1.056296 1.130400 17 0.902122 0.972850500 1.046248 1.122314500 1.201050 18 0.955188 1.030077 1.107792 1.188333 1.271700 19 1.008254 1.087303500 1.169336 1.254351500 1.342350 20 1.061320 1.144530 1 .230880 1.320730 1.413 30 1.591980 1.716795 1.846320 1.980555 2.119500 40 2.122640 2.289060 2.461760 2,640740 2.826 50 2.653300 2.861325 3.077200 3.300925 3.532500 60 3.183960 3.433590 3.692640 1 3.961110 4.239 81 — — — — ■ Diameter — in., lines, cm. ©urdjmeffer — jl., I., cm. High, 31 32 33 34 35 Etc. Square of Basis. — Quabratinljalt ber £vei§; unb ©vunbfladje. cc. 0.0754385 0.080384 0.0854865 0.090746 0.961625 Cube. ßuBuS." 0*01 0.000754385 0.000803840 0.000854865 0.000907460 0.000961625 0.02 0.001508770 0.001607680 0.001709730 0.001814920 0.001923250 0.03 0.002263155 0.002411520 0.002564595 0.002722380 0.002884875 0.04 0.003017510 0.003215360 0.003419460 0.003629840 0.003846500 0.05 0.003771925 0.004019200 0.004274325 0.004537300 0.004808125 0,06 0.004526310 0.004823040 0.005129190 0.005444760 0.005769750 0.07 0.005280695 0.005626880 0.005984055 0.006352220 0.006731375 0.08 0.006035080 0.006430720 0.006838920 0.007259680 0.007693 0.09 0.006789465 0.007234560 0.007693785 0.008167140 0.008654625 0.1 0.007543850 0.008038400 0.008548650 0.009074600 0.009616250 0.2 0.015087700 0.016076800 0.017097300 0.018149200 0.019232500 0.3 0.022631550 0.024115200 0.025645950 0.027223800 028848750 0.4 0.030175400 0.032153600 0.034194600 0.036298400 0.038465 0.5 0.037719250 0.040192 0.042743250 0.045373 0.048081250 0.6 0.045263100 0.048230400 0.051291900 0.054447600 0.057697500 0.? 0.052806950 0.056268800 0.059840550 0.063522200 0.067313750 0.8 0.060350800 0.064307200 0.068389200 0.072596800 0.076930 0.9 0.067894650 0.072345600 0.076937850 0.081671400 0.086546250 1 0.075438500 0.080384 0.085486500 090746 0.096162500 2 0.150877 0.160768 0.0170973 181492 0.192325 3 0.226315500 0.241152 0.256459500 0.272238 0.288487500 4 0.301754 0.321536 0.341946 0.362984 0.384650 5 0.377192500 0.401920 0.427432500 0.453730 0.480812500 6 0.452631 0.482304 0.512919 0.544476 0.576975 7 0.528069500 0.562688 0.598405500 635222 0.673137500 8 0.603508 0.643072 0.683892 0.725968 0.769300 9 0.678946500 0.723456 0.769378500 0.816714 0.865462500 10 0.754385 0.803840 0.854865 0.907460 0.961625 11 0.829823500 0.884224 0.940351500 1.998206 1.057787500 12 0.905262 0.964608 1.025838 1.088952 1.153950 13 0.980700500 1.044992 1.111324500 1.179698 1.250112500 14 1.056139 1.125376 1.196811 1.270441 1.346275 15 1.131577500 1.205760 1.282297500 1.361190 1.442437500 16 1.207016 1.286144 1.367784 1.451936 1.538600 17 1.282454500 1.366528 1.453270500 1.542682 1.634762500 18 1.357893 1.446912 1.538757 1.633428 1.730925 19 1.433331500 1.527296 1.624243500 1.724174 1.827087500 20 1.508770 1.607680 1.709730 1.814920 1.923250 30 2.263155 2.411520 2.564595 2.722380 2.884875 40 3.017540 3.215360 3.419460 3.629840 3.846500 50 3.771925 4.019200 4.274325 4 537300 4.808125 60 4.526310 4.823040 5.129190 5.444760 5.769750 82 Diameter— in., lines, cm, 2)urdj meffer— jl., L, cm. High, 36 37 38 39 40 Etc. Square o C Basis. — Ouabratinljalt bev Ärei§= xnib @rmibfläd)e. K. 0.101736 0.1074665 | 0.113354 0.1193985 0.1256 Cube. ßubu§. 0.01 0.001017360 0.001074665 0.001133540 0.001193985 0.001256 0*02 0.002034720 0. 002 149330 0.002267080 . 0.002387970 0.002512 0.03 0.003052080 0.003223995 0.003400620 0.003581955 0.003768 0.04 0.004069440 0.004298660 0.004534160 0.004775940 0.005024 0.05 0.005086800 0.005373325 0.005667700 0.005969925 0.006280 0,06 0.006104160 0.006447990 0.006801240 0.007163910 0.007536 0*07 0.007121520 0.007522655 0.007934780 0.008357895 " 0.008792 0.08 0.008138880 0.008597320 0.009068320 009551880 0.010048 0*09 0.009156240 0.009671985 0.010201860 0.010745865 0.011304 0.1 0.010173600 0.010746650 0.011335400 0.011939850 0.012560 0*2 0.020347200 0.021493300 0.022670800 0.023879700 0.025120 0*3 0.030520800 0.032239950 0.034006200 0.035819550 0.037680 0.4 0.040694400 0.042986600 0.045341600 0.047759400 0.050240 0.5 0.050868 0.053733250 0056677 0.059699250 0.062800 0*0 0.061041600 0.064479900 0.068012400 0.071639100 0.075360 0.7 0.071215200 0.075226550 0.079347800 0.083578950 0.087920 0.8 0.081388800 0.085973200 0.090683200 0.095518800 0.100480 0.9 0.091562400 0.096719850 0.102018600 0.107458650 0.113040 1 0.101736 0.107466500 0.113354 0.119398500 0.125600 2 0.203472 0.214933 0.226708 0.238797 0.251200 3 305208 0.322399500 0.340062 0.358195500 0.376800 4 0.406944 0.429866 0.453416 0.477594 0.5024.00 5 0.508680 0.537332500 0.566770 0.596992500 0.628 6 0.610416 0.644799 0.680124 0.716391 0.753600 7 0.712152 0.752265500 0.793478 0.835789500 879200 8 0.813888 0.859732 0.906832 0.955188 1.004800 9 0.915624 0.967198500 1.020186 1.074586500 1.130400 10 1.017360 1.074665 1.133540 1.193985 1.256 11 1.119096 1.182131500 1.246894 1.313383500 1.381600 12 1.220832 1.289598 1.360248 1.432782 1.507200 13 1.322568 1.397064500 1.473602 1.552180500 1.632800 14 1.424304 1.504531 1.586956 1.671579 1.758400 15 1.526040 1.611997500 1.700310 1.790977500 1.884 16 1 627776 1.719464 1.813664 1.910376 2.009600 17 1.729512 1.826930500 1.927018 2.029774500 2.135200 18 1.831248 1.934397 2.040372 2.149173 2.260800 19 1.932984 2.041863500 2.153726 2.268571500 2.386400 20 2.034720 2.149330 2.267080 2.387970 2.512 30 3.052080 3.223995 3.400620 3.581955 3.768 40 4.069440 4.298660 4.534160 4.775940 5.024 50 5.086800 5.373325 5.667700 5.969925 6.280 60 6.104160 6.447990 6.801240 7.163910 7.536 83 Diameter— in. , lines, cm. £uidj meffer— jl. f I, cm. High, Etc. 41 42 43 44 45 Square of Basis.— Ouctbwtinljalt bev § frei§* itnb ©nmbflädje. 2C. 0.1319585 0.138474 0.1451465 0.151976 0.1589625 Cube. M>u§. 0*01 0.001319585 0.001384740 0.001451465 0.001519760 0.001589625 0*02 0.002639170 0.002769480 0.002902930 0.003039520 0.003179250 0*03 0.003958755 0.004154220 0.004354395 0.004559280 0.004768875 0*04 0.005278340 0.005538960 0.005805860 0.006079040 0.006358500 0*05 0.006597925 0.006923700 0.007257325 0.007598800 0.007948125 0.06 0.007917510 0.008308440 0.008708790 0.009118560 0.009537750 0*07 0.009237095 0.009693180 0.010160255 0.010638320 0.011127375 0*08 0.010556680 0.011077920 0.011611720 0.012158080 0.012717 0*09 0.011876265 0.012462660 0.013063185 0.013677840 0.014306625 0*1 0.013195850 0.013847400 0.014514650 0.015197600 0.015896250 0*2 0.026391700 0.027694800 0.029029300 0.030395200 0.031792500 0*3 0.039587550 041542200 0.043543950 0.045592800 0.047688750 0*4 0.052783400 055389600 0.058058600 0.060790400 0.063585 0*5 0.065979250 069237 0.072573250 0.075988 0.079481250 0.6 0.079175100 0.083084400 0.087087900 0.091185600 0.095377500 0.7 0.092370950 0.096931800 0.101602550 0.106383200 0.111273750 0.8 0.105566800 8.110779200 0.116117200 0.121580800 0.127170 0*9 0.118762650 124626600 0.130631850 0.136778400 0.143066250 1 0.131958500 0.138474 0.145146500 0.151976 0.158962500 2 0.263917 0.276948 0.290293 0.303952 0.317925 3 0.395875500 0.415422 0.435439500 0.455928 0.476887500 4 0.527834 0.553896 0.580586 0.607904 0.635850 5 0.659792500 0.692370 ' 0.725732500 0.759880 0.794812500 6 0.791751 0.830844 0.870879 0.911856 0.953775 7 0.923709500 0.969318 1.016025500 1.063832 1.112737500 8 1.055668 1.107792 1.161172 1.215808 1.271700 9 1.187626500 1.246266 1. 306318500 1.367784 1.430662500 10 1.319585 1 384740 1.451465 1.519760 1.589625 11 1.451543500 1.523214 1.596611500 1.671736 1.748587500 12 1.583502 1.661688 1.741758 1.823712 1.907550 13 1.715160500 1.800162 1.886904500 1.975688 2.066512500 14 1.847419 1.938636 2.032051 2.127664 2.225475 15 1.979377500 2.077110 2.177197500 2.279640 2.384437500 16 2.111336 2.215584 2.322344 2.431616 2.543400 17 2.243294500 2.354058 2.467490500 2.583592 2.702362500 18 2.375253 2.492532 2.612637 2.735568 2.861325 19 2.507211500 2.631006 2.757783500 2.887544 3.020287500 20 2.639170 2.769480 2.902930 3.039520 3.179250 30 3.958755 4.154220 4.354395 4.559280 4.768875 40 5.278340 5.538960 5.805860 6.079040 6.358500 50 6.597925 6.923700 7.257325 7.598800 7.948125 60 7.917510 8.308440 8.708790 9.118560 9.537750 — 84 Diameter — in., lines, cm. £)urd)meffer— $1., I., cm. High, 46 47 48 49 50 Etc. Square of Basis. — Oitabrctttuljalt ber Ärei§= imb ©runbflädje. cc. 0.166106 0.1734065 0.180864 | 0.1884785 0.19625 Cube. ßubuS. 0.01 0.001661060 0.001734065 0.001808640 0.001884785 0.001962500 0.02 0.003322120 0.003468130 0.003617280 0.003769570 0.003925 0.03 0.004983180 0.005202195 0.005425920 0.005654355 0.005887500 0.04 0.006644240 0.006936260 0.007234560 0.007539140 0.007850 0*05 0.008305300 0.008670325 0.009043200 0.009423925 0.009812500 0.06 0.009966360 0.010404390 0.010851840 0.011308710 0.011775 0*07 0.011627420 0.012138455 0.012660480 0.013193495 0.013737500 0.08 0.013288480 0.013872520 0.014469120 0.015078280 0.015700 0.09 0.014949540 0.015606585 0.016277760 0.016963065 0.017662500 0.1 0.016610600 0.017340650 0.018086400 ' 8847850 0.019625 0.2 0.033221200 0.034681300 0.036172800 0.037695700 0.039250 0.3 0.049831800 0.052021950 0.054259200 0.056543550 0.058875 0.4 0.066442400 0.069362600 0.072345600 0.075391400 0.078500 0.5 0.083053 0.086703250 0.090432 0.094239250 0.098125 0.0 0.099663600 0.104043900 0.108518400 0.113087100 0.117750 0.7 0.116274200 0.121384550 0.126604800 0.131934950 0.137375 0.8 0.132884800 0.138725200 0.144691200 0.150782800 0.157 0.9 0.149495400 0.156065850 0.162777600 0.169630650 0.176625 1 0.166106 0.173406500 0.180864 0.188478500 0.196250 2 0.332212 0.346813 0.361728 0.376957 0.392500 • 3 0.498318 0.520219500 0.542592 0.565435500 588750 4 0.664424 0.693626 0.723456 0.753914 0.785 5 0.830530 0.867032500 0.904320 0.942392500 0.981250 6 0.996636 1.040439 1.085184 1.130871 1.177500 7 1.162742 1.213845500 1.266048 1.319349500 1.373750 8 1.328848 1.387252 1,446912 1.507828 1.570 9 1.494954 1.560658500 1.627776 1.696306500 1.766250 10 1.661060 1.734065 1.808640 1.884785 1. 962500 11 1.827166 1.907471500 1.989504 2.073263500 2.158750 12 1.993272 2.080878 2.170368 2.261742 2.355 13 2.159378 2.254284500 2.351232 2.450220500 2.551250 14 2.325484 2.427691 2.532096 2.638699 2.747500 15 2.491590 2 601097500 2.712960 2.827177500 2.943750 16 2.657696 2.774504 2.893824 3.015656 3.140 17 2.823802 2.947910500 3.074688 3.204134500 3.336250 18 2.989908 3.121317 3.255552 3.392613 3.532500 19 3.156014 3.294723500 3.436416 3.581091500 3.728750 20 3.322120 3.468130 3.617280 3.769570 3.925 30 4.983180 5.202195 5.425920 5.654355 5.887500 40 6.644240 6.936260 7.234560 7.539140 7.850 50 8.305300 8.670325 9.043200 9.423925 9.812500 60 9.966360 10.404390 10.851840 11.308710 . 11.775 — 85- Diameter — in., lines, cm. 5Durd imeffer— jl., I., cm. High. 51 52 53 54 55 Etc. Square of Basis. — DuabrctttnJjctlt her ftret§= ltnb ©ruubflädje. ■£>odj, JC. 0.2041785 0.212264 0.2205065 0.228906 0.2374625 Cube. £ufcu§. 0.01 0.002041785 0.002122640 0.002205065 0.002289060 0.002374625 0.02 0.004083570 0.004245280 0.004410130 0.004578120 0.004749250 0.03 0.006125355 0.006367920 0.006615195 0.006867180 0.007123875 0.04 0.008167140 0.008490560 0.008820260 0.009156240 0.009498500 0.05 0.010208925 0.010613200 0.011025325 0.011445300 0.011873125 0,06 0.012250710 0.012735840 0.013230390 0.013734360 0.014247750 0.07 0.014292495 0.014858480 0.015435455 0.016023420 0.016622375 0.08 0.016334280 0.016981120 0.017640520 0.018312480 0.018997 0*09 0.018376065 0.019103760 0.019845585 0.020601540 0.021371625 0.1 0.020417850 0.021226400 0. 022o50650 0.022890600 0.023746250 0*2 0.040835700 0.042452800 0.044101300 0.045781200 0.047492500 0.3 0.061253550 0.063679200 0.066151950 0.068671800 0.071238750 0.4 0.081671400 0.084905600 0.088202600 0.091562400 0.094985 0.5 0.102089250 0.106132 0.110253250 0.114453 0.118731250 0.6 0.122507100 0.127358400 0.132303900 0.137343600 0.142477500 0.7 0.142924950 0.148584800 0.154354550 0.160234200 0.166223750 0.8 0.163342800 0.169811200 0.176405200 0.183124800 0.189970 0.9 0.183760650 0.191037600 0.198455850 0.206015400 0.213716250 1 0.204178500 0.212264 0.220506500 0.228906 0.237462500 2 0.408357 0.424528 0.441013 0.457812 0.474925 3 0.612535500 0.636792 0.661519500 0.686718 0.712387500 4 0.816714 0.849056 0.882026 0.915624 0.949850 5 1.020892500 1.061320 1.10253^500 1.144530 1.187312500 6 1.225071 1.273584 1.323039 1.373436 1.424775 7 1.429249500 1.485848 1.543545500 1.602342 1.662237500 8 1.633428 1.698112 1.764052 1.831248 1.899700 9 1.837606500 1.910376 1.984558500 2.060154 2.137162500 10 2.041785 2.122640 2.205065 2.289060 2.374625 11 2.245963500 2.334904 2.425571500 2.517966 2.612087500 12 2.450142 2.547148 2.646078 2.746872 2 849550 13 2.654320500 2.759432 2.866584500 2.975778 3.087012500 14 2.858499 2.971696 3.087091 3.204684 3.324475 15 3.062677500 2.183960 3.307597500 3.433590 3.561937500 16 3.266856 3.396224 3.528104 3.662496 3.799400 17 3.471034500 3.608488 3.748610500 3.891402 4.036862500 18 3.675213 3.820752 3.969117 4.120308 4.274325 19 3.879391500 4.033016 4.189623500 4 349214 4.511787500 20 4.083570 4.245280 4.410130 4.578120 4.749250 30 6.125355 6.367920 6.615195 6.867180 7.123875 40 8.167140 8.490560 8.820260 9.156240 9.498500 50 10.208925 10.613200 11.025325 11.445300 11.873125 60 12 250710 12.735840 13.230390 13.734360 14.247750 Diameter — in., lines, cm. SDurdjtneffer — jl., I. cm. High, 56 57 58 59 60 Etc. Square of Basis. — QuabrcttinljaU bei* ÄreiS= nub ©n uibfTädje. K. 0.246176 0.2550465 0.264074 0.2732585 0.2826 Cube. ÄaBiiS. o.oi 0.002461760 0.002550465 0.002640740 0.002732585 0.002826 0*02 0.004923520 0.005100930 0.005281480 0.005465170 0.005652 0.03 0.007385280 0.007651395 0.007922220 0.008197755 0.008478 0*04 0.009847040 0.010201860 0.010562960 0.010930340 0.011304 0.05 0.012308800 0.012752325 0.013203700 0.013662925 0.014130 0.06 0.014770560 0.015302790 0.015844440 0.016395510 0.016956 0*07 017232320 0.017853255 0.018485180 0.019128095 0.019782 0.08 0.019694080 0.020403720 0.021125920 0.021860680 0.022608 0.09 0.022155840 0.022954185 0.023766660 0.024593265 0.025434 0.1 0.024617600 0.625504650 0.026407400 0.027325850 0.028260 0.2 0.049235200 0.051009300 0.052814800 0.054851700 0.056520 0.3 0.073852800 0.076513950 0.079222200 0.081977550 0.084780 0.4 0.098470400 0.102018600 0.105629600 0.109303400 0.113040 0.5 0.123088 0.127523250 0.132037 0.136629250 0.141300 0.Ö 0.147705600 0.153027900 0.158444400 0.163955100 0.169560 0.7 0.172323200 0.178532550 0.184851800 0.191280950 0.197820 0.8 0.196940800 0.204037200 0.211259200 0.218606800 0.226080 0.9 0.221558400 0.229541850 0.237666600 0.245932650 0.254340 1 0.246176 0.255046500 0.264074 0.273258500 0.282600 2 0.492352 0.510093 0.528148 0.546517 0.565200 • 3 0.738528 0.765139500 0.792222 0.819775500 0.847800 4 0.984704 1.020186 1.056296 1.093034 1.130400 5 1.230880 1.275232500 1.320370 1.366292500 1.413 6 1.477056 1.530279 1.584444 1.639551 1.695600 7 1.723232 1.785325500 1.848518 1.912809500 1.978200 8 1.969408 2.040372 2.112592 1.186068 2.260800 9 2.215584 2.295418500 2.376666 2.459326500 2.543400 10 2.461760 2.550465 2.640740 2.732585 2.826 11 3.717936 2.805511500 2.904814 3.005843500 3.108600 12 2 964112 3.060558 3.168888 3.279102 3.391200 13 3.210288 3.315601500 3.432962 3.552360500 3.673800 14 3.456464 3 570651 3.697036 3.825619 3.956400 15 3.702640 3.825697500 3.961110 4.098877500 4.239 16 3.948816 4.080744 4.225184 4.372136 4.521600 17 4.194992 4.335790500 4.489258 4.645394500 4.804200 18 4.441168 4.590837 4.753332 4.918653 5.086800 19 4.687344 4.845883500 5.017406 5.191911500 5.369400 20 4.923520 5.100930 5.281480 5.465170 5.652 30 7 385280 7.651395 7.922220 8.197755 8.478 40 9.847040 10.201860 10.562960 10.930340 11.304 50 12,308800 12.752325 13.203700 13.662925 14.130 f>0 14.770560 15.302790 15.844440 16.395510 . 16.956 g?— Diameter — in., lines, cm. £)urdj meffer— gl., 1., cm. High, 61 62 63 64 65 Etc. Square of Basis. — Ouabratinfjaft ber Jtrei§= uub ©ruubflädje. £otf), 2C. 0.2920985 0.301754 0.3115665 0.321536 0.33166625 Cube. ÄuBuS. 0*01 0.002920985 0.003017540 0.003115665 0.003215360 0.003316625 0.02 0.005841970 0.006035080 0.006231330 0.006430720 0.006633250 0*03 0.008762955 0.009052620 0.009346995 0.009646080 0.009949875 0*04 0.011683940 0.012070160 0.012462660 0.012861440 0.013266500 0*05 0.014604925 0.015087700 0.015578325 0.016076800 0.016583125 0,06 0.017525910 018105240 0.018693990 0.019292160 0.019899750 0*0? 0.020446895 0.021122780 0.021809655 0.022507520 0.023216375 0*08 0.023367880 0.024140320 0.024925320 0.025722880 0.026533 0*09 0.026288865 0.027157860 0.028040985 0.028938240 0.029849625 0*1 0.029209850 0.030175400 0.031156650 0.032153600 0.033166250 0*2 0.058419700 0.060350800 0.062313300 0.064307200 0.066332500 0.3 0.087629550 0.090526200 0.093469950 0.096460800 0.099498750 0*4 0.116839400 0.120701600 0.124626600 0.128614400 0.132665 0*5 0.146049250 0.150877 0.155783250 0.160768 0.165831250 0*6 0.175259100 0.181052400 0.186939900 0.192921600 0.198997500 o.y 0.204468950 0.211227800 0.218096550 0.225075200 0.232163750 0.8 0.233678800 0.241403200 0.249253200 0.257228800 0.265330 0.9 0.262888650 0.271578600 0.280409850 0.289382400 0.298496250 1 0.292098500 0.301754 0.311566500 0.321536 0.331662500 2 0.584197 0.603508 0.623133 0.643072 0.663325 3 0.876295500 0.905262 0.934699500 0.964608 0.994987500 4 1.168394 1.207016 1.246266 1.286144 1.326650 5 1.460492500 1.5087*0 1.557832500 1.607680 1.658312500 6 1.752591 1.810524 1.869399 1.929216 1.989975 7 2.044689500 2.112278 2.180965500 2.250752 2.321637500 8 2.336788 2.414032 2 492532 2.572288 2.653300 9 2.628886500 2.715786 2.804098500 2.893824 2.984962500 10 2.920985 3.017540 3.115665 3.215360 3.316625 11 3.213083500 3.319294 3.427231500 3.536896 3.648287500 12 3.505182 3.621048 3.738798 3.858432 3.979950 13 3.797280500 3.922802 4.050364500 4.179968 4.311612500 14 4.089379 4.224556 4.361931 4.501504 4.643275 15 4.381477500 4.526310 4.673497500 4.823040 4.974937500 16 4.673576 4.828064 4.985064 5.144576 5.306600 17 4.965674500 5.129818 5.296630500 5.466112 5.638262500 18 5.257773 5.431572 5.608197 5.787648 5.969925 19 5.549871500 4.733326 5.919763500 6.109184 6.301587500 20 5.841970 6.035080 6.231330 6.430720 6.633250 30 8.762955 9.052620 9.346995 9.646080 9.949875 40 11.683940 12.070160 12.462660 12.861440 13.266500 50 14.604925 15.087700 15.578325 16.076800 16.583125 . 60 17.525910 18.105240 18.693990 19.292160 19.899750 Diameter — in., lines, cm. £)urd »meffer— jl., 1, cm. High, 66 67 68 69 70 Etc. Square of Basis. — Quctbrctttnljalt ber Äret§s itnb @ritubflad)e. 2C. 0.341946 0.3523865 0.362984 0.3737385 0.38465 Cube. ßubu§. 0.01 0.003419460 0.003523865 0.003629840 0.003737385 0.003846500 0*02 0.006838920 0.007047730 0.007259680 0.007474770 0.007693 0*03 0.010258380 0.010571595 0.010889520 0.011212155 0.011539500 0*04 0.013677840 0.014095460 0.014519360 0.014949540 0.015386 0*05 0.017097300 0.017619325 0.018149200 0.018686925 0.019232500 0*06 0.020516760 0.021143190 0.021779040 0.022424310 0.023079 0*07 023936220 0.024667055 0.025408880 0.026161695 0. 026925500 0*08 0.027355680 0.028190920 0.029038720 0.029899080 0.030772 0.09 0.030775140 0.031714785 0.032668560 0.033636465 0.034618500 0.1 0.034194600 0.035238650 0.036298400 0.037373850 0.038465 0,2 0.068389200 0.070477300 0.072596800 0.074747700 0.076930 0,3 0.102583800 0.105715950 0.108895200 0.112121550 0.115395 0,4 0.136778400 0.140954600 0.145193600 0.149495400 0.153860 0.5 0.170973 0.176193250 0.181492 0.186869250 0.192325 0*6 0.205167600 0.211431900 0.217790400 0.224243100 0.230790 0*7 0.239362200 0,246670550 0.254088800 0.261616950 0.269255 0*8 0.273556800 0.281909200 0.290387200 0.298990800 0.307720 0,9 0.307751400 0.317147850 0.326685600 0.336364650 0.346185 1 0.341946 0.352386500 0.362984 0.373738500 0.384650 2 0.683892 0.704773 0.725968 0.747477 0.769300 3 1.025838 1.057159500 1.088952 1.121215500 1.153950 4 1.367784 1.409546 1.451936 1.494954 1.538600 5 1.709730 1.761932500 1.814920 1.868692500 1.923250 6 2.051676 2.114319 2.177904 2.242431 2.307900 7 2.393622 2.466705500 2.540888 2.616169500 2.692550 8 2.735568 3.819092 2.903872 2.989908 3.077200 9 3.077514 3.171478500 3.266856 3.363646500 3.461850 10 3.419460 3.523865 3.629840 3.737385 3.846500 11 3.761406 3.876251500 3.992824 4.111123500 4.231150 12 4.103352 4.228638 4.355808 4.484862 4.615800 13 4.445298 4.581024500 4.718792 4.858600500 5.000450 14 4.787244 4.933411 5.081776 5.232339 5.385100 15 5.129190 5.285797500 5.444760 5.606077500 5.769750 16 5.471136 5.638184 5.807744 5.979816 6.154400 17 5.813082 5.990570500 6.170728 6.353554500 6.539050 18 6.155028 6.342957 6.533712 6.727293 6.923700 19 6.496974 6.695343500 6.896696 7.101031500 7.308350 20 6.838920 7.047730 7.259680 7.474770 7.693 30 10.258380 10.571595 10.889520 11.212155 11.539500 40 13.677840 14.095460 14.519360 14.949540 15.386 . 50 17.097300 17.619325 18.149200 18.686025 19.232500 60 20.516760 21.143190 21.779040 22.424310 23.079 — 89 Diameter— in., lines, cm. SDurd&meffev— $!., I. cm. High, n 72 73 74 75 Etc. Square of Basis. — Quabratiuljcilt bev ftreigs itnb ©runbflädje. £od), cc. 0.3957185 0.406944 0.4813265 0.429866 | 0.4415625 Cube. £ubit§. 0*01 0.003957185 0.004069440 0.004183265 0.004298660 0.004415625 0*02 0.007914370 0.008138880 0.008366530 0.008597320 0.008831250 0*03 0.011871555 0.012208320 0.012549795 0.012895980 0.013246875 0*04 0.015828740 0.016277760 0.016733060 0.017194640 0.017662500 0*05 0.019785925 0.020347200 0.020916325 0.021493300 0.022078125 0,06 0.023743110 0.024416640 0.025099590 0.025791960 0.026493750 0*07 0.027700295 0.028486080 0.029282855 0.030090620 0.030909375 0*08 0.031657480 0.032555520 0.033466120 0.034389280 0.035325 0*09 0.035614665 0.036624960 0.037649385 0.038687940 0.039740625 0*1 0.039571850 0.040694400 0.041832650 0.042986600 0.044156250 0*2 0.079143700 0.081388800 0.083665300 0.085973200 0.088312500 0*3 0.118715550 0.122083200 0.125497950 0. 128959800 0.132468750 0*4 0.158287400 0.162777600 0.167330600 0.171946400 0.176625 0*5 0.197859250 0.203472 0.209163250 0.214933 0.220781250 0*0 0.237431100 0.244166400 0.250995900 0.257919600 0.264937500 0*7 0.277002950 0.284860800 0.292828550 0.300906200 0.309093750 0*8 0.316574800 0.325555200 0.334661200 0.343892800 0.353250 0*9 0.356146650 0.366249600 0.376493850 0.386879400 0.397406250 1 0.395718500 0.406944 0.418326500 0.429866 0.441562500 2 0.791437 0.813888 0.836653 0.859732 0.883125 3 1.187155500 1.220832 1.254979500 1.289598 1.324687500 4 1.582874 1.627776 1.673306 1.719464 1.766250 5 1.978592500 2.034720 2.091632500 2.149330 2.207812500 6 2.374311 2.441664 2.509959 2.579196 2.649375 7 2.770029500 2.848608 2.928285500 3.009062 3.090937500 8 3.165748 3.255552 3.346612 3.438928 3.532500 9 3.561466500 3.662496 3.764938500 3.868794 3.974062500 10 3.957185 4.069440 4.183265 4.298660 4.415625 11 4.352903500 4.476384 4.601591500 4.728526 4.857187500 12 4.748622 4 883328 5.019918 5.158392 5.298750 13 5.144340500 5.290272 5.438244500 5.588258 5.740312500 14 5.540059 5.697216 5.856571 6.018124 6.181875 15 5.935777500 6.104160 6.274897500 6.447990 6.623437500 16 6.331496 6.511104 6.693224 6.877856 7.065 17 6.727214500 6.918048 7.111550500 7.307722 7.506562500 18 7.122933 7.324992 7.529877 7.737588 7.948125 19 7.518651500 7.731936 7.948203500 8.167454 8.389687500 20 7.914370 8.138880 8.366530 8.597320 8.831250 30 11.871555 12.208320 12.549795 12.895980 13.246875 40 15.828740 16.277760 16.733060 17.194640 17.662500 50 19.785925 20.347200 20.916325 21.493300 22.078125 60 23.743110 24.416640 25.099590 25.791960 26.493750 90 — Diameter — in., lines, cm. £)urtf):nef|er — gl., I., cm. High, 76 4 4 78 79 80 Etc. Square of Basis.— Ouabvatinljalt ber Ävei§= unb ©runbflädje. £odj. 2C. 0.453416 0.4654265 0.477594 0.4899185 0.5024 Cube. stubm. 0.01 0.004534160 0.004654265 0.004775940 0.004899185 0.005024 0*02 0.009068320 0.009308530 0.009551880 0.009798370 0.010048 0.03 0.013602480 0.013962795 0.014327820 0.014697455 0.015072 0*04 0.018136640 0.018617060 0.019103760 0.019596740 0.020096 0*05 0.022670800 0.023271325 0.023879700 0.024495925 0.025120 0.06 0.027204960 0.027925590 0.028655640 0.029395110 0.030144 0*07 0.031739120 0.032579855 0.033431580 0.034294295 0.035168 0.08 0.036273280 0.037234120 0.038207520 0.039193480 0.040192 0.09 0.040807440 0.041888385 0.042983460 0.044092665 0.045216 0.1 0.045341600 0.046542650 0.047759400 0.048991850 0.050240 0*2 0.090683200 0.093085300 0.095518800 0.097983700 0.100480 0.3 0.136024800 0.139627950 0.143278200 0.146975550 0.150720 0-4 0.181366400 0.186170600 0.191037600 0.195967400 0.200960 0.5 0.226708 0.232713250 0.238797 0.244959250 0.251200 0.6 0.272049600 0.279255900 0.286556400 0.293951100 0.301440 0.7 0.317391200 0.325798550 0.334315800 0.342942950 0.351680 0.8 0.362732800 0.372341200 0.382075200 0.391934800 0.401920 0.9 0.408074400 0.418883850 0.429834600 0.440926650 0.452160 1 0.453416 0.465426500 0.477594 0.489918500 0.502400 2 0.906832 0.930853 0.955188 0.979837 1.004800 3 1.360248 1.396279500 1.432782 1.469755500 1.507200 4 1 813664 1.861706 1.910376 1 959674 2.009600 5 2.267080 2.327132500 2.387970 2.449592500 2.512 . 6 2.720496 2.792559 2.865564 2.939511 3.014400 7 3 173912 3.257985500 3.343158 3.429429500 3.516800 8 2.627328 3.723412 3.820752 3.919348 4.019200 9 4.080744 4 188838500 4.298346 4 409266500 4.521600 10 4.534160 4.654265 4.775940 4.899185 5.024 11 4.987576 5.119691500 5.253534 5.389103500 5.526400 12 5.440992 5.585118 5.731128 5.879022 6.028800 13 5.894408 6.050544500 6.208722 6.368940500 6.531200 14 6.347824 6.515971 6.686316 6.858859 7.033600 15 6.801240 6.981397500 7.163910 7.348777500 7.536 16 7.254656 7.446824 7.641504 7.838696 8.038400 17 7.708072 7.912250500 8.119098 8.328614500 8.540800 18 8.161488 8.377677. 8.596692 8.818533 9.043200 19 8.614904 8.843103500 0.074286 9.308451500 9.545600 20 9.068320 9.308530 9.551880 9.798370 10.048 30 13.602480 13.962795 14.327820 14.697555 15.072 40 18.136640 18.617060 19.103760 19.596740 20.096 50 22.670800 23.271325 23.879700 24.495925 25.120 60 27.204960 27.925590 28.655640 • 29.395110 30.144 — 91 — Diameter— in. , lines, cm. Sind; meffer— jL, l., cm. Hieb, 81 | 82 83 84 i 85 JitC. Square o l Basis. — Quctbratintjalt bei j?ret§= itnb ©rmtbflädje. £odi, 0.5150.385 0.527834 0.5407865 0.553896 0.5671625 Cube. föu&uS. O.Ol 0.005150385 0.005278340 0.005407865 0.005538960 0.005671625 0.02 0.010300TTO 0.010556680 010815730 0.011077920 0.011343250 0.03 0.015451155 0.015835020 0.016223595 0.016616880 0.017014875 0.04 0.020601540 0.021113360 0.021631460 0.022155840 0.022686500 0.05 0.025751925 0.026391700 0.027039325 0.027694800 0.028358125 0,06 0.030902310 0.031670040 0.032447190 0.033233760 0.034029750 0.0? 0.036052695 0.036948380 0.037855055 0.038772720 0.039701375 0.08 0.041203080 0.042226720 0.043262920 0.044311680 0.045373 0.09 0.046353465 0.047505060 0.048670785 0.049850640 0.051044625 0.1 0.051503850 0.052783400 0.054078650 0.055389600 0.056716250 0.2 0.103007700 0.105566800 0.108157300 0.110779200 0.113432500 0.3 0.154511550 0.158350200 0.162235950 0.166168800 0.170148750 0.4 0.206015400 0.211133600 0.216314600 0.221558400 0.226865 0.5 0.257519250 0.263917 0.270393250 0.276948 0.283581250 0.6 0.309023100 0.316700400 0.324471900 0.332337600 0.340297500 0.7 0.360526950 0.369483800 0.378550550 0.387727200 0.397013750 0.8 0.412030800 0.422267200 0.432629200 0.443116800 0.453730 0.9 0.463534650 0.475050600 0.486707850 0.498506400 0.510446250 1 0.515038500 527834 0.540786500 0.553896 0.567162500 2 1.030077 1.055668 1.081573 1.107792 1.134325 3 1.545115500 1.583502 1.622359500 1.661688 1.701487500 4 2.060154 2.111336 2.163146 2.215584 2.268650 5 2.575192500 2.639170 2.703932500 2.769480 2.835812500 6 3 090231 3.167004 3.244719 3.323376 3.402975 7 3.605269500 3.694838 3.785505500 3.877272 3.970137500 8 4.120308 4.222672 4.326292 4.431168 4.537300 9 4.635346500 4.750506 4.867078500 4.985064 5.104462500 10 5.150385 5.278340 5.407865 5.538960 5.671625 11 5.665423500 5.806174 5.948651500 6.092856 6.238787500 12 6.180462 6.334008 6.489438 6.646752 6.805950 13 6.695500500 6.861842 7 030224500 7.20064* 7.373112500 14 7.210539 7.389676 7.571011 7.754544 7.940275 15 7.725577500 7.917510 8.111797500 8.308440 8.507437500 16 8.240616 8.445344 8.652584 8.862336 9.074600 17 8.755654500 8.973178 9.193370500 9.416232 9.641762500 18 9.270693 9.501012 9.734157 9.970128 10.208925 19 9 785731500 10.028846 10.274943500 10.524024 10.776087500 20 10.300770 10.556680 10.815730 11.077920 11.343250 30 15.451155 15.835020 16.223595 16.616880 17.014875 40 20.601540 21.113360 21.631460 22.155840 22.686500 50 25.751925 26.391700 27.039325 27.694800 28.358125 60 30.902310 31.670040 32.447190 33.233760 34.029750 -92 — Diameter — in., lines, cm. üDurd) meffer— jfc, I., cm. High, 86 87 88 89 90 Etc. Square o I Basis. — Quabratin^alt bev jtrets^ nub @runbflctd)e. £od), K. 0.580586 0.5941665 0.607904 0.6217985 0.63585 Cube. £ubu§. 0.01 0.005805860 0.005941665 0.006079040 0.006217985 0.006358500 0*02 0.011611720 0.011883330 0.012158080 0.012435970 0.012717 0*03 0.017417580 0.017824995 0.018237120 0.018653955 0.019075500 0*04 0.023223440 0.023766660 0.024316160 0.024871910 0.025434 0.05 0.029029300 0.029708325 0.030395200 0.031089925 0.031792500 0.06 0.034835160 0.035649990 0.036474240 0.037307910 0.038151 0*07 0.010641020 0.041591655 0.042553280 0.043525895 0.044509500 0*08 0.046446880 0.047533320 0.048632320 0.049743880 0.050868 0.09 0.052252740 0.053474985 0.054711360 0.055961865 0.057226500 0,1 0. 058058600 0.059416650 0.060790400 0.062179850 0.063585 0.2 0.116117200 0.118833300 0.121580800 0.124359700 0.127170 0*3 0.174175800 0.178249950 0.182371200 0.186539550 0.190755 0.4 0:232234400 0.237666600 0.243161600 0.248719400 0.254340 0.5 0.290293 0.297083250 0.303952 0.310899350 0.317925 0.6 0.348351600 0.356499900 0.364742400 0.373079100 0.381510 0.7 0.406410200 0.415916550 0.425532800 0.435258950 0.445095 0.8 0.464468800 0.475333200 0.486323200 0.497438800 0.508680 0.9 0.522527400 0.534749850 0.547113600 0.559618650 0.572265 1 0.580586 0.594166500 0.607904 0.621798500 0.635850 2 1.161172 1.188333 1.215808 1.243597 1 271700 3 1.741758 1.782499500 1.823712 1.865395500 1.907550 4 2.322344 2.376666 2.431616 2.487194 2.543400 5 2.902930 2.970832500 3.039520 3.108992500 3.179250 6 3.483516 3.564999 ' 3.647424 3.730791 3.815100 7 4.064102 4.159165500 4.255328 4.352589500 4.450950 8 4.644688 4.753332 4.863232 4.974388 5.086800 9 5.225274 5.347498500 5.471136 5.596186500 5.722650 10 5.805860 5.941665 6.079040 6.217985 6.358500 11 6.386446 6.535831500 6.686944 6.839783500 6.994350 12 6.967032 7.129998 7,294848 7.461582 7.630200 13 7.547618 7.724164500 7.902752 8 083380500 8.266050 14 8.128204 8.318331 8.510656 8.705179 8.901900 15 8.708790 8.912497500 9.118560 9.326977500 9.537750 16 9.289376 9.506664 9.726464 9.948776 10.173600 17 9.869962 10.100830500 10.334368 10.570574500 10.809450 18 10.450548 10.694997 10.942272 11.192373 11.445300 19 11.031134 11.289163500 11.550176 11.814171500 12.081150 20 1 11.611720 11.883330 12.158080 12.435970 12.717 30 ] 17.417580 17.824995 18.237120 18.653955 19.075500 40 23.223440 23.766660 24.316160 24.871940 25.434 50 29.029300 29.708325 30.395200 31.089925 31.792500 60 34.835160 35.649990 36.474240 37.307910 38.151 — 93 — Diameter — in., lines, cm. ©urdjmeffer — jl., I. cm. High, 91 92 93 94 95 Etc. Square of Basis. — Quabratinfyatt bet itvetg; unb ©runbfläcfye. §od&, :c. 0.6500585 0.664424 0.6789465 0.693626 0.7084625 Cube. fiu&uS. urd)meffer — jl., 1., cm. High, 136 137 138 139 140 Etc. Square of Basis. — Ductbvattuljalt ber ftvei§= intb ©tuubflädje. £oä). ■ :c. 1.451936 1.4733665 1.494954 1.5166985 1.5386 Cube. tfu&uS. 1 0.014519360 0.014733665 0.014949540 0.015166985 0.015386 0.02 0.029038720 0.029467330 0.029899080 0.030333970 0.030772 0.03 0.043558080 0.044200995 0.044848620 0.045500955 0.046158 0.04 0.058077440 0.058934660 0.059798160 0.060667940 0.061544 0*05 0.072596800 0.073668325 0.074747700 0.075834925 0.076930 0,06 0.087116160 0.088401990 0.089697240 0.091001910 0.092316 0.0? 0.101635520 0.103135655 0.104646780 0.106168895 0.107702 0.08 0.116154880 0.117869320 0.119596320 0.121335880 0.123088 0.09 0.130674240 0.132602985 0.134545860 0.136502865 0.138474 0.1 0.145193600 0.147336650 0.149495400 0.151669850 0.153860 0.2 0.290387200 0.294673300 0.298990800 0.303339700 0.307720 0.3 0.435580800 0.442009950 0.448486200 0.455009550 0.461580 0.4 0.580774400 0.589346600 0.597981600 0.606679400 0.615440 0.5 0.725968 0.736683250 0.747477 0.758349250 0.769300 0.6 0.871161600 0.884019900 0.896972400 0.910019100 0.923160 0.? 1.016355200 1.031356550 1.046467800 1.061688950 1.077020 o.a 1.161548800 1.178693200 1.195963200 1.213358800 1.230880 0.9 1.306742400 1.326029850 1.345458600 1.365028650 1.384740 1 1.451936 1.473366500 1.494954. 1.516698500 1.538600 2 2.903872 2.946733 2.989908 3.033397 3.077200 3 4.355808 4.420099500 4.484862 4.550095500 4.615800 4 5.807744 5.893466 5.979816 6.066794 6.154400 5 7.259680 7.366852500 7.474770 7.583492500 7.693 6 8.711616 8.840199 8.969724 9.100191 9.231600 7 10.163552 10.313565500 10.464678 10.616889500 10.770200 8 11.615488 11.786932 11.959632 12.133588 12.308800 9 13.067424 13.260298500 13.454586 13.650286500 13.847400 10 14.519360 14.733665 14.949540 15.166985 15.386 11 15.971296 16.207031500 16.444494 16.683683500 16.924600 12 17.423232 17.680398 17.939448 18.200382 18.463200 13 18.875168 19.153764500 19.434402 19.717080500 20.001800 14 20.327104 20.627131 20.929356 21.233779 21.540400 15 21.779040 22.100497500 22.424310 22.750477500 23.079 16 23.230976 23.573864 23.919264 24.267176 24.617600 17 24.682912 25.047230500 25.414218 25.783874500 26.156200 18 26.134848 26.520597 26.909172 27.300573 27.694800 19 27.586784 27.993963500 28.404126 28.517271500 29.233400 20 29.038720 29.467330 29.899080 30.333970 30.772 30 43.558080 44.200995 44.848620 45.500955 46.158 40 58.077440 58.934660 59.798160 60.667940 61.544 50 72.596800 73.668525 74.747700 75.834925 76.930 60 87.116160 88.401990 89.697240 91.001910 92.316 — 103 Diameter — irr., lines, cm. £)urd)meffer— $1., I., cm. High, 141 142 143 144 145 Etc. Square of Basis. — Quabrattnlljalt ber ih'et§= nub ©ninbflädje. 1.5606585 1.582874 1.6052465 1.627774 1.6504625 Cube. $ubu§. 0.015606585 0.031213170 O.046819755 0. 062426340 0.078032925 0.093639510 0.109246095 0.124852680 0.140459265 0.156065850 0.312131700 0.468197550 0.624263400 0.780329250 0.936395100 1.092460950 1.248526800 1.404592650 1.560658500 3.121317 4.681975500 6.242634 7.803292500 9.363951 10.924609500 12.485268 14.045926500 15.606585 17.167243500 18.727902 20.288560500 21.849219 23.409877500 24.970536 26.531194500 28.091853 29.652511500 31.213170 46.819755 62.426340 78.032925 93.639510 0.015828740 0.031657480 0.047486220 0.063314960 0.079143700 0.094972440 0.110801180 0.126629620 0.142458660 0.158287400 0.316574800 0.474862200 0.633149600 0.791437 0.949724400 1.108011800 1.266299200 1.424586600 1.582874 3.165748 4.748622 6.331496 7.914370 9.497244 11.080118 12 662992 14.245866 15.828740 17.411614 18.994488 20.577362 22.160236 23.743110 25.325984 26.908858 28.491732 30.074606 31.657480 47.486220 63.314960 79.143700 94.972440 0.016052465 0.032104930 0.048157395 0.064209860 0.080262325 0.096314790 0.112367255 0.128419720 0.144472185 0.160524650 0.321049300 0.481573950 0.642098600 0.802623250 0.963147900 123672550 ,284197200 444721850 605246500 210493 ,815739500 6.420986 8.026232500 9.631479 11.236725500 12.841972 14.447218500 16.052465 17.657711500 19.262958 20.868204500 22.473451 24.078697500 25.683944 27.289190500 28.894437 30.499683500 32.104930 48.157395 64.209860 80.262325 96.314790 0.016277760 0.032555520 0.048833280 0.065111040 0.081388800 0.097666560 0.113944320 0.130222080 0.146499840 0.162777600 0.325555200 0.488332800 0.651110400 0.813888 0.976665600 1.139443200 1.302220800 1.464998400 1.627776 3.255552 4.883328 6.511104 8.138880 9.766656 11.394432 13.022208 14.649984 16.277760 12.905536 19.533312 21.161088 22.788864 24 416640 26.044416 27.672292 29.299968 30.927744 32.555520 48.833280 65.111040 81.388800 97.666560 0.0165Ö4625 0.033009250 0.049513875 066018500 0.082523125 0.099027750 0.115532375 0.132037 0.148541625 0.165046250 0.330092500 0.495138750 0.660185 0.825231250 0.990277500 1.155323750 1.320370 1.485416250 1.650462500 3.300925 4.951387500 6.601850 8.252312500 9.902775 11.553237500 13.203700 14.854162500 16.504625 18.155087500 19.805550 21.456012500 23.106475 24.756937500 26.407400 28.057862500 29.708325 31.358787500 33.009250 49.513875 66.018500 82.523125 99.027750 104 — Diameter — in., lines, cm. £)urd)meffev — gl., I., cm. 146 147 148 149 150 Square of Basis. — GuabratinljaU bev &ret§= nub ©n tnbflädje. K. 1.673306 1.6963065 1.719464 1.7427785 1.76625 Cube. £ubu§. 0.01 0.016733060 0.016963065 0.017194640 0.017427785 0.017662500 0.02 0.033466120 0.033926130 0.034389280 0.034855570 0.035325 0*03 0.050199180 0.050889195 0.051583920 0.052283355 0.052987500 0*04 0.066932240 0.067852260 0.068778560 0.069711140 0.070650 0.05 0.083665300 0.084815325 0.085973200 0.087138925 0.088312500 0.06 0. 100398360 0.101778390 0.103167840 0.104566710 0.105975 0.07 0.117131420 0.118741455 0.120362489 0.121994495 0.123637500 0*08 0.133864480 0.135704520 0.137557120 0.139422280 0.141300 0*09 0.150597540 0.152667585 0.154751760 0.156850065 0.158962500 0*1 0.167330600 0.169630650 0.171946400 0.174277850 0.176625 0.2 0.334661200 0.339261300 0.343892800 0.348555700 0.353250 0.3 0.501991800 0.508891950 0.515839200 0.522833550 0.529875 0.4 0.669322400 0.678522600 0.687785600 0.697111400 0.706500 0.5 0.836653 0.848153250 0.859732 0.871389250 0.883125 0.6 1.003983600 1.017783900 1.031678400 1.045667100 1.059750 0.7 1.171314200 1.187414550 1.203624800 1.219944950 1.236375 0.8 1.338644800 1.357045200 1.375571200 1.394222800 1.413 0.9 1.505975400 1.526675850 1.547517600 1.568500650 1.589625 1 1.673306 1.696306500 1.719464 1.742778500 1.766250 2 3.346612 3.392613 3.438928 3.485557 3.532500 3 5.019918 5.088919500 5.158392 5.228335500 5.298750 4 6.693224 6.785226 6.877856 6.971114 7.065 5 8.366530 8.481532500 8.597320 8.713892500 8.831250 6 10.039836 10.177839 10.316784 10.456671 10.597500 7 11.713142 11.874145500 12.036248 12.199449500 12.363750 8 13.386448 13.570452 13.755712 13.942228 14.130 9 15.059754 15.266758500 15.475176 15.685006500 15.896250 10 16.733060 16.963065 17.194640 17.427785 17.662500 11 18.406366 18.659371500 18.914104 19.170563500 19.428750 12 20.079672 20.355678 20.633568 20.913342 21.195 13 21.752978 22.051984500 22.353032 22.656120500 22.961250 14 23.426284 23.748291 24.072496 24.398899 24.727500 15 25.099590 25.444597500 25.791960 26.141677500 26.493750 16 26.772896 27.140944 27.511424 27.884456 28.260 17 28.446202 28.837210500 29.230888 29.627234500 30.026250 18 30.119508 30.543517 30.950352 21.370013 31.792500 19 31.792814 32.229823500 32.669816 33.112791500 33.558750 20 33.466120 33.926130 34.389280 34.855570 35.325 30 50.199180 50.889195 51.583920 52.283355 52.987500 40 66.932240 67.852260 68.778560 69.711140 70.650 50 83.665300 84.815325 85.973200 87.138925 88.312500 60 100.398360 101.778390 103.167840 104.566710 105.975 — 105 Diameter— in. , lines, cm. ' . ©urdjmeffer — $1., I., cm. High, 151 152 153 154 155 Etc. Square of Basis. — Quabrathifyctlt ber föxü$'- itnb (SruubjTädje. JC. 1.7898785 1.813664 1.8376065 | 1.861706 1.8859625 Cube. 5hibu§. 0.017898785 0.035797570 0.053696355 0.071595140 0.089493925 0.107392710 0.125291495 0.143190280 0.161089065 0.178987850 0.357975700 0.536963550 0.715951400 0.894939250 1.073927100 1.252914950 1.431902800 1.610890650 1.789878500 3.579757 5.369635500 7.159514 8.949392500 10.739271 12.529149500 14.319028 16.108906500 17.898785 19.688663500 21.478542 23.268420500 25.058299 26.848177500 28.638056 30.427934500 82.217813 34.007691500 35.797570 53.696355 71.595140 89.493925 107.392710 0.018136640 0.036273280 0.054409920 0.072546560 0.090683200 0.108819840 0.126956480 0.145093120 0.163229760 0.181366400 0.362732800 0.544099200 0.725465600 0.906832 1.088198100 1.269564800 1.450931200 1.632297600 1.813664 3.627328 5.440992 7.254656 9.068320 10.881984 12.695648 14.509312 16.322976 18.136640 19.950304 21.763968 23.577632 25.391296 27.204960 29.018624 30.832288 32.645952 34.459616 36.273280 54.409920 72.546560 90.683200 108.819840 0.018376065 0.036752130 0.055128195 0.073504260 0.091880325 0.110256390 0.128632455 0.147008520 0.165384585 0.183760650 0.367521300 0.551281950 0.735042600 0.918803250 1.102563900 1.286324550 1.470085200 1.653845850 1.837606500 3.675213 5.512819500 7.350426 9.188032500 11.025639 12.863245500 14.700852 16.538458500 18.376065 20.213671500 22.051278 23.888884500 25.726491 27.564097500 29.401704 31.239310500 33.076917 34.914523500 36.752130 55.128195 73.504260 91.880325 110.256390 0.018617060 0.037234120 0.055851180 0.074468240 0.093085300 0.111702360 0.130319420 0.148936480 0.167553540 0.186170600 0.372341200 0.558511800 0.744682400 0.930853 1.117023600 1.303194200 1.489364800 1.675535400 1.861706 3.723412 5.585118 7.446824 9.308530 11.170236 13.031942 14.893648 16.755354 18.617060 20.478766 22.340472 24.202178 26.063884 27.925590 29.787296 31.649002 33.510708 35.372414 37.234120 55.851180 74.468240 93.085300 111.702360 0.018859625 0.037719250 0.056578875 0.075438500 0.094298125 0.113157750 0.132017375 0.150877 0.169736625 0.188596250 0.377192500 0.565788750 0.754385 0.942981250 1.131577500 1.320173750 1.508770 1.697366250 1.885962500 3.771925 5.657887500 7.543850 9.429812500 11.315775 13.201737500 15.087700 16.973662500 18.859625 20.745587500 22.631550 24.517512500 25.403475 27.299437500 29.175400 31.061362500 32.947335 35.833287500 37.719250 56.578875 75.438500 94.298125 113.157750 — 106 — Diameter — in., lines, cm. $)urtf)tneffer — gl., I., cm. High, 156 157 158 159 160 Etc. Square of Basis. — Quabrcttinljalt ber Ätei§= itub ©rimbfladje. 2C. 1.910376 1.9349465 1.959674 1.9845585 2.0096 Cube. Mm3. 0.01 0.02 0*03 0*04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 0*3 0*4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 40 50 60 0.019103760 0.038207520 0.057311280 0.076415040 0.095518800 0.114622560 0.133726320 0.152830080 0.171933840 0.191037600 0.382075200 0.573112800 0.764150400 0.955188 1.146225600 1.337263200 1.528300800 1.719338400 1.910376 3.820752 5.731128 7.641504 9.551880 11.462256 13.372632 15.283008 17.193384 19.103760 21.014136 22.924512 24.834888 26.745264 28.655640 30.566016 32.476392 34.386768 36.297144 38.207520 57.311280 76.415040 95.518800 114.622560 0.019349465 0.038698930 0.058048395 0.077397860 0.096747325 0.116096790 0.135446255 0.154795720 0.174145185 0.193494650 0.386989300 0.580483950 0.773978600 0.967473250 .160967900 .354462550 .547957200 .741451850 .934946500 3.869893 5.804839500 7.739786 9.674732500 11.609679 13.544625500 15.479572 17.414518500 19.349465 21.284411500 23.219358 25.154304500 27.089251 29.024197500 30.959144 32.894090500 34.829037 36.763983500 38.698930 58.048395 77.397860 96.747325 116.096790 0.019596740 0.039193480 0.058790220 0.078386960 0.097983700 0.117580440 0.137177180 0.156773920 0.176370660 0.195967400 0.391934800 0.587902200 0.783869600 0.979837 1.175804400 1.371771800 1.567739200 1.763706600 1.959674 3.919348 5.879022 7.838696 9.798370 11.758044 13.717718 15.677392 17.637066 19 596740 21.556414 23.516088 25.475762 27.435436 29.395110 31.354784 33.314458 35.274132 37.233806 39.193480 58.790220 78.386960 97.983700 117.580440 0.019845585 0.039691170 059536755 0.079382340 0.099227925 0.119073510 0.138919095 0.158764680 0.178610265 0.198455850 0.396911700 0.595367550 0.793823400 0.992279250 1.190735100 1.389190950 1.587646800 1.786102650 1.984558500 3.969117 5.953675500 7.938234 9.922792500 11.907351 13.891909500 15.876468 17.861026500 19.845585 21.830143500 23.814702 25.799260500 27.783819 29.768377500 31.752936 33.737494500 35.722053 37.706611500 39.691170 59.536755 79.382340 99.227925 119.073510 0.020096 040192 0.060288 0.080384 0.100480 0.120576 0.140672 0.160768 0. 180864 0.200960 0.401920 0.602880 0.803840 1.004800 1.205760 1.406720 1.607680 1.808640 2.009600 4.019200 6.028800 8.038400 10.048 12.057600 14.067200 16.076800 18.086400 20.096 22.105600 24.115200 26.124800 28.134400 30.144 32.153600 34 163200 36.172800 38.182400 40.192 60.288 80.384 100.480 120.576 — 107 — Diameter — in., lines, cm. 3)itrd)meffev— $1. , L, cm. High, 161 162 163 164 165 Etc. Square of Basis.— Quctbrctttnfjalt ber ^rei§- inib @vunbflätf)e. £odj, K. 2.0347985 2.060154 2.0856665 2.111336 2.1371625 ; Cube. ßufiit§. O.Oi 0.020347985 0.020601540 0.020856665 0.021113360 0.021371625 0,02 0.040695970 0.041203080 0.041713330 0.042226720 0.042743250 0,03 0.061043955 0.061804620 0.062569995 0.063340080 0.061114875 0,04 0.081391940 0.082406160 0.083426660 0.084453440 0.085486500 0*05 0.101739925 0.103007700 0.104283325 0.105566800 0.106858125 0,06 0. 122087910 0.123609240 0.125139990 0.126680160 0.128229750 0*07 0.142435895 0.144210780 0.145996655 0.147793520 0.149601375 0,08 0.162783880 0.164812320 0.166853320 0.168906880 0.170973 0,09 0.183131865 0.185413860 0.187709985 0.190020240 0.192344625 0,1 0.203479850 0.206015400 0.208566650 0.211133600 0.213716250 0.2 0.406959700 0.412030800 0.417133300 0.422267200 0.427432500 0.3 0.610439550 0.618046200 0.625699950 0.633400800 0.641148750 0.4 0.813919400 0.824061600 0.834266600 0.844534400 0.854865 0.5 1.017399250 1.030077 1.042833250 1.055668 1.068581250 0.« 1.220879100 1.236092400 1.251399900 1.266801600 1.282297500 0.7 1.424358950 1.442107800 1.459966550 1.477935200 1.496013750 0.8 1.627838800 1.648123200 1.668533200 1.689068800 1.709730 0.9 1.831318650 1.854138600 1.877099850 1.900202400 1.923446250 1 2.034798500 2.060154 2.085666500 2.111336 2.137162500 2 4.069597 4.120308 4.171333 4.222672 4.274325 3 6.104395500 6.180462 6.256999500 6.334008 6.411487500 4 8.139194 8.240616 8.342666 8.445344 8.548650 5 10.173992500 10.300770 10.428332500 10.556680 10.685812500 6 12.208791 12.360924 12.513999 12.668016 12.822975 7 14.243589500 14.421078 14.599665500 14.779352 14.960137500 8 16.278388 16.481232 16.685332 16.890688 17.097300 9 18.313186500 18.541386 18.770998500 19.002024 19.234462500 10 20.347985 20.601540 20.856665 ' 21.113360 21.371625 11 22.382783500 22.661694 22.942331500 23.224696 23.508787500 12 24.417582 24.721848 25.027998 25.336032 25.645950 13 26.452380500 26.782002 27.113664500 27.447368 27.783112500 14 28.487179 28.842156 29.199331 29.558704 29.920275 15 30.521977500 30.902310 31.284997500 31.670040 32.057437500 16 32.556776 32.962464 33.370664 33.781376 34.294600 17 34.591574500 35.022618 35.456330500 35,892712 36.431762500 18 36.626373 37.082772 37.541997 38.004048 38.568925 19 38.661171500 39.142926 39.627663500 40.115384 40.606087500 20 40.695970 41.203080 41.713330 42.226720 42.743250 30 61.043955 61.804620 62.569995 63.340080 64.114875 40 81.391940 82.406160 83.426660 84.453440 85.486500 50 101.739925 103.007700 104.283325 105.566800 106.858125 60 122.087910 123.609240 125.139990 j 126.680160 128.229750 — 108 — Diameter — in., lines, cm. £ntrtf)tneffev — jl. , U, cm. High, 170 175 180 185 190 Etc. Square c >f Basis. — Quabrcttiutyalt bei* &xe\%: nub ©ruubflädje. •frod), 2C. 2.26865 2.4040625 2.5434 2.6866625 2.83385 Cube. Äubu§. 0*01 0.022686500 0.024040625 0.025434 0.026866625 0,028338500 0*02 0.045373 0.048081250 0.050868 0.053733250 0.056677 0*03 0.068059500 0.072121875 0.076302 0.080599875 0.085015500 0.04 0.090746 0.096162500 0.101736 0.107466500 0.113354 0*05 0.113432500 0.120203125 0.127170 0.134333125 0.141692500 0,06 0.136119 0.1.44243750 0.152604 0.161199750 0-170031 0*07 0.158805500 0.168284375 0.178038 0.188066375 0. 198369500 0*08 0.181492 0.192325 0.203472 0.214933 0.226708 0*09 O.2O417850O 0.216365625 0.228906 0.241799625 0.255046500 0*1 0.226865 0.240406250 0.254340 0.268666250 0.283385 0*2 0.453730 0.480812500 0.508680 0.537332500 0.566770 0*3 0.680595 0.721218750 0.763020 0.805998750 0.850155 0*4 0.907460 0.961625 1.017360 1.074665 1.133540 0.5 1.134325 1.202031250 5.271700 1.343331250 1.416925 o.6 1.361190 1.442437500 1.526040 1.611997500 1.700310 0.7 1.588055 1.682843750 1.780380 1.880663750 1.983695 0.8 1.814920 1.923250 2.034720 2.149330 2.267080 0.9 2.041785 2.163656250 2.289060 2.417996250 2.550465 1 2.268650 2.404062500 2.543400 2 686662500 2.833850 2 4.537300 4.808125 5.086800 5.373325 5.667700 3 6.805950 7.212187500 7.630200 8.059987500 8.501550 4 9.074600 9.616250 10.173600 10.746650 11.335400 5 11.343250 12.020312500 12.7)7 13.433312500 14.169250 6 13.611900 14.424375 15.260400 16.119975 17.003100 7 15.880550 16.828437500 17.803800 18.806637500 19.836950 8 18.149200 19.232500 20.347200 21.493300 22.670800 9 20.417850 21.636562500 22.890600 24.179962500 25.504650 10 22.686500 24.040625 25.434 26.866625 28.338500 11 24.955150 26.444687500 27.977400 29.553287500 31.172350 12 27.223800 28.848750 30.520800 32.239950 34.006200 13 29.492450 31.252812500 30.064200 34.926612500 36.840050 14 31.761100 33.656875 35.607600 37.613275 39.673900 15 34.029750 36.060937500 38.151 40.299937500 42.507750 16 36.298400 38.465 40.694400 42.986600 45 341600 17 38.567050 40.869062500 43.237800 45.673262500 48.175450 18 40.835700 43.273125 45.781200 48.359925 51.009300 19 43.104350 45.677187500 48.324600 51.046587500 53.843150 20 45.373 48.081250 50.868 53.733250 56.677 30 68.059500 72.121875 76.302 80.599875 85.015500 40 90.746 96.162500 101.736 107.466500 113.354 50 113.432500 120.203125 127.170 134.333125 141.692500 60 136.119 144.243750 152.604 161.199750 170.031 — 109 — Diameter— in., lines, cm. £)uvd)i neffer — jl., 1., cm. High, 195 200 205 210 220 Etc. Square o f Basis. — Quabratinljatt bev tot§= intb @runbfläd)e. 2C. 2.9849625 3.14 3.2989625 3.46185 3.7994 Cube. ^ubu§. O.Oi 0.029849625 0.031400 0.032989625 0.034618500 0.037994 0*02 0.059699250 0.082800 0.065979250 0.069237 0.075988 0.03 0.089548875 0.094200 0-098968875 0. 103855500 0.113982 0.04 0.119398500 0.125600 0.131958500 0.138474 0.151976 0.05 0.149248125 0.157 0.164948125 0.173092500 0.189970 0.06 0.179097750 0.188400 0.197937750 0.207711 0.227964 0.07 0.208947375 0.219800 0.230927375 0.242329500 0.265958 0*08 0.238797 0.251200 0.263917 0.276948 0.303952 0*09 0.268646625 0.282600 0.296906625 0.311566500 0.341946 0*1 0.298496250 0.314 0.329896250 0.346185 0.379940 0*2 0.596992500 0.628 0.659792500 0.692370 0.759880 0.3 0.895488750 0.942 0.989688750 1.038555 1.139820 0*4 1.193985 1.256 1.319585 1.384740 1.519760 0.5 1.492481250 1.570 1.649481250 1.730925 1.899700 0.6 1.790977500 1.884 1.979377500 2.077110 2.279640 0.7 2.089473750 2.198 2.309273750 2.423295 2.659580 0.8 2.387970 2.512 2.639170 2.769480 3.039520 0.9 2.686466250 2.826 2.969066250 3.115665 3.419460 1 2.984962500 3.140 3.298962500 3.461850 3.799400 2 5.969925 6.280 6.597925 6.923700 7.598800 3 8.954887500 9.420 9.896887500 10.385550 11.398200 4 11.939850 12.560 13.195850 13.847400 15.197600 5 14.924812500 15.700 16.494812500 17.309250 18.997 6 17.909775 18.840 19.793775 20.771100 22.796400 7 20.894737500 21.980 23.092737500 24.232950 26.595800 8 23.879700 25.120 26.391700 27.694800 30.395200 9 26.864662500 28.260 29.690662500 31.156650 34.194600 10 29.849625 31.400 32.989625 34.618500 37.994 11 32.834587500 34.540 36.288587500 38.080350 41.793400 12 35.819550 37.680 39.587550 41.542200 45.592800 13 38.804512500 40.820 42.886512500 45.004050 49.392200 14 41.789475 47.960 46.185475 48.465900 53.191600 15 44.774437500 51.100 49.484437500 51.927750 56.991 16 47.759400 54.240 52.783400 55.389600 60.790400 17 50.744362500 56.380 56.082362500 58.851450 64.589800 18 53.729325 58.520 59.381325 62.313300 68.389200 19 56.714287500 60.660 62.680287500 65.775150 72.188600 20 59.699250 62.800 65.979250 69.237 75.988 30 89.548875 94.200 98.968875 103.855500 113 982 40 119.398500 125.600 131.958500 138.474 151.976 50 149.248125 157.000 164.948125 173.092500 189.970 60 ; 179.097750 188.400 197.937750 207.711 227.964 — 110 — Diameter— in., lines, cm. ©urdjmeffer — jl. ; I., cm. High, 225 230 240 250 260 Etc. Square of Basis. — Duabratinfyalt bei* ÄrciSs nub @runbflctd)e. K. 3.9740625 4.15265 4.5216 4.90625 5.3066 Cube. ÄubiiS. 0.01 0.039740625 0.041526500 0.045216 0.049062500 0.053066 0*02 0.079481250 0.083053 0.090432 0.098125 0.106132 0*03 0.119221875 0.124579500 0.135648 0.147187500 0.159198 0*04 0.158962500 0.166106 0.180864 0.196250 0.212264 0.05 0.198703125 0.207632500 0.226080 0.245312500 0.265330 0*06 0.238443750 0.249159 0.271296 0.294375 0.318396 0*07 0.278184375 0.290685500 0.316512 0.343437500 0.371462 0*08 0.317925 0.332212 0.361728 0.392500 0.424528 0*09 0.357665625 0.373738500 0.406944 0.443562500 0.477594 0*1 0.397406250 0.415265 0.452160 0.490625 0.530660 0*2 0.794812500 0.830530 0.904320 0.981250 1.061320 0*3 1.192218750 1.245795 1.356480 1.471875 1.591980 0.4 1.589625 1.661060 1.808640 1.962500 2.122640 0.5 1.987031250 2.076325 2.260800 2.453125 2.653300 0.6 2.384437500 2.491590 2.712960 2.943750 3.183960 0*7 2.781843750 2.906855 3.165120 3.434375 3.714620 0.8 3.179250 3.322120 3.617280 3.925 4.245280 0.9 3.576656250 3.737385 4.069440 4.415625 4.775940 1 3.974062500 4.152650 4.521600 4.906250 5.306600 2 7.948125 8.305300 9.043200 9.812500 10.613200 3 11.922187500 12.457950 13.564800 14.718750 15.919800 4 15.896250 16.610600 18.086400 19.625 21.226400 5 19.870312500 20.763250 22.608 24.531250 26.533 6 23.844375 24.915900 27.129600 29.437500 31.839600 7 27.818437500 29.068550 31.651200 34.343750 37.146200 8 31.792500 33.221200 36.172800 39.250 42.452800 9 35.766562500 37.373850 40 694400 44.156250 47.759400 10 39.740625 41.526500 45.216 49.062500 53.066 11 43.714687500 45.679150 49.737600 53.968750 58.372600 12 47.688750 49.831800 54.259200 58.875 63.679200 13 51.662812500 53.984450 58.780800 63.781250 68.985800 14 55.636875 58.137100 63.302400 68.687500 74.292400 15 59.610937500 62.289750 67.824 73.593750 79.599 16 63.585 66.442400 72.345600 78.500 84.905600 17 67.559062500 70.595050 76.867200 83.406250 90.212200 18 71.533125 74.747700 81.388800 88.312500 95.518800 19 75.507187500 78.900350 85.910400 93.218750 100.825400 20 79.481250 83.053 90.432 98.125 106.132 30 119.221875 124.579500 135.648 147.187500 159.198 40 158.962500 166.106 180.864 196.250 212.264 50 198.703125 207.632500 226.080 245.312500 265.330 60 238.443750 249.159 271.296 294.375 318.396 —Ill — Diameter, — in., lines, cm. £)urd imeffev— gl., I., cm. High, 270 275 280 290 L 300 Etc. Square of Basis. — Duabratinljalt bet £rei§= unb ©runbflädje. 5.72265 5.9365625 6.1544 6.60185 7.065 Cube. &ubu§. 0*01 0.057226500 0.059365625 0.061544 0.066518500 0.070650 0.02 0.114453 0.118731250 0.123088 0.132037 0.141300 0*03 0.171679500 0.178096875 0.184632 0.198055500 0.211950 0.04 0.228906 0.237462500 0.246176 0.264074 0.282600 0*05 0.286132500 0.296828125 0.307720 0.330092500 0.353250 0,06 0.343359 0.356193750 0.369264 0.396111 0.423900 0*07 0.400585500 0.415559375 0.430808 0.462129500 0.494550 0*08 0.457812 0.474925 0.492352 0.528148 0.565200 0*09 0.515038500 0.534290625 0.553896 0.594166500 0.635850 0*1 0.575265 0.593656250 0.615440 0.660185 0.706500 0*2 1.14f530 1.187312500 1.230880 1.320370 1.413 0.3 1.716795 1.780968750 1.846320 1.980555 2.119500 0.4 2.289060 2.374625 2.461760 2.640740 2.826 0.5 2.861325 2.968281250 3.077200 3.300925 3.532500 0*0 3.433590 3.561937500 3.692640 3.961110 4.239 0.7 4.005855 4.155593750 4.308080 4.621295 4.945500 0.8 4.578120 4.749250 4.923520 5.281480 5.652 0.9 5.150385 5.342906250 5.538960 5.941665 6.358500 1 5.722650 5.936562500 6.154400 6.601850 7.065 2 11.445300 11.873125 12.308800 13.203700 14.130 3 17. 167950 17.809687500 18.463200 19.805550 21.195 4 22.890600 23.746250 24.617600 26.407400 28.260 5 28.613250 29.682812500 30.772 33.009250 35.325 6 34.335900 35.619375 36.926400 39.611100 42.390 7 40.058550 41.555937500 43.080800 46.212950 49.455 8 45.781200 47.492500 49.235200 52.814800 56.520 9 51.503850 53.429062500 55.389600 59.416650 63.585 10 57.226500 50.365625 61.544 66.018500 70.650 11 62.949150 65.302187500 67.698400 72.620350 77.715 12 .68.671800 71.238750 73.852800 79.222200 84.780 13 74.394450 77.175312500 80.007200 85.824050 91.845 14 79.117100 83.111875 86.161600 92.425900 98.910 15 85.839750 89.048437500 92.316 99.027750 105.975 16 91.562400 94.985 98.470400 105.629600 113.040 17 97.285050 100.921562500 104.624800 112.231450 120.105 18 103.007700 106.858125 110 779200 118.833300 127.170 19 108.720350 112.794687500 116.933600 125.435150 134.235 20 114.453 118.731250 123.088 132.037 141.300 30 171.679500 178.096875 184.632 198.055500 211.950 40 228.906 237.462500 246.176 264.074 282.600 50 286.132500 296.828125 307.720 330.092500 353.250 60 343.359 356.193750 369.264 396.111 423.900 112 — Diameter — in., lines, cm. ÜDurd jmeffer— jl,, 1. , cm. High, 310 320 325 350 375 Etc. Square of Basis. — Ductbratiuljali ber , ft'reiS? unb ©runbflädje.' £od), 7.54385 8.0384 8.2915625 9.61625 j 11.0390625 Cube. ßubiis. 0*01 0.075438500 0.080384 0.082915625 0.096162500 0.110390625 0*02 0.150877 0.160768 0.165831250 0.192325 0.220781250 0*03 0.226315500 0.241152 0.248746875 0.288487500 0.331171875 0.04 0.301754 0.321536 0.331662500 0.384650 0.441562500 0*05 0.377192500 0.401920 0.414578125 0.480812500 0.551953125 0,06 0.452631 0.482304 0.497493750 0.576975 0.662343750 0*07 0.528069500 0.562688 0.580409375 0.673137500 0.772734375 0*08 0.603508 0.643072 0.663325 0.769300 0.883125 0*09 0.678946500 0.723456 0.746240625 0.865462500 0.993515625 0*1 0.754385 0.803840 0.829156250 0.961625 1.103906250 0*2 1.508770 1.607680 1.658312500 1.923250 2.20781250o 0*3 2.263155 2.411520 2.487468750 2.884875 3.311718750 0.4 3.017540 3.215360 3.316625 3.846500 4.415625 0.5 3.771925 4.019200 4.145781250 4.808125 5.519531250 0.6 4.526310 4.823040 4.974937500 5.769750 6.623437500 0.7 5.280695 5.626880 5.804093750 6.731375 7.727343750 0.8 6.035080 6.430720 6.633250 7.693 8.831250 0.9 6.789465 7.234560 7.462406250 8.654625 , 9.935156250 1 7.543850 8.038400 8.291562500 9.616250 11.039062500 2 15.087700 16.076800 16.583125 19.232500 22.078125 3 22.631550 24.115200 24.874687500 28.848750 33.117187500 4 30.175400 32.153600 33.166250 38.465 44.156250 5 37.719250 40.192 41.457812500 48.081250 55.195312500 6 45.263100 48.230400 49.749375 57.697500 66.234375 7 52.806950 56.268800 58.040937500 67.313750 77273437500 8 60.350800 64.307200 66.332500 76.930 88.312500 9 67.894650 72.345600 74.624062500 86.546250 99.351562500 10 75.438500 80.384 82.915625 96.162500 110.390625 11 82.982350 88.422400 91.207187500 105.778750 121.429687500 12 90.526200 96.460800 99.498750 114.395 132.468750 13 98.070050 104.499200 107.790312500 125.011250 143.507812500 14 105.614900 112.537600 116.081875 134.627500 154.546875 15 113.157750 120.576 124.373437500 144.243750 165.585937500 16 120.701600 128.614400 132.665 153.860 176.625 17 128.245450 136.652800 140.956562500 163.476250 187.664062500 18 135.789300 144.691200 149.248125 173.092500 198.703125 19 143.333150 152.729600 157.539687500 182.708750 209.742187500 20 150.877 160.768 165.831250 192.325 220.781250 30 226.315500 241.152 248.746875 288.487500 331.171875 40 301.754 321.536 331.662500 384.650 441.562500 50 377.192500 401.920 414.578125 480.812500 551.953125 60 452.631 482.304 497.493750 576.975 662.343750 - 113 — Dia meter -»in., lines, cm. ©urdjmeffev — $1. , I., cm. High, 400 425 450 475 500 Etc. Square of Basis. — Quctbratinljialt bei f?rei§: nub ©ruubflädje. ■£od&, 2C. 12.56 14.1790625 15.89625 17.7115625 19.625 Cube. jhtfcus. 0.01 0.125600 0.141790625 0. 158962500 0.177115625 0.196250 0.02 0.251200 0.283581250 0.317925 0.354231250 0.392500 0*03 0.376800 0.425371875 0.476887500 0.531346875 0.588750 0*04 0.502400 0.567162500 0.635850 0.708462500 0.785 0.05 0.628 0.708953125 0.794812500 0.885578125 0.981250 0.06 0.753600 0.850743750 0.953775 1.062693750 1.177500 0.07 0.879200 0.992534375 1.112737500 1.239809375 1.373750 0.08 1.004800 1.134325 1.271700 1.416925 1.570 0*09 1.130400 1.276115625 1.430662500 1.594040625 1.766250 0.1 1.256 1.417906250 1.589625 1.771156250 1.962500 0.2 2.512 2.835812500 3.179250 3.542312500 3.925 0.3 3.768 4.253718750 4.768875 5.313468750 5.887500 0.4 5.024 5.671625 6.358500 7.084625 7.850 0.5 6.280 7.089531250 7.948125 8.855781250 9.812500 0.6 7.536 8.507437500 9.537750 10.626937500 11.775 0*7 8.792 9.925343750 11.127375 12.398093750 13.737500 0.8 10.048 11.343250 12.717 14.169250 15.700 0.9 11.304 12.761156250 14.306625 15.940406250 17.662500 1 12.560 14.179062500 15.896250 17.711562500 19.625 2 25.120 28.358125 31.792500 35.423125 39.250 3 37.680 42.537187500 47.688750 53.134687500 58.875 4 50.240 56.716250 63.585 70.846250 78.500 5 62.800 70.895312500 79.481250 88.557812500 98.125 6 75.360 85.074375 95.377500 106.269375 117.750 7 87.920 99.253437500 111.273750 123.980937500 137.375 8 100.480 113.432500 127.170 141.692500 157.0 9 113.040 127.611562500 143.066250 159.404062500 176.625 10 125.600 141.790625 158.962500 177.115625 196.250 11 133.160 155.969687500 174.858750 194.827187500 215.875 12 150.720 170.148750 190.755 212.538750 235.500 13 163.280 184.327812500 206.651250 230.250312500 255.125 14 175.840 198.506875 222.547500 247.961875 274.750 15 188.400 212.685937500 238.443750 265.673437500 294.375 16 200.960 226.865 254.340 283.385 314.0 17 213.520 241.044062500 270.236250 301.096562500 333 625 18 226.080 255.223125 286.132500 318.808125 353.250 19 238.640 269.402187500 302.028750 336.519687500 372.875 20 251.200 283.581250 317.925 354.231250 392.500 30 376.800 425.371875 476.887500 531.346875 588.750 40 502.400 567.162500 635.850 708.462500 785.00 50 628.0 708.953125 794.812500 885.578125 981.250 60 753.600 850.743750 953.775 1062.693750 1177.500 — 114 Diameter — in., lines, cm. SDurdjmeffer — $1., I.,cm. High, 525 550 575 600 625 Etc. Square of Basis. — Ductbrcttiuljalt ber Streik- itnb ©ruubflädje. £od). 2<\ 21.6365625 23.74625 25.9540625 28.26 | 30.664625 Cube. ÄufcuS. 0.216365625 0.432731250 0.649096875 0.865462500 1.081828125 1.298193750 1.514559375 1.730925 1.947290625 2.163656250 4.327312500 6.490968750 8.654625 10.818281250 12.981937500 15.145593750 17.309250 19.472906250 21.636562500 43.273125 64.909687500 86.546250- 108.182812500 129.819375 151.455937500 173.092500 194.729062500 216.365625 238.002187500 259.638750 281.275312500 302.911875 324.548437500 346. 185 367.821562500 389.458125 411.094687500 432.731250 649.096875 865.462500 1081.828125 1298,193750 0.237462500 0.474925 0.712387500 0.949850 1.187312500 1.424775 1.662237500 1.899700 2.137162500 2.374625 4.749250 7.123875 9.498500 11.873125 14.247750 16.622375 18.997 21.371625 23.746250 47.492500 71.238750 94.985 118.731250 142.477500 166.223750 189.970 213.716250 237.462500 261.208750 284.955 308.701250 332.447500 356.193750 379.940 403.686250 427.432500 451.178750 474.925 712.387500 949.850 1187.312500 1424.775 0.259540625 0.519081250 0.778621875 1.038162500 1.297703125 1.557243750 1.816784375 2.076325 2.335865625 2.595406250 5.190812500 7.786218750 10.381625 12.977031250 15.572437500 18.167843750 20.763250 23.358656250 25.954062500 51.908125 77.862187500 103.816250 129.770312500 155.724375 181.678437500 207.632500 233.586562500 259.540625 285.494687500 311.448750 337.402812500 363.356875 389.310937500 415.265 441.219062500 467.173125 493.127187500 519.081250 778.621875 1038.162500 1297.703125 1557.243750 0.282600 0.565200 0.847800 1.130400 1.413 1 695600 1.978200 2.260800 2.543400 2.826 5.652 8.478 11.304 14.130 16.956 19.782 22.608 , 25.434 28.260 56.520 84.780 113.040 141.300 169.560 197.820 226.080 254.340 282.600 310.860 339.120 367.380 395.640 423.900 452.160 480.420 508.680 536.940 565.200 847.800 1130.400 1413.0 1695.600 0.306640625 0.613281250 0.919921875 1.226562500 1.533203125 1.839843750 2.146484375 2.453125 2.759765625 3.066406250 6.132812500 9.199218750 12.265625 15.332031250 18.398437500 21.464843750 24.531250 27.597656250 30.664062500 61.328125 91.992187500 122.656250 153.320312500 183.984375 214.648437500 245.312500 275.976562500 306.640625 337.304687500 367.968750 398.632812500 429.296875 459.960937500 490.625 521.289062500 551.953125 582.617287500 613.281250 919.921875 1226.562500 1533.203125 1839.843750 115 Diameter-^-in., lines, cm. ©urdjmeffev— gl., I., cm. High, 650 675 700 725 750 Etc. Square of Basis. — Duabrcttiutyalt ber Ävet§= imb (Svuiibflädje. 6odi, 2C. 33.16625 35.7665625 38.465 41.2615625 44.15625 Cube. &ubu§. 0*01 0.331662500 0.357665625 0.384650 0.412615625 0.441562500 0*02 0.663325 0.715331250 0.769300 0.825231250 0.883125 0*03 0.994987500 1.072996875 1.153950 1.237846875 1.324687500 0*04 1.326650 1.430662500 1.538600 1.650462500 1.766250 0*05 1.658312500 1.788328125 1.923250 2.063078125 2.207812500 0,06 1.989975 2.145993750 2.307900 2.475693750 2.649375 0*07 2.321637500 2.503659375 2.692550 2.888309375 3.090937500 0.08 2.653300 2.861325 3.077200 3.300925 3.532500 0^09 2.981962500 3.218990625 3.461850 3.713540625 3.974062500 0*1 3.316625 3.576656250 3.846500 4. 126156250 4.415625 0.2 6.633250 7.153312500 7.693 8.252312500 8.831250 0.3 9.949875 10.729968750 11.539500 12.378468750 13.246875 0.4 13.266500 14.306625 15.386 16.504625 17.662500 0.5 16.583125 17.883281250 19.232500 20.630781250 22.078125 0.6 19.899750 21.459937500 23.079 24.756937500 26.493750 0.7 23.216375 25.036593750 26.925500 28.883093750 30.909375 0.8 26.533 28.613250 30.772 33.009250 35.325 0.9 29.849625 32.189906250 34.618500 37.135406250 39.740625 1 33.166250 35.766562500 38.465 41.261562500 44.156250 2 66.332500 71.533125 76.930 82.523125 88.312500 3 99.498750 107.299687500 115.395 123.784687500 132.468750 4 132.665 143.066250 153.860 165.046250 176.625 5 165.831250 178.832812500 192.325 206.307812500 220.781250 6 198.997500 214.599375 230.790 247.569375 264.937500 7 232.163750 250.365937500 269.255 288.830937500 309.093750 8 265.330 286.132500 307.720 330.092500 353.250 9 298.496250 321.899062500 346.185 371.354062500 397.406250 10 331.662500 357.665625 384.650 412.615625 441.562500 11 364.828750 393.432187500 423.115 453.877187500 485.718750 12 397.995 429.198750 461.580 495.138750 529.875 13 431.161250 464.965312500 500.045 536.400312500 574.031250 14 464.327500 500.731875 538.510 577.661875 618.187500 15 497.493750 536.498437500 576.975 618.923437500 662.343750 16 530.660 572.265 615.440 660.185 706.500 17 563.826250 608.031562500 653.905 701.446562500 750.656250 18 596.992500 643.798125 692.370 742.708125 794.812500 19 630.158750 679.564687500 730.835 783.969687500 838.968750 20 663.325 715.331250 769.300 825.231250 883.125 30 994.987500 1072.996875 1153.950 1237.846875 1324.687500 40 1326.650 1430.662500 1538.600 1650.462500 1766.250 50 1658.312500 1788.328125 1923.250 2063.078125 2207.812500 60 1989.975 2145.993750 2307.900 i 2475.693750 2649.375 — 116 — Diameter — in., lines, cm. £>urd)meffev — $., I., cm. High, Etc. §od), 2C. 775 800 825 850 875 Square of Basis. — Quabvctttnfyalt ber £rei3= mib ©ritubfläd&e. 47.1490625 50.24 53.456262 56.71625 60.1015625 Cube. ÄubuS. 0*01 0*02 0*03 0*04 0*05 0.06 0*07 0*08 0*09 0.1 0*2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 40 50 60 0.471490625 0.942981250 1.414471875 1.885962500 2.357453125 2.828943750 3.300434375 3.771925 4.243415625 4.714906250 9.429812500 14.144718750 18.859625 23.574531250 28.289437500 33.004343750 37.719250 42.434156250 47.149062500 94.298125 141.447187500 188.596250 235.745312500 282.894375 330.043437500 377.192500 424.341562500 471.490625 518.639687500 565.788750 612.937812500 660.086875 707.235937500 754.385 801.534062500 848.683125 895.832187500 942.981250 1414.471875 1885.962500 2357.453125 2828.943750 0.502400 1.004800 1.507200 2.009600 2.512 3.014400 3.516800 4.019200 4.521600 5.024 10.048 15.072 20.096 25.120 30.144 35.168 40.192 45.216 50.240 100.480 150.720 200.960 251.200 301.440 351.680 401.920 452.160 502.400 552.640 602.880 653.120 703.360 753.600 803.840 854.080 904.320 954.5600 1004.800 1507.200 2009.60 2512.00 3014.400 0.534562625 1.069125250 1.603687875 2.138250500 2.672813125 3.207375750 3.741938375 4.276501 4.811063625 5.345626250 10.691252500 16.036878750 21.382505 26.728131250 32.073757500 37.419383750 42.765010 48.110636250 53.456262500 106.912525 160.368787500 213.825050 267 281312500 320.737575 374.193837500 427.650100 481.106362500 534.562625 588.018887500 641.475150 "694.931412500 748.387675 801.843937500 855.300200 908.756462500 962.212725 1015.668987500 1069.125250 1603 687875 2138.250500 2672 813125 3207.375750 0.567162500 1.134325 1.701487500 2.268650 2.835812500 3.402975 3.970137500 4.537300 5. 104462500 5.671625 11.343250 17.014875 22.686500 28.358125 34.029750 39.701375 45.373 51.044625 56.716250 113.432500 170.148750 226.865 283.581250 340.297500 397.013750 453.730 510.446250 567.162500 623.878750 680.595 737.311250 794.027500 850.743750 907.460 964.176250 1020.892500 1077.608750 1134.325 1701.487500 2268.650 2835.812500 3402.975 0.601015625 1.202'»31250 1.803046875 2.404062500 3.005078125 3.606093750 4^207109375 4.808125 5.409140625 6.010156250 12.020312500 18.030468750 24.040625 30.050781250 36.060937500 42.071093750 48.081250 54.091406250 60.101562500 120.203125 180.304687500 240.406250 300.507812500 360.609375 420.710937500 480.812500 540.914062500 601.015625 661.117187500 721.218750 781.320312500 841.421875 901.523437500 961.625 1021.726562500 1081.828125 1141.929687500 1202.031250 1803.046875 2404.062500 3005.078125 3606.093750 — 117 — Diameter— in., lines, cm. 5)urd inteffer— jl. f I., cm. High, 900 925 950 975 1000 Etc. Square of Basis. — Cud )ratinf)alt ber j?rei§= unb @ritubf(äd)e. 2C. 63.583 67.1665625 70.84625 74.6240625 78.5 Cube. itubuS. 0.01 0.635850 0.671665625 0.708462500 0.746240625 0.785 0*02 1.271700 1.343331250 1.416925 1.492841250 1.570 0.03 1.907550 2.014996875 2.125387500 2.238721875 2.355 0*04 2.543400 2.686662500 2.833850 2.984962500 3.140 0*05 3.179250 3.358328125 3.542312500 3.731203125 3.925 0*06 3.815100 4.029993750 4.250775 4.477443750 4.710 0.07 4.450950 4.701659375 4.959237500 5.223684375 5.495 0.08 5.086800 5.373325 5.667700 5.969925 6.280 0.09 5.722650 6.044990625 6.376162500 6.716165625 7.065 0.1 6.358500 6.716656250 7.084625 7.462406250 7.850 0.2 12.717 13.433312500 14.169250 14.924812500 15.700 0.3 19.075500 20.149968750 21.253875 22.387218750 23.550 0.4 25.434 26.866625 28.338500 29.849625 31.400 0.5 31.792500 33.583281250 35.423125 37.312031250 39.250 0.6 38.151 40.299937500 42.507750 44.774437500 47.100 0.7 44.509500 47.016593750 49.592375 52.236843750 54.950 0.8 50.868 53.733250 56.677 59.699250 62.800 0.9 57.226500 60.449906250 63.761625 67.161656250 70.650 1 63.585 67.166562500 70.846250 74.624062500 78.500 2 127.170 134.333125 141.692500 149.248125 157.0 3 190.755 201.499687500 212.538750 223.872187500 235.500 4 254.340 268.666250 283.385 298.496250 314.0 5 317.925 335.832812500 354.231250 373.120312500 392.500 6 381.510 402.999375 425.077500 447.744375 471.0 7 445.095 470.165937500 495.923750 522.368437500 549.500 8 508.680 537.332500 566.770 596.992500 628.0 9 572.2Ö5 604.499062500 637.616250 671.616562500 706.500 10 635.850 671.665625 708.462500 746.240625 785.0 11 699.435 738.832187500 779.308750 820.864687500 863.500 12 763.020 805.998750 840.155 895.488650 942.0 13 826.605 873.165312500 921.001250 970.112712500 1020.500 14 890.190 940.331875 991.847500 1044.737775 1099.0 15 953.775 1007.498437500 1062.693750 1119.361837500 1177.500 16 1017.360 1075.665 1133.540 1193.985900 1256.0 17 1080.945 1142.831562500 1204.386250 1268.609962500 1334.500 18 1144.530 1209.99S125 1275.232500 1343.233125 1413.0 19 1208.115 1277.164687500 1346.078750 1417.857187500 1491.500 20 1271.700 1343.331250 1416.925 1492.481250 1570.0 30 1907.550 2014.996875 2125.387500 2238.721875 2355.0 40 2543.400 2686.662500 2833.850 2984.962500 3140.0 50 3179.250 3358.328125 3542.312500 3731.203125 3925.0 60 3815.100 4029.993750 I 4250.775 4477 443750 4710.0 — 118 Table of Comparison in Measure of Length, Foot to Meter. s&cvQU%ä)\tnQä*%ai>eUen im Sättflemnaf}, bei? ^ufj mm 9Weter* United States 1 line = 2.539954 mm. linch = 2.539954 cm., lfoot= 30.47973 cm., in general : 30.48. 5ßer. (Staaten 1 ßtnie= 2.539954 mm. 1 30a = 2.539954 cm. 1 ^u|3 = 30.47973 cm. im Sltlgemeinen : 30.48. "H-S C3 '£ V-9 O tin Yard Foot HS» 1 m. cm. mm. 7 O 3 21 m. 6 cm. 40 mm. Jjarb ■gufe in. cm. 59 mm. 2.539977 0.7433 1 61 18 2.6353 2 5.079954 22 6 70 5.5406 62 18 89 7.4326 3 7 619931 23 7 Ot 0.3379 21 63 19 20 2.2299 4 1 0.159908 8 24 7 31 5.1352 64 19 50 7.0272 5 1 2.699885 25 < 61 9.9325 65 19 81 1.8245 G 1 5.239862 26 7 92 4.7298 22 66 20 11 6.6218 7 1 7.779839 9 27 8 22 9.5271 67 20 42 1.4191 8 2 0.319816 28 8 53 4.3244 68 20 72 6.2164 9 2 2.859793 29 8 83 9.1217 23 69 21 03 1.0137 1 2 5.39977 10 30 9 14 3.9190 23.33 70 21 33 5.8110 2 5 0.79954 31 9 44 8.7163 26.67 80 24 38 3.784 3 7 6.19931 32 9 75 3.5136 30 90 27 43 1.757 4 10 1.59908 11 33 10 05 8.3109 33 33 100 30 47 9.73 5 12 6.99885 34 10 36 3.1082 66.67 200 60 95 9.46 6 15 2.39862 35 10 66 7.9055 100 300 91 43 9.19 7 17 7.79839 12 36 10 97 2.7028 133.33 400 121 91 8.92 8 20 3.19816 37 11 27 7.5001 166.67 500 152 39 8.65 9 22 8.59793 38 11 58 2.2974 200 600 182 87 8.38 10 25 3.99770 13 39 11 88 7.0947 233.33 700 213 35 8.11 11 27 9.39747 40 12 19 1.8920 266.67 800 243 83 7.84 1 30 4.7973 41 12 49 6.6893 300 900 274 31 7.57 2 60 9.5946 14 42 12 80 1.4866 333.33 1000 304 79 7.3 1 3 91 4.3919 43 13 10 6.2839 366.67 2000 609 59 4.6 4 1 21 9.1892 44 13 41 1.0812 1000 3000 914 39 1.9 5 1 52 3.9865 15 45 13 71 5.8785 1333.33 4000 1219 18 9.2 2 6 1 82 8.7838 46 14 02 0.6758 1666.67 5000 1523 98 6.5 7 2 13 3.5811 47 14 32 5.4731 2000 6000 1828 78 3.8 8 2 43 8.3784 16 48 14 63 0.2704 2333.33 7000 2133 58 1.1 3 9 2 74 3.1757 49 14 93 5.0677 2666.67 8000 2438 37 8.4 10 3 04 7.9730 50 15 23 9.8650 3000 9000 2743 17 5.7 11 3 35 2.7703 17 51 15 54 4.6623 3333.33 10000 3047 97 3.0 4 12 3 65 7.5676 52 15 84 9.4596 6666.67 20000 6095 94 6.0 13 3 96 2.3649 53 16 15 4.2599 10000 30000 9143 91 9.0 14 4 26 7.1622 18 54 16 45 9.0542 13333 33 40000 12191 89 2.0 5 15 4 57 1.9595 55 16 76 3.8515 16666.67 50000 15239 86 5.0 V 16 4 87 6.7568 56 17 06 8.6488 20000 60000 18287 83 8.0 17 5 18 1.554t 19 57 17 37 3.4461 23333.33 70000 21335 81 1.0 (i 18 5 48 6.3514 58 17 67 8.2434 26666.67 80000 24383 78 4.0 19 5 79 1.1487 59 17 98 3.0407 30000 90000, 27431 75 7.0 20 6 09 5.9460 20 60 18 28 7.8380 33333.33 100000 80479 73 — 119 — Table of Comparison in Square Measure, Foot to Meter, tfergfeicf)iings=Me(ren tm iluabrafmajj, öer Juß jum JRefet*. 1 sq. 1. = 6.151485 mm. 1 sq. in. = 6.451485 sq. cm. 1 sq. ft. = 0.09290137 sq. m.; in general = 0.0929 sq. m. 1 qf. = 6,451185 qmm. 1 q^l. = 6,451185 qcm. 1 qftj. = 0,09290137 qm. ; tin 2tüge= meinen = 0,0929 qm. sq. *■ sq. m. sq. dm sq. cm eq. mm. sq. ft. sq. m. sq. dm sq. cm. sq. mm. <*l. qm. qdm. qcm. qmm. qffe. qm. qdm. qcm. qmm. 1 06.151485 12.902970 19.354455 25.805940 32.257425 38.708910 45.160395 51.611880 2 3 4 5 6 7 8 9 18 27 37 4 S 55 65 74 83 58 87 16 45 74 03 32 61 02.768 2 04.152 3 05.536 4 06.920 5 08.304 6 09.688 11.072 8 12.456 9 58.063365 10 92 90 13.840 10 64.514850 11 01 02 19 15.224 20 01 01 02 03 03 04 05 05 06 12 19 25 32 29.02970 93.54455 58.05940 22.57425 87.08910 51.60395 16.11880 80.63365 45.1485 90.2970 35.4455 89.5940 25.7425 12 13 14 15 16 17 18 19 20 21 22 23 21 01 01 01 01 1 1 1 1 1 1 2 2 2 11 20 30 39 18 57 67 76 85 95 04 13 22 48 77 06 35 64 93 22 51 80 09 38 67 96 16.608 30 17.992 40 19.376 50 20.760 60 22.144 70 23.528 80 24.912 90 26.296 sq. in. 1 27.680 2 29.064 3 30.448 1 31.832 5 33.216 6 38 45 51 58 64 70.8910 16.0495 61.1880 06.3365 51.485 25 26 27 28 29 2 2 2 2 o 32 41 50 60 69 25 54 83 12 41 34.600 7 35.984 8 37.368 9 38.752 10 40.136 20 01 29 02.970 30 2 78 70 41.520 30 01 93 54.455 31 2 87 99 42.904 40 02 58 05.940 32 2 97 28 44.288 50 03 22 57.425 33 3 06 57 45.672 60 03 87 08.910 34 3 15 86 47.056 70 04 51 60.395 35 3 25 15 48.440 80 05 16 11.880 36 3 34 44 49.824 90 05 80 63.365 37 3 13 73 51.208 100 06 45 14.851 38 3 53 02 52.592 110 07 09 66.335 39 3 62 31 53.976 120 07 74 17.820 40 3 71 60 55.360 130 08 38 69.305 41 3 80 89 56.744 140 09 03 20.790 42 3 90 18 58.128 sq. ft. 1 09 29 01.384 43 3 99 47 59.512 120 — Table of Comparison in Square Measure, Foot to Meter. TJeryfeidjungs={EttlJeire im fluatafmajj, tier .fuß jum 311e(er. 1 sq. 1. = 6.451485 mm. 1 sq. in. == 6.451485 sq. cm. 1 sq. ft. = 0.09290137 sq. m.; in general = 0.0929 sq. m. 1 ql. = 6.451485 qmm. 1 q*l = 6.451485 qcm. 1 qfp. == 0.09290137 qm.; im 2Mge= meinen = 0.0929 qm. sq. ft. sq. m. sq. dm. sq. cm. sq. mm sq. ft. sq. m. sq. dm. sq. cm. sq. mm. qffc qm. qdm. qcm. qmm. 60.896 qtfc. qm. qdm. qcm. qmm. 44 4 08 76 86 i 98 95 19.024 45 4 18 05 62.280 87 8 08 24 20.408 46 4 27 34 63.664 88 8 17 53 21 792 47 4 36 63 65.048 89 8 26 82 22.176 48 4 45 92 66.432 90 8 36 11 23.560 49 4 55 21 67.816 91 8 45 40 24.944 50 4 64 50 69.200 92 8 54 69 26.328 51 4 73 79 70.584 93 8 63 98 27.712 52 4 83 08 71.968 94 8 73 27 29.096 53 4 92 37 73.352 95 8 82 56 30.480 54 5 01 66 74.736 96 8 91 85 31.864 55 5 10 95 76.120 97 9 01 14 33.248 56 5 20 24 77.504 98 9 10 43 35.632 57 5 29 53 78.888 99 9 19 72 37.016 58 5 38 82 80.272 100 9 29 01 38.4 59 5 48 11 81.656 200 18 58 02 76.8 60 5 57 50 83.040 300 27 87 04 15.2 61 5 66 69 84.424 400 37 16 05 53.6 62 5 75 98 85.808 500 46 45 06 92.0 63 5 85 27 87.192 600 55 74 08 30.4 64 5 94 56- 88.576 700 65 03 09 68.8 65 6 03 85 89.960 800 74 32 11 07.2 66 6 13 14 91.344 900 83 61 12 45.6 67 6 22 43 92.728 1000 92 90 13 84.0 68 6 31 72 94.112 2000 185 80 27 68.0 69 6 41 01 95.496 3000 278 70 41 52.0 70 6 50 30 96.880 4000 371 60 55 36.0 71 6 59 59 98.264 5000 464 50 69 20.0 72 6 68 88 99.648 6000 557 40 83 04.0 73 6 78 18 01.032 7000 650 30 96 88.0 74 6 87 47 02.416 8000 743 21 10 72.0 75 6 96 76 03.800 9000 836 11 24 56.0 76 7 06 05 05 184 10000 929 01 38 10 77 7 15 34 06.-568 20000 1858 02 76 80 78 7 24 63 07.952 30000 2787 04 15 20 79 i 33 92 09.336 40000 3716 05 53 60 80 7 43 21 10.720 50000 4,645 06 92 00 81 7 52 50 12.104 60000 5574 08 30 40 82 7 61 79 18.488 70000 6503 09 68 80 83 7 71 08 14.872 80000 7432 11 07 20 84 i 80 37 16.256 90000 8361 12 45 60 85 7 89 | 66 17.640 100000 9290 13 84 00 — 121 — Table of Comparison— Measure of Volume, Foot to Meter, ¥ergfeidjimgs=il(i6e(leii im Xürpermajj, bet Jug sum 31Mer. 1 cu. 1. = 16.886623 cu. mm. 1 cu. in. = 16.386623 cu. cm. 1 cu. ft. = 0.028316084 cu. m. general = 0.0283. in 1 tbl = 16,386623 kbmm. 1 fb]i. = 16,386623 kbcm. 1 fbfjj. = 0,028316084 kbm. meinen = 0,0283. im Mge- cu. 1. cu. m. cu. dm. cu. en i. cu. mm. cu. in. cu. m. cu. dm. cu. cm. cu. mm. fb(. kbm. kbdm. kben i. kbmm. Jbgl. 50 kbm. kbdm. kbcm. kbmm. 1 16.386623 .... 819 331.15 2 32.773246 -60 . 983 197.38 3 49.159869 70 . . 66i 147 063.61 4 65.546492 80 001 310 929.84 5 81.933115 90 001 474 796.07 6 98.319738 100 001 638 662.3 i 114.706361 200 003 277 324.6 8 131.092984 300 004 915 986.9 9 147.479607 400 006 554 649.2 10 163.86623 500 008 193 311.5 20 327.73246 600 009 831 973.8 30 . 491.59869 700 011 470 636.1 40 655.46492 800 013 109 298.4 50 819.33115 900 014 747 969.7 60 . 983.19738 1000 016 386 623.0 70 oo: L 147.06361 700 011 470 636.1 80 00 L 310.92984 20 ■ ■ > ■ 327 732.46 90 00 L 474.79607 PTl 8 131 092,984 100 00 L 638.6623 cu. ft. 1 '028 316 084 200 oo; } 277.3246 056 632 168 300 00- 1 915.9869 3 084 948 252 400 001 5 554.6492 4 113 264 336 500 00* 3 193.3115 5 141 580 420 600 00! ) 831.9738 6 169 896 504 700 01 L 470.6361 i 198 212 588 800 01* 1 109.2984 8 226 528 672 900 01' i 747.9607 9 254 844 756 cu.iu.l OK 3 386.623 10 283 160 840 2 03: I 773.246 11 311 476 924 3 04< ) 159.869 12 339 793 008 4 06; ) 546.492 13 368 119 092 5 08. L 933.115 14 396 425 176 6 09* 3 319.738 15 424 741 260 7 11- V 706.361 16 453 057 344 8 lS] L 092.984 17 481 373 428 9 14- " 479.607 18 509 689 512 10 m 5 866.23 19 538 005 596 20 32" ' 732.46 20 566 321 680 30 49] - 598.69 21 594 637 764 . 40 65i > | 464.92 22 622 953 848 122 — Table of Comparison — Measure of Volume, Foot to Meter. Itogfeidjungs-tEalielTen im Körpermaß, öer Jug jum Jliefer. 1 cu. 1. = 16.386623 cu. mm. 1 cu. in. = 16.386623 cu. cm. 1 cu. ft. = 0.028316084 cu. hi.; in general = 0.0283, 1 m. = 16,386623 kbmm. 1 fbjl. = 16,386623 kbcm. 1 fbffe. = 0,028316084 kbm. ; im 9(ttse= meincu — 0,0283. cu. ft. c ii. m. cu. dm. cu. cm. cu . mm. cu. ft. cu. m. cu. dm. cu. cm. cu.mm. fbffe. k bm. kbdm. kbcm. kbmm. - rof&. kbm. kbdm. kbcm . kbmm. 23 651 269 932 63 001 783 913 292 24 679 586 016 64 001 812 229 376 25 707 902 100 65 001 840 545 460 26 736 218 184 66 001 868 861 544 27 764 534 268 67 001 897 177 628 28 792 850 352 68 001 925 493 712 29 821 166 436 . 69 001 953 809 796 30 849 482 520 70 001 982 125 880 31 877 798 604 80 002 265 286 720 32 906 114 688 90 2 548 447 560 33 934 430 772 100 2 831 608 400 34 962 746 856 200 5 663 216 800 35 991 062 940 300 8 494 825 200 36 i" 018 379 024 400 11 326 433 600 37 l 046 695 108 500 14 158' 042 00 38 l 075 011 192 600 16 989 650 400 39 l 103 327 276 700 19 821 258 800 40 l 132 643 360 800 22 652 867 200 41 i 160 959 444 900 25 484 475 600 42 l 189 275 528 1000 28 316 084 43 l 217 591 612 2000 56 632 168 44 l 245 907 696 3000 84 948 252 45 l 274 223 780 4000 113 264 336 46 l 302 539 864 5000 141 580 420 47 [)i 330 855 948 6000 169 896 504 48 01 359 172 032 7000 198 212 588 49 01 387 488 116 8000 226 528 672 50 31 415 804 200 9000 254 844 756 51 31 444 120 284 10000 283 160 840 52 01 472 436 368 20000 566 321 680 • • • 53 01 500 752 452 30000 849 482 520 54 01 529 068 536 40000 1132 643 360 55 01 557 381 620 50000 1415 804 200 56 01 585 700 704 60000 1698 965 010 57 01 614 016 788 70000 1982 125 880 58 01 642 332 872 80000 2265 286 720 59 01 670 648 956 90000 2548 447 560 60 01 698 965 040 100000 2831 608 400 61 01 727 281 124 200000 5663 216 800 62 J 0< 01 755 597 208 300000 8494 825 200 • • V — 123 Comparison of the Square Yard to Square Meter. Uergfeidjimg bee Xluabraf=3]aib jum fluaöraf=31tefcr. 1 square yard = 0.836112 sq. m. | 1 Quabratgarb == 0.836112 qm. sq. sq. m. sq. yds. sq. in. sq. yds. sq. m. sq. nails 1 0.0528056 38 31.772256 81 67.725072 2 0.1056112 39 32.608368 82 68.561184 sq. 3 0.156514 40 33.444480 83 69.397296 qtrs. 1 0.209028 41 34.280592 84 70.233408 2 0.418056 42 35.116704 85 71.069520 sq. 3 0.627084 43 35.952816 86 71.905632 ydsl 0.836112 44 36.788928 87 72.841744 2 1.672224 45 37.625040 88 73.677856 3 2.508336 46 38.461152 89 74.513968 4 3.344448 47 39.297264 90 75.350080 5 4.180560 48 40.133376 91 76.186192 6 5.016672 49 41.969488 92 77.022304 7 5.852784 50 41.8056 93 77.858416 8 6.688896 51 42.641712 94 78.694528 9 7.525008 52 43.477824 95 79.530640 10 8.361120 53 44.313936 96 80.366752 11 9.197232 54 45.150048 97 81.202864 12 10.033344 55 45.986160 98 82.038976 13 10.869456 56 46.822272 99 82.865088 14 11.705568 57 47.658384 100 83.6112 15 12.541680 58 48.494496 200 167.2224 16 13.377792 59 49.330608 300 250.8336 17 14.213904 60 50.166720 400 334.4448 18 15.050016 61 51.002832 500 418.0560 19 15.886128 62 51.838944 600 501.6672 20 16.722240 63 52.675056 700 585.2784 21 17.558352 64 53.511168 800 668.8896 22 18.394464 65 54.347280 900 752.5008 23 19.230576 66 55.183392 1000 836.1120 24 20.066688 67 56.019504 2000 1672.2240 25 20.902800 68 56.855616 3000 2508.3360 26 21.738912 69 57.691728 4000 3344.4480 27 22.574024 70 58.527840 5000 4180.56 28 23.411136 71 59.363952 6000 5016.6720 29 24.247248 72 60.200064 7000 5852.7840 30 25.083360 73 61.036176 8000 6688.8960 31 25.919472 74 62.872288 9000 7525.0080 32 26.755584 75 62.7084 10000 8361.12 33 27.591696 76 63.544512 20000 16722.24 34 28.427808 i i 64.380624 30000 25083.36 35 29.263920 78 65.216736 40000 33444.48 36 30.100032 79 66.052848 50000 41805.60 37 30.936144 80 66.888960 60000 50166.72 124 — Comparison of the Cubic Yard to the Cubic Meter. Uergfeidjung ber 3{u6ik=3Jaib jnm 3Mik=J1Mer. 1 cu. yard : = 0.764534268 cu. m. cu. m. CU. 111. cu. 111. cu. yds. kbm. cu. yds. 41 kbm. cu. yds. kbm. 0.25 0.191133567 31.345904988 84 64.220878512 0.50 0.382267134 42 32.110439256 85 64.985412780 0.75 0.573400701 43 32.874973524 86 65.749947048 1 0.764534268 44 33.639507792 87 66.514481316 2 1.529068536 45 34.404042060 88 67.279015584 3 2.293604804 46 35. 168576328 89 68.043549852 4 3.058137072 47 35.933110596 90 68.808084120 5 3.822671340 48 36.6976448.64 91 69 572618388 6 4.587205608 49 37.462179132 92 70.337152656 7 5.351739876 50 38.226713400 93 71.101686924 8 6.116274144 51 38.991247668 94 71.866221192 9 6.880808412 52 39.755781936 95 72.630755460 10 7.645342680 53 40.520316204 96 73.395289728 11 8.409876948 54 41.284850472 97 74.159823996 12 9.174411216 55 42.049384740 98 74.924358264 13 9.938945484 56 42.813819008 99 75.688892532 14 10.703479752 57 43.578353276 100 76.453426800 15 11.468014020 58 44.343887544 200 152.906853600 16 12.232548288 59 45.107421812 300 229.360280400 17 12.997082556 60 45.871956080 400 305.813707200 18 13.761616824 61 46.636590348 500 382.267134 19 14.526151092 62 47.401124616 600 458.720560800 20 15.290685360 63 48.165658884 700 535.173987600 21 16.055219628 64 48.930193152 800 611.627414400 22 16.819753896 65 49.694727420 900 688.080841200 23 17.584288164 66 50,459261688 1000 764.534268 24 18.349822432 67 51.223795956 2000 1529.068536 25 19.113356700 68 51.988330224 3000 2293.602804 26 19.877890968 69 52.752864492 4000 3058.137072 27 20.642425236 70 53.517398760 5000 3822.671340 28 21.406959504 71 54.281933028 6000 4587.205608 29 22.171493772 72 55.046467296 7000 5351.739876 30 22.936028040 73 55.811001564 8000 6116.274144 31 23.700562308 74 56.575535832 9000 6880.808412 32 24.465196576 75 57.340070100 10000 7645.342680 33 25.229630844 76 58.104604368 20000 15290.685360 34 25.994165112 77 58.869138636 30000 22936.028040 35 26.758799380 78 59.633672904 40000 30581.370720 36 27.523233648 79 60.398207179 50000 38226.713400 37 28.287767916 80 61.162741440 60000 45872.056080 38 29.052302184 81 61.927275708 70000 53517.398760 39 29.816836452 82 62.691809976 80000 61162.741440 40 30.581370720 83 63.456344244 90000 100000 68808.084120 76453.426800 — 125 — Table of.Comparison, Gallon to Liter. T?ergreicgungs=SaBe(Te, hie flaflfone jum Cifer. 1 Gill = 0.1182909375 Liter. 1 ©id = 0,1182909375 filter. 1 Pint = 0.47316375 Liter. 1 $tut = 0,47316375 filter. 1 Quart = 0.9463275 Liter. 1 Quart = 0,9463275 fitter. 1 Gallon — 3.78531 Liter (Wine- l@alloiie= 3,78531 fitter (2Seui; gallon). galloue). Gallon Liter. Gall. Liter. Gall. Liter. Gallon. 1 Liter. ©altone £tter. ®aU. Siter. 68 utter. (Ballone. iJiter; gill 1 0.1182909375 31 117.34461 257.40108 600 2271.186 2 0.236581875 32 121.12992 69 261.18639 700 2649.717 3 0.3548728125 33 124.91523 70 264.97170 800 3028.248 pt.l 0.47316375 34 128.70054 71 268.75701 900 3406.779 qt. 1 0.9463275 35 132.48585 72 272.54232 1000 3785.31 2 1.892655 36 136.27116 73 276.32763 2000 7570.62 3 2.8389825 37 140.05647 74 280.11294 3000 11355.93 gal.l 3.78531 38 143.84178 75 283.89825 4000 15141.24 2 7.57062 39 147.62709 76 287.68356 5000 18926.55 3 11.35593 40 151.4124 77 291.46887 6000 22711.86 4 15.14124 41 155.19771 78 295.2541S 7000 26497.17 5 18.92655 42 158.98302 79 299.03949 8000 30282.48 6 22,71186 43 162,76833 80 302.82480 9000 34067.79 7 26.49717 44 166.55364 81 306.61011 10000 37853.10 8 30.28248 45 170.33895 82 310.39542 20000 75706.20 9 34.06779 46 174.12426 83 314.18073 30000 113559.30 10 37.8531 47 177.90957 84 317.96604 40000 151412.40 11 41.63841 48 181.69488 85 321.75135 50000 189265.50 12 45.42372 49 185.48019 86 325.53666 60000 227118.60 13 49.20903 50 189.26550 87 329.32197 70000 264971.70 14 52.99434 51 193.05081 88 333.10728 80000 302824.80 15 56.77965 52 196.83612 89 336.89259 90000 340677.90 16 60.56496 53 200.62143 90 340.67790 100000 378531.00 17 64.35027 54 204.40674 91 344.46321 200000 757062.00 18 68.13558 55 208.19205 92 348.24852 300000 1135593 19 71.92089 56 211.97736 93 352.03383 400000 1514124.0 20 75.7062 57 215.76267 94 355.81914 500000 1892655.0 21 79.49151 58 219.54798 95 359.60445 600000 2271186.0 22 83.27682 59 223.33329 96 363.38976 700000 2649717.0 23 87.06213 60 227.11860 97 367.17507 800000 3028248.0 24 90.84744 61 230.90391 98 370.96038 900000 3306779.0 25 94.63275 62 234.68922 99 374.74569 1000000 3785310.0 26 98.41806 63 238.47453 100 378.531 2000000 7570620.0 27 102.20337 64 242.25984 200 757.062 3000000 11355930.0 28 105.98868 65 246.04515 300 1135.593 4000000 15141240.0 29 109.77399 66 249.83046 400 1514.124 5000000 18926550.0 30 113.5593 67 253.61577 500 1892.655 6000000 12271860.0 — 126 — Table of Comparison, Liter to Gallon. Ttogfeidjumjs^aBettc, bei* Cifer 511 bei* <§adbne. 0.5 Liter = 1 Pint == 0.1320765 Gall. 1 Liter = 2 Pints = 0.2644 Gall. (Wine-gallon). 0.5 2ttcr=l ©d;op. == 0.1320765 ©all. 1 gitev = 2 ©djop. = 0.2644 @aü. (28eütgaüone). Liter. Gallon. Liter. Gallon. Liter. Gallon. Liter. Gallon. giter. ©attone. gitev. 36 (Ballone. Sit er. 72 ©allone. Siter. ©allone. liter 0.5 0.1320765 9.509508 19.019016 900 237.7377 1 0.264153 37 9.773661 73 19.283169 1000 264.1530 2 0.528306 38 10.937814 74 19.547322 2000 528.306 3 0.792459 39 10.301967 75 19.811475 3000 792.459 4 1.056612 40 10.566120 76 20.075628 4000 1056.612 5 1.320765 41 10.830273 77 20.339781 5000 1320.765 6 1.584918 42 11.094426 78 20.603934 6000 1584.918 7 1.849071 43 11.358579 79 20.868087 7000 1849.071 8 2.113224 44 11.622732 80 21.132240 8000 2113.224 9 2.377377 45 11.886885 81 21.396393 9000 2377.377 10 2.641530 46 12.151038 82 21.660546 10000 2641.530 11 2.905683 47 12.415191 83 21.924699 20000 5283.06 12 3.169836 48 12.679344 84 21.188852 30000 7924.59 13 3.433989 49 12.943497 85 22.453005 40000 10566.12 14 3.698142 50 13.207650 86 22.717158 50000 13207.65 15 3.962295 51 13.471803 87 22.981311 60000 15849.18 16 4.226448 52 13.735956 88 23.245464 70000 18490.71 17 4.490602 53 14.000109 89 23.509617 80000 21132.24 18 4.754754 54 14.264262 90 23.773770 90000 23773.77 19 5.018907 55 14.528415 91 24.037923 100000 26415.30 20 5.283060 56 14.792568 92 24.302076 200000 52830.60 21 5.547213 57 15.056721 93 24.566229 300000 79245.90 22 5.811366 58 15.320874 94 24.830382 400000 105661.20 23 6.075619 59 15.585027 95 25-094535 500000 132076.50 24 6.349672 60 15.849180 96 25.358688 600000 158491.80 25 6.603825 61 16.113333 97 25.622841 700000 184907.10 26 6.867978 62 16.377486 98 25.886994 800000 211322.40 27 7.132131 63 16.641639 99 26.151147 900000 237737.70 28 7.396284 64 16.905792 100 26.4153 1000000 264153.0 29 7.660437 65 17.169945 200 52.8306 2000000 528306.0 30 7.924590 66 17.434098 300 79.2459 2000000 792459.0 31 8.188743 67 17.698251 400 105.6612 4000000 1056612.0 32 8.452896 68 17.962404 500 132.0765 5000000 1320765.0 33 8.717049 69 18.226557 600 158.4918 6000000 1584918.0 34 8.981202 70 18.490710 700 184.9071 7000000 1849071.0 35 9.245355 71 18.754863 j 800 211.3224 8000000 2113224.0 APPENDIX. Metric Measure and Weight Sys- tem in France. The unit of the metric measure of length is called Meter, and is a forty- millionth of the earth's meridian which passes through Paris, or one ten-millionth of a quadrant of such a meridian. The unit of the measure of surface is called Are, and is a square, each side of which is 10 meters in length. The unit of the measure of capacity, such as is used for the measurement of dry and liquid articles, is called Liter, and in capacity is equal to a cube each side of which is 1/10 meter. A cubed meter is called Stere and con- tains 1000 liters. The unit of weight is called Gram, and is the absolute weight of 1/1000000 cu. cm. of pure water at its temperature of greatest density (4 degrees C). Each of the above named units is divided and multiplied and varies in a tenfold ratio. This accounts for the names: Decimeter, Centimeter, Mil- limeter, Dekameter, Hektometer, Kil- ometer, Myriameter, Decigram, Cen- tigram, etc. 1 meter = exactly = 0.513074 Parisian Toise, or — 443.2959 duodeci- mal lines of the former Parisian foot, if the matter of the meter is in melt- ing ice, but the Toise is of iron and has -f- 13 degrees Reaumur (55| degrees Fahrenheit).* f By -\- 13 degrees Reaumur a meter of platina = 443.357 Parisian lines; iron — 443.379 Parisian lines; brass * Laplase Exposition du Systeme du mode, 2d Ed. t Vega Logarithmen. Hnbang- WUm in ftvantvcxti). ©ie ©ruubetu^ett beS fiängenmaJBeS §en)t dieter, nub tft ber jefjitmiiiionte Ifyeil beS ^artfer ^Jceribianquabrauten, ober eigentlich ber r)unberttaufenbfte Xfyetl eines (SeuteftmaTgrabeS beS bitrdt) 5ßariS geljenbeu, auf bent StJceereSIjortsout rebucirten QfrbmertbianS, unter ber geo= graptyifdjen r>on 50 @rab ber (Sentefimals (lint raiding. 2)te beS §(äd)eu= unb $elb= tnafceS Reifet Are, nub ifi ein Quabrat, beffeu ©ette 10 9fteter lang tft. 2)ie (Stn= rjeit beS ^orjImafteS ut fliiftgen unb trocfeuen SBaaren Ijeifjt Siter, unb tfi am 3jnljalte einem Söürfel gtetdt), beffeu ispette 1/10 Sfteter beträgt; ein fu&irter «fleeter $et(?t ©tere, unb enthält 1000 8iter§. £>te (Sint)ett beS ©eroidjtS ^eipt ©rantm, unb tft baS abfolute ©eroicfjt einer Quantität beS beftilltrten Staffers, baS fid) im gujtaube [einer größten 2Ser= bicrjtung (ungefähr Beim 4. Gent=@rabe beS QnedfUoer=£{jermometerS) im utft= teeren Raunte fceftnbet, unb beffeu Volu- men 1/1000000 5?u6tf=2tteter beträgt. Jebe ber angeführten (Stn^etten rotrb in Heinere Steile nad) bem ©ecimalfnfteme eingeteilt, daraus ftnb bie ^Benennun- gen erftärlict) : ©ecimeter, (Zentimeter, SJctttimeter, 2)efameter, £ettometer, Ätlo= meter, 9Jh)riameter, ©ecigramnte, dentin gramme jc. ©in 3tteter genau = 0,513074 ^arifer £oiS ober = 443,2959 ©ttobecimal Suiten beS ehemaligen ^arifer ^uf^eS, menu fidt) bie ^ftateriebeS 9JceterS in fdjmeljenbem (Stfe beftnbet, bie £oife aber uon (Sifen tft unb + 13 @rab Reaumur = 61i g a & ven= tyeit Ijat* 33ei -|- 13 @rab Reaumur tft ein * u§a(t eines ÄretfeS gleid) ber s }3eripl)erie mal ben falben 9tabiu§ tjt, fo ntujj bie ^ertpljerte eines ÄreifeS, beffeu «WabtttS gleid) 1 ift = 2 Pi fein. ©efct man ben R. eines feife§ gletd) 1, fo ift ber Suljalt be§ eingefdjrteJbeuen regulären 4 ©eit§ gleid) 2, nub roeil bie ©eite be§ etugefd)rtebeuen regulären 4 ©ett§ gleid) bem ©urdjmeffer, alfo = 2 tft, fo tft ber Sntyalt = 4. £terau§ folgt [djon, baft Pi jroifdjeu 2 nub 4 liegen mutf. Sßereconet matt nun oermtttelft ber bei= ben g-ormeln bie 3>njjalte be§ ein* unb um= gefdjrtebenen regulären 8 <©ett§, unb au§ btefen rateber bie be§ etn=unb umgefd)rte= beneu regulären 16 ©ett§ u. f. to., fo rotrb mau immer engere ©renken für bie ait- närjernbe SBejttmmuug oon Pi finben muffen. 3" nadjftefyenbent ©amenta ift bie ausgeführte 9ted)nung 6i§ git 128 ©eit§ enthalten: Number of Sides, ©eitenanjaf)!. Volume of Inscribed Polygon. Snljalt beg eingefd^rie* benen ^otqgonS. Volume of Circumscribed Polygon. Snljalt be§ umidjriebencn Sßolt)jon§. 4 2.000000 4.000000 8 2.828428 3.313712 16 3.061464 3.182604 32 3.121446 3.151729 64 3.136551 3.144122 128 3.140334 3.142227 As the area of the inscribed polygon of 128 sides is equal to 3.140334 and that of the circumscribed polygon of 128 sides is equal to 3.142227 ©a nun ber^nbalt ber eiugefdjriebenen 128<5eit§ gletd) 3,140334 ...., ber beo umgefd)riebeneu 128 ©eit§ gleid) 3,142227 ... tft, Pi aber jroifdjen btefen betbeu — 129 — and as Pi must lie between these numbers, it is concluded "that Pi = 3.14, computed correctly to two deci- mal places. Remark: The number Pi is irra- tional and cannot, therefore, be given in a finite decimal, and in employing it, one must be contented with a fixed number of decimal places, seldom more than 4 to 7 are required. Com- puted to 7 decimal places, Pi = 3.141- 5927. For business purposes = 3.14. 3(U}leit Hegen mufj, jo folgt baft Pi = 3,14 bi§ 2 ©ecimalfteUen richtig bered)«ei ift. 21 it m e r t u it g : £te 3 a ^f Pi ift iv- vattonel «üb fa«« batyev b«vd) feine e«b-- ltd;e Slusaljt do« ©ecimalftetten a«ge= gebe« werben, i« be« 2fiuoe«b««ge« mufi ma« [id) baljer mit einer beftimmte« 2(n= let mttttftycn 9ft<*fje uttfc i$mid)tc, 1. Measure of Length. — s^ängenmaft. (The Unit is the Meter.— ©te (Stttt>ett bübet ba§ Bieter ober ber (©tab.) Kilometer. A. kilometer. Km. 1 Meter. B. WlzUi (©tab). M. 1 Hektometer. Jpcftometer. Hm. 10 1 Decimeter. ^Decimeter. dm. 10 1 Mile. 1 Weile Dekameter. ^efametev (Äette). Dm. 100 = 10 = 1 = Centimeter. (Seiitimetev (IftetigoK). cm. 100 - 10 1 Meter. lUetev (©tab). M. 1000 100 10 Millimeter. 2Kiaimeter. mm. 1000 100 10 Dekameter. Meter. 750 Defametev (ßüte) = 7500 Sfteter (©tab). 2. Measures of Surfaces. — ^läcfyenma^e. (The Unit is the Square Meter. — 5)tc (Sirtljett bübet bno Cuabratmeter ober ber Cuabratftab.) Sq. Km. Sq. Hm. Sq. Dm. Sq. Meter. Sq. dm. Sq. cm. Sq. mm. 1 = 100 = 1000 = 100000 = 1 = 100 . ' = 10000 = 1 = 100 = 1 = 100 = 10000 = 1000000 1 = 100 = 10000 1 = 100 * According to law of the German Empire, 1871.— Wod) bem ©efetje bes 5)tutfd)en üteicrjee, 1871. — 130- 3. Measures of Volume. — Körpermaße. (The Cubic Meter is the basis. The Unit is one Cubic Decimeter and is called Liter. — IDit Wrunb; (age btibet ba§ ftubifmetet ober jtubifftab. £>te ©infjeit i ft bet taufenbfte S^etl be§ £ubifmeter3 unb Reifet ba$ it'itec ober jfartne.) Cubic Dekameter. Cubic Meter. Cubic Decimeter. Cubic Centimeter. Cubic Millimeter, ftubtt'befameter. ftubtfmeter. Jhibifbectmeter. Äubitunttmeter. .fubtfmtUimeier. cu. Dm. 1 cu. m. cu. dm. cu. cm. = 1000 = 1000000 1 = 1000 = 1000000 1 = 1000 1 4. Measures of Capacity. — ^otjlma^e. cu. mm. = 1000000000 = 1000000 = 1000 Kiloliter. tfitoliter. Hektoliter. Dekaliter. Liter. £eftoltter (ft-ajj). Jjef alitor. Sit« (Äaiuie). Pint. ©poppen. 1 = 10 == 100 = 1000 1 = 10 = 100 1 = 10 1 = 2000 = 200 = 20 — 2 Hektoliter. £eftoliter ($af?) 1 üßeiiföeffel; Siter Otauue). = 2 = 100 1 = 50 1 5. Weights. — (Sertncbte. Pint. ©poppen = 200 = 100 = 2 (The Unit of Weight is the Kilogram = two pounds. — Die (Sinbeit be§ @eroid)te§ btibet bctS Üüogramm = ^roei ^Jfunb.) It is the weight of a liter of pure water at a temperature of 4° C. — G§ ifi ba§ ©ereilt etue§ gtter§ beftiUtrteu Stoffer bet + 4° C. Ton. Hundred-weight. Kilogram. Pound. Dekagram. A. dornte. Centner. Kilogramm, ^fuub. X>er'agrainm. Cwt.— Ctr. 20 1 Kg.-Klgr. 1000 50 1 B. Gram. @ramm g- ®r. 1 Decigram. recigmmni. dg. 5Dgr. 10 1 Pound. «Pfunb. lb.— «Pfb. 2000 100 2 1 Centigram. Gtenttgrftrnm. eg. Sgr. 100 10 1 "Dceutotb. 100000 5000 100 50 1 = Gram. ©vainni- G.— @r- 1000000 50000 1000 500 10 Milligram. Milligram tu. mg. >lKgr. 1000 100 10 — 131 — 6. gäblmafte. 1 «Ballen: lOSftieS; 1 3*ic§ : 10 23ud&; 1 S8ud^ : 24 ©d&vetfc, 25 «Bogen ©tu* Rapier. 1 ©d)Ocf: 4 9ttanbel; 19Jcanbel: 15 ©tue!. 1 ©d&odf: 60@tücf (Ritten = ©arbeit); 1 (Steige: 15 ©tue!. 1 ©ufcenb : 12 ©tue!. 1 Zimmer ($elle ?c): 4 ©edjer ober 40 ©tue!; 1 ©ed&er : 10 ©tücf. * Table of Comparisons. — * Stet gleicfMutft* = ZabeiUn. United States Measures and Weights in the Metrie Measure and Weight. — 23er. Staaten 2fta£je unb ©erotdjte im metrtjdjen 2Rafj unb ©eroidjt. A. Measure of Length. — iämienmaft. 1 Yard 1 Foot 1 Inch 1 Fathom, 2 yards. 1 Cable, 240 yards. . 1 Chain, 22 yards . . 1 Mile 1 Furlong, i mile. . 1 Pole, perch or rod, 5.5 yards. 1 Meter 1 Meter 0.914398 30.47973 2.53998 1.8288 192.45 20.12 1609 201.2 m. cm. cm. m. m. m. m. m. 5.09 m. 1.09363 yard. 3.2809 feet. 1 garb 1 S"f 1 Sou 1 gaben, 2 2)arb.. 1 Kabellänge, 240 ?)arb 1 8tnf, 22 3)arb... 1 ÜReile. ;., 1 $ndong,i beetle, 1 ftitttje, 5.5 2)arb. 1 «fleeter 1 «fleeter 0,904398 m. 30,47973 cm. 2,53998 cm. 1,8288 m. 192,45 20,12 1609 201,2 5,029 m. m. m. m. m. 1,09363 3,2809 ?)arb. B. Measure of Surface. — ^lädjenmafi. 1 Sq. Yard = 0.836112 sq. m. 1 Sq. Foot = 0.09290137 sq. m. 1 Sq. Inch = 6.451485 sq. cm. 1 Sq. Line = 6.451485 sq. mm. 1 Sq. Acre, 4840 sq. yards = 40.467838 Are. 1 Sq. Meter = 10.7643 sq. feet. 1 Are = 2.47114 Acres. 1 qbr. 2)arb == 0,836112 qbr. m. 1 qbr. §ufj = 0,09290137 qbr. m. 1 qbr. 3,0 a = 6,451485 qbr. cm. 1 qbr. Suite = 6,451485 qbr. mm. 1 qbr. 9kre, 4840 qbr. ?)arb = 40,467838 Are. 1 qbr. 2«etev = 10,7643 qbr. ftufc. 1 2Xre =2,47114 3Icre§. * All relative numbers of the tables of comparison of measure and weight are taken from Edward Braesike and Siegfried's tables of mint measure and weight. * ©ämmtltc&e SSerftättniKjafjIen ber t Petg(etrintng§tabfQ'ert ber ÜJtafse unb (*eroid)tc finb oon (5 b to a rb 23 r ä )' i t e unb ® t e g f r i e b' § Wüuy-, ?lHaf?s nnb ©erotdjtSs'Jabetlen entnommen. — 132- C. Measure of Volume. — Körpermaß. 1 Cubic Foot . . = 0.028316084 cu. m. 1 Cubic Inch.. = 16.386623 cu. cm. 1 Cubic Line. . = 16.386623 cu. mm. 1 Cubic Meter = 35.3166 cu. feet. 1 ßubiffujj. ...,..= 0,028316084 kbm. 1 tfubifjoU = 16,386623 kbcm. 1 tfublflinte == 16,386623 kbmm. 1 Äubifmeter . . , . . = 35,3166 Äubiffuf . D. Measure of Capacity. — £}or?lmafj& 1 Barrel, 36 gallons. . = 163.6 liters. | 1 göft, 36 ©attonen. . . = 163,6 Sitcr. 1 Barrel, 196 lbs. = 88.9 kg.; by Fish, 90 kg; Rosin, 127 kg. 1 ftafe, 196 §Pfb. = 88,9 kgr. ; bet gifd&eu, 90 kgr. ; £arj, 127 kgr. 1 Bushel = 36.3477 liters. 1 Gallon (wine gal.). = 3.78531 liters. 1 Gallon (i bushel) = 4.405 liters. 1 Pint (i gallon). . , . = 0.473 liter. lSBuf&ei 1 ©aüone (2Betn) . . . 1 ©aüone (i$8uf$el). l$iutc(i (Motte).. = 36,3477 gitcr. = 3,78531 fitter. = 4,405 fitter. = 0,473 fitter. F. Weights. — (Seandjte. 1 Hundred-weight = 112 lbs. = 45.359264 kg. rondo. 1 Quarter = 12.7005 kg. 1 Ton (long) — 2240 pounds = 10160.4754 kg. 1 Ton (short) = 2000 lbs. = 907 . 1853 kg. 1 Pound (avoirdupois — avdp. or lbs.) = 453.59265 kg. r. 0.453.6 kg. 1 Ounce (avdp.) = 284.3954 gr. 1 Grain (or Grain troy), Gold, Silver, Mint and Apothecaries weight = 0.06479895 gr. 1 Pound, troy, Gold, Silver, Mint and Apoth. weight = 373.59265 gr. 1 Ounce, troy = 480 grains, Gold, Silver, Mint and Apothecaries weight = 31.103496 gr. 1 Kilogram — 2.20463 pounds avdp. 1 Kilogram = 2.67924 pounds troy. 1 Gentner = 112 «ßfunb = 45,359265 kgr. rondo. 1 Duarter (i Gentner) = 12,7005 kgr. 1 Sonne (grofje) = 2240 $funb = 10160,4754 kgr. 1 £onne(fcir$e)= 2000 $ f.== 907,1853 kg. 1 $funb (avoirdupois — avdp. ober lbs.) = 453,59265 kgr., r. 0.453,6 kgr. 1 Uuje (avdp.) = 284,3954 gr. 1 ©rain (audi) Grain troy), @o!b=, <&iU ber=, üftünjs unb 2(pot|cfer=@en)tc^t = 0,06479895 gr. 1 «jSfunb (troy) @olb=, @itber=, Mu$= unb 2Iport). =@eroicf)t = 373,59265 gr. 1 Uitae(troy)= 480 grains, @o!b=, Bih bers, $Mu^ unb 2lpot^.;@eioidit = 31,103496 gr. 1 Kilogramm = 2,20463 «Pfunb avdp. 1 Kilogramm = 2,67924 $fuub troy. — 133 — OS O* SO o CO ""^ SO o iO o so lO lO 00 00 so o T— 1 1—1 o 1— I o 1-i £- t-" to ^ J— 1 1—1 -< •J9J8 ^ UBI8ST1JI OS 00 lO OS — O* 00 00 r- © iO OS «3 05 o 00 CO 00 O f 1— 1 t- so lO *tf ■t— I T—{ •3)l31fl5 3£j ■-l\tiUi) qun -}^ -J3S5 •9DM •gng; pus -g «q C9 O 6.644 6.214 00 SO o 1— 1 so 00 OS •3]13lU33g) 3^ilj6u|) qun u3;ddJ2) -33$ •Sua pun 'S "II T-l OS o so OS © Ol so o "tf CO SO »O tO ^* X 00 d •aprnqs'sstAiS •aatt 3^)Uqupno& LO OS' — — — „' *J SO Ol SO SO o lO o 05 O? 00 o o so CO lO tH 7— 1 00 CO to CO Oi Ol oi 03 H H I— 1 1=1 o o X o O d x X o o . ^■s ^. ^: ° S a; « ? g i^ 'S = as •1« 60 s 02 < — ^g ^ s _ ^5 © « cr. 3 c !=1 s ^^ •- s Q a X X :: DG >-• p ■5 3 -s 3 5 o c Ü c X ö 5 'S CD Si- 'Ö a -d (fl 3 S SO x" iJ £ & 1 ■^ O Q «5 r cfijjse?iese aa.2§ c "3 I® LÖ « 2 ; s s ; S rt-Hi-ii-iriiirtVii^i-IrilS I IE 31 J! S (C I « i< i a i-3 u 4) ? hfi'O II ^ 6X5=] 3 ■> S3 — " '-I 6X1 Ö o = 'S so a +* mX S-ö 2 sj =- — OS'S xP > iß Q «O > — o »-< c - a -3 134 — Table of Comparison — Foreign Measure of Length to the Meter. Belgium: Germany : Denmark: = 0.6277 m. England: — 0.9144 m. France: 1 as @ 10 EUROPE. : Same as France. Same as France. 1 Ell = 2 ft. @ 12 in. ; 1 ft. = 0.31385 m. 1 Yard — 3 ft. @ 12 in. 1 ft. — 0.3047945 m. Meter == 10 dm. @ 10 cm. @ 10 mm. Greece: The new Pike (meter) = 10 Palmen @ 10 in. @ 10 lines. Italy: Metro (meter) = 10 Palmi @ 10 Diti @ 10 Atomi. Luxemburg: Same as France. Netherlands: 1 El (meter) @ 10 Palmen @ lODuimen @ 10 Strepen. Norway: Same as France. Austria ~ Hungary: Same France. Portugal: Same as France. Roumania: Same as France Russia. 1 Foot @ 12 in lines = 0.3047945 m. (same England). Sweden: 1 Foot @ 10 in. @ lines == 0.2969 m. Switzerland: Same as France. Servia: Same as France. Spain, Official: Same as France. Turkey, Official: 1 Zirai-a'chary or Meter with decimal divisions. Until now: 1 Pik (Pik Halebi) or Bazar-Arschine @ 8 Rub @ 2 Girah = 0.6858 m. 1 Endase or short Ell @ 8 Rub @ 2 Girah = 0.6528 m. The Halebi (Arschine) = 0.708647 meter. AFRICA. 1. Abyssinia: The Pik (Ell) = the Turkish = 0.6857878 m. 2. Egypt: The Pik (Ell) (5) 6 Krat = 0.677 m. 10, 11 12. 13, 14, 15 16 17 18, 19, as 10 4 Rup 1 gufc = 3 gufe @ 12 1 3"fi = (Europa. ,- Zeigten: 2Bte $ranfreid). , ©eutfdjtanb: 2ßie granfretd) . ©änemarf: 1 (Sue @ 2 gufe @ 12 3od = 0,6277 3Reter; 0,31385 «Meter. . (Sitglanb: 1 2)arb = ^od = 0,9144 öfterer; 0,3047945 Sfteter. . §ranfietd&: 1 öfterer = 10 ©ecimeter ju 10 Centimeter ju 10 «JJUtttmeter. , @rtecr)eniaub: ©teneuepfe(2fteter) = 10 Jahnen @ 10 Soil @ 10 ßtnteu. , Italien : «Metro («Meter) = 10 «Palmi @ 10 ©ttt @ 10 Storni. , Suremourg: 2ßie ^ranfretcr;. Wieberlanbe : 1 @i (2Reter) @ 10 «Palmen @ 10 ©utmen @ 10 ©trepen. «ftorroegen: «löte ^ranfretd). Defterreia> Ungarn : SSie granr"retd) Portugal : 2Bie graufreid). Rumänien : 2öte granfretd). «Rufelanb: 1 gufe @ 12 3ol( @ 10 Linien = 0,3047945 «Meter. 2öie @ng= lanb. , ©djroeben : 1 ftufe @ 10 3oU @ 10 giuten = 0,2969 Sfteter. ©djroeij: «iöte graufretd). , (Serbien: «Bie granfretd). , (Spanien: Offtjiell, rote ftrcuif'reid). , dürfet: OffisietC — 3ir>avT- a'd^art) ober «Meter mit ©ecimat=Uuterabtl)et= ungeit. «Bt§f,er: 1 $tf (W £alebt) ober 93ajaar^rfd)tne @ 8 ftub @ 2 ©trait) = 0.6858 SOleter. 1 Cntbafe ober rurjc ©tie @ 8 «Rub @2 ©irälj = 0,6528 äReter. ©er £alebi (Slrfd&m) = 0,708647 Steter. 21 f r i f a. 1. «Hbgffiuteu : ©er q3if (@ac) = ber titrfifdjen = 0,6857878 m. 2. 51egt)pten: ©er «ßtf (©He) @ 4 «Rup @ 6 Ärat = 0.677 m. 15 16, 17, 18 19 135 - 3. Capeland: The old Amsterdam and Rhineland Foot ==• 12 in. (g 12 lines = 0.313946 m. 4. Morocco: The Dhra'a, Canna, Codo, Cubit or Ell Tannin = 0.570723 m. 5. Tripoli: The Dhra'a (Pik, Ell) = 0.671 m, 6. Tunis: The Dhra'a a arabrv (Ell) = 0.4883 m. AMERICA — THE GREATER ANTILLES. 1. Cuba: The Pie (foot) = 12 Pulga- das @ 12 Linias @ 12 Puntos = 0.282566 m. 2. Hayti or St. Domingo: The Pied = 12 Panies @ 12 Lignesa @ 12 Points = 0.3248394 m. 3. Jamaica (British): Same as Eng- land. 4. Porto Rico (Spanish): Same as Cuba; also the metric measure. THE LESSER ANTILLES. 1. British Possessions : Anguilla, Antigua, Barbadoes, Barbida, Dom- inica, Grenada, Montserrat, Nevis, St. Cristoph, St. Lucie, St. Vincent, Tabago, Tortola, Trinidad and Vir- gin, measures same as the old and new English. 2. French Possessions: Guadeloupe, Marie Galante, Martinique, Les Saintes and St. Martin, in general, same as in France. 3. Netherland Possessions: Aruba, Curacao, Eustace, Saba and St. Martin, measures are the English, and partly the old Amsterdam measures. 4. Danish Possessions: St. Croix, St. Jean and St. Thomas, measures are the Danish and partly the old Ams- terdam. 5. Argentine Republic: Buenes Ay- res, Catamarca, Cordova, Corri- entes, Entre Rios, Sujug, Mendoza, Rioja, Salta San Juan, Santa Fe, 3. Äaolanb: £er alte 2(mftei*bamer Dtyeiul. $u&= 12 3ott @ 12 fitnicu = 0,313946 m. 4. 9floroffo : £>te Dhra'a, (Saiina, (Sobo, duhit ober Glle o. £auin= 0,570723 m. 5. Tripoli : £)er £>t)ra'a (^if, @Uc) = 0,671 m. 6. XuuiS : £)er ©Ijra'a, a arabry ((Site) = 0,4883 m. 21 m e r t F a — gro§ß Antillen. 1. duba: ©er $ie (ftufj) = 12 $utga= ba% ju 12 Siuia§ $u 12 juntos = 0,282566 m. 2. «öagti ober ©t. Domingo : £)er ^ieb = 12 ^anieS @ 12 Signe§ @ 12 joints = 0,3248394 m. 3. 3 am( *ifa OBritttfd)): toie (Snglaub 4. Querto 3^ifo (©panifä)): rote auf @uba; audj ba§ metrifdje Waft. Kleine Antillen. 1. 33rittifdt)e SBefifcuiigeu : anguilla, Siuttgua, 23arbaböe3, 23arbiba, §Dotm= utt'a, ©renaba, 2Jcontferrat, ^eoig, ©t. (Sljrtftopf), ©t. Suae, ©t. ^titjeitg, £abago, tortola, £riuibab u. ^trgtit. 2ftaj3e roie bie alten unb neuen eugli= fdjen. 2. granjöf. SSefifcuugen : ©uabetoupe, ataxia ©alanta, £e3 ©atnte§ unb ©t. Martin, im Slllgemetnen rote hierauf; reidj. 3. 9fcieberlänbi[ä)e 33e(t£uitgen: Struba, (Suraccao, Chtftace, ©aba. üftafte [tub bie engiifdjen, aud) jum ^Ijetf bie alten Slmfterbamer. 4. £äut|"d)e 23ejt$ungen : ©t. (Srotr, ©t. 3 eau un0 ©*• Bornas, yjlafyt ftub bie bänifdjen, jum £r)etl audt) bie alten 2lmfterbamer. 5. 2lrgeutiui|d)e 9£epubltf: 99ueno§ 2lore§, (Satantara, (jorbooo, (Sorrten- te8, ©utre 9ftio§, 3»S U 9/ 2Renbo$a, D^ioga, ©alta, ©an ^uau, ©anta $ee, ©anttago bei (5ft era, Xucamon, 1 $ie (gufj) @ 12 $ulgaba§ gu 12 SincaS 31t 12 juntos = 0,28866 m. — 136 — Santiago del Estero, Tucuman = 1 Pie (foot) == 12 Pulgadas @ 12 Li- neas @ 12 Puntos = 0.28866 m. 6. Brazil: Same as France. 7. Canada: Same as England and France. CENTRAL AMERICA. 1. Costa Rica, Guatemala, Hondu- ras (republic), Honduras (British), Mosquito, Nicaragua, San Salva- tor. Measures in Costa Rica are mostly Castilian. 2. Chili: Same as France. 3. Guiana, British: Berbica, Dem- erara, Essequebo, measures are partly the old Amsterdam and part- ly English. 4. French Possession: Cayenne, same as France. 5. Dutch Possession: Surinam, same as Holland. 6. British — Hudson-Bay-Company : Same as England. 7. Danish— Iceland: The Allen (Ell) = 0.570643 m. 8. Mexico: The Vara or Ell = 0.8477 m 9. New Granada : The Vara = 0.8 m. 10. Peru: Pie (foot) = 12 Pulgados @ 12 Lineas = 0.2825 m.: The Codo =1* Pie's = 0.42375 m. 11. Uruguay: Castilian measures. 12. Venezuela: Measures Castilian and partly British. ASIA — ARABIA. 1. Hadramand, Hadschar, Yemen, Muscat, Nejed, Oman, Hedjaz, Si- nai, Betelfaki (Yemen): The Covid (Cubit, Ell) = 0.4571937 m; the great Covid = 0.68579055 m. ; the Goess = 0.63499125 m. 2. Djedda (Hedjaz): The Covid (Ell) = 0.48259345 m. 3. Lohmia (Yemen): Same as Bet- elfaki. 6. 33rafüten: wie $ranfreidj. 7. (Sauaba: rote (Sngtanb unb $ranf= reidj. £entra!=21mertfa. 1. (Softa=3ftifa, ©uatemala, .!ponbura§ (9?epuMtf), £onbura§ Oörittifdj), 9tto§; qutta, Nicaragua, <&a\\ ©attmtor. Wla% e [tub in (5ofla=9ftico metftenä bie cafttltfdjen. 2. (Srjile: 2öie granfretd). 3. ©niana OBritttfdj), 23eroica, ©enters ara, ©ffeqnebo. ^ftafje ftnb trjett§ bie alten 2lmfterbamer, nnb trails bie eng= tifdjen. 4. ^ranjöfifc^e ©eftfeungen : (Sagenue. 2Gie granfreid). 5. ^tebetlänbifc|e 23eft£ttng : ©urtnam. me ^ottanb. 6. ©rtttifdje ©efifcung: £ubfou -- ©at> Gompang. 2öie (Sngtanb. 1. SDänifd^c SBefifcung: 3§lanb. 3Me 2TOen (©tie) = 0.570643 üfterer. 8. äfterico : S5te «ara ober (Me == 0,8477 Steter. 9. 9fau=@ranaba: . S)te 23ara = 0,8 2fteter. 10. «pern : Pie (ftufc) == 12 '$utgaba§ ju 12 Stnea§ = 0,2845 Sfteter. ©er Gobo = 1£ q3ie§ = 0,42375 Steter. 11. Uruguay: Wa^e ftnb bie cafttli- fdjen. 12. SBenejuela : 9#af3e ftnb bie cajlili* jdjen, sum £r)etl attdj btebrittifdjen. 2J f t e n — Arabien. 1. £abramanb, #abf<$ar, Renten, 9tta§= fat, Webtet, 3(men, .£>ebga§, ©inai, SBettelfane (fernen): ©er <5ot)tt (ib = 0,68579055 Stteter. ©er ©öj3 = 0,63499125 SReter. 2. ©iebba(£ebia§): ©er (Somb (©tie) 0,48259345 ütteter. 3. Sofntia (Semen). Sie in 93ettelfaft. 137 — 4. Muskat (Imanat): The Covid (Ell) = 0.964 m. 5. Mocha (Yemen): Same as Betel- faki. ASIATIC RUSSIA. Legal as in European Russia. ASIATIC TURKEY. I. Armenia. IL Asia Minor. —1, Smyrna; 2, Trapezunt; 3, Tschesme: measures same as Turkey. III. Mesopotamia. — 1, Bagdad: lPik(Ell) = 0.80263m.;2, Bassora: the Fik of Had- dad = 0.8686 m. IV. Syria. — Acre, Aleppo, Beirut, Damascus, Cyprus, Sidon, Tripoli : in general, same as in Turkey. 6. China: the Tschich of merchants @ lOTsuna @ 10 Fan = 0.374648 m. 7. Japan: the Kane sasi (foot) = 10 Sun @ 10 Bun @ 10 Rin = 0.303 m. 8. Batavia( India): the Amsterdam- Rhineland Voet = 12 Duimen @ 12 Streepen = 0.313946 m. 9. Bombay (India) and Calcutta (Bengal): the Cubit (Haut) = 0.45719 m. 10. Persia: 1 Foot = 24 Fingers = 0.50798 m. 11. Turkestan. — 1, Bokhara; 2, Khi- va: the Haze (Ell) = 1.06678 m. AUSTRALIA. New Zealand, etc. , Sandwich Isles : measures same as English ; also, as the Lesser Antilles. 4. üfta§fat (Snianat) : SDer (Sonib ((Stte) = 0,964 Sfteter. 5. hoffet (fernen): Sie 93ettelfafi. 21fiattfd?es Hußlanb. (Sefefcttd) roieimeuropäifd)en 9hif?lanb 2Xfiatifd?c Orfci. I. Armenien. IL Äletnafteu(^atoüen):l. ©mprnct 2. £rapesimt; 3. £fdje§me; 9ttafce rote bie Xürfet. III. ^efopotamieu— l.SBagbab: 1 *ßif (@Üc) = 0,80263 Steter. 2. 93affora: ©er ^3icf tron £abbab = 0,8686 ÜJietcr. IV. ©grien: Slcre, 2ltteppo, Beirut, SDamaSfuS, Wtcofia (3nfel <5t>* pern), ©aiba (©ibon), Tripoli. ^rnMgern einen rote in ber^ür; fei. 6. <5&ina : ©er £f $id& ber ^aufteilte @ 10 £fnn @ 10 gern = 0.374648 Steter. 7. Sapan : ©a§ tae fafi (gufc) == 10 eaiftfier< (S§ tft getDOIjulid), bte ©cfyroere eine§ gerotffett $törper§ al§ (Sinljeit angttne^ men unb nad^er tn^o^IenauSjubntdfen, — 139 The weight which denotes the press- ure of a body upon its basis, and which, therefore, decreases and in- creases according to the quantity of mass, is called the absolute weight ; the other, however, which tells us what relation it has to the gravity of a like quantity of water, is called the specific weight. Table of comparison of specific weight, water by melting ice and temperature of 4 degrees C. taken at 1000. roie oft fo fdjroer eine anbere Seltene »on gleichem Volumen fei. £)a§ @enud)t, roeldEjeg ben £)mcf 6ejeic^= net, beneiu.f?örpetauffeineUuterlageau§= üht, alfo mit ben Quantitäten ber $ftaffe ao= unb guuimmt, tjetftt bag abfolute — ba§ aubere hingegen, ba§ un§ fagt, in meinem SSer|ältniffe jene§ &ur ©cjtoeve einer gleidj grofen Sftenge 2Bafffer fteljt, ba§ fpejiftfdje @eraitf)t.— 23ergleid)ung§= Xabeöe be§ fpejtftfdjen @erctdjte§, ba§ 2ßaffev beim fdjmeljeuben (Sife unb £em= pevatur oou 4° C. gu 1000 angenommen. Oil of citron. Kalium Turpentine oil Ice Linseed oil. . . . Bodies. Density.— £)td)te. Äötper. Cork. 0.240 ftorf Poplar-wood, dry 0.383 ^appelfyolg, trocf en Lindenwood 0.439 £inbenfjol& Linden wood, fresh 0.817 £mbeul)oIg, frtfdje§ Silver-leaved fir-tree 0.555 ©beltanne Beech-wood 0.590 Sucfyenljolj Beech-wood, fresh 0.982 SSuäjenfyofj, frtfd^eä Nut-wood 0.677 yiu%baum$o{$ Ether 0.713 2letfjer Spirit of wine, free from water. . 0.793 2Beingeift, raaffevfvet 0.852 Gitronenb'l 0.865 Galium 0.872 Terpentinöl 0.916 @iS 0.953 Seinöl Poppvoil 0.929 Wtofynol Olive oil 0.915 Oltoenöt Natrum 0.972 ^atrum Rhenish wine 0.999 9%$etmoein Water 1.000 Staffer Sea water 1.026 9Jteerroaffer Milk 1.030 2JWd& Oak-wood, dry 1.170 @id)enIj)ot$, trocfen Phosphorus 1.826 ^oSpIjor Sulphuric acid 1.848 ©djtoefelfäure Ivory 1.917 dlfenoeiu Sulphur 2.033 ©djraefet Sandstone 2.151 — 2.350 <5aubfteinoon Mirror-glass 2.370 ©piegetglaS Basalt 2.176—3.970 SSafalt oon Bottle glass ■ 2.660 ftlafd&englaS Aluminum, forged 2.670 aluminum, gefcfjmtebet Marble 2.717—2.744 Marmor oon Granite 2.576—2.800 @ranitoon Diamond 3.520 £)iamant Ponderous spar 4.426 ©djtoerfpatf) — 140 Bodiee. Density.— £>id)te. Äörpcr. (fronte 2tntimon Sinl 3"!" .(Stfen, gefcrjmtebet Chrome 5.900 Antimony 6.712 Zinc 7.037 Tin 7.291 Iron, forged 7.788 Steel. 7.816 Copper, forged 8.878 Tupfer, gefdjmtebet Bismuth 9.822 SötgmutJ) Silver 10.474 ©Über Lead 11.352 <ßlei Mercury 13.598 Duedfilber Iridium 18.600 ^ribiitm Gold 19.325 .@olb Platina 22.100 ^lattn Application : Since, for instance' each body under otherwise equal cir" cumstances has one and the same density, this is one of the most im- portant distinctions of various bodies. Were anyone to sell me pure silver, a cubic centimeter must weigh = 10.474 grams. If its density is less, it is supposable that copper, and if it is greater, that lead has been added to the silver. If I have rafters made of oak-wood which weigh 1170 kilograms, rafters of fir- wood, which have exactly the same volume, will weigh only 555 kilograms. A flask, which, filled with water, contains 10 kilograms, must, if filled with sulphuric acid, take up 18 kilo- grams, because it is nearly twice as dense as water, etc. Tenacity : The force with which some bodies resist an attempt to pull their particles asunder is called tenacity. By absolute tenacity we understand the force with which a body resists the tearing when it is lengthwise strained. As easily seen , the tenacity is proportioned to the area of the cross-section of a body to be pulled asunder. For many practical purposes it has been important to ascertain the force, 21 n ro e n b it n g : £>a 3. 33. ein jeher Körper unter übrigens gleiten Umftän= beu ftet§ eine unb biefelbe$)td)te befifct, fo tffc btefeä eine ber rc*td)ttgfteit Unterfd)et= buugen oerfcr)tebener Körper. Söürbe mir 3 e w a "b reinjies» ©über oerfaufen, fo muft ein Jhtbücentimeter = 10.474 ©ramm rotegen. 3>ft f e " ie ©tdjte geringer, fo famt man oorauSfe^en, baft Tupfer, ift fie gröft er, baft 33tet bem ©il= ber jugefefet roorben ift. Saffe id) ein @e= bält oon (Stdjenfjolj anfertigen, roeld)e§ 1170 ÄUogramm rotegt, fo wirb ein @e= bäl! oon Sannenfjolj, ba§ genau fooiel ÄuBtfutljalt l>at aB jeite§, nur 555 $\\o- gramm toiegen. ©ine ^ a f^ e / ^ xt m ^ Staffer angefüllt, 10 Kilogramm bcffel* ben faftt, mufe, mit ©d)toefelfäure gefüllt, 18 Kilogramm baoon aufnehmen, toetl biefe beinahe uod) einmal fo btdjt aB Staffer ift u. f. to. $ e ft i g f e t 1 : 5Die Äraft, mit toeldjer ein Körper ber Trennung fetner £ljeild)en roiberfteljt, nennt man feine geftigfett. Unter ab] oluter ^-eftigfett oerftefytman bie föraft, mit melier ein Körper beut fyx- reiften toiberftebt, menu er ber Sänge nad) angefpannt toirb. 2ßie leidjt eiuutfe^en. roädjft biefelbe mit bem Querfdjnitte be§ ju jerreiftenben Äörper§. $ür manche pratttfd)e 3toede roare§ toidjttg, btetoft ju ermitteln unb man t)at gefunben, baft ein @eioi$t oon 60 Kilogramm erfovbet= 141 and it has been found that it requires a weight of 60 kilograms to tear an iron wire with a diameter of one milli- meter. With an equal diameter, it requires kilograms to tear the following : Rod-iron. 45; steel, 30 to 40; cast iron, 14; brass wire, 30 to 60; copper wire, 21; glass rods or tubes, 2.5; spun lead, 1.75; oak-wood, 18; white beech, 14. silver-fir, 9; hemp rope, 6. In cases where these accounts are to be practically used, for the sake of safety, only one-third of the above ca- pacity of bearing is taken. In the most commonly used ther- mometers, the distance between the freezing and the boiling-point is di- vided into 80 equal parts. This divi- sion was at first made by Reaumur, and after him the instrument is yet to-day called. In France and in scien- tific works, the thermometer of 100 degrees or Centigrade of Celsius is used, on which the boiling-point is denoted by 100. In England, a differ- ent division was accepted from Fahr- enheit, and the following table will show most clearly a comparison of the various divisions. Via) ift, um einen @ifenbrar)t oon einem yjliUimeUx £)urd)meffer ju jerreifcen. 23et gteid) ftarfem ©urdjmeffer ftnb an Kilogramm erforberlid) jur gerreifnmg ber nadifolgeitben Äörper: ©tabeifen, 45; <5tQ%l, 30 bi§ 40; @a£etfen, 14; 2ftefftngbra|t, 30 big 60; £upferbraf}t,21; @fa§ftäbe obereren, 2,5; Sleibraljt, 1,75; @id)enljol$, 18; 2Seipudjeit, 14; Sßeifetaune, 9; >£>anf= fetle,<6. 3u Säßen too au3 biefen Angaben eine orafttfdje Sdtrcenbung gemacht roerben foil, barf, ber ©icfyerfyett raegen, bodj nnr ber britte Xfjetl ber angegebenen Xraa,= fraft angenommen roerben. 23et ben meiflen gercöljulid) gebraudp ten £r)ermometern ift bie Entfernung jtni= fdjeu @efrier= nnb «Siebepunft in 80 gleite Steife geteilt, 2)iefe (Sintrjeilung rottrbe juerft oon Reaumur gemalt, nnb nad) tljm roirb ba§ 3 n l"h"ument nod) r)eute be= naunt. 3 n Sranfreicr) nub in roiffen= fd^aftlidr)eu Werfen bebient man fid; meift be§ fyunbertt^eiltgen ober (Senteftmal- Xr;ermometer§ con @etftu§, an melden ber ©tebepunft mit 100 besetztet ift. 3" (Sngtanb ift oon Jafjrenrjeit roieber eine ganj aubere (Stnfrjeiutng angenommen raorben, unb bie folgenbe £afel roirb am beutltdjften eine 23ergtetd)ung biefer oer= f^iebenen (5tntr)eUuugeu geben: The degrees of heat are expressed by -\-, and those of cold by — . Zero O is the freezing point of water, by Fahrenheit + 32°. As we see, 5 degrees of the thermo- meter of 100 parts are equal to 4 degrees of the one of 80 parts, and 9 degrees Fahrenheit. Fahren- Celsius. Reaumur. heit. — 20 — 16 — 4 — 10 — 8 + 14 32 + io + 8 50 20 16 68 30 24 86 40 32 104 50 40 122 60 48 140 70 56 158 80 64 176 90 72 194 100 80 212 ©te SMrmegrabe raerbeu mit -f- unb bie föältegrabe mit — bejeicrjnet. vtuU= pimft O ber ©efrterpunft be§ 2öaffer§, bet gar)ren= f,eit + 32°. me man fietjt, ftnb je 5 ©rab be§ 100=trjeiltgen Xr)ermonte= ter§ gteid) 4 @rab be§ 80; ^eiligen unb 9 @rab gaty* renljeit. — 142 As remarkable we will give some temperatures. 2H§ bemerfen§Koett^ treuen roir einige Temperaturen mit. Freezing point of spirit of wine Freezing point of mercury Freezing point of water . . Greatest density of water Warmth of room Blood-heat of persons .... Boiling point of ether .... Melting point of wax .... Ignition of phosphorus . . Boiling p't of sp. of wine. Boiling point of water. . . Melting point of sulphur Melting point of lead Boiling point of mercury Melting point of silver . . . Melting point of cast iron Melting point of gold. . . . Melting point of rod iron Reau- Fahren- Celsius. mur. heit. — 72° — 90° —130° — 32 — 40 - 40 + 32 + 3i + 4 39* 16 20 68 29 37 97i 28 35 95 54 68 153* 60 75 153* 62 78 171* 80 100 212 87 109 287f 267 334 632f 288 360 680 800 1000 2120 980 1200 2237 1000 1250 2282 1280 1600 2912 ©efrierpunft beg SBeingeifxeS ©efrterpunft be§ QuecffilberS ©efrierpunft be§ 23taffer§. . . ©rö'jjte £)id)te be§ Staffers. . gimmertoärme Körper; ober SBlutioärme be§ SJcenfdjen ©tebepunft be§ 2letljer§ ©djmeljpunÜ be§ 2öad)fe§. . (Sntjünbung be§ $j3ljo§p£or§. ©tebepunft be§ 2öetngeifte§. ©iebepuuft be§ Staff er§ ©djmelgpunft be§ ©djroefeB ©djmeljpunft be§ 23lete§ ©tebepunft be§ QuecfftlberS. ©c^metjpunft be§©ilber§.. ©djmeljpunft be§ ©ufjeifenS ©c^meljpunft be§ @olbe§.. ©ajmel^punft beg ©tabetfenS The force with which bodies are expanded by heat is exceedingly great. The strongest vessels often can. not resist it, if, being filled with liquid or air, closed tightly and then heated. Of solid bodies it is often, especially in putting together machines, of impor- tance to know how much they will expand by certain differences of tem- perature, wherefore determinations of the kind have been made with the greatest exactness. It has been shown that for a rising of the temperature from degree to 100 degrees C. — 212 degrees Fahr., the following bodies expand length- wise as much as the fraction denotes: platina, 1/1167; glass, 1/1147; steel £)te ©eroalt, mit roefdjer bie Körper buret) bie 2ßärme ausgebest werben, tft aufjerorbentlid& grojj. 3Me (tärfften @e= fäjje oermögen oft ntdjt berfelben 31t Tüiberftej)en,roenn fie, mit glüffigfeit ober Stift gefüllt, feft oerfcf)loffen unb bann er= Ijifct toerben. 33 et ben feften Körpern tft e§ tu oieter SBejieljung, namentlich bei ber 3ufamtnenfefcung t)0n 9JtafcI)inen, 0011 SBtdjtigjfeit Ju raiffen, rate ftarf fie )\ä) bei gemiffen Uuterfdjiebeu ber Xem= peratur an§bel)uen, roeSIjalb 23eftimmun= gen ber 2trt mit ber größten ©enauigf'eit angeftellt roorben fiub. OB l)at ftd) er= geben, baft für eine (Srpfjuug ber Ztm- peratur oon 0° big 100° C. ='212° $alp reuljeit bie folgenben Körper um ben bei= gefegten 93vud)tl)eil iljrer Sänge naü) ftc§ ausbeuten: Platin um 1/1167, ©la§ 1/1147, ©tal)I (geprtet) um 1/807, (5-ifeu 1/819, Tupfer 1/584, 3»effing 143 (hardened), 1/807; iron, 1/819; cop- per, 1/584; brass, 1/531; lead, 1/351; zinc, 1/340; consequently an iron rod with a length of 819 lines by degree has a length of 820 lines by 100 degrees C. = 212 degrees Fahr. If the above figures are multiplied by 2, we have the increase of the area, and if they are multiplied by 3, the product gives the increase of the cube for the same degree of heating. 1/531, Viet 1/351, 3tnf 1/340. gotg= lid) f)at $. 23. ein (Stfenftab, ber bet @rab 819 Stuten lang mar, bet 100° C. = 212 galjrenfyeit bte Sänge oon 820 Stuten. SEBemt bte Dorfteljeuben Safyltn mit 2 multtpltcht roerben, fo erhält man bte Vergrößerung be§ $Iädjen= tu!jalte§, unb raeun fte mit 3 multtpltctrt toerbeu, fo gibt ba§ ^robuft bie Ver- größerung ibre§ ftubifinljalteS für ben= felben @rab ber (Srroävmung an.