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RRM tts HVA ian ey Pesce tyinn whi We. . yee asy p { woah Ww vy tyt sas bese 4 } At y pen thhs eae? agen Ae Bee ‘Osay med sie! ty re Mia anitenes a) nu ap eer 0 Ds na) * HY () 41 | ee Pet (" Fees Berit y baal tt id | ‘ BY , Md : ry ah (| ‘ iy * ‘ ae Basse tam an ; lig Hibs cry i) Nes Ne i ie ( ope i " Rn Hat Ue cua si i oe 5 ie ' i heh | seal a ete tks ¥ PN, Hi | ; i Uses a wt beh 1 + Chih Ppapse ute A ny 4 ri K ry dd : Aaah } A Cs yaet boat 91) # wile ebe Lobe bebheot WD aya } 4 i an i ia WW ashe ! ae wh wort ” i ‘ in itt} i tt piety! ea at f i i ‘ i Mh BM ey “y f 7 y tbe aN) Oo enn SERACR TT ant) i bi Me) Pe ; ii ah reread i Dd aha , Hal Aw Bh al We CU pSiaet tt aN Seat eau ir ; ae Pa 5 Haiti sisectemtnce ape unite fant Sects pi } LaLa i a he ary at F it He ies ihe iy a Ot gi Mt a ‘vt by fhe ie ii Lena AROSE ACES MEL Al ta tt se ney Chart bet DORR 2 is oo} ay fi ‘ Pherae be HS , ) ‘ ti ae Rae ie i} Uh I bes! ee eet bi us SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOR, KAXY. 292000000% ‘© PVERY MAN IS A VALUABLE MEMBER OF SOCIETY WHO BY HIS OBSERVATIONS, RESEARCHES AND EXPERIMENTS PROCURES KNOWLEDGE FOR MEN.”’—SMITHSON, WASHINGTON CER Y: PUBLISHED BY THE SMITHSONIAN INSTITUTION, 1897. wy da aM ant - . Hae. a ae ‘ay? i a , aaa 1| ADVERTISEMENT. The present series, entitled “Smithsonian Miscellaneous Col- lections,” is intended to embrace all the publications issued di- rectly by the Smithsonian Institution in octavo form; those in quarto constituting the “ Smithsonian Contributions to Knowl- edge.” The quarto series includes memoirs, embracing the records of extended original investigations and researches, re- sulting in what are believed to be new truths, and constituting positive additions to the sum of human knowledge. The octavo series is designed to contain reports on the present state of our knowledge of particular branches of science; instructions for collecting and digesting facts and materials for research; lists and synopses of species of the organic and inorganic world; mu- seum catalogues; reports of explorations; aids to bibliographical investigations, etc., generally prepared at the express request of the Institution, and at its expense. In the Smithsonian Contributions to Knowledge, as well as in the present series, each article is separately paged and indexed, and the actual date of its publication is that given on its special title-page, and not that of the volume in which it is placed. In many cases works have been published and largely distributed, years before their combination into volumes. Ss. P. LANGLEY, Secretary S. I. (iii) ; nd nae i 2) i 1 y ' Tas ; ny a Ly i wf ' ea y , ie Coil a. mo Peele / 7 7 , rs wv i Ks v4 7S ite Ta hie uae ; « ine - tte ii : Hae F Th on : away hae a avid Cera a ante ae a eer iyi Tay pooh I in Malin Inet) Cea : zai? Cig 7 ; : Te (her ra) ice ub 7 ire ue mM ar ae oy ie aan . D re ye ; 5 eh Tr hon a e bi 7 ay cL eon [ ve a nae a Me kh if . MB tie't ae ao 7 a 7 i I My hi o 7 . . 4 hah Ee) ay & a ie 7 Bi xt ioe! A o 7 x fs it ‘ib, . md Ke ie noe ee ye hae | pee 1 ies a ie us See a Se Va 7 See prong eet oN 5 oe emma ca ev A hae f ; =p fi Si aan J . e e et, - mit " 7 ; i, ; one 7 a in a ante Wo eee oe sty, re Ma F aay — 7 eh ah i ee Tag ae Rae Ou 7. ie Wins . a Oe: ea oe a 7 oe . i. 7 7 ‘ ; 4) iP him “i " way _ z - 5 | Af 1" art ea bain . F oes ne i ; ‘ ' Be Ki Acie move an, Sh at eirgee uae , bs it Rpaeas ? ~ fo we 7 p ) Pv anfh he ros was ae - ; 7 : 1 ) ive ie > i. : » vy, 4 Oe Pua al 4 if Wer — i “4 7 7 Wy : at eee) am : t ra iy / a { ty a vy : : wy . >» > oe yt 7 7 me 7 Wile a Wy i aaa Ty a i Bey i see, oe. i, oj fi. ; i te Shere - 7 BA | i if Tad ray a Pr . wi yey ork i, ae) rae / i a =e e ' ; : ay a 7 Piles i eee | ‘ i its ; oF 1 ae Pre = I ai Ps, Sih ery en 7 7 ns ; a) ais 7 ar saa) a) | a 1 ; 7 i - (oer - oa) v A aft ae) aah ai 7 i DW Oe su OM i Tal tee J) D ; Te im : as SA 4 ri eh 4 7 Y wy an in ie ui Fj T's ~ : , a - } A lie #0) Why ine ae BLE fos u mere sy at Dee ana hie 7 V - ity " : me - me i my ae 7 gb / r a oat 7 ae mag re ay a ay cy. Ly ve i Se ee a ye. a } 7 i ri ne ; mi 7 ‘ ; aan ay wen a yh it i‘ 7) ey (aan « AY a ri i / / a), ’ mite wy i my : a ta a ee " 7 ae - x oo a Noe eal iF . rot ri Ter) ee ii) ; he pt ; ris aa AY) Cr wir a . a ei i re | ae = i's i te oa = 17 iy ms as a Pi, bs at ans ee he yell on ae ae ak a) OA) im ee ae i Z ; Me aap = : a ° r i Gia ' yp Pons ren Gal g nied 7 1 i UR aes ' ee Bae ny Ue. teh eae iy rar - neor 5 in iN ; : (bes si ee i) ie ns mona) Ls nae REL aN Petal . i, " ae 7" eet i nue ny a aA eae cn i) i Sy nlp & oe a ial rite es iv ry7at to 5 peel ; an ai . = 1 o¢ ty Poe rk \ Ms Th he hen 4 oe yi es ee OF CMs ocuard Manda tiara ME A a a a OY) Pt tee os oi Ras ae ae Be ieee tie 4 ae . nia sa ive 2 i‘ Diet Pi be = ; unvaall } Oey if eet ial ci ai ae OF es TABLE OF CONTENTS. ArvicLE I. (844.) SmrrasontAN METEOROLOGICAL ‘TABLES. 1893. Pp. Lrx, 262. ArticLte II. (854.) SmrrHsonrIAN GEOGRAPHICAL TABLES. PRE- PARED BY R.S. Woopwarp. NoveMBER, 1894. Pp. ov, 182; Articne IIT. (1038.) Smirusonran PuystcaAL TABLES. PRE- PARED BY THOMAS GRAY. OcrToBER, 1896. Pp. sexxiy, 30L. (v) CORRIGENDA. € Page lii, line 14, for January 10 vead January 1.0. Page 133, Table 39, 7th column, for 6.230 read 6.330. Pages 136, 137, Table 41, the top argument should be printed without the de- gree (°) mark. Pages 222, 223, for TABLE 86 read TABLE 83. | 6.0 Page 232, in argument of Table 92, for | 5.0 bee he Be | 4.0 | | 6.0 | Page 249, Ter Bagnéres-de- PEIEEOUTS read Bagnéres-de-Bigorre. Bordeaux Or 21 E. ‘« Bordeaux o° 31’ W. [ieyon 2° 20h. ‘¢ Lyon 4° 47° E ‘© Marseille enw “* Marseille Ge Pe Dy COMPic:du-Viidi 25812) We ‘© Pic-du-Midi o° 8’ E. ‘“* Toulouse o° 54’ W. _ ‘© Toulouse 1° 26’ E. Page 257, last line, for Thorshaven, Férvé Island 62° 22’ N, read Thorshavn, Farée Islands 62° 2’ N. fee ge195 Sou 2, 61 e peak. 2%6U7 Tae \) == ae — - — ea wan i ™ we fa ea ar ~ ae : i ~ a ay ' —_ or a 4 7 ri 6 : q : ; ’ : ‘or S . 7 rr Lo td ; i ny : ed 7 ie a ' - 7 7 7) lle ' c af : —_ iy © f ’ - = : a i ‘ - 7 p : a an 7 ae x : ; fell, ee <7 \ aes ne 7h) : ; 7 7) : - ‘ : +O-0 nd me ¥ V) 7 - oy i oy ae _ . La Cy . > a. a) ; a ; a 7 Py’ _ Cpa a woe y hn erly a : Cay Fy oni rome > ; oo 7 — tl bla fod 7 ae = i. a we Sn) . a fe ' ~~ ass a 7h a ary a : a ee iat r a) if : - t 1/sies wi i 7 Oa 7 - > ; Be ae 7 ae | ey ait) as ae a i in ys 26s ba | gt 9 vee ag a - is VP tie at : neal! 1% 1 eh i aia ty ec va . a oy a hie ae an lad ia iby oi i, i) F ; ne i 7 SAW ii Det 7. < iW aah Tale » sf i wif a, x mw 4) a 4 7 =" PO a) (Pier ea an ae. ; . edt. cele ee _ Ao eh Piebta! Vi a ae oC 7 che ie meee ii) See oP a a t a sp ce = Cvaer / ees a tt, one “a os - iar 2. = A : ; \ aah ssi i ie eee: 2 1, =| ue, aie AL rt. \ f yy as ay ij 44 om 5 De a’ an aa ee ii ¥ Y ae ats 7 cennh fide A et a i oy i eo pie fe * alae eA eet h) i foi) te ae Tek ah ee er wae by Vie NS ae a ie | a 1) elo) ii lel ah SDAA aia Weds ay Be METEOROLOGICAL TABLES PREPAC E In connection with the system of meteorological observations estab- lished by the Smithsonian Institution about 1850, a collection of meteorological tables was compiled by Dr. ARNox~p Guyot, at the request of Secretary Henry, and published in 1852 as a volume of the Miscellaneous Collections. Five years later, in 1857, a second edition was published after careful revision by the author, and the various series of tables were so enlarged as to extend the work from 212 to over 600 pages. In 1859 a third edition was published, with further amendments. Although designed primarily for the meteorological observers report- ing to the Smithsonian Institution, the tables obtained a much wider circulation, and were extensively used by meteorologists and physicists in Europe and in the United States. After twenty-five years of valuable service, the work was again revised by the author; and the fourth edition, containing over 700 pages, was published in 1884. Before finishing the last few tables, Dr. Guyot died, and the completion of the work was intrusted to his assistant, Prof. WM. Liprry, JR., who executed the dfities of final editor. In a few years the demand for the tables exhausted the edition, and thereupon it appeared desirable to recast entirely the work. After very careful consideration, I decided to publish the new tables in three parts: METEOROLOGICAL TABLES, GEOGRAPHICAL TABLES, and Puysicart TasiEs, each representative of the latest knowledge in its field, and independent of the others; but the three forming a homo- geneous series. Although thus historically related to Dr. Guyot’s Tables, the present work is so substantially changed with respect to material, arrange- ment, and presentation that it is not a fifth edition of the older tables, but essentially a new publication. V v1 PREFACE. In its preparation the advantage of conformity with the recently issued Jnternational Meteorological Tables has been kept steadily in view, and so far as consistent with other decisions, the constants and methods there employed have been followed. The most important difference in constants is the relation of the yard to the metre. The value provi- sionally adopted by the Bureau of Weights and Measures of the United States Coast and Geodetic Survey, I mettre — 39.3700 inches; has been used here in the conversion-tables of metric and English linear measures, and in the transformation of all formule involving such conversions. : A large number of tables have been newly computed; those taken from the /nternational Meteorological Tables and other official sources are credited in the introduction. To Prof. Wm. LiBBEy, JR., especial acknowledgments are due for a large amount of attention given to the present work. Prof. LIBBEY had already completed a revision, involving considerable recomputation, of the meteorological tables contained in the last edition of Guyot’s Tables, when it was determined to adopt new values for many of the constants, and to have the present volume set with new type. This involved a large amount of new computation, which was placed under the direction of Mr. GrorGre E. Curtis, who has also written the text, and has carefully prepared the whole manuscript and carried it through the press. To Mr. Curtis’s interest, and to his special experi- ence as a meteorologist, the present volume is therefore largely due. Prof. LinBEY has contributed Tables 38, 39, 55, 56, 61, 74, 77, 89, and go, and has also read the proof-sheets of the entire work. I desire to express my acknowledgments to Prof. CLEVELAND ABBE, for the manuscript of Tables 32, 81, 82, 83, 84, 85, 86; to Mr. H. A. HAZEN, for Tables 49, 50, 94, 95, 96, which have been taken from his Fland-book of Meteorological Tables; and also to the Superintendent of the United States Coast and Geodetic Survey, the Chief Signal Officer of the Army, and the Chief of the Weather Bureau, for much valuable counsel during the progress of the work. S. P. LANGLEY, Secretary. PApee OF CONTENTS. INTRODUCTION. PAGE Description and use of the Tables xi tov lix THERMOMETRICAL TABLES. TABLE PAGE Conversion of thermometric scales — ! Reaumur scale to Fahrenheit and Centigrade 2 2 Fahrenheit scale to Centigrade 3 3 Centigrade scale to Fahrenheit 7 4 Centigrade scale to Fahrenheit, near ne seule nett of water . eer 9 5 Differences F ateeatiere to geese Cbarierade 9 6 Differences Centigrade to differences Fahrenheit 9 7. Reduction of temperature to sea level—English measures 10 g Reduction of temperature to sea level— Metric measures Il 9 Correction for the temperature of the mercury in the thermometer stem. For Fahrenheit and Centigrade thermometers 12 BAROMETRICAL TABLES. Reduction of the barometer to standard temperature — 10 English measures 14 11 Metric measures ee ae 34 Reduction of the barometer to standard gravity at latitude 45°— 12 English measures 58 13 Metric measures Seen cm 59 Reduction of the barometer to sea level — English measures. 14 Values of 2000 60 15 Correction of 2000 # for aed 69 i6 B, — B=B(10"—1) 70 Reduction of the barometer to sea level — Metric measures. 17 Values of 2000 ee, 78 18 Correction of 2000 # for ieanide oe Ces go 19 a eT ONT), eg, i cei) Sw. gs 9g! viii TABLE 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 } 43 37 38 39 40 4| 42 TABLE OF CONTENTS. BAROMETRICAL TABLES.—Continued. Determination of heights by the barometer — English measures. Values of 60368 [1 + 0.0010195 x 36] log ier SIN octet Term for temperature : Correction for latitude and neem of mercury Correction for an average degree of humidity Correction for the variation of gravity with altitude Determination of heights by the barometer — Metric measures. Values of 18400 log Ee Term for temperature Correction for humidity : Correction for latitude and weight of mercury Correction for the variation of gravity with altitude Difference of height corresponding to a change of 0.1 inch in the barometer — English measures : Difference of height corresponding to a change of 1 millimetre in the barometer — Metric measures Determination of heights by the barometer. Formula of Babinet . Barometric pressures corresponding to the temperature of the boiling point of water — English measures Metric measures HYGROMETRICAL TABLES. Pressure of aqueous vapor (Broch) — English measures Metric measures Pressure of aqueous vapor at low temperatures (C.F. Marvin)— English and Metric measures cyte Weight of aqueous vapor in a cubic foot of saturated air— English measures Weight of aqueous vapor in a cubic metre of saturated air— Metric measures : elk . Reduction of psychrometric observations rir ae measures. Pressure of aqueous vapor ners Values of 0.000367 B(¢—4,) € ae = =) : 1571 Relative humidity —Temperature Fahrenheit ii 128 "| 142 PAGE I0O 104 106 108 109 IIo Liet Pr 114 rs 116 117 118 119 IIg y22 130 122 133 134 136 TABLE 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 7I\ TABLE OF CONTENTS. HYGROMETRICAL TABLES.—Continued. Reduction of psychrometric observations — Metric measures. Pressure of aqueous vapor , —4, Values of 0.000660 B (¢ — ¢,) (x = = ) Relative humidity —Temperature Centigrade . Reduction of snowfall measurements. Depth of water corresponding to the weight of snow (or rain) collected in an 8-inch gage . ‘ Rate of decrease of vapor pressure with aniende : WIND TABLES. Mean direction of the wind by Lambert’s formula— Multiples of cos 45°; form and example of computation . Values of the mean direction (a) or its complement (go — a) Synoptic conversion of velocities . Miles per hour into feet per second Feet per second into miles per hour Metres per second into miles per hour Miles per hour into metres per second Metres per second into kilometres per hour Kilometres per hour into metres per second . . . .. , Beaufort wind scale and its conversion into velocity . GEODETICAL TABLES. Relative acceleration of gravity at different latitudes Length of one degree of the meridian at different latitudes Length of one degree of the parallel at different latitudes . Duration of sunshine at different latitudes . Declination of the sun for the year 1894 Relative intensity of solar radiation at different fapiandes CONVERSION OF LINEAR MEASURES. Inches into millimetres Millimetres into inches Feet into metres Metres into feet Miles into kilometres . Kilometres into miles . ae Interconversion of nautical and statute ee : Continental measures of length with their metric and paoteh equivalents PAGE 142 143 144 146 148 149 154 155 155 156 157 158 159 160 162 165 166 177 178 180 187 200 202 204. 206 208 208 x TABLE OF CONTENTS. CONVERSION OF MEASURES OF TIME AND ANGLE. TABLE PAGE 72. Axe: into time: =. Pecsae "5. oe Wy Pe) ea, oe) eS 73 Timeintoarc . . ; ; ote tb | eee 74 Days into decimals ae a year ana nets wea Oe a oo ee ee 75 Hours, minutes and seconds into decimals of a day. . . . . 216 76 Decimals of a day into hours, minutes and seconds. . . . . 216 77. Minutes and seconds into decimals of an hour « «2. ayeed7 78° Mean time at apparentimoon) 92) (a2 ce fina. ce ea 79 ‘Sidereal time into mean solar time . . . . . 4 | . . . 298 so Mean solartime into siderealtime ........ .. 218 MISCELLANEOUS TABLES. 81 Density of air at different temperatures Fahrenheit . . . . 220 Density of air at different humidities and pressures— English measures. 82 Term for humidity: auxiliary to Table 83 292). eet 83 Values of i Be Chee enone 222 29.921 29.921 84 Density of air at different temperatures Centigrade. . . . . 224 Density of air at different humidities and pressures — Metric measures. 85 Term for humidity: auxiliary to Table 86 . . . . . 225 86 Values of ate SI re OOISE OSI82 226 760 760 87 Conversion of avoirdupois pounds and ounces into kilogrammes . 226 88 Conversion of kilogrammes into avoirdupois pounds and ounces 230 39. Conversion of grains intogrammes: (07 2) Se ee ee 90 Conversion «of srammes into grains un ee ee 91 Conversion of units of magnetic intensity. . . 4 O22 92 Quantity of water corresponding to given eats oe mince oiyes2 93 Dates of Dove’s pentades . . . a ks a eS eee 94 Division by 28 of numbers from 28 to 867 O72 fs) ms. ae Bailast Rese 95 Division by 29 of numbers from 29 to 898971. =~ 2 = =a 234 96 Division by 31 of numbers from 31 to 960969 . . . . . . 235 97 °-Natural sines and’ cosines“. ©2160, .) :) 0 eee 93 “Natural tangents and cotangents.. ©. <% |. (<0 :/) awe aS 99° Logarithms: of ‘numbers. 72.45) Se eee eee (00, LIST ‘OF METEOROLOGICAL, STATIONS 7. 5 70. st ee ee APPENDIX. Constants’ 12. 4... % Mel i ete Ae eS Synoptic conversion aE merch aa tet units.:.. “Sateen wee OO Dimensions of: physical. quantities 9 7 5 1 ee PNPERODUCT LON: DESCRIPTION AND USE OF THE TABLES. THERMOMETRICAL TABLES. COMPARISON OF THERMOMETRIC SCALES. Conversion of readings of the Reaumur thermometer to readings of the Fahrenheit and Centigrade thermometers. WABEE 1. The argument is given for every Reaumur degree from + 80° to — 40° Reaumur, and the corresponding readings Fahrenheit and Centigrade are given to hundredths of a degree, permitting the exact values to be expressed. A column of proportional parts gives the values corresponding to tenths of a Reaumur degree. By the help of the column of proportional parts, the table is also conveniently used for converting Fahrenheit to Centigrade and Reaumur, and Centigrade to Fahrenheit and Reaumur throughout the thermometric scale from the boiling point of water to — 60° F. or — 51° C. The formule expressing the relation between the different scales are given at the bottom of the table, where F° = Temperature Fahrenheit. C° = Temperature Centigrade. R° = Temperature Reaumur. Examples: To convert 18°3 Reaumur to Fahrenheit and Centigrade. From the table, 180 R.= 72°50 f= 22°50 C. From column Prop. Parts, 0.3 = 0.675 = 0.375 13 2. = 932 F.—" 22:90 CG. To convert 147°7 Fahrenheit to Centigrade and Reaumur. From the table, 146°75 F.= 63°75C. = 510k. From column Prop. Parts, 0.95 = 0.53 = 0.4 Tay ee) 04S (C.——= 25 1.4K. To convert 16°9 Centigrade to Fahrenheit and Reaumur. From the table, 16°25 C.= 61°25F. = 13:08. From column Prop. Parts, 0.65 = 7, = 0.5 1699 C.= 624 F. = 13°5R xi xii INTRODUCTION. TABLE 2. Conversion of readings of the Fahrenheit thermometer to readings Centigrade. The conversion of Fahrenheit temperatures to Centigrade temperatures is given for every tenth of a degree from + 130°9 /. to—7o°9 fF. ‘The side argument is the whole number of degrees Fahrenheit, and the top argument, tenths of a degree Fahrenheit ; interpolation to hundredths of a degree, when desired, is readily effected mentally. The tabular values are given to hundredths of a degree Centigrade. : The formula for conversion is Ge = 5: (F° Ales 225) 9 where F° is a given temperature Fahrenheit, and C° the corresponding temperature Centigrade. Example: To convert 79°7 Fahrenheit to Centigrade. The table gives directly 26°50 C. For conversions of temperatures above 131°, use Table 1. TABLE 3. Conversion of readings of the Centigrade thermometer to readings fahrenheit. The conversion of Centigrade temperatures to Fahrenheit temperatures is given for every tenth of a degree Centigrade from + 50°9 to — 50°%9 C. The tabular values are expressed in hundredths of a degree Fahrenheit. The formula for conversion is —_ 9 Ce | 32° 5 where C° is a given temperature Centigrade, and /° the corresponding temperature Fahrenheit. For conversions of temperatures above the upper limit of the table, use Tables 1 and 4. TABLE 4. Conversion of readings of the Centigrade thermometer near the boiling point to readings Fahrenheit. This is an extension of Table 3 from g0°%0 to 1o0°9 Centigrade. Example: To convert 95°74 Centigrade to Fahrenheit. From the table, 95-70 C. By interpolation, 0.04 204°26 F. 0.07 I 95-74 C. = 204°33 F. THERMOMETRICAL TABLES. xiii Conversion of differences Fahrenheit to differences Centigrade. TABLE 6. The table gives for every tenth of a degree from 0° to 20°9 /. the corresponding lengths of the Centigrade scale. Conversion of differences Centigrade to differences Fahrenhett. TABLE 6. The table gives for every tenth of a degree from 0° to 9°9 C. the corre- sponding lengths of the Fahrenheit scale. Example: To find the equivalent difference in Fahrenheit degrees for a difference of 4°72 Centigrade. From the table, 4:70 C. = 8°46 F. From the table by moving the decimal point for 0.2, 0.02 0.04 Ae Ca Sh Owe REDUCTION OF TEMPERATURE TO SEA LEVEL. English Measures. TABLE 7. Metric Measures. TABLE 8. These tables give for different altitudes and for different uniform rates of decrease of temperature with altitude, the amount in hundredths of a degree Fahrenheit and Centigrade, which must be added to observed tem- peratures in order to reduce them to sea level. The rate of decrease of temperature with altitude varies from one region to another, and in the same region varies according to the season and the meteorological conditions ; being in general greater in warm lati- tudes than in cold ones, greater in summer than in winter, and greater in cyclones than in anti-cyclones. For continental plateau regions, the reduction often becomes fictitious or illusory. The use of the tables there- fore requires experience and judgment in selecting the rate of decrease of temperature to be used. The tables are given in order to facilitate the reduction of temperature either upwards or downwards in special investigations, but the reduction is not ordinarily applied to meteorological observations. The tables, 7 and 8, are computed for rates of temperature change ranging from 1° Fahrenheit in 200 feet to 1° Fahrenheit in goo feet, and from 1° Centigrade in 100 metres to 1° Centigrade in 500 metres; and for altitudes up to 5,000 feet and 3,000 metres respectively. Example, Table 7: Observed temperature at an elevation of 2,500 feet, Bae Reduction to sea level for an assumed decrease in tem- perature of 1°/. for every 300 feet, + 873 Temperature reduced to sea level, 60°83 F. Xiv INTRODUCTION. Example, Table 8: Observed temperature at an elevation of 500 metres, T2e5 Ck Reduction to sea level for an assumed decrease in tempera- ture of 1° C. for every 200 metres, + 2°55 Temperature reduced to sea level, 150°C, CORRECTION FOR THE TEMPERATURE OF THE MERCURY IN THE THER- MOMETER STEM. TaBLeE 9. Fahrenheit thermometers ; Centigrade thermometers. When the temperature of the thermometer stem is materially differ- ent from that of the bulb, a correction needs to be applied to the observed reading in order to correct it for the difference in the length of the mer- cury column caused by this difference in its temperature. ‘This correction frequently becomes necessary in physical experiments where the bulb only is immersed in a bath whose temperature is to be determined, and in meteorological observations it may become appreciable in wet-bulb, dew point, and solar radiation thermometers, when the temperature of the bulb is considerably above or below the air temperature. If / be the average temperature of the mercury column, ¢ the observed reading of the thermometer, z the length of mercury in the stem in scale degrees, and a the apparent expansion of mercury in glass for 1°, the correction is given by the expression — an ( —?2) in which, for Centigrade temperatures, a = 0.000154 or 0.000155. The average temperature of the mercury column can not be directly observed and is difficult to determine, for it differs from the temperature of the glass stem by an amount depending on the conduction of heat between the bulb and the mercury column. Practically however it is possible to use the actually observed temperature of the glass stem as the value of “” by making a small compensating change in the value of a, and this appears to be the simplest method that has been proposed. Mr. T. E. Thorpe (Journal of the Chemical Society, vol. 37, 1880, p. 160) has determined by a series of experiments that the proper thermometric cor- rections will be obtained by this method if 0.000143 be used as a coefficient (for Centigrade temperatures) instead of the value of a given above, and this value has been adopted in the present tables. The correction formule are, then, T = ¢— 0.0000795 x (¢ — +f) Temperature Fahrenheit. T= ¢— 0.000143 2 (¢# —?¢) Temperature Centigrade. in which 7 = Corrected temperature. ¢ = Observed temperature. ?’ = Mean temperature of the glass stem. m= Length of mercury in the stem in scale degrees. BAROMETRICAL TABLES. xV When ?# is ) Cer adie 1 + m (f— 32°) in which B= Observed height of the barometer in English inches. ¢ = Temperature of attached thermometer in degrees Fahrenheit. m = 0.0001818 X 2 = O.O00IOI J = 0.0000184 X 2 = 0.0000102 The combined reduction of the mercury to the freezing point and of the scale to 62° Fahrenheit brings the point of no correction to approximately BAROMETRICAL TABLES. xvii 28°5 Fahrenheit, and this is therefore the standard temperature to which all readings are reduced. For temperatures above 28°5 Fahrenheit, the correction is subtractive, and for temperatures below 28°.5 Fahrenheit, the correction is additive, as indicated by the signs (+ ) and (—) inserted throughout the table. The table gives the corrections for every half degree Fahrenheit from o° to 100° The limits of pressure are 19 and 31.6 inches, the corrections being computed for every half inch from 19 to 24 inches, and for every two-tenths of an inch from 24 to 31.6 inches. Example: Observed height of barometer — eon te Attached thermometer, 54°5 F. Reduction for temperature =— 0.068 Barometric reading corrected for temperature ea TABLE 11. TABLE 11. Reduction of the barometer to standard temperature—Metric measures. For the metric barometer the formula for reducing observed readings to the standard temperature, 0° C., becomes ome) ine 1 + mt in which C and @ are expressed in millimetres and ¢ in Centigrade degrees. I —O,OCOLS 1G 4.) — ©, 0000184. In the tables, the limits adopted for the pressure are 440 and 795 mil- limetres, the intervals being 10 millimetres between 440 and 600 milli- metres, and 5 millimetres between 600 and 795 millimetres. The limits adopted for the temperature are o° + and + 35°8, the intervals being 0’5 and 1°0 from 440 to 560 millimetres, and o?2 from 560 to 795 millimetres. For temperatures above o° Centigrade the correction is xegative, and hence is to be subtracted from the observed readings. For temperatures below o° Centigrade the correction is fosztive, and from o° C. down to — 20° C. the numerical values thereof, for ordinary baro- metric work, do not materially differ from the values for the corresponding temperatures above o° C. Thus the correction for — 9° C. is mawmerically the same as for + 9° C. and is taken from the table. In physical work of extreme precision, the numerical values given for positive temperatures may be used for temperatures below 0° C. by applying to them the following corrections : XvViii INTRODUCTION. Corrections to be applied to the tabular values of Table 11 in order to use them when the temperature of the attached thermometer ts below 0° Centigrade. PRESSURE IN MILLIMETRES. Temper- ature. l 450 | 500 550 | 600 | 650 | 700 | 750 | | | | CG mm. | mm. mm. | mm. mm. | mm mm ee 0.00 | ©:007 9/5 10:00) 1020057) #aO!00 | 0.00 0.00 = © -00 | .0O .0O | -0O -0O | oo .0O | | | —I10 0.00 | 0.00 0.00 0.00 0.00 | +0.01 | +0.01 Il -0O | .0O .0O .0O +o0.01 | .O1 .O1 I2 ZOOF 5} .0O .0O0 + 0.01 .O1 | .OI LOL 13 .0o | oO | +0.01 -O1 .O1 -O1 -OI —14 .00 | +0.01 | .O1 yop. || O14 OI .O1 | | —I15 + 0.01 + 0.01 +0.01 | +0.01 +0.01 | +0.01 + 0.01 16 OI OL, |
    ) in which & is 2 constant depending on the ellipticity of the earth ; and the correction becomes C=—kcos2¢ Bj. The value of & adopted here is that determined by Prof. Harkness,* k = 0.002662. The correction is the same numerically for ¢ = 45° + a and ¢= 45° —a. It is negative for latitudes below 45° and positive for latitudes above 45° TABLES 12,13. TaBLeE 12 (English measures) gives the correction in thousandths of an inch for every degree of latitude and for each inch of barometric pres- sure from 19 to 30 inches. TABLE 13 (JZetric measures) gives the correction in hundredths of a millimetre for each 20 millimetres barometric pressure from 520 to 770 mil- limetres. Example: Barometric reading (corrected for temperature) at Dodge City; latitude 37° 45’, = 27.434 Gravity correction for latitude from Table 12, — 0.018 Barometer reduced to latitude 45°, = 272450 *Wn. HARKNESS: Zhe solar parallax and its related constants. Washington, 1891, 4°, pp. 169. xx INTRODUCTION. REDUCTION OF THE BAROMETER ‘TO SEA LEVEL. The fundamental formula for reducing the barometer to sea level and for determining heights by the barometer is the original formula of Laplace, amplified into the following form— A+h, Z=K (1 +09)(— ee) (1 + kcos2 9) (14+55 *) tog & in which # = Height of the upper station. h, = Height of the lower station. Z=h—h,. p = Atmospheric pressure at the upper station. p. = Atmospheric pressure at the lower station. R = Mean radius of the earth. 6 = Mean temperature of the air column between the altitudes hand h,. e = Mean pressure of aqueous vapor in the air column. 6 = Mean barometric pressure of the air column. ¢ = Latitude of the stations. &A = Barometric constant. a = Coefficient of the expansion of air. k = Constant depending on the figure of the earth. The pressures £, and # are computed from the height of the column of } eacbe : : mercury at the two stations ; the ratio BR of the barometric heights may be substituted for the ratio = if B, and # are reduced to the values that would be measured at the same temperature and under the same relative value of gravity. The correction of the observed barometric heights for instrumental tem- perature is always separately made, but the correction for the variation of gravity with altitude is generally introduced into the formula itself. If &,, B represent the barometric heights corrected for temperature only, we have the equation Poe PB p being a constant depending on the variation of gravity with altitude. B Z log Pe = log —+ lo (1 - bbs ); oC pe eecweet tire ‘ ue : . Since — is a very small fraction, we may write R Nap. log ( tesa = ee and log (1 -|- Ee He M being the modulus of common logarithms. M, BAROMETRICAL TABLES. xxi By substituting for 7 its approximate value Z= XK log = , we have _hK K e, log ( ee ae M \og gz With these substitutions the barometric formula becomes a K (1 +06)(— aoe aye) + bcos 26)(2 +E) pe (« is EM ) log 2 As a further simplification we shall put B = 0.3785) y = cos 2¢ and nat uw, and write the formula— B a7.) (1 + 1) log 3 Z=K (1 +46) (>) (1 ty (1+" Values of the constants.—The barometric constant A is a complex quantity defined by the equation AX Bn. ox MN icy B, is the normal barometric height of Laplace, 760 mm. A is the density of mercury at the temperature of melting ice. M. Marek (Zvavaux et Mémoires du Bureau international des Poids et Mesures, t. II, p. D 55) gives the value, A = 13.5956, and finds that different specimens of mercury purified by different processes differ from this by several units in the fourth decimal. The International Meteorological Committee have taken the value A, = 13.5958, and for the sake of uniformity this value is here adopted. 8 is the density of dry air at o° C. and under the pressure of a column of mercury B&B, at the sea level and at latitude 45° The value adopted by the International Bureau of Weights and Measures (7vavaux et Mémotres, Pe gp. A54) is 5 = 0.001293052. M (the modulus of common logarithms) = 0.4342945. These numbers give for the value of the barometric constant K = 18400 metres. Xxii INTRODUCTION. For the remaining constants, the following values have been used : a = 0.00367 for 1° Centigrade... (International Bureau of Weights and Measures: TZravaux et Mémoires, t. I, p. A 54.) y= cos 2¢=0.002662 cos 2¢. (Harkness: The solar parallax, etc., See pois) R = 6367324 metres. (A.R. Clarke: Geodesy, 8°, Oxford, 1880.) tee BAM = 0.002396. (Ferrel: Report Chief Signal Officer, 1885, Pt 2,°D-9393-) In reducing the barometer to sea-level, 4, =o, and the factor (1 + —) becomes ( I+ yi Taking the product of this factor and A (1 +486), and neglecting the term in @ Z, the formula becomes in metric measures Z (metres) = (18444 + 67.53 4° “ + 0.003 Z) : (1y) log + Bis I—p B and in Anglish measures B Z, (feet) =1(56573-— 12aerae 4-1 a. 002 Z)(- _ ae + y) log at The form adopted for the tables is that of M. Angot.* Taking the formula in English measures, let vos I Y= 56573 + 123.10 40.0032 I1—f Z ; : ; Bev ak Then disregarding the small correction for gravity, m = log RB gives an approximate value of &,, and the correction to be added to the observed pressure to obtain the sea-level pressure is G— hs or): If m, be the value of mm corrected for gravity, we have m : m, = -——_ Or, approximately, = m — my. 1+¥ The correction for gravity is therefore made by applying to the approxi- mate value 7 the small correction my. With this corrected value of mm, the reduction to sea-level is given by the expression B(10" — 1). The above fraction designated mm contains the altitude Z, the mean temperature #, and the humidity factor In the Swzthsonian tables, I =p meteorological and physical, by Dr. A. Guyot, the distinguished author *A. ANGOT: Annales du Bureau Central Météorologique. Année 1878, t. I, p. C. 13. ee BAROMETRICAL TABLES. Xxili in treating of this humidity factor in connection with hypsometric tables took the following position : ‘To introduce a separate correction for the expansion of aqueous vapor ‘‘is in the writer’s view, a doubtful improvement. The laws of the distri- ‘“ bution and transmission of moisture through the atmosphere are too little ‘known, and its amount, especially in mountain regions, is too variable, and ‘“depends too much upon local winds and local condensation, to allow a ‘reasonable hope of obtaining the mean humidity of the layer of air between ‘“the two stations by means of hygrometrical observations made at each of “them. ‘These doubts are confirmed by the experience of the author and ‘“of many other observers, which shows that, on an average, Laplace’s “method works not only as well as the other, but more uniformly well. At ‘any rate the gain, if there be any, is not clear enough to compensate for ‘the undesirable complication of the formula.”’ Since this position was taken by Dr. Guyot forty years ago, there has been no such advance in our knowledge as to impair the practical conclusion in conformity with which he constructed his hypsometric table. Accord- ingly in treating this portion of the formula in the construction of the present tables for the reduction of the barometer to sea level, it has been deeined advantageous to retain the method adopted by Guyot, and to incorporate the humidity factor in the temperature term, thereby assum- ing the air to contain the average degree of humidity corresponding to the actually prevailing condition of temperature. In evaluating the humidity factor as a function of the air temperature, the tables given by Prof. Ferrel (Jeteorological researches. Part tii.—Baro- metric hypsometry and reduction of the barometer to sea level. Report, U. 5. Coast Survey, 1881. Appendix 10.) These tables by interpolation, and by extrapolation below o° /., give the following values for f: For Fahrenheit temperatures, B 6 B 6 B F. Fe 0.00104 36° | 0.00267 62° 0.00724 -OOIII 38 .00293 64 .00762 -oo118 4o .003 22 66 .oo801 -O0126 42 .00353 68 .00839 .OO134 44 .00386 70 .00877 .O0O143 AS .00421 72. .OOQT4 .OO153 48 .00458 -OO163 50 .00496 76 0.00990 .OO174 52 .00534 80 .O1065 .00187 54 .00572 84 -OLI4I .00203 56 .00610 88 .O1217 .00222 58 .00648 92 .01293 0.0243 60 .00686 96 .01369 xxiv INTRODUCTION. For Centigrade temperatures, vk AD The practical tables consist essentially of two mutually dependent parts:—the first gives values of 2000 in a table of double entry of which the altitude of the station and the mean temperature of the air between the station and sea level are the arguments; the second gives the reduction to sea level in a table of double entry of which the arguments are 20007 and the observed barometric height corrected for temperature. In addition, a subsidiary table gives the small correction for latitude to be applied to the values of 2000. This correction, while of theoretical interest, seldom becomes of practical importance, since its effect is in general overshadowed by the relatively large uncertainties incident to the determination of the true mean temperature. The mean temperature of the air column is to be obtained from the observed temperature at the station by employing some assumption as to the rate of change of temperature with altitude. In the discussion of barometric observations made in the mountain and plateau regions of the United States, it has been found that this rate of change is a climatic factor which needs to be determined for every station for different seasons of the year, and for different atmospheric conditions. When the results of such investigations are embodied in tables for reduction to sea level, the tables and the method of their use may be simplified and the labor of obtaining the reduction greatly abridged; but in the nature of the case, these special methods can not be utilized in the construction of general tables which are to be applicable to all phases of topography and climate. Whatever method be used for obtaining the mean temperature of the air column (8) from the observed temperature at the station, the former and hence the latter is subject to the important condition that it shall not contain the diurnal fluctuation. Hence in reducing to sea level any indi- vidual observation of the barometer, the simultaneous observation of air temperature used in obtaining @ should be reduced to the daily mean by a correction, or, better, the actual mean temperature of the preceding twenty- four hours should be taken. i i I ee i Me ee BAROMETRICAL ‘TABLES. xxV TABLES 14, 16, 16. TABLES 14,15,16. Reduction of the barometer to sea level — English measures. Table 14 gives values of 2000 x m. m= = : ~ 56573 + 123.19+0.003Z2 1+f8 The temperature 6 varies by intervals of 2° from — 20° F. to 96° /., except near the extremities of the table where the interval is 4’ The alti- tude Z varies by intervals of 100 feet from 100 to gooo feet. The values of 20007 are given to one decimal. In order to facilitate interpolations for .:ractions of a roo feet in altitude, the tabular differences for 100 feet have been added on each line. Table 15 gives a small correction to 2000 m for latitude, computed from the expression 2000 72 X 0.002662 cos 29. The arguments are 2000m, which varies by tens from 10 to 350, and the latitude, which varies by 5° from 0° to go? The correction is to be subtracted for latitudes below 45° and added for latitudes above 45° The tabular values are given to one decimal. Table 16, with the value of 2000 thus corrected, gives the correction which must be applied to the barometric reading B (corrected for tem- perature) to reduce it to sea level. The arguments are 2, which varies by 0.5 inch from 31.00 inches to 19.5 inches, and values of 2000m, which are given for every unit from 1 to 334. The reduction values B,— 2 are given to o.or inch. Example: Let B= 26.24 inches be the barometric reading (corrected for temper- ature) observed at a station whose altitude is 3572 feet, and latitude 32° Suppose the mean temperature of the air column 6270.14 Table 14 gives (p. 63) with Z = 3, 500 feet and 0 = 62°8 /., 2000 = 108.0 The difference for 72 feet is 22 The approximate value of 2000 7 is EXO:2 Table 15, with 2000 m = 110 and latitude = 32°, gives the subtractive correction 0.1. Hence the corrected value of 2000 is 110.1. With 2000m = 110.1 and B= 26.24, Table 16 (p. 72) gives the reduc- tion to sea level, 3.55 inches. Accordingly the barometric pressure reduced to sea level is B, = 26.24 + 3.55 = 29.79 inches. xXvV1 INTRODUCTION. TABLES 17, 18,19. Reduction of the barometer to sea level—Metric measures. For reducing to sea level readings of the metric barometer, the baro- metric formula in metric measures derived on page xxii is treated in the same manner as the formula in English measures just described in detail, and the method of construction of the tables is the same. Table 17 gives values of 2000 7. ee I om 18444 + 67.539+0.003Z 1+B8° The temperature @ varies by intervals of 2° from — 16° C. to + 36° C. except near the extremities of the table where the interval is 4? The alti- tude Z varies by 10 metres from 10 to 3000 metres. ‘The values of 2000 m are given to one decimal. Table 18 gives the small correction to 2000 m for latitude. The argu- ments are 2000, which varies by tens from 10 to 350, and the latitude which varies by 5° from o° to go? ‘The correction is to be subtracted for latitudes below 45° and added for latitudes above 45° The tabular values are given to one decimal. ‘The value of 2000 thus corrected is then used in entering Table 19. Table 19 gives the correction which must be applied to the barometric reading & (corrected for temperature) to reduce it to sea level. The argu- ments are 4, which varies by 10mm. from 790 mm. to 480 mm., and values of 2000 m which vary by units from 1 to 345. The tabular values B,—B are given to 0.1 mm. Example: Let & = 648.7 mm. be the barometric reading observed and corrected for temperature at a station whose altitude is 1353 metres and latitude ° 32: Suppose the mean temperature of the air column #@= 14°3 C. Table: 17 gives (p..83) fon 0 —t4and Z—-145355) 2000 77)— 13856 The proportional part for 0°3 is oh Hence the approximate value of 2000 ™ is 138.45 Table 18, with 2000 m = 138 and latitude 32°, gives the subtractive correction 0.15. Hence the corrected value of 2000 m is 138.3. With this value and & = 649mm. as arguments, Table 19 gives 8, —B = 112.0mm. Accordingly the barometric reading reduced to sea level is 5, = 648.7 4- 112-0 — 700, 7 mm: THE DETERMINATION OF HEIGHTS BY THE BAROMETER. TABLES 20, 21, 22, 23, 24. Lnglish Measures. The barometric formula developed in the preceding section (see p. xxi) is arranged in the following form for determining heights by the barometer. | 4 BAROMETRICAL TABLES. XXVii Z=K (log B, — log B) ie + a6) (x + B) (1+ cos 2$) (1+ 7) Ga) in which K (log B,—log B) is an approximate value of 7 and the factors in the brackets are correction factors depending respectively on the air temperature, the humidity, the variation of gravity with latitude, the varia- tion of gravity with altitude in its effect on the weight of mercury in the barometer, and the variation of gravity with altitude in its effect on the weight of the air. With the constants already given, the formula becomes in English measures : Z (feet) = 60368 (log B, — log BZ) | [1 + 0.002039 (9 — 32°)] | (1 + B) | (1 + 0.002662 cos 2¢) (1 + 0.00239) Z+2h, Coat R In order to make the temperature correction as small as possible for average air temperatures, 50° F. will be taken as the temperature at which the correction factor is zero. "This is accomplished by the following trans- formation : 1 + 0.002039 (6 — 32°) =[1 + 0.002039 (8 — 50°)] [1 + 0.0010195 x 36°]. The second factor of this expresssion combines with the constant, and gives 60368 (1 + 0.0010195 X 36°) = 62583.6. The first approximate value of Z is therefore 62583.6 (log B, —log #). In order further to increase the utility of the tables, we shall make a further substitution for log &, —log 4, and write 62583.6 (log B, — log B) = 62583.6 log eS — log =F). Table 20 contains values of the expression 62583.6 log “2 for values of B varying by intervals of 0.01 inch from 12.00 inches to 30.90 inches. The first approximate value of Z is then obtained by subtracting the tabular value corresponding to B, from the tabular value corresponding to B (& and B, being the barometric readings observed and corrected for temperature at the upper and lower stations respectively). XXViii INTRODUCTION. Table 21 gives the temperature correction Z X 0.002039 (8 — 50°). The side argument is the mean temperature of the air column (@) given for intervals of 1° from 0° to 100° F. ‘The top argument is the approximate difference of altitude Z obtained from ‘Table 20. For temperatures above 50° /., the correction is to be added, and for temperatures below 50° /., the correction is to be subtracted. It will be observed that the correction isa linear function of Z, and hence, for example, the value for 7= 1740 is the sum of the corrections in the columns headed 1000, 700, and 4o. In general, accurate altitudes can not be obtained unless the temperature used is freed from diurnal variation. Table 22 gives the correction for latitude, and for the variation of gravity with altitude in its effect on the weight of the mercury. When altitudes are determined with aneroid barometers the second factor does not enter the formula. In this case the effect of the latitude factor can be obtained by taking the difference between the tabular value for the given latitude and the tabular value for latitude 45° The side argument is the latitude of the station given for intervals of 2? The top argument is the approximate difference of height Z. Table 23 gives the correction for the average humidity of the air at different temperatures; the values of the factor (1 + 8) adopted by Prof. Ferrel and given on page xxiii have been used. ‘This correction could have been incorporated with the temperature factor in Table 21, but it is given separately in order that the magnitude of the correction may be apparent, and in order that, when the actual humidity is observed, the correction may be computed if desired, by the expression Ze (0.378 5) where ¢ is the mean pressure of vapor in the air column, and 6 the mean barometric pressure. The side argument is the mean temperature of the air column, varying by intervals of 2° from — 20° F. to 96° /., except near the extremities of the table where the interval is 4° The top argument is the approximate difference of altitude Z. Table 24 gives the correction for the variation of gravity with altitude in its effect on the weight of theair. The side argument is the approximate difference of altitude Z, and the top argument is the elevation of the lower station /,. The corrections given by Tables 22, 23 and 24 are all additive. BAROMETRICAL ‘TABLES. XXix Example: Let the barometric pressure observed, and corrected for temperature, at the upper and lower stations be, respectively, B = 23.61 and B,=29.97. Letthe mean temperature of the air column be 35° /, and the latitude 44°16’. ‘To determine the difference of height. Feet. Table 20, argument 23.61, gives 6420 Table 20, BS 20,07.) — 64 Approximate difference of height (7) = 6484 Table 21, with Z= 6484 and 0 = 35° F., gives — 198 Table 22, with Z= 6300 and ¢= 44’, gives + 16 Table 23, with Z = 6300 and = 35: /, gives + 17 Table 24, with Z= 6300 and #, =0, gives + 2 Final difference of height (7) = 6321 If in this example the barometric readings be observed with aneroid barometers, the correction to be obtained from Table 22 will be simply the portion due to the latitude factor, and this will be obtained by subtracting the tabular value for 45° from that for 44°, the top argument being Z = 6300. This gives 16 —15 =I. TABLES 25, 26, 27, 28, 29. Metric Measures. The barometric formula developed on page xxi is, in metric units, (1 + 0.00367 8 C.) (1 + 0.3785) (1 + 0.00266 cos 2 ¢) (1 + 0.00239) , Z+2h,) lea 6 367 323 Z (metres) = 18400 (log B,& log B) The approximate value of Z (the difference of height of the upper and lower station) is given by the factor 18400 (log B, —log B). This expression is computed by means of two entries of a table whose argument is the barometric pressure. In order that the two entries may result at once in an approximate value of the elevation of the upper and lower stations, a transformation is made, which gives the following identity: ; ; 60 7O@ 18400 (log B, —log B) = 18400 (Jog i — log B. ? . TABLE 25. Table 25 gives values of the expression 18400 log im for values of B varying by intervals of 1 mm. from 300 mm. to 779 mm. ‘The first approxi- mate value of Z is then obtained by subtracting the tabular value corresponding to &, from the tabular value corresponding to & (2 and #&, being the barometric readings observed and reduced to o° C. at the upper and lower xxxX INTRODUCTION. stations respectively). The first entry of Table 25 with the argument B gives an approximate value of the elevation of the upper station above sea level, and the second entry with the argument 2, gives an approximate value of the elevation of the lower station. Table 26 gives the temperature correction : 0.00367 8 C. x Z. The side argument is the approximate difference of elevation Z and the top argument is the mean temperature of the air column. ‘The values of Z vary by intervals of 100 m. from 100 to 4ooo metres and the temperature varies by intervals of 1° from 1° C. to 10° C. with additional columns for 20°, 30°, and 40° C. Attention is called to the fact that the formula is linear with respect to 6, and hence that the correction, for example, for 27° equals the correction for 20° plus the correction for 7? When the table is used for temperatures below o° C., the tabular correction must be subtracted from, instead of added to, the approximate value of Z. . Table 27 (pp. 112 and 113) gives the correction for humidity resulting from the factor 0.37 ; x Z=PZ. e b argument is the mean pressure of aqueous vapor, ¢, which serves to repre- sent the mean state of humidity of the air between the two stations. e=%3(f+/,) (f and Ff being the vapor pressures observed at the two stations) has been written at the head of the table, but the value to be assigned to ¢ is in reality left to the observer, independently of all hypothesis. ‘The top argument is the mean barometric pressure $(B X B,). The vapor pressure varies by millimetres from 1 to 40, and the mean barometric pressure varies by intervals of 20mm. from 500mm. to 760 mm. Page 112 gives the value of 0.378 = multiplied by 1oo00. ‘The side The tabular values represent the humidity factor 6 or 0.378 £ multiplied by 10000. Page 113 gives the correction for humidity, with Z and 10000 x 0.3785 (derived from page 112) as arguments. The approximate difference of altitude is given by intervals of 100 metres from 100 to 4000 metres, and the values of roooof vary by intervals of 25 from 25 to 300. The tabular values are given in tenths of metres to facilitate and increase the accuracy of interpolation. Table 28 gives the correction for latitude, and for the variation of gravity with altitude in its effect on the weight of the mercurial column. When altitudes are determined with aneroid barometers, the latter factor does not enter the formula. In this case the effect of the latitude factor can be obtained by subtracting the tabular value for latitude 45° from the tabular value for the latitude in question. The side argument is the approximate difference of elevation Z, varying by intervals of 100 metres from 100 to 4000. The top argument is the latitude varying by intervals of 5° from 0° to 75° BAROMETRICAL TABLES. xxxi TABLE 29. Table 29 gives the correction for the variation of gravity with altitude in its effect on the weight of the air. The side argument is the same as in Table 28; the top argument is the height of the lower station varying by intervals of 200 metres from o to 2000, with additional columns for 2500, 3000 and 4000 metres. Example: Let the barometric reading (reduced to 0° C.) at the upper station be 655.7mm.; at the lower station, 772.4mm. Let the mean temperature of the air column be 6=12°3 C., the mean vapor pressure e=g mm. and the latitude $= 32° Table 25, with argument 655.7, gives I179 metres. ‘Taplez2s;. Ee AT 2A — 129 Approximate value of Z —ALZOG Table 26, with Z= 1300 and 0 = 12°3 C, gives 59 Table 27, with e=gmm. and Z= 1370, gives a Table 28, with Z= 1370 and ¢= 32°, gives 5 Table 29, with Z= 1370 and 2, =0, gives oO Corrected value of 7 1379 Metres. TABLE 30. Taste 30. Difference of height corresponding to a change of 0.1 inch in the barometer—English measures. If we differentiate the barometric formula, page xxvii, we shall obtain, neglecting insensible quantities, dB 2 ; d Z = — 26281 PR (« -+ 0.002039 (8 — 32 )) (1 + B) _in which & represents the mean pressure of the air column d@Z. Putting dB =0.1 inch, 2020.10 7-0 0 dZ=— B 1 + 0,002039 (6 — 32°) ) (1 + 8) The second member, taken positively, expresses the height of a column of air in feet corresponding to a tenth of an inch in the barometer on the parallel of 45° latitude. Since the last factor (1 + 8), as given on page xxiii, is a function of the temperature, the function has only two variables and admits of convenient tabulation. Table 30, containing values of dZ for short intervals of the arguments B and 6, has been taken from the Report of the U. S. Coast Survey, 1881, Appendix 10,—Barometric hypsometry and reduction of the barometer to sea level, by Wm. Ferrel.* * Due to the use of a slightly different value for the coefficient of expansion, Prof. Ferrel’s formula, upon which the table is computed, is bea aor ( + 0.002034 (9 — 32°) (t+ 8): XXxXii INTRODUCTION. The temperature argument is given for every 5° from 30° F. to 85° F, and the pressure argument for every 0.2 inch from 22.0 to 30.8 inches. This table may be used in computing small differences of altitude, and, up to a thousand feet or more, very approximate results may be obtained. Example: Mean pressure at Augusta, October, 1891, 29.94; temperature, 60°8 F. Mean pressure at Atlanta, October, 1891, 28.97; temperature, 59°4 Mean pressure of air column, bi—2OrA 5c 0 —(60"r Entering the table with 29.455 and 60°r1 as arguments, we take out 94.95 as the difference of elevation corresponding to a tenth of an inch difference of pressure. Multiplying this value by the number of tenths of inches difference in the observed pressures, viz. 97, we obtain the difference of elevation 921 feet. TABLE 31. Difference of height of air corresponding to a change of 1 millimetre in the barometer—Metric measures. This table has been computed by converting Table 18 into metric units. The temperature argument is given for every 2° from — 2° C. to + 36° C.; the pressure argument is given for every millimetre from 760 to 560 mm. TaBLe 32. Sabinet’s formula for determining heights by the barometer. Babinet’s formula for computing differences of altitude* represents the formula of Laplace quite accurately for differences of altitude up to 1000 metres, and within one per cent for much greater altitudes. As it has been quite widely disseminated among travellers and engineers, and is of con- venient application, the formula is here given in English and metric measures. It might seem desirable to alter the figures given by Babinet so as to con-_ form to the newer values of the barometrical constants now adopted ; but this change would increase the resulting altitudes by less than one-half of one per cent without enhancing their reliability to a corresponding degree, on account of the outstanding uncertainty of the assumed mean temperature of the air. The formula is, in English measures, Z (feet) = 52404 [1 = a a and in metric measures, 2(4,+4)1,8,-—B 1000 B,+ B’ in which Z is the difference of elevation between a lower and upper station at which the barometric pressures corrected for all sources of instrumental error are &, and B, and the observed air temperatures are /, and /, respectively. Z (metres) = 16000 [: le Cope Rendus, Pane 1850, vol. xxv., page 309. 4 BAROMETRICAL ‘TABLES. XxXXtiil For ready computation the formula is written BL,—B n= OK Bee Re and the factor C, computed both in English and metric measures, has been kindly furnished by Prof. Cleveland Abbe. The argument is 3 (¢, + 7) given for every 5° Fahrenheit between 10° and 100° /., and for every 2° Centigrade between 10° and 40° Centigrade. In using the table, it should be borne in mind that on account of the uncertainty in the assumed temperature, the last two figures in the value of C are uncertain, and are here given only for the sake of convenience of interpolation. Consequently one should not attach to the resulting altitudes a greater degree of confidence than is warranted by the accuracy of the temperatures and the formula. The table shows that the numerical factor changes by about one per cent of its value for every change of five degrees Fahrenheit in the mean temperature of the stratum of air between the upper and lower stations ; therefore the computed difference of altitude will have an uncertainty of one per cent if the assumed temperature of the air is in doubt by 5° / With these precautions the observer may properly estimate the reliability of his altitudes whether computed by Babinet’s formula or by more elaborate tables. Example: Let the barometric pressure observed and corrected for temperature at the upper and lower stations be, respectively, B = 635 mm. and B,=730mm. Let the temperatures be, respectively, ¢= 15° G? 4,=20° C. To find the approximate difference of height. 20° +1 eas ° With 3,12) = 2 — 17°5 C., the table in metric measures gives BL—B C— Y7 120 mlettes. B. om ae The approximate difference of height = 17120 x 95 = II91.5 metres. 1365 THERMOMETRICAL MEASUREMENT OF HEIGHTS BY OBSERVATION OF THE TEMPERATURE OF THE BOILING POINT OF WATER. When water is heated in the open air, the elastic force of its vapor gradually increases, until it becomes equal to the incumbent weight of the atmosphere. ‘hen, the pressure of the atmosphere being overcome, the steam escapes rapidly in large bubbles and the water boils. ‘The tem- perature at which water boils in the open air thus depends upon the weight of the atmospheric column above it, and under a less barometric pressure the water will boil at a lower temperature than under a greater pressure. Now, as the weight of the atmosphere decreases with the elevation, it is obvious that, in ascending a mountain, the higher the XXXIV INTRODUCTION. station where an observation is made, the ower will be the temperature of the boiling point. The difference of elevation between two places therefore can be deduced from the temperature of boiling water observed at each station. It is only necessary to find the barometric pressures which correspond to those temperatures, and, the atmospheric pressures at both places being known, to compute the difference of height by the tables given herein for com- puting heights from barometric observations. From the above, it may be seen that the heights determined by means of the temperature of boiling water are less reliable than those deduced from barometric observations. Both derive the difference of alti- tude from the difference of atmospheric pressure. But the temperature of boiling water gives only zuzdirectly the atmospheric pressure, which is given directly by the barometer. "This method is thus liable to all the chances of error which may affect the measurements by means of the barometer, besides adding to them new ones peculiar to itself, the prin- cipal of which is the difficulty of ascertaining with the necessary accuracy the true temperature of boiling water. In the present state of ther- mometry it would hardly be safe, indeed, to rely, in the most favorable circumstances, upon quantities so small as hundredths of a degree, even when the thermometer has been constructed with the utmost care; more- over, the quality of the glass of the instrument, the form and substance of the vessel containing the water, the purity of the water itself, the position at which the bulb of the thermometer is placed, whether in the current of the steam or in the water, —all these circumstances cause no inconsiderable variatiorfs to take place in the indications of thermometers observed under the same atmospheric pressure. Owing to these various causes, an obser- vation of the boiling point, differing by one-tenth of a degree from the true temperature, ought to be still admitted as a good one. Now, as the tables show, an error of one-tenth of a degree Centigrade in the temperature of boiling water would cause an error of 2 millimetres in the barometric pressure, or of from 70 to 80 feet in the final result, while with a good barometer the error of pressure will hardly ever exceed one-tenth of a millimetre, making a difference of 3 feet in altitude. Notwithstanding these imperfections, the hypsometric thermometer is of the greatest utility to travellers and explorers in rough countries, on account of its being more conveniently transported and much less liable to accidents than the mercurial barometer. A suitable form for it, designed by Regnault (Annales de Chimie et de Physique, Tome xiv, p. 202), consists of an accurate thermometer with long degrees, subdivided into tenths. For observation the bulb is placed, about 2 or 3 centimetres above the surface of the water, in the steam arising from distilled water in a cylin- drical vessel, the water being made to boil by a spirit-lamp. . | HYGROMETRICAL TABLES. XXXV TABLES 33, 34. Barometric pressures corresponding to the temperature of boiling water. TABLE 33. English Measures. TABLE 34. Metric Measures. Table 33 is a conversion into English measures of Table 34. The argument is the temperature of boiling water for every tenth of a degree from 1850 to 212°9 Fahrenheit. The tabular values are given to the nearest 0.01 inch. Table 34 is Regnault’s table of barometric pressures corresponding to temperatures of boiling water, revised by A. Moritz (Acad. Sct. Bull., St. Petersburg, xiii., 1855, col. 41-44). ‘To the degree of precision here desired, these values do not differ from the more recent reduction by Broch. The argument is given for every tenth of a degree from 80/0 to 10079 Cx eine tabular values are given to the nearest 0.1 mm. HYGROMETRICAL TABLES. PRESSURE OF AQUEOUS VAPOR IN SATURATED AIR. Tables 35, 36, and 43, giving the pressure of aqueous vapor in saturated air, are based upon Dr. Broch’s reduction of the observations of Regnault (Travaux et Mémoires du Bureau international des Poids et Mesures, t. I, p. A 19-39). This reduction assumes that the observations may be repre- sented by the empirical formula bt + cf? + dts + ett + fs 1+ at Fie TO in which / is the pressure of aqueous vapor expressed in millimetres of standard mercury, that is at o° C. and at latitude 45° and sea level, its density being 15.59593. ¢, the temperature expressed in normal Centigrade degrees. a = 0.003667458 By using the simultaneous values of / and / given by Regnault’s observations, Dr. Broch obtained a series of observation equations whose solution by the method of least squares gave the following values for the coefficients : a 4.568 685 9 Ree TOs ea eo OO Lc. ¢€=—I105 X 1.416 112 423 2—, 1G" 420.035'336 308 e€=— 109 X 2.646 535 103 a tO X03 77/150 From this formula Broch’s tables of vapor pressure were computed. XXXVI INTRODUCTION. TABLE 35. Pressure of aqueous vapor—English measures. This table is a conversion into English measures of Table 36. It gives the vapor pressure in saturated air for temperatures varying by o°2 from — 20°0 to 214°0 Fahrenheit. The tabular values are given in inches to four decimals. A column of differences for 0°71 is added for convenience in interpolating. TABLES 36, 43. /vessure of aqueous vapor.—Metric measures. These tables, taken from Broch, give the pressure of aqueous vapor to hundredths of a millimetre for temperatures varying by o21 C. from — 29°0 to 10079 Centigrade. ‘The values for temperatures between 0° C. and 45° C. are given in Table 43, the remainder in Table 36. TABLE 37. Pressure of aqueous vapor at low temperature.—(C. F. Marvin.) Broch’s vapor pressures at temperatures below o° C. (32° F.) as given in Tables 35 and 36, when compared with the actual observed values of Reg- nault are found to be systematically too large. This discrepancy signifies that the empirical formula adopted by Broch fails to represent accurately the law of variation of vapor pressure for temperatures both above and below the freezing point. Moreover, the failure in the application of the formula might be inferred from the laws of diffusion following from the kinetic theory of gases, for these give no reason to suppose that the function expressing the relation between vapor pressure and temperature is continuous between the two states of water and ice. Under proper conditions water can be cooled far below o° C. (32° /) before solidifying, so that at the same temperature we may have it either in the liquid or the solid state, and experiments confirm the theory of diffusion in showing that the pressure of the vapor is different according as it is in contact with its liquid or its solid at the same temperature. ‘The method hitherto employed of combining vapor pressures above and below freezing, and attempting to represent them by a single continuous function, must therefore be considered as radically erroneous. ; Recognizing the systematic errors of the vapor pressures given by 3roch’s formula for temperature below freezing, the Chief Signal Officer lately authorized a new determination by direct observation. ‘This experi- mental investigation has been carried out by Prof. C. F. Marvin, from the results of which (Annual Report Chief Signal Officer, 1891; Appendix No. 10,) Table 37 is reproduced. The interpolation between the observed press- ures which were noted at intervals of about 5° /., was effected graphically and not by mathematical formula. The vapor pressures were determined for the case of the vapor in con- tact with ice and not a water surface. For the temperature of melting ice (0° C. or 32°F.) all values agree. Below this temperature Marvin’s vapor pressures are slightly smaller than Regnault’s, but differ from the latter less than any other tabular values. L. HYGROMETRICAL ‘TABLES. XXXvVii The argument of the table is given for every two-tenths of a degree Fahrenheit from — 60°0 to 32°0 Fahrenheit. The tabular values are given in millimetres and inches to three and four decimals respectively. TABLES 38, 39. TaeLe 38. Weight of aqueous vapor in a cubic foot of saturated air— English measures. TaBLe 39. Weight of aqueous vapor in a cubic metre of saturated air— Metric measures. The weight of aqueous vapor in a cubic metre of saturated air is given by the expression asd F 1 --at’ 760’ a is the weight of a cubic metre of dry air (free from carbonic acid) at temperature o° C., and pressure of 760 millimetres of standard mercury at 45° latitude and sea-level: a=1.29278 kg. (Bureau International des Poids et Mesures: 7ravaux et Mémoires, t. I, p. A 54.) 8 is the density of aqueous vapor: §= 0.6221 F is the pressure of aqueous vapor in saturated air whose temperature is ¢; Broch’s values are adopted, expressed in millimetres. a is the coefficient of expansion of air for 1° C.: a = 0.003667 ¢ is the temperature in Centigrade degrees. Whence we have W (grammes) = 1.05821 x aE ooushn? Table 39 is computed from this formula and gives the weight of vapor in grammes in a cubic metre of saturated air for dew-points from — 29° to 40° C., the intervals from 6° to 4o° C. being o?r C. The tabular values are given to three decimals. The weight W7’ of aqueous vapor in a cubic foot of saturated air is obtained by converting the foregoing constants into English measures. The weight of a cubic foot of dry air at temperature 32° /. and at a pressure of 760 mm. or 29.921 inches is 1292.78 X 15.43235, a’ (grains) = == FOWL OA. (grains) (@sse8sa: 564.94 We have therefore, . . ‘ / 6 fl W” (grains) = cee ‘ ; 29.921 Pep ate = 32 2 nue - ad i i = — — ate? pee 0.002037 (¢’ — 32°) The temperature / is expressed in degrees Fahrenheit ; the vapor pressure /’, expressed in inches, is obtained from Table Bo: XXXVili . INTRODUCTION. Table 38* gives the weight of aqueous vapor in grains in a cubic foot of saturated air for dew-points given to every 0°5 from —19°5 to 115° /, the values being computed to the thousandth of a grain. The computation of Tables 38 and 39 has been furnished by Prof. Wm. ~~» Libbey, ike REDUCTION OF OBSERVATIONS WITH THE PSYCHROMETER AND DETERMINATION OF RELATIVE HUMIDITY. The psychrometric formula derived by Maxwell, Stefan, August, Regnault and others is, in its simplest form, IS =i A BE—4); in which ¢ = Air temperature. ¢, = Temperature of the wet-bulb thermometer. J = Pressure of aqueous vapor in the air. /, = Pressure of aqueous vapor in saturated air at temperature /,. 4 = Barometric pressure. A =A quantity which, for the same instrument and for certain conditions, is a constant, or a function depending in a small measure on /,. The important advance made since the time of Regnault consists in recognizing that the value of 4 differs materially according to whether the wet-bulb is in quiet or moving air. ‘This was experimentally demonstrated by the distinguished Italian physicist, Belli, in 1830, and was well known to Espy, who always used a whirled psychrometer. ‘The latter describes his practice as follows: ‘‘ When experimenting to ascertain the dew-point by means of the wet-bulb, I always swung both thermometers moderately in the air, having first ascertained that a moderate movement produced the same depression as a rapid one.”’ The principles and methods of these two pioneers in accurate psychrom- etry have now come to be adopted in the standard practice of meteor- ologists, and psychrometric tables are adapted to the use of a whirled or ventilated instrument. Tne factor A depends in theory upon the size and shape of the ther- mometer bulb, largeness of stem and velocity of ventilation, and different formulze and tables would accordingly be required for different instruments. But by using a ventilating velocity of three metres or more per second, the differences in the results given by different instruments vanish, and the same tables can be adapted to any kind of a thermometer and to all changes of velocity above that which gives sensibly the greatest depression of the wet- bulb temperature; and with this arrangement there is no necessity to measure or estimate the velocity in each case further than to be certain that it does not fall below the assigned limit. *The table has been computed with the factor 11.7449, which results from Clarke’s value for the conversion of the metre, instead of with the value 11.7459 above derived. HYGROMETRICAL TABLES. XXxXix The formula and tables here given for obtaining the vapor pressure and dew-point from observations of the whirled or ventilated psychrometer are those deduced by Prof. Wm. Ferrel (Annual Report Chief Signal Officer, 1886, Appendix 24) from a discussion of a large number of observations. Taking the psychrometric formula in metric units, pressures being expressed in millimetres and temperatures in Centigrade degrees, Prof. Ferrel derived for 4 the value : A = 0.000656 (1 + 0.0019 ¢,) In this expression for 4, the factor depending on /, arises from a similar term in the expression for the latent heat of water, and the theoretical value of the coefficient of /, is 0.00115. Since it would require a very small change in the method of observing to cause the difference between the theoretical value and that obtained from the experiments, Prof. Ferrel adopted the theoretical coefficient o.oo115 and then recomputed the obser- vations, obtaining therefrom the final value A =0.000660 (I + 0.001154). With this value the psychrometric formula in metric measures becomes S=f,— 0.000660 B (¢ — #,) 4 + 0.00115 4) In order to adapt the formula to convenient tabulation, Prof. Ferrel substituted ¢—/, for ¢, in the last factor, a modification which produces appreciable error only in extreme cases. ‘The error in the computed vapor pressure will be E =0.00000076 B (¢— #,) (¢— 24,). Expressed in English measures, the formula is e /=f, — 0.000367 B (¢—4,) (1 + 0.000644) and with the same modification in order to render the formula more con- venient for tabulation, we have S=f, — 0.000367 B (¢—#,) (1 + 0.00064 (¢—4,)), -a which f= Vapor pressure in inches. 7, = Vapor pressure in saturated air at temperature /,. ¢= Temperature of the air in Fahrenheit degrees. ¢, = Temperature of the wet-bulb thermometer in Fahrenheit degrees. £& = Barometric pressure in inches. TABLES 40, 41. Reduction of Psychrometric Observations—English measures. TaBie 40. Pressure of aqueous vapor. —_ TaBLe 41. Values of 0.000 367 B(t—4,)(1 “+ d ae) These two tables provide for computing the vapor pressure and dew- point from observations of ventilated wet- and dry-bulb Fahrenheit ther- mometers. xl INTRODUCTION. Table 40, with the wet-bulb temperature /, as an argument, gives the value of f, the first term of the formula for the vapor pressure f, given above. It is simply an abbreviation of Table 35 for temperatures above 32° F., and of Table 37 for temperatures below 32° /, reprinted for convenience. Table 41, with ¢—/, and B as arguments, gives the value of the second term of the formula, viz: Ze, 0.000 367 B (¢ — ¢,) (: + a) The top argument is given for every half inch from 30.5 to 18.5 inches; the side argument, ¢—/7,, is given for every whole degree up to 4o° F Tabular values are given to thousandths of inches. With the two tables we then have, J (vapor pressure) = Table 40 — Table 41. The value of ¢ in Table 4o, corresponding to the vapor pressure thus obtained, is the dew-point. Examples: 1. Given ¢ = 84°3; ¢, = 66°7, and B = 30.00 inches, to find the vapor pressure and dew-point. Table 40, with ¢, = 66°7, gives 7, = 0.654 inches. Table 41, with ¢— ¢, = 84°3 — 66°7 = 17°6 and B= 30.00 inches as arguments, gives 0.196 inch as the value of the last term of the expression above. Hence we have the vapor pressure J = 0.654 — 0.196 = 0.458 inch. The temperature (Table 40) corresponding to this value of / is the dew-point, d = 56°6 7. 2. Given ¢=34°5; ¢,=29°4, and B= 22.3 inches, tg find the vapor pressure and dew-point. Table 40, with ¢,= 29°24, gives 4, = 0.162 inch. Table 41, with ¢—7,=34°5—209°4=5°1 and B= 22.5 inches (the nearest value in the table to 22.3 inches) as arguments, gives 0.042 inch as the value of the second term of the expression for f Hence we have the vapor pressure / = 0.162 — 0.042 = 0.120 inch. The temperature in Table 40, corresponding to this value of f is the dew-point, d= 22°0. NoTE—In using Table 4o, the proportional part for tenths of the argument, ¢—Z,, may be easily obtained by taking one-tenth of the tabular value belonging to the same number of degrees; for instance, in the first example, the tabular value for 17° is 0.189, and the proportional part for 0% is one-tenth the tabular value for 60, viz., one-tenth of .066, or .007. Hence we get 0.189 + 0.007 = 0.196. TABLE 42. Lelative humidity— Temperature Fahrenheit. Table 42 gives the relative humidity of the air in hundredths, having given the air temperature ¢ and the dew-point d in Fahrenheit degrees. TYGROMETRICAL TABLES. xli It is computed by the formula - Relative humidity = Z. fand F are the maximum pressures of vapor corresponding respectively to the temperatures @ and ¢ as given in Table 35 for temperatures above 32° /. and in Table 37 for temperatures below 32° /. , The top argument is /—d, extending by half degree intervals from o° to 15° /., and by increasing intervals from 15° to 75° /. The side argument is the air temperature /, given for intervals of four degrees from — 32° to 120° /. Example: Let the air temperature be 62° 7. and the dew-point 51° /., to find the relative humidity. With ¢—d = 11° for the top argument, and ¢ = 62° for the side argument, the table gives 67.5 per cent as the relative humidity. TABLES 43, 44. Reduction of Psychrometric Observations—Metric measures. TABLE 43. Pressure of aqueous vapor. pay TABLE 44. Values of 0.000660 B (¢t—1?,) (x + ae : These two tables provide for computing the vapor pressure and dew- point from observations of ventilated wet and dry-bulb thermometers Centigrade. Table 43, with the wet-bulb temperature 7, as an argument, gives the value of f,, the first term of the formula for the vapor pressure /, viz: f=f,—0.000660 B (¢—#,) [1 + 0.00115 ¢—4,)]- It gives the vapor pressure to hundredths of a millimetre from — 30%0 C. to 45:9 C., the intervals being 1° for temperatures below o° C. and o’1 for temperatures above o° C. Table 44, with the depression of the wet-bulb ¢—/,, and the barometric pressure B as arguments, gives the value of the second term of the formula. The top argument is given for every 1o millimetres from 770 to 460 mm. ; the side argument /—/, is given for every whole degree up to 20. Tabular values are given to hundredths of a millimetre. From the two parts of the table we then have Vapor pressure, f (mm) = Table 43 — Table 44. The temperature in Table 43, corresponding to the vapor pressure thus obtained, is the dew-fornt. xii INTRODUCTION. Example: Given ¢= 10°94 C.; ¢,=8?3 C. and 8 = 740 mm., to find the vapor pressure and dew-point. Table 43, with the argument 7, = 8°3 C., gives f, =8.15 mm. Table 44, with ¢—7¢,—2°1 and 8=740 as arguments, gives I.03 mm. as the value of the last term of the expression for Hence we have the vapor pressure, f=8.15— 1.03 =7.12mm. ‘The value of the temperature in Table 40, corresponding to this vapor pressure, is the dew-point d = 6°3 C. TaBLe 45. Relative humidity —Temperature Centigrade. Table 45 gives the relative humidity of the air in hundredths, having given the air temperature ¢ and the dew-point d in Centigrade degrees. It is computed by the formula Relative humidity = PP f and F being the maximum pressures of aqueous vapor corresponding to the temperatures d and /as given in Tables 36 and 43. The top argument is the dew-point d, extending by 5° intervals from ales LOLsOm Ce. The side argument is the depression of the dew-point ¢—d, given for every 072 C. from o%o to 10°0; for every 075 from 10°%0 to 20°0, and for every I~ from 20:0 td 30.0: Example: Given the air temperature 21° C. and the dew-point 17° C., to determine the relative humidity. With ¢—d= 4° C. for the side argument, and @—17> © for the top argument, the table gives 78 per cent as the relative humidity. REDUCTION OF SNOWFALL MEASUREMENT. The determination of the water equivalent of snowfall has usually been made by one of two methods: (a) by dividing the depth of snow by an arbitrary factor ranging from 8 to 16 for snow of different degrees of com- pactness; (4) by melting the snow and measuring the depth of the resulting water. The first of these methods has always been recognized as incapable of giving reliable results, and the second, although much more accurate, is still open to objection. After extended experience in the trial of both these methods, it has been found that the most accurate and most convenient measurement is that of weighing the collected snow, and then converting the weight into depth in inches. ‘The method is equally applicable whether the snow as it falls is caught in the gage, ora section of the fallen snow is taken by collecting it in an inverted gage. WIND TABLES. xiii TABLE 46. Tasie 46. Depth of water corresponding to the weight of snow (or rain) collected in an 8-inch gage. The table gives the depth to hundredths of an inch, corresponding to the weight of snow or rain collected in a gage having a circular collecting mouth 8 inches in diameter —this being the standard size of gage used throughout the United States. The argument is given in avoirdupois pounds, ounces and quarter ounces in order that it shall be adapted to the customary graduation of commercial scales. Example: The weight of snow collected in an 8-inch gage is 2 Ibs. 2% 0z. To find the corresponding depth of water. The table gives directly 1.18 inches. ; TABLE 47. TaBLe 47. Rate of decrease of vapor pressure with altitude. From hygrometric observations made at various mountain stations on the Himalayas, Mount Ararat, Teneriffe, the Alps, and also in balloon ascensions, Dr. J. Hann (Zeztschrift fir Meteorologie, vol. ix, 1874, p. 193-200) has deduced the following empirical formula showing the average relation between the vapor pressure /, at a lower station and / the vapor pressure at an altitude # metres above it : Vane ae ue This is of course an average relation for all times and places from which the actual rate of decrease of vapor pressure in any individual case may widely differ. Table 47 gives the values of the ratio us for values of # from 200 to We 6000 metres. An additional column gives the equivalent values of / in feet. WIND TABLES. CALCULATION OF THE MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. Lambert’s formula for the eight principal points of the compass is a SN SW) C08 45" N—S+(WE+NW—SE—SW) cos 45° a is the angle of the resultant wind direction with the meridian. E, NE, N, etc., represent the wind movement from the corresponding directions East, Northeast, North, etc. In practice instead of taking the total wind movement, it is often considered sufficient to take as proportional cat! o— xliv INTRODUCTION. thereto the number of times the wind has blown from each direction, which is equivalent to considering the wind to have the same mean velocity for all directions. If directions are observed to sixteen points, half the number belonging to each extra point, should be added to the two octant points between which it lies; for example, VV =6 should be separated into V= 3 and NE=3; ESE=4 intoH=2and SE=2. The result will be approximately identical with that obtained by using the complete formula for sixteen points. TABLE 48. Aultiples of cos 45°; form for computing the numerator and . denominator. TaBLe 49. Values of the mean direction (a) or tts complement (go°—a). . Table 48 gives products of cos 45° by numbers up to 209, together with a form for the computation of the numerator and denominator, illustrated by an example. ‘The quadrant in which a lies is determined by the follow- ing rule: When the numerator and denominator are positive, a lies between N and £. f When the numerator is positive and the denominator negative, a lies between S and £. When the numerator and denominator are negative, a lies between Sand W. When the numerator is negative and the denominator positive, a lies between VV and WV. Table 49 * combines the use of a division table and a table of natural tangents. It enables the computer, with the numerator and denominator of Lambert’s formula (computed from Table 48) as arguments, to take out directly the mean wind direction a or its complement. The top argument consists of every fifth number from 10 to 200. The side argument is given for every unit from 1 to 50 and for every two units from 50 to 150. ‘Tabular values are given to the nearest whole degree. Rule for using the table: Enter the table with the larger number (either numerator or denomi- nator) as the top argument. If the denominator be larger than the numerator, the table gives a. If the denominator be smaller than the numerator, the table gives go: —a. a is measured from the meridian in the quadrant determined by the rule given with Table 48. *From Hand-book of Meteorological Tables. By H. A. Hazen. Washington, 1888. A corrected copy of the table has been kindly furnished for the present volume by the author. WIND TABLES. xlv E le: a= ani a tan) ai meee; Table 49 gives 90° —a = 32° a— 5 53, M7, Notr.—If the numerator and denominator both exceed 150 or if either exceeds 200, the fraction must be divided by some number which will bring them within the limits of the table. The larger the values, provided they are within these limits, the : : . — 138 easier and more accurate will be the computation. For example, let tan a — a 1 The top argument is not given for 18, but if we multiply by 5 or to and obtain = or _ the table gives, without interpolation, 90° — a = 38° and a= NV 52° W. CONVERSION OF VELOCITIES. : : es TABLE 50. TABLE 50. Synoptic conversion of velocities. This table*, contained on a single page, converts miles per hour into metres per second, feet per second and kilometres per hour. The argu- ment, miles per hour, is given for every half unit from o to 78. Tabular values are given to one decimal. For the rapid interconversion of velocities, when extreme precision is not required, this table has proved of marked convenience and utility. TABLE 51. TABLE 51. Conversion of miles per hour into feet per second. The argument is given for every unit up to 149 and the tabular values are given to one decimal. TABLE 52. TABLE 52. Conversion of feet per second into miles per hour. The argument is given for every unit up to 199 and the tabular values are given to one decimal. TABLE 53. TABLE 53. Conversion of metres per second into miles per hour. The argument is given for every tenth of a metre per second up to 60 metres per second, and the tabular values are given to one decimal. TABLE 54. TABLE 54. Conversion of miles per hour into metres per second. The argument is given for every unit up to 149, and the tabular values are given to two decimals. *From Hand-book of Meteorological Tables. By H. A. Hazen. Washington, 1888. With permission of the author. xlV¥i INTRODUCTION. TABLE 55. Conversion of metres per second into kilometres per hour. The argument is given for every tenth of a metre per second up to 60 metres per second, and the tabular values are given to one decimal. TABLE 56. Conversion of kilometres per hour into metres per second. The argument is given for every unit up to 200, and the tabular values are given to two decimals. TaBLe 57. Leaufort wind scale and its conversion into velocity. The personal observation of the estimated force of the wind on an arbitrary scale is a method that belongs to the simplest meteorological records and is widely practiced. Although anemometers are used at meteor- ological observatories, the majority of observers are still dependent upon estimates based largely upon their own judgment, and so reliable can such estimates be made that for many purposes they abundantly answer the needs of meteorology as well as of climatology. A great variety of such arbitrary scales have been adopted by different observers, but the one that has come into the most general use and received the greatest definiteness of application is the duodecimal scale introduced into the British navy by Admiral Beaufort about 1800. The definitions of the successive grades of the Beaufort scale were made in terms of the effect of the wind on the sails of a full-rigged ship, so that navigators of all nations have generally acquired a very uniform and definite idea of their meaning and a very considerable expertness in the use of the scale. The Table gives the designations of the 12 grades together with several conversions of the scale into wind velocities as made by different meteorologists. A committee appointed by the Royal Meteoro- logical Society to establish a conversion of the Beaufort scale into wind velocity made a preliminary report (Quart. Journal Roy. Meteorological Soc., vol. 13, 1887), but did not consider their work sufficiently complete to present a definite conversion table. GEODETICAL TABLES. TABLE 58. Relative acceleration of gravity at sea-level at different latitudes. The formula adopted for the variation of gravity with latitude is that of Prof. Harkness * £6 =L 45 (1 — 0.002662 cos 2h) in which gy is the acceleration of the gravity at latitude ¢, and g,, the acceleration at latitude 45° S¢ 45 The table gives the values of the ratio to six decimals for every 10’ of latitude from the equator to the pole. * WM. HARKNESS: The solar parallax and its related constants. Washington, 1891. " GEODETICAL TABLES. xlvii LENGTH OF A DEGREE OF THE MERIDIAN AND OF ANY PARALLEL. The dimensions of the earth used in computing lengths of the meridian and of parallels of latitude are those of Clarke’s spheroid of 1866.* This spheroid undoubtedly represents very closely the true size and shape of the earth, and is the one to which nearly all geodetic work in the United States is now referred. The values of the constants are as follows : a, semi-major axis = 20926062 feet; log a = 7.3206875. 6, semi-minor axis = 20855121 feet; log 6=7.3192127. 2s 62 pees “2 = 0-006 76866 ; log e? = 7.8305030— Io. With these values for the figure of the earth, the formula for computing any portion of a quadrant of the meridian is Meridional distance in feet = [5.5618284] A ¢ (in degrees), — [5.0269880] cos 2¢ sin A 4, + [2.0528] cos 4¢ sin 2A 9, in which 2¢=¢,+ ¢,, A¢=$¢,—%,, $1, $= end latitudes of are. For the length of 1 degree,the formula becomes : 1 degree of the meridian, in feet = 364609.9 — 1857.1 cos 26 + 3.94 COS 49. The length of the parallel is given by the equation 1 degree of the parallel at latitude ¢, in feet = 365538.48 cos $ — 310.17 Cos 3p + 0.39 COS 59. TABLE S59. Taste 59. Length of one degree of the meridian at different latitudes. This gives for every degree of latitude the length of one degree of the meridian in statute miles to three decimals, in metres to one decimal, and in geographic miles to three decimals—the geographic mile being here defined to be one minute of are on the equator. The values in metres are computed from the relation: 1 metre = 39.3700 inches. The tabular values represent the length of an arc of one degree, the middle of which is situated at the corresponding latitude. For example, the length of an arc of one degree of the meridian, whose end latitudes are 29° 30’ and 30° 30; 1s 68.879 statute miles. TABLE 60. TaBLe 60. Length of one degree of the parallel at different latitudes. This table is similar to Table 59. * Comparisons of standards of length, made at the Ordnance Survey office, South- ampton, England, by Capt. A. R. Clarke, R. E., 1866. xlviii INTRODUCTION. TABLE 61. Duration of sunshine at different latitudes for different values of the sun's declination. Let Z be the zenith, and WA the hori- zon of a place in the northern hemisphere. FP the pole; QEO' the celestial equator; RR’ the parallel described by the sun on any given day; S the position of the sun when its upper limit appears on the horizon; PN the latitude of the place, ¢. ST the sun’s declination, 6. PS the sun’s polar distance, 90° — 8. ZS the sun’s zenith distance, z. ZPS the hour angle of the sun from meridian, ¢. y the mean horizontal refraction = 34’ approximately. s the mean solar semi-diameter = 16’ os 2=90°+7+s5=90° 50’ In the spherical triangle ZPS, the hour angle ZPS may be computed from the values of the three known side by the formula sin } ZPS = [ind GS + PZ— PS) sind ZS + PS— PZ) sin PZsin 2S or sin 2 =, [sind @-+ 8—9) sin §@— 34 #) cos ¢ cos 8 The hour angle ¢, converted into mean solar time and multiplied by 2, is the duration of sunshine. Table 61 has been computed for this volume by Prof. Wm. Libbey, jr. It is a table of double entry with arguments 8 and ¢. For north latitudes northerly declination is considered positive and southerly declination as negative. The table may be used for south latitudes by considering southerly declination as positive and northerly declination as negative. The top argument is the latitude, given for every 5° from o° to 40°, for every 2° from 40° to 60°, and for every degree from 60° to 80° The side argument is the sun’s declination for every 20’ from S 23° 27’ HOV 22097) The duration of sunshine is given in hours and minutes. To find the duration of sunshine for a given day at a place whose latitude is known, find the declination of the sun at mean noon for that day in the Nawtical Almanac, and enter the table with the latitude and declination as arguments. CONVERSION OF LINEAR MEASURES. xlix Example: To find the duration of sunshine, May 18, 1892, in latitude 49° 30’ North. From the Nautical Almanac, 6 = 19° 43’ /V. From the table, with 8=19° 43’ V and ¢=49° 30’, the duration of sunshine is found to be 15% 31”. TABLE 62. TABLE 62. Declination of the sun for the year 1894. This table is an auxiliary to Table 61, and gives the declination of the sun for every third day of the year 1894. These declinations may be used as approximate values for the corresponding dates of other years when the exact declination can not readily be obtained. Thus, in the preceding example, the declination for May 18 may be taken as approximately the same as that for the same date in 1894, viz. 19° 37’. RELATIVE INTENSITY OF SOLAR RADIATION AT DIFFERENT LATITUDES FOR DIFFERENT SEASONS OF THE YEAR. TasLe 63. WWean vertical intensity for 24 hours of solar radiation J and the solar constant A in terms of the mean solar constant A,. This table is that of Prof. Wm. Ferrel, published in the Axnwal Report of the Chief Signal Officer, 1885, Part 2, and in Professional Papers of the Signal Service, No. 14, where the formulz and constants will be found. It gives the mean vertical intensity for 24 hours of solar radiation / in terms of the mean solar constant 4, for each tenth parallel of latitude of the northern hemisphere, and for the first and sixteenth day of each month ; also the values of the solar constant 4 in terms of 4,, and the angular motion of the sun in longitude for the given dates. CONVERSION OF LINEAR MEASURES. The relation here adopted between the metre and the English measures of length is that used and officially authorized by the U. 5. Bureau of Weights and Measures, viz: I metre = 39.3700 inches. TABLE 64. TABLE 64, Inches into millimetres. The argument is given for every hundredth of an inch up to 32.00 inches, and the tabular values are given to hundredths of a millimetre. A table of proportional parts for thousandths of an inch is added on each page. Example: To convert 24.362 inches to millimetres. The table gives (p. 184) (24.36 + 0.02) inches= (618.75 + 0.05 mm.) = 618.80 mm. 1 INTRODUCTION. TABLE 65. Millimetres into inches. From o to 4oo mm. the argument is given to every millimetre, with subsidiary interpolation tables for tenths and hundredths of a millimetre. The tabular values are given to four decimals. From 400 to 1000 mm., covering the numerical values which are of frequent use in meteorology for the conversion of barometric readings from the metric to the English barometer, the argument is given for every tenth of a millimetre, and the tabular values to three decimals. : Example: To convert 143.34 mm. to inches. The table gives 143 + .3 + .04 mm. = 5.6299 + 0.0118 + 0.0016 inches = 5.6433 inches. TABLE 66. feet into metres. From the adopted value of the metre, 39.3700 inches— 1 English foot = 0.3048006 metre. Table 66 gives the value in metres and thousandths (or millimetres) for every foot from o to 99 feet; the value to hundredths of a metre (or centimetres) of every 10 feet from 100 to 4ooo feet ; and the value to tenths of a metre of every 10 feet from 4000 to gogo feet. In using the latter part, the first line of the table serves to interpolate for single feet. Example: To convert 47 feet 7 inches to metres. 47 feet 7 inches = 47.583 feet. The table gives 47 feet = 14.326 metres. By moving the decimal point, 0.583 « = 0.178 47.583 feet = 14.504 metres. TABLE 67. Metres into feet. I metre = 39.3700 inches = 3.280833 + feet. From o to 500 metres the argument is given for every unit, and the . tabular values to two decimals; from 500 to 5000 the argument is given to every 10 metres, and the tabular values to one decimal. The conversion for tenths of a metre is added for convenience of interpolation. Example: Convert 4327 metres to feet. The table gives (4320 + 7) metres = (14173.2 + 23.0) feet = 14196.2 feet. CONVERSION OF MEASURES OF TIME AND ANGLE. li TABLE 68. Miles into kilometres. TABLE 68. 1 mile = 1.609347 kilometres. The table extends from o to 1000 miles with argument to single miles, and from rooo to 20000 miles for every 1000 miles. The tabular quantities are given to the nearest kilometre. TABLE 69. Kilometres into miles. TABLE 69. 1 kilometre = 0.621370 mile. The table extends to 1000 kilometres with argument to single kilo- metres, and from 1000 to 20000 kilometres for every 1000 kilometres. Tabular values are given to tenths of a mile. Example: Convert 3957 kilometres into miles. The table gives (3000 + 957) kilometres = (1864.1 + 594.7) miles = 2458.8 miles. TABLE 70. LInterconversion of nautical and statute miles. TABLE 70. The definition of the nautical mile here used is that adopted by the U. S. Coast and Geodetic Survey. A nautical mile is equal to the length of one minute of arc on the great circle of a sphere whose surface is equal to the surface of the earth. Computed on Clarke’s spheroid of 1866, the nautical mile thus defined equals 6080.27 feet. (/efort, U. S. Coast Survey, 1881, page 354.) The table gives, for nautical and statute miles from 1 to 9, the equivalent in statute and nautical miles, respectively, to four decimals. TABLE 71. TABLE 71. Continental measures of length with their metric and English equivalents. This table gives a miscellaneous list of continental measures of length alphabetically arranged, with the name of the country to which they belong and their metric and English equivalents. CONVERSION OF MEASURES OF TIME AND ANGLE. TABLE 72. Arc into time. i = = 07067. TABLE 72 Example: Change 124° 15’ 24”7 into time. From the table, 124: a Soo OC 15/ — I oO 24” = 1.600 Cn — 047 Soap A047 lii INTRODUCTION. TABLE 73. Time into are. 8 ee Example: Change 84 17™ 18647 into arc. From the table, gh = 120° Ww = 4 15) 1s = re 0.64 = 9.60 By moving the decimal point, .0co7 = 0.10 124° 15 24:7 TABLE 74. Days into decimals of a year and angle. The table gives for the beginning of each day the corresponding decimal of the year to five places. Thus, at the epoch represented by the beginning of the 15th day, the decimal of the year that has eiapsed since January 10 : , I : : is computed from the fraction rae . The corresponding value in angle obtained by multiplying this fraction by 360°, is given to the nearest minute. Two additional columns serve to enter the table with the day of the month either of the common or the bissextile year as the argument, and may be used also for converting the day of the month to the day of the year, and vice versa. Example: To find the number of days and the decimal of a year between February 12 and August 27 in a bissextile year. Aug. 27: Day of year = 240; decimal of a year = 0.65435 BRED: 125 hae Ask eM hah = 0.11499 Interval in days =197; interval in decimal of a year =0.53936 The decimal of the year corresponding to the interval 197 days may also be taken from the table by entering with the argument 198. TaBLe 75. fours, minutes and seconds into decimals of a day. The tabular values are given to six decimals. Example: Convert 55 24™ 23%4 to the decimal of a day: Sty) sOl208ec8 2447 = 016667 22 266 By interpolation, or by moving the decimal for 48 0.4 = 5 612352 71 CONVERSION OF MEASURES OF TIMB AND ANGLE. liii TaBLe 76. Decimals of a-day into hours, minutes and seconds. OEE y Example: Convert 04225 271 to hours, minutes and seconds : 0.22 day = 4" 48™ + 28™ 48% = 55 16™ 488 0.0052 day = 7™ 12° + 17528 = 7) £20.25 0.000071 day = 6805 + 0.09 = 6.14 55 24™ 2394 TaBLE 77. Minutes and seconds into decimals of an hour. yen a The tabular values are given to six decimals. Example: Convert 34™ 287 to decimals of an hour. ati O500067 238 = 7778 oy = 194 0.574.639 TABLE 78. Mean time at apparent noon. cays This table gives the time that should be shown by a clock when tlic sun crosses the meridian, on the rst, 8th, 16th, and 24th days of each month. ‘The table is useful in correcting a clock by means of a sun-dial or noon-mark. Example: To find the correct mean time when the sun crosses the meridian on December 15, 1891. The table gives for December 16, 118 56™. By interpolating, it is seen that the change to December 15 would be less than one-half minute ; the correct clock time is therefore 4 minutes before 12 o’clock noon. ; ; : TABLES 79, 80. TABLE 79. Sidereal time into mean solar time. TABLE 80. Mean solar time into sidereal time. According to Bessel, the length of the tropical year is 365.24222 mean solar days,* whence 365.24222 solar days = 366.24222 sidereal days. Any interval of mean time may therefore be changed into sidereal time by increasing it by its part, and any interval of sidereal time I 365.24222 may be changed into mean time by diminishing it by its ; *The length of the tropical year is not absolutely constant. The value here given is for the year 1800. Its decrease in 100 years is about 0.6s. liv INTRODUCTION. Table 79 gives the quantities to be subtracted from the hours, minutes and seconds of a sidereal interval to obtain the corresponding mean time interval, and Table So gives the quantities to be added to the hours, minutes and seconds of a mean time interval to obtain the corresponding sidereal interval. The correction for seconds is sensibly the same for either a sidereal or a mean time interval and is therefore given but once, thus forming a part of each table. Examples : Change 14" 25™ 3652 sidereal time into mean solar time. Given sidereal time 144 o5™s 2022 Correction for 14 ee on 2a =— 4.10 3682 =— IO —— 2 20.or amie 21.8 Corresponding mean time — 14 23. s1ae4! 2. Change 13" 37™ 2257 mean solar time into sidereal time. Given mean time a 130 37 oos7 Correction for 12" =—= = omy 13212 Bas =-+ 6.08 2257, = + 0.06 ape ytAee7, =e 14.3 Corresponding sidereal time = 13) 330), | 37-0 MISCELLANEOUS TABLES. DENSITY OF AIR AT DIFFERENT TEMPERATURES, HUMIDITIES AND PRESSURES. The following tables (81 to 86) give the factors for computing the density of air at different temperatures, humidities and pressures. The formula from which they have been computed is, in metric measures, 3 — 0:001 29305 (i7arrrons..i| (eas t -O1008'07+7 760 in which 6 is the weight of a cubic centimetre of dry air expressed in grammes, under the standard value of gravity at latitude 45° and sea level. 6 is the barometric pressure in millimetres. é is the pressure of aqueous vapor in millimetres. # is the temperature in Centigrade degrees. For dry atmospheric air (containing 0.0004 of its weight of carbonic acid) at a pressure of 760 mm. and temperature 0° C., the absolute density, MISCELLANEOUS ‘TABLES. lv or the weight of one cubic centimetre, is 0.00129305 gramme. _ (Inter- national Bureau of Weights and Measures: Zvavaux et Mémoires, t. I, p. A 54.) In English measures, the formula becomes ~ IX 0.0020389 (¢— 32°) 29.921 0.001 29305 b — 0.378 a where 4 is defined as before, but 6 and e are expressed in inches and ¢ in Fahrenheit degrees. Thus by the use of tables based on these two formule, lines of equal atmospheric density may be drawn for the whole world (neglecting slight variations in gravity), whether the original observations are in English or metric measures. Prof. Cleveland Abbe has kindly fur- nished for the present volume the logarithms of the density given in the accompanying tables (81 to 86). TABLE 81. TABLE 81. Density of air at different temperatures Fahrenheit, This table gives the values and logarithms of the expression 0.00129305 7 0.0020389 (¢ — 32°) for values of ¢ extending from — 45° /% to 140° /, the intervals between o Ff, and 110° /. being 1° The tabular values are given to five significant figures. TABLES 82, 83. Density of air at different humidities and pressures—English measures. TABLE 82. TZerm for humidity; auxiliary to Table 83. —WO53 70 € 29.921 Table 82 gives values of 0.378 e to three decimal places as an aid to the use of Table 83. The argument is the dew-point given for every degree from — 40° /. to 140° / A second column gives the corresponding values of the vapor pressure (¢) according to Broch. b TABLE 83. Values of Table 83 gives values and logarithms of ae = e188 for values 29.921 29.921 of 4 extending from 10.0 to 31.7 inches. The logarithms are given to five significant figures and the corresponding numbers to four decimals. Example: The air temperature is 68° /., the pressure is 29.36 inches and the dew- point 51° #. Find the logarithm of the density. Table 81, for = 68° /., gives 7.08085 — 10 Table 82, for dew-point 50°, gives 0.378 e = 0.141 inch, Table 83, for 4 = 6 — 0.378 ¢ = 29.36 — 0.14 = 29.22, gives 9.98941 — 10 30 Logarithm of density = 7.07056 — 10 lvi INTRODUCTION. TABLE 84. Density of air at different temperatures Centigrade. This gives values and logarithms of the expression 0.001 29305 Ste 2S Teo loos OTT for values of ¢ extending from — 34° C. to 69° C. The tabular values are given to five significant figures. Density of air at different humidities and pressures—Metric measures. TABLE 85. Zerm for humidity: values of 0.378e. 56 — 0.378 760 Table 85 gives values of 0.378e¢ to hundredths of a millimetre for dew- points extending by intervals of 1° from — 30° C. to 50° C. ‘The values of Broch’s vapor pressures (¢) corresponding to these dew-points are given in a second column to hundredths of a millimetre. The table is thus conveniently used when either the vapor pressure or the dew-point is known. : : h —0o. Table 86 gives values and logarithms of a Yims for values of 760 760 h extending from 300 to 800mm. ‘The barometric pressure 4 is the barom- eter reading corrected for temperature and 0.378 e is the term for humidity obtained from Table 85. The logarithms are given to five significant figures and the corresponding numbers to four decimal places. TABLE 86. Values of = TABLE 87. Conversion of avotrdupots pounds and ounces into kilogrammes. The latest comparisons made by the International Bureau of Weights and Measures between the Imperial standard pound and the ‘‘kilogramme proto-type’’ result in the relation : I pound avoirdupois = 453.592 4277 grammes. This value has been adopted by i. United States Bureau of Weights and Measures and is here used. For the conversion of pounds, Table 87 gives the argument for every tenth of a pound up to 9.9, and the tabular conversion values to ten-thousandths of a kilogramme. For the conversion of ounces, the argument is given for every tenth of an ounce up to 15.9, and the tabular values to ten-thousandths of a kilo- gramme. TABLE 88. Conversion of kilogrammes into avoirdupots pounds and ounces. From the above relation between the pound and the kilogramme, 1 kilogramme = 2.204622 avoirdupois pounds. —= 35.274 avoirdupois ounces. MISCELLANEOUS TABLES. ; lvii The table gives the value to thousandths of a pound of every tenth of a kilogramme up to 9.9; the values.of tenths of kilogrammes in ounces to four decimals ; and the values of hundredths of a kilogramme in pounds and ounces to three and two decimals respectively. 3 spice TABLES 89, 90. TABLE 89. Conversion of grains into grammes. TABLE 90. Conversion of grammes into grains. From the above relation between the pound and the kilogramme, I gramme = 15.432356 grains. I grain = 0.06479892 gramme. Table 89 gives to ten-thousandths of a gramme the value of every grain from 1 to gg, and also the conversion of tenths and hundredths of a grain for convenience in interpolating. Table 90 gives to hundredths of a grain the value of every tenth of a gramme from 0.1 to 9.9, and the value of every gramme from 1 to 99. The values of hundredths and thousandths of a gramme are added as an aid to interpolation. J The computation of these two tables has been furnished by Professor William Libbey, who has ysed the relation, 1 gramme = 15.432 531 grains. This value is practically identical with the relation above adopted, differing from it by about 1 part in 3,000,000. TABLE 91. Conversion of units of magnetic intensity. cme, This table gives the conversion factors from 1 to 9 for converting Eng- lish measures of magnetic intensity into C. G. S. measures, and vice versa. The English unit of magnetic intensity is the force which, acting for I second on a unit of magnetism associated with a mass of 1 grain, produces a velocity of 1 foot per second. The C. G. S. unit of magnetic intensity is the dyne—the force which, acting upon one gramme for 1 second, generates a velocity of 1 centimetre per second. The Gaussian unit of magnetic intensity, which has been extensively used, is a force which, acting upon a mass of 1 milligramme for I second, generates a velocity of 1 millimetre per second. By using the dimensions of magnetic intensity [3/12 Te the inter- conversion of these units is easily made. tr ¢. GG. S: anit = Gaussian units 10 = 10 Gaussian units TC enon unit = J 15-492956 M Rnglish units .03280833 L = 21.6882 English units lviii INTRODUCTION. TABLE 92. Quantity of water corresponding to given depths of rainfall. This table gives for different depths of rainfall over an acre and a square mile the total quantity of water measured in imperial gallons and tons respectively. TABLE 93. Dates of Dove's pentades. For tabulating and averaging meteorological data, Dove divided the year into seventy-three intervals of five days each, which have been called, Dove’s pentades, and this system of averaging has been used in the publication of a very considerable amount of meteorological data. ‘Table 93 gives the initial and terminal dates of each pentade throughout the year. TABLE 94. Division by 28 of numbers from 28 to 867 972. TaBLe 95. Division by 29 of numbers from 29 to 898 971. TABLE 96. JLiviston by 31 of numbers from 31 to 960 969. The frequent occasion in meteorological work to divide by the numbers 28, 29 and 31 renders useful the division tables compiled by Mr. H. A. Hazen (Handbook of Meteorological Tables, Washington, D. C., 1888), the use of which has been kindly granted. As here printed, the dividend is given in plain type and the quotient in heavy-face type, and in order that one shall never be mistaken for the other, a column is given containing the letters D and Q successively, which designates that all figures on a line with D are dividends, and all on a line with Q are quotients. The four columns to the right of this D-Q column give the last two figures of the dividend and of the quotient, namely, the units and tens. ‘The ten columns to the left side of the D-Q column give the preceeding figures of the dividend, namely, the hundreds, thousands, and tens of thousands. ‘These two parts of the dividend—to the left and right of the D-Q column—are always to be taken on the same horizontal line. Kach dividend is an exact multiple of the divisor, hence each quotient is exact or without remainder. For example, the dividend 17360 in Table 94 is found in two parts ; 173 is found in the column headed 600 on the left-hand side of the D-Q column, and 60 in the same horizontal row in the third column on the right- hand side. The hundreds figure of the quotient is given in bold-face type at the top, middle and bottom of the page, and each one obtains for all the dividend figures in its own column. ‘The units and tens figures of the quotient are found, as already stated, on the right side of the D-Q column directly under the last two figures of the dividend. ‘Thus in the above example, for dividend 17360 the hundreds figure of the quotient is 6 and the units and tens will be 20, or the quotient of 17360 divided by 28 is 620. When any given dividend MISCELLANEOUS ‘TABLES. lix is not an exact multiple of the divisor, the nearest even multiple as given in the table must be used. For example, 23979 + 28 =856; the 8 is in the 9th column above 239 and the 56 is under 68, the nearest figure to 79 in the right-hand part of the table. The last column, which is separated from the rest of the table by a triple line, is to be used when the quotient exceeds three figures, or 999. The bold-face figures in this column give the thousands and tens of thousands figures of the quotient, and the plain figures are the multiples thereof by the divisor. To use the column, find in it the number which, with three ciphers added, comes nearest to (but is less than) the dividend ; the heavy-face figures beneath it will be the first figures of the quotient. Subtract this multiple number from the given dividend, and with the remainder enter the main body of the table to obtain the last three figures of the quotient as already described. For example: Divide 833885 by 28. The nearest figure to 833000 in the last column is 812000 and the quotient 29000. 833885 — 812000 = 21885. Under 218 we have 7, and under 96, the nearest figure to 85 on the right, we find 82. 833885 + 28 = 29782. TABLE 97. TaBLce 97. Natural sines and cosines. TABLE 98. Taste 98. Natural tangents and cotangents. : TABLE 99. TasBLe 99. Logarithms of numbers. TABLE 100. TasLe 100. List of meteorological stations. This list of meteorological stations has been compiled for this volume from data furnished by the United States Weather Bureau. A geographical arrangement has been adopted as being most serviceable for the purposes for which the table will most generally be used. In making the selection of stations from the vast number available, the object has been to choose such of the higher order stations as will fairly represent the varied climatic conditions of each country. With few excep- tions, the stations are active; in all cases there are published observations, which may generally be found in the monthly and annual reports ‘of the national meteorological services of the countries in which the stations are situated, or by which they are politically controlled. So far as known, the list contains all first order stations, z. e., those at which the principal meteorological elements are either recorded continuously and automatically, or are observed at hourly or bi-hourly intervals; such stations are designated by an asterisk (**). The names of the stations have been given in the native orthography, which is in all cases the form adopted by the national meteorological service in its official publications. GEORGE E. CURTIS. THERMOMETRICAL TABLES. Conversion of thermometric scales — ! Reaumur scale to Fahrenheit and Centigrade Busts Fahrenheit scale to Centigrade se te Centigrade scale to Fahrenheit . ... . Centigrade scale to Fahrenheit, near the boiling point of WaALCE S75 “s< Differences Fahrenheit to differences Centigrade Differences Centigrade to differences Fahrenheit Reduction of temperature to sea level— English measures Reduction of temperature to sea level — Metric measures Correction for the temperature of the mercury in the ther- mometer stem. For Fahrenheit and Centigrade ther- mometers TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE ww TABLE 1. REAUMUR SCALE TO FAHRENHEIT AND CENTIGRADE. _ : Fahrenheit | Centigrade || j,y, | Fahrenheit |Centigrade Fahrenheit Centigrade ° ° +212°00 |+100%00 |] +40° | +122°00 | +50°00 209.75 | 98.75 39 | 119.75 | 48.75 207.50 97-50 | 38 117.50 47.50 205.25 96.25 |} 115.25 46.25 203.00 95.00 x 113.00 | 45.00 +32°00 |= ofoo 29.75 |— 1-25 27.50 2.50 25.25 3-75 23.00 5-00 on Sra anhoerai +200.75 |+ 93-75 ff +110.75 | +43.75 +20.75 |— 6.25 198.50 92.50 é 108.50 42.50 18.50 7.50 196.25 91.25 Ee 106.25 16.25 8.75 194.00 g0.00 |; 104.00 : 14.00 10.00 191.75 88.75 1OI.75 75 |] Tr75 |e L25 TNT ONT ST HNW fp mI NO HW bH H ° +189.50 87.50 jf + 99.50 3 | + 9.50 |—I2.50 187.25 86.25 97-25 36. 7325 13.75 185.00 85.00 95.00 ; | 5.00 15.00 182.75 83.75 | 92.75 3-75 |i 2.75 16.25 180.50 82.50 | g0.50 : | + 0.50 17.50 on beYannhaba? +178.25 81.2: 88.25 25 | ‘ —18.75 176.00 30. / 86.00 30. : 20.00 L73e75 : | : 83.75 | 75 Il : 21.25 171.50 .50 | 81.50 aC : 22.50 169.25 125, | 79.25 125 | ' 23.75 o +167.00 Taye 77.00 5. | ae —25.00 164.75 ; 74.75 -75 ill Bs 26.25 162.50 . 72.50 27.50 160.25 : 70.25 28.75 158.00 70. 68.00 00 | .00 | 30.00 | | +155-75 65-75 75 Il 4.25 |—31.25 153.50 Z 63.50 | ; 50 | 32.50 151.25 : Le ail 61.25 i Hs || Seis 149.00 . 59-00 : 31.00 | 35.00 146.75 sae 56.75 ‘ 33.25 | 36.25 +144.50 at é | 35.50 | —37-50 142.25 | 39:75: fl elie 140.00 | 40.00 || .05| 0.09 137-75 | 41.25 | .10 18 135.50 a 2.50 oa 42.50 | = | +133.25 |+ 56.25 | + 25 | (43275 Mego o eae -50 | -9o 131.00 55.00 ff d 41.00 5.00 | i 49.00 | 45.00 75 | 1.35 | . | +/ ie 128.75 | 53-75 |} 38-75 3°75.) 51.25 | 46.25 ff 1.00] 1.80 126.50 52.50 | 36.50 | 50 |} 38 | 53.50 | 47.50 124.25 51.25 34-25 |+ 1.25 | ; 55-75 | 48.75 +122.00 |+ 50.00 |] + + 32.00 | + 0.00 |] —58.00 | —50.00 WWD WD WwW ww wo ol ) SMITHSONIAN TABLES. TABLE 2. FAHRENHEIT SCALE TO CENTIGRADE. Cc. Cc. Cc. Cc c. Cc. Cc Cc. Cc. Cc. +54°44 | +54°50 | +54°56 | +54°61 | +54°67 | +54°72 | +54°78 | +54°83 | +54°89 | +54°94 | 53:89] 53-94] 54-00] 54.06] 54.11] 54.17] 54.22] 54.28] 54.33] 54.39] 53°3 53-39| 53-44] 53-50] 53-56] 53.61] 53-67] 53.72] 53-78] 53-83 52.78| 52.83} 52.89] 52.94] 53.00] 53.06] 53.11] 53.17| 53-22 53-28 | 52.22| 52.28] 52.33] 52.39] 52.44] 52.50] 52.56] 52.61] 52.67] 52.72 | | +51.78 | +51.83 | +51.89 | +51.94 | +52.00 | +52.06 | +52.11 | +52.17 ; f SLO Sessile 5L SO SL MAl 5.501)" 50-501|| Fier 50.56] 50.61] 50.67! 50.72] 50.78] 50.83] 50.89] 50.94] 51.00} 51.06 50.00] 50.06] 50.II}| 50.17] 50.22] 50.28] 50.33] 50.39] 50.44| 50.50 49-44) 49-50) 49.56| 49.61) 49.67] 49.72] 49.78] 49.83] 49.89] 49.94 +48.89 | +49.94 | +49.00 | +49.06 | +49. 11 | +49.17 | +49.22 | +49.28 | +49.33 | +49.39 48.33| 48.39] 48.44] 48.50] 48.56] 48.61] 48.67| 48.72] 48.7 48.83 47.78| 47-83| 47-89] 47.94| 48.00] 48.06] 48.11] 48.17] 48.22] 48.28) 47.22] 47-28] 47-33] 47-39| 47-44] 47-50| 47.56] 47.61| 47.67] 47.72 72| 46.78) 46.83] 46.89] 46.94] 47.00] 47.06] 47.11] 47.17} +46. 11 | +46. 17 | +46.22 | +46.28 | +46.33 | +46.39 | +46.44 | +46.50 | +46.56 | +46.61 45.56| 45-61) 45.67] 45.72| 45-78] 45.83} 45-89] 45.94] 46.00] 46.06 | 45.00| 45.06) 45-11] 45.17] 45.22] 45.28) 45.33] 45-39] 45-44] 45.50 44.44| 44.50] 44.56] 44.61] 44.67] 44.72| 44.78] 44.83] 44.89] 44.94] 43-89| 43-94| 44-00} 44.06] 44.11] 44.17] 44.22] 44.28] 44.33] 44.39 | +43.33 | +43-39 | +43-44 | +43.50 | +4356] 4-43-61 | +43.67 | +43.72 | +43-78 | 143-83 | 2.78 2.83] 42.89] 42.94] 43.00 43.06 | 43.00) (43007! 143322) 7432281 42.22 2.28)|" (42°33 2.39| 42.44] 42.50] 42.56} 42.61] 42.67} 42.72] 41.67] 41.72] 41.78} 41.83] 41.89] 41.94] 42.00] 42.06) 42.11] 42.17] AIL] 41.17] 41.22] 41.28] 41.33] 41.39] 41.44] 41.50] 41.56 41.61 | sil +40.56 | +40.61 | +40.67 | +40.72 | +40.78 | +40.83 | +40.8g | +40.94 | +41.00 +41.06 | 40.00] 40.06} 40.11] 40.17] 40.22] 40.28} 40.33] 40.39| 40.44] 40.50) 39-44| 39-50) 39-56] 39.61] 39.67] 39-72} 39-78] 39.83) 39-89] 39-94 | 38.89} 38.94 39-00 | 39-06 BOnnl 33 ). 17} 39:22 39.28 39-33 39-39 38.33| 38-39] 38-44] 38.50] 38.56] 38.61| 38.67] 38.72]. 38.7 38.83 | +37.78 | +37-83 | +37-89 | +37-94 | +38.00 +38.06 | +38.11 | +38.17 | +38.22 | +38.28 37-22| 37-28| 37-33} 37-39] 37-44] 37-50] 37-56] 37-61] 37-67) 37-72 36.67| 36.72] 36.78] 36.83] 36.89] 36.94] 37.00] 37.06] 37.11} 37-17 36.11} 36.17} 36.22] 36.28} 36.33] 36.39] 36.44] 36.50] 36.56 36.61 35:50) 35-91) 35 67| 35-72| 35-781 35-83| 35-89] 35-94| 36.00] 36.06 435.00 | +35.06 | 135-11 | +35.17 | +35-22]+35-28 | +35-33 | +35-39 | +35-44 | 35-50 | 34.44! 34.50) 34.56] 34.61] 34.67] 34.72] 34.78| 34.83] 34.89] 34-94) 33.89} 33-94| 34.00] 34.06] 34.11] 34.17] 34.22] 34.28 34-33] 34-39) 33-33 33-39) 33-44) 33-50} 33-56] 33-61) 33-67) 33-72] 33-78] 33-83 22.7 32.83} 32-89] 32.94] 33-00] 33.06] 33.11] 33.17] 33-22| 33-28 4-32.22 |+32.28 | +32.33 | $32.39 | +32.44 | +32.50 | +32.56 | +32.61 | +32.67 | +32.72 | 31.67 31.72 | 31.78] 31.83] 31.89] 31.94] 32.00| 32.06] 32.II| 33.17 Silat 31-17 | 31.22] 31:28) 21-331 35-39] 35.441 3-50) 31.56) 35-65 30.56| 30.61} 30.67) 30.72] 30.78] 30.83] 30.89] 30.94] 31.00 31.06 30.00! 30.06} 30.11 30.17| 30.22] 30.28] 30.33] 30.39] 30.44] 30.50 | | | 129.44 | +29. 50 | +29.56 | +29.61 | +29.67 | +29.72 | +29.78 | +29.83 | +29.89 | +29.94 25.59| 28.94| 29.00] 29.06] 29.11] 29.17] 29.22| 29.28] 29.33] 29.39 28.33 | 28.39] 28.44] 28.50) 28.56] 28.61| 28.67| 28.72) 28.78| 28.83 27.78| 27.83] 27.89] 27.94] 28.00] 28.06) 28.11] 28.17] 28.22] 28.28 27.22} 27.28| 27.33] 27.39| 27-44] 27.50] 27.56 | 27-61), °27:67 |) 27.72) +26.67 | +26.72 | +26.78 | +26.83 | +26.89] +26.94 | +27.00 | +27.06 | +27.11 | +-27.17 | | | [5 ey eS es ee ees Perr ty. 48-0) cowl .0 4 ay eS ae 5 | 6 SMITHSONIAN TABLES, TABLE 2. FAHRENHEIT SCALE TO CENTIGRADE. 3 4 5 8 Cc. C. Cc. Cc. 426% 72 | +26°78 | +26°83 | +26°89 | +26°94 427°00 27°11 26.28} 26.33] 26.39 26.56 25.72) 257Omme5.o3 26.00 25.17 )|| 25.22) 225.28 25-44] 25.50 24.61} 24.67] 24.72 24.89] 24.94 +24.06 | +24.11]+24.17 +24.33 | +24.39 23.50| 23.56] 23.61 227 O23 OR 22.94| 23.00] 23.06 22°22 ees 25 22.39| 22.44] 22.50 22567) 822072 21.83| 21.89] 21.94 22.11 | 22.07, +21.28 | +21.33 ]+21.39 +21.56]-+21.61 20.72| 20.78] 20.83 21.00] 21.06 20.17] 20.22} 20.28 20.44] 20.50 19.61} 19.67] 19.72 19.89| 19.94 19.06] 19.11] 19.17 19.33} 19.39 +18.50 | +18.561+18.61 +18.78 | +18.83 17.94] 18.00] 18.06 18.22} 18.28 17.39| 17.44] 17.50 W7.67| Lye72 16.83} 16.89] 16.94 L72LU)|) L7el7 16.28] 16.33] 16.39 16.56| 16.61 +15.72 | +15.78]+15.83 +16.00 | +16.06 15.17| 15.22] 15.28 15-44] 15.50 14.61| 14.67] 14.72 14.89} 14.94 14.06)|| SI4 TE TAL 14.33| 14.39 13.50| 13.56] 13.61 0307 13.83 +12.94 | +13.00]-+13.06 +13.22 | +13.28 12.39] 12.44] 12.50 12:67)|) 12.72 11.83] 11.89] 11.94 T2500) Les 11.25), T3313 TL-50)|) Leon 10.72| 10.78] 10.83 II.00| 11.06 +10.17 | +10.22}+10.28 +10.44 | +10.50 9.61| 9.67] 9.72 9.89} 9.94 9.06} 9.II} 9.17 9-33} 9-39 8.50 8.56 8.61 8.78 8.83 7.94 8.00 8.06 8.22 8.28 + 7.39|+ 7-44|+ 7-50 + 7.67|+ 7-72 6.83 6.89 6.94 7a eli], 6.28 6.33 a 6.56 6.61 B72 5.78 5.83 6.00 6.06 5.17 5.22 5 28 5.44 5-50 F 4:62)/-- 4-671 4.72 + 4.89|+ 4-94 4.06; 4.11] 4.17 4.33| 4-39 3.50} 3-56] 3.61 3-78} 3-83 2.94 3.00 3.06 3.22 3.28 2.39 2.44 2.50 2.67 2.72 + 1.83/+ 1.89]+ 1.94 + 2.11 |-+ 2.17 2\}+ 1.28/+ 1.33]+ 1.39 + 1.56/-+ 1.61 + 0.72|+ 0.78]+4 0.83 +- 1.00|+ 1.06 + 0.17] + 0.22]+ 0.28|+ 0 + 0.44]+ 0.50 10.39 |= sOd 3 0.20 |i. 0122 — 0.1I]— 0.06 .00|— 0.94|— 0.89]— 0.83 — 0.67|— 0.61 1 | ae | 3 4 5 .8 9 SMITHSONIAN TABLES. TABLE 2. FAHRENHEIT SCALE TO CENTIGRADE. tO wo wHN nn & oo SMITHSONIAN TABLES. FAHRENHEIT SCALE TO CENTIGRADE. [co Tf a2] ea eee e. |. Vea Teel ce pee eee ce eameates =. Cc c c. c C. c Cc. : Cc: —28789 | —28°94 | —29°00| 29°06 | —29°11 ] —29°17 —29°22 | —29°28 | —29°33 | —29°39 | 29.44] 29.50} 29.56] 29.61] 29.67] 29.72| 29.78] 29.83] 29.89] 29.94) 30.00} 30.06] 30.11] 30.17} 30.22] 30.28] 30.33] 30.39] 30.44] 30.50] 30.56] 30.61] 30.67] 30.72] 30.78] 30.83] 30.89] 30.94] 31.00] 31.06 BI.I1 ||) 3.07) | 31.22)] | Sr-28)) Vari) si-30)|\ sr Aq) em. 50) |e 5 Ol] meaeon —31.67 | —31.72 | —31.78 | —31.83| 31.89] —31.94 | —32.00 | —32.06 | —32.11 | —32.17 32.22} 32.28) 32.33] 32-39] 32-44] 32.50] 32.56] 32.61] 32.67] 32.72 32.78| 32.83] 32.89] 32.94] 33-00] 33.06] 33.11] 33.17] 33-22] 33-28] 33-33| 33-39} 33-44) 33-50] 33-56] 33-61) 33-67] 33.72| 33-78] 33.83) 33-89] 33-94| 34-00] 34.06] 34.11] 34.17] 34.22] 34.28] 34.33] 34.39) —34-44 | —34.50 | —34.56 | —34.61 | —34.67 | —34.72 | —34.78 | —34.83 | —34.89 | —34.94 | : 35-00} 35.06] 35-11] 35-17] 35-22] 35.28] 35-33] 35-39] 35-44] 35-50| 32 | 35-56) 35.61) 35-67] 35-72] 35-78] 35-83] 35-89] 35-94] 36.00] 36.06) oa 36.11} 36.17] 36.22] 36.28] 36.33] 36.39] 36.44] 36.50] 36.56] 36.61] 34 36.67} 36.72] 36.78) 36.83] 36.89] 36.94] 37.00] 37.06] 37.II] 37.17 —35 |—37-22 | —37.28 | —37.33 | —37-39 | —37-44 | 37-50 | —37-56 | —37-61 | —37-67 | —37.72| 26 37-78 | 37-83] 37-89] 37-94] 38.00] 38.06] 38.11} 38.17] 38.22 38.28 | 37 38.33] 38.39] 38.44] 38.50} 38.56] 38.61] 38.67] 38.72] 38.78} 38.83] 38 | 38.89] 38.94) 39.00} 39.06) 39.11] 39.17} 39-22| 39.28] 39.33] 39.39) 39 | 39-44} 39-50; 39.56] 39.61] 39.67] 39.72) 39.78} 39.83] 39.89 39594) ] | —40 |—40.00 | —40.06 | —40.1I | —40.17 | —40.22 | —40.28 | —40.33 | —40.39 | —40.44 | —40.50| 4I 40.56| 40.61| 40.67] 40.72} 40.78] 40.83} 40.89] 40.94] 41.00] 41.06] 42 AI.IL] 41.17| 41.22] 41.28] 41.33] 41.39] 41-44] 41.50] 41.56 41.61, 2 41.67} 41.72] 41.78] 41.83] 41.89] 41.94] 42.00] 42.06] 42.11} 42.17] 44 42.22| 42.28 2.33) || | A2.39)|) W424 2.50] 42.56] 42.61] 42.67] 42.72] —43.22 | —43.28 —45 |—42.78 | —42.83 | —42.89 | —42.94 | —43.00 ] —43.06 | —43. 7 gE: 43-78} 43.83 | I 46 3-33} 43-39] 43-44] 43.50] 43-56] 43.61] 43.6 47 43-89] 43-94] 44.00] 44.06] 44.11] 44.17] 44.2 | 44-33] 44.39! 48 44.44| 44.50| 44.56| 44.61] 44.67| 44.72} 78| 44.83| 44.89] 44.94) 49 45.00] 45.06] 45.11] 45.17] 45.22] 45.28] 45.33] 45-39| 45-44] 45.50] é -72 | —45.78 | —45.83 | —45-89 | —45.94 | —46.00 | —46.06 | 51 46.11] 46.17| 46.22] 46.28] 46.33] 46.39| 46.44] 46.50| 46.56] 46.61 | 2 F | 46.89] 46.94] 47.00] 47.06} 47.11] 47.17]| 3 47.22| 47.28} 47.33| 47-39| 47-44] 47.50] 47.56) 47.61| 47.67] 47.72 4 47-78| 47.83! 47.89] 47.94| 48.00] 48.06] 48.11] 48.17} 48.22] 48.28] | ol Oo | _ U ou oO | _ ok On | a On oO ~sI | > on “I nN —55 |—48.33 | —48.39 | —48.44 | —48.50 | —48.56 | —48.61 | —48.67 | —48.72 | —48.78 | —48.83 56 48.89 | 48.94| 49.00] 49.06] 49.II] 49.17 49.22 49.28 49-33 | 49.39 | 57 49-44} 49.50} 49.56] 49.61| 49.67] 49.72] 49.78] 49.83] 49.89] 49.94 58 50.00} 50.06) 50.11} 50.17] 50.22] 50.28] 50.33] 50.39] 50.44] 50.50} 59 50.56| 50.61] 50.67] 50.72| 50.78] 50.83} 50.89] 50.94] 51.00] 51.06 | | | —60 [—5I.11| —51.17 | —51.22 | —51.28 | —51.33 |] —51.39 | —51-44 | —51.50 | —51.56 | —51.61 | 61 51.67| 51.72) 51.78 | 51-83) 51-89)) (51-94,| §2:00)|' 52!06'| 5250) 52507, 62 52.22| 52.28) 52.33] 52.39] 52-44} 52.50] 52.56] 52.61) 52.67] 52.72] 63 52.78] 52.83} 52.89] 52.94] 53-00] 53.06] 53.11] 53-17| 53-22] 53-281] 64 | 53-33] 53-39] 53-44] 53-50} 53-56] 53-61| 53.67) 53-72] 53-78] 53-83 | —65 | —53-39 | —53-94 | —54.00 | —54.06 | —54.11] —54.17 | —54.22 | —54.28 | —54.33 | —54.39 66 54-44] 54.50] 54.56] 54.61) 54.67] 54.72] 54.78] 54.83] 54.89] 54.94) 67 55-00] 55.06} 55.11 | 55.17 99-22 55-28} 55-33| 55-39] 55-44] 55-50|] 68 55-56) 55.61| 55-67] 55-72| 55-78} 55-83| 55-89] 55.94] 56.00] 56.06) 69 56.11| 56.17| 56.22| 56.28] 56.33] 56.39] 56.44] 56.50] 56.56] 56.61| --70 |—56.67 | —56.72 | —56.78 | —56.83 | —56.89 | —56.94 | —57.00 | —57.06 | —57.11 | —57.17]| -O oe Fy 3 4 [oh | an at 8 9 SMITHSONIAN TABLES. CENTIGRADE SCALE TO FAHRENHEIT. 0 wk F F. +-122°00]+-122°TS 120.20] 120.38 118.40} 118.58 116.60) 116.78 114.80] 114.98 +113.00]/+-113.18 III.20] I11.38 109.40} 109.58 107.60] 107.78 105.80] 105.98 +104.00}+-104.18 102.20} 102.38 100.40} 100.58 98.60} 98.78 96.80} 96.98 + 95.00] + 95.18 93-20] 93.38 91.40} 91.58 89.60] 89.78 87.80] 87.98 + 86.00] + 86.18 84.20} 84.38 82.40} 82.58 80.60} 80.78 78.80} 78.98 + 77.00} + 77.18 75-20} 75.38 73-40} 73-58 7TGO|)e7le7S 69.80} 69.98 + 68.00] + 68.18 66.20} 66.38 64.40) 64.58 62.60} 62.78 60.80} 60.98 + 59.00] + 59.18 57-20} 57-38 55-40} 55.58 53-60] 53-7 51.80} 51.98 + 50.00) + 50.18 48.20] 48.38 46.40} 46.58 44.60) 44.78 42.80] 42.98 + 41.00) + 41.18 39-20} 39.38 37-40| 37.58 35-60; 35.7 33-80] 33-98 at + 32.00] + 32.18 SMITHSONIAN TABLES, eee Lee III.92 110.12 108.32 106.52 +4-104.72 48.92 74 3 F. F. -+122°36|]+122°54 120.56) 120.74 118.76] 118.94 116.96] 117.14 115.16] 115.34 +113.36/+113.54 I11I.56} 111.74 109.76| 109.94 107.96} 108.14 106.16} 106.34 +104.36|+104.54 102.56] 102.74 100.76] 100.94 98.96} 99.14 97-16) 97.34 + 95-36] + 95-54 93-56} 93-74 91.76} 91.94 89.96} 90.14 88.16} 88.34 + 86.36] + 86.54 84.56} 84.74 82.76] 82.94 80.96} 81.14 79-16} 79.34 + 77-36 + 77-54 75-56} 75-74 73-7 73-94 71.96] 72.14 70.16] 70.34 + 68.36} + 68.54 66.56) 66.74 64.76] 64.94 62.96) 63.14 61.16) 61.34 + 59-36) + 59-54 57-56} 57-74 55-76} 55-94 53-96} 54.14 52.16] 52.34 + 50.36] + 50.54] + 50.72 48.56} 48.74 46.76} 46.94 44.96} 45.14 43.16] 43.34 + 41.36) + 41.54 39-56} 39-74 37-76| 37-94 35-96} 36.14 34-16} 34.34 + 32.36) + 32.54 “7 3 F. 122°90 121.10 119.30 117.50 115.70 +-113.90 112.10 110,30 108.50 106.70 -+-104.90 103.10 IOI.30 99-59 97-70 + 95-90 94.10 92.30 90.50 88.70 -+ 86.90 55.10 83.30 81.50 79-79 74.30 70.70 + 68.90 67.10 65.30 63.50 61.70 + 59.90 58.10 56.30 54-50 52.70 + 50.90 49.10 47.30 45-50 43-70 + 41.90 40.10 38.30 36.50 34-70 +77.90| 76.10} 72.50 F. +123°08 121.28 119.48 117.68 115.88 +114.08 112.28 110.48 108.68 106.88 +105.08 103.28 101.48 99.68 97.88 + 96.08 94.28 92.48 90.68 88.88 + 87.08 85.28 83.48 81.68 79.88 + 78.08 76.28 74.48 72.68 70.88 + 69.08 67.28 65.48 63.68 61.88 + 60.08 58.28 56.45 54.68 52.88 + 51.08 49.28 47.48 45.68 43.88 + 42.08 40.28 38.48 36.68 34.88 + 33.08 6 TABLE 3. aig 8 F. F. +123°26|+123°44 121.46] 121.64 119.66) 119.84 117.86) 118.04 116.06] 116.24 +114.26/+114.44 112.46] 112.64 110.66} 110.84 108.86] 109.04 107.06] 107.24 +105.26)/+-105.44 103.46| 103,64 101.66} ror.84 99.86] 100.04 98.06] 98.24 + 96.26) + 96.44 94.46] 94.64 92.66} 92.84 90.86} 91.04 89.06] 89.24 + 87.26) + 87.44 85.46, 85.64 83.66} 83.84 81.86) 82.04 80.06] 80.24 + 78.26] + 78.44 76.46} 76.64 74.66) 74.84 72.86| 73.04 71.06} 71.24 + 69.26) + 69.44 67.46, 67.64 65.66} 65.84 63.86] 64.04 62.06) 62.24 + 60.26} + 60.44 58.46] 58.64 56.66} 56.84 54.86) 55.04 53-06] 53-24 + 51.26) -+ 51.44 49.46] 49.64 47.66} 47.84 45.86] 46.04 44.06] 44.24 + 42.26) + 42.44 40.46} 40.64 38.66} 38.84 36.86] 37.04 35-06] 35.24 + 33-26] + 33.44 ait 8 F; +123°62 121.82) 120.02) 118.22! 116.42) +1 14.62) 112.82) 111.02 109.22) IAG +105.62) 103.82) 102.02) 100.22, 98.42 + 96.62 94.82 93-02 g1.22 89.42 + 87.62 85.82 84.02 82.22) 80.42 78.62 76.82 75.02 7.2022 71.42 + 69.62 67.52 66.02 64.22 62.42 + 60.62 58.82 57.02| 55.22 53-42 + 51.62 49.82 48.02) 46.22 44-42) oo 42.62) 40.82) 39-02) 37-22 35-42 + 33:62 a 9 | TABLE 3. CENTIGRADE SCALE TO FAHRENHEIT. —40.00 41.80 43.60 45.40 47.20 —49.00 50.80 52.60 54.40 56.20 —55.00 F. °Q | +31.82 30.02 28.22 26.42 24.62 |-+22.82 21.02 19.22 17.42 15.62 +13.82 12.02 10.22 8.42 6.62 + 4.82 == 13.02 |-+ 1.22 — 0.58 — 2.38 18. 58 20.35 —22.18 23.98 25.78 27.58 29.38 —31.18 32.98 34.78 36.58 38.38 —40.18 41.98 43.78 45.58 47.38 —49.18 | 50.98 52.78 | 54.58 56.38 F. +31°64 29.84 28.04 26.24 24.44 +22.64 20.84 19.04 17.24 15.44 +13.64 11.84 10.04 8.24 6.44 + 4.64 + 2.84 + 1.04 — 0.76 — 2.56 — 4.36 6.16 7-96 9.76 11.56 —13.36 15.16 16.96 18.76 20.56 —22.36 24.16 25.96 27.76 29.56 —31.36 33.16 34.96 36.76 38.56 —40.36 42.16 43.96 45.76 47.56 —49.36 51.16 52.96 | 54-76 56.56 —58.18 | —58.36 F. +31°46 29.66 27.86 26.06 24.26 +22.46 20.66 18.86 17.06 15.26 +13.46 11.66 9.86 8.06 6.26 + 4.46 + 2.66 + 0.86 — 0.94 — 2.74 — 4.54 6.34 8.14 9.94 11.74 —13-54 15-34 17.14 18.94 20.74 —22.54 24.34 26.14 38.74 —40.54 42.34 44.14 45-94 47.74 —49.54 51.34 53-14 | 54-94 56.74 —58.54 —49.90 51.70 53-50 55.30 57-10 —58.90 +30°92 29.12 27.32 25.52 23.72 +21.92 20.12 18.32 16.52 14.72 +12.92 Ti c2 9-32 7-52 5-72 + 3-92 + 2.12/44 == 0.32 — 1.48 — 3.28 — 5.08 6.88 8.68 10.48 12.28 —14.08 15.88 17.68 19.48 21.28 —23.08 24.88 26.68 28.48 30.28 —32.08 33.88 35.68 37-48 39.28 —41.08 42.88 44.68 48.28 —50.08 51.88 53-68 55.48 57.28 —59.08 6 ALL F. +30°74 28.94 27.14 25.34 23.54 +21.74 19.94 18.14 16.34 14.54 +12.74 10.94 9-14 7-34 5-54 3-74 1.94 O.14 1.66 — 3.46 5.26 7.06 8.86 10.66 12.46 —14.26 16.06 17.86 19.66 21.46 —23.26 25.06 SMITHSONIAN TABLES, TABLE 4. CENTIGRADE SCALE TO FAHRENHEIT—Near the Boiling Point. 5 a : F. F. F. F. | 212°72] 212°90| 213°08| 213°26| 213-44 210.92] 211.10] 211.28] 211.46| 211.64 209.12] 209.30} 209.48] 209.66 | 209.84 207.32] 207.50| 207.68] 207.86) 208.04 205.52 205.70| 205.88 | 206.06| 206.24 203.72} 203.90] 204.08} 204.26] 204.44 201.92] 202.10] 202.28] 202.46| 202.64 200.12] 200.30] 200.48 | 200.66 | 200.54 198.32] 198.50] 198.68] 198.86] 199.04| 199.22 196.52] 196.70] 196.88 | 197.06| 197.24) 197.42 194.72 | 194.90] 195-08 | 195.26 195.44 | 195-62 | TABLE 5. DIFFERENCES FAHRENHEIT TO DIFFERENCES CENTIGRADE. N @ h o N © fo) CO YAHOO, & OWNIN - WOW CON ‘oO = Cnn N™NIH 48 oO WO G2 nko bd afPPowhnd nek wnw nN ARUI WIN AH Oo Onn ake ww O10 oO» Of OV IID NHBYY Com CS am nN we TAA SIH DO Cour ~1 & Ow D SIND QU DI DAN OWI NN eH OO NO NSH DOL aonn O19! 60 ON ° 790 Mone a- tO 2.88 4.68 6.48 8.28 HO Urn: Rw NHN NHN OMI U1 G2 NN HN ND IW HOO. oO 10.08 11.88 13.68 15.48 17.28 Se Re EQ 5 OnWU Hep H f$HHHH Nw CuI HW fPOnHO POND NR NHN N NON N | Qu HO OrWUNT |. SMITHSONIAN TABLES. TABLE 7. REDUCTION OF TEMPERATURE TO SEA LEVEL. ENGLISH MEASURES. DIFFERENCES BETWEEN THE TEMPERATURE AT ANY ALTITUDE . AND AT SEA LEVEL. ALTITUDE IN FEET. 100 200 300 400 , 500 600° 700 800 | 900]1!000, 2000 3000 4000 5000 | | j | | Ref oP) Re [FS | oFs) | Sha] i ee | ona inte ge dae ees Foi a ie 0250 | 1°00 | 1250 | 2°00 | 2°50 | 3°00 | 3°50 | 4200 | 4°50] 5°00! 10°00 | 15°00 | 20°00] 25°00 0.49 | 0.98 | 1.46] 1.95 | 2.44] 2.93 | 3.41 | 3.90| 4.39 4.88 | 9-76 | 14.63 | 19.51 24.39 0.48 | 0.95 | 1.43 | 1.90] 2.38 | 2.86 | 3.33 | 3.81] 4.29] 4.76| 9.52] 14.29] 19.05 23.81) 0.47 | 0.93 | 1.40] 1.86] 2.33 | 2.79 | 3-26 | 3.72 | 4.19 | 4.65 | 9.30 | 13.95 | 18.60} 23.26! 0.45 | 0.91 | 1.36] 1.82] 2.27 | 2.73 | 3-18 | 3.64 | 4.09 4.55 | 9.09 | 13.63 | 18.18} 22.72! 0.43 | 0.87] 1.30] 1.74] 2.17] 2.61 | 3.04] 3.48] 3.91 | 4.35 | 8.70 | 13.04 17.39] 21.74 0.42 | 0.83 | 1.25 | 1.67 | 2.08 | 2.50] 2.92] 3.33 | 3.75] 4.17| 8.33 | 12.50] 16.67] 20.83, 0.40 | 0.80| I.20| 1.60] 2.00] 2.49] 2.80] 3.20| 3.60] 4.00| 8.00! 12.00] 16.00] 20.00 0.38 | 0.77] I.15| 1.54] I.92] 2.31 | 2.69] 3.08] 3.46] 3.85 | 7-69] 11.54] 15.38] 19.23) 0.37 | 0.74| 1.11 | 1.48] 1.85 | 2.22} 2.59] 2.96| 3.33] 3-70| 7-41 11.11] 14.81] 18.52! 0.36] 0.71 | 1.07] 1.43 1.79| 2 14 | 2.50| 2.86] 3.21] 3.57] 7-14] 10.71 | 14.29] 17.86] 0534] O169}| 1.03)|' 1238 -)-7.31k2707 | 2-4 | 2876) osTo 3.45 | 6.90 | 10.34| 13.79] 17.24 0.33 | 0.67 | 1.00.| 1.33} 1.67 |'2.00| 2.33, | 2:67] 3.00|/3.33)| 6.67) 10.00) 13:33 16.67, 0.32 | 0.65 | 0.97 | I.29| 1.61] 1.94] 2.26] 2.58] 2.901 3.23} 6.45) 9.68] 12.90] 16.13} 0.31 | 0.62 | 0.94 | 1.25 | 1.56| 1.87 | 2.19] 2.50] 2.81] 3.12| 6.25} 9.37] 12.50 15.62! 0.29 | 0.59 | 0.88 | 1.18 | 1.47 | 1.76 | 2.06| 2.35 | 2.65] 2.94| 5.88] 8.82] 11.76 14.71] 0.28 | 0.56 | 0.83 | 1.11 | 1.39 | 1.67] 1.94] 2.22] 2.5012.78| 5.56} 8.33] 11.11] 13.89] 0.26 | 0.53 | 0.79 | I.05 | 1.32| 1.58] 1.84] 2.10] 2.37] 2.63} 5-26] 7.89| 10.53| 13.16] 0.25 | 0.50] 0.75 | I.00,| 1 25 | 1.59] 1.75 | 2.00} 2.25 2.50 | §.00} 7.50} 10.00 12.50) 0.24 | 0.48| 0.71 | 0.95 | 1.19 | 1-43 | 1.67| 1.90| 2.14 2:38) 4.76| 7.14] 9.52 11.90 0.23 | 0.45 | 0.68 | 0.91 | 1.14] 1.36] 1.59] 1.82] 2.05] 2.27] 4-55| 6.82] 9.09] 11.36) 0.22 | 0.43 | 0.65 | 0.87 | 1.09] I.30] 1.52] 1.74] 1.96]2.17| 4-35] 6.52 8.70| 10.87] 0.21 | 0.42 | 0.62 | 0.83 | 1 4.17| 6.25| 8.33] 10.42 6.00} 8.00} 10.00 5-77| 7-69] 9.62/ 8 = 8 0.20 | 0.40 | 0.60] 0.80 | I.00| 1.20] 1.40] 1.60 0.19 | 0.38} 0.58 | 0.77 0.96 | 1.15] 1.35 | | | al 2 I .04| 1.25] 1.46| 1.67 | 1.87 I I xP PP ° Co on TS oO nN oS oO nr 0.19 | 0.37'|.0.56| 0.74'!'0,93)}' 1.11 | 1230) }.1-48))) 1.67 }1585)1! 3.701) 5.50)l 7A 220 0.18 | 0.36] 0.54 | 0.71 | 0.89] I.07 | 1.25] 1.43] 1.61] 1.79] 3-57] 5.36) 7.14] 8.93 0.17 | 0.34] 0.52 | 0.69| 0.86| 1.03 | 1.21 | 1.38] 1.55 1.72| 3-45] 5.17| 6.90] 8.62) 0.17 | 0.33 | 0.50] 0.67 | 0.83)| 1.00) 1.17.) 1233-150] 1.671) 3°33, 5:00 1116.67.) (6:33 0.16 | 0.32 | 0.48 | 0.65 | 0.81 | 0.97 | 1.13 | 1.29] 1.45] 1.61) 3-23] 4.84| 6.45] 8.06) | | 0.77 | 0.92} 1.08 | 1.23 | 1.38 0.71 | 0.86} 1.00] I.14] 1.29 A nN A w - 0.46 | 0.6 0.14 | 0.29 | 0.43 | 0.5 5 -54| 3.08| 4.62] 6.15 7-69) 43), 2.86)| ¥4520)) 5 a7 74 0.13 | 0.27 | 0.40 | 0.53 | 0.67 | 0.80 | 0.93 | 1.07 | I. 2.67] 4.00] 5.33} 6.67) 0.12 | 0.25 | 0.37 | 0.50| 0.62] 0.75 | 0.87] I.00| 1.12] 1.25| 2.50| 3.75} 5.00] 6.25 0.12 0.24 | 0.35 | 0.47 | 0.59| 0.71 | 0.82] 0.94] 1.06] 1.18] 2.35] 3-53] 4-71 5.88 tS tS NS , | O.II | 0.22 | 0.33 | 0.44 | 0.56] 0.67 | 0.78 | 0.89] I.00] 1.11 | 3-33| 4-44 5:56 Tabular values are to be added to the observed temperature to obtain the temperature at sea level. SmiTHSONIAN TABLES. 10 REDUCTION OF TEMPERATURE TO SEA LEVEL. METRIC MEASURES. AND AT SEA LEVEL. TABLE DIFFERENCES BETWEEN THE TEMPERATURE AT ANY ALTITUDE Rate of decreas of ature 100 c. 1°00 0.98 0.96 0.94 0.93 | 0.91 0.87 120 | 0.83 125 | 0.80 130 | 0.77 135 | 0.74 | LeTAGn NOL 7 | 145 | 0.69 | 150 0.67 [e555 10.05 160 | 0.62 | 170 | 0.59 | 180 | 0.56 | 190 } 0.53 | 200 | 0.50 | | 210 | 0.48 | | 220 | 0.45 230 | 0.43 | 240 | 0.42 250 | 0.40 | | 260 | 0.38 270 | 0.37 | 280 | 0.36 | 290 | 0.34 300 | 0.33 | 320 | 0.31 | | 340 | 0.29 360 | 0.28 | | 380 | 0.26 | | 400 | 0.25 | 420 | 0.24 | | 440 | 0.23 | 460 | 0.22 | 480 } 0.21 | 500 0.20 300 400 | 500. 600 Gy |e: Cc C: 3°00 | 4200 | 5:00 6200 2.94 | 3-92 | 4.90 | 5.88 2.88 3.85 | 4.81 | 5.77 2:83) | 3.775 ag2 | 5.66 2.78 | 3.70 | 4.63 | 5.56 2.73 | 3-64 | 4-55 | 5-45 2.61 | 3-48 | 4.35 | 5.22 PASO esas ae (eae | 5.00 2.40 | 3.20 | 4.00 | 4.80 2.31 | 3.08 | 3.85 | 4.62 2.22 | 2.96 | 3.70 | 4.44 2.14 | 2.86 | 3.57 | 4-29 2507) || 2-76) | 3-45_ || 4-14 2500) || 2367) 73°33 ||)4.00 1.94 | 2.58 | 3.23 | BVO7 TsO7 | 2250) |e sek 3.75 1.76 | 2.35 | 2-94 | 3-53 1.67 | 2.22 | 2.78 | 3.33 1.58 | 2.10 | 2.63 | 3.16 1.50 | 2.00 | 2.50 | 3.00 1.43 | 1.90 | 2.38 | 2.86 TagGuluxsSon| 2.27 120735 1:30 || 3.74. | 2:17 | 2.61 1.25 | 1.67 ee ae 1.20 | 1.60 } 2.00 | 2.40 1.15 | 5A) |) 1.92 | 23, Terr | T-48 |) F.85 | 2.22 1-07) | 1243 |) 1-79) ||) 25% 103°)" 1.36 | 1-72), 2.07 I-00) v1.33) |) £67, | 2:00 0.94 | 1.25 | 1.56 | 1.87 | 0.88 | 1.18 | 1.47 | 1.76 O:83) |) ILE |) 130) |) 1/07 0:79 | F.05-| I.32°} 1.58 O275 T.00 | 1.25 | 1.50 0.71 | 0.95 | I-19 | 1-43 | Goxtetsii |) KoKohe 4) aeeng P| a ce{e) 0.65 | 0.87 | I.09 | 1.30 0.62 | 0.83 | 1.04 1.25 0.50 1.00 1.20 ALTITUDE IN METRES. 0.60 | 700 Oo ~# Oe on uv 2 CO mn DW © ce Lal “IQ O 0 ann na wt BR HEEYD N oO w nan HW OH WwW ° w Ow > OW PPE Ne} NS 69 50 4I 33 19 yy PV 94 me eH Hw NN -75 .67 1.59 1.52 monn 80 | 59 | 06 | 84 | 1.46 | | 1.40 | | 800 | er 8°00 7.84 .69 55 Sy GEO Di ON ia Ny Bw we KH NK N .52 -74 1.67 1.60 Ss ee .9O | CU ONE Ons On ON Osea eh RS O WK x ow yy NNN non uw DW W GW Oo HH RH HN N .OL 62 29 00 74 50 29 .09 gI -75 .60 46 21 10 00 14 05 96 37 .50 10°00 9.80 9.62 9-43 | g. 26 9.09 8.70 8.33 $.00 7-69 7.41 7-14 6.90 6.67 6.45 6.25 5.88 5-56 5.26 5.00 4.7 4.55 4.35 4.17 8 2 Oe oo y 70 Ye eH ¢ worn nn 78 wb ww NHN W 08 OO | BR KH NHN ND ND I Io. aes 8 ANA AAI BEER yg Hoon Noun DD Tabular values are to be added to the observed temperature to obtain the temperature at sea level. SMITHSONIAN TABLES. It 3000 CG 30°00 29.41 28.85 .30 .78 27 .09 | OC 5¢ ) .OO fF eC on nn Wd to > 6 CO TABLE 9. CORRECTION FOR THE TEMPERATURE OF THE MERCURY IN THE THERMOMETER STEM. T— ¢t—0.0000795 » (t/ —¢) — Fahrenheit temperatures. T = t— 0.000143 (¢/— 7) — Centigrade temperatures. T — Corrected temperature. ? — Observed temperature. ?’— Mean temperature of the glass stem and mercury column. n — Length of mercury in the stem in scale degrees. CORRECTION FOR FAHRENHEIT THERMOMETERS. Values of 0.0000795 # (¢/ —?) WSNNN NWO U1 NO CORRECTION FOR CENTIGRADE THERMOMETERS. Values of 0.000143 (¢/—?7) 20>.) ; 50° Cc. | : Cc. °o | ° 0.03, | | 0.07 0.06 0.14 0.09 j pea O. 21 0.11 ’ | | 0.29 0.14 | “ 0.36 0.17 | : 0.43 0.20 | 0.50 0:23. | 10.3 | 0.57 0.26 | 0.64 0.29 0:72 J oe than ¢ the correction is to be eer 7 lia When 7 is 1 Tess : BAROMETRICAL TABLES. Reduction of the barometer to standard temperature — English measures TABLE Metric measures ‘ Reduction of the barometer to feeandard ari at Taide 45°— English measures TABLE Metric measures “ys Reduction of the barometer to sea Si a — Boece measures. Values of 2000 . : TABLE Correction of 2000 for ine rode! B,— B = B(10* — 1) tees Reduction of the barometer to sea level — Medic measures. Values of 2000 . TABLE Correction of 2000 for aera B,— B= B (10" — 1) é Determination of heights by the Eeromets _— erent measures. Values of 60368 [1 + 0.0010195 X 36] log = of = Ute PABER J Term for temperature 2 Correction for latitude and eee Bie mercury . Correction for an average degree of humidity Correction for the variation of gravity with altitude . Determination of heights by the barometer — Metric measures. Values of 18400 log ne TABLE 25 Term for temperature 26 Correction for humidity . : 27 Correction for latitude and meet oa mercury . 28 Correction for the variation of gravity with altitude . 29 Difference of height corresponding to a change of o.1 inch in the barometer— English measures . . TABLE 3 Difference of height corresponding to a change of 1 mulheneee in the barometer— Metric measures . . .. . . TABLE 3 Determination of heights by the barometer. Formula of Babinet : TABLE 32 Barometric pressures ere pordinie "a the jnpereee of ne boiling point of water — English measures TABLE 33 Metric measures 34 13 TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. HEIGHT OF THE BAROMETER IN INCHES. 19.5 | 20.0 | 20.5 21.0 23.0 | 23.5 Inch. | Inch. Inch. Inch. Inch. | Inch. +0.051 |+-0.052 |+0.053 |+-0.055 +0.060 |+0.061 +0.050 |+0.051 |+0.053 |+0.054 +0.059 |+0.060 .049 .050! .052 .053 ; ‘ ; .058 -059 .048} .049] .O51 .052 : : ; .057 .058 | .047| .049 .050 -O51 , ‘ .056 .057 .046 | .048 .049 .050 : : .055 -056 NN E+ maou +0.046 .047 .048 |+-0.049 +0.054 |+0.055 045} .046 -047 .048 : 5 : .053 -054 .044 .0O45 .046 -O47 : ‘ .052 .053 .043 -O44 -045 .046 : ; .O51 -052 042] .043] .044 -O45 : , -049 -O51 | | | .040 |+0.041 |+-0.042 |+0.043 |+0.044 |+o. +0.048 |+0.049 .039| .040 -O41 | .042 -043 : : ; -O47 048 £038} ..039 | “odo:| | jor SOA ee : .046 .037 .038 -039 | .040 -O41 : -O4; : -O45 .037 .038 .038 .039 -040 -O41 - 0% : +044 nf ow omone 10 601 ae VU SUG. n 0 | | | +0.037 |+0.038 -038 |+-0.039 -O40 +-0.043 | .036] .037] .038] .038]| .039| . 042 035 .036 .037 .038 .038 : : .O41 .034 .035 | .036 .037 .037 : -040 -033| .034] .035 .036 .036 . .039 | .032 +-0.033 .034 |+0.035 -035 .038 co 9° C1 O'OnS Pe Oo 0 a NY Oo BUI ON .033 .034 .034 ; : .037 .032 -033 .034 : .036 .031 .032 .033 .033 .03¢ .035 .030 .031 .032 : .034 -O3T | ~ .032 -030 | -O31 -030 | -030 029 | 9.028 |+0.028 |+-0.029 |4-0.030 }-0.031 |+0. 033 .027| .028 .025 -029 -030 : -O: .032 .026 .027 .027 .028 .029 : : .031 .025 .026| .026 .027 .028 : ; .030 .024 025 | .025 .026 .027 ‘ : .029 | | | 023 |+0.024 |+0.024 .025 .026 : k .027 .023 .023 .024 .024 .025 ‘ ; .026 -022 | .022 .023 .023 .024 : : .025 -O2] sO2T. | 3,022 -O22 -023 ° . -024 -020 -O20 | -O21 -O21 5022 e 2 -023 | | } | | | | .O1g .O1g 020 .020 .O21 .O18 .O138 | .o1g -O19 -020 .O17 .o18 .o18 .o18| .o19 .O16 .O17 .O17 sOL7, 018 .O15 -016:| 016 O16 .O17 -O14 |+0.015 |+0.015 .O16 |+0,016 O14 O14 | -O14 -O15 -O15 .O13 .O13 .O13 .OI4} .O14 .O12 .O12 .O12 .O13 .O13 .OL] OI! OI .O12 .O12 | | O10 -++-0.010 |+-0.010 ,OII |4+0.011 .009| .009|} .o10 .o10| .OI0 | .008 .008 | .009 .009| .009 .007 .008 .008 008 .008 | .006 .OO7 .007 .OO7 .007 | = oO HNN on ft & Go SMITHSONIAN TABLES. 14 TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. HEIGHT OF THE BAROMETER IN INCHES. 19250 1'20:0) 920755) 21,0) (62165) 22.0) | 2255 | 2S.0 | 23.5 Inch. Inch. | Inch. Inch. Inch. “ Inch. Inch, Inch. i+0.006 |+0.006 +0.006 |+0.006 |+0.006 |-+-0. +0.006 |+0.007 |+0.007 -005 -005| = .005 .005 .005 : .005 .005 .006 -004 “ -O04 -OO4 -OO4 : -OO4 -OO4 -005 -003 2 .003 .003 .003 : -003 .003 .003 -002 .002 -002 .002 . 002 002 .002 |+0.001 +o.oo1 |+0.001 |+-0.001 +o.oo1 |+0.001 +0.001 0.000 | 0.000} 0.000] 0. 0.000 | 0.000 | 0.000 '—0.001 |—0.001 |—0.001 —0.001 |—0.001 .OO1 .002 .002 .002| . .002 .002 .003 | .003 .003 | .003 | .003 —0.004 |—0.004 |—0.004 |—0.004 |—0.004 .004 .005 .005 .005 .005 005 | .005 .005 .006 .006 .006 .006 .0O7 .0O7 .007 | .007} .008 .008 0,008 |—0.009 —0.009 009 |) 009)”: -O10 | s010)|) -O10)|) 2018 FOU me .O12 S014" .013 | Oates w os \—0,013 |—O. .O14 .O14 : .O15 .O15 : .O16 .O16 : .O17 .O17 O18 | W G2 Gd EONS) nono —o.018 \—0.019 .O1g : .020 | .020 : .O21 .021 : .022 .022 : .023 .023 ; —0,024 .024 ; .025 | .025 : .026 iy O27 Ve. O20) |\—0.029 .030 .031 .032 | -033 ° {o) CR Gd G2 GH Go “SIND BW |\—0.034 | .035 .036 | -037 | .038 ° 0.0 Oo On —0.039 |—0.040 | .040| .O4I .O41 -042 | -042 .043 «O43, -O44 0.45 ome > & o SMITHSONIAN TABLES. TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. HEIGHT OF THE BAROMETER IN INCHES. 19.0 || 19.5 |) 20,.0'| 2075 | 21.0) 21.5 | 22.0) 22.5)|\'2a- On eor> Inch. | Inch. Inch. Inch. Inch. | Inch. Inch. Inch. Inch. Inch. —0.038 |—0.039 |—0.040 —0.041 |—0.042 |—0.043 |—0.044 |—0.045 |—0.046 |—0.047 .039 .040 O41 | .042 .043 .044 -045 .046 0.47 .048 -039 .O40 .O41 .042 -O44 -045 -046 -O47 .048 -049 -040 .O4I} .042 -043 -044 -046 -047 .048 -049 -O50 .O41 .042 -043 | .044 .045 -O47 .048 -049 .050 .O51 .042 |—0.043 |0.044 |—0.045 046 |—0.047 |—0.049 |—0.050 |—0.051 .052 .043| -044 .O45 .046 -O47 -048 -O50 .O51 .052 -053 -O44 -045 .046 -O47 .048 -O49 -O51 .052 -053 .054 -045}| .046] .047 .048 -049 .050 -052 -053 -054 .055 .045 .047| .048 .049 | 050 .O51 .053 .054 .055 .056 9.046 ;—0.047 |\—0.049 .050 —0.051 |—0.052 |—0.054 |—0.055 |—0.056 .057 .047| .048 .050} .O51 -052 .053 .055 .056 .057 .058 .048 -O49 .050 .052 .053 .054 .056 -057 .058 .059 .049 .050 .O51 -053 .054 .055 -057 .058 -059; .060 .050} .O5%| .052} .054 .055 .056 .058} .059 .060 on J NNO aod. nou ono ol a OoOnNonNoe On + + Go nnn n a a a oO Vv “SIST OV ON oun now un 0.052 |—0.053 .055 .056 |—0.057 |—0.059 .060 |—0.061 .053 .054 .055 -O57 .058 .060 .O61 .062 .064 .054 .055 .056 .058 .059 .061 .062 .063 .065 .055 .056 .057 .059 .060 .061 .063, .064 .066 .055 .057 .058| .060} .061 .062 .064| .065) .067 encn ol 5 OS no 9.056 |—0.058 |—0.059 —0.061 |—0.062 |—0.063 \—0.065 |—0.066 .057 .059 .060 .062 -063 .064 .066 .067 .069 .058 .060 .061 .062 -064 .065 .067 .068 .059 .060 .062 .063 .065 .066 .068 .069 .060 .O61 .063 .064 .066 .067 .069 .O71 061 .062 |—0.064 —0.065 |—0.067 |—0.068 0.070 | 9.072 .062 .063 .065 .066 0.68 .069 .O71 .073 | .062 .064 .066 .067 .069 .O70 .072 .063 .065 .067| .068 .070 507 U)|s O73 .064) .066 .067 | .069 .O71 -072)| .074:| 9.065 |—0,067 .068 .070 |—0.072 .073 |—0.075 .066 .068 .069 .O71 .073 .074 .076 .067 .069 .070 .072 .074 .075 LO7y .065 .069 .O7I .073 .O75 .076 .078 .069 {070} |, 2072||/4 074 .076 .077 .079 | 0.069 |—0.071 .073 |—0.075 |—0.077 |—0.078 |—0.080 | .O70 .072 .074| .076 .078 .079 .OS1 .O71 .073 .075 .077 .079 .080 .082 .072 .074 .076 .078 .079 O81 .083 .073 .075 | .077 .079 .080 .082 .084 .074 | .076 |—0.078 |—0.080 |—0.081 | 9.083 | 9,085 | .075 | .077| .079 .080 .082 .084 .086 .076 -078 | .079 O81 .083 .085 .087 .076 .078 | .080 .082 .084 .086 .088 1077 079) .O8I | -083 | .085 .087 .089 | | | .076 —0.078 .080 |—0.082 |—0.084 |—0.086 |—0.088 .0gO -077| .079 -O81 .083 .085 .087 .089 -OgI .078| .080 .082 -084 .086 .088 .0gO .092 079} .081] .083] .085] .087] .089] .og1| .093 .080 .082 .084 .086 .088 .0gO .092 NI w ONnoNne sSININI™N app w SMITHSONIAN TABLES. 16 TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. HEIGHT OF THE BAROMETER IN INCHES. | a | a | LT Inch. | Inch. Inch. Inch. .086 .088 .0gO .087 .089 -O91 .087 -0gO .092 .088 -O9I .093 —0.089 |—0.09I |—0.094 .0gO .092 .095 -093 .096 -094 | -097 -095 | -097 | —0,096 |—0.098 097 .099 -098 . 100 -099 IOI -I00| .102 IOI . 103 .102 - 104 .103 -105 .103 . 106 .107 . 109 -110 DUE e012 Dalle 114 sLr4 DES .116 Ligiy/| 118 | 11g «L2ZO 2d £22 .124 25 .126 NT 7, .128 .129 .130 .130 .132 -133 134 .108 | 122 | Inch. Inch. —0.083 |—0.085 |—0.087 |—0.089 |—0.091 |—0.093 .092 .093 .094 -095 —0.096 -097 .098 -099 . 100 -094 -095 .096 097 —o0,098 -099 .100 IOI .102 .103 -104 -105 -106 .107 .108 .109 .1IO0 Str .112 Me -II4 BLS -116 SLL, .118 119 .120 +121 .122 RI23 .124 Bias .126 3127 .128 .129 .130 <3 .132 Sra -134 a5 -136 Inch. —0.095 |—9.097 .098 * .100 101 .102 .103 .104 -105 .106 .107 .108 .109 .110 errr 112 Era .II4 “ads BLLO oy) .118 -119 -120 sL20 SMITHSONIAN TABLES. 17 TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. 7 aaa HEIGHT OF THE BAROMETER IN INCHES, 24.2 | 24.4 24.6 | 24.8 Inch. | Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch, H-0.063 +0.063 +0.064 |4-0.064 |+-0.065 |+0.065 |+0.066 |+0.066 |++0.067 |+-0.067 +0.061 ;+0.062 +0.063 |+0.063 |-+0.064 |+-0.064 |+-0.065 |+0.065 |+-0.066 |+-0.066 .060| .0o61 .061 .062 .062 .063 .063 .064 .064 .065 .059 .060 .060 | .061 .O61 -062 .062 .063 .063 .064 £0558 .059 .059 .060 .060 .O61 .O61 .062 .062 .063 -057 .058} .058]) .059 .059} .059} .060] .060] .o61 061 oy “oO o ONDNO NONUON ONOMNOS UOMO RHR .056 |+0.056 |+0.057 |+-0.057 |+-0.058 |+0.058 |+0.059 |+-0.059 |+-0.060 |+0.060 -055 -055 .056 .056 .057 .057 .058 .058 .059 -059 .054 .054 -055 .055 .056 .056 .057 .057 .057 .058 .053 | -053 .054 .054 .054 -055 .055 .056 .056 -O57 .052| .052 .052 .053 .053 .054 .054 .055 .055 .056 -O51 |+0.051 |+-0.051 .052 .052 |4+0.053 |+0.053 |4-0.053 |+-0.054 |+0.054 .049 -050 .050 .O51 .O51 .052 .052 .052 .053 .053 .049 .049 .050 .050 .050 .O51 .O51 .052 -052 | .048 -045 | .048 -O49 -049 -050 -050 -050 -O51 | .047 .047 | .047 .048 -045 .048 -049 .049 -050 45 \+0.045 |-+0.046 |+-0.046 :047 |+0.047 |4-0.047 |+0.048 .048 |+0.048 .044 .045 .045 -045 .046 .046 -047 .047 .O47 .043 .O44 .O44 -O44 -O45 -O45 .O45 .046 .046 | .042 -042 .043 .043 .044 .044 -044 -045 -O45 -O41 -O4I | .042 -042 -042 -043 -043 -043 +044 IVWAAM APSO Sp 090 ) |+0.040 .040 |+0.041 .O41 |4+0.041 |+0.042 |+0.042 .042 |+0.043 ® 039 .039 | .039 .040 .040} .040] .O4I -O41 -O41 -035 .038 .038 .039 -039 -039 .040 .O40 -O40 -037 .037 .037 .038 .038 .038 .038 -039 -039 .036 .036 .036 .036 .037 .037 £037, .038 .038 +0.034 |4+-0.035 |-+0.035 |+-0.035 |+0.036 |+-0.036 |+0.036 .036 |4+0.037 -033 -034 +034 -034 -034 -035 +035 -035 -036 .032 .032 -033 : -033, .034. -034 -034 -034 .031 .031 .032 : -032 .032 -033 -033 -033 -030 -030 -030 A -031 -O31 -O31 -032 +032 .029 |+0.029 |+0.029 +0.030 |4-0.030 |+-0.030 |4-0.031 |+0.03 4 .028 .028 .028 : .029 .029 -029 .029 +030 5027 1 4.027'| 2 AOz7ane .028{ .028] .028] .028| .028 .026 .026 .026 : .026 .027 .027 .027 .027 024] 025 | 0251] 1% .025| .026| .026| .026| .026 .023 .024 |+0.024 +0.024 |+0.024 |+-0.025 |4-0.025 |4+0.025 .022 .022 .023 3 .023 .023 .023 .O24 .024 .O2I1 .O2I O22 .022 .022 022 -O22 023 .020 .020 .020 .O21 O21 O21 O21 O21 .O19 -O1g .O19 .020 .020 .020 .020 .020 .018 |+0.018 |+0,018 0.018 |+0.019 |+0.019 |+0.01g |+0.019 .O17 .O17 .O17 .O17 .O17 O18} .o18| .O18 .O16 -O16 .O16 .O16 .O16 .O16 .O17 -O17 Lo15'| , 20154), j-01s 5015 || ..015 |. -OlSi Orsi 2OnG .O13 .O14 .O14 -O14 .O14 -O14 -O14 -O14 -OI2 |+0.012 |+0.013 +0.013 |-+0.013 |+0.013 |+0.013 |+9.013 -OII JOLT -OII : oO .025 .028 .028 .029 .029 .030 .029 .029 .030 .030 :0 .031 .031 .030| .030 .031 FOOT .032 -032 O No Ne} oO oe ).031 |—0.032 |—0.032 |—0.032 .032 .033 033 .033 033 -034] -034] .034 -035 -035 -035 -035 .036| .036 .036 .037 | 2 09 DW GD GD G2 G2 —0.033 .033 -034 -034 -035 -035 .036 .03 .037| .03 -037 |—0.037 |—0.037 |—0.038 02 .038 .039 .038 .038 .038 .039 20; : .040 .O40 .039 .039 .040 .040 :C ’ .O41 .O41 .040 .O4 -O41 ‘ ; .042 .O41 .042 .042 : 04: .043 —0.042 |—0.043 |—0.043 , : .O44 .044 .044 .044 : .O4! 045 | -045| .045 .045 : : .047 .046 .046 .O47 : : .048 .047 .048 .048 : .049 SMITHSONIAN TABLES, TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. pienoned HEIGHT OF THE BAROMETER IN INCHES. mometer ) Fahren-| 54.0 | 24.2 | 24.4 | 24.6 | 24.8 | 25.0 | 25.2 | 25.4 | 25.6 Inch. | Inch. | Inch, Inch. | Inch, | Inch. Inch, Inch, Inch. —o0,.048 —o0.048 |—0.048 |—0.049 —0.049 —0.050|—0.050 |—0.051 |—0.051 .049 .049 | .049 FOS5O)| 1) 2 O50:| ln .O51 .O51 .052 .052 .050 050} .O51| .O51| .051 : -052 .053 -053 .053 051 O51 .052 .052| .053 : .053 .054 .054 055 .052 .052 .053 505311 054i) = | .055 .055| .055 .053 .053 —0.054 .054 |\—0.055 |—o. —0.056 |—0.056 |—0.057 | 20541) 2055), 7-055 -055 .056 ; .057 .057 .058 055} .056| .056 FOS) POSi7 ; .058 .058 -059 -056 10574) PLOS7Al BOSS .058 3 .059 .060 .060 .057 .058 .058 .059 .059 é .060 .061 O61 | .058 f .059 —0.060 —o0.060 |—o, 0,061 |—0.062 .062 $O60)| 7 |) F£OGON) 061/811. 061 : .062 .063| .063 A909) |e | =4062)|| | :062°|) 063 .062 .064 .064 | .065 £0621" L% | .063 .063 .064 : .065 .065 .066 .063| .063; .064 .064 .065 é | 066 .066 .067 .064 : .065 —0.065 —0.066 : |\— 0.067 .068 —0.068 | .065 : | .066 <0674) ) .067 : .068 .069 .069 | 066). | 067 .068 .068 F .069 .070| .070 SOOT? Ne .068 | .06g .069 : .O70 LO7E | 072 .068 | . .069| .070|] .070 : 1 O07 25love .073 | .073 |—0.073 0.074 .074 -074| .075 .O75 .076| .076 .076 207/7,\) 4.0777 :O77, .078 .078 | .069 —o. .070 |—0.071 |—0.072 | .070 : :072)\,) -072 -073 | .O71 : :073 1073), O74 .073 2073) <074'| 17074 .075 | .074| .07 .075 (075 | 7 -O76il ODO OV O° NNININN SDH WN Q | | .075 : .076 .077 |—0.077 |—0.078 .078 .079 |—0.080 10761 Vine | = 4.077.) | 4078)) 9.078 |) c070:|" i080) O80; 99 OL 5O777)| bys .078 .079 .079 .080 O81 .O81 -082 .078 ‘ | .079| .080 -O81 O81 .082 .082 .083 .079| . | .080] .o81 .082| .082 083 | .084] .084 | .080 |—o. O81 —0.082 |—0.083 |—0.083 |—0.084 |—0.085 —0.085 .081 .082| .083] .083 .084 .085 .085 .086 | = .087 .082} .083 .084} .084 .085 .086 .086 .087 | .088 .083} .084| .085 .085 .086 .087 .087 .088} .089 | .084 .085 .086 .087 | .087 .088 .089 | .08g .09O | .085 .086 —0.087 —0.088 |—0.088 |—0.089 |—0.090 —0.090 |~—0.091 .087 | .087] .088 .089 .089 -OgO .Og! .092 .092 .088 | .088 .089 .0gO .091 .Og! .092 -093 | .093 .089 .089 .09O .OgI | .092 .092| .093 .094 095 | .090 | .O9I Og] 5092'|, 5098 |) 1<4094|' 4.094 095 096 | O09! .0g2 .092 0,093 .094 |—0.095 |—0.095 .096 —0.097 | .0G2 -093, .094| .094 .095 .096 .097 .097 | —.098 | .093 .094} .095| .095 .096| .097 .098 .098 -099 .094} .095 .096 .096 | 097| .098| .099] .100| .100| -095 .096 .097 .098 | .098 | = .099 . 100 101 . 102 0.096 es? —0.098 |\—0.099 |\—O. 100 |_o. 100 IOI . 102 |--0. 103 |—O. .097 .098 .099 | .100 101 101 .102 .103 104 .098 .099| .100 | - 101 .102 - 103 - 102) . 104 .105 . 100 | -100| .IOI - 102 .103 - 104 .105 . 105 . 106 | -IO!I | .101 | . 102 .103 . 104 - 105 . 106 109) 107 | i i Pe SMITHSONIAN TABLES. 20 TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. Inch. oO. 102 -103 .104 .105 .108 - 109 .I110 114 SEES .116 .118 -119 .120 eI e122 .123 124) S125 .126 .128 .129 G2 WD G2 GG + & ow SMITHSONIAN TABLES. . 106 | PLO? | -IIl LZ —0. 103 .104 -105 -106 .107 .108 . 109 .I110 et Dn2 -116 rez a) = ake .118 119 .120 roy 5L22 23 .124 | .130 | Inch, \—0. 103 |—0. 104 |—0. 105 Toa 2005) HEIGHT OF THE BAROMETER IN Inch, - 104 .106 .107 .108 | - 109 | -I1O oeaed ern2y aes 114 | Sn S7, .118 119 .120 SLT P22 ar .124 | 125 .126 | .128 .129 | .130 ee SS Gr G2 Ge Ge Go un Nv + nan 1 SI OUI new NnN Inch. -105 -106 .108 . 109 -I10 a ee | Inch. Inch, 106 NOT .108 .110 aod “102 ae .114 115 .116 Ese .118 .120 .121 B22 “123 .124 .125 .126 5127) .128 .130 rei .132 | men -134 135 .136 Lagat 7 |—O1.39 |—O. .140 141 | 142 -143 9.144 -145 .146 -147 | -149 .150 .107 .108 109 “IIo Sil TL 114 BTS; .116 aL .118 -IIg | 2 a2 0. 123 | .124 -125 .126 m277 128 | .130 IS .132 -133 -134 -135 | .136 | -137 .138 I40 | 151 ERG .153 154 | 155 -156 -158 -159 .160 .I161 | -14I | 142 | -143 | 144 -145 .146 | -147 -149 .150 | 24.2 24.4 24.6 24.8 | 25.0 | 25.2 Inch. —0.106 —0.107 .108 il) and sus .116 an —o. 11g .120 .122 123) 109 -I110 olan Ra 118 aT 25 .126 27 site} | .129 ara prez T22 rere) -134 135 126 ais, .135 .140 LAL INCHES. —o.108 |—o. . 109 iO -III nil Lore .1I4 -116 .117 118 | 119 | 4 | | 20 ok22 -124 | a25 |—0- .126 | 27, e125) | .129 .130 |—o. .132 | 133 | 134 136 | 137 -149 .150 51 .152 1153 | | 25.4 | 25.6 Inch. Inch, -110 sa ~LI2 Bt -114 Pas Sey SS. 119 or .128 .129 .130 -134 -135 | 136 | -143 | -144 -145 .146 -148 108 .120 121 .122 123 25, | 126 | 131 22 137 | .138 -140 141 .142 -154 -156 J -157 -158 .159 .160 |—o. -161 -162 -164 .165 TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. = Attached | Ther- mometer | Fahren- heit. 2.0 063 2.5 .062 3.0 H-o.061 3-5 -059 4.0 .058 4.5 057 5.0 .056 5.5 140.055 6.0 054 6.5 052 7.0 .O51 7a5 050 8.0 }+-0.049 8.5 .045 g.0 .046 9-5 045 10.0 044 10.5 }+0.043 II.o .042 11.5 .O4I 12.0 .039 12.5 .038 13.0 }4+-0.037 3°5 3 14.0 03 14.5 033 15.0 032 15.5 }4+0.031 16.0 .030 16.5 .029 17.0 .027 7a .026 } 18.5 .024 | 19.0 .023 19.5 .022 | 20.0 020 | 20.5 }|+0.019 | 21.0 O18 21.5 .O17 | 22.0 o16 22:5 o14 23.0 }+0.013 P2855 or2 24.0 Or! 24.5 -O10 | 25.0 .009 SMITHSONIAN TABLES. HEIGHT OF THE BAROMETER IN INCHES. 26.2 | 26.4 Inch. Inch. +0.068 |+-0.069 +0.067 |+0.068 .066 .066 .065 .065 .064 .064 .062 .063 +0.061 |+0.062 .060 .060 -059 059 .058 .058 .056 057 +0.055 |+0.056 -054 054 +9053 053 -052 052 .050 O51 +0.049 |+0.050 .048 .048 | -O47 -O47 | .046 .046 -O44 045 +0.043 |-+0.044 .042 042 .O4I | .O4I -040 040 .038 039 +0.037 |+0.038 .036 036 .035 | 035 -034 034 -032 033 +0.031 |+0.032 .030 030 .029 | 029 .028 | .028 .027 | 027 | +0.025 |+0.026 -024 .02 .023 | 02: .022 | 022 .O21 | O21 +0.01g |4+-0.020 O18 O18 147 : 9». IZ 150 | LAS! Wed : leet Th .149 eS 10s a5 3y LI51 SS 2a oes 154 AUS 2 weds le Aalls LD} am a > HH ne Om eet et mannan NID on .157 158 | .160 a 162 | on \o al et et ed nonin Sonu be ent an iilon lilo! nour COnI DUI D 5 163 | 164 | . 166 | .167 | .168 DAD kn .170 171 | 2) 174 | -175 a a | Du NH as “I > -176 |—0. 7 -177 | 791) .180 "181 | Dou nee PII SIS Ovr.o | ° ee .183 |—o. .184 .185 | .187 | .188 DoW ow Ns mers ss Now WMO Oo SMITHSONIAN TABLES. TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. HEIGHT OF THE BAROMETER IN INCHES. | 30.0 | 30.2 30.4 30.6 | 30.8 | 31.0 | 31.2 | 31.4 | 31.6 | ES Inch. Inch. | Inch. Inch. Inch. Inch. Inch. Inch. Inch. | +0.078 [+0.079 +-0.079 |+-0.080 |+-0.080 |+-0.081 |+0.081 |++-0.082 |+-0.082 +0.077 |+0.077 |+0.078 |4+-0.078 |+0.079 |+0.079 |+0.080 |+0.080 |+-0.081 .076 | .076 .077 .077 .078 .078 : -O79 .080 .074| .075 .0O75 .076 .076 .077 : .078 .078 -073| .073 .074 .074 .0O75 -O75 5 .076 -0O77 -O71 | .072 .072 .073 .073 LOTAN |) a | .075 .075 9.070 +0.070 .O71 .O71 072 .072 ; 073 |+0.074 .069 .069 .070} .070 .070 .O71 .O71 .072 .072 .067| .068] .068| .069] .069| .070} .070| .070| .o71 .066 .067| .067 .068 .068 .069 .069 .069 .065 .065 | .066 .066 .067 .067| .068 .068 .064 |+-0.064 |+0.064 |+0.065 |+0.065 |+0.066 |-+0.066 .062 .063 .063 .063 .064 .064 | = .065 .061 | = .061 .062 .062 .062 .063 .063 .059| .060 .060 .061 .061 .O61 | .062 .058| .058] .059] . .060) .060| .060 WIIDAAA WHEY w nondg -057 |+0.057 .057 .058 .058 +0.059 '+0.059 1055 | .056 .056 : .057 .057| .058 .054| .054 -055 .055| .055 .056 | .056 -O53 -053 -053 -054| .054] .054} .055 -O51 -052 052 -O; 053 -053 +053 .050 |+0.050 -050 |+0. O51 |+0.051 +0.052 .048 -O49 .O49 ; .050 050) .050 .046| .047]|- .047 .047 .048 .O% .048 .049| .049 .045 5 | .046 .046 .046 .047 .047 .047| .048 .044 -044| .044 .045 -045 .045 .045 -046 | .046 +0.042 .043 |+0.043 |+0.043 |+0.044 |4-0.044 |+0.044 |4+0.044 +0.045 .O41 ‘ | .042 .O42 .042 042 .043} .043| .043 -O40 -040 | -O40 -O4O0 -O4I -O41 -O41 -O42 | -O42 .038 .039} .039 .039 .039 .O40 : -040 .O40 .037 .02 .037 .038 .038 .038 .038 .039 | .039 +0.036 |+0.036 |+-0.036 .036 .037 .037 -037 |4+-0.037 .037 034} .03¢ -035| -035}] -035| .035| .036| .036| .036 -033 -O3. .033, -034 -034 -034 aC -034| .035 .032 Aor -032:15) 032 .032 .033 LoKk .033 .033 .030 .030| .031 .031 .031 .031 .03 .032| .032 0.029 +0. 9.029 |+0.02¢ 9.030 .030 |-+-0. .030 |+0.030 2 3 3 30 | 3 .027 .028 .028 .028 .028 .028 : -029 -029 .026 i | .026 .027 .027 .027 : .027 | —.027 .025| .025 .025 .025 .025 .026 Z .026| .026 .023 | .024| .024 .024 .024 .024 02. .024| .025 +0.022 |-+0. 022 |+-0.022 |40.023 |+0.023 |+0.02: .023 |-+0.023 021 : .O21 .021 021 2021, | tke .022 .022 -O19 -O19 -O20 | .020 .020 .0O20 4 -020 | -020 .O18 | .018 .o18 .o18 .o18 .O19 é .O19 .O19 FOL/) U.OL7 -OL7.|'" OL7 .O17 .O17 eC -OL7, 2017) +0.015 |+0.015 +0.015 .O16 .O16 .O16 : +0.016 .O16 .O14| O14 O14 .O14 POLAT SOLAN yt O15) | O05 SOL3.|| psOLRyi| 1 2013 -O13) -O13 .O13 Koy -O13 .O13 .OIL SOLL.|' }2OLE .OIl SOLde || OL ; .O12 .O12 .O10 SOLO! +2010 .O10 .O1O .O10 ‘ .O10 0.10 SMITHSONIAN TABLES. TABLE 10. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. ENGLISH MEASURES. 30.4 31.6 Inch. Inch. Inch, Inch, Inch. +0.009 |-+-0.009 f -OC +-0.009 |+-0.009 -007 -OO7 : : -OO7 : ; .005 .008 .006 : : : 006] . : .006 .006 -OO4 ° : : -O05 . -OO5 -OO5 -005 -003 . : . -003 : : -003 -003, +0.002 ‘ +0,002 5 +0.002 |+-0.002 0.000 R f i ; A 0.000 | 0.000 —0O.OOI le ° ~OC —0O.OOI |—O.OOI 002 : 5 4 ; .OC .002 .002 -OO4 ‘ -O0O04 : : +002 . -OO4 —0.005 |—0.005 |—0.005 ' —0.005 .006 .006 .007 : : : ; .007 .008 .008 .008 : . 4 a .008 .009 .009 -009 2 .OC : ‘ .O10 .OLL OIL} .OII ; : 7 : OI —0.012 .O12 |—0.012 : 5012 .O13 SOL3;| ) 2 > SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 600 mm. 605 mm. Attached Ther- : 0°2 0°4 mometer. nim, mm, mm, mm. mim, mm, mm. mim. nim. mim, 0.00 0.02 : 0.06 0.08 0.00 0.02 0.04 0.06 0,08 10 on2 ST? 6 .18 LO AiG: -I4 .16 Lo .20 322 : <25 ‘ .20 a2 ; .26 29 sor : 35 es .30 232 2 36 39 41 : -45 ; .40 -41 43 45 wn OO oe a 49 51 : 55 ae -49 51 : 55 5 61 : .65 : 59 61 65 -70 é : BY, -69 wt -75 .SO .82 82 8 -79 SI 85 gt 95 J Com Co RO? wnt Din SIST SINS No} © a dC -OL «LO I 05 I 1.20 I I 14 24 -34 -44 30 .40 a | SOY = ey SS eS HS SS HHH HO belt) et te ¢ 1.50 1.60 1.70 1.79 1.89 “54 I I ies I I I Es x I I I. I I I Te I I I Tie I mH OOO Le oe oe oe | ¢ 1.99 2.09 2.19 2.28 2.38 NOH H NNNNA NNN NN PHN oer NR NN ND He PY NP yPPNW Nw hd bh a) 2.48 2.58 2.68 2377 2.87 Poa kee wow KH NH NN PPPPNb NNN NN era bo vwHH HN Le N pPPPs O 1 \o 2.97 3-07 3.16 3.26 3.36 to Co Go G2 Go Go Ww Whe © OP G2 G2 GW lo WwW nh CR G2 Oo Ww Ne C2W WON WwWwW dr WWW N BW WO Onur an Ww Co W Wd» 3.46 Go o Oe Oo w _ Nn 2 o>) On | | © On | SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER WEIGHT OF THE BAROMETER 610 mm. ; 615 mm. Attached | | | Ther- SOPs we Os 5 SG iO: : : : o°6 | mometer. | Ce min. tm. mm. mm. | mim. mm. . niin. 0 0.00 0.02 0.04 | 0.06 | 0.08 0,00 0.02 | 0.06 I .10 S12) |) ata ee ON eer co .10 2 2 20 222\||_5 vad <26 | saee 20 .20 22 3 130 $32 14 130 Hea 2201) ee 32 4 .40 2429 9-44 .46 .48 .40 42 5 0.50 0.52 0.54 0.56 0.58 50 0.52 6 .60 502); jae 04: .66 .68 .60 62 7 -79 -72 -74 .70 | =79 -79 72 5 .50 .52 54 .86 | .88 .50 .82 9 .gO 92 | -94 .96 | .95 .gO .92 | | 10 0.99 1.01 1.03 L05,¢||| 1c 07 00 .02 1! 1.09 Tors Tale C25 Lely, .10 oe 12 1.19 e223 25) | 27, .20 222 3 1. 2¢ Desh ess 1.35 i377, 30 S32 14 1.39 1.41 1.43 1.45 1.47 .40 .42 | | 15 1.49 ESL tes ee ledS 1.57 T.50 a2 ie 16 1.59 1.61 [-63 | © 1-65.) 1:67 1.60 .62 Ke 17 1.69 Levfil D734) M7 |) ear 1.70 Be i te) 1.79 1.81 1.83 1.55 1.57 1.50 .52 r. 19 1.59 LOL 4 1.93 1495 |) 1.97 1.90 .g2 i | 20 1.99 2.01 2.03 B05 | 2:07 2.00 2.02 De 2% Di 21 2.09 2.00} | 2.12 254 |! “2516 2.10 22 2s 2. 2s 22 2.18 2.20 222 D2A» |) 12626 2.20 222 Dy 23 2 23 2.28 RAO | 2.32 2 Ant 2E 26 2.20 Dee De 25 Ds 24 2.38 2.40 2.42 2.44 | 2.46 2.40 2.42 Di De 2.4 25 2.48 2.50 | 2.52 2.54 2.56 2.50 2.52 2.: 2.: or 26 2.55 2.60 | 2.62 | 2.64 | 2.66 2.60 2.62 2. 2" 2: 27 2.68 2:70 2472 27 Ao | h2s 70 2.70 2172 2. 2 2: ' 28 2.78 2.90) | 2502 2.84 | 2.86 2.80 2.82 2.1 2! 2 29 2.88 2.90 | 2.91 2.93 2.95 2.90 2.92 2. 2. 2: 30 2.97 2.99) | 3.01 3.03 3.05 3.00 2°02 a a 2 31 3.07 2.09.'|7 3201 3-13 | 3-15 3.10 3,12 Bs 2% a 32 an7 2.19 "|| 322% BUDO a4 Ne Qk2s 3.20 B22 Bt a. Be 4 z |) are Sie at mana e 0 2 aa 5 3 2 33 3-27 3-29 | 3-31 3290) | -or a0 330 332 3: Se 3 34 3°37 3-39 | 3-41 3-43 3°45 3-40 3.42 3: 3 3 35 3-47 3-49 | 3.51 | 93°53, | 3°55" | «3-49 3 3: SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 620 mm. 625 mm. | Attached | | | Ther- | 0°0 | 022 | 0% | 076 | 0°8 | 020 | 0°2 | 0% | 076 | o°8 | mometer. | Cc mim. mum. mm, mm. nim. mm. mm. mm. mm. mm. O° 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 0.08 I .10 .12 14 16 18 .10 ae 14 .16 oS | 2 .20 = 22 2 .26 .28 -20 22 -24 27 -29 3 30 | .32 34 -36 .38 31 33 “35 37 -39 4 -40 43 45 -47 -49 40 43 45 47 -49 5 0.51 0.53 0.55 0.57 0.59 0.51 0.53 0.55 0.57 0.59 6 61 63 65 .67 .69 61 63 65 .67 .69 7 71 -73 5 -77 79 -71 7 -75 .78 .80 8 SI .83 55 .87 .89 .82 84 86 88 go 9 -9I 93 +95 -97 -99 92 94 -96 98 | 1.00 10 1.01 T.03 1.05 1.07 1.09 1.02 1.04 1.06 1.08 I.10 i wr eal els 1.15 T.L7, I.19 Tal2 I.14 1.16 1.18 1.20 12 E21 1.23 1.25 1.27 1.29 1.22 1.24 1.26 1.28 1.30 | 13 1.31 [33 1.35 1237 1.39 1.32 1.34 nay) 1.39 1.41 ae te 1.41 1.43 1.46 1.48 1.50 1.43 1.45 1.47 1.49 I.51 P15 Toso) te 5 4 1.56 1.58 1.60 1.53 1.55 57 1.59 1.61 Lo 1.62 | 1.64 1.66 1.68 I.70 1.63 1.65 Toy 1.69 1eAee | 17 72 1.74 er], 1.78 1.80 1.73 1.75 Lap 1.79 1.81 18 1.82 1.84 1.86 1.88 1.90 1.83 1.85 1.87 1.89 I.9I 19 1.92 1.94 1.96 1.98 2.00 1.93 1.95 1.97 1.99 2.01 | 20 2.02 2.04 2.06 2.08 2.10 2.04 2.06 2.08 2.10 212 21 2512 2.14 2.16 218 2.20 2.14 2.16 2.18 2.20 2522 22 222 2.24 2.26 2.28 2.30 2.24 2.26 2.28 2.30 Paved |) ee Bea? Ne aeaA |e eesOn te 2-35. |) 2:40) 1)" 21340 || 12.965) 2:38) || \2.40n)|) 92,4201 lh 2 2.42 2.44 2.46 2.48 2550) || 2544 2.46 2.48 2.50 2.52 25 2.52 2.54 2.56 2.58 2.60 2.54 2.56 2.58 2.60 2.62 26 2.62 2.64 2.66 2.68 2.70 2.64 2.66 2.68 2.70 D2 27 272 2.74 2.7 2.78 2.80 2.74 2 2.78 2.80 2.82 28 2.82 2.84 2.86 2.88 2.90 | 2.85 2.87 2.89 2.91 2.93 2 2.92 | 2.94 2.96 2.98 3.00 | 2.95 2.97 2.99 3.01 3.03 30 gr02" |) 3:04 3.06 3.08 sar 3.05 3.07 SOON senr Bars 31 Sone ese lA: 3.16 S515 3.20 aUT5 3.17 3.19 oT Rto3 32 3-22 | 3.2 3.26 | 3.28 3.30 3-25. | 3-27 3.29 3-31 3-33 33 3-32 | 3-34 | 3-36 | 3-38 | 3.40] 3-35 | 3-3 3-39 | 3-41 | 3-43 3 3-42 | 3-44 | 3.46] 3.485 | 3.50] 3-45 | 3-47 | 3-49 | 3-51 | 3.53 35 3-52 | 3.54 | 3-56 | 3-58 | 3.60] 3.55 | 3-57 | 3-59) 3.61 | 3.63 SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 630 mm. 635 mm. | Attached | | | | | Ther- 0°0 | Of2 | O°4 | 0°6 0°38 0°2 0°4 0°6 0°8 _mometer. | | Cc. nm. mim, mm. | mm. mim. mim, mm. mm. mm. 0° 0.00 0.02 0.04 | 0.06 0.08 0.02 0.04 0.06 0.08 I .10 a2 -14 .16 1g 51 15 k7 19 2 221 23 -25 E27 .29 22) as 2277 .29 3 +31 +33 +35 37 -39 -33 35 37 +39 4 -41 -43 -45 -47 -49 -44 .46 .48 .50 5 0.51 0.53 0.56 0.58 0.60 0.54 0.56 0.58 0.60 6 .62 64 .66 .68 .70 64 .66 .68 -70 7 “f2 -74 7 .78 .80 -75 rly | -79 81 | 8 .82 .84 .86 .88 .gO 85 .87 .59 OI | 9 +92 “95 -97 -99 T.O1 “95 -97 -99 I.02 | 1.03 1.05 1.07 1.09 Teli Te 1.06 1.08 I.10 Im # 113 1.15 Lel7 1.19 e221 re 1.16 1.18 1.20 122 ¥.22 1:25 L:2 1.29 Deo Its 1.26 1.28 1.30 Ieee 1.34 1.36 1.38 1.40 1.42 Me 37) 1.39 1.41 1.43 1.44 1.46 1.48 1.50 1.52 tes 1.47 1.49 TSH L533) 4 1.54 1.56 1.58 1.60 1.62 1.55 1.57 1.59 1.61 1.63 1.64 1.66 1.68 1.70 72 1.66 1.68 1.70 e722 1.74 1.74 17.7 1.79 1.81 1.83 1.76 1.78 1.80 1.82 1.84 1.85 1.87 1.89 1.9 1.93 1.86 1.88 1.90 1.92 1.94 1.95 1.97 1.99 2.01 2.03 1.96 1.99 2.01 2.03 2.05 2.05 2.07 2.09 2200 2°13 2.07 2.09 2.11 255 2.05 2.15 27, 2.19 2.21 2.24 27 2.19 2-27. 2.23 252 2.26 2.28 2.30 2:22 2.34 22 212 23T | 2s3A| 2.36 2.36 2.38 2.40 2.42 2.44 2.38 2.40 2.42 2.44 2.46 2.46 2.48 2.50 2552 2.54 2.48 2.50 2.52 2.54 2.56 2.56 2.58 2.60 2.62 2.64 2.58 2.60 2.62 2.64 2.66 | 2.66 2.68 2.70 2:73 2.75 2.69 27 272 2.75 2.97 4M 77 2.79 2.81 2.83 2.85 2.79 2.81 2.83 2.85 Dy feh7h | 2.87 2.89 2.91 2.93 2.95 2.89 2.91 2.93 2.95 | 2.97 2.97 2.99 3.01 3.03 3.05 2.99 3.01 2.02 3.05 | 3.08 3:07 ||= 3:09 2. R1 2512 3.15 3.10 3.12 a4 3.16 3.18 | 27 3.19 2:21 3:22 3.25 3.20 3.22 3.24 3.26 2°28 ail 3-28 | 3-30 | 3-32 | 3-34 | 3-36 | 3-30 | 3.32 | 3-34 | 3-36 | 3.38 | 3-38 | 3.40 | 3.42 | 3:44 | 3.46 ] 3-40 | 3.42 | 3.44 | 3.47 | 3.49 3-48 | 3.50 | 3.52 | 3-54 | 3-56] 3-51 | 3.53 | 3-55 | 3-57 | 3-59 3.58 | 3.60 | 3.62 | 3.64 3.66 | 3.61 3.63 3.65 3.67° || 23'5one a a a, er RT a EE SMITHSONIAN TABLES, > ° TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. _ FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER 640 mm. HEIGHT OF THE BAROMETER 645 mm. Attached Ther- o°0 =| «6(0°2 0°4 0°6 0°0 o°2 0°4 0°6 0°8 mometer. | oh mm. nim. | mim, mim. min, nim. mm. mm. mm. mm. o° 0.00 | 0.02 0.04 | 0.06 | 0.08 | 0.00 | 0.02 0.04 | 0.06 | 0.08 I .10 ane 15 7 19 rr 203 15 7 19 2 227 .23 225 277 29 e211 23 225 27 .29 3 3 33 60) @) .30 .40 32 -34 36 38 .40 4 -42 -44 .46 .48 .50 .42 -44 .46 .48 ‘Sir | 5 0.52 0.54 0.56 0.59 0.61 0.53 0.55 0.57 0.59 0.61 6 .63 .65 .67 | .69 7 63 65 .67 .69 72 7] “73 -75 Sf -79 SI -74 -76 -78 .80 .82 8 .84 .56 88 gO .92 .84 .86 .88 .go -93 9 94 .96 .95 1.00 1.02 95 .97 -99 1.01 1.03 1.04 1.06 | 1.09 I.11 les 1.05 1.07 1.09 1.12 Et ~~ | 2 oC r 1.15 Leaky 1.19 E-21))|) 1:28 1.16 1.18 1.20 i222 I. 24 1.25 127, a2) Lee on | ee 1.26 1.28 1.30 i232 1.35 1.36 1s 1.40 1.42 1.44 1.37 1.39 1.41 1.43 T.45 1.46 1.48 1.50 | 1.52 1.54 1.47 1.49 1.51 1.53 1.56 1.56 1.59 1.61 1.63 1.65 1.58 1.60 1.62 1.64 1.66 1.67 1.69 Tey 1.73 7/5 1.68 I.70 1272 1.74 177 eo fef| 1.79 1.51 1.53 1.56 1.79 1.51 1.83 1.85 1.87 1.88 1.90 1.92 | 1.94 1.96 1.59 LO) | 0592 1.95 1.97 1.98 2.00 2.02 | 2.04 2.06 2.00 2.02 2.04 2.06 2.05 | 2.08 2.10 Dee 2.15 27 2.10 22112 2.14 | 2.16 2.18 2.19 Dei 22am eae? S 227 220 2523 BEG) |e 22237 2.2 252 2°35 Dag 225 D237 2.31 2.33 2:25 237 2.39 2.40 2.42 2.44 2.46 2.48 2.41 2.43 2.46 2.48 | 2.50 2.50 2.52 2.54 2.56 2.558 2.52 2.54 2.56 2.55 2.60 2.60 | 2.62 | 2.64 | 2.66 | 2.69 | 2.62 | 2.64 | 2.66 | 2.69] 2.71 2571 2.73 2.75 2p 2.79 2.73 2.75 eG fy | 2.79 | 2.51 2.81 2.83 2.85 2.87 2.89 2.83 2.85 2.87 2.89 | 2.92 2.91 2.93 2.95 | 2.98 3.00 2.94 2.96 | 2.98 3.00 2.02 3.02 3.04 3.06 3.08 3.10 3.04 3.06 | 3.08 3.10 2.12 Bei 3.14 3.16 3.18 3.20 3.14 B07) | 3219 2597 3522 2422 3.24 B52] 3.29 ae 2225 227 3° 2C 3.31 earn 3-33 S290) | Oso! 3°39 3-41 3-35 3-37 3-39 3-42 3-44 3-43 | 3-45 | 3-47 | 3-49 | 3-51 | 3-46] 3.48 | 3.50] 3.52 | 3.54 3.53 3.55 3.5° 3.60 3.62 3.56 3.58 | 3.60 3.62 3.64 3-64 | 3.66 | 3.68 | 3.70 | 3-72 | 3.67 | 3-69 | 3-71 | 3-73 | 3-75 ' SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. Attached Ther- mometer. GC. mim, 0 0.00 I a 2 21 3 32 4 42 5 0.53 6 .64 dh 74 5 55 9 95 10 1.06 II ro 12 27 13 1.38 14 1.48 15 1.59 16 1.69 17 1.80 15 1.91 19 2.01 20 2.12 21 2522 22 2.33 23 2.43 24 2.54 25 2.64 26 2.75 27 2.85 28 2.96 29 3.06 30 3.17 31 2.27, 32 2.30 33 3.45 34 3-59 35 3.69 SMITHSONIAN TABLES, NEIGHT Hee OH n oO NR eee R®WNN NNKHNN NNN HN ww WD Go WW GW Or 05 2 .40 ON H O.o on! 1 nba ns nnn OF THE 650 mm. mim. Oo. Oe WO NN LH RHHN ND RS) ete at as el ee G2 G2 G2 G2 Gr O4 “15 £25 330 47 -57 65 78 .59 OO 79 .gO OO Au fw bd cal GW wb DN A a | ay BAROMETER mim. oO to G2 Ge Qo & ° to nN ON NHR ee Rm NH GO wNHN G2 G2 GW G2 Ge 06 Lyi .28 .38 -49 9.59 .70 mm & OH bd 1 VN / - .56 ~ A L Ww NN au Oo on + & Ww ~ oO mm. 0.05 .19 C G2 On Nee RR ont co Rew NH bh Dui — WD b& to to con WWNNH ND \O ne BQ Ww WG G2 G2 G2 G2 Go I Ww Ont Don © WNHNHNN wRKRNHK HN NO Re ee Re Se HH G2 Gs G2 G2 G2 Dun wn — G2 HEIGHT OF THE BAROMETER 655 mm. mm. 0.02 = n> 24 34 -45 0.56 66 77 .88 .95 .09 .20 30 41 a a .62 -73 54 -94 .05 Dee Ale NNNNN pozane Se eras 1™ a ~ \o C2 G2 G2 G2 G2 O20 NNN Aur — G2 vd HO” baer BWwWWNR HOO Ge ~I 2 4 f 0°4 nim. 0.04 Ls .26 36 47 0.55 .65 -79 -9O 1.00 ee Ree 32 43 54 a 64 -75 .56 .96 .07 NR ee 18 25 39 -49 60 NNNNN S SI Rw HK -O2 rr 24 34 45 55 G2 Oe 2 G2 G2 Ge & mim. 0.06 I I 1.35 oe I NUR Re on mm iS} ty ° ww HH a _ nN CONT NI_N OD Dur & G2 G2 G2 G2 G2 Go oe al Ne} | | | | nim, 0.09 .19 30 .4I ae SO OS 2 1 NNR AH O = NNNK to ne Oe WonnL ‘Oo Oo TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF TITE BAROMETER 660 mm. 665 mm. Attached Ther- : 3 0°4 mometer. mim. | MM, mm, mm, mim. mm. Mit. Min. ° 0,02 .O: 0.06 0.09 0.00 : 0.04 0.07 0.09 3 : 7 wLG) : wll 15 cece .24 : [25700 12 . .26 .25 -30 es ae .39 AI a 3: -37 239 le eel -45 AT || 50. | 52 4: ; .45 50) 4] 52 56 255 9.60 .6 se ae 59 | .61 .63 oy fe he ay v7 6: 3 .69 HZ TA .78 “OOu i ecO2 ; 7 .78 , | 02 55 5 .93 z A SC : -93 .95 .03 .O8 .95 Ae : | I.04 14 .25 330 .46 57 15 e260 +37 -47 55 NAA G: 0 I 2 3 4 5 6 7 Pa} 9 0 L 3 4 mn &O NH & + oa ul amuses nO nN On & G2 G2 N 605 .78 -59 OG): mali a on .69 50 “JI NN eRe 1S lon ll on ll on El | NO me we Ro \O NO Be Ae me oe wee ee RN Re RB NNR NO bw — YU ~ tN RN Nh NR wRHN NHN Row NHN Hur bv & Gb BR wR NH bh RwKHHN HN NKHHNK NH Dui Ww vy to hm Nw bh te wWwNNHN BwNN A BR wRwHN bh An fo vd Dun On & Go NR KN KH bd RO tb aS) mm Com] nur PENN WO NN KN in tn f& Go Go PeNNN ea yeRNN i) 2 N i) N yg yh o& Ye N N NS Een HH OO G2 G2 bo Ge 2 nN 1 G2 G2 G2 Ga &? Dur —& &W to Hew hn LN G2 G2 G2 G2 YG G2 Ge Ge Ge Ge nes ~I™ we SI YS G2 G2 G2 G2 Gd G2 G2 G2 G2 Go G2 G2 G2 Go Go G2 G2 G2 G2 G2 SI OU & Go nN Re G2 G2 Ge Ge Go 2 G2 G2 G2 ¢ e 2 2 we Ge co - Oe “I n Go we >) SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 675 mm. eee ——— | Attached | Ther- ; : : 0°2 : : 0°38 mometer. C. mim. ‘ mim. 0° 1027 | .O7 0.09 I ns | 5 2 -24 ) -35 4 .46 5 0.57 6 .68 | 7 -79 8 , -gO | A 9 Ti: I I I.O1 I TAG I 10 Tt 1 I i I Ter? Te Ie Te Il ie Tis I Te I 122 is ies T; 12 Te i I if I 1.34 Te i Ti. 13 I Ti I T. I 1.45 ie I. Te 14 I.! Le I Tee I 1.56 Te ie Le 15 Te Te I 1 ie 107) I Te Te 16 Ti Tt: I Ts i Te Ls Ts 17 1.8 [ I iT Me I L Te 18 1 Te 2 2 i 2. 2: 2: 19 Bi 2. 2 Py Ds 2. 2s D4 20 2: a 2 2 os 2 2 23 21 oF 2 2 2 2: 2 2 2: 22 2: 2 2 2 2. 2 2 2. |} 23 2 Di 2 2 2: 2 2 2 | 2 2 2" 2 2 2: 2 2 2. 25 2 2. 2: 2. 2 Dae 2: 2.8 2. 26 2. 2. 2. 2 2 2.88 or 2) 2 a7 2 2. 2: a3 2 2.99 ai a 2: 25 2. 3: 3: 3. 3 3.09 ae 3. Bs 29 2 2 3.20 Bt 2 3.20 3. Be a 30 3. 3-2 BBL oi sors 3-2 3-31 | 3.3: 3-36 | 3.3 31 3. 3-4¢ 3-42 3.4 3-4 3:42 | 3-4 3:47 3-4 33 3 3:50 | 3-53 |" 3 3-5 353, “6 sone 3-57 | 3-60 33 2. 3.61 3.63 a 3.6 3.64 | 3.6 3.68 207 34 a: 3-72 | 3-74 «| 3; 3-7. 3°75. We aae7, 3-79 | 3-81 35 3 3.85 3.84 3.86 3.88 | 3.90 | 3.92 SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 680 mm. 685 mm. Attached Ther- : 0°2 : : : : 0°2 0°4 0°6 0°38 mometer. min. mm. mm. mm. mm. mm. mn. mm, min. 0.00 | 0.02 0.04 | 0.07 0.09 ! 0.02 0.04 | 0.07 0.09 01 ae .16 18 .20 : 08 .16 .18 20) 22 22 S27 : Set! : 25 27 .29 31 33 36 BG : .42 : =20 38 .40 43 44 47 . : 53 . -47 -49 51 “54 Oe .56 58 ‘ ; ; . .58 .60 63 | 65 .67 .69 ay) ; : : .69 .72 74 .78 .80 : : : : .80 83] “85 .89 OI : : : : .92 94 | .96 ‘ .02 : .03 5 .07 _ = La = HH rH H, WO KOIADT LWnNnHOO Ki = 18 -30 41 152 .63 ans .24 “35 .46 57 14 E25 236 47 ‘59 Te Bs We Woz ve HHH RO = = aS eS et OO OS cipro tenetniolis OOS ie ses te so He Re eH — HR HH a | DUE wWN -70 .O1 2 03 .14 25 eo) -74 .85 .96 .O7 19 .30 41 aD -63 -74 35 .96 -O7 | 18 o~] on) PPA H PEE NN An NN AA H NN HHH NON HA Aw NN AAH NO Be ee Re N NAR eS NO ND HHH PRN tO NNN ND N NX oe N PHP ‘ NNNNVL NNNNN ts NY N No NS NPNNN NNN NN NN NS N N WWNNN WWwWwNN Www n bd Www NL WwWwwnN DOW NN WON ND WWwWwNN WWD bd Nv oO Cnt OV wn Oo Oo to Go W Ga DH GW OG) SOU WD nabkpw nN G2 G Ca G G2 G2 G2 Oe OG» OG Go GO» C2 DG OG) Go WWWWW WWWwNN WW Go &» G2 G2 Ga Gn Gd G2 DH G2 G2 Gd ¢ WN A Ww ol a CO OV 2 ~~ > on \O un oy we os) wae \O me Swf Hsonian TABLES. 45 TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 630 mm. 695 mm. Attached Ther- 0°0 0:2 0°4 | O°6 3 0°0 0:2 0°4 0°6 mometer. M11. mn. | mm. mm. mm, mim. mim. mn. 0.02 0.05 0.07 0.09 0.00 | 0.02 0.05 Ass LG 18 .20 Situ 14 16 25 27, -29 ae .23 25 aif 36 30m (ime. 4 1 As 34 36 39 -47 | si = : -45 45 | .50 HwWNR OO 59) |/0! 63 a m5 7 0.59 61 .70 £7 74 : .68 -70 73 SI 8: .56 zc -79 .82 84 .92 .95 .97 ‘ 91 AK .95 -O4 . : -IC 5O2,)|| : .O7 no .18 4 .4I 252 .62 x nui w bv SID Hui & wv al 72 ag 4 5 -74 -97 05 .20 NNN HH NN DH HH NN RAH NN Hee NON HH He NON A AR Ae NON RAH NN HHH oe NS .30 42 53 2 / N N NHN N NN HH N NwHKH NN WKN NH No wet NH b wR HNK HN WD w RNN KN Rw NHK ND SI DUB Go CNT AS NNNHNN HD Oe ee) ~ ~I > 7 .95 .10 N A J vw HWN ° . ae | 1 O202&® NN as! \O NNwK HN \o Wo N 9 Perey nN w » Ye N N oe Y» y bv nb WwW Y ow S) Peownn» oe H w wo WY Ye es) & ts) Or om w oN te G2 w 2N HO O» G2 G2 G2 OG? Pri Nun Ane vs G2 G2 G2) G2 Ga An nul erate: G2 DW G2 G2 Se G2 G2 2 G2 Gd GK» G2 Ga Go Go G2 G2 OG) GD Go W G2 G G2 2 C2 HRW WG G2 G2 WW G2 Go G2 Se -& W ol 6 > % SMITHSONIAN TABLES, TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. OF THE BAROMETER 700 mm. WEIGHT HEIGHT OF THE BAROMETER 705 mm. Attached ° ) ° } oO | °C o r c Ther- 0:0 O22 1) 10:4. 1 2-026 0°2 0:4 0:6 0°8 mometer. | Ge mia. mm. | nim. mm, mim. mim, mim. mii. mini, | 0 0.00 O.02 | 0.05 0.07 0.09 0,00 0.02 0.05 0.07 0.09 I ait 14 16 LS teeter .12 14 .16 18 21 2 28 S22 yah eT, -30 32 aoe 25 .28 208) 320 Wn, ‘3 34 37°} -39 | -41 “43 35 37 | -39 40 | .44 4 46) 45 |) “50 53 55 AG" |)" 2.43) |" 7.5% Han) y55 | 5 0.57 | 0.59 | 0.62 | 0.64 | 0.66 | 0.58 | 0.60 | 0.62 | 0.64 | 0.67 6 .69 | ar | 73 75 78 .69 Es ai .76 .78 7 .8o | 82 | .85 .87 .89 .SI .83 | 085 .87 -9O » » | ~ 8 gl | “oA || 206) |) 98) 1.00 .g2 SOA § G7 .99 1.01 9 1.03 | 1.05 1.07 I. 10 Ter? 1.04 1.06 | 1.08 1.10 Lig 10 TVAS |e LO) |\ tear U2 1 23 Ted Ty, 1.20 1322 1.24 II 1.26 | 1.28 | 1.30 I.32 5 1.26 1,29 Ta3t 1.33 1.36 12 1.37 1.39 1.42 | 1.44 1.46 1.38 Ke) 1.43 1.45 1.47 13 1.48 I.51 | 1.53 1355 1.57 1.49 1.52 SA 1.56 1.59 I4 1.60 162)0 |e. Od! 1.67 1.69 1.61 1.63 1.65 1.68 1.70 15 1.71 Lovf3 1.7 a7 fey |Ne Aigtsle, 1-72 L75 7, 1.79 1.51 16 1.82 1.85 1.87 1.89 | 1.92 1.84 1.56 1.88 1.QI 1.93 17 1.94 1.96 1.98 2.01 | 2.03 1.95 1.98 2.00 2.02 2.04 18 2.05 2.07 2.10 DA 2 | e254 2.07 2.09 731 601 DErA 2.16 19 2.17 2.19 221 2328 2.26 2ET Sa 2320 222 2.25 2:27, 20 DED Sel 28 On |e 2.30 2385 2ZAy7 | e2-30) | F232 2.34 2.36 | 2.39 21 2.39 2.42 2.44 2.46 2.48 2.41 2.43 2.46 2.48 2.50 22 2.51 2556 2.55 2.57 2.60 2.52 255 2.57 2.59 2.62 23 2.62 2.64 2.67 2.69 2.71 2.64 2.66 2.65 2.71 273 24 Dea 2.76 2.78 2.80 2.82 2.75 2.798 2.80 2.52 2.54 25 2.85 2.87 2.89 2.91 2.94 2.87 2.59 2.91 2.94 2.96 26 2.96 2.95 ALO 3.03 3.05 2.98 3.00 3.03 3.05 3.07 27 3.07 2.10 2a 3.14 | 3.16 2uO ani) 3.14 3.16 3.19 28 3.19 3.21 3-23 3-25 | 3.28 220 3.23 3.25 3.28 3-30 29 3-30 3 32 3-34 3-37 | 3-39 3-32 3-35 3-37 3-39 3-41 | 30 3-41 3-44 3-46 | 3.48 | 3:50 | 3-44 | 3-46 | 3.48 |. 3.51 a.53 31 3-93 | S59 | 3-57 | 3-59) || “3-52 | 3-55° 1 3:57 |, 3:60 | 3.62° | 3.64 32 3-64 | 3.66 | 3.68 | 3.71 | 3.73 | 3-66 | 3.69 | 3.71 | 3.73 | 3.76 ~e 7 > + @ 2 4 . : 97 5& 2 R | a 2? .c ? S me 33 BnT5 BOT 3.50 3.52 3.54 3-79 | 3.80 | 3.82 3.85 3.87 34 3.87 3.59 3-91 3.93 3-96 | 3-89 | 3.92 3-94 3.96 3.98 35 3.98 1.00 1.02 4.05 | 4.07 4.01 | 4.03 4.07 | %.10 SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. THE BAROMETER NEIGHT OF HEIGHT OF THE BAROMETER 715 mm. Attached | Ther- 0°6 0°2 0°4 0°6 o°8 mometer. CG; mm. mn, | mm. min, mm. mm, mm. mim. mm, mm. 0° 0.00 0.02 | 0.05 0.07 | 0.09 0.00 0.02 0.05 0.07 0.09 I a Gt 16 19 | 21 Sie: 14 .16 .19 220 2 a28 26 | .28 220) 220) .26 .28 -30 233 3 235.) 0237, | 4230) Needed 35 .37 -40 |. 42h aa 4 5400)|) ¢ s40P\| wees 7530 | m5 47 -49 51 54 .56 5 0.58 0.60 0.63 0.65 0.67 0.58 | 0.61 0.63 0.65 0.68 6 708i) M7 -74 a/OM N79 .70 V2 75 Td -79 7 SI .83 .56 .88 | .90 .82 84 .86 .89 -9I 8 .93 .95 .97 1.00 1.02 93 .96 .98 1.00 1.03 | 9 1.04 1.07 1.09 LLL T..13 1.05 1.07 1.10 110) 1.14 | 10 1.16 1.18 1.20 1.23 1.25 Fl] 1.19 121 1.24 1.26 II 27 1.30 1.32 1.34 137, 1.28 ao 0 ie) 1.35 1.38 12 1.39 1.41 1.44 1.46 1.48 1.40 1.42 1.45 1.47 1.49 3 1.50 1.53 1.55 1.57 1.60 1.52 1.54 1.56 1.58 1.61 14 1.62 1.64 1.67 1.69 ral 1.63 1.65 1.68 [70 | (Ta72 15 1.74 1.76 1.78 1.80 1.83 1.75 0.77, 1.79 1.82 1.84 16 1.85 1.87 1.90 1.92 1.94 1.86 1.89 1.91 1.93 1.96 7 1.97 1.99 2:01 2.04 2.06 1.98 2.00 2.03 2.05 2.07 18 2.08 2:10 DI 205 2517, 2:10 2.12 2.14 Dal, 2.19 19 2.20 222 2.24 2:27, 2.29 2.21 2.24 2.26 2.28 2.30 20 2531 2.33 2.36 2.38 2.40 2a2 2.35 2527, 2.40 2.42 21 2-2 2.45 2.47 2.50 2.52 2.44 2.47 2.49 2.51 2.54 22 2.54 2.57 2.59 2.61 2.63 2.56 2.58 2.61 2.63 2.65 22 2.66 2.68 2.70 2:73 2.75 2.68 on D2 2.75 2.77 2 2077 2580'sl (2,62 2.84 2.86 | 2.79 | 2.81 2.84 | 2.86 2.88 25 2.89 2.91 2.93 2.96 2.98 2.91 2.93 2.95 2.98 3.00 26 3.00 3.03 3.05 3.07 3.09 3.02) ||, 3:05 3.07 3.09 oan 27 2.12 2514 3.16 3.19 3.21 3.14 3.16 3.19 220 2428 28 2522 3.25 3.28 3.30 3.32 3.25 3.28 3.30 2022 ahah 29 3-35 | 3-37 | 3-39 | 3-42 | 3-44 | 3-37 | 3-39 | 3-42 | 3.44 | 3.46 30 3.46 | 3.48 | 3.51 | 3-53 | 3:55 | 3-49 | 3-51 | 3.53 |) 3:55 | eas 31 3.58 3.60 3.62 3.65 3.67 3.60 3.62 3.65 3.67 3.69 32 3.69 |, 3-72 | 3:74 | -3-760N 93-789) 3-72 | 3-74. || 23.7018 g-7On) sean 22 3.81 3.83 3.85 3.87 3.90 3.83 3.86 3.88 3.90 3.92 34 3-92 3-94 3-97 3-99 4.01 3-95 3-97 3-99 4.02 4.04 35 4.03 4.06 4.08 4.10 4.13 4.06 4.09 ASIT 4.13 4.16 SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 720 mm. 725 mm. Attached | Ther- : eeGs2ns|) 0:4-/0 026 0°83 : : 0°4 0°6 mometer. | | mm. | mim. mim. mm. mim. mm. min. mm. O° 0.02 | 0.05 0.07 0.09 0.00 | 0.05 0.07 .16 .19 21 : aouiare sity) .19 25 ok aa : : .28 aan .40 -42 4: 36 | . .40 .43 52 54 : . area 52 54 .63 .66 : D: : 64 .66 -75 : 8 : ; -76 -78 .87 ; : 5 : .88 .gO .99 : 0. : e -99 .02 .IO : isl A + N = © “SI01 —& b O O ang mwWNFHO”O Con! 4 _ - _ I 22 “34 .46 -57 -69 25 37 .49 222) -35 -47 58 .70 ot oe | — = SH ee | Hee OO oe 82 94 05 17 29 .o1 92 04 16 27 yePyor NPY aw pePynn Cine PN rn pyro yPPyon NON HS -39 oes .62 yPPNN RO NN H NY oP Poe yRPHNN PHN’ NPNNN NNN NN yy x 2 & WwWwwn ¢ WwWwWWN www N OD On G2 Ge WD Wwwwn OR W G2 G2 Go C2 OR OW OD G2 G2 Ge - NS Dui m~arunr Oo Mm Go Gs G2 nN On CONT U1 Ge W G2 Ge Gd Oo NI O1W WR WH GW & GD G) GD Go 8 ao & DW Oo WD On & RWWW Ww coal SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 730 mm. 735 mm. Attached Ther- 0°0 0°2 0°4 0°6 0°6 0°38 | mometer. C. mm. mm. mim. mm. mm 0° 0.00 | 0.02 0.05 0.07 0.07 | 0.10 7 x12 14 7, .19 .19 .22 2 .24 .26 .29 eau 31 34 3 .36 .38 -41 -43 43 .46 4 .48 .50 152 255 55 .58 5 0.60 0.62 0.64 0.67 0.67 0.70 6 ail -74 -76 -79 79 .82 7, .83 .86 .88 .9I gI -94 8 -95 .98 1.00 1.02 Te 1.03 1.06 9 1.07 1.10 I.12 I.14 Tele 1.08 1.10 T0g 05 T7 10 1.19 120 1.24 1.26 1.29 I.20 Te?! 1.25 127 1.29 II Ts P38 1.36 1.38 1.40 12 1.34 137 1.39 1.41 12 1.43 1.45 1.48 1.50 1.52 1.44 1.46 1.49 1.51 1.53 13 1.55 1557 1.59 1.62 1.64 1.56 1.58 1.61 TO3 1.65 14 1.67 1.69 1.70 1.74 1.76 1.68 1.70 172 Ta75, 777) 15 1.78 1.81 1.83 1.86 1.88 1.80 1.82 1.84 1.87 1.89 16 1.90 1.93 1.95 1.97 2.00 1.92 1.94 1.96 1.99 2.01 17 2.02 2.05 2.07 2.09 Dele 2.04 2.06 2.08 2.11 2a 18 2°TA 2.16 2.19 PGA 2522 2205 2.18 2.20 2.23 2.25 19 2.26 2.28 2.31 2.33 2.35 227, 2.30 2.32 2.35 2.37 20 2.38 2.40 2.42 2.45 2.47 2.39 2.42 2.44 2.46 2.49 |} 21 2.50 2.52 2.54 2.57 2.59 2.51 2.54 2.56 2.58 2.61 22 2.61 2.64 2.66 2.68 Day. 2.63 2.66 2.68 2.70 2473 23 2.73 2.76 2.78 2.80 2.83 Des Br 2.80 2.82 2.85 24 2.85 2.87 2.90 2.92 2.94 2.87 2.89 2.92 2.94 2.97 reo 2.97 2.99 3.02 3.04 3.06 2.99 3.01 3.04 3.06 3.08 26 3.09 3.11 2°12 3.16 3.18 250 Bor 2.16 3.18 3.20 27 3.20 2723 B25 3.28 3.30 2523 3.25 By) 3.30 3.32 25 3.32 3-35 | 3-37 | 3-39 | 3-42 1 3.35 | 3.37 3-39 | 3-42 | 3.44 29 3-44 | 3-46 | 3.49 | 3.51 | 3.54 ] 3-46 | 3.49 | 3-51 | 3-54 | 3.56 | -30 3.56 | 3.58 | 3:61 | 3863) 3.65 1 93.58) 93.61 | 3,630 sor i anuoS 31 3.68:.|" «3.70. | 3-72. | 3.759 B77 3-70) || 3.73.1 oS-75 egeee ae ance 32 3-79 | 3.82 | 3.84 | 3.87 | 3.89 ]| 3.82 | 3.84 | 3.87 | 3.89 | 3.92 33 3-91 | 3-94 | 3-96 | 3.98 | 4.01 | 3.94 | 3.96 | 3.99 | 4.01 | 4.03 24 4.03 4.05 4.08 4.10 4.12 4.06 4.08 4.11 4.13 4.15 35 4.15 4.17 4.20 4.22 4.24 4.18 4.20 4.22 4.25 4.27 | | | | | SMITHSONIAN TABLES TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. 740 mm. "Attached Ther- , mometer. CG: ak I 2 1 3 | 4 5 6 7 8 9 lO.” r 12 T3 ee | ) 15 it 16 Te 17 oF 18 Dk es 5x9 2 20 2.41 2.43 2.46 21 2.53 2.55 2.58 22 2.65 2.67 2.70 23 DEF 2.79 2.82 24 2.89 2.91 2.94 25 3.01 3.03 3.06 26 Bats 3.15 3.18 27 3.25 BuO F 3.30 25 3-37 | 3-39 | 3-42 29 3-49 3-51 3-54 30 3.61 | 3.63 | 3.66 | 3I 3278) WBS) | So) 32 B1S5 || 0SeO7)) | B09 33 3:97 3-99 4.01 34 4.09 4.11 4.13 35 4.21 4.23 4.25 SMITHSONIAN TABLES. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 745 mm. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. METRIC MEASURES. Attached Ther- mometer. Cc. . o° 0.00 I 12 2 25 3 -37 4 -49 5 0.61 6 73 7 .86 8 .98 9 1.10 10 22 II 35 12 1.47 13 1.59 14 rai 15 1.83 [> 2916 1.96 17 2.08 15 2.20 19 BRD 20 2.44 21 2.56 22 2.69 23 2.81 24 2.93 25 3.05 26 207 a 3.29 28 3.41 29 3-54 30 3.66 31 3-78 32 3.90 33 4.02 34 4.14 35 4.26 SMITHSONIAN TABLES. HEIGHT OF THE BAROMETER 750 mm. 0°2 0°4 0°6 0°0 mm, mm. mm. mm. 0.02 0.05 0.07 0.00 mT 17 .20 12 27, .29 a2 By +39 -42 -44 -37 -51 54 .56 -49 0.64 | 0.66 , 0.69 0.62 7 -78 SI -74 .88 -9I 93 .86 1.00 1.03 1.05 .99 rete T.15 ETE et 1.25 1.27 1.30 1.23 Tay 1.39 1.42 1.35 1.49 1.52 1.54 1.48 1.61 1.64 1.66 1.60 1.74 La7 1.78 Taj 1.86 1.88 I.9I 1.85 1.98 2.00 2.03 1.97 2.10 ante 2.15 2.09 2.22 2525 DOr 20 2.34 2.37 2.39 2.34 2.47 2.49 2552 2.46 2.59 2.61 2.64 2.58 Dust 272 2.76 2.70 2.83 2.86 2.88 2.83 2.95 2.98 3.00 2.95 3.07 3.10 p12 3.07 3520 B22 3.24 3.19 3-32 3-34 3-37 3-31 3-44 | 3.46 | 3.49 3-44 3.56 3.58 3.61 3.56 3.68 3.71 273 3.68 3.80 3.83 3.85 3.80 3-92 3-95 3-97 3-92 4.04 4.07 4.09 4.05 4.17 4.19 4.21 4.17 4.29 4.31 4-33 4.29 RH HO Dw HHH RR on Ow PHYA - iS QNNHN ony MOI DABRWNHH O HOARN CONN nv ON UG aN SHOW wW Ww ®W WW N HO w = HEIGHT OF THE BAROMETER 755 mm. 0.69 oI -94 1.06 1.18 Tar 1.80 TABLE 11, REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 760 mm. 765 mm. _ Attached Ther- 0°0 0°2 0°4 0°6 0°8 | mometer. mim. mm, Imm. mm. mm, 0,00 ; y 7 0.10 She fs : ; -22 225 ae -3/ .50 ° .62 -74 .87 -99 .12 CONIA fHWNHOO _ al 24 36 49 61 73 86 98 10 23 35 47 He eH Oe HH RH ameter aheetens ¢ NNNAHH NM NNN NNNNN NNNNhH PQ & ys Oe Ww He COOT BW H COQAW HO G2 G9 Gs & ALW WH Hw CODW Con ONTO Cony Coun Gs BEY HOO GY BLL PER YY Oo N HO RO MOU “IU1 NS O © New On NO to P PREYS EOE fF REY YY > oo i) OH _> Oo wn Ww \o |B FEEEO KOH SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 770 mm. 775 mm. | Attached | Ther- : 0°2 0°4 | mometer. ° WO OIDWA PWN HOO Lal e eee eS eH = Se ee eH I. I 2. 2 2. 2 2.2 2 2. 2 ®WONHNNN © oom! com Oo NI DALW ND MAW OOM WO WAW BHD SOOO w O -_ PELY EYYYY YWHDHND Sos Ww do eo wom Co | P RRREE SOOO &! |} & WNHO SMITHSONIAN TABLES. 54 TABLE 11 REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 780 mm. 785 mm. Attached Ther- : 0°2 : : : 0°0 0°2 0°4 mometer. mm, mim. 0.03 0.05 ay 18 .28 -35 -41 43 -53 .56 0.66 .69 -79 SI -92 +94 1.04 .O7 .20 ° WO ONAT AWNH OO me HH I ts I I Te i I Te i I Ts I I 1.8 iT See Se eS eS Se eH ee ° onl RoNNN Lal Pye) Ro wHN HD N NNN WN PPR! NR NN ND A PHNNS WNN NN ey PPD WoNnNNN WNNNN eye» ee GQ o WNHO DO NALW HN OnNUN 2 EQ QO moO IAW on 2 Qo Mui w ONT H®W®W® GQ SOO nar Ones 2 OQ GG IAnNH Nv moun om G2 Cann + ono One ) ST DUNO ~~ mur vs oO oO 8 8 WN OO Dw COU W WH OO me COUwW oO DW QW NH [ooo nie) A PF REREY EOEWYG CS a P PRLYOY Bf PREYO f REREY p PRESY & Wwnovw P PRERY nN BW HOW Oo W®WNH _ oO on 4 OV 4 oO > CO SMITHSONIAN TABLES. TABLE 11. REDUCTION OF THE BAROMETER TO STANDARD TEMPERATURE. METRIC MEASURES. FOR TEMPERATURES ABOVE 0° CENTIGRADE, THE CORRECTION IS TO BE SUBTRACTED. HEIGHT OF THE BAROMETER HEIGHT OF THE BAROMETER 730 mm. 795 mm. | Attached Ther- : : : : : : o°4 0°6 | mometer. mm, mm. . mm. O° 0.05 0.10 ; 0.05 .18 : -23 z : .18 5 : 36 : : ai “44 . “49 . . -44 7 : .62 . ; -57 .70 : 0.75 .6: : .70 .83 5 .88 . : .83 -95 : 1.01 : : .96 08 r.13 : : 1.09 22 = H _ — 21 OONIADT HhWnH OO 30. 48 61 -74 87 +34 47 60 73 85 Hy OO Hee ee ¢ Sn en | HHH HOW . Castes 99 I2 25 38 51 64 77 go 03 16 NNN ND NNNNH NNN NH NNN ON “I WwWNNN YPRPNN ®WWwWNNN WOwWNNN HK OMON coum Nw Z520 Aw ONS HR Osan ow SSW WW WQwWNNN N “SIAL WW C2 G2 G2 Ge G2 SIAN & Wb “TIS NWO OD Ce WB &® GH W 2 WD 2 Go Go msn & oo ano co on 8 & Ow oO aun NWO Do Do Dw P PEPEY HOWOW on SNR Sy ree a elas na BWNn OW) NR oH nN \o SP PEELOE YY > WN HO ~¢ n WN we | Ne) | ea Ea Aa ae © SMITHSONIAN TABLES. TABLE 12. REDUCTION OF THE BAROMETER TO STANDARD GRAVITY. ENGLISH MEASURES. Reduction to Latitude 45°. From latitude 0° to 45°, the correction is to be subtracted. From latitude go° to 45°, the correction is to be added. HEIGHT OF THE BAROMETER IN INCHES. Latitude. 21 24 25 26 Inch. Inch. | Inch. Inch. 0.056 0.064 | 0.067 0.074 0.055 0.063 | 0.066 0.073 .055| . : .062| .065] . : 2078) .054] . : 200212065)" : .O72 .054]| . : .o61| .064 : .072 SO58i 5 : .061 | .063 : .O71 .053 | O. 0.060 | 0.063 0.070 FO52)|". : .059| .062] . 2 .069 S051 |" * : .058] .o61] . .066| .068 3050)|, : -057,| .060)|"~. : .067 .049] . ‘ .056] .059 ‘ .066 .048 | 0. 0.055 | 0.058 0.065 O47] . : .054| .056 : .063 .046| . : .053] .055| .- ; .062 .045| .O< ; .052| .054 : .060 .044] . ; .050 ).043 | O. 0.049 SOAZIK I: : .047 .040| . : .046 AOZ(s) | : -044 2037) : .043 .036 0.041 5034)|' = : .039 -033 .031 .030 .028 .026 .025 .023 .O21 .01g .O17 .O15 -O14 .O12 0.010 .008 .006 .004 -002 0.000 SMITHBONIAN TABLES. 58 TABLE 13. REDUCTION OF THE BAROMETER TO STANDARD GRAVITY. METRIC MEASURES. Reduction to Latitude 45°. From latitude 0° to 45°, the correction is to be subtracted. From latitude go° to 45°, the correction is to be added. HEIGHT OF THE BAROMETER IN MILLIMETRES. Latitude. 540 |560 580 | 600 | 620 | 640 | 660 | 680 | 700 | 720 | 740 | 760 | 780 mm. mm. }mm.} mm.| mm. | mm, |} mm.; mm. | mm. | mm. }/ mm. 1.44 1.54 | 1.60| 1.65] 1.70] 1.76] 1.81 | 1.86] 1.92] 1.97 | 2.02 On 1.63 | 1.68 1.78 | 1.84 | 1.89 | 1.94] 1.99 1.61 | 1.67 1.77 | 1.82 | 1.87 | 1.93] 1.98 1.60} 1.65 | 1.70] 1.76] 1.81 | 1.86] 1.91 1.59 | 1.64 99 | 1.74] 1.79] 1.84] 1.89 I is I Te 7a | OZ T2MMat7 if, | eo2)| ale Oi7) 352) | 1.41 5 i 1.39 .50| I. 1.35 48/1 1.37 47 | 1 OG) G2 G2 G2 Gd non vfbo oan OQ .60 -70| I.75 |/T.80| 1.85 .58 68)) 1273) G79) 163 -45 I I 256i: 1.65 | 1.70| 1.75 | 1.80 I I -43 41 39 -36 53 BO) les Of Neliey 72) || leery, .60 | 1.65 | 1.69 | 1.74 el ee | NN Go G2 G2 NO HOON NOH WU S57 ile Ole| ke OO!| zit .54| 1.58 | 1.63 | 1.67 -50 | 1.54 | 1.59 | 1.63 -46] 1.51] 1.55] 1.59 -43| 1.47 | 1.51 | 1.55 © G2 Ont Www RRO HOR Cn tS & WON NON & Oo Go Non — OO NN G2 Ge Go e OofN -39 | 1-43 | 1-47 | 1.51 -35 | 1.38 | 1.42 | 1.46 230) E6340 )0.38)| 1-42 226) e208 || des 20 D625) | 25)) Ws 2 Or 0 HoH nn ~ oo a e rt et et et ‘KS ~ STO)|ele20) || de 2 Boe Li |. 05, |e Boi 06 (I. LO}| 1.13)) 1.16 (OL L- O40 1.07 | 110 .96 | 0.99 | 1.02 TN Cr.o ox 1 1 -91 | 0.94 | 0.96 | .85| .87 AO POL It On: ETA FO) ae 268)!" 70 ~ ~ ~ to I On Oo a> UY an AQ - MwWn~N Nn Q—sI CO CO ON 1 Cy nr oO © HAA~AINI C NN NNIW .62| 0.64 56] .58 .50] .51 -44) «45 SOueSo © u oO Cus nun tht Ww hkh bu Nv “ST Oo OO fin _ au ZT Ol32 225) 220 - LQ) ..19 eels .06| .07 LS) BNI H oO Lal = ° n 9 8 0,00 | 0,00 SMITHSONIAN TABLES. TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Zz I fs Values of 2000 X m. (gare eee ‘Tp Mean Tem- Differ- perature ALTITUDE OF STATION IN FEET (Z). nen | of air for | 100 @Fahr, | 100 | 200} 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000] coc. | —20° 3.7 | 74] Itt], 14:8}; 16.59) 22.2 | 25:9.) 20:6 |) ss -2 ee 0 wee — 16 Bu] 7,3, ‘T2.0.| 14.65). 18:3) 22.037 2516)] 220:34// 933-07] eso ounces —I12 3.6 73 10.9 14.5 18.1 27.8] 25.41 (20.0 |) 32.7 | sO. 218 iate — 8 3.6 7.2 | To:8 |" T4.40|| T8iol ers6n 125226 28250 |) 32:40 86.01les-O — 6 3.6 7:2 | 10:7 | “14.3¢)) 729) (25 es.) 28.6) ] 32:2 ees eo — 4 3.6 7.1 |, 10:7 | 24.35)) 27-04|21-ga| 925 ON 28-55] 32010 | eae anrere — 2 BG FeE | LOZ || LAS2 A778) ST sued onl 25-4 lees T.On ene 5 ahaa 0 Ba5 ne LOG Ky ASE L774} 22a) e247 le 20.888 BO is oso ama + 2 3.5 7.0 10.6 14.1 07-60) 20 24-08 2O.0 B07 sees 5s2 aoe 4 35 7-0 | 10.5 | 14.0,| 17-5'| |21.0') 24.55 |, 28.0 | 31-5)| 35-010 3.5 6 3.5 7.0 10.5 13.9 17-4 | 20.9 DAVARI Me 2720) 1 93 0-4e 54.0 ese 8 3.5 G59) V1O.4N |) 130 a7. 4: | 2018))||) 2463412728) este aA Talons 10 B55 6.9: |'_To.4 |, 13:8°| 17.35" 20179) s24%2s| 27-7." sicm Wiegasomecns 12 3.4 6.9) |) 20:3 4|\ 03.8) |) 1752) |= 2016) | e24lr |} S27e5e | ssc On| pasted ames 14 2eA| GO] |) 10! 30/5 1307; 1751) || £20561 2At0! |f 27 Aa BOsoal mode onset 16 Bed. 6:8 |) Tol2_ || 13°65} 17.0 | 2055)" 2359) |27-38 ie sOs7 | oa eet 18 3.4 6:8 | 10:2"| 13.6 | "17-0) |v 20:48|" 23:8) 272282016) esd Ona 20 3.4 6.8 | I0.1 13:5 | 16.9.4 .20.35|.42307 0 27a) 2O:Ael eo sacar meeary 22 3.4 6:7 || 10:2 | 13555) e618) | 20725) 23560 2610" aesO.culleSou7mlieoee 24 3.4 6:7 |! 10.4) |)" 13:4)" 16:8) || 20.57 323550| 26°Sa| a 0:2 ie 53:5uleoeaal 26 B08 6.7 | «10.0,| + 13.4] 16.7. 20:0: |* 23:44) «26.7 Pisor |) aaed eee 28 Bee 6:7 || I0:0))| 913-3 | +16.671" 2o!0 12353, 26:64|8 29-0) | 38-3es.s | 30 203 6.6 9:9) 13°2>|) 16:6.) 19°09) |) 423-2) |= 26u5n| 20:00 63S a aS call 32 258 6.6 9:9 | 13.2 | 16.5 | 19.8 | "23.571. 26:49)" 20:7 |" 33-OnIN3 3 34 aaa 6.6 9:9) 1351 16.4 | 19/7 | 23.04. (26.3 1420.6)! @ 3280 Tina 36 253 6.5 OSn near 16.4 | 19.6] 22.9] 26.2] 29.4] 32-7 | 3.3 38 2.3 6.5 9.8} 13.0] 16.3] 19.5 | 22.8] 26.0] 29.3] 32. 3:3 40 2°2 6.5 O57))|)| 13:04] 6:2 LOIS) 22/7) ||| 825-0) 11 20:25| 3 224aaeee 42 B12 6.5 9:7 | 12.9) 16:0 | 19.47) 22164) 125-8) ||| 29:1 n32-30ins-e 44 3-2 6.4 9.6 | “22.9 |= 16.0 | 19.37) earn | 25.70) 28-00) aeaenes 46 B72 6.4 9.6 | 12.8] 16.0] 19.2 | 22.4] 25.6] 28.8] 32.0] 3.2 48 3.2 6.4 9:6 | “22.7 *15:9"| 1910} 2203) ] -25.5./) 28.7 | VoL Onis = 50 2.2 6.3 9-5 | 12.7] 15.9] 19.0] 22.2] 25.4 28.6 | 31.7 | 3.2 | 52 Bae 6.3 O5e| L216 52a Mo.0n 5 22) x 25.35) 20.Aql | SILOMies 2 54 Ba 6.3 9.4 12.6 L507 i) soso 122.0 2522 28.3 OTe Sal ese 56 2.5 6.3 9.4 | 12.5%) -The7 1 18:8 || (219) 25. | 22a egies aeseue 58 200 6.2 9.4 |' 12.5 | 15.6.) 18.7 | (25:8) 25-0. || acre) ee Qie2 ase 60 3.1 6.2 9:3 | 12:4) 915.5 18.6 | 21.7 , 24.8 | 28:0) ) 30.0 [93-1 | 62 3.1 6.2 9.3| 12:4. | 15:5] 18.6.) 20.6 1 124.77) %27-00) W30.Q aaa) 64 BA0 6.2 9.2 T29 15.4 18.5 21.6 DASO a 27e7 ZOrOnlesatal 66 Bal 6.1 9.2 | 12.3] © 05.3) 28.40|" 2.5 || 42425 2720 3087 eer 68 Bar 6.1 9.2 12:2) r5.3, |) 18.3) 25-4) SAA 27-5) |e oC OMS aoa 70 3.0 6.1 Q.T) | F225) 15.2182") :21.3 (24 Sa 27 640) ee A ee 72 3.0 6.1 Q-L | “T2.0) er5. || 08.2) 20.2 |S 2Ah on 27-3) oOo ao.o 76 ZL0N| O10 9.0] 12.0] 15.0] 18.0| 21.0] 24.0] 27.0] 30.0] 3.0 80 3.0 | {6:0 8.9] 11.9| 14.9|-17.9| 20.9] 23.8 | 26.8] 29.8] 3.0 84 3.0] 5.9 8.9} 11.8 14.8] 17.7 | 20.7) 23.6'|" 26.6) (29.6 }) 370 88 2.9 5.9 S90 | LLe7 14.7 17.6 | 20.5 | 23.5 | 26.4| 29.3 | 2:9 g2 2.9 5.8 8.7 | 11.6 | THs | 07.4 | 20.4 1 923.27 eeG.28| e209: ee.G 96 2.9 5.8 8.7 | 11.5 | 14:4] 17.3 | 20.2] 23.1 | 26.07) §28.9 1p2:9 SMITHSONIAN TABLES. TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Values of 2000 X m. m Zz I ~~ 56573+123-10+.0032 1+ | Mean Tem- | perature of air column. OFahr. 1100 ALTITUDE OF STATION IN FEET (2). 40.7 40.3 39-9 nuw oo OO Nano Row O2 02 G) Gd Go nannn oO OO AINOHK BAUOO HKRAUDO Ob NO QOoww HBR um nn Hit wo nun SR CA oneien Hoe na NEUODH BRADHH NDOOaN = BRERER aanne SRR ARR PARA b ha ae ORR DG ANIM AAIAIN CO OWMMM WPWW WOO WW GD Oo Ww anna anno UN Si CICS CD ace cP oe ty \O ~ ca 0 oO \O oy WONT O B® UST OG) 0) Od GO) Go AANA ANAADAD AD o aw Ow No ~ 2 G2 GW OG O92 wWXW WW WwW WW W BPWWWW HWW W WW oo FR HNN NNNNN WWWWW OW RAR SHH UNI ADAD aww MOH Wf OG) G» Os in1tn wn wn U1 tw NNN OO on ¢ 2 G00 G0 Oo A~I OO OV nw ONO on C1 exe nNhUS Vee Ss Ovo ne nw on U1 G2 Ga Go Go G “IsI™ PBMAAHD AAD HDAIAW AIAN H HHHoH OO doe VI RL RuE Cn ol Ol & onc 7) O Dw0 4 vy UNTO HE OOH BODO? b On anno 0 O OV rat. ¢ NOR FAONHL N ¢ NNNND QDQOoWOWw HhpPbLLHY WWWWD WWW®® WWW) Ww NOOHW fF G0 Go Go Go -— SS eR DA ¢ WUK ADAH No OOM Doo BWWWW WWWWW WWW WD vo OnR UO CO m Go G2 Ge Wo C ww UI Wn OAWUINT O BHO CO umn ~ Se aiaens sais . ON DH UN ORL ~m>tndcrd1 cic CMtiiind Ua ¢ DHHD OO OY nN OA RPNTI HR HU NI CON OAH NNNKR® OO OHnaHLE SHEESH o) WH WWWWW Oo oo WO PNOGME BE AAAAM ADAA G2) O22 GD GW Nanni Un Un NOH AH P PYEHY FO OOO0O0 OO WOO wW Ww NOnNMO WU AN onnnanan an aA UMN > ou NOs Tiel I Oba wd OG Go Gd Go Go OP HH Oo Sale oe = Oo on oO “I vy SMITHSONIAN TABLES. TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Values of 2000 < m. Mean Tem- perature of air column. I 6 Fahr. ue —20° 77-6 —16 76.9 —I2 76.2 ro 75-5 |} — 6 75-2 5 74.5 =e 74-5 0 74-2 + 2 73-9 4 73-5 6 1 8 72.9 10 72.6 12 72.3 14 72.0 16 71.6 18 7 | 20 71:0 22 70.7 24 79-4 26 7OsL 28 69.5 30 69.5 22 69.2 34 69.0 36 68.7 38 68.4 | 40 68.1 42 67.8 44 67.5 46 Tis 48 66.9 50 66.6 52 66.3 54 66.1 56 65.8 58 65.5 60 65.2 62 64.9 | 64 64.7 66 64.4 68 64.1 | 70 63.9 | 72 63.6 | 76 63.1 80 62.6 | 84 62.1 88 61.6 g2 61.1 96 60.6 2200 | 2300 | 2400 | 2500 $153 80.6 79.8 Ox NHHNO FN OLN RARER GOGEE SANAAH DII STST STS ST ONTNTNSIONN ONNNNT SD OST OST ST DAOKMO wna Z MN SS eee 56573+123.16+.003Z Space 1+B $5.0 $4.2 53-5 82.7 82.3 82.0 81.6 81.2 $0.9 $0.5 80.2 79.8 2030 PAPO O WOOONADA ONUONH UOMO HUI ONMN cy O HANNNKH&® SCWwoOHLH S£$UNNMNMD DAN WN SS SS SS ST SST TS SST ST WOON 80.8 $0.5 s1~ ee on 00 CO.0 10 eon On SSSI SIS oo SAGER RAMAA AAI HNO WHAONMN ONMNCOH OAOHMN OH SINININ STN SINTON NTN ONT ST STS So NST ST SSS So Ne OO ow 69.8 69.2 SMITHSONIAN TABLES. 92.4 91.5 90.7 89.9 89.5 89.1 88.7 88.3 | 87.9 87.5 87.2 86.8 8.3 oO NY PEGEA AA HAIN HNORWOMNH STO WNOW A O NS OV Nd ALTITUDE OF STATION IN FEET (2). 2600 | 2700 | 2800 | 2900 | 3000 96.1 | 99.8 | 103.5 | 107.2] II0.9} 3.7 95-2 | 98.9 | 102.5 | 106.2} 109.8] 3.7 94.3 | 98.0 | 101.6} 105.2} 108.8] 3.6 93:5 Q7.I | 100.7] 104.3] 107.9} 3.6 93.1 | 96.6 | 100.2] 103.8] 107.4] 3.6 Pah \) Clay 99.8 | 103.3 | 106.9] 3.6 92.2 | 95.8] 99.3] 102.9] 106.4] 3.5 g1.8 | 95.4 98.9 | 102. 106.0] 3.5 91.4 | 95.0] 98.5] 102.0] 105.5] 3.5 91.0 | 94.5 98.0] IOI.5 | 105.0] 3.5 90:6 | 94.1 | °97:6:| BOTT || To4:6il se55 go. 2 93-7 97.2 | 100.7 | 104.1] 3.5 89.9 | 93-3 | 96.8 100.2 | 103.7] 3.5 89.5 | 92.9 | 96.3] 99.8] 103.2] 3.4 89.I | 92°5 95:9] 99.4} 102.8] 3.4 88.7 | 92.1 95-5 98.9 102.3} 3.4 88.3 | 91.7 | 95-1] 98.5} IOT.9] 3.4 875914) (Ol-3 all) C4574" nOoas elo. Simon 8720%,| 29059) |," 94°35) 1O7-74| tOL.O ea A 87.2 | 90.6 | 93-9] 97.3] 100.6] 3.4 86.8 | 90.2 | 93.5} 96.9] 100.2] 3.3 86.5 | 89.8 | 93.1] 96.4] 99.8] 3.3 86.1 | 89.4 | 92.7] 96.0 99-3] 3-3 85-7 89.0 92.3] 95.6] 98.9] 3.3 85.4 | 88.7 O191|) 995.2) 1) 98:5 85.01], 88.3)|. 29L-5\|) (94.811 Oo. tleaes 84.6 | 87.9] 91.2] 94.4] 97-7] 3-3 $4.3 87.5 90:8)|| {94-01 9 7e2)1i8352 83.9 | 87.1 90.4] 93.6) 96.8] 3.2 83.6 | 86.8 | 90.0] 93.2] 96.4] 3.2 83.2 | 86.4 89.6| 92.8] 96.0] 3.2 82.8 | 86.0 | 89.2] 92.4] 95.6]| 3.2 82.5 | 85:7 | 88:8) (92:01) “95-2)1e3%2 82.1 | 85.3 | 88.4] 91.6] 94.8] 3.2 81.8 | 84.9 | 88.1] 91.2] 94.4] 3.1 81.4 | 84.6 07.7 |, 90:8)||) OAFON 35m Si.L |) Sd. 2) |) S7-sh OOM al OZcOlmaeL S087) I 1O3s0 87.04 90.1 O852) [eau 80.4 | 83.5 86.6] 89.7] 92.8] 3.1 80.1 $3.1 86:2)]/ SSOr3i | O24 iesed 79.7, ||| 02-0 85.9] 88.9| 92.0] 3.1 79.4 | 82.5 85.5| 88.6] 91.6] 3.1 79.1 82.1 85.1 08:2) OL. 2118350 Fer. | mite 84.8] 87.8] 90.9] 3.0 78.1 SI. S450 37.0 ey GOsta esto 775 \ vols 83.4| 86.4] 89.4] 3.0 76.8 | 79.8 S207 WE S5a7 ||) oc-Ole.O 7G: 2a a7 OeL 82.1] 85.0] 87.9] 2.9 75.6 | 78.5 81.4| 84.3] 87.2] 2.9 75,0 | 77.9 |. 80.8) 93.71] S6.5)162:9 TABLE 14, REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Z I ” ~ 56573-+123.10-+.0032 1+-8 Values of 2000 * m. Mean Tem- perature of air column. 6 Fahr. ALTITUDE OF STATION IN FEET (Z). 3100 | 3200 | 3300 | 3400 | 3500 | 3600 | 3700 | 3800 | 3900 —20° 114.5 | 118.2] 121.9] 125.6] 129.3] 133.0] 136.7] 140.4 144.1 —16 113.5 | 117.2] 120.8] 124.5 | 128.1] 131.8] 135.5 | 139.1 | 142.8 -—I2 112.5 | 116.1 | 119.7 | 123.3 | 127.0] 130.6| 134.2] 137.9| 141.5 III.5 | 115.1 | 118.7] 122.3 | 125.9] 129.4] 133.0] 136.6| 140.2 IIT.O | 114.5} 118.1] 121.7] 125.3] 128.9| 132.4] 136.0| 139.6 110.5 | 114.0} 117.6] 121.2] 124.7] 128.3] 131.9] 135.4| 139.0 110.0 | 113.5 | 117.1 | 120.6] 124.2] 127.7] 131.3] 134.8] 138.4 109.5 | 113.0] 116.6] 120.1 | 123.6] 127.2] 130.7| 134.2| 137.8 109.0 | 112.5 | 116.1] 119.6] 123.1 | 126.6] 130.1 | 133.6] 137. 108.5 | 112.0] I15.5| 119.0] 122.5 | 126.0] 129.5] 133.0 108.1 | 111.6] 115.0} 118.5 | 122.0] 125.5 | 129.0 132.5 107.6 | II. | 114.5 | 118.0] 121.5 | 124.9| 128.4 131.9 WWWW WWW 107.1 | 110.6 | 114.0] 117.5] 121.0 EAS tak 27. Gh sata 106:7 | LIO:T | 113:6,|' 117-0.| 120.4 : Lesa L307 106.2 | 109.6 | 113.1 | 116.5 | 119.9 53) || £26:8'! 130:2 105.8 | 109.2 | 112.6] 116.0] 119.4 5 126.2 | 129.6 105.3 | 108.7 | 112.1] 115.5 | 118.9 EQ alial25 570) L2Qsi 104.9 | 108.2} III.6| 115.0] 118.4 .8 | 125.1 | 128.5 104.4 | 107.8} III. | 114.5] 117.9 ; 124.6 | 128.0 104.0 | 107.3 | I10.7| 114.0] 117.4 : T2450 L277 103.5 | 106.9 | 110.2] 113.5] 116.9 : 123.6 | 126.9 103.1 | 106.4 | 109.7 | 113.1] 116.4 : 123.0] 126.4 102.7 | 106.0} 109.3 | 112.6] 115.9 : L225 aeL25eS 102.2 | 105.5 | 108.8] 112.1] 115.4 é 1225 One 2523 101.8 5. 108.3 | I11.6] I14.9 120.5) || 12483 IOI.3 F 107.9 | I1I.2]| 114.4 U2T.Oi| L2As2 100.9 . LO7EAG eT LO:7;,| STI3¢6 120245 | 12307 LLQSOy 12352 119.4 | 122.6 TIS.9)| 1227 118.4 | 121.6 e749) a 2a I17.4.| 120.5 116.9 | 120.0 116.4] 119.5 II5.9} II9.0 TE5.4) |) TrIse5 108.7 : II14.9| 118.0 108.2 ene Luqeds lems 107.8 EO) |) 1632) Pol 172O 107.3 24S) TIS) 5), Loss 106.9 : I13.0| 116.0 WWW WW WOW» WOwWwWWw BHAARA PARAM AnDAAN AAAD auN He ARH OW W®WARU WH : 1H MDWOKf ODHRNW OMNO AN DH 1 G Go Go OOS NY WWWWwW WWWWW Ww t 0 OOHHN NO c < Do wha oO OM aH a tN Nsw Nb W Go We Wo 100.5 100.0 99.6 99.2 98.8 98.3 97-9 97-5 97.1 96.7 96.3 d 102.5 | 105. 95-9 5. 102.0} 105. 95.5 3.5 | IOI.6] 104. 95.1 8. IOI.2]| 104. 94.7 2 100.8 | 103. 94.3 ; 100.3 | I03. 93-9 . 99:9 93.1 3 99.1 5 105.1 : DCTS T || Sigs Lae 92.3 a -3| 104.3 i TLIO Ties 91.6 : 97-5 3 103.4 F 109.3 | I12.3 90.9 ‘ 96.7 102.6 -5 | 108.4] II1.4 90.1 : 96.0 101.8 ‘ 107.6 | 110.5 107.0| II0.2]| 113.4 106.5 | 109.7] I13.0 106.0 | 109.3 | 112.5 105.6 | 108.8] 112.0 105.1 | 108.3] I1I.5 Mon! ene Mu Oe G2 G Go Go NNN NN | 104.7 | 107.9] III.o [04.2 | I07 I10.5 | 103.8] 106. 110.1 103.3 | 106 109.6 | 102.9] 106. 109.1 CON Der Of ¢ Oo I NNYKO NDNON DN OY NO wHH ND HRN NW Ww Ax NNT He HNN "G2 C) Ge Go Go H NS HH Mo WHAH OMoOok 5 NO OO} OH OH HOHNIN YUN 106.4 2 112.5 | 115.5 106.0 : II2.0] I15.1 oO % Ox HO 2 COW WHO Oo Ww 89.4 ‘ 95.2 IOI.O .8| 106.7 | 109.6 SMITHSONIAN TABLES. TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Values of 2000 < m. m= Z I 56573+123.18+.003Z 1+8 Mean Tem- perature of alr column. 6 Fahr. ALTITUDE OF STATION IN FEET (Z). 4400 | 4500 | 4600 162.6} 166.3 | 170.0 161.1 | 164.8] 168.4 159.6 | 163.3 | 166.9 158.2| 161.8] 165.4 157.5 | 161.1] 164.7 156.8} 160.4] 163.9 156.1] 159.6] 163.2 | 155.4] 158.9} 162.5 154.7 | 158.2] 161.8 154.0] 157.5] I61.0 153-4| 156.9] 160.3 152.7] 156.2] 159.6 152.0] 155.5] 159.0 151.4] 154.8] 158.3 150.7 | 154.2| 157.6 150.1} 153.5 | 156.9 149.5 | 152.9] 156.2 148.8 | 152.2] 155.6 148.2} 151.6} 154.9 147.6] 150.9] 154.3 146.9] 150.3] 153.6 146.3} 149.6] 153.0 145.7] 149.0] 152.3 145.1 | 148.4] 151.7 144.5 | 147.7] I51.0 143.8} 147.1] 150.4 143.2] 146.5 142.6] 145.8 142.0| 145.2 141.4 | 144.6 140.8 | 144.0 140.2} 143.4 139.6} 142.7 139.0] 142.1 138.4 | I41.5 137.8 | 140.9 137.2 | 140.3 = eS = i GD id id ¢ &® > AD WI Go o> HRHNN NNNNND WOWWWW OoOAAL SPHHA ANN AKDDAA Ann — eS Re G Go G ¢ m= s“T tb ON Ow On I 2 ~ ~ HAA Oe WW WWW HHN®WW HH Me et Mt el 0D WON | ¢ DR Go DH WD DV ON NI DMOO re) Ana RH He eH ~ ha NN Ww cof CO mH Os HH WO WH GW HWW Gb. ~ mH Nh Ge Go NO NH ew SHU DAD oH GH © rs O HAH 2 G2 G2 G2 ° oORn Oo WWWWW GW nv wun ~ CO.O IN 0 SP PPELHY OH HEHYH GCHOHHDA GHHHH HOHHY HOOD HBHWHO DHWEW WHEW Gh © O00059 OO H Ww SMITHSONIAN TABLES. 64 TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Values of 2000 X m. m Zz I ~ §6573+123.18+.0032 1+8 Mean Tem- perature of air palnme: 5200/5300 5800 | 5900 6 Fahr. ALTITUDE OF STATION IN FEET (Z). 192.1 | 195.8 é 214.3 | 218.0 190.4} 194.0 5. 27253 5|' 2IGLO 188.7 | 192.3 ; 210.4] 214.0 187.0] 190.5 ; 20855) 202.0 186.1 | 189.7 ‘ : 207.6] 211.2 185.3 | 188.9 : 206.7 | 210.2 184.5 | 188.0 5: 205.7 | 209.3 ikere7/ || ake ey : 204.8 | 208.4 182.8 | 186.4 : ; .4.| 203.9] 207.5 182.0} 185.5 : ; 203.0] 206.5 181.3 | 184.7 : -7 | 202.2] 205.6 180.5 | 183.9 ; 201.3 | 204.8 | H nu ANI CEH GW PANO NF AOC HHHNND NKHNKKN OHHH GQoOARAR RABRAG ADiOaan Anan TOu7 eles el ; 200.4} 203.9 178.9 | 182.3 ; 199.5 | 203.0 178.1] 181.6 ; 198.7 | 202.1 177.4| 180.8 : : 197.8] 201.2 176.6 | 180.0 : 197.0} 200.4 175.9] 179.2 ‘ 196.2 | 199.5 B75 eos ; 195.3 | 198.7 WA SAN LI 7e7, ¢ 194.5 | 197.8 073 OiL77.0 ¥ 3 193-7 | 197.0 172.9 | 176.2 ; 192.9] 196.2 172.2| 175.5 : 192.0} 195.3 171.4 | 174.7 4. I9QI.2] 194.5 170.7 | 174.0 33. 190.4 | 193.7 170.0 | 173.2 : : 189.6 | 192.9 169.3 | 172.5 32. 188.8 | 192.0 ww WW WW WW OD WWWW®W WWW Wo 168.5 | 171.8 5 188.0} I9gI.2 167.8 | 171.0 : 187.2] 190.4 167.1 | 170.3 79. 186.4 | 189.6 166.4 | 169.6 79. 185.6] 188.7 165.6] 168.8 : 184.8 | 187.9 164.9 | 168.1 164.2 | 167.4 163.5 | 166.7 162.8| 166.0 162.1} 165.3 184.0] 187.1 183.2] 186.3 182.4 | 185.5 181.6 | 184.7 180.8 | 184.0 SS oe NSN NNINININ Q RAAAT 161.5 | 164.6 180.1 | 183.2 160.8] 163.9 : : 17973) | lO2-4. 160.1 | 163.2 ‘ ; 178.6 | 181.6 159.4] 162.5 : : 177.8 | 180.9 158.8 | 161.8 77 |weboOs L YW wWww WD WO G) DW WW OW Bee ee Re 159.1) eLolet 176.3] 179.4 157-5 | 160.5 175.6] 178.6 156.2 | 159.2 aoa 154-9 | 157-9 172.8 | 175.7 153-6] 156.6 L704 | 74.3 152.4] 155.3 170.0 | 172.9 PSI Aae 168.6 | 171.5 oO NH NNWWW WwW ow OO 000 150.0] 152.9 167.3 | 170.2 SMITHSONIAN TABLES. 65 TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Z I 2 xX m. m= ————————§$§__—_—_—— -—— Values of 2000 X m 565734-123.10 4-.003z rp ee ALTITUDE OF STATION IN FEET (2). of air pe ae 6500 | 6600 6700 6800 6900 7000 —20° 229.1 | 232.8] 236.4 | 240.1 | 243.8] 247.5] 251.2] 254.9] 258.6 225.4 — 16 223.3 | 227.0| 230.6| 234.3 | 237.9] 241.6| 245.3 | 248.9 | 252.6] 256.2 —I12 221.3 | 224.9| 228.5 | 232.2] 235.8] 239.4] 243.0] 246.7 | 250.3| 253.9 3,| 222.9] 226.5] 230.1] 233.7| 237.3| 240.9] 244.5 | 248.1] 251.6 3,| 221.9| 225.5 | 229.1 | 232.6] 236.2] 239.8] 243.4 | 246.9] 250.5 .4 | 220.9| 224.5 | 228.0] 231.6] 235.2| 238.7 | 242.3 | 245.8] 249.4 4 4 219.9| 223.5 | 227 230.6 | 234.1 | 237.7] 241.2] 244.8] 248.3 2T90)|) 222. 5220: 214.5 | 218.0] 221.5 | 225. 213.5 | 217.0] 220.5 212.6 | 216.1 | 219.6] 223. QUT) 215.2)| 218501) 222° 229.6 | 233.1 | 236.6) 240.1 | 243.7] 247.2 228.5 || 232.1 | 235.6)|| 230.1 | 242/61) 246.5 227.5 | 231.0| 234.5| 238.0] 241.5] 245.0 226.6 | 230.0] 233.5 | 237.0] 240.5] 244.0 225.6 | 229.0] 232.5 | 236.0] 239.4] 242.9 vd iS) ASG PEKKA BYWEY HOY HHOOO OOHH HHHBDKH KHDNKHDNN OHHOoOHW GHOAAA PAH ANUAUAH AADAA avr~ 10 210.8 | 214.2] 217.7| 221.1] 224.6] 228.0] 231.5 | 235.0| 238.4] 241.9 12 209.9 | 213.3 | 216.7| 220.2 | 223.6] 227.1} 230.5 | 233.9] 237-4] 240.8 14 209.0 | 212.4] 215.8| 219.2] 222.7] 226.1] 229.5| 232.9| 236.4] 239.8 | 16 208.1 | 211.5| 214.9| 218.3 | 221.7| 225.1 | 228.5 | 231.9] 235.3| 238.8 | 18 207.2 | 210.6| 214.0] 217.4] 220.8] 224.2] 227.6] 230.9] 234.3 | 237-7 20 206.3 | 209.7] 213.1 | 216.4 | 219.8| 223.2] 226.6] 230.0] 233.3] 236.7 22 205.4 | 208.8] 212.2] 215.5 | 218.9] 222.3] 225.6] 229.0] 232.4] 235.7 24 204.6 | 207.9 | 211.3] 214.6] 218.0] 221.3] 224.7 | 228.0] 231.4] 234.7 26 203.7 | 207.0] 210.4] 213.7] 217.0| 220.4] 223.7 | 227.0] 230.4 | 233.7 28 202.8 | 206.2} 209.5 | 212.8| 216.1] 219.4] 222.8] 226.1 | 229.4] 232.7 | 30 202.0 | 205.3 | 208.6| 211.9] 215.2] 218.5] 221.8] 225.1] 228.4] 231.8 32 201.1 | 204.4| 207.7| 211.0] 214.3 | 217.6) 220.9] 224.2] 227.5] 230.8 34 200.2 | 203.5 | 206.8] 210.1 | 213.4] 216.7| 219.9] 223.2 | 226.5 | 229.8 36 199.4 | 202.7] 205.9| 209.2| 212.5] 215.7| 219.0] 222.3 | 225.5 | 228.8 38 198.5 | 201.8] 205.0| 208.3 | 211.6] 214.8] 218.1 | 221.3] 224.6] 227.8 40 197.7 | 200.9| 204.2] 207.4] 210.6] 213.9] 217.1 | 220.4 | 223.6 226.8 2 196.8 | 200.1 | 203.3 | 206.5 | 209.7| 213.0] 216.2] 219.4] 222.6] 225.9 44 196.0 | 199.2 | 202.4 | 205.6] 208.8] 212.1] 215.3 | 218.4 | 221.7 | 224.9 46 195.2 | 198.4 | 201.5 | 204.7] 207.9] 211.1 | 214.3] 217.5 | 220.7} 223.9 48 194.3 | 197.5 | 200.7] 203.9] 207.0| 210.2] 213.4] 216.6] 219.8 | 223.0 50 193.5 | 196.6] 199.8| 203.0] 206.2 | 209.3 | 212.5] 215.7 | 218.8 | 222.0 52 192.6 | 195.8] 199.0] 202.1 | 205.3 | 208.4] 211.6] 214.7 | 217.9| 221.1 54 191.8 | 195.0] 198.1 | 201.3 | 204.4 | 207.5] 210.7 | 213.8] 217.0] 220.1 56 I91.0| 194.1 | 197.3| 200.4 | 203.5 | 206.7] 209.8] 212.9| 216.0] 219.2 58 190.2 | 193.3 | 196.4| 199.5 | 202.7| 205.8] 208.9] 212.0] 215.1] 218.3 60 189.4 | 192.5 | 195.6| 198.7] 201.8] 204.9] 208.0] 211.1 | 214.2 62 188.6 | 191.7] 194.8] 197.9| 201.0| 204.1] 207.2] 210.2] 213.3 | 216.4 64 187.8 | 190.9 | 194.0] 197.0| 200.1 | 203.2 | 206.3] 209.3 | 212.4] 215-5 66 187.0 | 190.1 | 193.1 | 196.2] 199.3| 202.3] 205.4| 208.5] 211.5 | 214.6 68 186.2 | 189.3 | 192.3] 195.4] 198.4 | 201.5 | 204.6| 207.6] 210.7 | 213.7 70 185.5 | 188.5] 191.5 | 194.6] 197.6 | .200.7| 203.7} 206.7] 209.8] 212.8 72 184.7 | 187.7] 190.8| 193.8] 196.8] 199.8] 202.9] 205.9] 208.9] 211.9 2| 189.2] 192.2] 195.2] 198.2] 201.2] 204.2] 207.2] 210.2 80 181.7 | 184.7] 187.6] 190.6] 193.6] 196.6] 199.6] 202.5 | 205.5 | 208.5 84 180.2 | 183.2] 186.1} 189.1] 192.0] 195.0] 197.9] 200.9] 203.8| 206.8 7 184.6 | 187.6] 190.5 | 193.4] 196.3] 199.3] 202.2] 205.1 183.2 | 186.1] 189.0] 191.9] 194.8] 197.7 | 200.6] 203.5 96 175.9 | 178.8 | 181.7] 184.6] 187.5 | 190.3 193.2 | 196.1 | 199.0} 201.9 P PYHYY OO GBOKHHY OYWHE HHOHHY WHOOH OHOWWH KOO © 00000 00 OHHHH SMITHSONIAN TABLES. 66 TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES, Values of 2000 X m. m Z ~ §6573+123.10 +.0032 zr ry Mean Tem- _ perature of air column. 6 Fahr. 7500 ALTITUDE OF STATION IN FEET (Z). 4) 277.1 C 9| 274.5 | 278.2] 281.9] 285.5 | 289.2] 292.8 -4| 272.1 | 275.7} 279.3 | 282.9 | 286.6| 290.2 oO 8 7 2 — 16 259.9 | 263.6 | 267.2) 2 2 - to to wn = oO tN OV _ No tO ON aay co AnI~NI 269.6 | 273.2] 276.8| 280.4] 284.0] 287.6 268.4 | 272.0| 275.6| 279.1 | 282.7] 286.3 267.2 | 270.8| 274.3 | 277.9] 281.5 | 285.0 251.8 | 255.4 | 258.9 | 262.5 | 266.0] 269.6] 273.1 | 276.7 | 280.2] 283.8 | 254.3 | 257.8] 261.3 | 264.9| 268.4] 271.9] 275.4] 279.0| 282.5 249.6 | 253.1 | 256.7} 260.2 | 263.7] 267.2| 270.7} 274.2| 277.8] 281.3 248.5 | 252.0] 255.5 | 259.0] 262.5] 266.0] 269.5 | 273.0] 276.5 | 280.0 247.5 | 250.9| 254.4| 257.9| 261.4| 264.9] 268.4] 271.8] 275.3] 278.8 8 246.4 | 249.8 | 253.3 | 256.8} 260.3 | 263.7 | 267.2| 270.7| 274.1| 277.6 10 245.3 | 248.8 | 252.2] 255.7] 259.1 | 262.6] 266.0] 269.5 | 272.9] 276.4 12 244.3 | 247.7 | 251.1] 254.6] 258.0) 261.4] 264.9] 268.3 | 271.8] 275.2 14 243.2 | 246.6] 250.1] 253.5 | 256.9 | 260.3 | 263.8] 267.2] 270.6] 274.0 16 242.2 | 245.6 | 249.0] 252.4] 255.8] 259.2] 262.6] 266.0] 269.4] 272.8 18 241.1 | 244.5 | 247.9] 251.3] 254.7} 258.1] 261.5 | 264.9] 268.3] 271.7 Aen OO nk aw to n 2 “I PPRPAPXAHP POR HWHW OOWWW HOW W BHWWWW WHWHW WWWW WH to HHHNN NNNNHD OWWWH WHORAKR RARA Anan Aaan oa 20 240.1 | 243.5 | 246.9] 250.2] 253.6] 257.0] 260.4] 263.8] 267.1] 270.5 22 239.1 | 242.4] 245.8] 249.2] 252.5 | 255.9] 259.3 | 262.6| 266.0] 269.4 24 238.1 | 241.4] 244.8} 248.1 | 251.5 | 254.8] 258.2] 261.5 | 264.9] 268.2 26 237-1 | 240.4 | 243.7} 247.1 | 250.4 | 253.8] 257.1 | 260.4] 263.8] 267.1 28 236.1 | 239.4 | 242.7| 246.0] 249.4] 252.7| 256.0] 259.3 | 262.7] 266.0 30 235.1 | 238.4 | 241.7] 245.0| 248.3 | 251.6] 254.9] 258.2] 261.5] 264.8 | 32 234.1 | 237.4 240.7] 243.9] 247.2] 250.5 | 253.8] 257.1] 260.4] 263.7 | 34 233.1 | 236.3 | 239.6] 242.9] 246.2| 249.5] 252.8] 256.0] 259.3 | 262.6 36 232.1 | 235.3 | 238.6] 241.9] 245.1 | 248.4| 251.71 254.9 258.2 | 261.5 38 231.1 | 234.3 | 237.6 | 240.8 | 244.1 | 247.3] 250.6] 253.9] 257.1] 260.4 40 230.1 | 233.3 | 236.6] 239.8] 243.0] 246.3] 249.5 | 252.8] 256.0] 259.2 42 229.1 | 232.3 | 235.5 | 238.8] 242.0] 245.2] 248.4 | 251.7| 254.9] 258.1 44 228.1 | 231.3 | 234.5 | 237.7| 241.0] 244.2] 247.4| 250.6] 253.8] 257.0 46 227.1, | 23013] 233-5 |. 236-7) 239.9 | 243.1 | 246.3 || 249:5 | 252.7) 255.9 48 226.2 | 229.3 | 232.5] 235.7] 238.9] 242.1] 245.3| 248.4] 251.6] 254.8 50 225¢2)|§ 220.4) 221523407 5237.0) 241.0) 2442 | 247-4) | 2505 |) 25327 52 224.2 | 227.4] 230.5 | 233.7] 236.8] 240.0] 243.2] 246.3] 249.5] 252.6 54 223.3 | 226.4 | 229.5 | 232.7| 235.8] 239.0] 242.1 | 245.3] 248.4] 251.5 56 222.3 | 225.4] 228.6| 231.7] 234.8] 238.0] 241.1] 244.2] 247.3] 250.5 538 221.4 | 224.5 | 227.6| 230.7] 233.8] 236.9] 240.1 | 243.2] 246.3 | 249.4 60 220.4 | 223.5 | 226.6| 229.7| 232.8] 235.9] 239.1 | 242.2] 245.3] 248.4] 3.1 | 62 219.5 | 222.6] 225.7} 228.8] 231.9] 235.0] 238.0] 241.1 | 244.2] 247.3] 3.1 64 218.6 | 221.7 | 224.7| 227.8] 230.9] 234.0| 237.0] 240.1 | 243.2| 246.3] 3.1 | 66 217.7 | 220.7 | 223.8| 226.9] 229.9| 233.0] 236.1] 239.1 | 242.2| 245.2 ae | 68 216.8 | 219.8 | 222.9] 225.9| 229.0] 232.0] 235.1] 238.1 | 241.2| 244.2] 3.0 70 215.9 | 218.9 | 221.9) 225.0 | 228.0| 231.1 | 234.1 | 237.1 | 240.2] 243.2] 3:0 72 215.0) || 200.0) |1 227,01) 224014 227.1 | 230:1)| 233.1 | 23612'\) 230.2 || 242/31) 3.0 76 2S. 2) || 21652)| e262) 22252 225.2)|| 228'2)| s23me2 | 2a4noi| 227.2 ..|| 24022111 3.0) | 80 ZT 5 | 214.4 | 217.4 | 220.4] 223.4] 226.4] 229.3 232.3] 235.3| 238.3] 3.0 84 209.8 | 212.7 | 215.7| 218.6| 221.6] 224.5| 227.5 | 230.4| 233.4| 236.3] 2.9 388 208.1 | 211.0| 213.9| 216.9] 219.8] 222.7| 225.6| 228.6] 231.5] 234.4] 2.9 92 206.4 | 209.3 | 212.2] 215.1 | 218.0] 220.9] 223.8] 226.7] 229.7 | 232.6] 2.9 | 96 204.8 | 207.6} 210.5 213.4 | 216.3 | 219.2| 222.1 | 224.9] 227.8| 230.7] 2.9 | | SMITHSONIAN TABLES, 67 TABLE 14. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Values of 2000 X m. Mean Tem- _ perature of air column. 6 Fahr. —20° — 16 —I12 MAL NO nk aw Do Gao NH ANI & Abo DL OV 241. Mm = 56573-+123-1 O-+.0032 Z ALTITUDE OF STATION IN FEET (Z). nN On COsOo! C010 Nw NON NOON Sh ann on NIWO AN WHC ww fh ans 245. 243. WNNN ND 39-4 8400 8500 310.3 | 314.0 307.5) | 31r-i 304.7 | 308.3 302.0 | 305.5 300.6 | 304.2 299.3 | 302.8 297-9 | 301.5 296.6 | 300.2 295.3 | 298.8 294.0 | 297.5 292.7 | 296.2 291.5 | 294.9 290.2 | 293.7 289.0 | 292.4 2357 a7, | e2O lar 286.5 | 289.9 285.3 | 288.7 284.0 | 287.4 282.8 | 286.2 281.6 | 285.0 280.5 | 283.8 279.3 | 282.6 278.1 | 281.4 276.9 | 280.2 275.7 | 279.0 274.5 | 277.8 273.4 | 276.6 DOD e275 A 271.0| 274.3 269.9 | 273.1 268.7 | 271.9 267.5 | 270.7 266.4 | 269.6 265.3 | 268. 264.1. | 267.38 263.0] 266.1 261.9] 265.0 260.8 | 263.9 259.7 | 262.8 258.6 | 261.7 257.5 | 260.6 256.4 | 259.5 255.4] 258.4 254-3 | 257-3 259.2) S25 552 250.2 | 253.1 248.1 | 251.1 246.1 | 249.1 244.2 | 247.1 242.2 | 245.1 8600 317-7 314.8 BII.9 309.1 307.8 306.4 305.0 303-7 302.4 301.0 299-7 298.4 297.1 295.8 294.6 293-3 292.1 290.8 289.6 288.3 287.1 285.9 284.7 283.5 282.3 281.1 279-9 278.7 277-5 276.3 275.1 273-9 2727 27126 270.4 269.3 268.1 267.0 265.9 264.7 263.6 262.5 261.4 260.4 258.2 256.1 254.1 252.0 250.0 248.0 8800 B25or 322.1 319.2 316.3 314.9 313-5 312.1 Z1Os7 309.4 308.0 306.7 395-3 304.0 302.7 301.4 300. I 298.5 297.6 296.3 295.0 293.8 292.6 291.3 290.1 288.5 287.6 286.4 285.2 283.9 282.7 281.5 280.3 279.1 277-9 27 O47, 275-5 274.3 273.2 272.0 270.9 269.8 263.6 267.5 266.4 264.2 262.1 260.0 257-9 255.8 253.8 8900 328.8 325.8 322.8 319-9 318.5 Bla. 315-7 314.3 312.9 311.5 310.2 308.8 397-5 306.2 304.8 393-5 302.2 300.9 299.7 298.4 297.1 295-9 294.6 293-4 292.1 290.9 289.6 258. 4 287.2 285.9 284.7 283.5 |. 282.2 281.0 279.8 278.6 277-5 276.3 275 ai 274.0 272.8 277 270.6 269.4 267.2 265.1 262.9 260.8 258.7 250.7 HHHHD RNHKDKDHN OHHH GORA BARRA AUDA AaDaAD aU P PP YEW GH POHHH OBYWWY GHOHHH BWWHH HHOWYWY SHODDY BHYYO OOH WO 0 00000 00 OHHH SMITHSONAN TABLES. 68 TABLE 15. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Correction of 2000 m for Latitude: 2000 m X 0.002662 cos 2. For latitudes 0° to 45°, the correction is to be subtracted. For latitudes 45° to go°, the correction is to be added. LATITUDE. 5 10° 15° 20° 25° 30° 35° 40° 45° 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 O.1 o.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Oar o.1 O.1 O.1 O.1 0.0 0.0 0.0 0.0 O.1 I 0.1 0.1 O.1 O.1 0.0 0.0 0.0 O.1 0.1 O.1 0.1 Op Ont 0.0 0.0 0.0 0.2 0.2 Oo. O.1 O.1 O.1 O.1 0.0 0.0 0.2 0.2 0.2 O.I O.1 oO. oO. 0.0 0.0 0.2 0.2 0.2 0.2 O.I Or O.I 0.0 ofo | 0.2 0.2 0.2 0.2 0.2 O.1 o.1 0.0 0.0 0.3 0:3 0.2 O:2 0.2 O.1 O.1 0.0 0.0 0.3 0.3 0.3 0.2 0.2 O.1 OnE O.1 0.0 0.3 os 0.3 0.2 0.2 0.2 0.1 0.1 0.0 0.3 0.3 0.3 0.3 0.2 0.2 O.1 0.1 0.0 | 0.4 0.4 0.3 03 0.2 O12 O.1 O.1 (ahyey | | 0.4 0.4 0.3 0.3 0.3 0.2 O.1 0.1 0.0 0.4 0.4 0.4 0.3 0.3 0.2 O.1 O.1 0.0 0.4 0.4 0.4 0.3 0.3 Ore 0.2 0.1 0.0 0.5 0.5 0.4 0.4 0.3 0.2 0.2 0.1 | 0.0 0.5 0.5 0.4 0.4 0.3 0.3 0.2 OI | 0.0 0.5 0.5 0.5 0.4 0.3 0.3 0.2 O.1 0.0 0.6 0.5 0.5 0.4 0.4 or 0.2 O.I 0.0 0.6 0.6 0.5 0.4 0.4 0.3 0.2 O.1 0.0 0.6 0.6 0.5 0.5 0.4 0.3 0.2 Ou 0.0 0.6 0.6 0.6 0.5 0.4 0.3 O.2 O.T 0.0 0.7 0.6 0.6 0.5 0.4 0.3 0.2 O.1 0.0 0.7 0.7 0.6 0.5 0.4 O13 0.2 o.1 0.0 0.7 0.7 0.6 0.6 0.5 0.4 0.2 O.1 0.0 0.7 0.7 0.6 0.6 0.5 0.4 0.3 O.1 0.0 0.8 (oer 0.7 0.6 0.5 0.4 0.3 oO.I 0.0 0.8 0.8 0.7 0.6 0.5 0.4 0.3 Our 0.0 0.8 0.8 0.7 0.6 0.5 0.4 0.3 0.1 0.0 0.8 0.8 0.7 0.7 0.5 0.4 0.3 O.I 0.0 0.9 0.8 0.8 0.7 0.6 0.4 0.3 0.2 0.0 0.9 0.9 0.8 0.7 0.6 0.5 0.3 0.2 0.0 0.9 0.9 0.8 0.7 0.6 0.5 Os 0.2 0.0 85° 80° AOee |) sO 65° 60° Boe 50° 45° | | SMITHSONIAN TABLES. TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. B.—B = B (107-1). Top argument: Height of the barometer (B). Side argument: Values of 2000 7 obtained from Table 14. HEIGHT OF THE BAROMETER IN INCHES. 31.0 | 30.5 . 29.5 | 29.0 | °28:5)))/)28:0 27-5 Inches. | Inches. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. 0.04 0.04 0.03 0,03 0.03 0.07 Q,07 0.07 0.07 0.07 O.1I O.1I 0.10 0.10 0.10 0.14 0.14 0.14 0.13 0.13 0.18 0.18 : 0.17 0.17 oO 16 0.21 0.21 0.20 0.20 0.20 0.25 0.25 0.24 0.23 0.23 0.29 0.28 0.27 Or; 0.26 0.32 0.32 0.31 0.30 0.30 AQrNI NDA fBWN — S © 0.36 0.35 0.34 0.34 0:32 0.40 0.39 0.38 0.37 0.36 0.43 0.42 : 0.41 0.40 0.40 0.47 0.46 : 0.44 0.44 0.43 0.50 0.50 0.48 0.47 0.46 ee Now How ew a 0.54 0.53 0.51 0.51 0.50 0.58 : ! 0.55 0.54 0.53 0.61 0.58 0.57 0.56 0.62 0.61 0.60 0.65 0.64 0.63 0.69 0.68 0.66 0.72 0.71 0.70 0.74 0.73 0.77 0.7 0.81 0.80 H OO 0.85 0.83 0.88 0.87 0.90 0.93 0.97 .0O 04 .07 .10 ao 17, 25 24 27 31 1.34 1.38 1.41 1.45 1.48 1.52 SMITHSONIAN TABLES. 7O 89 TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Bo—B = B (10”"—1). Top argument: Height of the barometer (B). Side argument: Values of 2000 77 obtained from Table 14. Inches. 1.57 1.60 1.64 1.68 7 1.75 1.78 1.82 1.86 1.89 1.93 1.96 2.00 2.04 2.07 Zod Inches. 1.54 1.58 1.61 1.65 1.68 72 75 79 82 86 Le oe oe oe | -90 93 -97 -0O 04 NN RA Oe 07 II 15 18 22 NNNNN 25 29 33 36 4o 43 47 5k 54 PPV NNNNH HEIGHT OF THE BAROMETER IN INCHES. 28.5 Inches. 1.52 1.55 1.58 1.62 1.65 .69 72 76 ‘79 83 en | NOS eH OO \o Oo 28.0 1.52 1.56 1.59 1.62 66 .69 et SS Oe Ot \O J ° 2 NNNNDND oO “I NNNNN No WN 38 PHN a nN yRPRe S i) I ° Inches. = Inches. .46 .50 I I 2 2 2 2 2 3 I if 1.60 NNNNN NNNNDHND NwNNN NNN N Se oH oe A ae Se ee NNNNN 27.5 “53 56 162 66 70 73 76 .SO 83 .87 .go -93 -97 00 03 07 10 14 17 2I 24 27 ei 34 38 4I 45 48 51 55 58 62 65 69 WD 76 79 53 .86 .gO -93 97 -0O 27.0 Inches. 1.44 1.47 1.50 1.53 Leys 1.60 1.63 1.67 1.70 re73 1.76 .8o .83 86 go NNNNN NNNNN NNNN ND NNN HH ee Oe on Ww i] Fe} ° oe ~I NNNNN ea) QI 2.84 2.88 2.91 2.95 26.5 Inches, 1.70 1.73 1.76 1.80 1.83 1.86 1.90 26.0 | 25.5 ae Inches. | Inches. ” 28 N s~Is n 2.81 SMITHSONIAN TABLES. TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. B.—B= B (10”—1). Top argument: Height of the barometer (B). Side argument: Values of 20007 obtained from Table 14. HEIGHT OF THE BAROMETER IN INCHES. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 3.06 3.00 2.95 2.89 2.84 2.78 3.09 3.04 2.98 2.93 2.87 2.82 3.13 3.07 3.02 2.96 2.91 Be Ohms 2.0n 3.05 2.99 2.94 2.88 3.14 3.09 3.03 2.97 2.91 3.18 3.12 3.06 3.01 2.95 3.21 3.16 3.10 3.04 2.98 3.19 Bons 3.07 3.01 3722 Bry, Bene 3.05 3.26 3.20 Z.04 3.08 Bali] 3.11 B21 3.14 3.18 3.20 $283 902. RO AWOnhnd Pe YG O AW Oo PO GG o WOO NN Nf ONTO Ow O@ 3 Goo RN ao, 3- 3: 3. 3: 3: 3- 3: 46 5 5 5 6 6 6 7 7 7 8 8 COR HNO WwW Wo BNR ON DW W 2 G) bo eo £64 CoH QP ys OO Wo ao rH cour NON O BAN H SIINNAD DNL $HWWw NK BNI OH NANDA UANHPHH 2 G2 G2 Go G2 OD wonnrd o Ww CO Mm abv ex COO MN OLB HR 2 MI G2 0 An COM OOO & oo ¢ Om | AnNnwoun COMINIITIA ADAnAUNUMNH Ron PEWEe WHO go Ne} PR REYLEO SEWYY O 3 = 4 O0 MOM NIN Qo NNN DADDY NALLHL BW YEOH WHEY IBRO VWHROUA He COOH CO BH OP wo Co Ow N £0 co CO DAnwowi PERWE BOWE WHO ar oie Ow < WO QU a > > \o 4 O oO NO co WNNN NON bn SESE HEEYY » O° _ BS = Ww Fmart ak Cat red ruran on oa aso oa ere ON COWM OMMON NNAAAN + aS Sop aEsS O00 Oo AWN ours ise NH N woocnnxl ea ° NOANWO DWO OO ae — nan Pehaior oe oon eee foo vo Ee) oy ap Sw ON Ww By Nd N BP PRESSE PRESS on a SMITHSONIAN TABLES. 72 amet TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Bo—B = B (10”-1). Top argument: Height of the barometer (B). Side argument: Values of 2000 77 obtained from Table 14. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 4.37 4.29 4.20 4.12 4.41 4.32 4.24 4.15 4.44 4.36 4.27 4.19 4.48 4.22 51 4.25 OO > O° O > o WD &. ase DADUN on wows OV CO mun AW O sIsI “I O71 OF nui COf H NIU a ns & HID HSI ow WwW dv b&b COUN w ~I nN D0 Ov W n> DARDDUN OR mun on OO OnmM AN WO VU oon ™ SIO20 OV SINS DOD aun SIP ONG oO nnnpb hHHWW oO ° yuan BRAS REESE BEEE Our H S888 Oo OWOWO eu OOonrInsIs! an & wo Aunap FRESE BRESEE HESEE FF HOOOUWO OO DOO NOUN CO NH OPH COUNT HD Anu NO UI NO DANwo VAN NH HHO NOUN BREED PREAH FERRE FREER HERES “I tN COO0DD OMMMY IIAAD BARODA YNOMNNnNHO UNOUNH Soe aEe OOWDO ~ Oo DY HN wnown © WNN ONBWO DA ee RN Re DO OD DWOINIA ADMIN pee w HANI ° nRooN Oo AW OOO OM ounnon mnonrIN mnnown mourn © > & © woh DH % “IG NN NH He AWO DY =A OrORo Our 0 0OWWOoO nan moun 4. 4. A. 4. 4. 4. A. A. 4. 4. 4. 4. 4. 5. 5. ee 5. 5 5: ee = 5 5. Fe ie Be 5. 5. 5 5. ie nN Unni nv a O WO ONW O NHR HO mm COU HH CO AAANH AANA ANANTH AAKNSE PPPEH AAAAR HHHRH HESS ANNAN ANAAA ANSEL BEEEH F SIAN aAnppP — Annu — WWW & O DAWWO Av COW euIh ON ANNAN AMAA AACA ANNA APLEHL HEHPHS HEFEH HHESHE SE NwoOunbd © “I ~I Oo On Ov _ un SMITHSONIAN TABLES. TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. B.—B = B (10””—1). Top argument: Height of the barometer (B). Side argument: Values of 2000 #2 obtained from Table 14. HEIGHT OF THE BAROMETER IN INCHES. 25.5 | 25.0 | 24.5 | 24.0 | 23.5 | 23.0 | 22.5 | 22.0 | | i Inches. Inches. Inches. Inches. Inches. Inches. | Inches. | Inches. 5.87 5-64 5-53 5-41 | 5.91 5.68 5.56 5.94 5 5-98 6.02 Yu ~J] an nn I on £ n oC” nonoun on WO AW O co oO De SINT OO OV nun & & DW G2 W a4 mun H On Aw O ang nn HAO gigi nan H OU H C rH oO ° on) PAA NAY ONT C0009 © Of SIO ANngan mMHO OW) OOo ODnmm Ano uv NAAM IAD Onn WO DAW Ow our DW O our ° OOOO © Omonns! NN HH He aN HON DMO On~s! Cura nnn ANwo aN ann Annan Oo =O DW O DAN DHDADH AKRAM Ww ®W NNN HR eNH ONT KH HHO; OH Of O09 OMWOMWMO AANA 90000 OMDMOMNI NO ANWO SI “IS WO DW O n> Cura AnNWO mnmC jon) . p on 5: 5: 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. Arann BHR&W& bd Rn OUNHN an aw - OWNHN ND No HH HO \o ANOoMmW wNnounnm® Nw OU HOOOUWO WO” NO ANWO ANNO DO nat RRO N WODANKNO WAN NN eee \o 0 mH “IO OO ANWO DANwo abv SANNA NIQ OO QU. Row HN eH onnon O a no. Om ons] Cour ms SIUIAADAD Annpp WBoOwWNDN O AWWO WNN bd — OH II NAN ADADAA DAAAH DAADAHA AHAAHR DAADH gunn OO Con] Anvnwound eH OR HNI fF ON W NO O DW HONnnwoO NANOUWN NHN oOOoOUmUMmw) D ADDAN DADAH AAHDAH AAADAH AHRAAHD naunun D AADAN AAHDAH DAAHDAH AADAH AHAUU ND ADANADAN DAAAAHA DADADHD DADAM BUNAM Naga ONINYIAN DANUNbpP Pwww'r N AUN. HHH GW ND NDDADHA DAHAAD nN BH HRWW o No) ° on = “I al ° SMITHSONIAN TABLES, 74 TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Bo—B= B (10”—1). Top argument: Height of the barometer (B). Side argument: Values of 2000 77 obtained from Table 14. HEIGHT OF THE BAROMETER IN INCHES. | 23.5 23.0 22.5 22.0 21.5 | 21.0 Inches. Inches. Inches. Inches. Inches. Inches. | Inches. .I0 6.95 6.80 .65 6.51 6.98 6.84 i 6.54 7.02 6.87 : 6.57 7.05 6.90 : 6.60 7 ey : 6.64 SESS STE 6.67 6.70 Se nese NInwIs > B&W Ww FHT R O onsen a HOR HF CO NWO NH CO Oo C©0O NB OL nn O00 ww 7. Te Fife ie We ‘fs 7. Te 7- Ta fie ds Te Te Tia de Ti 7. Je T= BAIS SS Seat C00 OOD KM ONNIANR AQAuunuwnsp Onn ONWWO DA DU ee Ga! ROR HN LOIS Sil SS Sa Seay Saray NANNANN HPHAHRWW Wh PHN HRO NR ON W SINAN NNN NINN RH W NHN NNN ANNNN NANHAA DNNANHAAD HH PONBAH WOonn Ua Se Rb OM H © Ree DANN BAN eH ae SHAH W Oo NAH ONS 1 20 ODO MM DOIN YIAT oo 4 a ICO SS Staion DX ONN ON Ona a Cmurik © Wa WN _ ate tetiet Stet Sten Sr ay 3 OV Sera I HROURO 29 DOO MH MUIUD & PRODHS 20 90 90 90 G0 MOO HAW O DNWMN Ooonn OM I~] ° a ae DN ADNNN NO ANWO AW O On Se ee © AAAI OO OMWO MM oo tbo ° wo nN “I SMITHSONIAN TABLES. 75 TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Bo—B = B (10””—1). Top argument: Height of the barometer (B). Side argument: Values of 200077 obtained from Table 14. HEIGHT OF THE BAROMETER IN INCHES. 2000 m. 23.0 22.5 22.0 | 21.5 | 21.0 20.5 20.0 Inches. Inches. | Inches, | Inches. Inches. Inches. Inches. 270 8.39 8.20 8.02 7.84 7.66 271 8.42 8.24 8.06 7.87 7.69 272 8.46 8.27 8.09 7.91 7.72 273 8.49 8.31 8.12 7.94 Te. 274 8.53 8.34 8.16 7-97 7-79 275 8.57 8.38 8.19 8.01 7.82 276 8.60 8.42 8.23 8.04 7.85 277 8.45 8.26 8.08 7.89 7.70 278 8.49 8.30 8.11 7.92 778 279 8.52 8.33 8.14 7-95 TI 280 8.56 8.37 8.18 7.99 7.80 lon S20 8.59 8.40 8.21 8.02 7.83 282 8.63 8.44 8.25 8.05 7.86 283 8.67 8.47 8.28 8.09 7.90 284 8.70 8.51 8.32 8.12 7.93 285 8.74 8.54 8.35 8.16 7.96 286 8.7 8.58 8.38 8.19 7.99 287 8.81 8.61 8.42 8.22 8.03 288 8.85 8.65 8.45 8.26 8.06 289 8.88 8.68 8.49 8.29 8.09 290 8.92 8.72 8.52 8.32 8.13 291 8.95 8.76 8.56 8.36 8.16 292 8.99 8.79 8.59 8.39 8.19 | 293 9.03 8.83 8.63 8.43 8.22 294 9.06 8.86 8.66 8.46 8.26 295 9.10 8.90 8.70 8.49 8.29 8.09 | 296 9.14 8.93 8.73 8.53 8.32 S120 a] 297 8.97 8.7 8.56 8.36 8.15 | 298 9.00 8.80 8.60 8.39 8.19 | 299 9.04 8.83 8.63 8.42 8.22 300 9.08 8.87 8.66 8.46 8.25 301 9.11 8.go 8.70 8.49 8.28 302 9.15 8.94 8.73 8.52 8.32 303 g.18 8.97 8.77 8.56 8.35 304 9.22 9.01 8.80 8.59 8.38 305 9.26 9.04 8.83 8.62 8.41 306 9.29 9.08 8.87 8.66 8.45 | . 307 9.33 9.12 8.90 8.69 8.48 308 9.36 9.15 8.94 8.72 8.51 309 9.40 9.19 8.97 8.76 8.54 310 9.44 9.22 g.O1 8.79 8.58 311 9-47 9.26 9.04 8.83 8.61 | "Saat 9.51 9.29 9.08 8.86 8.64 313 9.54 9.33 g.11 8.89 8.68 314 9.58 9.36 9.15 8.93 8.71 315 9.62 9.40 9.18 8.96 8.74 SMITHSONIAN TABLES. 76 TABLE 16. REDUCTION OF THE BAROMETER TO SEA LEVEL. ENGLISH MEASURES. Bo—B = B (10”—1) Top argument: Height of the barometer (B). Side argument: Values of 20007 obtained from Table 14. HEIGHT OF THE BAROMETER IN INCHES. 2.0 21.5 21.0 20.5 20.0 19.5 | Inches. | Inches. Inches. Inches. Inches. Inches. 9.62 | 9.40 9.18 8.96 8.74 8.52 65 9.43 9.21 g.00 8.75 8.56 6 9.47 9.03 8.81 8.59 7 9.51 9.06 8.84 8.62 7. 9.54 9.10 8.88 8.65 Oo NN COUN NS 9. 9: 9- 9: 9.8 9.13 8.91 "4 *8:69 9.17 8.94 oe 9.20 5.98 9.23 g.O1 9.04 \o n co COU DAnNnwon i) IAA HHL WwW No) 9.08 g. II 9-14 g.18 9.21 oOmn~Is DOO Do 9. 9. 9. 9. 9. 9. 9. 9. 9. 2 ww DNQDUNN NO 9.24 9.28 9.31 9-34 9.38 ‘o \O & Aer Oo \O 1 “I a WYONG WVYHVoN YHOwoYOD WYO Om COxnI SIS] Oe SMITHSONIAN TABLES. NI en TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. of 2000 =< m. q Z I n=O COC 18444+-67.530+-.0032 1+ 8 Values Altitude in SMITHSONIAN TABLES. MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). | metres. a | Zz - 16°} — 12°} — 8°} —4°| —2°| 0° + 2° | + 4° | + 6° | +8° | + 10° 10 Te Vode fee eo Det Teak ee Te Te it 10 1.0 20 2.3 Dea glee 2e2 252 22 292 ONT gi 2 2a Dat 30 Bus 3-4 | 3-3 ane 2.3 3.2 22 352 ano ar aur 40 4.6} 4.5 4.5 4-4 4.4 4.3 4.3 4-3 4.2 4.2 4.2 50 B On| ost te 5:0 i s5 sb ate BAe 5A | 5-3 5-3 5-2 5.2 60 6.9 6.8 | 6.7 6.6 6.5 6.5 6.4 6.4 6.3 6.3 6.2 70 8.1 TOM 7eo 77 7.6 7.6 Hae Tels 7.4 TES, 732 80 g.2 g.1 8.9 8.8 8.7 8.7 8.6 8.5 8.5 8.4 8.3 go 10.4 | 10.2 | 10.0 9.9 9.8 9.7 9.7 9.6 9.5 9.4 9.4 100 Tes | LES | I1.2 | 11.0 | 10.9 | 10:8 | 10.7 | 10-7, | 10:6 | "140-55| "rom: 110 T2-7 02.5) | 12.3) | P25 |) 12.08 erie on) ere Sai |l ele, |e On || ree an mene: 120 Tessa 0g.O5\" 1354 i ns2 3.0) 13208 | 12.9") |(eratS) | ere7 ale 12s On aeins 130 Eso) |i E457 | TAS edo | As oan ere TAO Es On xs.7 13-6) etaes 140 T6.1 | 15/9 | 15.6 | 15-4 | 15:3 | 15-1 | 5-0) 14-9) | alo) | raz ese 150 17-3, | 17.0 | 16.7. | T6)5) e164. || Mer6so a eer Oar 1620) ||) 15:9) | 15-7a| 5.0 160 18.4} 18:1.|°17-8) | 1726.0) 1754) 07.3 e720 TOO nl SG ones liad 170 1956) |) 19:3 4} 19:0) 18.7 ||/5rSs5, | rS.48 |) Sree a ler oa [8,018 L750 ele 180 20:7 || 20.4, | 20.1 |, 1958*)| 19:6> | 19.5) || #1953) L912 a 19:0 \TStO) neta, 1g0 21.9 | 21.5 | 21.2 | 20.9 | 20.7 | -20:6':|, 20:4 || 20:2.) "20.1 |) 19.9) | arG:8 200 23:0 | 22.7 | 22.2 | 22.0 1221.8, |421-6" | 21.5) || orator are || On|m2Oso 210 24.2 | 23.8 |: 23.4 | 23.1 9) 22:0) ze | 22:6 1) oon ore opto iene 220 25:3 | 24-9) | 24:5 ||| 2422')| 2430 823735523565 oat 22 6o Ieoot tale atG 30 2625, | 2650) | 2527.0 25e8) ae yuk PHI) | PYIS7/ 24.5 2453552450 23.9 240 27.6 || 27.2: 26:8 | 26:4: 1526720)" 26:00)/025:9) | 225 Olmos ena eo 5e 2m nse 250 28.8, |.28.3° | 27-9 °| 2725 i 27.30 |\22720) 926.5 '5|26:00 260126; alo oro 260 29:9 |29.5,"| 29.0 || 28:69 28°39) 925.1 e270 27270 |e e7eb el ee en eel 270 31.1, ||30.6 | 30.2 | 29577 162054.8) (20.25 |2orONl 28: S255 25sec oal 280 32.2 | 31-7 | 31-2 || 30.8 | 30.5.) 30:3: || 30.5 |) 20:59)" 2016" S20. Au open 290 33.4 || 32-9 | 32:4 || 31.0) |" 3r.6.4) S31. zai siemen| 830-05 se Or7alm 30. Ann ore 300 34.5. "| 34.0 | 33.5) 1 33:0 ||" 32e7 11 93 2)5 | aaron a2: = ota leo Teo eae 310 35-7 | 35-1 | 34-6 | 34.1 | 33-8 | 33-5 | 33-3 | 330 | 32:8 | 32.5 | 32:3 320 | 36.8 | 36.3 | 35-7 | 35-2 | 34-9 | 34.6 | 34.4 | 34-1 | 33-8 | 33-6 | 33-3 339 | 38.0 | 37-4 | 36.8 | 36.3 | 36.0 | 35.7 | 35-4 | 35-2 | 34-9 | 34-6 | 34.3 340 | 39.1 | 38.5 | 37-9 | 37-4 | 37-1 | 36.8 | 36.5 | 36.2 | 35.9 | 35.7 | 35-4 350 | 40.3 | 39-7 | 39-0 | 38.5 | 38.2 | 37.9 | 37-6 | 37-3 | 37.0 | 36.7 | 36.4 360 41.4 | 40.8 | 40.2 | 39.5 | 39.2 | 38.9 | 38.6 | 38.4 | 38.1 | 37-8 | 37.5 | 370 42:6) 41.9) | 41-3: | 4016: 5|40.3" 1/9400 ||| 3957-9 30:4) |e eons | sosoulmsos> | 380 43.7 3.1 | 42.4 | 40-7 \FAn.4 ||) 41.1} 40:8 |e40%5) | Aor ieaoron| 30.0 | 390 44.9. | 44.2 | 43.5, | 42:8 | 42.5 | 42.2 '| aro | 4.5 | S428 40:08 e4016 400 46.0 | 45.3 | 44.6 | 43.9 | 43-6 | 43.3 | 42.9 | 42.6 | 42.3 | 42.0 | 41.6 410 47.2 | 46.4 | 45-7 | 45.0 | 44.7 | 44.4 | 44.0 | 43.7 | 43.3 | 43-0 | 42.7 420 48.3 | 47-6 | 46.9 | 46.1 | 45.8 | 45.4 | 45.1 | 44.7 | 44.4 | 44.1 | 43.7 430 49.5 | 48.7 | 48.0 | 47.2 | 46.9 | 46.5 | 46.2 | 45.8 | 45.5 | 45-1 | 44.8 440 50.6 | 49.8 | 49-1 | 48.3 | 48.0 | 47.6 | 47.2 | 46.9 | 46.5 | 46.2 | 45.8 450 51.8 | 51.0 | 50.2 | 49.4 | 49.1 | 48.7 | 48.3 | 47.9 | 47.6 | 47.2 | 46.8 460 52.9 | 52.1 | 51.3 | 50.5 | 50.1 | 49.8 | 49.4 | 49.0 | 48.6 | 48.2 | 47.9 470 BACT | 53-2 | 52.4. 1) 5a Om eym.2 || 50.0.8! e5Os5 50.1 49-7 | 49.3 | 48.9 480 B52 54-4 wl 5305 ll 5 2e7, 2.3 | 52.9) || 5005 |) Slake || Onze 50:3) | 50:0 56. 55-5 | 54-7 | 53.8 eA Be 52s : ’ i 56.6 | 55.8 | 54.9 w— TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Values of 2000 X m. m Z ~ 18444+-67.530-+ .003z I I+B MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (@). Altitude in : metres. + 12° | -+ 14°| + 16°| + 18°} + 20° + 22°] + 24° | + 26° | + 28° | + 32° SU CONS Nee HO mee RO RRR OO 70D 0 O COM Oye Orit Caries AAD ARON H cont NAO PHI AM PY! Or ANnaAQanN NOM oe) AnAN ane e eh WWWN Nh 3 90 H ! Fone WNNH NN HHH _ ° H n HO NOH to — SS OO MnO nN 4 4 Os Ln oe oe oe | | Oe SO Doo BAROAMAH DADWAY Ccomt OF DID AE — Se SIAR BENAD OKIAM BHONAH DSO a= CaN ae OMS O SOO SECO BE ANUAAA ADIYNY IYHMMHHH OO NHR ee OO Ne Hee Oo i OO CGNID nf HH OH OH vv PE OtesO -7 = “7 -7 8 vv ON NN BREEAM AnNaaAnK ADNAADATD Anarnn U- NO NNN ND I 2 3 A. 5. Ov ¢ NS to 1 fs COMI DG Cont OV RRM ¢ OO DINARS A n> NYHNNNYH NNN SONCOR TIONS On) HNNNWH Wa &® NNN ND FAG DADAM Anninbh HAHAHA H CH dW to OO & ty oN ONNINN AD ADDU UMBHP POWWW WNHNNHNHD Ww to 90 ne nl AHN OW 0 | WWWwWW GWNHNHN bd &» G OG > Oo G G2 Go OG) GO) G2 Oo obo Nw CO G2 G2 G2 Go G2 Avil wn i | Ww WwHWWW OYWNNK NNYNNHNN oO woow o 3 Fea COS ene Coats EN ii Cle ES ORE COT HH HHH HRW WWWWW WWOWWNH NNNHNNHD NNNNDND >I OV CON Dn OWN HO O ON WN _ ODIA AhONH O22 2 2 G2 Ga & Ga Go Ww Faeroe ka MOCO ONCE) C2 NBEO =FHANND NNNWW WOWWHLE fm Go G2 G2 Go OIWAR R&P CONTEC ACoA moonoo SO WONN DH SIAM WN WWW WwW C G2 G2 G2 OG) Go 5 0 f 4 aD Ny Nw a 9 © D 02 GP she HO Nu =O GW O20) Ww WwW Oo ~ARA HR HPwdWWW WWWWW MOMMD OD0000 OHH pf n A DAWA ° 0D MONININI SININIDD a = SALAH WWWOWW WWWWH NNHNNN > 2 co DYES CSAC xO > a ” br & na PIAAE HNEOO DAan~~! SPER BHAPHW WWWWW hHH HH AHHWO SDN W NW Nothin SMITHSONIAN TABLES TABLE 17: REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Values of 2000 * m. SMITHBONIAN TABLES, Z 18444-+67.536+.003Z m — 80 eee ss I+B MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). _—— — —————— — —————————— —————————— — 16° | —12° | —8° | —4° | —2° o° +2° |; +4° 575 | 56.6] 55.8] 54.9 | 54-5] 54.2] 53:7] 53- 58.7 57.8 | 56.9 56.0| 55.6) 55.2} 54.8] 54. 598 | 58.9 | 58.0] 57.1 56.7 | 56.3] 55.8] 55. 61.0} 60.0! 59.1 58.2 57-0 |) 5ie3 56.9 | 56. 62.1 61.2 | 60.2 59.3 | 58.9 | 58.4 | 58.0] 57.5 63.3 | 62.3 | 61.4 | 604} 60.0] 595] 59.0] 58.6 64.4 | 63.4] 62.5 | 61.5 | 61.1 | 60.6] 60.1] 59.7 65:6 ||| 64:6 | 63.6] 62:6) (62.1 | (617 | 6r-2)| 60:7, 66.7 |" 65.7 | 64.7 63.7) ||) 163-2) 62:75 62:25 || vO1es, 67.9 | 66.8] 65.8] 64.8] 64.3 | 63.8 | 63.3 | 62.9 69.0 | 68.0} 66.9] 65.9 | 65.4} 64.9} 64.4 | 63.9 70.2 | 69.1 | 68.0 | 67.0] 66.5 | 66.0} 65.5} 65.0 7 AG) 670.2 69.2 68.1 67.67 O7a0 66.6 | 66.0 72.5 71.4 7023 69.2 | 68.7 | 68.2 67.6 | 67.1 73.7 | 72:5.| 71.4] °70.3'| 69.87) <692°| 63:70) 568.2 FARO | 73-6 | 072.5 71.4 | 70.9] 70.3} 69.8] 69.2 76.0 74.8 73.6 72.5 | 72.0 71.4 70.9 70.3 TUN VTS |) 74:74 73-8)" 78.0) 72. 5a eon eee 78-3 | 77-0.| 75.9. \' 7427 | “74-0 | 73.0) “73:08 72:4 79-4 | 78.2 | 77.0 | 75.8) 75.2 | 74.6) 74.1 | 73- 80:6'1 79.3.) . 78:0) || 76:97 |) $763) e757) |e See 81.7 | 80.4 | 79.2 FSOn | 777d 170. ea Oe a5: 82.9} 81.6] 80.3 79:1 | 78:5 TON Ges 76. 83:0 | | 82-79)|" S04 80.2 79:67) 79:0. || G7S8:400 G7: 65:2) )'33.8 | S25 |) °Sr-35!) (Sou BSO.lle ona. 86.3 | 85.0 | 83.7 82:49) SieSa| olka OOl Sale Z0: 87.5 86.1 84.8 32.5) | @S2.90 | ns2-29|) ol-Onl mote 88.6 | 87.2] 85.9 | 84.6 | 83.9] $3.3 | 82.71) 82. 89.8 |..¥88.4 | 87:0.| 85:7 |, 85:0: |, #S4-ael, 433.7 Bal 90.9 | 89.5 | 88.1 86.8 | 86.1] 85.5} 84.8] 84.2 92.1 90.6 | 89.2 87.9 | 87.2 | 86.5] 85.9] 85.2 93-2 | 91.8] 90.4 89.0 | 88.3 | 87.6} 87.0] 86.3 94.4] 92.9] 91.5 go. 89.4 | 88.7 | 88.0] 87.4 95-5 | 94.0] 92.6 | 91.2] 90.5] 89.8] 89.1 $8.4 96.7 | 95.2 | 93.7 | 92.3] 91.6] 909] 90.2] 89.5 97:8 | 96.3 94.5 93-4 | 92.7 92.0 | 91.2 90.5 99:0 | 97-4| 95:9 | 94.5 | 93.8 | 93.0] 92.3] 91.6 100.1 98.6 | 97.0'| 95:6: 704.85 ie 79420 i) 193-4) | 9 2i7 101.3 | 99.7 | 98.2 | 96.7] 95.9] 95.2] 94.5 | 93.7 102.4 | 100.8 | 99.3 | 97-8] 97.0] 96.3 | 95.5 | 94.8 103.6 | 102.0 | 100.4 | 98.9] 98.1] 97-4] 96.6] 95.9 TO427* | (103-1. | TOL. 5+] sLOO!O | 99:2 9 98O5:4 9! 1707.7. 96.9 105.9 | 104.2 | 102.6 | IoI.1 | 100.3 99.5 98.8 98.0 107.0 | 105.4 | 103.7 | 102.2 | IOI.4 | 100.6 | 99.8 | 99.1 108.2 | 106.5 | 104.9 | 103.3 | 102.5 | IOI.7 | 100.9 | I00.1 109.3 | 107.6 | 106.0 | 104.4 | 103.6 | 102.8 | 102.0 | IoI.2 110.5 | 108.8 | 107.1 | 105.5 | 104.7 | 103.9 | 103.1 | 102.3 I11.6 | 109.9 | 108.2 | 106.6 | 105.7 | 104.9 | 104.1 | 103.3 £12.8 | 111.0 | 109.3 | 107.6 | 106.8 | 106.0 | 105.2 | 104.4 113.90 | EI2s19 | L10.4. | 108:7))| 8197-0} || 107-1 || 06:39 oO 5.5 II5.I | 113.3 | 111.5 | 109.8 | 109.0 | 108.2 | 107.3 | 106.5 i> - eee TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Values of 2000 X m. Altitude metres. 840 850 900 940 950 990 1000 SMITHSONIAN TABLES, mM Z —~ 18444+67.530+.0032 MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). + 12° 51.6 52-7 53-7 94-7 55.5 56.8 57:8 58.9 99:9 60.9 62.0 63.0 100.2 IOI.2 102.2 103.3 + 14° 55.2 52.3 53:3 54-3 | 99:3 56.4 57-4 58.4 59-4 60.5 61.5 62.5 63.5 64.6 65.6 66.6 71.7 72.8 7235 74.8 75.8 76.9 77-9 78.9 79-9 8I.0 WmOMCM ARK 8 HOOO om Wa “SIor Oo DX Hn NEB OR OsCOee © Oo 90 0° DOV 1S Ow as He 96.6 97.6 98.7 99.7 100.7 101.7 + 18° | + 20° GOS! |e SOU 51.5 | 51.1 B25 hh 93:5 | 53-1 94:5 | 54.1 95-0) | 90-2 6 56.1 ae 58.1 59.1 60.1 61.1 62.1 a. 63.1 64.6 | 64.1 65.6 | 65.1 66.6 | 66.1 67.05 |G 68.6 | 68.1 69.6 | 69.1 FOU 7 Oak eal eafled FTA e721 73-7 | 73-1 74-7 | 74.1 79:7 | 75-1 76.7 76.1 71-7 \- 77-1 78.7 78.1 79:7 | 79.1 80.8 | 80.1 81.8 | 81.2 82.8 | 82.2 3:9) | Os. $4.8 | 84.2 85.8 | 85.2 86.8 | 86.2 87.8 | 87.2 88.8 88.2 89.8 | 89.2 g0.8 | 90.2 91.9 | 91.2 92.9 | 92.2 93-9 | 93.2 94-9 | 94.2 95-9 | 95.2 96.9 96.2 97-9 | 97.2 98.9 | 98.2 99:9 | 99.2 100.9 | 100.2 -+ 22° 8I 49-7 50.7 51.7 52.7 53-7 93.8 94.8 95-7 96.7 97-7 98.7 93.1 94.1 95.0 96.0 97-0 98.0 OKO EOC MO 0 COornasn SNS NSINITNT © C + 32° | + 36° 47-9 | 47.2 48.9 |} 48.2 49.5 | 49.1 50.8 50.1 51.8 51.0 52:4 ||| 52.0 53-7 | 52-9 54.6 | 53-9 55-6 | 54.8 56.5 | 55-7 57-5 | 56.7 58.5 57.6 59.4 58.6 60.4 59.5 61.3 | 60.5 62.3, |, 6%-4. 63.3 | 62.4 64.2 | 63.3 65.25) 6402 66.1 | 65.2 67.1 66.1 68.0 | 67.1 69.0 | 68.0 70.0 | 69.0 70.9 | 69.9 71.9 | 70.9 72.8} 71.8 TOCOn 2 ES 74.8 | 73-7 75-7 | 74.6 76.7 | 75.6 77-5 | 76.5 78.6 | 77.5 79-5 | 78.4 80.5 | 79.4 81.5 | 80.3 82.4 | 81.3 |] 83.4 | 82.2 84.3 $3.1 85.3 | 84.1 86.3 | 85.0 87.2 | 86.0 | 88.2 | 86.9 | 89.1 | 87.9 g0.1 | 88.8 | gI.I 89.8 | 92.0 | 90.7 93.0 | 91.6 93-9 | 92.6 | 94-9 | 93-5 95-9 | 94-5 TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Values of 2000 < m. m Z I ~ 18444+-67.530-+-0032 I+ MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). ‘Altitude in — 16° | —12° | —8° | —4° | —2° 0° | +2°) +4° | +6° | +8° |}+10° ; 113.3 | I11.5 | 109.8 | 109.0 | 108.2 | 107.3 | 106.5 | 105.7 | 104.9 | 104.1 f) IOIO 114.4 | 112.7 | 110.9 | II0.1 | 109.3 | 108.4 | 107.6 | 106.8 | 105.9 | 105.1 1020 | 115.5 | 113.8 | 112.0 | IIL-2 | TI0.3 | 109.5 | 108-7 | 107.8} 107-0) TeG-2 1030 116.7 | 114.9 | 113.1 | 112.3 | IXI.4 | 110.6 | 109.7 | 108.9 | 108.0 | 107.2 1040 | 117.8 | 16.0 | 114.2 | 113.4 | 112.5 | 111.6 | 110.8 | 109.9 | 109.1 | 108.2 1050 | 120.8 | 118.9 | 117.1 | 115.3 | 114.5 | 113.6 | 112.7 | 111.8 | III.O | IIo.1 | 109.3 1060 | 122.0 | 120.1 | 118.2 | 116.4 | 115.6 | 114.7 | 113.8 | I12.9 | 112.0 | III.2 | II0.3 TO7O || 123.1 | 127.2 | II9.3 | 117.5.| 116.6-| 115-7 | 114-9 | TI4O || 113-1 | Liz) ce 1080 | 124.3 | 122.3 | 120.5 | 118.6 | 117.7 | 116.8 | 115.9 | I15.0 | 114.2 | 113.3 | 112.4 1090 | 125.4 | 123.5 | 121.6 | 119.7 | 118.8 | I17.9 | I17.0 | I16.1 | 115.2| 114.3 | 113.4 1100 | 126.6 | 124.6 |} 122.7 | 120.8 | 119.9 | 119.0 | 118.1 | 117.2 | 116.3 | 115.4 | 114.5 TLIO! {°127.9 | 125.7 | 123.8) I21.9'| I2L0 | 1207 | 1O.27| (01S:2) | 00734 OA att PI20: | 128.9 | 126.9 | 124.9:| 123.0’) 122-15| T21-27| 20.2 | 19.3) ne 4 | 7-5 ete I130 130.0 | 128.0 126.0, [ L24.1 | T22to" 22 2421s 20 An SLO lA a ar 18.5 117.6 1140 }| 131.2 | 129.1 | 127.2 | 125.2 | 124.3 | 123.3 | 122.4 | 121.4 | 120.5 119.6 | 118.6 1150 | 132.3 | 130.3 | 128.3 | 126.3 | 125.4 | 124.4 | 123.4 | 122.5 | 121.6 | 120.6 | 119.7 1160 | 133.5 | 131.4 | 129.4 | 427.4 | 126.4 | 125.5 | 124.5.| 123.6 | 122.6 | 121.7 | 120.7 1170 | 134.6 | 132.5 | 130.5 | 128.5 | 127.5 | 126.6 | 125.6 | 124.6 | 123.7 | 122.7 | 121.8 1180 | 135.8 | 133.7 | 131.6 | 129.6 | 128.6 | 127.6 | 126.7 | 125.7 | 124.7 | 123.8 | 122.8 II90 | 136.9 | 134.8 | 132.7 | 130.7 | 129.7 | 128.7 | 127.7 |. 126.8 | 125.8 | 124.8) 123.6 1200 | 138.1 | 135.9 | 133-8 | 131.8 | 130.8 | 129.8 | 128.8 | 127.8 | 126.8 | 125.9 | 124.9 | 1210 | 139.2 | 137.1 | 135.0 | 132.9 | 131.9 | 130.9 | 129.9 | 128.9 | 127.9 | 126.9 | 125.9 1220 | 140.4 | 138.2 | 136.1 | 134.0 | 133.0 | 132.0 | 131.0 | 130.0 | 129.0 | 128.0 | 127.0 | 3230-] r4r-s |.130.3 | 137.2 | 135.0 | 134.0 || 233.t0) %32/od|P13%O9) etgo.Onie120.0n| arene | 1240 | 142.7 | 140.5 | 138.3 | .136.2 | 135.2 | 134.1 | 133-1 | 132.1 | 131.1 | 130.1 | 129.0 W 1250 | 142-8 | 4.6 | 139.4 | 13733 | 136.3 | 035221) 7394-25) ese | gem rst tal gow [£260 4:145.0 | 142.7 | 140:5 | 138.4 | 1237-3.) 36.3) || 13533 34.2 | 133.2 22 Tal eroid 1270 | 146.1 | 143.9 | 141.7 | 139.5 | 138.4 | 137.4 | 136.3 | 135-3 | 134.2 | 133.2 | 132.2 | 1280 }| 147.3 | 145.0 | 142.8 | 140.6 | 139.5 | 138.5 | 137.4 | 136.3 | 135.3 | 134.2 | 133.2 | 1290 | 148.4 | 146.1 | 143.9 | 141.7 | 140.6 | 139.5 | 138.5 | 137-4 | 136.3 | 135.3 | 134.2 | 1300 | 149.6 | 147.3 | 145.0 | 142.8 | 141.7 | 140.6 | 139.5 | 138.5 | 137.4 | 136.3 | 135.3 | I310 | 150.7 | 148.4 | 146.1 | 143- 142.8 | 141.7 | 140.6 | 139.5 | 138.5 | 137.4 | 136.3 | 1320 | 151.9 | 149.5 | 147.2 | 145.0 | 143.9 | 142.8 | 141.7 | 140.6 | 139.5 | 138.4 | 137.4 | 1330 | 153.0 | 150.7 | 148.3 | 146.1 | 145.0 | 143.9 | 142.8 | 141.7 | 140.6 | 139.5 138.4 1340 | 154.2 | 151.8 | 149.5 | 147.2 146.1 | 145.0 | 143.8 | 142.7 | 141.6 | 140.5 | 139.5 | 1350 | 155.3 | 152.9 | 150.6 | 148.3 | 147.2 | 146.0 | 144.9 | 143.8 | 142.7 | 141.6 | 140.5 | 1360 | 156.5 | 154.1 | 151.7 | 149.4 | 148.2 | 147.1 | 146.0 | 144.9 | 143.7 | 142.6 | 141.5 1370 | 157.6 | 155.2 | 152.8 | 150.5 | 149.3 | 148.2 | 147.1 | 145.9 | 144.8 | 143.7 | 142.6 1380 | 158.8 | 156.3 | 153.9 | 151.6. | 150:4. | 149.3 | 1148.1 | 147.0-|145.9)| 144-70) 143,0 1390 | 159.9 | 157-5 | 155.0 | 152.7 | 151.5 | 150.4 | 149.2 148.1 | 146.9 | 145.8 | 144.7 1400 | 161.1 | 158.6 | 156.2 | 153.8 | 152.6 | 151.4 | 150.3 | 149.1 | 148.0 | 146.8 | 145.7 I4io | 162.2 | 159.7 | 157.3 | 154.9 | 153.7 | 152.5 | I51.4 | 150.2 | 149.0 | 147.9°| 146.7 1420 | 163.4 | 160.8 | 158.4 | 156.0 | 154.8 | 153.6 | 152.4 | 151.3 | 150.1 | 148.9 | 147.8 1430 | 164.5 | 162.0 | 159.5 | 157.1 | 155.9 | 154.7 | 153.5 | 152.3 | 151.1 | 150.0 | 148.8 1440 | 165.7 | 163.1 | 160.6 | 158.2 | 157.0 | 155.8 | 154.6 | 153.4 | 152.2 | I51.0 | 149.9 1450 | 166.8 | 164.2 | 161.7 | 159.3 | 158.1 | 156.8 | 155.7 | 154.5 | 153.3 | 152.1 | 150.9 1460 | 168.0 | 165.4 | 162.8 | 160.4 | 159.1 | 157.9 | 156.7 | 155.5 | 154.3 | 153-1 | 151.9 | 1470 }| 169.1 | 166.5 | 164.0 | 161.5 | 160.2 | 159.0 | 157.8 | 156.6 | 155.4 | 154.2 | 153.0 | 1480 | 170.3 | 167.6 | 165.1 | 162.6 | 161.3 | 160.1 | 158.9 | 157.6 | 156.4 | 155.2 | 154.0 1490 | 171.4 | 168.8 | 166.2 | 163.7 | 162.4 | 161.2 | 159.9 | 158.7 | 157.5 | 156.3 | 155-1 1500 162.3 | 161.0 | 159.8 | 158.5 | 157.3 | 156.1 | | 172.6 | 169.9 | 167.3 | 164.8 SMITHSONIAN TABLES. ee a TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Values of 2000 * m. Altitude in was 418° 100.9 IOL.9 103.0 104.0 105.0 106.0 107.0 108.0 109.0 I10.0 III.0 112.0 reget II4.1 TESS TI6.1 TL yal TIS.1 119.1 120.1 4 Ny N Ne) nO TesT 12201: 123.1 124.2 125.2 OO O 12 it) 2 I2 I2 DI DAG ° 126.2 T2172 128.2 129.2 130.2 | NO ONS 131.2 Z mM ~ 18444+-67.53 0+.003z 1+8 + 20° | + 22° 99.4 100.4 IOI.4 102.4 103.4 104.4 105.4 106.4 107.4 108.4 109.4 110.4 TII.4 112.4 113.4 114.4 115.3 116.3 pas 118.3 119.3 120.3 1213 122.3 123.3 124.3 125.3 T2683 127.3 128.3 129.3 130.3 Tie 132.2 133.2 134.2 135.2 36.2 137.2 138.2 39.2 140.2 141.2 142.2 143.2 144.2 145.2 146.2 147.2 148.2 149.1 + 24° 98.7 99-7 100.7 IO1.7 102.6 103.6 104.6 105.6 106.6 107.6 108.6 109.6 110.5 II1.5 112.5 TL35 114.5 115.5 116.5 117.4 118.4 119.4 120.4 121.4 122.4 123.4 124.4 H tO CO Se ee i PHOS NW G2 G2 Gy W ee WO WWI God SI OU GW Ro NH NHN i) oe + 26° 98.0 99.0 99-9 100.9 IOL.9 102.9 103.9 104.8 105.8 106.8 107.8 108.8 109.7 110.7 Tele 7 [12.7 113.6 114.6 115.6 116.6 117.6 118.5 119.5 120.5 121.5 122.5 123.4 124.4 125.4 126.4 127.4 128.3 129.3 130.3 030.3 11323 133.2 134.2 135.2 136.2 137.2 138.1 139.1 140.1 I41.1 TA 1 143.0 144.0 145.0 146.0 147.0 + 28° 97-3 98.2 99.2 100.2 IOI.1 102.1 103.1 104.1 105.0 106.0 107.0 108.0 108.9 109.9 110.9 I11.8 112.8 113.8 114.8 I15.7 116.7 707 118.6 119.6 120.6 121.6 122.5 123.5 124.5 125.5 126.4 ~ nH Nv S iw 128.4 HH No 52 OG WWW WWW © SO HR HHH G Se AIAAD nNf&wWnH Lao) — Oo ‘0 - 95-9 96.8 97.8 98.7 99-7 100.6 IO1.6 102.6 103.5 104.5 105.4 106.4 107.4 108.3 109.3 T10.2 III.2 TT2s1 LIST TI4.1 115.0 116.0 116.9 117.9 1138.9 119.8 120.8 LOK 7 1227 123.6 124.6 125. 126.5 127.5 128.4 129.4 130.3 131.3 13253 133.2 138.0 139.0 139.9 140.9 141.8 142.8 143.8 SMITHSONIAN TABLES. 83 TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Z, I Values of 2000 X m. m= UYVEN a Eee ; itp Altitude MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). in tres. netics 12° | _a | —2° +6° | +8° | +10° 164.8 | 163.5 : 158.5 | 157.3 | 156.1 165.9 | 164.6 : 159.6 | 158.4 | 157.1 167.0 | 165.7 : 160.7 | 159.4 | 158.2 168.1 | 166.8 ; 161.7 | 160.5 | 159.2 169.1 | 167.9 : 162.8 | 161.5 | 160.3 1500 I510 1520 1539 1540 1550 : 1560 | 179.5 | 1570 } 180.6 1580 | 181.8 1590 | 182.9 | “SJ ONT HAE ® vv OON OA en ee io 170.2 | 169.0 ‘ 163.8 | 162.6 | 161.3 L713 PL7Olo : 164.9 | 163.6 | 162.3 C7224) |) L7itel : 165.9 | 164.7 | 163.4 17355 L722 : 167.0 | 165.7 | 164.4 L7A.6) | 27233 : 168.1 | 166.8 | 165.5 | 1600 | 184.1 | 175.7 | 174.4 2 169.1 | 167.8 | 166.5 1610 | 185.2 : 176.8 | 175.5 A. 170.2 | 168.9 | 167.5 1620 | 186.4 | 183.: 177.9 | 176.6 ; 171.2 | 169.9 | 168.6 1630 | 187.5 ; 179.0 | 177.7 : 172.3 | 170.9 | 169.6 | 1640 | 188.7 5. 180.1 | 178.8 : 173.3 | 172.0 | 170.7 | 1650 | 189.8 36. 181.2 | 179.8 3 174A rz 20 |) 7a | 1660 | I9I.o | 188. 182.3 | 180.9 ‘ 175-4. \LZAL |) £7227 10670; I} 192:2 | 189: 183.4 | 182.0 30. 176.5 | 175.1 | 173.8 | 1680 | 193.3 | aK 184.5 | 183.1 : 23 d 177.6 | 176.2 | 174.8 | 1690 } 194.5 A 185.6 | 184.2 ; 178.6 | 177.2 | 175.9 1700 | 195.6 : 186.7 | 185.3 : L7Q\7 | L7S:3) |p L7O.9 1710 | 196.8 : 187.8 | 186.4 35. 180.7 | 179.3 | 177.9 1720 | 197.9 | 8 188.9 | 187.5 36. 181.8 | 180.4 | 179.0 1730 } I99.1 : 190.0 | 188.6 as 182.8 | 181.4 | 180.0 1740 | 200.2 : I9I.I | 189.7 : 183.9 | 182.5 | 181.1 1750 | 201.4 | . T.Q2\2)| #19017 : 185.0 | 183.5 | 182.1 | 1760 | 202.5 | & 193.3 | I91.8 3 186.0 | 184.6 | 183.1 | 1770 | 203.7 | 200.5 194.4 | 192.9 : : 187.1 | 185.6 | 184.2 | 1780 } 204.8 | ; 195.5 | 194.0 ; 188.1 | 186.7 | 185.2 | 1790 | 206.0 : 196.6 | 195.1 : 189.2 | 187.7 | 186.3 | 1800 | 207.1 | 203. 197.7 | 196.2 : 190.2 | 188.8 | 187.3 | 1810 | 208.3 5. 198.8 | 197.3 5. 191.3 | 189.8 | 188.3 1820 | 209.4 : 199.9 | 198.4 : 192.4 | 190.9 | 189.4 | 1830 | 210.6 a 201.0 | 199.5 : 193.4 | I9I.9 | 190.4 | 1840 | 211.7 8. 202.1 | 200.6 : 194.5 | 193.0 | I9QI.5 | 1850 | 212.9 4 203.2 | 201.6 ; 195.5 | 194.0 | 192.5 1860 } 214.0 : 204.3 | 202.7 : 196.6 | 195.1 | 193.6 1870 | 215.2 8 205.4 | 203.8 : : 197.6 | 196.1 | 194.6 1880 | 216.3 : 206.5 | 204.9 3. 198.7 | 197.2 | 195.6 1890 } 217.5 : 207.6 | 206.0 : 199.7 | 198.2 | 196.7 1900 | 218.6 5. 208.7 | 207.1 ; 200.8 | 199.3 | 197-7 | I910 | 219.8 K 209.8 | 208.2 3 201.9 | 200.3 | 198.8 1920 | 220.9 At 210.9 | 209.3 : 202.9 | 201.3 | 199.8 1930 } 222.1 8. 212.0 | 210.4 8. y 204.0 | 202.4 | 200.8 1940 | 223.2 : 203.0 | 2aa.4: 4 205.0 | 203.4 | 201.9 1950 | 224.4 | 220. 2TA2 || 2725 ! 206.1 | 204.5 | 202.9 | 1960 | 225.5 : 215.3% 2136 , 207.1 | 205.5 | 204.0 1970 | 226.7 2 216.4 | 214.7 j 208.2 | 206.6 | 205.0 1980 | 227.8 : 217.5 | 215.8 : 209.3 | 207.6 | 206.0 1990 |} 229.0 A 218.6 | 216.9 5. 210.3 | 208.7 | 207.1 2000 | 230.1 : 219.7 | 218.0 : 211.4 | 209.7 | 208.1 e OO “I Oo Hoe ISINT NINNI™N OO IED BW NY HO Cn OW ON OW) HH ~ ~ sO OY SONNINNISI OwHOWw on Dur vv H on Lal _ mor 4 \O wo oO SMITHSONIAN TABLES, 84 TABLES tsa REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Values of 2000 x m. Z 7 Altitude in ee Oe Sear + 36° | 153-7 | 152.5 | 151.4 | 150.3 | 149.1 | 148.0 143.8 | 141.7 | 154.7 | 153.6 | 152.4 | 151.3 | 150.1 | 149.0 144.7 | 142.7 155.8 | 154.6 | 153.4 | 152.3 | I5I.I | 150.0 145-7 | 143.6 156.8 | 155.6 | 154.4 | 153.3 | 152.1 | I51.0 146.6 | 144.5 157.8 | 156.6 | 155.4 | 154.3 | 153-1 | 152.0 147.6 | 145.5 158.8 | 157.6 | 156.4 } 155.3 | 154.1 | 153.0 148.6 | 146.4 159.9 | 158.7 | 157-5 | 156.3 | 155.1 | 154.0 149.5 | 147.4 160.9 | 159.7 | 158.5 | 157-3 | 156.1 | 154.9 150.5 | 148.3 161.9 | 160.7 | 159.5 | 158.3 | 157-1 | 155-9 151.4 | 149.3 162.9 | 161.7 | 160.5 | 159.3 | 158.1 | 156.9 152.4 | 150.2 164.0 | 162.7 | 161.5 | 160.3 | 159.1 | 157.9 153-3 | 151.2 165.0 | 163.7 | 162.5 | 161.3 | 160.1 | 158.9 L543) || T5200 166.0 | 164.8 | 163.5 | 162.3 | 161.1 | 159.9 155.3) (53:0 167.0 | 165.8 | 164.5 | 163.3 | 162.1 | 160.9 156.2 | 154.0 168.1 | 166.8 | 165.5 | 164.3 | 163.1 | 161.9 157-2 | 154.9 169.1 | 167.8 | 166.5 | 165.3 | 164.1 | 162.8 158.1 | 155.9 170.1 | 168.8 | 167.5 | 166.3 | 165.1 | 163.8 159.1 | 156.8 : 171.1 | 169.8 | 168.6 | 167.3 | 166.0 | 164.8 160.1 | 157.8 5 | 172.2 | 170.9 | 169.6 | 168.3 | 167.0 | 165.8 161.0 | 158.7 5 | 173.2 | 171-9 | 170.6 | 169.3 | 168.0 | 166.8 162.0 | 159.7 1700 | 175.6 | 174.2 | 172.9 | 171.6 | 170.3 | 169.0 | 167.8 162.9 | 160.6 1710 | 176.6 | 175.2 | 173.9 | 172.6 | 171.3 | 170.0 | 168.8 163.9 | 161.5 1720 } 177.6 | 176.3 | 174.9 | 173.6 | 172.3 | 171.0 | 169.7 164.8 | 162.5 1730 | 178.7 | 177-3 | 175-9 | 174.6 | 173.3 | 172.0 | 170.7 165.8 | 163.4 L740 |) 79.7 | 178.3 | 177-0 | 175-6 | 174.3 | 173-0 | 171.7 166.8 | 164.4 1750 | 180.7 | 179.3 | 178.0 | 176.6 | 175.3 | 174.0 | 172.7 ; 167.7 | 165.3 1760 | 181.7 | 180.4 | 179.0 | 177.6 | 176.3 | 175.0 | 173.7 : 168.7 | 166.3 1770 }| 182.8 | 181.4 | 180.0 | 178.6 | 177.3 | 176.0 | 174.7 | 173. 169.6 | 167.2 1780 | 183.8 | 182.4 | 181.0 | 179.7 | 178.3 | 177.0 | 175.7 : 170.6 | 168.2 1790 | 184.8 | 183.4 | 182.0 | 180.7 | 179.3 | 178.0 | 176.7 : 171.6 169.1 1800 | 185.9 | 184.5 | 183.1 | 181.7 | 180.3 | 179.0 | 177.6 | 176.3 | 175.0 | 172.5 | 170.0 1810 | 186.9 | 185.5 | 184.1 | 182.7 | 181.3 | 180.0 | 178.6 | 177.3, T7OOM | L735: e710 1820 | 187.9 | 186.5 | 185.1 | 183.7 | 182.3 | 181.0 | 179.6 | 178.3 | 177.0 | 174.4 | 171.9 | 1830 | 189.0 | 187.5 | 186.1 | 184.7 | 183.3 | 181.9 180.6 | 179.3 | 178.0 | 175.4 | 172.9 | 1840 | 190.0 | 188.6 | 187.1 | 185.7 | 184.3 | 182.9 | 181.6 | 180.3 178.9 | 176.3 | 173.8 1850 | 191.0 | 189.6 | 188.1 | 186.7 | 185.3 | 183.9 | 182.6 | 181.2 | 179.9 | 177.3 174.8 1860 | 192.1 | 190.6 | 189.2 | 187.7 | 186.3 | 184.9 | 183.6 182.2 | 180.9 | 178.3 | 175.7 | 1870 | 193.1 | 191.6 | 190.2 | 188.7 | 187.3 | 185.9 | 184.5 | 183.2 | 181.8 | 179.2 176.7 | 1880 | 194.1 | 192.7 | 191.2 | 189.7 | 188.3 | 186.9 | 185.5 | 184.2 | 182.8 | 180.2 177.6 | 1890 | 195.2 | 193.7 | 192.2 | 190.8 | 189.3 | 187.9 186.5 | 185.1 | 183.8 | 181.1 | 178.5 | 1900 | 196.2 | 194.7 | 193.2 | 191.8 | 190.3 | 188.9 | 187.5 | 186.1 | 184.8 | 182.1 | 179.5 | 1910 | 197.2 | 195.7 | 194.2 | 192.8 | 191.3 | 189.9 | 188.5 | 187.1 | 185.7 | 183.1 | 180.4 | 1920 | 198.3 | 196.8 | 195.3 | 193.8 | 192.3 | 190.9 | 189.5 188.1 | 186.7 | 184.0 | 181.4 1930 | 199.3 | 197.8 | 196.3 | 194.8 | 193.3 | 191.9 | 190.5 | 189.1 | 187.7 185.0 | 182.3 | 1940 | 200.3 | 198.8 | 197.3 | 195.8 | 194.3 | 192.9 | I9I.5 | 190.0 188.7 | 185.9 | 183.3 | 1950 | 201.4 | 199.8 | 198.3 | 196.8 | 195.3 | 193-9 | 192.4 | IgI.0 | 189.6 186.9 | 184.2 | 1960 | 202.4 | 200.8 | 199.3 | 197.8 | 196.3 | 194.9 | 193.4 | 192.0 | 190.6 187.8 | 185.2 | 1970 | 203.4 | 201.9 | 200.3 | 198.8 | 197.3 | 195.9 | 194.4 | 193.0 191.6 | 188.8 | 186.1 | 1980 | 204.5 | 202.9 | 201.4 | 199.8 | 198.3 | 196.9 | 195.4 | 194.0 | 192.5 189.8 | 187.0 | 1990 | 205.5 | 203.9 | 202.4 | 200.8 | 199.3 | 197.9 | 196.4 | 194.9 | 193-5 | 190.7 188.0 | 2000 | 206.5 | 204.9 | 203.4 | 201.9 | 200.3 | 198.8 | 197.4 | 195.9 | 194.5 | 191.7 | 188.9 2 pe ad SMITHSONIAN TABLES. TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Wh I Values of 2000 < m. m= 18444-+-67.530+.0032 1+ | Altitude MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). . — 16° | —12° | —8° | —4° | —2° 0° +2° | +4° | +6° | +8° | +10° | 220.1 |/226:5 ||.223.0)|| 219-7 || 218.0) ("276.39 214-7) | 213.0) |) armed | Peoos7m|E2oosr 231.3 | 227.7 | 224.2 | 220.8 | 219.1 | 217-4 | 215-7 | 214.1 | 212.41) 210.55) 209.2 232.4) |9228:8) || 225.3 || 221-9) | 220:2))| 258:5) 9276.8) | 215 0208 5s onion oro 233°6) || 229:9'| 226.4 |) 223.0) | 221-3) 219:63|/217.98) 216.2) 21405) |Rororon liom 234.7 | 231.1 || 227.5 | 224.0 | 222.3)|:220.65|°210.0 127723 | 215.6 ons on met ors 22510) | 232.2| 228.6 | 225-1 || 223-45 220-73 | §220.07 8218.25) 26.7 || 21h on mamcee 237.0 | 233.3 | 229.7 | 226.2 | 224°5 | 22273) |i2ar1 | 219.4) 207-7 | 216.0nlearA A 238.2 | 234.4 | 230.9 | 227.3 | 225.6 | 223.9 | 222.2 | 220.5 | 218.8 | 217.1 | 215.4 239.3 | 235.6 | 232.0 | 228.4 | 226.7 | 225.0 | 223.2 | 221.5 | 219.8 | 218.1 | 216.4 2A0.5\'| 236:7 | 233.1 |'229.5' | (22728 | 226.1 ||| 224%3 122916) 22019) 2rQ 24) aris 241.6 | 237.8 | 234.2 | 230.6 | 228:9 | 227-1 |225:4\ | 223°7 || 227.9) || 22007) Dressel 242.8 | 239.0 | 235.3 | 231.7 | 230.0 | 228.2 | 226.5 | 224.7 | 223.0 | 221.3 | 219.6 243.9 | 240.1 | 236.4 | 232.8 | 231.1 | 229.3 | 227.5 | 225.8 | 224.0 | 222.3 | 220.6 2A5:1 | 2AT.2.| 237.51 233.9, | 232:2"| 220-4 228:6)| (226.0 | 225°1 | 222A Gi ooo 246.2 | 242.4 | 238.7 | 235.0 | 233.2 | 231.5 | 220:7 | 227.9 | 226.2 | 224:4 | 229.7 247-4. | 243.5 ||| 239:8 || 236114 234'3)| 232°5, || 8220:8) 18220.08|227-2) soon Sn eaoa, 248.5 | 244.6 | 240.9 | 237.2 | 235.4 | 233.6 | 231.8 | 230.0 | 228.3 | 226.5 | 224.8 249.7 | 245.8 | 242.0 | 238.3 | 236.5 | 234.7 | 232.9 | 231.1 | 229.3 | 227.6 | 225.8 250.8 | 246.9 | 243.1 | 239.4 | 237.6 | 235.8 | 234.0 | 232.2 | 230.4 | 228.6 | 226.8 248.0 | 244.2 | 240.5 | 238.7 | 236.9 | 235.1 | 233.2 | 231.4 | 229.7 | 227.9 S og Pe oO 253-1 | 249.2 | 245.4 | 241.6 | 239.8 | 237.9 | 236.1 | 234.3 | 232.5 | 230.7 | 228.9 254.3 | 250.3 | 246.5 | 242.7 | 240.9 | 239.0 | 237.2 | 235.4 | 233.6 | 231.7 | 230.0 255.4 | 251.4 | 247.6 | 243.8 | 242.0 | 240.1 | 238.3 | 236.4 | 234.6 | 232.8 | 231.0 256.6 | 252.6.) 248.7 |/244°9, | 243-0 || 241-2) |7239.3) || 23725. | 235-71) 23308) 232.0 257-7 | 253-7 | 249.8 | 246.0 | 244.1 | 242.3 | 240.4 | 238.6 | 236.7 | 234.9 | 233.1 258.9 | 254.8 | 250.9 | 247.1 | 245.2 | 243.4 | 241.5 | 239.6 | 237.8 | 235.9 | 234.1 260.0 | 256.0 | 252.0 | 248.2 | 246.3 | 244.4 | 242.6 | 240.7 | 238.8 27,0) |225.2 261.2 | 257.1 | 253.2 | 249.3 | 247.4 | 245.5 | 243.6 | 241.8 | 239.9 38.0 | 236.2 262.3 | 258.2 | 254.3 | 250.4 | 248.5 | 246.6 | 244.7 | 242.8 | 241.0 | 239.1 | 237.2 263.5 | 259.4 | 255.4 | 251-5 | 249.6 | 247.7 | 245.8 | 243.9 | 242.0 | 240.1 | 238.3 264.6 | 260.5 | 256.5 | 252.6 | 250.7 | 248.8 | 246.9 | 245.0 | 243.1 | 241.2 | 239.3 265.8 | 261.6 | 257.6 | 253.7 | 251.8 | 249.8 | 247.9 | 246.0 | 244.1 | 242.2 | 240.4 266.9 | 262.8 | 258.7 | 254.8 | 252.9 | 250.9 | 249.0 | 247.1 | 245.2 | 243.3 | 241.4 |f 2.4 | 268.1 | 263.9 | 259.8 | 255.9 | 253.9 | 252.0 | 250.1 | 248.1 | 246.2 | 244.3 | 24 269.2 | 265.0 | 261.0 | 257.0 | 255.0 | 253-1 | 251.1 | 249.2 | 247.3 | 245.4 | 243.5 270.4 | 266.1 | 262.1 | 258.1 | 256.1 | 254.2 | 252.2 | 250.3 | 248.3 | 246.4 | 244.5 271.5 | 267.3 | 263.2 | 259.2 | 257.2 | 255.2 | 253.3 | 251.3 | 249.4 | 247.5 | 245.6 272.7 | 268.4 | 264.3 | 260.3 | 258.3 | 256.3 254.4 | 252.4 | 250.5 | 248.5 | 246.6 273.8 | 269.5 | 265.4 | 261.4 | 259.4 | 257.4 | 255.4 | 253-5 | 251.5 | 249.6 | 247.6 275.0 | 270.7 | 266.5 | 262.5 | 260.5 | 258.5 | 256.5 | 254.5 | 252.6 | 250.6 | 248.7 | | | | 276.1 | 271.8 | 267.7 | 263.6 | 261.6 | 259.6 | 257.6 | 255.6 | 253.6 | 251.7 | 240.7 277-3 | 272.9 268.8 | 264.7 | 262.7 | 260.7 | 258.7 | 256.7 | 254.7 | 252.7 | 250.8 278.4 | 274.1 | 269.9 | 265.8 | 263.7 | 261.7 | 259.7 | 257.7 | 255.7 | 253.8 | 251.8 279.6 | 275.2 | 271.0 | 266.9 | 264.8 | 262.8 | 260.8 | 258.8 | 256.8 | 254.8 | 252.8 280.7 | 276.3 | 272.1 | 268.0 | 265.9 | 263.9 | 261.9 | 259.9 | 257.9 | 255.9 | 253. 281.9 | 277.5 | 273.2 | 269.1 | 267.0 | 265.0 | 262.9 | 260.9 | 258.9 | 256.9 | 254.9 2460 | 283.0 | 278.6 | 274.3 | 270.2 | 268.1 | 266.1 | 264.0 | 262.0 | 260.0 | 258.0 | 256.0 2470 | 284.2 | 279.7 | 275.5 | 271.3 | 269.2 | 267.1 | 265.1 | 263.1 | 261.0 | 259.0 | 257.0 2480 | 285.3 | 280.9 | 276.6 | 272.4 | 270.3 | 268.2 | 266.2 | 264.1 | 262.1 | 260.1 | 258.0 2490 | 286.5 | 282.0 | 277-7 | 273-5 | 271.4 269.3 | 267.2 | 265.2 | 263.1 | 261.1 | 259.1 287.6 | 283.1 | 278.8 _ 2500 274.5 || 272.5,|1270:4 | 268.3 "| 26612.)| 264%2 41226212 4 260m SMITHSONIAN TABLES. 86 TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Zz, Values of 2000 < m. m= : 18444+-67.539 +.003Z 1+ Altitude MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). in metres. 2 Yi? | +14" | + 16° + 24° | + 26° | + 28° | +32° 2000 | 206.5 | 204.9 | 203.4 2010 | 207.6 | 206.0 | 204.4 ; 196.9 2020 | 208.6 | 207.0 | 205.4 : ; 197.9 2030 | 209.6 | 208.0 | 206.4 3 | 198.8 2040 | 210.7 | 209.0 | 207.5 : 199.8 2050 | 211.7 | 210.1 | 208.5 .3 | 200.8 2060 } 212.7 | 211.1 | 209.5 A. 3 | 201.8 2070 | 213.8 | 212.1 | 210.5 22) (5202-6 2080 | 214.8 | 213.1 | 211.5 : 203.7 2090 } 215.8 | 214.2 | 212.5 : 204.7 2100 | 216.8 | 215.2 | 213.5 52) 20557 2110 | 217.9 | 216.2 | 214.6 .2 | 206.7 2120 | 218.9 | 217.2 | 215.6 32) || 20727 2130 | 219.9 | 218.3 | 216.6 .2 | 208.6 2140 | 221.0 | 219.3 | 217.6 .2 | 209.6 2150 | 222.0 | 220.3 | 218.6 2|—20!6 2160 } 223.0 | 221.3 | 219.6 12) |G 201.6 2170 | 224.1 | 222.4 | 220.7 : 212.6 2TSO! Il) 225.0 |) 222.40 || 220-7 ale 20355 2190 | 226.1 | 224.4 | 222.7 ; 214.5 2200)8) 22722) | 225-4. 223-7 BT ees es 2210) || 228'2; | 2265; ||| 224:7; : 216.5 2220) 220.2) || 227-5; || 225.7 ae | P2725 2230 228.5 | 226.8 .I | 218.4 | 2240 3 | 229.5 | 227.8 .O | 219.4 2250 3 | 230.6 | 228.8 .O | 220.4 2260 | 233.4 | 231.6 | 229.8 .O | 221.4 2270 .4 | 232.6 | 230.8 .O | 222.4 2280 .4 | 233.6 | 231.8 20) (522328 2290 5 | 234.7 | 232:9 © || 224°3 2300 Py 123527 1233.9 20 || 225-3 2310 5 | 236.7 | 234.9 <0 |9226:3 2320 16 |) 237-75 | 235.9 LON 22723 2330 40.6 | 238.7 | 236.9 2340 41.6 | 239.8 | 237.9 2350 | 242.7 | 240.8 | 239.0 2360 43.7 | 241.8 | 240.0 | 2370 -7 | 242.8 | 241.0 2380 45. 243.9 | 242.0 2390 | 246.8 | 244.9 | 243.0 2400 7.8 | 245.9 | 244.0 2410 |} 248.8 | 246.9 | 245.1 2420 : 248.0 | 246.1 2430 | 250.9 | 249.0 | 247.1 2440 248.1 2450 249.1 2460 250.1 2470 251.2 241.9 2480 252.2 242.9 2490 253-2 243-9 5 2500 254.2 244.9 | 243.1 NN NO CO G2 O23 G2 N NR HH NN BWW WW GW ® OO NH OM HHYKND GBwHwOWHh BRRRGM Me AID ARONA hy NWN O09 SON'S booAR ain Ax Go Go Gs Go Go NOHNNHNN OWN H NNN NH Oo NN ND to oa Oo ° —lMNHDNNHNDM WOUWUNU Co SI DAR to BS Co \O 2 J yy + + wo Co >) Oo yoyo =~ UO . PS G2 ) G2 Od e NNNHN NH NNNNN Ro NN to ow w bh WN noua un nN uUbond +H HH eH O &HHoWwW GG GGG to NH No Oo on No on SMITHSONIAN TABLES. TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Z I Values of 2000 x m. to — 18444--67.530 --.003Z . TB MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). — - ———S —————— | ————— | 293.4 | 288.8 | 284.4 | 280.0 | 277.9 | 275.8 | 273.7 | 271.6 | 269.5 | 267.4 | 265.3 294.5 | 289.9 | 285.5 | 281.1 | 279.0 | 276.9 | 274.7 | 272.6 | 270.5 | 268.4 | 266.4 295-7 | 291.1 | 286.6 | 282.2 | 280.1 | 277.9 | 275.8 | 273.7 | 271.6 | 269.5 | 267.4 296.8 | 292.2 | 287.7 | 283.3 | 281.2 | 279.0 | 276.9 | 274.8 | 272.6 | 270.5 | 268.4 298.0 | 293.3 | 288.8 | 284.4 | 282.3 | 280.1 | 278.0 | 275.8 | 273.7 | 271.6 | 269.5 299.1 | 294.5 | 290.0 | 285.5 | 283.4 | 281.2 | 279.0 | 276.9 | 274.8 | 272.6 | 270.5 300.3 | 295.6 | 291.1 | 286.6 | 284.4 | 282.3 | 280.1 | 278.0 | 275.8 | 273.7 | 271.6 301.4 | 296.7 | 292.2 | 287.7 | 285.5 | 283.4 | 281.2 | 279.0 | 276.9 | 274.7 | 272.6 302.6 | 297.8 | 293.3 | 288.8 | 286.6 | 284.4 | 282.3 | 280.1 | 277.9 | 275.8 | 273.6 303-7 | 299.0 | 294.4 | 289.9 | 287.7 | 285.5 | 283.3 | 281.1 | 279.0 | 276.8 | 274.7 304.9 | 300.I | 295.5 | 291.0 | 288.8 | 286.6 | 284.4 | 282.2 | 280.0 | 277.9 | 275.7 306.0 | 301.2 | 296.6 | 292.1 | 289.9 | 287.7 | 285.5 | 283.3 | 281.1 | 278.9 | 276.8 307.2 | 302.4 | 297.8 | 293.2 | 291.0 | 288.8 | 286.5 | 284.3 | 282.1 | 280.0 | 277.8 308.3 | 303.5 | 298.9 | 294.3 | 292.1 | 289.8 | 287.6 | 285.4 | 283.2 | 281.0 | 278.8 309-5 | 304.6 | 300.0 | 295.4 | 293.2 | 290.9 | 288.7 | 286.5 | 284.3 | 282.1 | 279.9 310.6 | 305.8 | 301.1 | 296.5 | 294.2 | 292.0 | 289.8 | 287.5 | 285.3 | 283.1 | 280.9 311.8 | 306.9 | 302.2 | 297.6 | 295.3 | 293.1 | 290.8 | 288.6 | 286.4 | 284.2 | 282.0 312.9 | 308.0 | 303.3 | 298.7 | 296.4 | 294.2 | 291.9 | 289.7 | 287.4 | 285.2 | 283.0 314.1 | 309.2 | 304.5 | 299.8 | 297.5 | 295.2 | 293.0 | 290.7 | 288.5 | 286.3 | 284.0 315.2 | 310.3 | 305.6 | 300.9 | 298.6 | 296.3 | 294.1 | 291.8 | 289.5 | 287.3 | 285.1 316.4 | 311.4 | 306.7 | 302.0 | 299.7 | 297.4 | 295.1 | 292.9 | 290.6 | 288.4 | 286.1 317-5 | 312.6 | 307.8 | 303.1 | 300.8 | 298.5 | 296.2 | 293.9 | 291.7 | 289.4 | 287.2 318.7 | 313-7 | 308.9 | 304.2 | 301.9 | 299.6 | 297.3 | 295.0 | 292.7 | 290.5 | 288.2 319.8 | 314.8 | 310.0 | 305.3 | 303.0 | 300.6 | 298.3 | 296.1 | 293.8 | 291.5 | 289.2 321.0 | 316.0 | 311.1 | 306.4 | 304.1 | 301.7 | 299.4 | 297.1 | 294.8 | 292.5 | 290.3 322.1 | 317.1 | 312.3 | 307.5 | 305.1 | 302.8 | 300.5 | 298.2 | 295.9 | 293.6 | 291.3 323.3 | 318.2 | 313.4 | 308.6 | 306.2 | 303.9 | 301.6 | 299.2 | 296.9 | 294.6 | 292.4 324.4 | 319.4 | 314.5 | 309-7 | 307-3 | 305.0 | 302.6 | 300.3 | 298.0 | 295.7 | 293.4 325-6 | 320.5 | 315.6 | 310.8 | 308.4 | 306.1 | 303.7 | 301.4 | 299.0 | 296.7 | 294.4 326.7 | 321.6 | 316.7 | 311.9 | 309.5 | 307-1 | 304.8 | 302.4 | 300.1 | 297.8 | 295.5 327.9 | 322.8 | 317.8 | 313.0 | 310.6 | 308.2 | 305.9 | 303.5 | 301.2 | 298.8 | 296.5 329.0 | 323.9 | 318.9 | 314.1 | 311.7 | 309.3 | 306.9 | 304.6 | 302.2 | 299.9 | 297.6 330.2 | 325.0 | 320.1 | 315.2 | 312.8 | 310.4 | 308.0 | 305.6 | 303.3 | 300.9 | 298.6 331.3 | 326.1 | 321.2 | 316.3 | 313-9 | 311-5 | 309.1'] 306.7 | 304.3 | 302.0 | 299.6 332-5 | 327-3 | 322.3 | 317-4 | 314.9 | 312.5 | 310.1 | 307.8 | 305.4 | 303.0 | 300.7 333-6 | 328.4 | 323.4 | 318.4 | 316.0 | 313.6 | 311.2 | 308.8 | 306.4 | 304.1 | 301.7 > a ° 2 2 ee) 5 334.8 | 329.5 | 324.5 | 319.5 317.1 | 314.7 | 312 309.9 | 307.5 | 305.1 | 302.8 335-9 | 330-7 | 325.6 | 320.6 | 318.2 | 315.8 | 313.4 | 311.0 | 308.6 | 306.2 | 303.8 337-1 | 331.5 | 326.7 | 321.7 | 319.3 | 316.9 | 314.4 | 312.0 | 309.6 | 307.2 | 304.8 335.2 | 332-9 | 327.9 | 322.8 | 320.4 | 317.9 | 315.5 | 313.1 | 310.7 | 308.3 | 305.9 339-4 | 334-1 | 329.0 | 323.9 | 321.5 | 319.0 | 316.6 | 314.2 | 311.7 | 309.3 | 306.9 340.5 | 335-2 | 330.1 | 325.0 | 322.6 | 320.1 | 317.7 | 315.2 | 312.8 | 310.4 | 308.0 341.7 | 336.3 | 331.2 | 326.1 | 323.7 | 321.2 | 318.7 | 316.3 | 313.8 | 311.4 | 300.0 342.8 | 337-5 | 332-3 | 327-2 | 324.7 | 322.3 | 319.8 | 317.3 | 314.9 | 312.5 | 310.0 344.0 | 338.6 | 333.4 | 328.3 | 325.8 | 323.3 | 320.9 | 318.4 | 315.9 | 313.5 | 311.1 345-1 | 339-7 | 334-5 | 329.4 | 326.9 | 324.4 | 321.9 3195 | 317.0 | 314.6 | 312.1 SMITHSONIAN TABLES. TABLE 17. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Z I Values of 2000 X m. m= TORRE op core ‘ +B Altitude MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). in metres. Zs ia} SIN] eG a OR bo x OV oO NY HNN ons ~ OO oom NN Go Go Hb HHO O NNN HD SIs NI Dur => WN ¢ NwWN ND GG Od I ON co 280.0 281.0 CMMmMmMm cm NRHHN ND NNN NH ND MnO NH NNHNNHNH YNHHHN MH HARROD NHHNHN Our & Od NNONN ON ee ~ On WWwO OwWworw DAR ODE WWwowo 5 A COC S) to ie) CO ar oon sa NON ND Is] DARE GQNHAOO KITA os “I 4 tO NN bh 2M MmOMOM DAMM] ty oO we ° HNU1 4 ° AnH UMMOSOO tO \o “I Mmm mMoo bo HN H NN Oo Ny YN H COmoomrn~s SSIS SINS. to \O ~ \o Ss Co ‘o ° 2 oe © \O PCOnMeMnM MOO ISNIN NSN SIN Ooms NO NNN ND KR NH HN DN WDOOODD OODOGO wb ww HH Nw NHN b . ANI bd nan nnnnn Nom i Rint OOIDHN BONE | N DANS®WN me WWWWN nn annonce w&® ty CO oes tO Co } OG SMITHSONIAN TABLES. TABLE 18. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Correction of 2000m for Latitude: 2000 7 « 0.002662 cos 2g. For latitudes 0° to 45°, the correction is to be subtracted. For latitudes 45° to go°, the correction is to be added. LATITUDE. 3S °o eH me He O S we He O b ww RH boH Rb we HN ORO FOF OSC Rw NKR N os o nN yb oN oN ° ty O49 O20R2 GO Oo 990 bv nN NH oO oO +H BWW WH Ww bhA B&O AnkR Bd & & O & nin n CP OFC Ogee O52 OF. O39 WD G Oo on on ow NA AW ANA navAMN 3 3 3 4 4 5 5 4 0.3 4 4 ‘5 5 fon oO fon pay orgie) WO) Ne. SoS SSS oO on nn Sauda 4 COSY 50.01% 49.3 1948.6) 247-9 age 61 54.6 | -53.8 | 53-1 | 52.4 | 51-77] 50:9.) 50.2 | 40.5, 1" 48:7 4 eA8:0 62 55.5 || *54.0 || 64-07] 53.3) | 52: 513 || SLL) | 50:3 || 40:67 948.3 63 56.4 | 55-7 | 54-9 | 54-2°| 53.4 | 52.7 O19 | $1.2 | $0.4 49.6 64 57-3 | 50.6: | 55:8 1055-0 "| 954-3.) (53-51) 528/11 52:07) e502) song 65 58.3 | 57-5.| 56:7), 55-9.| 55-2 | -54-4 | 53-6 | 52.8}! 952-0 vi paes 66 59.2 | 58.4 | 57.6 | 56.8 | 56.1 55:3: 854-5) | 95337 1) 52-0) (952.1 67 60.1 | 59.3 | 58.5 | 57-7 | 56.9 | 56. | 55-3 | 54.5 | 53-7 | 52.9 68 60.3 | 59-4 | 58.6 | 57-8 | 57.0 | 56.2 | 55.4 | 54.6 | 53.7 69 61.2 | 60:4, | 5055-) 58-7. |)57-9) || 57.0.4] 56.2151 55-40n mega 70 62:1 || 61.3" |) 60:4.) 5956 Wh 5827) | 95759) Sede 5 Olen oe 71 63.0 ||) 6252.1) (61.3 3 6075 4] 50.6) ||| 58:84 5 7-957 laos 72 | 64.0 || 63.2 || 16252° |" (61-4, | “60.5 |) 59:6. |) 58:85 | 5720) |) 5720 73 64:9 | 64:0") “63° || 162.3.) 6154. |) 16055) |) 59:6.)| 500715729 | 74 65.8 | 64.9 || 64.0 | 63:1 | 62.3) 61-4 | (60:5 | 59:69 58:7 75 66.7 | 658.41) 164.9 |}'.64:0 |) 63.1) || 62-2, 9| 16r- 60.4 | 59.5 76 67:7 | 66.8 1|.-65-8:1|" (64.9:7| 64.0 || (637% ||| 6220) a #Oraes God! 77 68.6 | 67.7 | 66.7 | 65.8 | 64.9 | 64.0 | 63.0 | 62.1 | 61.2 78 69.5 | 68.6 | 67.6 | 66.7 | 65.8 | 64.8 | 63.9 | 63.0 | 62.0 7 69:5) "| 763.6°7|°%67.6 |) 66372), "6537 allOd: Fal O3-318|| 0270 70.4 | 69.5 |. 68:5 | 67:5 | 66:6: 165.6 9) 64.6. 46357 71.4 | 70.4 | 69.4 | 68.4 67.4 66.5 |.65.5 | 64.5 | 7233)" 7Lsge|"'70.3 |) 6O53) |, 1685.26) Onegai me Oona aImOsse 73.2) i V72s2"94\\ *7:1,2) || ©7012) 4) 6.25 Oo.2 O72 2a ORS FAT 72 oi 72%. FIT, || 7OoL 69.0 | 68.0 | 67.0 | 75.0 | 74.0 ||| 73:0 4|)) 72.0 || 7O%9)||GO:9) |) 168:0 14] RO 7e6 SMITHBONIAN TABLES. TABLE 19. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. — B=B (107-1). Height of the barometer (B). Values of 200072 obtained from Table 17. HEIGHT OF THE BAROMETER IN MILLIMETRES. | 700 | 690 680 670 660 650 640 630 Top argument: Side argument: 710 114 115 116 Tel7) 118 11g 120 121 122 123 sIsI“] Ne HN OO NN TAKES “I CWO O O MM Or =I PH OO % oh haa mMmo KES HAN ooo Sxcx woo 87.9 88.8 89.7 90.6 SMITHSONIAN TABLES. SINISI DD £ sa n pA OW RNHWL ss aaeone ° ss Oe Am CO oonIsIs HOO Sm mm. 7-5 68.4 69.3 70.2 Fle 72-9 73-7 74.6 75-5 76.4 77-3 78.2 79-1 80.0 80.9 $1.8 82.7 83.6 84.5 85.4 86.3 88.1 99.9 91.8 os 7 95-4 96.3 97-3 98.2 99.1 100.0 100.9 101.9 102.8 103.7 104.6 105.6 106.5 mm. 66.6 67.4 68.3 69.2 70.1 79.9 71.8 72.7 95-0 95-9 96.8 97-7 98.6 99:5 100.4 101.3 102.2 103.1 104.1 105.0 105.3 min. 65.6 66.5 67.3 68.2 69.0 69.9 70.8 71.6 72-5 73-4 74-2 75.1 76.0 76.8 77-7 78.6 79-5 80.3 81.2 82.1 83.0 83.9 84.7 85.6 86.5 87.4 88.3 89.1 go.0 90-9 g1.8 92.7 93.6 94-5 95-4 96.3 97-2 98.1 98.9 99.8 100.7 IO1.6 102.5 103.4 104.3 mm. 64.6 65.5 66.3 67.2 68.0 68.9 69.7 70.6 71.4 72-3 Fou: 74-0 74-9 75-7 76.6 77-4 78.3 79.2 80.0 80.9 81.8 82.6 83.5 84.4 87.0 87.8 88.7 91.3 92.2 93-1 94-0 94-8 95-7 96.6 97-5 98.4 99-3 100. I IOI.O IOI.9 93-4 93 mm. 62.7 63.5 64.4 65.2 77-3 78.1 78.9 79-7 80.6 81.4 82.2 83.1 83.9 84.7 $5.6 86.4 87.2 88.1 88.9 89.8 90.6 91.4 92.3 93-1 94.0 94.8 95-7 96.5 on SO HIA HO UIST O TABLE 19. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. B.—B=B (10”—1). Top argument: Height of the barometer (B). Side argument: Values of 200077 obtained from Table 17. HEIGHT OF THE BAROMETER IN MILLIMETRES. 680 670 660 | 650 640 630 | 620 610 mm. mm. mm. mm. mm, a mm. mm, mm, 106.8 | 105.3 | 103.7 | 102.2 | 100.6 : 97.5 96.0 94.4 107.7 | 106.2 | 104.6 | 103.0 | IOI.5 : 98.4 96.8 95.2 LO8=6" }| LOFT ||| TO5.5 4/0329) || 19202 8 99.2 97.6 96.0 109.6 | 108.0 | 106.4 | 104.8 | 103.2 : 100.0 | 98.4 96.9 110.5 | 108.9 | 107.3 | 105.7 | IO4.1 : TOO) | #9933) || sOVe7 I11I.4 | 109.8 | 108.2 | 106.6 | 104.9 : IOI.7 | 100.1 98.5 EL223) | L1O.7 | LOOsT io 7eA) | 10523 : 102.6 | 100.9 99.3 TL3-2' | TLL.6) ||’ LLOsO! | TOSs3) 4106.7 5. TO3.45 || LOLS" | LOOs TL4s2) | L255. | LOOM |»10972) || 10776 5. 104.2 | 102.6 | 100.9 TES S10 |) LEZ! || LEIS) eLTOse |) TOSsA| eS as on | o Se eS ee SP HAD ARKOP as e co Hoo a0 + G2 G2 G2 Oo 161.1 : : T5355 e4 elo dO. 162.0 ; ‘ 154.4 | I51.9 162.9 ; : 155-3 || 152.6 163.9 : : 156.2 | 153.6 164.8 : : 157.1 | 154.5 165.7 es : 157.9 | 155-4 166.6 : : 158.8 | 156.2 167.6 : : 159.7 | 157.1 168.5 : : 160.6 | 158.0 169.4 8 : 161.5 | 158.8 170.4 : : 162.4 | 159.7 171.3 3 : 163.3 | 160.6 17202 : .8 | 164.2 | 161.5 165.1 | 162.3 165.9 | 163.2 166.8 | 164.1 167-72) 205-0 168.6 | 165.9 169.5 | 166.7 170.4 | 167.6 mann or Our —& f Go ANAOON 171.3 | 168.5 = on “I o SMITH8ONIAN TABLES. 95 TABLE 19. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. B.— B=B (10”—1). Top argument: Height of the barometer (B). Side argument: Values of 200077 obtained from Table 17. HEIGHT OF THE BAROMETER IN MILLIMETRES. 590 | 580 | 570 | 560 | 550 | 540 S E mn. mm. mm. mm. mm. mm. 165.7 | 162.9 | 160.1 | 157.3 4. I51.7 166.6 | 163.8 | 160.9 | 158.1 55. 152.5 167.4 | 164.6 | 161.8 | 158.9 3 153.3 168.3 | 165. 162.6 | 159.8 . 154.1 169.2 | 166. 163.5 | 160.6 3 154.9 BEEN SINNSISN T7Os1 | 167-2) 1 1643) | TO reA: 3 155-7 170.9: |" 168.0) 165:m | 162.3 i 156.5 171.8 | 168.9 | 166.0 | 163.1 : 157-3 172.7 | 169.8 | 166.8 | 163.9 : 158.1 17326) || 3:70. OM LOZ 57) «| eho =i ‘ 158.9 171.5 | 168.5 | 165.6 : 159.7 172.4 | 169.4 | 166.4 : 160.5 17322 a7 Orn lG7ee 4.3 | 161.3 D7 ATS) L700 ||| MOSsr ! 162.1 175.0 | 172.0 | 168.9 : 162.9 175.8 | 172.8 | 169.8 : 163.7 T7037 073074) LOL : 164.5 077.68) T7AL5 | R75 : 165.3 L/S. 50 |e LT5eA (| L72es ; 166.1 £7913). |) 176:20)| sb 73e0 3 167.0 190.2% | 277500) |) L7ALO : 167.8 TOLe Le 7O.O» PL 7A.o : 168.6 182.0 D5 a7 : 169.4 182.8 } 176.5 : 170.2 183.7 177.4 A. 171.0 184.6 178.2 : L729 185.5 179.1 5. 7207 186.4 179.9 : 173.5 187.2 180.8 : 174.3 188.1 181.6 : 175.1 189.0 182.5 : 176.0 189.9 183.3 f 176.8 190.8 184.2 : 177.6 191.7 185.1 ; 178.4 192.6 185.9 ‘ 179.3 193.4 186.8 : 180. I 194.3 187.6 A. 180.9 195.2 188.5 ; 181.8 196.1 189.4. : 182.6 197-0 190.2 : 183.4 197.9 191.1 : 184.3 198.8 191.9 : 185.1 199.7 192.8 ; 185.9 200.6 193.7 ; 186.8 201.5 194.6 : 187.6 202.4 195.4 : 188.4 SMITHSONIAN TABLES. g6 TABLE 19. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. B.— B= B (10”—1). Top argument: Height of the barometer (B). Side argument: Values of 200077 obtained from Table 17. HEIGHT OF THE BAROMETER IN MILLIMETRES. mm. mm. . . . mm. 195.4 191.9 : ; 178.0 196.3 192.8 : : 178.8 197.2 193.6 ‘ 3s 179.6 198.0 194.5 j ; 180. 4 198.9 195.4 : 34. 181.1 199.8 196.2 : ‘ 181.9 200.7 197.1 : Ff 182.7 201.5 197.9 : : 183.5 202.4 198.8 . ‘ 184.3 203.3 199.7 : : 185.1 204.2 200.5 : : 185.9 205.0 201.4 2 ; 186.7 205.9 202.3 : : 187.5 206.8 203.1 : s 188.3 207.7 204.0 ; : . 189.1 208.6 204.9 : : 190.0 209.5 205.7 : 4.5 190.8 210.3 206.6 ; Se 191.6 | 21Ie2 207.5 : : 192.4 20 2h 208.3 8 ; 193.2 213.0 209.2 s ; 194.0 213.9 210.1 : : 194.8 214.8 211.0 : : 195.6 215.7 211.8 : 4. , 196.4 216.6 SIG : é 197.2 217.5 213.6 : ‘ 198.1 218.4 214.5 : : 198.9 219.3 215.4 ; ‘ 199.7 220.2 216.2 : ; 200.5 221.1 27ST : : 201.3 222.0 218.0 ’ : 202.1 222.9 218.9 : : 203.0 223.8 219.8 8 : 203.8 224.7 220.7 : : 204.6 225.6 2205 : : 205.4 226.5 222.4 : i 206.3 22774 22252. 5. ; 207.1 228.3 224.2 ; 5 207.9 229.2 225.1 : : 208.7 230.1 226.0 _ : 209.6 231.0 226.9 3 : 210.4 231.9 227.8 : : 211.2 232.8 228.7 : 21251 233.8 229.6 ‘ ; 212.9 234.7 230.5 ‘ : 213.7 235.6 231.4 : : 214.6 SMITHSONIAN TABLES. 97 TABLE 19. REDUCTION OF THE BAROMETER TO SEA LEVEL. METRIC MEASURES. Bo— B = B (10”—1). Top argument: Height of the barometer (B). Side argument: Values of 200077 obtained from Table 17. HEIGHT OF THE BAROMETER IN MILLIMETRES. 550 540 mm. mm. HNO NNNHNH HD Oo Oe © Go O bo HHH ND O» G Go G2 Go nN & ON ty Nw NHN NW WNNN bd OO Gon “I QMO ON oO HoH N ND NHN Nb Dur & & Oo Y DN Oro G2 Go CON Qn NOS oo > cn a NONNN ND Or Gs Go Oo” U1 NY NNN G2 Go G2 Go ALORA DAE Yo & ANO O NHN HD Wb HHL SOROS HNNW 0 Oa SI OV An CO O G2 Go G2 G2 O 24 25 25 25 25 PA AAA “INT CWO O & na a e NHNHN HD G2 G2 G2 G2 2 DADA -anNT OO to ar ° Ww SMITHSONIAN TABLES, 98 TABLE 20. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Values of 60368 [1 + 0.0010195 x 36] log Barometric ; Pressure. | - .Ol .02 .03 .04 05 oo .07 .08 .09 29.90. B ee re _——————h Inches. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. 12.00 | 24814 | 24791 | 24769 | 24746 | 24723 | 24701 | 24678 | 24656 | 24633 | 24611 12.10 | 24588 | 24566 | 24543 | 24521 | 24499 | 24476 | 24454 | 24431 | 24409 | 24387 12.20 | 24365 | 24342 | 24320 | 24298 | 24276 | 24253 | 24231 | 24209 | 24187 | 24165 12.30 | 24143 | 24121 | 24098 | 24076 | 24054, | 24032 | 24010 | 23988 | 23966 | 23944 12.40 | 23923 | 23901 | 23879 | 23857 | 23835 | 23813 | 23791 | 23770 | 23748 | 23726 12.50 | 23704 | 23682 | 23661 | 23639 | 23617 | 23596 | 23574 | 23552 | 23531 | 23509 12.60 | 23488 | 23466 | 23445 | 23423 | 23402 | 23380 | 23359 | 23337 | 23316 | 23204 12.70 | 23273 | 23251 | 23230 | 23209 | 23187 | 23166 | 23145 | 23123 | 23102 | 23081 12.80 | 23060 | 23038 | 23017 | 22996 | 22975 | 22954 | 22933 | 22911 | 22890 | 22869 12.90 | 22848 | 22827 | 22806 | 22785 | 22764 | 22743 | 22722 | 22701 | 22680 | 22659 13.00 | 22638 | 22617 | 22596 | 22576 | 22555 | 22534 | 22513 | 22492 | 22471 | 22451 13.10 | 22430 | 22409 | 22388 | 22368 | 22347 | 22326 | 22306 | 22285 | 22264 | 22244 13.20 | 22223 | 22203 | 22182 | 22162 | 22141 | 22121 | 22100 | 22080 | 22059 | 22039 13.30 | 22018 | 21998 | 21977 | 21957 | 21937 | 21916 : 21896 | 21876 | 21855 | 21836 13.40 | 21815 | 21794 | 21774 | 21754 | 21734 | 21713 | 21693 | 21673 | 21653 | 21633 13.50 | 21612 | 21592 | 21572 | 21552 | 21532 | 21512 | 21492 | 21472 | 21452 | 21432 13.60 | 21412 | 21392 | 21372 | 21352 | 21332 | 21312 | 212y2 | 21272 | 21252 | 21233 13.70 | 21213 | 21193 | 21173 | 21153 | 21134 | 21114 | 21094 | 21074 | 21054 | 21035 13.80 | 21015 | 20995 | 20976 | 20956 | 20936 | 20917 | 20897 | 20878 | 20858 | 20838 13.90 | 20819 | 20799 | 20780 | 20760 | 20741 | 20721 | 20702 | 20682 | 20663 | 20643 14.00 | 20624 | 20605 | 20585 | 20566 | 20546 | 20527 | 20508 | 20488 | 20469 | 20450 14.10 | 20431 | 20411 | 20392 | 20373 | 20354 | 20334 | 20315 | 20296 | 20277 | 20258 > 14.20 | 20238 | 20219 | 20200 | 20181 | 20162 | 20143 | 20124 | 20105 | 20086 | 20067 14.30 } 20048 | 20029 | 20010 | IgggI | 19972 | 19953 | 19934 | 19915 | 19896 | 19877 14.40 | 19858 | 19839 | 19821 | 19802 | 19783 | 19764 | 19745 | 19727 | 19708 | 19689 14.50 | 19670 | 19651 | 19633 | 19614 | 19595 | 19577 | 19558 | 19539 | 1952I | 19502 14.60 | 19483 | 19465 | 19446 | 19428 | 19409 | 19390 | 19372 | 19353 | 19335 | 19316 14.70 | 19298 | 19279 | 19261 | 19242 | 19224 | 19206 | 19187 | 19169 | I9I50 | 19132 14.80 | 19114 | 19095 | 19077 | 19059 | 19040 | 19022 | 19004 | 18985 | 18967 | 18949 14.90 | 18931 | 18912 | 18894 | 18876 | 18858 | 18840 | 18821 | 18803 | 18785 | 18767 15.00 | 18749 | 18731 | 18713 | 18694 | 18676 | 18658 | 18640 | 18622 | 18604 | 18586 15.10 | 18568 | 18550 | 18532 | 18514 | 18496 | 18478 | 18460 | 18442 | 18425 | 18407 15.20 | 18389 | 18371 | 18353 | 18335 | 18317 | 18300 | 18282 | 18264 | 18246 | 18228 15.30 | 18211 | 18193 | 18175 | 18157 | 18140 | 18122 | 18104 | 18086 | 18069 | 18051 15.40 | 18033 | 18016 | 17998*| 17981 | 17963 | 17945 | 17928 | 17910 | 17893 | 17875 15.50 | 17858 | 17840 | 17823 | 17805 | 17788 | 17770 | 17753 | 17735 | 17718 | 17700 15.60 | 17683 | 17665 | 17648 | 17631 | 17613 | 17596 | 17578 | 17561 | 17544 | 17526 15.70 | 17509 | 17492 | 17474 | 17457 | 17440 | 17423 | 17405 | 17388 | 17371 | 17354 15.80 | 17337 | 17319 | 17302 | 17285 | 17268 | 17251 | 17234 | 17216 | 17199 | 17182 15.90 }| 17165 | 17148 | 17131 | 17114 | 17097 | 17080 | 17063 | 17046 | 17029 | 17012 16.00 | 16995 | 16978 | 16961 | 16944 | 16927 | 16910 | 16893 | 16876 | 16859 | 16842 16.10 16825 | 16808 | 16792 | 16775 | 16758 | 16741 | 16724 | 16707 | 16691 | 16674 16.20 | 16657 | 16640 | 16623 | 16607 | 16590 | 16573 | 16557 | 16540 | 16523 | 16506 16.30 | 16490 | 16473 | 16456 | 16440 | 16423 | 16406 | 16390 | 16373 | 16357 | 16340 16.40 | 16324 | 16307 | 16290 | 16274 | 16257 | 16241 | 16224 | 16208 | 16191 | 16175 16.50 | 16158 | 16142 | 16125 | 16109 | 16092 | 16076 | 16060 | 16043 | 16027 | 16010 16.60 | 15994 | 15978 | 15961 | 15945 | 15929 | 15912 | 15896 | 15880 | 15863 | 15847 16.70 | 15831 | 15815 | 15798 | 15782 | 15766 | 15750 | 15733 | 15717 | 15701 | 15685 16.80 | 15669 | 15652 | 15636 | 15620 | 15604 | 15588 | 15572 | 15556 | 15539 | 15523 16.90 | 15507 | 15491 | 15475 | 15459 | 15443 | 15427 | I541I | 15395 | 15379 | 15363 17.00 | 15347 | 15331 | 15315 | 15299 15283 | 15267 | 15251 | 15235 | 15219 | 15203 SMITHSONIAN TABLES. 100 TABLE 20. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. 29.90 Values of 60368 [1 + 0.0010195 * 36] log a" Barometric Pressure. | -00 Ol .02 .03 .04 -05 .06 .07 208) a e.09 B. Inches. Feet. Feet. Feet. | Feet. Feet. Feet. Feet. Feet. BEC een. 17.00 | 15347 | 1533I | 15315 | 15299 | 15283 | 15267 | 15251 | 15235 | 15219 | 15203 17.10 15187 | I5172 | 15156 | 15140 | 15124 | 15108 | 15092 | 1507 15061 | 15045 17.20 | 15029 | 15013 | 14997 | 14982 | 14966 | 14950 | 14934 | 14919 | 14903 | 14887 17.30 | 14871 | 14856 | 14840 | 14824 | 14809 | 14793 | 14777 | 14762 | 14746 | 14730 17.40 | 14715 | 14699 | 14684 | 14668 | 14652 | 14637 | 14621 | 14606 | 14590 | 14575 17.50 | 14559 | 14544 | 14528 | 14512 | 14497 | 14481 | 14466 | 14451 | 14435 | 14420 17.60 14404 | 14389 | 14373 | 14358 | 14342 | 14327 | 14312 | 14296 | 14281 | 14266 | 17.70 14250 | 14235 | 14219 | 14204 | 14189 | 14173 | 14158 | 14143 | 14128 | 14112 | 17.80 | 14097 | 14082 | 14067 | 14051 | 14036 | 14021 | 14006 | 13990 | 13975 | 13960 17.90 } 13945 | 13930 | 13914 | 13899 | 13884 | 13869 | 13854 | 13839 | 13824 | 13508 18.00 | 13793 | 13778 | 13763 | 13748 | 13733 | 13718 | 13703 | 13688 | 13673 | 13658 18.10 | 13643 | 13628 | 13613 | 13598 | 13583 | 13568 | 13553 | 13538 | 13523 | 13508 | 18.20 | 13493 | 13478 | 13463 | 13448 | 13433 | 13418 | 13404 | 13389 | 13374 | 13359 | 18.30 | 13344 | 13329 | 13314 | 13300 | 13285 | 13270 | 13255 | 13240 | 13226 13211 | 18.40 | 13196 | 13181 | 13166 | 13152 | 13137 | 13122 |"13107 | 13093 | 13078 | 13063 | 18.50 | 13049 | 13034 | 13019 | 13005 | 12990 | 12975 | 12961 | 12946 | 12931 | 12917 18.60 | I2902 | 12888 | 12873 | 12858 | 12844 | 12829 | 12815 | 12800 | 12785 | 12771 | 18.70 | 12756 | 12742 | 12727 | 12713 | 12698 | 12684 | 12669 | 12655 | 12640 | 12626 | 18.80 | 72611 | 12597 | 12583 | 12568 | 12554 |} 12539 | 12525 | 12510 Boe | 12482 | 18.90 | 12467 | 12453 | 12438 | 12424 | 12410 | 12395 | 12381 | 12367 12352 | 12338 19.00 | 12324 | 12310 | 12295 | 12281 | 12267 | 12252 | 12238 | 12224 | 12210 | 12195 19.10 I218r | 12167 | 12153 | 12138 | 12124 | 12110 | 12096 | 12082 | 12068 | 12053 19.20 | 12039 | 12025 | I201I | 11997 | 11983 | 11969 | 11954 | II940 | 11926 | IIgI2 19.30 11898 | 11884 | 11870 | 11856 | 11842 | 11828 | 11814 | 11800 | 11786 | 11772 19.40 11758 | 11744 | 11730 | 11716 | 11702 | 11688 | 11674 | 11660 | 11646 | 11632 19.50 | 11618 | 11604 | 11590 | 11576 | 11562 | 11548 | 11534 | 11520 | II507 | 11493 19.60 | 11479 | 11465 | 11451 | 11437 | 11423 | 11410 | 11396 | 11382 | 11368 | 11354 19.70 | 11340 | 11327 | 11313 | 11299 | 11285 | 11272 | 11258 | 11244 | 11230 | 11217 19.80 11203 | 11189 | III75 | 11162 | 11148 } 11134 | III2I | 11107 | 11093 11080 19.90 | 11066 | 11052 | 11039 | 11025 | I10II | 10998 | 10984 | 10970 | 10957 | 10943 | 20.00 | 10930 | 10916 | 10903 | 10889 | 10875 | 10862 | 10848 | 10835 | 10821 | 10808 | 20.10 10794 | 10781 | 10767 | 10754 | 10740 | 10727 | 10713 | 10700 | 10686 | 10673 20.20 | 10659 | 10646 | 10632 | 10619 | 10605 | 10592 | 10579 | 10565 | 10552 | 10538 20.30 10525 | 10512 | 10498 | 10485 | 10472 | 10458 | 10445 | 10431 | 10418 | 10405 20.40 | 10391 | 10378 | 10365 | 10352 | 10338 | 10325 | 10312 | 10298 | 10285 | 10272 20.50 | 10259 | 10245 | 10232 | I02Ig | 10206 | IoIg2 | 10179 | 10166 | 10153 | 10139 20.60 | 10126 | 10113 | IOI0o | 10087 | 10074 | 10060 | 10047 | 10034 | I002I | 10008 20.70 | 9995 | 9982 | 9968} 9955 | 9942] 9929 | 9916 | 9903 | 9890 9877 20.80 | 9864 | 9851 | 9838 | 9825 | 9812] 9799] 9786 | 9772 | 9759 9746 20.90 | 9733 | 9720| 9707 | 9694 | 9681 | 9668 | 9655 | 9642 | 9629 | 9617 21.00 | 9604 9591 | 9578 | 9565 | 9552} 9539} 9526 9513 | 9500 | 9487 | 21.10 | 9474 | 9462 9449} 9436 | 9423] 9410| 9397| 9384] 9372 9359 | 21.20 | 9346 | 9333 | 9320 | 9307 | 9295 | 9282 | 9269) 9256) 9244 | 9231 | 21.30 9218 | 9205 | 9193 | 9180} 9167 9154 | 9142] 9129] 9116} 9103 21.40 gogI 9078 | 9065 | 9053 | 9040 9027 | 9OI5 goo2 | 8989 | 8977 21.50 8964 | 8951 | 8939 | 8926} 8913} 8901 | 8888 | 8876] 8863 | 8850 21.60 8838 | 8825 | 8813 | 8800] 8788] 8775 | 8762] 8750] 8737 | 8725 21.70 8712 | 8700 | 8687 | 8675 | 8662 8650 | 8637 | 8625 | 8612} 8600 21.80 8587 | 8575 8562 | 8550] 8538 8525 8513 8500 | 8488 | 8475 21.90 8463 | 8451 | 8438 | 8426] 8413] 8401 | 8389] 8376 8364 | 8352 22.00 8339 | 8327 | 8314 | 8302 | 8290] 8277 | 8265 | 8253 | 8240 | 8228 SMITHSONIAN TABLES, IOI TABLE 20. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. 29.90 Values of 60368 [1 + 0.0010195 x 36] log = Barometric | ae ee : : ; ; z .06 .07 .08 B. Feet. Feet. Feet. Feet. Feet. 8277 | 8265 | 8253 | 8240 | 8228 8154 | 8142 | 8130 | 8118 | 8105 8032 | 8020 | 8008 | 7995 | 7983 7910 | 7898 | 7886 | 7874 | 7862 7789 | 7777 | 7765 | 7753 | 7740 7668 | 7656 | 7644 | 7632 | 7620 7548 | 7536 | 7524 | 7512 | 7500 7428 | 7416 | 7404 | 7392 | 7380 7309 | 7297 | 7285 | 7273 | 7261 7190 | 7178 | 7166 | 7155 | 7143 7072 | 7060 | 7048 | 7037 | 7025 6954 | 6943 | 6931 | 6919 | 6907 6837 | 6825 | 6814 | 6802 | 6790 6721 709 | 6697 | 6686 | 6674 6604 | 6593 | 6581 | 6570 | 6558 6489 | 6477 | 6466 | 6454 | 6443 6374 | 6362 | 6351 | 6339 | 6328 6259 | 6247 | 6236 | 6225 | 6213 6145 | 6133 | 6122 | 6110 | 6099 6031 | 6020 | 6008 | 5997 | 5986 5918 | 5906 | 5895 | 5884 | 5872 5805 | 5794 | 5782 | 5771 | 5760 5693 | 5681 | 5670 | 5659 | 5648 5581 | 5570 | 5558 | 5547 | 5536 5469 | 5458 | 5447 | 5436 | 5425 5358 | 5347 | 5336 | 5325 | 5314 5248 | 5237 | 5226 | 5215 | 5204 5138 | 5127 | 5116 | 5105 | 5094 5028 | 5017 | 5006 | 4995 | 4985 4919 | 4908 | 4897 | 4886 | 4876 4810 | 4800 | 4789 | 4778 | 4767 4702 | 4691 | 4681 | 4670 | 4659 4594 | 4584 | 4573 | 4562 | 4551 4487 | 4476 | 4465 | 4455 | 4444 4380 | 4369 | 4358 | 4348 | 4337 LS) UT a ~ O i) wt a oO 4273 | 4263 | 4252 | 4241 | 4231 4167 | 4156 | 4146 | 4135 | 4125 4061 | 4051 | 4o4o | 4030 | 4oI9 3956 | 3945 | 3935 | 3924 | 3914 3851 3841 3830 3820 3809 D 3 Row NN onororon 3746 | 3736 | 3726 | 3715 | 3705 1 be 3642 | 3632 | 3622 | 3611 | 3601 26.20 * 358 3539 | 3528 | 3518 | 3508 | 3497 26.30 | 3435 | 3425 | 3415 | 3404 | 3394 26.40 3373, | 3332 | 3322 | 3312 | 3301 | 3291 26.50 1327 3230 | 3219 | 3209 | 3199 | 3189 SMITHSONIAN TABLES. 102 TABLE 20. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Values of 60368 [1 + 0.0010195 x 36] log 79-70. Barometric Pressure. ] - 3 - ‘ ; : .06 .07 .08 B. Inches. Feet. 26.50 3209 26.60 3107 26.70 3905 26.80 2904 26.90 2803, 27.00 2703 27.10 2602 27.20 2502 27.30 33 2403 27.40 2304 27.50 2205 27.60 2107 27-79 2009 27.80 IgII 27.90 1814 28.00 1717 28.10 1620 28.20 1524 28.30 / 1428 28.40 1332 28.50 1237 28.60 II42 28.70 1047 28.80 953 28.90 859 29.00 765 29.10 672 29.20 & 579 29.30 486 29.40 394 29.50 2 302 29.60 29.70 29.80 29.90 30.00 30.10 30.20 30.30 30.40 30.50 30.60 30.70 30.80 SMITHSONIAN TABLES, TABLE 21. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Term for Temperature: 0.002039 (@— 50°) Z. ( added. \ subtracted. f above 50° F.) (below 50° F. j For temperatures the values are to be Mean APPROXIMATE DIFFERENCE OF HEIGHT OBTAINED FROM TABLE 20. | Temperature. 80 | 100 600 | 700 , 800 Feet. | Feet. ’ a s : .| Feet. oO oO Bie OnOn OR OrOcO [ONO SS Se eS Oe He ee Q°0).070 HHH ee HOO°O WWNNN NNHHRH HHO OONN AUB WONNH HOUND OAH DND NN HHH HHH He NHOOW OONNADA ADANHLHW NNH SS Se eS eS OOO MO ONNNA ADANUNLHP PWWNHNH NHHO NN 2 N I I I Ir I bo S to “NI tO SS Se eH eH SO eS oo IW WWW WD PID AHWN MKPONINT NNNDAD DADUNU ANPHHp HHWWW +H 46 tS NH OVO Co ph Sw 444 Cm NAM MWMOONNNNNN DADADA DU ANHPHHP HHPHWW WWW NH HH HNN a \O DANDDAADUUNNNN ANNKAHPH HHHPAH PWWWW WWWWH NNNNN BD NHNNNNNKN NNNNNKN NNN HH co HAHAHA R PRWWW WWWWWH WWWWHNHN NHNNNHND NNONNND NHHHH Ow nv woOL GA AN OW O nn HO SMITHSONIAN TABLES. 104 TABLE 21. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Term for Temperature: 0.002039 (9— 50°) Z. added. above 50° F.) subtracted below 50° F. | the values are to be | For temperatures | Mean APPROXIMATE DIFFERENCE OF HEIGHT OBTAINED FROM TABLE 20. Temperature. nnn mn & 4 On onl ara NIN OHNO G DI SMITHSONIAN TABLES. TABLE 22. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Correction for Latitude and Weight of Mercury: z (0.002662 cos 2@+-0.00239). SMITHSONIAN TABLES. 106 ++ HOOHH | Lati. | APPROXIMATE DIFFERENCE OF HEIGHT OBTAINED FROM TABLES 20-21. tude. 500 | [000 4000 | 4500 Feet. Feet Feet. Feet. | Feet. | Feet Feet. 3 +5 +8 +Io | +13 |/+15 | +18 | +20 | +23 3 5 8 Io 13 15 18 20 22 3 5 8 Io 13 15 18 20 23 2 5 7 Io 12 15 7 20 De 2 5 a Io 12 15 17 20 22 {0 |}+2 +5 +7 +1o | +12 | +15 | +17 | +20 | +22 ere 2 5 Ti. Io 12 I4 07 19 22 14 2 5 7 9 I2 I4 17 19 21 16 2 5 Ti 9 I2 I4 16 19 21 18 2 5 7 9 II 14 16 18 20 20 | +2 +4 +7 + 9 |+1r | +13 | +16 | +17 | +20 | +22 22 2 4 6 9 II 13 15 17 19 22 24 2 4 6 3 10 13 15 17 19 21 26 2 4 6 8 10 12 14 16 18 20 | 28 2 4 6 8 ro 12 14 16 17 19 SO00f 2 4 6) E27 Oa eee 5 7 || 32 2 4 5 i 9 IL 12 14 16 18 34 2 3 5 7 8 10 12 I4 15 17 36 2 3 5 6 8 10 IL 13 14 16 38 2 3 5 6 8 9 IL 12 14 15 AOE 3. a) A OE Zoe tO ae ee 42 I Z 4 5 Te Wn te 9 II 12 13 44 I 2 4 5 6 7 9 Io II I2 45 Ptr pee 164 1 ebos ck 6 ee 7 at Sl t0n] Ihe) 4-22 AG OP TN 2 eS te a lie On ete er i Olean =f LO} =f at 48 I 2 3 4 5 6 7 3 10 IL 50 I 2 3 4 5 6 7 9 10 62. --2 +2 oS aS apa atone pat Oa Ae aa teeth tone 54 I 2 2 3 4 5 5 6 Zz 8 56 I I 2 ZB 4 5 6 7 7 58 I I 2 2 3 4 4 5 6 6 60 I [ 2 2 3 3 ‘4 4 5 2 62 09) 5-a fe islet iteeea nce oS Sect Sales ee octets 64 oO I I 2 2 2 3 3 3 4 66 oO I I I 2 2 2 2 3 3 68 oO fe} 16 i I I 2 2 2 2 70 oO oO i i I I I I 2 2 7 [P+ oO oO oO o}+ rier) -rltiz lit tisk 2 74 oO oO oO oO oO oO I I 16 |e a 76 oO oO oO oO oO Oo Oo oO oO oO 783 oO oO oO Oo oO oO ° oO oO Oo 80 oO oO Oo Oo oO Oo Oo oO o|-— tr. AN C.O O NOwBRN TABLE 22. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Correction for Latitude and Weight of Mercury: z (0.002662 cos 2 d + 0.00239). | 6000 7000, 8000 | 9000 |10000| 11000 Feet. + IOI IOI 101 100 oo +98 96 95 93 gt +89 86 83 Noho doa who nn HOOHN HOOHN SMITHSONIAN TABLES. 107 TABLE 23. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Correction for an Average Degree of Humidity. APPROXIMATE DIFFERENCE OF HEIGHT OBTAINED FROM TABLES 20-21. Mean Temper- : ature. | 500 | 1000 | 2000 | 3000 4000 | 5000 6000 7000 8000 | 9000 |10000/20000 F Feet. | Feet. | Feet. | Feet. | Feet. | Feet. | Feet. | Feet. | Feet. | Feet. | Feet. | Feet. —20° oO oO oO oO Oo Oo Oo +1 +1 +1 +1 +2 |— 16 oO oO o |+1 +1 +1 +1 I 2 2 2 4 | —12 oO o |+1 I I 2 2 2 3 3 3 6 — 8 oO Oo I I 2 2 3 3 4 4 4 9 — 6 oO oO I I 2 2 3 3 4 4 5 10 — 4 o | +1 I 2 2 B 3 4 4 5 6 Il — 2 oO i I 2 2 3 4 4 5 6 6 12 0 oO I I 2 3 3 4 5 5 6 Fl 14 Fae oO I I 2 3 4 4 5 6 7 7 15 4 oO I 2 2 3 4 5 6 af 7 8 16 6 oO I 2 3 4 4 5 6 7 8 9 18 8 oO I 2 3 4 5 6 7 8 9 10 19 109-E 1 I 2 3 4 5 6 7 8 9 Io 21 12 I I 2 2 4 6 7 8 9 Io II 22 14 I I 2 4 5 6 7 8 9 II 12 24 16 I I 3 4 5 6 8 9 10 II 13 25 (. 438 I I 3 4 5 7 8 9 II 12 13 27 | 20 I I 3 4 6 7 9 10 II 13 14 29 I, 222 I 2 3 5 6 8 9 Tal ToD 14 15 31 2 I 2 3 5 Fi 8 Io Ir 13 15 16 33 j 26 I 2 Bi 5 7; 9 10 12 14 16 17 35 28 I 2 4 6 i 9 II 13 15 17 19 37 30 I 2 4 6 8 10 12 14 16 18 20 4 22 I 2 4 7 9 II me 16 18 20 22 44 34 I 2 5 7 IO 12 15 17 19 22 24 49 36 I 3 5 5 II 13 16 19 2 2 27 53 38 I 3 6 9 12 15 18 21 23 26 29 59 40 2 2 6 10 13 16 19 23 2 29 22 64 | 42 2 4 7 ET 14 18 21 25 2 32 35 71 | 44 - 4 8 12 15 19 23 27 3l 35 39 77 46 2 4 8 13 17 21 25 29 34 38 42 84 45 2 5 9 14 18 23 27 32 37 41 46 92 50 ° 5 10 15 20 25 30 35 40 45 50 99 52 3 5 II 16 21 27 32 37 43 45 53. 4 107 54 3 6 II 17 23 29 34 40 46 51 57 an ale: 56 3 6 12 18 24 30 37 43 49 55 61 122 58 3 6 13 19 26 | 32 | 39 | 45 52 | 58 65 | 130 60 3 7 14 21 27 34 41 48 55 62 69 | 137 62 4 7 14 22 29 36 43 51 58 65 72 \ 145 64 4 8 15 23 30 38 46 53 61 69 7 152 66 4 8 16 24 32 4o 48 56 64 72 So 160 68 4 8 17 25 34 42 50 59 67 7 84 | 168 70 4 9 18 26 35 44 53 61 70 79 88 | 175 72 5 9 18 27 37 46 55 64 73 82 gI | 183 76) 5 20° | 30°) 4007) 49° "| 59 |), 69) a76) 4 BSG 99 | 198 80 5 21 32 43 53 64 75 85 96 106 | 213 84 6 23 34 46 EF 68 80 gI 103 DA e225 88 6 24 Y/ 49 61 73 85 97 IIo 122 243 92 6 26 39 52 65 78 OL © |103) | TK6)) || 120) 8255 96 7 27 4I 55 68 82 96 IIo 123 a7; 274 SMITHSONIAN TABLES. TABLE 24. DETERMINATION OF HEIGHTS BY THE BAROMETER. ENGLISH MEASURES. Correction for the Variation of Gravity with Altitude: sae HEIGHT OF LOWER STATION IN FEET (/,). 7000 8000 | 9000 10000|12000 1000 | 2000 | 3000 | 4000 | 5000 | 6000) | Feet. | Feet. | Feet. Feet. | Feet. | Feet. | Feet. oO oO +1 +1 I 2 2 oO SMITHSONIAN TABLES. 109 TABLE 25. DETERMINATION OF HEIGHTS BY THE BAROMETER. METRIC MEASURES. Values of 18400 log 2829. Barometric Pressure. mm, 300 310 320 330 349 350 360 3/9 350 399 400 410 420 430 440 450 460 479 450 490 500 510 520 530 540 550 560 579 580 59° 600 610 SMITHSONIAN TABLES. IIO an = eT a nd il TABLE 26. DETERMINATION OF HEIGHTS BY THE BAROMETER. METRIC MEASURES. Term for Temperature: 0.00367 @ X Z. pair ve) eaters we © Pe added. For temperatures { subtracted. MEAN TEMPERATURE OF AIR COLUMN IN CENTIGRADE DEGREES (6). HHHO 8 w OO ONIN PONH : ° WOW NN “INT OVO OF non —& momn \o SMITHSONIAN TABLES. TABLE 27. DETERMINATION OF HEIGHTS BY THE BAROMETER. METRIC MEASURES. Correction for Humidity: Values of 10000 #. Ea ea rae eee Pie aa Arse aap mm. Aun —& & DOnWN Oo SMITHSONIAN TABLES. II2 TABLE @2/, DETERMINATION OF HEIGHTS BY THE BAROMETER. METRIC MEASURES. Correction for Humidity: 10000 3 x z. Top argument: Values of 10000 § obtained from page 112. Side argument: Approximate difference of height (z). Approximate Difference of Height. ze ONO OE Ow nn mMuw oo Aw oO ou 33-3 25.0): 35-0 36.8 27.5 : 38.5 28.8 4. 40.3 30.0 : 42.0 2.8 : 43.8 32-5 . 45-5 33-8 5 | 47-3 : 25.0") 742: 49.0] 56.0 36.3 : 50.8| 58.0 3. 4. 4. 4. 4. 5.0 Seo 5-5 5.8 6.0 6. 6. 6. a 7 & 0 Muw 37-5 : 52.5} 60.0 38.8 54.3 | 62.0 40.0 56.0] 64.0 41.3 57.8| 66.0 42.5 : 59.5 | 68.0 43.8 : 61.3 | 70.0 45.0 | 54.0] 63.0] 72.0 46.3 | 55-5 64. 8} 74.0 47.5 | 57-0)| 66.5)|' 76,0 48.8 | 58.5] 68.3] 78.0 50.0 | 60.0] 70.0] 80.0 62.5 | 75.0] 87.5 | 100.0 75.0 | 90.0] 105.0 | 120.0 7.5 | 105.0] 122.5 | 140.0 SMITHSONIAN TABLES. 113 TABLE 28. DETERMINATION OF HEIGHTS BY THE BAROMETER. METRIC MEASURES. Correction for Latitude and Weight of Mercury: z (0.002662 cos 2 ¢ + 0.00239). | Approximate LATITUDE (¢). difference of Height. ol ol ° metres. 100 200 300 400 by by HH NO NHR ! oH OH NOR OH HH HO HrRO;O HrHOO o0o0o°o OBOr Ore) 0000 B oo00 B 500 600 700 S800 goo BHRWOWN WWWwh hd WwWNNN WNNN HH RONN HH ON HAR SS Se Se eS HHOOO 0-00. 070 (a) {ef {e) {e) fe) On — 4 G2 Go On — Go Go > BO b {000 I10oO 1200 1300 1400 Dann fp HWW bd 1 ee) WWwWWwWwW bd He HHH ee He o0000 o0o0000 SINT DN OV NN NOU SINAN NIDDM 1500 1600 1700 1800 1900 oo cmon! oOo OnN NI NSNITAADDAD UANPpf DNDAUUN NY wYHKHNHN Se RS eS = = ae ee 0. 0°0' O70 appHR LE Oo 2000 2100 2200 2300 2400 oon NON RRR HH o0o0000 SINDDD UANnnnp & BW & Aunmuniwn abRAS BO & & WOoNNN 0 © Morn sl ONNNN 2500 2600 2700 2800 2900 COWO © mMmoonnl Go Gs G2 Go Go wNN NN HAR Coo0o00 3000 3100 3200 3300 3400 3500 3600 Om onrni NN AAD NNNNN HHH HA o0000 anu ann phALHL ALA WW OH W O22 02 NN NNN NH Hee AW He x O00 E | WWWwWNN HHH eH o0000 mH NHOW © OnNInNININI ST RAAAO Dunn NNNNH HOOO0O0 00 WOW ONN OD AO NN DOAUNS HEH hh G2 Go Go 2 ak BHWWW HoH NN al SMITHSONIAN TABLES. 114 i a ty TABLE 29. DETERMINATION OF HEIGHTS BY THE BAROMETER. METRIC MEASURES. Correction for the variation of gravity with altitude: “o = _— n g % u ay = ce 4 Z S u < H n 4 S S _ i ° H x oO _ B = Approxi- mate difference 2500 3000) 4000 OO HANA AN NAN OMNOMOS oats st ttTOMW IW WO 0 \O eH RH HH HR RR NN NANAANAN eh oD 09 ON OD tT ATIND WH 1. n OnnnRR DACA me INO 0 0 OoOn~oano a 9 eNO OO trates m., OOR HH HHH HH HHANA NANAAN oF) 0 0 0 OD gegs st st Nn N 69 6) 6D 69 MMmMmMmwo O MO ovo ttt in wy MO h>AD OV ttt io INO AO OV NN eh 69 6 e969 69 69 SS 9 oF) 6) 0) 0 0 200 400/600 800) 1000 1200 | 1400 1600 | 1800 | 2000 9059 09 aotststa tTNO ~O oats st TNO ~O meng eo st - ~ ° H Nn H NAN HOO | 9 ON OH e9 0 0 OF) OD of height. Zz SMITHSONIAN TABLES. FIs TABLE 30. DIFFERENCE OF HEIGHT CORRESPONDING TO A CHANGE OF 0.1 INCH ENGLISH MEASURES. IN THE BAROMETER. 3] Feet. | 119.2 118.2 L701 116.1 114.0 Ere. I 112.1 roced 110.2 109.3 108.4 107.5 106.6 105.8 115.0 | 35° 120.5 119.4 118.3 | eC 7a 116.3 TLS. 114. LT. LL2.3 2 G2 GO) OG SMITHSONIAN TABLES. Feet. ‘ Feet. tor.8 IOI.1 45° 100.3 99.6 98.9 98.1 97-4 96.7 96.1 95-4 94.7 94.1 93-4 92.8 92.1 91.5 90.9 | 90.3 89.7 89.1 88.5 88.0 50° Feet. mH HHH Ro NNN NHN Onn ts me NOOB 60° Feet. ae 127. DART A L205O 123.6 | 124.9 122.5 | 123.8 |pRemeAn | oo 120.3 | 121.6 119.3 | 120.6 118.3 | I19.5 L173) LISS T1623 || IL7.5 116.5 115.6 114.6 LIae7, IIl.o I1O.1 109.3 108.4 107.6 106.8 106.0 105.2 104.4 102.5 | 103.6 101.8 | 102.8 LOT, ©) | PLo2s1 100.3 | IOI.3 99.6 | 100.6 98.8 | 99.9 98.1 |} 99.2 97-5 | 98.5 96.8} 97.8 96.1} 97.1 95-4{ 96.5 94.8) 95.8 94.1} 95.1 93-5 | 94-5 92.9} 93.9 92.3) || 93:2 91.7 | "92.6 OL. 13] 92:0 990-5} 91.4 89.9| 90.8 65° Feet. 128.5 | 12762 126.2 125.1 124.0 122.9 121.8 | 120.8 119.8 118.8 | Dje0 116.8 115.9 114.9 E222 TEs 110.4 109.6 108.7 107.9 107.1 106. 3 105.5 104.7 103.9 103.2 102.4 LOW IOI.O 100.2 99.5 98.8 98.2 97-5 96.8 96.1 95-5 94.9 94.2 93-6 93-0 92.4 91.8 | 70° | 75° Keet. | Feet. 129.8) |) 1ate2 128.7 | 130.0 127.5, | 128.8 126.4 | 127.7 125.3 | 126.6 124.2 | 125.5 123.1 | 124.4 122 PLZ 303 T2120} 2243) 120:0)]|| L2T.3 120.2 119.2 118.3 TL7.3 116.4 115.4 T14.5 T1336 mot, III.9 III.o 110.1 109.3 108.5 107.7 106.9 106. I 105.3 104.6 103.8 TOSST 102.3 101.6 100.9 100.2 98.5 | 99.5 97.8 | 98.8 G7s1s|) 19832 96.5 | 97-5 95.8| 96.8 95.2] 96.2 94.6| 95.6 94.0} 94.9 93-3| 94-3 92.7 | 93-7 MEAN TEMPERATURE OF THE AIR IN FAHRENHEIT DEGREES. 80° Feet. 132.5 Ties 130.2 129.0 L27203 126.8 T25-7 124.6 T2255 12285 121.5 120.5 119.5 118.5 TeliS oy7) 114.8 113.9 113.0 112.1 Thos 110.4 109.6 108.8 108.0 107.2 106.4 105.6 104.9 104.1 103.4 102.7 101.9 IOI.2 100.5 99-9 99.2 98.5 97.8 97.2 96.5 95-9 95-3 94.7 85° Feet. 133-9 132-7) LG 130.3 129.2 128.1 127.0 125.9 124.8 123.8 LOOT 127 120.7 119.7 116.9 116.0 TS er 114.2 Tress 112.4 III.6 MIO, 109.9 109. I 108.3 107.5 106.7 105.9 105.2 104.4 103.7 103.0 102.3 101.6 100.9 100. 2 99-5 98.8 98.2 97-5 96.9 96.2 95.6 TABLE 31. DIFFERENCE OF HEIGHT CORRESPONDING TO A CHANGE OF 1 MILLIMETRE IN THE BAROMETER. METRIC MEASURES. MEAN TEMPERATURE OF THE AIR IN CENTIGRADE DEGREES. Barometri Pressure. — 2° 0° oe 4° 6° 8° 10° 12° 14° 16° Metres. | Metres. | Metres. | Metres. | Metres. | Metres. | Metres. | Metres. | Metres. Metres. | 10.48 | 10.57 | 10.65 | 10.73 | 10.81 | 10.89 10.98 | 11.06 | II.15 | I1.23 10.62 | 10.71 | 10.79 | 10.87 | 10.95 | 11.04 | 11.13 | I1.2I | 11.30 | 11.38 10.77 | 10.85 | 10.93 | I1.02 | II.IO | I1.19 TT 200 We sO! | LAS) |) os 5 4: 10.91 | 11.00 | 1%.08 | 11.17 | 11.26 | 11.35 | I1.43 | 11.52 OL ew ls 7O) Prog) Mmc rs) |e Ur 24-} 10.92. | 11.427) 11.50 | 1-59) |. 21.60) |) 22.77 11.86 HISoN |) Teese) LEO) LEAS | B58 | 10167 | 1.75 11.85 | LL-94) ||| 12:03 | 11.30" | £1.47 | 21:56 |: 11-65 | 11.74 TL.O8 ||| LL-92 T2000 ||) 3i2-20 10.55 | 11-63 | 11.72 | 11.82 | TI.9g1 | 12.00 | 12.09 : [2,298 12,36 11.72 | 11.80 | 11.89 | 11.99 | 12.08 | 12.18 | 12.27 ; 12.46 | 12.56 15-59) -EL.98 | 12.07 |) 22-17 || 12.26 12.36 | 12.46 : 565 +|| 12575 12.07 | 12.16 | 12.26 | 12.35 | 12.45 | 12.55 | 12.65 : .84 | 12.94 12.26 | 12.35 | 12.45 | 12.54 | 12.64 | 12.74 | 12.84 .04 | 13.14 12.45 | 12.55 | 12.64 | 12.74 | 12.84 | 12.94 | 13-04 2: 2A) 13s3 5m 12.65 | 12.75 | 12.84 | 12.94 | 13.04 | 13-15 | 13-25 3. 13.45 | 13.56 12.85 | 12.96 | 13.05 | 13.15 | 13.25 | 13-36 | 13-46 13.67 | 13.78 12.06) |) 13.07) |) 13:27, 2637, | 13-47) | 13-55: | 13-00 13.89 | 14.01 13.28 | 13.39 | 13.49 | 13-59 | 13-70 | 13-80 | 13.91 14.13 | 14.24 E3257 |) L202) | 13.72 | 13.621) 13:93 || %4.03' | 14.15 14.37 | 14.48 13.74 | 13.85 | 13.96 | 14.06 | 14.17 | 14.28 | 14.39 14.62 | 14.73 | 13.98 | 14.09 | 14.20 | 14.31 | 14.42 | 14.53 14.64 14.88 | 14.99 14.23 | 14.34 | 14.45 | 14.57 | 14.68 | 14.79 | 14.90 15.14 | 15.25 MEAN TEMPERATURE OF THE AIR IN CENTIGRADE DEGREES. Barometric Pressure. 18° 20° 22% 24° 26° 28° 30° S2y 34° 36° mm. Metres. | Metres. | Metres. | Metres. | Metres. | Metres. | Metres. | Metres. Metres. | Metres. 760 11.32 | 11.41 | 11.49 | 11.58 | 11.66 | 11.75 | 11.84 | 11.92 | 12.0% | 12.10 750 EEA7 | uu.56 | I-64 | t1.73 | 11-62 | 11-91 |* 12.00 | “12-08 || 12.17 12.26 740 EE-03)) eL1e72) | 11-80 | 11.892) Tk.9S" |, “12.07 [2.16 | £2.24) || T2533) |) 12542 | 730 11.79 | 11.88 | 11.96 | 12.05 | 12.15 | 12.23 | 12.32 | 12.41 12.50 | 12.59 | 720 11.95 | 12.04 | 12.13 | 12.22 | 12.32 | 12.40 | 12.49 | 12.58 12.68 | 12.77 | 710 12.12 | 12.21 | 12.30 | 12.39 | 12.49 | 12.58 | 12.67 | 12.76 12.86 | 12.95 700 [2.29 | 12:39)| 12:48 || 12:57 | 12:67 |, 12.7 12.85 | 12.94 | 13.04 | 13.13 | 690 12.47 | 12.57 | 12.66 | 12.75 | 12.85 | 12.94 | 13.04 | 13.13 | 13-23 | 13-32 | 680 12.66 | 12.75 | 12.85 | 12.94 | 13.04 | 13.13 | 13.23 | 13-32 | 13.42 | 13.52 670 12.85 | 12.94 | 13.04 | 13.14 | 13.23 | 13-33 | 13-43 | 13-52 | 13.62 | 13.72 660 J 13.04 | 13.14 | 13.24 | 13.34 | 13-43 | 13-53 13.63 | 13.73 | 13.83 | 13-93 650 | 13.24 | 13-34] 13-44 | 13-54 | 13-64 | 13-74 | 13-84 | 13-94 | 14.04 | 14.15 | 640 13.45 2.55 | 13-05, || 13-75.| 13-05 3-96 | 14.06 | 14.15 | 14.26 | 14.37 630 13.66 | 13.76 | 13.87 | 13.97 | 14.07 | 14.18 | 14.28 | 14.35 | 14.49 14.60 620 13.58 3.98 | 14.09 | 14.20 | 14.30] 14-41 | 14.51 14.62 | 14.72 | 14.83 610 I4.II | 14.21 | 14.32 | 14.43 | 14.54 | 14.64 | 14.75 14.86 | 14.96 | 15.07 | 600 14.35 | 14.45 | 14.56 | 14.67 | 14.78 | 14.89 | 15.00 | 15.1I | 15.21 | 15-32 590 14.59 | 14.70 | 14.81 | 14.92 | 15.03 | 15.14 | 15.25 | 15.36 | 15.47 | 15-59 | 580 14.84 | 14.95 | 15.07 | 15.17 | 15.29 | 15.40 | 15.52 15.63 | 15.74 | 15.86 | | 570 15.10 | 15.21 | 15.33 | 15-44 | 15.56 | 15.67 | 15.79 | 15.91 | 16.02 16.14 16.42 | 560 15.37 Deal 15.60 | 15.72 15.84 15.95 | 16.07 | 16.19 | 16.30 SMITHSONIAN TABLES. TABLE 32. DETERMINATION OF HEIGHTS BY THE BAROMETER. Formula of Babinet. ae C (in feet) = 52494 ra! + - aS as —English Measures. 2 Sees C (in metres) = 16000 [r+ 2het Mee] —Metric Measures. In which Z — Difference of height of two stations in feet or metres. &., & = Barometric readings at the lower and upper stations respectively, corrected for all sources of instrumental error. /,, == Air temperatures at the lower and upper stations respectively. Values of C. ENGLISH MEASURES. METRIC MEASURES. Feet. Metres. 4.18639 15360 . 19000 15488 -19357 15616 -19712 15744 - 20063 15872 49928 50511 51094 51677 52261 . 20412 16000 .20758 16128 . 21101 16256 .21442 163584 16512 52844 53428 54011 54595 55178 16640 16768 16896 17024 17152 55761 56344 56927 57511 58094 2 2 a2 “2 2: 17280 17408 17536 17664 17792 Ro ww YN N 58677 17920 18048 18176 18304 59260 59544 60427 SMITHSONIAN TABLES. BAROMETRIC Tempera- ture. Inches. 17.05 17.42 17.81 18.20 18.59 19.00 19.41 19.82 20.25 20.68 21.13 21.58 22.02 22.50 22.97 23-45 23-94 24.44 24.95 25.46 25-99 26.52 27.07 27562) 28.18 28.75 29-33 29.92 Inches. | Inches. | Inches.} Inches. } Inches, | Inches.| Inches.} Inches. | Inches. TABLE 33. PRESSURES CORRESPONDING TO THE TEMPERATURE OF THE BOILING POINT OF WATER. ENGLISH MEASURES. ot | o72 | 083 | 0% | 0% | O°6 | 0°7 | o°8 | o°9 B7.GO)|/eU7s02s)) 17.06: | 17.20. 1.7.23|| 17.27 | n7.an | 17-95 17.39 17.46 | 17.50 | 17.54 | 17.58 | 17.61 | 17.65 | 17.69 | 17.73 eri 17.84 | 17.88 | 17.92 | 17.96 | 18.00 | 18.04 | 18.08 | 18.12 | 18.16 18.24 | 18.27 | 18.31 | 18.35 | 18.39 | 18.43 | 18.47 | 18.51 | 18.55 | 18.63 | 18.67 | 18.71 | 18.75 | 18.79 | 18.83 | 18.87 | 18.91 | 18.95 19.04 | 19.08 | 19.12 | 19.16 | 19.20 | 19.24 | 19.28 | 19.32 | 19.36 19.45 | 19.49 | 19.53 | 19.57 | 19.61 | 19.66 | 19.70 | 19.74 | 19.78 19.87 | 19.91 | 19.95 | 19.99 | 20.04 | 20.08 | 20.12 | 20.17 | 20.21 20.29 | 20.34 | 20.38 | 20.42 | 20.47 | 20.51 | 20.55 | 20.60 | 20.64 20.73 | 20.77 | 20.82°| 20.86 | 20.90 | 20.95 | 20.99 | 21.04 | 21.08 21.17 | 21.22 | 21.26 | 21.30 | 21.35 | 21.39 | 21.44 | 21.48 | 21.53 | 21.62 | 21.67 | 21.71 | 21.76 | 21.80 | 21.85 | 21.89 | 21.94 | 21.99 22.08 | 22.12] 22.17 | 22.22 | 22.26 | 22.31 | 22.36 | 22.40 22.45 22.54 | 22.59 | 22.64 | 22.69 | 22.73 | 22.78 | 22.83 | 22.88 23.02 | 23.07 | 23.11 | 23.16 | 23.21 | 23.26 | 23.31 | 23.36 23-50 | 23.55 | 23:60 |) 23.65 | 23.70 | 23.75 | 23:80 | 23.85 23.99 | 24.04 | 24.09 | 24.14 | 24.19 | 24.24 | 24.29 | 24.34 24.49 | 24.54 | 24.59 | 24.64 | 24.69 | 24.74 | 24.80 | 24.85 25.00 | 25.05 | 25.10 | 25.15 | 25.21 | 25.26 | 25.31 | 25.36 25-52) | 25-57 | 25:02 || 25.67) |) 25°73) 1° 25.78 || 25.83) | 25.88 26.04 | 26.10 | 26.15 | 26.20 | 26.25 | 26.31 | 26.36 | 26.42 26.58 | 26.63 | 26.68 | 26.74 | 26.79 | 26.85 | 26.90 | 26.96 27.12 | 27.10 | 27-23 | 27.29 | 27.34 | 27.40 | 27:45 | 27.51 27.67 | 27.73 | 27-79 | 27.84 | 27.90 | 27.95 | 28.01 | 28.07 28.24 | 28.29 | 28.35 | 28.41 | 28.46 | 28.52 | 28.58 | 28.64 28.81 | 28.87 | 28.92 : 29.04 | 29.10 | 29.16 | 29.21 29.39 | 29.45 | 29.51 : 29.62 | 29.68 | 29.74 | 29.80 29.98 | 30.04 | 30.10 ; 30.28 | 30.34 | 30.40 Tempera- o7 | 0o°2 0°3 0°4 0°5 0°6 mm. mm. mm. | mm. mm. mm. mm. 5 | 359.0 | 360.4 361.9 363.3 | 364.8 | 366.3 | 367.8 3 | 373-8 | 375-3 | 376.8 | 378.3 | 379.8 | 381.3 | 382.9 5 | 389.0 | 390.6 | 392.2 | 393-7 | 395-3 | 396.9 | 398.5 3.| 404.9 | 406.5 | 408.1 | 409.7 | 411.3 | 413.0 | 414.6 6 | 421.2 | 422.9 | 424.6 | 426.2 | 427.9] 429.6 | 431.3 4 | 438.1 | 439-9 | 441-6 | 443.3 | 445.1 | 446.8 | 448.6 8 | 455-6 | 457.4 | 459. >| 462.8 | 464.6 | 466.4 8 | 473-7 | 475-5 | 477-: 488.5 | 490-4 492.3 | 494.2 | 496. 4 9 Oo 7 2 4 3 an 479.2 | 481.0 | 482.9 | 484.8 2 3 I | 498.0 | 499.9 |.501.8 | 503.8 507.6 | 509 S1I.5 | 513-5 | 515-5 | 517-4 | 519.4 | 521.4 | 523.4 | 527-4 | $29 531-4 | 533-4 | 535-5 | 537-5 | 539-6 | 541.6 | 543.7 547-8 | 549 551-9 | 554-0 | 556.1 | 558.2 | 560.3 | 562.4 | 564.6 568.8 | 571 573-1 | 575-3 | 577-4 | 579.6 | 581.8 | 584.0 | 586.1 590.5 | 592 595-0 | 597.2 | 599.4 | 601.6 | 603.9 | 606.1 | 608.4 612.9 | 615 617.5 | 619.8 | 622.1 | 624.4 | 626.7 | 629.0 | 631.4 636.0 | 638 640.7 | 643.1 | 645.5 | 647.9 | 650.2 | 652.6 | 655.0 | 659.9 | 662 664.7 | 667.1 | 669.6 | 672.0 | 674.5 | 677.0 | 679.4 | 684.4 | 686.9 | 689.4 | 691.9 | 694.5 697.0 | 699.5 | 702.1 | 704.6 | 709.7 | 712.3 | 714.9 | 717.5 | 720.1 | 722.7 | 725.3 | 727.9 | 730.5 | 735-8 | 738.5 | 741.2 | 743.8 | 746.5 | 749-2 | 751-9 | 754-6 | 757.3 | 762.7 2 | 782.0 84.8 765.5 | 768.2 | 770.9 | 773-7 | 776.5 | 779. SMITHSONIAN TABLES. 11g HYGROMETRICAL TABLES. Pressure of aqueous vapor (roch) — English measures Metric measures Pressure of aqueous vapor at low temperatures (C. 7. Marvin)— English and Metric measures Weight of aqueous vapor in a cubic foot of saturated air — English measures Weight of aqueous vapor in a cubic metre of saturated air — Metric measures . Reduction of psychrometric observations — English measures. Pressure of aqueous vapor . yee j 1 S es 1 Values of 0.000367 B (¢ — 4)(1 — a Temperature Fahrenheit . Relative humidity Reduction of psychrometric observations — Metric measures. Pressure of aqueous vapor . Values of 0.000660 B (¢ — AC + io 7 Relative humidity — Temperature Centigrade Reduction of snowfall measurements. Depth of water corresponding to the weight of snow (or rain) collected in an 8-inch gage Rate of decrease of vapor pressure with altitude I21 TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE 35 36 43 oT 40 4 42 43 44 45 46 2 47 TABLE 35. PRESSURE OF AQUEOUS VAPOR. (Broch.) ENGLISH MEASURES. Vapor Pressure. Inch, 0.0167 0.0168 -O170 | .0172 | .O174 .0176 0.0177 | .O179 .OISI .0183 -O185 .O187 .O189 .OIQI .0193 0195 .O197 -O199 .O201 .0203 .0205 -0207 -0209 -O2TL .0213, | .O216 | .O218 .0220 0 -] S) » O NO bw bt Nw h “I U1 t > a O LU © NWN NN G2 2 Or WN \o N n> ~ © fot \O 0241 -O244 .0246 | -0O249 | .O25I 1.0254 .0256 -0259 .0261 .0264 | .0267 .0269 .0272 -0275 Diff. for O°! lal SS ARS Se SS SS eS Oe I I I I H Temper- ature. RK KW CO OO ONE DO ON NNNINI NI ORR AD ONER DAO OKRA OKKRDO Or © PEPE Oe EEE NAUNT ADAAD ds HH HH NNNN ND NA DAW ONL AN O ~ O ° co Vapor Pressure. Inch. 0.0277 0.0280 .0283 .0286 .0289 .0292 .0294 .0297 .0300 .0303 .0306 .0309 .0312 -0315 .0318 .0322 ).0325 .0328 .0331 -0334 .0338 .0341 -0344 -0347 .0351 .0354 | .0358 .0361 .0305 .0368 .0372 -0375 -0379 0383 .0386 .0390 -0394 -0397 | .O401 .0405 -O409 .O413 .O417 .O421 .0425 | .0429 0.0433, | .0437 .O44I -0445 al NdoOdHNNH YN NNHNNNH KN NHNNKHNKHKH KH NNNNH KH NHNNNHND HSH HNKHNH YH HNNNHN KH NHNNNDHND KY NNHH Temper-| Vapor ature. | Pressure. Inch. 0.0449 -0454 -0458 .0462 -0467 -O471 +0475 .0480 .0484 .0489 9.0493 -0503 .0507 .O512 Nvynnhd NAR NO 0.0517 .0522 .0526 .0531 -0536 0.0541 AALNO .0551 .0556 .0561 MOAR N © 0.0567 .0572 -0577 .0582 .0588 DAR NO -0593 .0598 .0604 .0609 .O615 ARAL nN © .0620 .0626 .0632 -0037 .0643 WIVINM DADAP AAAAMW EEE YWHOHO ALN © Cn co .0649 .0655 .o661 .0667 | .0673 .0679 | .0685 | .0691 .0697 .O704 .0498 | 0546 | for of! BNWWWwW WD WwOWwWWwW NH NNHNNH NHN NNHNNH KH NHNNNN HY NNNN BDBWWWW WD WWWW WD WWWW WD WwWWW Temper- ature. F 10°0 10.2 10.4 10.6 10.8 11.0 Tale II.4 11.6 SMITHSONIAN TABLES E22 Vapor Pressure. Inch. 0.0710 .0716 .0723 -0729 .0736 0.0742 | -0749 .0756 .0762 | .0769 0.077 .0783 -0790 -0797 .0804 0.0811 .0818 .0825 .0832 .0840 0.0847 .0854 .0862 .0869 .0877 0.0885 .0892 .0gO0O .0908 .0g16 0.0924 .0932 .0940 .0948 .0956 0.0965 -0973 .O9SI .0990 -0999 . 1007 1016 . 1024 . 1033 . 1042 . 1051 . 1060 . 1069 .1078 . 1087 AnanafP APHRAH HL HHHAH HPAPHAALHP HP ARALR HP AHAH HARDER BP BPOWHW YH HWHWW &H WHWWW PRESSURE OF AQUEOUS VAPOR. (Broch.) ENGLISH MEASURES. Temper-| Vapor ature. | Pressure. F. Inch. | 20°0 | 0.1097 20.2 1106 | 20.4 -III5 20.6 ~2I25 20.8 . 1134 21.0] 0.1144 21.2 .1154 21.4 .1163 21.6 ~LL73 21.8 .1183 22.0] 0.1193 22.2 .1203 22.4 1202 22.6 212298 22.8 .1234 23.0] 0.1244 23.2 ~1255 23.4 . 1265 [= 23.6 .1276 23.8 .1287 24.0 | 0.1297 24.2 .1308 | 24.4 Sa TO 24.6 .1330 24.8 -1341 25.0} 0.1352 25.2 1364 25.4 1375 | 25.6 1386 | 25.8 1398 | 26.0] 0.1409 26.2 1421 26.4 1433 26.6 1445 26.8 1457 27.0] 0.1469 27.2 [451 27-4 1493 27.6 1505 27.5 1518 28.0] 0.1530 25.2 1543 25.4 1555 28.6 15658 25.95 1551 29.0} 0.1594 | 29.2 . 1607 | 29.4 . 1620 | 29.6 .1633 | 29.5 . 1646 | _ Diff. for | O°! NADNDADAD WANA nnn nn aAnnin nA aAannn wn anon NSININI “IS Temper- ature. oO AALN G2 G2 Oo RAKRNOS WWWwWWW WHWww WwW DAADRNOS IIVIN DADA®S AAA G Aa bd oO 62 62 G2 Go W OD 2 2 Go W Go Ge to to 60 Ona. N oO Vapor Pressure. Inch. 0. 1660 .1673 .1687 . 1700 Ae. 0.1728 .1742 .1756 .1770 .1784 0.1799 .1813 .1828 .1842 .1857 0.1872 .1887 . 1902 -LOL7 -1933 0.1948 . 1964 -1979 -1995 .2011 0.2027 2043 | .2059 .2076 . 2092 0.2109 2125 .2142 .2159 .2176 0.2193 .2210 NO NNN bY O21028 ND tN Temper- Vapor Pressure. Inch, 0.2465 2484 2503 .2523 .2542 0.2562 | .2582 . 2601 S202 .2642 0.2662 | .2683 | .2703 .2724 -2745 .2766 .2787 O .2808 .2830 | .2851 0.2873 . 2895 -2917 -2939 .2962 0.2984 3007 -3030 -3053 . -3076 a VY 9.3099 O2 G2 G2 G2 Go WNNNN OV Diff. for O°! a a G2 WWW GH GO) 02 ee Temper- ature. ol NRRNN AAP NOS noun bo 62 Oo Go WW oui OI DARKS wm A niminimn I w AD NMnan ow pp noo nee OO ww TABLE 35. Vapor oo | Pressure. 0°! | Inch... | 0.3598 me -3625 | 1 -3652 | 1) | 3679 14 | 3706 sy 0.3734 -3761 a -3789 14 3817 | 1A -3845 | 0.3874 | 3902 si 3931 | 14 | 3900 1 oe 3989 0.4018 | : .4048 | = | -4077 | 15 4107 | 15 4137 | : 0.4168 2 4198 3 | 422 i 4259 | 16 -4290 || 0.4322 ass hee -4395 | 16 AAT] | 5G 4449 6 0.4481 75 4513 4546 ie 4579 | ae 4612 4 17 0.4645 | 4679 | 5. API2G oe 4746 | 57 .4780 J : 17 0.4815 | |, -4849 | 5. .4884 18 -4919 18 -4954 5 18 0.4999 | 18 5025 18 5061 18 5097 18 | 513 SMITHSONIAN TABLES. TABLE 35. PRESSURE OF AQUEOUS VAPOR. (Broch.) ENGLISH MEASURES. _Temper-| Vapor eo Temper-| Vapor aoe Temper-| Vapor ae Temper-| Vapor rt | ature. | Pressure. 0°! ature. | Pressure. ature. | Pressure. ature. | Pressure. 0°! F. Inch. | Inch. Inches. Inches. | 60°0 | 0.5170 0.7320 1.0219 1.4081 | 60.2 -5207 | -7370 .0286 -4170 44 | 60.4] .5244 | 7420 0354 4259 i 60.6 .5282 AT .0422 -4349 45 60.8 -5319 a7522 -0490 -4439 ve 61.0 | 0.5357 0.7573 1.0558 1.4530 46 61.2 5395 -7625 .0627 -4621 6 61.4 -5433 .7676 .0697 -4712 fe 61.6 5471 7728 .0767 .4805 Ae 61.8 .5510 .7781 .0837 .4897 a | 47 62.0] 0.5549 0.7834 1.0907 1.4990 47 62.2 .5598 -7887 | .0978 .5084 62.4 .5628 .7940 . 1050 : -5178 47 62.6 .5067 -7994 | -II2I | 36 92.6 -5273 a 62.8 .5707 .8048 | . 1194 - 92.8 5368 " 63.0 | 0.5748 a 73.0 | 0.8102 1.1266 Se 93.0] 1.5464 - 63.2 | .5788 | 35 | 73-2-| -8157 | 19339°] o24 | 93:2" || 25560 48 63-4] .5829| 3, | 734 | -8212 -tAr3)| 241 93.4.) ) 25657 49 63.6 -5870 | 3, 723.6 .8267 1457), | ent 193-6 5755 63.8 5911 73.8 .8323 1561 | 37 93.8 15853 49 21 leno? 4 64.0 | 0.5952 " 74.0 | 0.8379 1.1635 | oe 94.0] 1.5951 a 64.2 | .5994| 5, | 74-2 | -8435 | -1710 | 39 | 94.2 | .6050 £6 64.4 .6036 | a 74.4 .8492 1786 | 30 94.4 .6149 50 64.6 .6078 | 74.6 .8549 .1862 | 38 94.6 .6249 6 64.8 6120 | 77 74.8 .8606 | .1938 e 94.8 .6350 5 21 38 I 65.0] 0.6163 75.0] 0.8664 I.2015 | E 95.0] 1.6451 = 65.2 .6206 | re 75.2 .8722 .2093 | 39 95.2 .6552 oe 65.4 .6249 ~ 75.4 .8780 e207 081" 95-4 .6655 Be 65.6 -6293 ee 75.6 .8839 22005 seo 95.6 .6758 ae 65.8 16387) |g 75.5 .8898 -2327 | © 95-8 6861 | > 22 3 2 66.0) 0.6351 | ., | 76.0] 0.8957 1.2406 os 96.0] 1.6964 ss 66.2 -6425 | 3. 76.2 .9OI7 .2455 | ie 96.2 .7069 52 66.4 .6470 es 76.4 .9077 .2565 Hh 96.4 -7174 = 66.6 6514 es 76.6 .9137 .2645 | ao 96.6 -7279 J2 66.8 .6560 23 76.8 .9198 52726) ae 96.8 -7385 53 23 eons 53 67.0) 0.6605 | 92 | 77.0} 0.9259 1.2807 | ,, | 97.0] 1.7492 4 67.2 6651 Be 792 .9321 .2559 | ce 97.2 -7599 i 67-4 | .6697 | 3° | 77-4| -9383 2971 | Ay | 97-4] +7707 | ay 67.6 .6743 om 77.6 -9445 +3054 | Ao 97.6 -7815 54 67.8 | .6789| “2 | 77.8] .9507 3137 97.8 | .7924 23 42 55 68.0) 0.6836 78.0| 0.9570 1.3220] ,, | 98.0] 1.8034 68.2 .6883 oe 78.2 .9633 23304 He 98.2 .8144 2 68.4 .6930 2 78.4 .9697 3388 a 98.4 8254 | £6 68.6 | .6978 | 24 | 786} .9761 3473 | 42 | 986 | 8366] 2¢ 68.8 | .7026| 74 | 788] 9825 .3558 | 49 | 98.8] .8477 a es 5 69.0} 0.7074 = 79.0 | 0.9890 1.3644 a 99.0] 1.8590 57 69.2 -7123 a 79-2 -9955 +3731 43 99.2 -8703 57 69.4 | .7172 : 79.4 | 1.0021 .3818 41 | 99-4 .8817 ey 69.6 eal ae 79.6 .0087 +3905 A4 99.6 .8931 57 69.8 | .7270 a5 | 79:3} -0153 3993 | 44 | 992 -9046 | 58 SMITHSONIAN TABLES, TABLE 35. PRESSURE OF AQUEOUS VAPOR (Broch.) ENGLISH MEASURES. Temper-| Vapor Vapor ae Temper-| Vapor a Temper-| Vapor te ature. | Pressure. 0°! Pressure. A ature. | Pressure. 0°! ature. | Pressure. nt | F. Inches. Inches. F. Inches. Inches. | 100°0] 1.9161 8 25705 |) tL 2020)|) ed253 6 4.5044 100.2 | .9277 28 5915 es 120.2 4445 a6 -5286 ae | | 100.4 -9394 59 -6066 76 120.4 -4637 97 “5539 | nog 100.6 .Q511 .6217 "6 120.6 .4831 7 S579) |e 100.8 .9629 59 .6369 | 120.8 .5026 a .6020 | *Y | 77 123 | 101.0] 1.9747 22 2.6522 es 121.0] 3.5221 a 4.6267 E IOI.2 .9867 SS .6676 77 121.2 -5417 = .6515 eu > / ; = ae Zz ror | 998° | Go Pelee eee $784 | t35 | fp LORS | A{OLO7 1 Go ope? 78 “S°T3 | 100 ho |e Te6u | 101.8 .0228 - .7142 : 121.8 .6012 .7266 3 I 7 100 12 | 102.0] 2.0349 | 6, 2.7299 $3 122.0] 3.6213 non 4.7519 127 | Pe ae te er a eee | ees | a8 | 22 | | 6 oe 2 ce pe ae “681 162 "8081 ie | pee oo 62 “7775 Sonata Soo bo eres 0204 129 | 102.8 .0842 és -7935 5 122.8 .7023 ae 8541 | S | oO 103.0 | 2.0967 6: 2.8096 81 123.0| 3.7228 103 4.8800 ae | x 3 3 5 c 30 | Bre) eee ee ea | ee ele | eee le Pel aais ee isse)| 82 | rane || s4849 | 204 soebo | 138 1038 ee oe 8747 ee 8 ‘058 104 ve 132 | 64 82 105 132 104.0] 2.1601 64 2.8912 83 124.0] 3.8267 105 5.0110 | ,,, | m9 5 5 27 DI 104.2 pk 65 O18 83 ee eal Ob a 133 | | 0: cs 80 65 ae SA ea 8 a 106 0 2 134 | | 104. esate Eats -94 84 4. -29°3 | 107 he 135 | | 104.8 .2120 ee .9580 A 124.8 -QI17 "1179 107 135 | 105.0} 2.2251 | 66 2.9749 e 125.0] 3.9332 | 168 5.1450 se | | 105.2 -2384 66 -9919 85 125.2 -9548 109 22 136 sr) ea nr eee pal peer a eta 19 | 237 es a |e 10433 86 aes ee uS eo enae 5: - Nn N Inch. 0.0011 .OOIT .OOI2 .0013 0.0014 .OOT5 .OOI7 .oo18 .OOIg 0.0020 .0022 .0023 .0025 .0027 0.0028 .0030 .0032 34 .0036 0.0038 .OO4I .0043 .0045 -0047 0.0050 .0053 .0056 .0059 .0063 0.0067 .0072 .0077 .OOSI .0087 0.0092 .0097 .O103 -O109 .O116 0.0122 .O130 .0138 -O146 -O155 0.0164 130 mm. oO. ° a -23 -247 2 3 NN ON N No WWW WW ONTO T o> Jes 4 “I CO OOH OH Inch. 0.0067 .OO7 1 .007 .0080 .0085 0.0091 .0096 .O102 .O108 .O115 0.0121 .0128 .0136 .O144 .0153 0.0162 0°6 mm. 0.027 .029 .031 .033 0.035 .038 .O41 -044 -O47 0.051 .055 -059 .063 .067 0.071 .076 .OSI .086 .Ogt 0.096 -159 .180 .192 . 204 e2L7, 0.230 .244 -259 274 291 0.308 Inch. mm, 0.0010 .OOII .OO12 .0013 0.0028 TABLE 37. PRESSURE OF AQUEOUS VAPOR AT LOW TEMPERATURES. (C. F. Marvin.) ENGLISH AND METRIC MEASURES. Tempera- 0°0 0°2 0°4 0°6 0°8 ture. F. Inch. mm. Inch. mm. Inch. mm. Inch. min. Inch. mim, —15° | 0.0168 | 0.427 | 0.0166 | 0.422 | 0.0164 | 0.417 | 0.0162 | 0.412 | 9.0160 | 0.407 14 0178 | .452 .0176 | .447 .O174 | .442 .O172 437 0170 | .432 13 0188 | .478 | .o186| .473 | .0184 | .468 | .o182 | .462] .o180| .457 12 0199 | .505 | .0196| .499] .0194| .494 | .o192 .488 | .o190 | .483 II 0210 | .534 .0208 | .528 .0206 | .522 .0203 516 .0201 510 —10 | 0.0222 | 0.564 | 0.0220 | 0.558 | 0.0217 | 0.552 | 0.0215 | 0.546 | 0.0213 | 0.540 9 .0234 | .595 .0232 598 .022 592 .0227 576 .0224 .570 8 .0247 | .627 .0244 | .620 .0242 614 .0239 | .607 .0237 .601 | 7 .0260 | 661 | .0257 |° .654 | .0255 | .647| .0252| .640| .0249 | .633 6 .0275 | .698 | .0272| .691 .0269 | .683 | .0266| .676 | .0263 | .669 | | —§5 | 0.0291 | 0.738 | 0.0287 | 0.730 | 0.0284 | 0.722 | 0.0281 | 0.714 | 0.0278 | 0.706 | 4 | 2.055 STAR As (Ps shos .1266 | 3.215 1278 | 3.245 .1290 | 3.276 25 | 0.1302 | 3.307 | 0.1314 | 3.338 | 0.1327 | 3-370 | 0.1339 | 3.402 | 0.1352 | 3-434 26 1365 | 3-466 | .1377 | 3-498 | -1390 | 3.531 .1403 | 3.564 1416 | 3.597 27 -1430 | 3.631 1443 | 3-665 .1456 | 3.699 | .1470 | 3.733 1483 | 3-768 28 1497 | 3.803 Thi |p stsso 1525 | 3.874 1539 | 3-910 | .1554 | 3-946 29 .1568 | 3.982 .1582 | 4.018 | .1596 | 4.055 -I61I | 4.093 .1626 | 4.131 30 | 0.1641 | 4.169 | 0.1656 | 4.207 | 0.1671 | 4.245 | 0.1687 | 4.284 | 0.1702 | 4.324 232i 1718 | 4.364 | .1734 | 4.404 | .1750 | 4.444 | .1766 | 4.485 | .1782 | 4.526 32 1798 | 4.568 | SMITHSONIAN TABLES, 131 TABLE 38. WEIGHT OF AQUEOUS VAPOR IN A CUBIC FOOT OF SATURATED AIR. ENGLISH MEASURES. Temper-| gg | Qo5 | Temper-| go ° me : 0°5 ature. ature. Grains | Grains Grains | Grains Grains | Grains troy. | troy. troy. y. 5 troy. troy. 0.230 | 0.224 1.675 é 8.240} 8.372 .242 3230) 1 1.743 77 8.508 | 8.644 -254 1.812 8 8.782] 8.923 .267 P.602 5s 9.066 | 9.210 | 956 | I. 9.356 | 9.504 034 | 2.073 | 9.655 | 9.807 113 : 9.962 | 10.118 194 : 10.277 | 10.438 279 : 10.601 | 10.766 Rowe eH Nw HN 366 457 559 646 746 10.934 | II.103 11.275 | 11.450 11.626 | 11.805 11.987 | 12.170 12.356 | 12.545 bY HNHD i &» 2 OH W m1 Oo NNNNN NNKNNN \O 12.736 | 12.930 TANT 2 7 |eler eos 13.526 | 13.730 13.937 | 14.146 14.359 | 14.573 .849 955 064 177 204 BON HO Eg rd WwWwon hn Bw wHH Hh Wb ALAR PP 3.414 | 3. 14.790 | 15.011 3-539 | 3. 15.234 | 15.460 ) é 15.689 | 15.920 16.155 | 16.393 16.634 | 16.877 Sen aoc 2 2 o ) 2 2 4 5 2 2 5 / 5 2 2 5 2) 2 2 d d ao So Oo 17.124 | 17.374 17.626 | 17.883 18.142 | 18.404 18.671 | 18.940 4.685 : 19.212 | 19.487 oO BWW 4.549 | 4. 19.766 | 20.049 5-016 | 5. 20.335 | 20.624 -I9QI | 5.280 | 18 20.917 | 21.214 379 | 5. 3 21.514 | 21.817 DOOM FO: 22.125 | 22-436 LAD AL nor on STA 5) | 5.02 22.750 | 23.070 5.941 aC 3.392 | 23.718 9.142 R245" 24.048 | 24.382 | 349 -456 | 24.720 | 25.062 P5Ose |KO: 25.408 | 25.758 mannnn DANADAaUUN OV 782 89! 26.112 | 26.470 009 : c 26.832 | 27.199 241 Ka | 2 27.570 | 27.946 | 480 60 2: 28.325 | 28.708 726 | 7.85 : 29.096 | 29.489 SNe 7.980 | 8. | 29.887 SMITHSONIAN TABLES, TABLE 39. WEIGHT OF AQUEOUS VAPOR IN A CUBIC METRE OF SATURATED AIR. METRIC MEASURES. Temper- ature. Temper- O20) 05 || aig | 70) | Oc2° | r0%4. |, O76" | Ors Gram’s. C. Gram ’s,| Gram’s. C. Gram’s.| Gram’s.| Gram’s.| Gram’s.| Gram’s.| 0.496 | —17° | 1.375 | 1.321 — | B-407 1 74-359")| 3-321 3.659 | 3.607 | 3.556 3.926 | 3.871 3.817 4.211 | 4.152 | 4.095 4.513 | 4.451 | 4.390 5 .542 16 1.489 | 1.432 4 3 2 I O | 4.835 | 4.769 | 4.704 0 I 2 3 4 3 593 15 I.61I | 1.549 .647 14 1 742))|) 22676 .706 3 1.882 | 1.811 .770 2.032 | 1.956 0.839 2.192 | 2.111} + 913 2.363 | 2.276 -992 2.546 | 2.453 1.078 2.741 | 2.642 1.170 2.949 | 2.843 1.269 3.171 | 3.058 | + 4.835 | 4.901.| 4.969 5.176 | 5.247 | 5.318 5.538 | 5.613 | 5.689 5.922 | 6.002 | 6.082 6.230 | 6.414 | 6.499 6.761 | 6.851 | 6.941 0°0 orl O°2 | 0°3 | 0°4 0°5 0°6 0°7 Gram's.| Gram’s. | Gram’s.| Gram’s. | Gram’s.| Gram’s. | Gram’s. | Gram’s. | Gram’s. 7.266 7-313 7-361 7.409| 7.457 7.506 7-555 7-614 7-753 | 7.803] 7.853] 7.904] 7.955| 8.007] 8.058] 8.IIO | 8.268 | 8.321] 8.374| 8.428] 8.482] 8.536] 8.591] 8.646 8.813 | 8.869} 8.926] 8.982] 9.039] 9.097] 9.155| 9.213 9.389 | 9.448] 9.508] 9.568] 9.628] 9.689] 9.750} 9.811 | 9.997 | 10.060 | 10.123 |] 10.186} 10.250] 10.314 | 10.378 | 10.443 | 10.640 | 10.706 | 10.773 | 10.840} 10.907 | 10.975 | II.043 | II.1II | [i316 || 11388 | 11.458 || LI.529 | 112600|| 10-672)) 11.744 | 1x. 11.888 | 12.035 | 12.108 | 12.182 | 12.257 | 12.332 | 12.407 | 12.483 | 12.559 | 12.635 | 12.790 | 12.867 | 12.945 | 13.024 | 13.103 | 13.182] 13.262} 13.3, 13.423 | 13.505 | 13.586 | 13.668 | 13.750] 13.833 | 13.916 : 14.085 e 14.254 | 14.339 | 14.425 | 14.511] 14.598 | 14.685 | 14.773 : 14.950 | 15.039 | 15.128 15.218 | 15.308 |} 15.399] 15.491 | 15.583] 15.675 ay 15.861 | 15.955 | 16.049 16.144 | 16.239 | 16.335 | 16.431 | 16.528 | 16.625 : 16.821 ; | 17.019 17.118 | 17.218 | 17.319 | 17.420 | 17.522] 17.624 3 17.830 .934 | 18.039 18.143 | 18.248 |} 18.353 | 18.460 | 18.568 | 18.676 .784 | 18.893 | 19.002 | 19.111 19.222 | 19.332] 19.444] 19.556] 19.668] 19.751 8 20.009 .124 | 20.239 20.355 | 20.471 | 20.588 20.824 | 20.943 : 21.182 .303 | 21.424 21:546 | 21.668 | 21.791 -914 | 22.038 | 22.163 37 | 22.414 .541 | 22.668 22.796 | 22.925 : 24.109 | 24.244 25.487 | 25.629 26.933 | 27.082 28.450 | 28.605 54 -184 | 23.314 | 23.445 24.653 | 24.790 26.058 | 26.202 2752272002 29.077 | 29.235 23-709 25.067 26.492 27.988 29-555 oO ° ow NN HN Com U1 Go “SINNIW O Doo I NOH eR NON HN WD ONAHLW MOO U1 Owh nN NHK HN O OHDUW 2 . 202 Oo oO on 30.039 | 2 31.704 33-449 35-275 37-187 30.696 32.392 34-169 36.030 37-976 39.187 . 39.805 | 40.012 41.279 a -924 | 42.142 43.465 . 4. 44.367 45-751 | 45-985 : 46.693 48.138 | 48. , 49.123 : as 50.377 O > 094 -903 795 780 NU NO Co 0 “I DAnIO O HHO Sf ONIN DAL OH ¢ G2 2 GO CONN ae G2 G2 G2 G2 WG SIUIO HO Ge G2 Go G2 Go G2 G2 G2 OG» G2 DAR O DR W G2 Go Oo man ca &) G2 G2 G2 OD un ov wun Or on “I 40.853 43.020 5.286 fete tO uw nvr» Oo aN OAOwn : 133 TABLE 40. REDUCTION OF PSYCHROMETRIC OBSERVATIONS. ENGLISH MEASURES. Pressure of Aqueous Vapor. ' Tempera: Inch. 0.007 .O13 -022 +Q -035 0.038 .063 .103 7 56 6 Cor SINT Go Go Go Oo HD PWN HO NIH bh O SMITHSONIAN TABLES, 2 Inch. 0.006 -OI2 -O2T .036 0.040 .066 .108 O°! Inch. 0.165 2172 -181 2° Inch. 0.006 .OIl ~020 -034 0.042 .070 .rL3 O°2 Inch. 0.166 “A> ISI .189 .196 204 see) R220 .230 -239 9.248 .258 .268 -279 .289 301 e212 324 3° 4° Inch. 0.006 .OIL .O19 .033 0.044 Inch. 0.005 .O10 .o18 -031 0.047 NS Ne m No t b Go G2 Go Go Ga MNO NH O wo N UO t. $. Oo Go Oe OOD MOO n 134 Inch. 0.168 .176 .184 -19I .199 .207 215 .224 .233 242 .251 .261 S27 L .282 -293 304 -316 328 -340 +353 367 .380 +394 -409 .424 .440 -456 473 .490 .508 .526 “545 505 585 .606 627 .649 .672 .695 .720 aa Inch, 0.005 .008 .O15 .026 0.054 .089 -143 Inch. 0.169 esis .185 -193 -200 .208 <217 «22 +234 -244 253 .263 Inch. 0.171 .179 .186 194 - 202 .210 | .219 2277 .236 .246 +255 .265 .276 .286 -297 -309 -321 -333 “345 -358 TaBLE 40. REDUCTION-OF PSYCHROMETRIC OBSERVATIONS. ENGLISH MEASURES. Pressure of Aqueous Vapor. eee oco | ol jaz | 0:3 | O24 | O°5 | O°6 | 0°77 | o's | 0% Inch. Inch. | Inch. | Inch. Inch. Inch, Inch, Inch. Inch, | Inch. 0.732 | 0.734 | 9.737 | 0.739 | 9.742 | 9.744 | 9.747 | 0.750 | 9-752 | 9-755 0.757 | 0.760 | 0.762 | 0.765 | 0.768 } 0.770 | 0.773 | 9.775 | 9-77 0.781 | 0.783 | 0.786 | 0.789 | 0.791 | 0.794 | 9.797 | 9.799 0.802 | 0.805 | 0.807 0.810 | 0.813 | 0.816 | 0.818 | 0.821 | 0.824 | 0.827 | 0.830 | 0.832 0.835 0.838 | 0.841 | 0.843 | 0.846 | 0.849 | 0.852 | 0.855 | 0.858 0.861 | 0.863 | 0.866 | 0.869 | 0.872 | 0.875 | 0.878 | 0.881 | 0.884 | 0.887 | 0.890 | 0.893 0.896 | 0.899 | 0.902 | 0.905 | 0.908 | o.gir | 0.914 | 0.917 | 9.920 | 0.923 0.926 | 0.929 | 0.932 | 0.935 | 0.938 | 0.941 | 0.944 0.948 | 0.951 | 0.954 | 0.957 | 0.960 | 0.963 | 0.966 | 0.970 | 0.973 | 0.976 | 0.979 | 0.982 0.986 0.989 | 0.992 | 0.995 | 0.999 | I.002 | I.005 | I.009 | I.012 | 1.015 | 1.019 1.022 | 1.025 | 1.029 | 1.032 | I.035 | I.039 | 1.042 | 1.046 | 1.049 | 1.052 1.056 | 1.059 | 1.063 | 1.066 | 1.070 | 1.073 | 1.077 | 1.080 1.084 | 1.087 1.091 | 1.094 | 1.098 | 1.101 | I.105 | I.109 | 1.112 | 1.116 | I.1Ig | 1.123 Pale7) |) TelZo || 11340) 12138" )| Tor4k | 1.145) t.149) || 1.052 1.156 | 1.160 mxor | ter67 | 1.072 | 1.175 || 1-179 | 1-182 | 1-186.) 1.190}, 1-194: 1.195 1.201 | 1.205 | 1.209 | I.213 | 1.217 | 1.221 | 1.225 | 1.229 | 1.233 \ereo37 1.241 | 1.245 | 1.248 | 1.253 | 1.256 | 1.260 | 1.264 1.269 | 1.273 | 1.277 1.281 | 1.285 | 1.289 | 1.293 | 1.297 | 1-301 | 1.305 | 1.310 | 1.314 | 1.318 | 132271915326) |) 1.330) || 1.335) |) 2-339 |) £-343 | 2-347 | 1-352 1.356 | 1.360 1.364 | 1.369 | 1.373 | 1.377 | 1-382 | 1.386 | I.390 | 1.395 | 1-399 | 1-404 1.408 | 1.413 | 1.417 | 1.421 | 1.426 | 1.430 | 1.435 | 1.439 | 1-444 | 1.448 1.453 | 1.458 | 1.462 | 1.467 | 1.471 | 1.476 | 1.480 | 1.485 | 1.490 | 1.494 E499 | 1.504 | 1.508 | 1.513 | 1-519 | 1-523 | 1.527-| 1.532)| 2-537 | 1-542 E546 |) 1551 | E556'| 1.560 | 1.566 | 2.571 | 1.576 | 1-580") 1-585 | I.590 I.595 | 1.600 | 1.605 | 1.610 | I.615 | 1.620 | 1.625 | 1.630 1.635 | 1.640 1.645 | 1.650 | 1.655 | 1.660 | 1.665 | 1.671 | 1.676 | 1.681 | 1.686 | 1.691 1.696 | 1.702 | 1.707 | 1.712 | 1.717 | 1.723 | 1.728 | 1.733 ; 1-738 | 1-744 Te7ZAG | ele 550s BGO lela 705) eke ee kari 1.781 | 1.787 | 1.792 | 1.798 1.803 | 1.809 | 1.814 | 1.820 | 1.825 | 1.831 | 1.837 | 1.842 1.848 | 1.853 || 1.859 | 1.865 | 1.870 | 1.876 | 1.882 | 1.887 | 1.893 | 1.899 | 1.905 | I.g1o | 1.916 1.922 | 1.928 | 1.934 | I.939 | 1.945 | 1.951 | 1-957 1.963 | 1.969 1.975 | 1-981 | 1.987 | 1.993 | 1.999 | 2.005 | 2.011 | 2.017 | 2.023 | 2.029 2.035 | 2.041 | 2.047 | 2.053 | 2.059 | 2.066 | 2.072 2.078 | 2.084 | 2.090 2.097 | 2.103 | 2.109 | 2.116 | 2.122 | 2.128 | 2.134 | 2.141 | 2.147 | 2.154 2.160 | 2.166 | 2.173 | 2.179 | 2.186 | 2.192 | 2.199 | 2.205 | 2.212 | 2.219 | 2.225 | 2.232 | 2.238 | 2.245 | 2.252 | 2.258 | 2.265 | 2.272 | 2.278 | 2.285 2.292 | 2.299 | 2.305 | 2.312 | 2.319 | 2.326 | 2.333 | 2-340 | 2.346 | 2.353 2.360 | 2.367 | 2.374 | 2.381 | 2.388 | 2.395 | 2.402 | 2.409 2.416 | 2.423 2.431 | 2.438 | 2.445 | 2.452 | 2.459 | 2.466 | 2.474 2.481 | 2.488 | 2.495 2.503 | 2.510 | 2.517 | 2.525 | 2.532 | 2.539 2.547 | 2.554 | 2.562 | 2.569 2.576 | 2.584 | 2.591 | 2.599 | 2.607 | 2.614 | 2.622 | 2.629 2.637 | 2.645 2.652 | 2.660 | 2.668 | 2.675 | 2.683 | 2.691 | 2.699 | 2.706 | 2.714 | 2722 2730)\| 2.738 | 2.746 |, 2.754.) 2.762) 12.770 | 2.777, 2.785 | 2.793 | 2.801 2.810 | 2.818 | 2.826 | 2.834 | 2.842 | 2.850 | 2,858 | 2.866 | 2.875 | 2.883 2.891 | 2.899 | 2.908 | 2.916 | 2.924 | 2.933 | 2.941 | 2.950 | 2.958 2.966 2.975 | 2.983 | 2.99 3.000 | 3.009 | 3.017 | 3.026 | 3.035 | 3-043 | 3.052 3.061 | 3.069 | 3.078 | 3.087 | 3.095 | 3-104 | 3-113 | 3-122 | 3.131 | 3-140 3.148 | 3.157 | 3-166 | 3.175 | 3-184 | 3.193 | 3-202 | 3.211 | 3-220 | 3.22 3-239 | 3.248 | 3.257 | 3-266 | 3.275 | 3.284 | 3-294 | 3-303 | 3-312 | 3-321 3-331 | 3-340 | 3-349 | 3-359 | 3-368 | 3-378 | 3-387 | 3-397 | 3-406 | 3-416 | SMITHSONIAN TABLES, TABLE 41. REDUCTION OF PSYCHROMETRIC OBSERVATIONS. ENGLISH MEASURES. Values of 0.000367 B (t— t)(1 +8 tesco / — Barometric pressure. ¢— Temperature of the dry-bulb thermometer. ?, — Temperature of the wet-bulb thermometer. BAROMETRIC PRESSURE IN INCHES (£4). i—iZ, | | ¢ Cc 2 30°5 | 30°0 | 29°5 29°0 | 28°5 | 28°0 | 27°5 | 27°0 | | F. Inch. | Inch. | Inch. | Inch. | Inch. | Inch. ] Inch. | Inch. | Inch. [° }o.or1 | 0.01 | O.OTL | O.OIL | 0.010 | 0.010 | 0.0TO | 0.0T0 | 0.0rO 2 :022 | .022:| .022)| .02T || .02T ||" .02% |) :020)| 20201). 0r9 3 .034 | .033 +033 -032 | .O3I1 -O31 -030} .030] .029 4 .045| -044] .043] .043] .042]| .O41 | .040] .040| .039 5} 0.056 | 0.055 | 0.054 | 0.053 | 0.052 | 0.052 | 0.051 | 0.050 | 0.049 6 .067 | .066} .065} .064] .063] .062] .o61] .060| .059 7 .079, |) .O77 |, <.076:| 2075 073 | .072]| .07I| .070] .068 5 .o9g0| .088] .087} .086] .084] .083] .o81| .o80] .078 | : > | 9 -Io1}| .099] .098] .096| .095] .093] .ogt| .ogo}] .088 10 J 0.113 | O. III | 0.109 | 0.107 | 0.105 | 0.103 | 0.102 | 0.100 | 0.098 II 1244) 2022) |) 2020) 2eEtS 106) | RIA. |) Ll) Ons LOS G2 T3G Aly LSS |) eee Dall 220 T26i| dee 2AY ot 22) | 20) eee os 13 £147) “204485 A | er 4o) ee ately || aenieye}ill —atgtoy ||" cavzdy, i4 2158) 056") .0533)° 050s) 2 04Sa| 2045 | dail 140) 1s, er 15 | 0.170 | 0.167 | 0.164 | 0.161 | 0.158 | 0.156 | 0.153 | 0.150 | 0.147 16 18D |" .278)| .275)|. 3272) |: ~169)|' 5.166" 1635" Colmes 7 17 -LQ2)|° <189)| 3186) 3-153) =2TS0ll a7 7 | yak7a|| 7) |e LOZ IS .204 200| .197]| .194 L9QO))|' -187" |) SS45|" LSON a7 19 .215 212)\\) 42003) ©2205 200 || .198\|.LO44|" On |) 37 20 | 0.227 | 0.223 | 0.219 | 0.216 | 0.212 | 0.208 | 0.204 | 0.201 | 0.197 21 2238!) 234); 32303) B22261)" 2.223) OTONM 25 pe2ln | e2Or 22 .250'| #246) "2427| 3227 23311) 220). 225)! Hae2is peels 23 261 257 || 253°). -248°| 2445" 22401) 42261) est 227, 24 273 268) .264| © 2259)| - 255") .2501| .246)| "241 |) 5237 25 [0.284 | 0.280 | 0.275 | 0.270 | 0.266 | 0.261 | 0.256 | 0.252 | 0.247 26 296)! .291)|' 286i) 2280277) (e 27.2) a2678| 26 2ql mea 27 -307 |) 32023] *.2074|" £202) |" 287 E2821) M7 7allh 2729267, 28 -319| -314] .309] .303 ©2989), 92293) 3288°)| 262) 22771 29 +331 | -325| .320] .314 309 304.| .298| .293| .287 | 30 | 0.342 | 0.337 | 0.331 | 0.325 | 0.320 | 0.314 | 0.309 | 0.303 | 0.297 31 | -354| -348) -342] .336] -331| -325| -319| -313} -307 32 | -365| -359| -354] -348| .342] .336] .330] -324| .318 33. | -377| -371| -365] -359| -352| -346] .340| .334) .328 34 | -389| .382] .376] .370| .363| .357| -351| 344] -338 35 | 0.401 | 0.394 | 0.387 | 0.381 | 0.374 | 0.368 | 0.361 | 0.355 | 0.348 36 | -412| .405| .399| 392] -385] -378| -372| -365| -358 37, 424} .417| .410| .403 1396)), -399 | 8921) ©3751" Ea0° 38 436| .428| .421| .414| .407]| .400] .393] .386] .379 - a9 ~ > 4Q 39 -447| .440| .433] -425| -418] .411} .403] .396] .389 40 10.459 | 0.452 | 0.444 | 0.437 | 0.429 | 0.422 | 0.414 | 0.406 | 0.399 SMITHSONIAN TABLES. Inch. 0.O0TO oO. .057 .067 .077 .086 oO. 203 sie oO. .252 .O19 .029 .038 048 .096 . 106 pes, m5 135 144 -154 .164 -174 .183 193 Bn 1225 o 23 3 242 2262 2272 .282 .292 . 302 Az 5222 oO. 351 301 sB7L 381 22 "IO 341 26°5' | 2670 |:25°5.|525°0 Inch. | Inch. | 0.009 vel 019 | .Or8 | .028 cee .038 | .037 0.047 | 0.046 .056 | .055 | 066 | .064 | .075 | .074 .085 | .083 0.094 | 0.092 -104| .102 SLisy |e on “1235 ||) -L20 5132) |) l30 0.142 | 0.139 i dgit)|| Aawsks} .161 | .158 £70) S267, .180| .176 0.190 | 0.186 -199| -195 .209 | .205 12101202. +226 || ..224)) 0.238 | 0.233 +247 | .243 1257 || 2252 2207 seo #270) Nee eval 0.286 | 0.281 .296| .290 .306 | .300 5305) |' 5309) -325 | -319 0.335 | 0.328 | -345 | -338 -354| -347 -364| .357} -374 -367 | 0.384 | 0.37 TABLE 41. REDUCTION OF PSYCHROMETRIC OBSERVATIONS. ENGLISH MEASURES. t—t Values of 0.000367 B (4) (1 - 4571)" #& —= Barometric pressure. ¢— Temperature of the dry-bulb thermometer. ¢, = Temperature of the wet-bulb thermometer. BAROMETRIC PRESSURE IN INCHES (A). 24°5 23°5 | 23°0 | 22°5 | 22°0| 21°5 | 21°0 25 | 20°0 | Inch. .| Inch. | Inch. | Inch. } Inch, | Inch. | Inch. .| Inch. Taehe hice lanich: | 9.009 0.009 |0.008 j0.008 |0.008 |0.008 |0.008 0.007 |0.007 |0.007 018 .017 | .017 | .o16 | .o16 | .o16 | .o15 OI5 | .O14 | .o14 | .o14 028 | . 026 | .025 | .025 | .024 | .024 | .023 022 | .021 | .021 | .020 .036 635 | .034 | .033 | .032 | .032 | .031 | 029 | .029 | .028 | .027 No" O45 0.043 |0.042 0.041 |0.040 |0.040 |0.039 0.037 (0.036 0.035 0.034 \ o 2 = .054 | - .052 | .O51 | .050 | .049 | .048 | .046 | . .044 | .043 | .042 | .04 c 0637) |\= .061 | .059 | .058 | .057 | .055 | -054 | . 052 | .050 | .049 | .048 O72" Pe .070 | .068 | .066 | .065 | .063 | .062 | . .059 | .057 | .056 | .055 Kotshie || 078 | .076 | .075 | .073 | .07I | .070 | . 066 | .064 | .063 | .061 AON ar WwW \o .0gO 0.087 |0.085 |0.083 |0.081 |0.079 |0.077 |0. 0.074 |0.072 (0.070 |0,068 ELOON|Pc .095 |°.093 | .ogI | .089 | .087 | .085 | . .O8I | .079 | .077 | .075 .I09 | . | .104 | .102 | .100 | .097 | .095 | .093 | - 089 | .086 | .084 | .082 stato Je | te oT | LO TOS) |) LOG. || LOSs|| . LOM 7. 096 | .093 | .OgI | .089 027, : TOPs | LON | kkzal aus er GPs LOO! |i .104 | .1O1 | .098 | .095 9.136 oO. 0.131 |0.128 |0.125 |0.122 |O.1Ig |O.117 |oO. III |0.108 j0.105 |o.102 145 | - | PLO L3Onl 033) | SON |e 270) 124) |r. Hidit) |pecpeatsy |p asiieey || sia Co) -I55 | - TAS ml ll Sa LA 2a els Op ecko 51 eeles 21h. 20) [23a eZON en deles, 164 | . SER 7 | eL5A |g k | Lay |ed sy | AO 3 D3At ZO. |) L271) 024 SUS les TOON LO2e | USO L555 2p LAo: kes AL | else say en ss .182 |o. 0.175 |0.171 |0.167 |0.163 |0.160 |0.156 |o. 0.148 |0.144 |O.14I |0.137 .IQI | . 163) |) 160 | .£76 | 2172 || 168! || 164) ||: 156) |) 2052-148 | 044 s2O le. 2192 | 3188 |) =184 | .180)} . 7 lie | .164 | .160 | .155 | .151 210) || "- e2OKy | elO7 98 LOZ" |NLOON |e. -160)|| | 170 | .067. | -163) |) 150 -210)||) -205) ||-20L |! 196) |): eLSSh |) e193) | 079) |) 274) |) 0709 LOS bb NRHN on + Oe uni .210 0. : 9.196 /0. .186 |o.181 |0.177 218) |\ : P2OR aE .194 | .189 | .184 e227 alles : SPA .201 | .196 | .191 2235 23 2 | .219 | .214 | .209 | .203 | .199 | . 244 |. lbe2e ‘ ¢ 2168 22th || 22008). nN 4 NO by bv Oo Ne vow iy bv > 0 9 CO io On & G2 G2 NY 2601 | .269 278 .286 252 .218 | .226 233 241 .248 oO coml Su by bb mn WW Co Nv 2 bbb meni OU ons bby bH r _— NW tN G2 G2 G Go N Wh Nh vt ‘Oo are &WNN HH nun io to to bbbt Man~TO nN S mW + to \O GP to oO .295 304 ‘3 L2 aBOn 330 ao oD nN a O — me th bbb C~I SI OV woo b&b Drewun on iv Cnr “I on to WW G2 G2 O2 OW \O nmnewn Go Go Go Go Go G2 G2 Ge Go G2 G2 Ge Ge HH 1) SO Ooo Ro nNNH NN NY STIOUUW eH fo SI | | | Ba) ; ; ; [0.301 |0.293, |0.286 |0.278 | aes SMITHSONIAN TABLES. TABLE 42. RELATIVE HUMIDITY. TEMPERATURES FAHRENHEIT. DEPRESSION OF THE DEW-POINT (¢—@). | 2°0 | 2°5 | 3°0 | 3°5 | 4°0 | 4°5 | 5°0 | 5°5 | 6°90 | 6°95 | 790 | 7°95 65 | 63 65 aa Oo Sel Toad baal oad f& & G2 G2 Go ss NN HAH SMITHSONIAN TABLES. 138 TABLE 42, RELATIVE HUMIDITY. TEMPERATURES FAHRENHEIT. 9°5 | 10°O| 10°5 | 1170 | 11°5 ees 14°5 1520, + a av anm “STD D mm OO O & GH Ww Spend ees ed eel Ww WN N “I ° on mn NIN SIN “I oO ~I on > im ° nn uo SIN DON GW on a om Ro ee Dn Dd oO 0 a nur NO “JI ° OO SJ SST ST NT VON BWW Ww N ST ST) SJ to “I Oo O OO NaN “TN oonnn SINT SI NI SI oO Oy sNNT nn psp & NNNN NI ef WW NNN NN Ww WwW KN N STS ST Now ow “I “I “I NS oO “I~ No nw on wn O22 WwW N CO NN NIN SJ nu & & sss SI SI ~I Ce on) ST eS ak ew SS SSeS & WN NHN NHN H PT one at ce No FF ~~ Oo “I on ~I > SMITHSONIAN TABLES. TABLE 42. RELATIVE HUMIDITY. TEMPERATURES FAHRENHEIT. DEPRESSION OF THE DEW-POINT (/—@). hee 8S? | 207 218 DW Go nn & WW WH W fw wn GO Ww Ov as Oo WwW “I W Ww co NO a On oO & GG Oo to WwW wns bd © \O 0 ty nN “I oo as & G . CO's) ‘SJ ON, Gt oo rs oe Go NO = oO to © to oO W &% Go Ww aA pp PB Oo WH G OG) YW Oo nv oO \o us oD \ .o ass O & © DD GF W ww nn Oo oon! on “UO W HD GD WwW ON me BW G% WwW ¢ wn GW to w So aS O w ~ oO oO w Gn & Ww | aml SOL <= con] a = Oo ‘oO W W OW n > > Ge > 4 NS O Gd GH WwW x > to NS OG G Oo = ®O NK b ee NC) - n> ASS NO = Ww ¢ © oO WwW OF DW Oo on W &% G “SIO OH n ww ics) oD i) Oo tN > a —~ oo \o i GW oH GW Oo WwW Ww ay oO - oO ft Oo O° G2 G2 Ww N G6) GS 765 Oo as 4 Ow am STENTONOUCn oo a WW DW WwW On a= ww oer nN Ww oO oO nu ¢ Oo Nn w oO DW WwW co w re Oo onn > > $f oO \o GO GW Oo co nonn WwW ND KN HF HS > to 4 oo » Oo & \O n num + fw = Pret Nok: SMITHSONIAN TABLES. TABLE 42. RELATIVE HUMIDITY. TEMPERATURES FAHRENHEIT. DEPRESSION OF THE DEW-POINT (/—@). 33° | 36°) 39° | 42°; 45°| 48° 51° | 54° 57° |, 60° 63° | 66° 69° | 72°| 75° D5 nes 15 Bi lerr TOM ener |e 9 8 PF ta? eer | .TO" |) 8 7 17 | 14 | 12 | 10 8 Paleo ISOs LS |p 22) ||) LO 9 7, 6 5 4 | ie) af Gi ey |p eae 9 376 5 4 4 LOM Loe LA) LE 10 8 | 7 6 5/ 4 3 LOM |) 16) |er4, || 12." ro Oia waza 6 5 4 3 2 208 eet STA.) 12: | 10 Sap es 6 Sal aa 4 3 aoe an ere. | 1s. | 13° |) 1 S| PS. ine7 Ga eosin le eAs teases 2 2 | | | | 22g | PLOu a LOD CAG) |e 124 LOM) BAS 77 Gries 4 | 4 3 2 2 23 | 20/87 || 15 all oa| 9/| 8 7 6 5 4 ie 2 2 SAR ea Loa PSiih 13. fe Die AKO: |e 1S 7 6 5 4 Aw | aes 2 Beales 1 | ron) Tor end) |e r2 4) 10 9 8 6 5 5 4| 3 3 267223 2/20 pdfs yekote NS | a 9 8 7 6 5 4 4 3 | = | Zon een Mert 08) | eTOm RT| tae tog neo, ee 77 ie Oke Seles ae |e 29 | 25 | 22 | 19 | 16 | 14 | 12 | x1 Gul Saley7eiesGn kanal apes BON 620.1) 235 520 107 | 15 Hears |e Cle lO 8 7a © 5 5 4 BOM 27 Aleeds ||| Sra roe r6, | tA | 2121) 1° 9 8 7 6 5 4 | | Bi e2or W 24e 22 XQ) | E7 oes, rs | 9 ones, 6 5 4 | | | | | | ie ets Na 22 i 20. |-18y|e15"\| 13! |) 124) To)! 9 Ss 7 6 5 32) |) 290)-26: | 23.1 2018 | 16 | 14 |\,72.) 11 Gal So | 7 shecGn ea 33) |) 29 )2 25h 297) 07115) |) 13 | Bx) | To 9 8] 7 6 | 33, (6300 27) | 2a 20 LOM OL7 15 14 | 12 IO OF |S lie od 6 34 | 30 | 27 | 25 | 22 | 20] 18 | 16] 14 | 12 | 11 | 10| 8] 7 | 6 | | | 84 | B1 |) 28) 25) 230) 20} -a8 | 16. | 14 ) 13) f keen. aS 8 "7 a5. | g2-| 29 | 26 ZEN LG) Hak] |e h Se | LS Vetere Rs lec 8 7 36. 1..32, | 29 | e6: | 24 "| 25 | xg | 17 | Th) a4 | ee a | 10 |) 9, | 8 | Bor Sota SOM 27 te 24a le 220 208 | TS> 6.0) 14! 2) ur 10 9 8 BT eSS On Sze leone 120s | Gee TO. |S eal er seumemezen|s mT 9 8 | | | | | | | PAO Mees asia 2) 25238 eon Ig | 17 15 | 14 12 | Il 10 9 | | | | | SMITHSONIAN TABLES. I4t TABLE 43. REDUCTION OF PSYCHROMETRIC OBSERVATIONS. METRIC MEASURES. Pressure of Aqueous Vapor. (Broch.) Tempera- ture. Bo 39 4° Be 6° ae 8° Cc. — 30° — 20 0.35 0.32 0.29 0.23 : 0.19 0.87 | 0.79 0.73 : 0.61 55 0.50 I.99 | 1.84 1.69 1.44 1.22 4.25 | 3.95 | 3.67 ae Syl .9: 27D O17 0.46 1.22 oO 2.50 Tempera- OFS} O22 0°3 0°5 0°6 0°7 0°8 | $s |FE | | | mm. mn, min. mm. mm. min. | | | mm. | mm. mm, ; mim. mim, mm. mm. mm. 4.64 | 4.67 4:74 | 4.77 | 4.80 | 4.84 | 4.87 | 4.98 5.02 5.12 5.06 | 5.20 5222 5-35 | 5-39 ; 5-50 | 5-54 | 5-58 | 5.62 | 5.74 | 5-78 . 5-90 | 5.94 | 5.99 | 6.03 | 6.20 22 6.33 | 6.37 6.42 6.46 6.64 : oy) 6.78 6.83 6.88 6.92 Fauve) ; E 7526 Tea 7230 7.42 7.62 Ts : 7.78 EOS 7.88 8.15 : : a 8.38 8.43 8.72 8 ; : 9.02 9.32 9.48 See |e 9.64 9.96 : : 22 ELOwO 10.64 : 8: : 10.99 11.36 250 .598 | II. nie 12,12 227) 35 4 12.51 | 12.92 £G 7 P2o els .24. C3077 .95 ’ 5 14.21 14.67 4.56 : 5. 15.14 15.62 5.8 : : 16.12 16.63 Rox 92 .04 | 17.15 17.69 - ‘ 3 18.24 18.81 : LO. |) LO: 19.39 19.99 : SS .48 | 20.61 21.24 3 ; 6: : 21.89 22.55 BO: 4 ay 23.24 23.94 oex 3 p 24.66 25.40 a 25. : 26.16 26.94 . : 250) |) 27274. 28.56 8 29. : 29.40 30.26 : 30. : 31.15 32.99 34-92 36.95 39.08 41.32 NO vy bd t Agi GW bt oO Onl 32.06 33-94 35-92 38.00 40.19 42.48 43.67 44.89 : 5. 46.14 47.42 47.94 3.20 | 48.2 48.73 50.07 50.61 8 : 51.44 52.54 | 53-41 | 53. ; 54.28 55-75 56.35 | 56.65 | 56.95 | 57.26 | : 58.80 59.43 | 59.7. : 60,38 61.99 62.65 | 62. 2.30 a O3.04" | 65.33 66.01 56. 2 : 67.05 68.82 69.54 i 70. | 70.63 | 72.48 7222 ; -98 | 74.36 WH WD WW AA N DHWwWwWf & GG GW GW 2 WWwWWwWwWW NNN N Oo 2 G2 G2 Go WOnTIOO G2 G2 G2 Ge Go WO NIU A _ NS & Oo OV WO CONIA PWN HO > ase tN ft ort Oo» \O IwWwWw WwW & SMITHSONIAN TABLES. 142 TABLE 44. REDUCTION OF PSYCHROMETRIC OBSERVATIONS. METRIC MEASURES. Values of 0.000660 B (t— —+) (14858 873 ¢—= Temperature of the dry-bulb thermometer. 7, = Temperature of the wet-bulb thermometer. .~}|/ mm, | mm.; mm. . mm. mm. mm. | mm. | mm. | mm.; mm. | mm. mm, | 0.50 | 0.50 | 0.49 | 0.48 | 0.47 | 0.46 | 0.46 | 0.45 | 0.44] 0.44 | 0.43 | 0.42 | T.00 | 0.98 | 0.97 | 0.96 0.94 | 0.93 0.92 | 0.90 | 0.89 | 0.88 | 0.87 | 0.85 | 0.84 | | 1.49] 1.47| 1.45| 1.43 | I-41 | 1.39] 1.37] 1.35] I-33] 1-32| 1.30| 1.28 1.26 | I.99| I.97| I.94| I. 1.89 | 1.86 | 1.83 | 1.81 | 1.78] 1.75 | 1.73 | 1-70 1.67 | 2.46 | 2.43 2.17 | 2.13 | 2.09 2.95 | 2.91 2.59 | 2.55 | 2.51 3.45 | 3-40 3-04 | 2.99 |} 2.94 | 3-95 | 3-59 3.48 4.44 | 4.38 3-91 4.94 5-44 5-94 6.45 | 6.95 | 7.46 7-96 8.47 8.98 9.49 10. 14|10.00) 32 OV N 2.26 | 2.23 2.71 2:07 eaee7 13a .2)) 3-63 | 3.58 | 4-09 eS) 4.54 5.00 5.46 5-92 6.39 32 | | 2.79 3.26 Of OOM) Code t one P20 Oo ty Sa Go STW Oo 2 I HOD HANAN MmMnurwo OONIN”G Bw wbv Dur ¢ fw&nh bd ape ono Ono “I G2 Mm & Mh & I on DQ vx CO = f ~I OO OV oO KH OVW DAG HO ONO NON NR Re oO OV crit G2 \O COU Co f OAH WHAT N to om MWMADIN HHwWbvwbv DANAE RO o DANN Fe ww Noh ON UNS ° On H OVN SIO HAH OO f On O12 AN COO Ok MINN “SIOOnNS mMOonun to ty NIG Om HONO UU HS 4 yw G2 HO DU WADA ¢ OD Ar U1 6.85 7-32 7:79 8.25 8.72 9.60 | 9.46 | 9. 9.19 On ~ oN Po Om Peas n+ ne HMI O Ul Oe mPhon PMAOAIMAHD DINAH SWwwnn 5 S OAINAINATIAYD Anak COmnINI ON ON aya ¢ ~ O NINN NO NT NTO Oy whhu PRIMI AD ANY Oo MHANKA Ow THU OW tO NTI G2 \O on oO eI oC OV na © 0 “I oo BAROMETRIC PRESSURE IN MILLIMETRES (BS). 610/600 | 590) 580 570| 560 550 | 540 | 530/520) 510 500 490 | 480 -|/ mm. | mm./ mm. | mm, | mm.| mm. / mm, / mm. }/ mm. | mm. |} mm. ; mm, | mim. | mm. 0.41 | 0.40 | 0.40 | 0.39 | 0.38 | 0.38 | 0.37 | 0.36 | 0.36 | 0.35 | 0.34 | 0.34 | 0.33 | 0.32 0.81 | 0.80 | 0.78 | 0.77 | 0.76 | 0.75 | 0.73 | 0.72 | 0.70 | 0.69 | 0.68 | 0.67 | 0.65 | 0.64 | 1.20] I.17| 1.15] I.13| 1.12] I.10| 1.08] 1.06] 1.04] 1.02] 1.00] 0.98 | 0.96 | 1.60 | 1.57| I.54| 1.51| 1.49] 1.46| I.44| 1.41 | 1.38] 1.36| 1.33 | I-30| 1.28 1.99 | 2.39 | 2.80 3.20 a ron) 93 | 1.90 | 1.86 | 1.83 | 1.80] 1.76] 1.73 | 1.70] 1.66 2.24 | 2.20] 2.16] 2.12] 2.08} 2.04 | 2.00 2.61 | 2.56| 2.52 | 2.47 2.43 | 2.3 38 | 2.33 | 2.99 | 2.94 | 2.88 | 2.83 | 2.78 | 2.72 | 2.67 | 3-31 | 3-25 3-13 Ge 3-00 3.67 | 3.61 4.05 | 3-97 4.42 | 4.34 4-79 | 4-79 5-17 | 5-07 5-54 3} 5-92 | -30 | 6.67 7°05 7-43 > ~ “I D+ G2 Go n> G2 \ t CO Qe ~ VY NN ND HH No O02 NNN WOwNN n HH Hl ann WwWh dH “I 4 an No} oO ~I oO rs 1 cot CO Dv WO VHANWO = Cou eon Oo Aw © »ne OAS O ow On Oo HW co Conn Coun G) 1G OO WH > oO Oo & OW Afb pw iS) mur as SI WOM HAT WwoOUui ° nub Ww 1 ew SIG \O Oo om & & Ww NO Cour Mw “IG =~ o o~ CO et 4 00 Oy 2 > QO DAnNwo DAwvw0o Cnt on An +e Hreui nak “I Go aN Coun eH © ON Ne) no DAA AHREY & > Y -— © III DN WN SE OnkALK mur DAUM HPHREWW SII DAD 0 DAwHWO ALK me Ol CRON H HNWHL Wr IID DNDN nS Nn ny Of wh N SIOUUNNUI > NDA OU ND DUN Ons OL Won OWN NOY won “I SE a CON OO OWN wNIWO BS ND HAANAN SEEDY a Dn BD GW GW ere = | “I CO ae “I “I Oo oO “I & “I oO’ ON NO CO Go oO co to & ;o SMITHSONIAN TABLES. TABLE 45. RELATIVE HUMIDITY. TEMPERATURE CENTIGRADE. Depres- DEW-POINT (@). sion of the dew-point. ase | + 20° | + 25° | +30° Cro CoOmmm On NW 3:0 3.2 3-4 3.6 3.8 Se TTT nan An “I o © ape CAL N NNN na ans Nw Norio OI monk nNO 4 Oo NSINTNININI SINNNN 2 ° SMITHSONIAN TABLES. TABLE 45. RELATIVE HUMIDITY. TEMPERATURE CENTIGRADE. sion of the dew-point. | Depres- DEW-POINT (d). ee 1 I8e -| +10° | +15° | + 20°] + 25° | +30° | | ARAN MO HW SEAS 41 40 DH Cro OD am & 1% 2 OH Ww ao OW Ww Oo om Go G G2 Go mr NO O2 G) G2 G2 Wwhui ° 2 1S) BRN®O OO NNN NN = = Se et Mn ANI CWO _ aS SMITHSONIAN TABLES. 145 TABLE 46. REDUCTION OF SNOWFALL MEASUREMENTS. Depth of water corresponding to the weight of snow (or rain) collected in an 8-inch gage. Weight Oz. Oz. of 0 is Snow. 4 Lb.Oz.| Inch, | Inch. | Inch. Inch’s|Inch’s|Inch’s|Inch’s}Lb.Oz.|Inch’s|Inch’s|Inch's Inch’s } 0.00 } 0. 0.02 0.83 | 0.83 | 0.84 |0.85 [2 13 | 1.55 | 1.56 | 1.57 | 1-57 | 5030. LO5 Mallen 86 | .87 | .88 | .89 | 2 14] 1.58 | 1.59 | 1.60 | 1.61 07/808) | -OOu| 2: :69) | 90)! OL i) 292 fi2!" 15)|/1.620 | 1:63) |G 2 8) 64! SLOU| : : : 94 | .94 | .95 SLA ali : ; : -97 | .98 | .99 oo OL | T0104] 1202 .04 | 1.05 | 1.06 .08 | 1.08 | I.09 1.65 1.69 172 1.75 1 oF 22 24 .28 a ourr tN 0 I 2 3 4 5 6 7 8 9 WO WW &w G3 INLD 34 38 .41 WwwWw Ww OON AC HLWNHO ) CONT CVO WW 6202 > W HHHNNN n TABLE 47. RATE OF DECREASE OF VAPOR PRESSURE WITH ALTITUDE. (According to the empirical formula of Dr. J. Hann). if a h —=I0- 6517 Jo J, fo = Vapor pressures at an upper and a lower station respectively. h Difference of altitude in metres, Difference of Altitude. ——=s Difference of Altitude. Fi - | Difference of Altitude. d. ca So So To metres. Feet. metres, Feet. metres. Feet. 200 656 0.93 1S00 5905 0.53 3400 T1155 0.30 400 1312 87 2000 6562 49 3600 IISII 28 600 1968 SI 2200 7218 .46 3800 12467 .26 | 800 2625 75 2400 7874 43 4000 13123 BD | > | 1000 3281 0.70 2600 $530 0.40 4500 14764 0.20 1200 3937 65 2800 g186 aif 5000 16404 7 1400 4593 61 3000 9542 35 5500 18045 14 1600 5249 57 3200 10499 32 6000 19685 12 SMITHSONIAN TABLES, WIND TABLES. Mean direction of the wind by Lambert’s formula — Multiples of cos 45°; form and example of computation . Values of the mean direction (a) or its complement (90 — a) Synoptic conversion of velocities Miles per hour into feet per second Feet per second into miles per hour Metres per second into miles per hour Miles per hour into metres per SECON aieun ee ae cmyeare to é Metres per second into kilometres per hour Kilometres per hour into metres per second Beaufort wind scale and its conversion into velocity 147 TABLE TABLE § TABLE TABLE TABLE TABLE | TABLE TABLE |! TABLE on On Go TABLE 48. MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. E—W+ (NE + SE—NW—SW )cos 45° N-—S+(NE4+ NW-—SE— SW) cos 45° Multiples of cos 45°. tana = Number, Ort a No} iON Hw DOW SONIC Ot rman NDAUNL ON HH Nn on & DOW OW HO \o OO OM] ARN OM MON nu Cony DaW& Od Nigu SO. ow NICs oor 0° WO ONNAHD UANHW bv E-—W | NS | NE-sW SE= NE | | [ — 20 | [-s1 cos 45° |[ — 22 ]x COS 45° Numerator(7). te =f [ — 22.6 ] + [ — 15.6 = [—43.2 ] | Gafiominwtor(a) i [ — 20 | 4- i — 22.6 i] -- [ — 15.6 i [ —27.0] ais the angle between the mean wind direction and the meridian. The signs of the numerator (7) and denominator (7) determine the quadrant in which a lies. When wz and d are positive, a lies between N and E: E=NE. When 2 is positive and d negative, a lies between S and E: GaeG When x and d are negative, a lies between S and W: —=SW. When 2 is negative and d positive, a lies between N and W: 148 TABLE 49. MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. Values of the mean direction (a) or its complement (go —“). a= tan-1n/d DENOMINATOR OR NUMERATOR (@ OR 7). o oO 20/| 25 | 30 45 | 50| 55| 60/| 65/ 70/| 75| 80| 85 ° ° ° ° ° ° ° o ° - ° NAAN WN He - ~} H ne MI AU WN eH _ OO COND NWN CONIA PWN He Dur wn —& Go H oni 4 HO HOW OD OAR \O Hi COO O MON DM FW NH O H 4 OnemMDNIAMNS WNNH tN OW ON DANHH WNHHH RH H HHOWMTONN DAUHL ©DNN H Ro ww N OO ONIN nN mns1 Ow N it _ -& Oo 1 HH HOW OMOODNIAD ANLLW WNHH Wn ° H uo H Bb wHH KN Cn DUN O OD 1) >¢ Oo > Ww ° NO Re mH RH Owo CO ON OV 2 G2 &» WwW Ww HD PWN H NO nN NS I 2N oO O&» Go Oo On NHN NH Du w bi NN 2 b ee ta — ONNH O rs) On O° aS n O° G» G2 G2 Od Os by NNN HN OoOnn \o nun —& + wR wHN DN nm INIA ange OwWwo Oe Dan SNNH WWWwww Wa Wd \O WWWWOH W Od G2 G2 Ge G2 = hWWNN NNHOO WwNN bd , Nb bhH Hb mons Oo Oo G2 G2 G2 G2 OG a v HHO pH NAR OW} Ga I G2 G2 GO NNDDUMNUW DD DW Ww GW Oo One G2 WwW bo On G2 G2 G2 WwNNr > iS} oO om GO ON oo as Ww 1) SMITHSONIAN TABLES 149 TABLE 49. MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. Values of the mean direction (4) or its complement (go°—a). DENOMINATOR OR NUMERATOR (d OR 2”). 2 or a. 115 120 125 130 135 140 145 150 I re ie o° 0° 0° 0° Oz OF 0° 0° 2 I I I I I I I I I I 3 2 2 I I I I I I I I 4 2 2 2 2 2 2 2 2 2 2 5 3 3 2 2 2 2 2 2 2 2 6 3 3 3 3 3 3 3 2 2 2 7 4 4 3 3 3 3 3 3 3 3 5 4 4 4 4 4 4 3 3 3 3 9 4 4 4 4 4 4 4 4 + 3 10 5 5 5 5 5 4 4 4 4 4 II 6 6 5 5 5 5 5 4 4 4 12 7 6 6 6 5 5 5 5 5 5 re 7 7 6 6 6 6 6 5 5 5 | 14 8 7 7 7 6 6 6 6 6 5 15 8 8 7 7 a, 7 6 6 6 6 (bers 9 8 8 8 7 7 7 7 6 6 a oy 9 9 8 8 5 7 7 7 7 6 | 18 ro 9 9 9 8 8 8 7 7 ai 1g 10 10 9 9 9 8 8 8 7 7 20 II 10 Io 9 9 9 8 8 8 8 21 II II 10 10 10 9 9 9 8 8 22 12 II II 10 10 10 9 “9 9 8 23 12 I2 Il II 10 10 10 9 9 9 24 13 12 12 II II 10 10 10 9 9 25 13 13 26 14 13 27 14 14 28 15 14 29 15 15 , 30 16 15 i 3r 16 16 32 17 16 33 17 17 34 18 17 35 18 18 36 1g 18 o7 19 19 38 20 19 39 20 20 40 21 20 4! 2T 20 42 22 21 43 22 21 44 23 22 45 22 22 46 24 23 47 24 23 48 25 24 49 25 24 50 25 24 SMITHSONIAN TABLES. 150 TABLE 49. MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. Values of the mean direction (@) or its complement (go’—4). DENOMINATOR OR NUMERATOR (d OR 7). 155 | 160 | 165 175 185 | 190 | 195 | 200 ° ° ° ° ° 0° oF E xe O ° HR HO ° HHHO ee ke O | = He RO H HHO ln lo to to O20203 NN WwNN KN WwNHN HK ®W NNN N ®ONN NH Woh bh WQ&wWh th an Ww Aye 4 4 5 5 6 6 6 7 7 7 8 8 8 9 ODO OOONN NNAA UANPHLH WWWNHN COONININ AHA UALPHPHRW CONINNN DADAM AHHH wW NNN AD ADAAaNUNN LHPHAPW WY POI NNIAADAD ANNES HHPHWW 00 0 COOONN NADH MPOONN NNADA AnNnnf HPPWWW WNNNH ODD MMH OCNINNNDHD DANN HHHW YH OOD OCORHRMMON NNNADAD DAUM HHPLPWW WNHNNHN SMITHSONIAN TABLES. TABLE 49. MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. Values of the mean direction (a4) or its complement (go°- a). n a—ftan-1 —- ad DENOMINATOR OR NUMERATOR (d OR 2). | 70 | 75 95 100/105); 110) 115 |120 ° CG G2 G2 Go Go On DU 2 Ne} fee NRO 4 + Nn rh Oe GH G2 WG Oo ONIN DUN SMITHSONIAN TABLES, 152 TABLE 49. MEAN DIRECTION OF THE WIND BY LAMBERT’S FORMULA. Values of the mean direction (a) or its complement (90° —a). n DENOMINATOR OR NUMERATOR (d OR 7). or sf 1301 135 | 140 | 145 | 150 | 155 | 160 165/170 175 | 180) 185 | 190 | 195 | 200: mao ae | 205) tO) Use|, wor x75) 17] ) La) TO” T6°| o©5°] I5-) Lac 44 agi || 20) To") x9 18] oxy | 174) Te 16) “IG. 153) 15°) a5} 21 20°] 20°| Z9 | 19,| 1S) } 1189)) 27 | 147 16) |perOule 5a seco 22| 21] 20] 20] 19] 19] 18] 18] 17] 17] 16 16 | 16 22 22 21, |) 2 | 8201 |) £G*|| 2G | TOs) akon eye 7 AZ 16 23 22 22952 af | 20) || eTQ:|)" EG) Lou) 2 LO} A177, 17 | 24 23 220" 1224 2ir 271 | 20) 9204) uO) eL9 15 1S 1) 25 24 2B0\ 22) eno |e 20 2) 20m 20))|| a9 19 18 18 25 24 2A 23 22 22 21 21 20) | 20 1g 1g 18 26 25 DA ty 2An| 23, |), 222° (12 22))| 2k 20) 20 ZOU ASL 29 27 261) 25) | 24) |) 245|) 23) 22)|( 922) 2 || 2h 20 20) | LO 272620) | 25) eae) 24-|) 23, (e229 22) 205) 2b 2 eed Bol ee27o| w2Ouls 2orl 25) 240 245| 23) 220) 9225) 20. 28 ee 28 | 28] 27] 26] 25] 25 | 24} 23 Bue 22) 122m ee ies eee BoM es ez ale 2726 |( eon) 250 242 oel 25 ee eee eee ee Bon We2Qul G25.) 27oNe2 7 20) 25r\) 25) Ae) 23n Mean aa ee 30 | 29| 29| 28| 27] 26| 26| 25| 24] 24] 23 | 23] 22 2 30 | 29] 28] 28] 27] 26| 26] 25) 24) 24) 23) 23 251) 3 30 | 29 | 28| 28| 27] 26) 26] 25] 24| 24] 23 We 2 |) 3r ly 30) |) B04) 2on)) 28: 277) 27 26m 2A wees) | ee Aw lees: | Sah 320| Bis 304 12g.) 29. |) 20) 527 427 26 |" 25) | 2 24 | 33 | 32] 32) 31] 30| 29] 28| 28] 27 26) 26} 25] 25 | 34 | 33 | 32) 33 | 30| 30] 29] 28) 28). 27 26)1| 268 S25 34 | 34|° 33 | 32| 31 | 30| 29] 29] 28| 27) 27 | 26) 26 | 35 | 34| 331 32| 3z| 3z| 30] 29| 29| 28} 27] 27] 26) SOV es Sule SA Soe esas la eGOn le oOn 29 28 28 272i, 36 | 35 | 34| 33] 33| 32| 32 | 30| 30| 29] 28) 28) 27 |] 37 | 36| 35| 341 33} 32| 31] 32} 30| 29| 29) 28) 27 S70) Oi G5) ail 34 |, 33.) S2 |b | 30°29: || 208); sae Ba) acl 930 |. Gat ub34-1 33) | 3270321 Bit Sal 303) 204 eee BSS P aI eSOt! Gor a5 a Nes4e 65) (Oe Wr Skul Shei oos|e Saal are Bode SO S37 alison sabe wedulh GS lw Sou|) o> kha) pons oe, | lee Boal eso), S70) BO" aon! Sant a4 [oe | S24) /92)) OP) 6 307) oe Aon) 39.) 38:7) | 930 | 135 |. 34 | 34 33) 32) - 32 1 Sh oe 4o| 39| 38} 37 | 36] 36] 35 | 34] 33) 33-| 32) 3%) 3% At | “40 1) =39 |; 38 | 37 | 36} 35'|' 34 1°34 | 33.) 32.) 327) 38 4r| 40] 39] 38] 37| 36] 36] 35] 34] 33] 33) 32) 3! 42| 4z.| 40} 30) 38) 37'| 36) 35 | 35.) 34) 33) 32) 3? Bue Aw 400 3603S) i370! 37. | Sort. 30.) B43 35 |e 42| 41 | 40| 40} 39] 38| 37] 36) 35] 35] 34} 33) 33 | 43 2} '4r| 40 | 39 | 38 | 37 | 37 | 36 35) 34) 34) 33) 43 | 42| 41} 4o| go] 39] 38] 37| 36] 35] 35| 34] 33) 44| 43 2} 4r| 40| 39| 38} 37| 37] 36| 35} 34) 34 44| 43) 42| 4} 40| 39] 39] 38| 37] 36] 36) 35) 34| 45| 44| 43| 42| 41 | 40| 39| 38| 37] 37] 36] 35] 35 45| 44| 43| 42] 4r| 40] 39] 39] 38] 37] 36] 36] 35 44 | 4gi\942 | 4a) 4x)! wo} 39.1, 48:1) 38) 137.)30 |) 35 45 | Aa) \ Ag) 42) e40 |, A939. esos) 88, B7_| SSui".38 44| 43| 42| 42| 42] 40] 39| 38] 38] 37] 36| AS. | ae Laz) | ade eae Ry fOr SON 39, 1°38: 374" 37 45 | 44| 43| 42] 41] 41] 40) 39] 38) 39 | 37 | | SMITHSONIAN TABLES. 153 TABLE 50. SYNOPTIC CONVERSION OF VELOCITIES. Miles per hour into metres per second, feet per second and kilometres per hour. “Miles | Metres Feet |Kilome-| Miles | Metres Kilome-[ Miles | Metres | Feet | Kilome- per per per per per p per per per | tres per hour. | second. second. | - | hour. | second. - | hour. | second.| second.| hour. 0.0 0.0 | 7 : 11.6 : 52-0) 23:25 | 7ormaleeat, 0.5 2. : 0.8 : 11.8 9 | y 52.5 2335) 7/7720 4 OASs 1.0 ; ; : : 12.1 : A3. 53.0) | 23°78 az7e7a) 1598 1.5 ; , y ; T2305 e40: 4. 53.5 23:9), || 78:50 || woos 2.0 ‘ 12.5 : 2 54.0 24.1 79.2 | 86.9 2.5 12.7 : 54.5 | 24.4 | 79.9 | 87.7 3.0 13.0 46. 55.0 | 24.6 | 80.7 | 88.5 3.5 13:2 : : 55-5 24.8 | 81.4 | 89.3 4.0 13.4 : Be 56.0 | 25.0 | 82.1 | go. 4.5 13.6 : 56.5 25.3 | 82.9 | 90.9 5.0 13.9 : 57.0 25.50 | 63:6" || ony 5.5 14.1 : 57-5 | 25-7 | 84.3 | 92.5 14.3 58.0 | 25.9 | 85.1 | 93.3 14.5 58.5 26.2 | 85.8 | 94.1 14.8 59.0 | 26.4 | 86.5 | 95.0 15.0 59.5 26.6 | 87.3 | 95.8 15.2 60.0 | 26.8 | 88.0 | 96.6 15.4 97-4 15.6 98.2 15.9 99.0 16.1 99.8 16.3 100.6 16.5 IOI.4 16.8 : 3. : 102.2 NNN HH DM HAW ORO | {OO COMINGS 7S © OOnR AM CAR HOY AbO on nnn un ID ARGON A to 3 ° HON O Nb NNNHN Sa NINN 17.0 : : 3. : 103.0 T7e2. : : 4. 8 : 103.8 17.4 ; 2. : : ; 104.6 17.7 . Be ; : .I_ | 105.4 17.9 3 : : 3 F 106.2 107.0 CAR mae o : 30.€ 107.8 18.6 : : 30.2 : 108.6 109.4 | 110.2 III.O 111.8 2 2 3 ay Be 3 4. 4. 4. 4. 4. 53 5: 5 5 6 6 6 6 6 DAR HON Now wh HD nebo —— NNN SI 5 O T1227 113.5 114.3 115.1 115.9 116.7 Ge 90 90 G0 G0 Oo ONN WoO Udo WNNHKR NH HN O sISIs DLIDA BRON? &» tO bo S CO WG ONO 117.5 118.3 119.1 119.9 120.7 121.5 co GW G2 OM BWW Nw PORN MAWAOD LN > DW GW G2 G2 Go Go OG» Go OG» G2 DH WII AUB g A MOKA 122.3 123.1 123.9 124.7 | 125.5 mW WWW WW WD 2&2 G2 G2 U2 eS > 0.0 n+. & on uo p On HERUODOD AUNOH< Psaanunn sus w se Oo SMITHSONIAN TABLES. 154 TABLE 51. MILES PER HOUR INTO FEET PER SECOND. 1 mile per hour = feet per second. Miles | per hour. Feet per|/Feet per/Feet per Feet per/Feet per/Feet per|Feet per|Feet per F eet te ‘eet per sec. sec. sec sec. sec sec, sec. sec sec. sec. 0.0 1.5 2.9 : : (Bs 8.5 10.3 11.7 14.7 16.1 17.6 : 20. 22.0 2355 24.9 29.3 30.8 32.3 s 5. 36.7 38.1 39.6 44.0 | 45.5 | 46.9 . 49. 51-3 | 52:8 | 54.3 58.7 60.1 61.6 : 4. 66.0 67.5 : eu 74.8 76.3 ; ! 80.7 82.1 88.0 89.5 90.9 . : 95-3 96.8 102.7 | 104.1 | 105.6 : 3 1aKoyfe} ||| aeierens 117.3 | 118.8 | 120.3 : ; 124.7 | 126.1 132.0 | 133.5 | 134.9 : BT. 139.3 | 140.8 146.7 | 148.1 | 149.6 , : 154.0 | 155.5 161.3 | 162.8 | 164.3 : ; 168.7 | 170.1 176.0 | 177.5 | 178.9 : 31. 183.3 | 184.8 190.7 | 192.1 | 193.6 : ; 198.0 | 199.5 205.3 | 206.8 | 208.3 : : 212 7)|| 20 AeT TABLE 52. FEET PER SECOND INTO MILES PER HOUR. oO 1 foot per second =4 miles per hour. Miles Miles Miles Miles Miles Miles Miles Miles Miles Miles per hr.} per hr.| per hr.; per hr.| per hr. | per hr. | per hr. -| per hr. | per hr;| 0.7 1.4 2.0 27, 3.4 4.1 0 Se 6.1 7.5 8.2 8.9 9.5 10.2 10.9 , iv 13.0 14.3 : 15-7 16.4 17.0 077 3.4 ). 19.8 2TK . 22.5 23.2 23-9 24.5 26.6 28.0 3 29.3 30.0 30.7 31.4 33.4 wh Nu On Co 34.8 ‘ 36.1 36.8 37.5 38.2 41.6 : 43.0 43.6 44.3 45.0 48.4 : 49.8 50.5 51.1 51.8 55-2 : 56.6 Bee 58.0 58.6 62.0 ; 63.4 64.1 64.8 65.5 40.2 47.0 93-9 | 60.7 7-5 | DOG HO ConshMN DONA, mW Uno Nn & Go 68.9 ' 70.2 : 71.6 75-7 0. 77-9 /7- 78.4 82.5 : 83.9 34. 85.2 89.3 g0.0 90.7 : 92.0 96.1 96.8 97.5 : 98.9 74-3 SI.1 88.0 94.8 101.6 Ge wo mon! Bs MOOI Dn ONNON 8 co : Oo wu AaI0 103.6 | 104.3 : 105.7 : Ts 4 108.4 LIOTS | |PILESE SON pene : 3 . II5.2 | D073 ||) eks:0 3, 119.3 Z : 21%, 120.0 | 124.I | 124.8 5 126.1 26.8 : 8. 128.9 | 130.9 | 131.6 53 | 133-0 : : 35. 135-7 | SMITHSONIAN TABLES, 155 TABLE 53. METRES PER SECOND INTO MILES PER HOUR. I metre per second — 2.236932 miles per hour. | Metres per second. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Miles | Miles | Miles Miles Miles Miles | Miles Miles Miles Miles per hr. | per hr.| per hr.| per hr.| per hr. | per hr. | per hr. | per hr.| per hr. | per hr. 0 0.0 O:2 0.4 0.7 0.9 Tet m2 1.6 1.8 2.0 I 22s 285 eT, 2.9 351 3.4 3.6 3.8 4.0 4.3 2 4.5 AF 4.9 5.1 5.4 5.6 5.8 6.0 6.3 6.5 3 6.7 G95) 872 7-4 7.6 7.8 8.1 8.3 8.5 8.7 4 8.9 9.2 | 9.4 9.6 9.8 10.1 10.3 10.5 10.7 II.O 5 Lie LI. | 6 11.9 12.1 12.3 12.5 12.8 13.0 13.2 6 13.4 13.6 13.9 14.1 14.3 14.5 14.8 15.0 15.2 15.4 7 1537, 15.9 16.1 16.3 16.6 16.8 7/0) 172 17.4 77 8 17.9 18.1 18.3 18.6 18.8 19.0 19.2 19.5 19.7 19.9 9 20.1 20.4 20.6 20.8 21.0 21a2 215 DI 21.9 2OuT 10 22.4 22.6 22.8 23.0 2252 23.5 23.7 23.9 24.2 24.4 II 24.6 24.8 25.1 25.3 25.5 25.7 25.9 26.2 26.4 26.6 12 26.8 27.1 2752 2765 Diet, 28.0 28.2 28.4 28.6 28.9 13 29.1 29.3 29.5 29.8 30.0 BON 30.4 30.6 30.9 ata 14 2162 3135 31.8 32.0 2210 BOA 32.7 220 Socr Be. 15 33:6'| 33:8: | 34:07] 9.3452" |) 34047 aA eA Ong 5at a 635 -om lmao 16 35.8 36.0 | 36.2 36.5 36.7 36.9 B71 37.4 37-6 37.8 17 38.0 | 38.3 | 385 | 38.7 | 389 | 39.1 | 39-4 | 39-6 | 39.8 | 40.0 18 40.3 40.5 40.7 40.9 Aire 2 AI.4 41.6 41.8 42.1 2.3 19 42.5 | 42.7 | 43.0 | 43.2 | 43.4 |, 43-6 | 43.8 | 44.1] 44.3 | 44.5 20 | 44.7 | 45.0 | 45.2 | 45.4 | 45-6 | 45.9 | 46.1 | 46.3 | 46.5 | 46.8 ZT 47.0 47.2 47.4 47.6 47.9 48.1 48.3 48.5 48.8 49.0 22 49.2 49.4 49.7 49.9 50.1 50.3 50.6 50.8 51.0 51.2 23 51.5 51.7 51.9 52.1 52.3 52.6 52.8 53-0 53.2 53-5 24 53-7 53-9 54-1 54-4 54.6 54.8 55-9 55-3 D020 |) oe 25 55-9 | 56.1 | 56.4.) 56.6 | 56,85) 57:01 57-3 1) (57-5 || Poder Wor 26 58.2 58.4 58.6 58.8 59.1 59.3 59.5 59.7 60.0 60.2 27 60.4 60.6 60.8 61.1 6153 61.5 61.7 62.0 | 62.2 62.4 28 62.6 | 62.9 63.1 63.3 63.5 63.8 64.0 | 64.2 64.4 | 64.6 29 64.9 65.1 65.3 65.5 65.8 66.0 66.2 66.4 66.7 66.9 30 67.1 67.3 67.6 67.8 68.0 68.2 68.5 68.7 68.9 69.1 ar 69.3 69.6 69.8 70.0 70.2 70.5 70.7 70.9 7XeL 71.4 | 32 71:6: |..'7I.8 |. 7210 |) 17223 A 72: 72.7 ||. 2.9, | “Zeal 73-4 | 73-6 33 73-8 74.0 74:3 74-5 74-7 74.9 75-2 75-4 75-6 75-8 34 70.0 | 76.3 | 7605 | 87617" P7720 17752 | aah 7g OMe 7 Ma 35 78.3 78.5 78.7 79:0) | 702 79.4 79:56) 11 179.0 al eLOOnL 80.3 36 80.5 80.8 81.0 81.2 81.4 81.6 81.9 82.1 82.3 82.5 37 82.8 | 83.0 | 83.2 83548307, 84.0 | 84.1 84.3 | 84.6 | 84.8 38 $5.0 85.2 85.5 85.7 85.9 86.1 86.3 86.6 86.8 87.0 39 87.2 87.5 87.7 87.9 88.1 88.4 88.6 88.8 89.0 89.3 40 89.5 89.7 89.9 | 90.2 | 90.4 90.6 | 90.8 | 91.0 | 91.3 | 91.5 41 QI.7 91.9 92.2 92.4 92.6 92.8 93.1 93-3 93-5 93-7 | 42 94-0 | 94.2 | 94.4 | 94.6 | 94.8 | 95.1 | 95-3 | 95-5 | 95-7 | 96.0 43 96.2 | 96.4 | 96.6 | 96.9 | 97.1 | 97.3 | 97-5 | 97-8 | 98.0 | 98.2 44 98.4 | 98.7 | 98.9 | 99.1 | 99.3 | 99.5 | 99.8 | 100.0 | 100.2 | 100.4 SmJTHSONIAN TABLES 156 Metres per second. TABLE 53. METRES PER SECOND INTO MILES PER HOUR. Miles per hr. 100.7 102.9 105.1 107.4 109.6 111.8 II4.1I 116.3 118.6 120.8 MILES PER HOUR 0.1 Miles per hr. 100.9 103.1 105.4 107.6 109.8 [i2.0 114.3 116.6 118.8 121.0 123.3 125.5 127.8 130.0 132.2 0.2 Miles per hr. LOD. 1 103.3 105.6 107.8 LIOCE e253 II4.5 116.8 119.0 120.3 Oo RNG anonn ) eat et eS et WWwWNNN oO Nv 0.3 Miles Der Ut. IOI.3 103.6 105.8 108.0 110.3 R25 114.8 117.0 I1g.2 eet, 123.7 126.0 128.2 130.4 R327 Miles per hr. ro1.8 104.0 106.3 108.5 110.7 113.0 115.2 117.4 119.7 121.9 124.2 126.4 128.6 130.9 meee Miles per hr. I02.0 104.2 106.5 108.7 IIt.o Tise2 115.4 D7, 119.9 T22er 124.4 126.6 128.9 TTT 133-3 1 mile per hour — 0.4470409 metres per second. 0.8 Miles per hr. 102.5 104.7 106.9 109.2 I1I.4 113.6 115.9 118.1 120.4 122.6 124.8 12721 129.3 131.6 133.8 0.9 Miles j per hr. 102.7 } 104.9 | 107.2 |} 109.4 | 111.6 113.9 116.1 118.3 20:6) 4 122750) a WWwWNNN BHONTU 0 MUW H TABLE 54. INTO METRES PER SECOND. Miles per hour. 0 metres per sec. 0.00 SMITHSONIAN TABLES. metres per sec. 0.45 4.92 9-39 13.86 18.33 22.80 27-27 31.74 36.21 40.68 45-15 49.62 54-09 58.56 63.03 metres per sec. 0.89 5.36 9.83 14.31 18.78 o2125 27.72 32.19 36.66 41.13 45.60 50.07 54-54 59.01 63.48 metres per sec. 1.34 5.81 10.28 14.75 19.22 | 23.69 28.16 32.63 37.10 41.57 metres per sec. 1.79 6.26 10.73 15.20 19.67 24.14 28.61 33-08 37-55 42.02 46.49 50.96 55-43 59.90 64.37 157 metres per sec. 2.24 6.71 11.18 15.65 20.12 24.59 29.06 33-53 38.00 42.47 46.94 51.41 55.88 60.35 64.82 metres per sec. 2.68 7-15 a oy 16.09 metres per sec. 3-13 7.60 12.07 16.54 21.01 co mnSo GO OPON DO nu WO bh nN Ww metres 3-58 0.05 12.52 16.99 21.46 25.93 30.40 34.87 39-34 43.81 48.28 52-75 57.22 61.69 66.16 per sec, metres | per sec. 4.02 8.49 12.96 17.43 21.91 | 26.38 | 30.85 35-32 39-79 44.26 48.7: 53-2¢ 57-67 62.14 66.61 TABLE 55: METRES PER SECOND INTO KILOMETRES PER HOUR. I metre per second — 3.6 kilometres per hour. | Metres per | iencande 00 | 0.1 0.2 | 0.3 0.4 0.5 0.6 0.7 | 0.8 | 0.9 km. km. | km. km. km. km. km. km. kin. per hr.| per hr.| per hr.| per hr.| per hr.| per hr.| per hr.| per hr.}| per hr. 0 0.0 0.4 0.7 I.I I.4 1.8 2X2 2.5 2.9 aro I 3.6 4.0 4.3 4.7 5.0 5.4 5.8 6.1 6.5 6.8 2 aD 7.6 7-9 8.3 8.6 9.0 9.4 9.7 10.1 10.4 3 10.8 Dl-2 Ts 11.9 12.2 12.6 13.0 13.3 1387) 14.0 | 4 14.4 14.8 15.1 15.5 15.8 16.2 16.6 16.9 1753 17.6 | 5 18.0 18.4 18.7 1g.1 19.4 19.8 20.2 20.5 20.9 202 6 216 22.0 22.3 2ONT 23.0 23.4 23.8 24.1 24.5 24.8 7 252 25.6 25.9 26.3 26.6 27.0 27.4 2a 28.1 28.4 8 28.8 29.2 29.5 29.9 30.2 30.6 31.0 31.3 Tay 32.0 9 32.4 | 32.8 | 33-1 | 33-5 | 33-8 | 34.2 | 34.6 | 34.9 | 35.3 | 35.6 10 36.0 36.4 36.7 Bia 37.4 37.8 38.2 38.5 38.9 39.2 IT 39.6 4o 2 40.3 40.7 41.0 41.4 41.8 42.1 42.5 42.8 12 43.2 | 43-6 | 43.9 | 44.3 | 44.6 | 45.0 | 45.4 | 45.7 | 46.1 | 46.4 13 46.8 | 47.2 | 47-5 | 47-9 | 48.2 | 48.6 | 49.0 | 49.3 | 49.7 | 50.0 14 50.4 50.8 RT 51.5 51.8 52.2 52.6 52.9 53.3 53.6 15 54.0 | 54.4 | 54-7 | 55-2 | 55-4 | 55-8 | 56.2 | 56.5 | 56.9 | 57.2 16 57.6 58.0 58.3 58.7 59.0 59.4 59.8 60.1 60.5 60.8 heen 61.2 61.6 61.9 62.3 62.6 63.0 63.4 63.7 64.1 64.4 8 64.8 65.2 65.5 65.9 66.2 66.6 67.0 67.3 67.7 68.0 19 68.4 68.8 69.1 69.5 69.8 70.2 70.6 70.9 718 71.6 | 20 72.0 | 72.4 | 72.7 | 73-0 | 73-4 | 73-8 | 74.2 | 74.5 | 74.9 | 75-2 oT 75.6 76.0 76.3 76.7 77.0 77-4 77.8 78.1 78.5 78.8 22 79.2 79.6 79.9 80.3 80.6 81.0 87.4) 81-7 82.1 82.4 23 $2.8 83.2 83.5 83.9 84.2 84.6 85.0 85.3 85-7 86.0 24 86.4 | 86.8 | 87.1 87.5 | 87.8 88.2 88.6 | 88.9 | 89.3 | 89.6 25 g0.0°| 90:4) || 90.7) | “ors gI.4 OL. SA 192.2 92.5 92.9 | 93.2 26 93-6 | 94.0 | 94.3 | 94.7 | 95-0 | 95-4 | 95-8 | 96.1 | 96.5 | 96.8 27 97-2 | 97-6 | 97.9 | 98.3 | 98.6 | 99.0 | 99.4 | 99.7 | Ioo.I | 100.4 28 100.8 | IOL.2 | IOL5 | TOL.9 | 102.2 ||, 102.6 | 103.0 | 103-3 || 103:7° || 10470 106.6 | 106.9 | 107.3 | 107.6 29 104.4 | 104.8 | 105.1 | 105.5 | 105.8 | 106.2 | 30 108.0 | 108.4 | 108.7 | 109.1 | 109.4 | 109.8 oT OM MG e-Noln| bering kewl amie nc A ant Woy |maaiel lesion Il sour. | atawlasy [| niy4is) 32 II5.2. | TE5:O. | 1T5-9) | Li6.38 | LL6/G | 117.0 | 7A ay, eo teeter 33 LIS.8" || TIO} 24/ LI9s50 | LTO. 9) | l20)29 || -120/6. | 12-0 S12 Tai ee alee sO 34 122.4 | 122.8 |) 122.1 | 123%5) | 12358 | 1243204) 1246) | encom er25. 3) we 5eO 35 [26.0 | 126.4 | 126.7, | 127.1 5) 127-4) || 127:8) \e128.2) | 128i 5nnes.95 | areo.2 36 129.6 .| 130.0; |.130:3) || 130:7 )|| 13L-0) | 131.4) 03r.8) reese 13255 iGieers 37 133-2 | 133-6 | 133-9 | 134-3 | 134.6 | 135.0 | 135.4 | 135.7 | 136.1 | 136.4 38 136.8: (13722: |) 137-5) | 13729, ||) 138:20 |, 138:60 39:0 4013053 302 7a tA OO 39 140.4 | 140.8 | I4I.I | I41.5 | 141.8 | 142.2 | 142.6 | 142.9 | 143.3 | 143.6 SI 40 144.0 | 144.4 | 144.7 | 145.1 | 145.4 | 145.8 4I 147.6 | 148.0 | 148.3 | 148.7 | 149.0 | 149.4 42 T5062. [051.6 |)" I50.9) || P5253 lel 52.OMl el5ac0 43 154.8 | 155.2 | 155-5 | 155.9 | 156.2 | 156.6 44 158.4 | 158.8 | 159.1 | 159.5 | 159.8 | 160.2 SMITHSONIAN TABLES, | 1 : TABLE 55. | METRES PER SECOND INTO KILOMETRES PER HOUR. eee “second, é 0.8 | 0.9 — km. km. sm, =m. km. km. per hr. Sper ur, | per hr. : . | pe r. | per hr; per hr. 162.4 ; 163.1 | 163.4 3.8 ; 164.9 | 165.2 166.0 : 166.7 | 167.0 Me ;. 168.5 | 168.8 169.6 ; 170.3 | 170.6 Fate : 172.1 || 172.4 173.2 ae T7e8.OF |) L74e2 : 5. 175.7 | 176.0 | 176.8 : alg 7 ialy AV lrg exe: . B: T7923) 79.64 180.4 By, ||) aitsyigae | aitsyeyel 31.8 32. 182.9 | 183.2 184.0 34.3 | 184.7 | 185.0 : : 186.5 | 186.8 187.6 a7: 188.3 | 188.6 39. : 190.1 | 190.4 191.2 : I9I.9 | 192.2 : iB 193.7 | 194.0 194.8 : 195.5 | 195.8 ; : 197.3 | 197.6 198.4 BS 199.1 | 199.4 8 200.5 | 200.9 | 201.2 202.0 ayy 202.7 | 203.0 A 204.1 | 204.5 | 204.8 | 205.6 ; 206.3 | 206.6 : 207.7 | 208.1 | 208.4 209.2 : 209.9 | 210.2 ; 25E, 3h 2 ial || 20220 DIS e2 L328 : 214.9 | 215.3 | 215.6 TABLE 56. KILOMETRES PER HOUR INTO METRES PER SECOND. 10 1 kilometre per ona AG metres per second. | ‘Kilome'res | per hour. | metres | metres | metres | metres | metres | metres | metres | metres | metres per sec. | per sec. | per sec. | per sec. | per sec. | per sec. | per sec. | per sec. | per sec. | per sec. 0.00 0.28 0.56 0.83 Ted 1.39 1.67 1.94 2522 2.50 | .78 3.06 3.33 3.61 3.89 4.17 4.44 4.72 5.00 5.28 | 5.56 5.83 6.11 6.39 6.67 6.94 722 7.50 7.78 8.06 | 3 8.61 8.89 9.17 9.44 9-72 | 10.00 | 10.28 | 10.56 | 10.83 | TsO) LLO7 al LUOAN | L2!225 | eT s5Om 1275.9 TesOG) | els-sanlh 1atoL metres | 14.17 | 14.44 | 14.72 | 15.00 | 15.28 | 15.56 | 15.83 | 16.11 | 16.39 16.94) |) 17.22.) 17-50: ||| 17-76) | 18.06 | 18533 | 18:61 |) 18:89) | 19.57 19:72) |"20;00))|| 20:28) ||. 20:56) ||) 20.83) 21.11 | 21.67 | 21.94 22.50 | 22.78 | 23.06 2x23 722.01 ((c23.09 aly | 24.4A | oAe72 25.28 | 25.56 | 25.83 |; 26.11 | 26.39 | 26.67 -94 | 27.22 | 27.50 28.06 | 28.33 | 28.61 | 28.89 | 29.17 9.44 : 30.00 | 30.28 30:83) ||| 30-11 || 31-39) | 31.67 | 31.94 | 32.22 | 32.50) | 22.78 |) 33.06 33-61 | 33-89 | 34-17 | 34-44 | 34.72 | 35.00 | 35.28 | 35.56 | 35.83 36.39 | 36.67 | 36.94 | 37-22 | 37.50 | 37-78 | 38.06 | 38.33 | 38.61 39.17 | 39-44 | 39.72 | 40.00 | 40.28 | 40.56 | 40.82 41.39 41.94 | 42.22 | 42.50 | 42.78 | 43.06 Baan By 8 44.17 44.72 | 45.00 | 45.28 | 45.56 | 45.83 | 46.11 ae : 46.94 47.50 | 47.78 | 48.06 | 48.33 | 48.61 | 48.89 : 49. 49.72 50.28 | 50.56 | 50.83 | 51.II | 51-39 | 51.67 : 52. 52.50 53-06 | 53-33 | 53-61 | 53-89 | 54-17 | 54.44 : : 55-25 SMITHSONIAN TABLES. TABLE 57. BEAUFORT WIND SCALE AND ITS CONVERSION INTO VELOCITY. Velocity in miles per hour. Designation. Calm. Light air. Light breeze. Gentle breeze. Moderate breeze. Fresh breeze. Strong breeze. Moderate gale. Fresh gale. Strong gale. Whole gale. Storm. Hurricane. * Velocity 3.3 is assigned to 0.5 grade. (a.) COLONEL SIR HENRY JAMES: Instructions for taking meteorological obser- vations; with tables for their correction and notes on meteorological phenomena, 8vo. Lond., 1860. (6.) GEORGE NEUMAYER: Discussion of the meteorological and magnetical observations made at the Flagstaff Observatory, Melbourne, during the years 1858 to 1863. 4to. JJannhetm, 1867. (c.) J. K. LAuGHTON: Physical geography and its relation to the prevailing winds and currents. 8vo. Lond., 1870. 2ded., 8vo. Lond., 1873. (d.) C.A.ScHorr; Meteorological observations in the Arctic seas. By Sir Francis Leopold McClintock, R. N. Made on board the Arctic searching yacht ‘‘Fox,”’ in Baffin Bay and Prince Regent’s Inlet, in 1857, 1858 and 1859. Reduced and discussed by Charles A. Schott. Sizithsonian Contributions to Knowledge, 146. Washington, 1862. (e.) Robert H. Scorr: An attempt to establish a relation between the velocity of the wind and its force (Beaufort scale). Quarterly Journal Meteorological Society, Lond., 1874-’75, ii, p. 109-123. Instructions in the use of meteorological instruments. Compiled by direction of the Meteorological Committee. 8vo. Lond., 1877. 160 GHODETICAL TABLES. Relative acceleration of gravity at different latitudes Length of one degree of the meridian at different latitudes . Length of one degree of the parallel at different latitudes Duration of sunshine at different latitudes Declination of the sun for the year 1894 Relative intensity of solar radiation at different latitudes for the first and sixteenth day of each month 161 TABLE TABLE TABLE TABLE TABLE TABLE 538 59 60 61 63 TABEE 58. RELATIVE ACCELERATION OF GRAVITY AT DIFFERENT LATITUDES. Ratio of the acceleration of gravity at sea level for each 10’ of latitude, to its acceleration at latitude 45°. S% S45 = I — 0.002662 cos 2 Latitude. 0’ 0.997 338 340 345 DI9 364 0.997 378 396 417 441 468 0.997 499 0.997 695 742 793 846 902 0.997 961 0.998 022 085 151 219 0.998 259 361 435 511 589 0.998 669 750 833 917 0.999 003 0.999 090 0.999 538 DR mn Se RTE TSE OR RRR SR RE TS SE SMITHSONIAN TABLES, 10’ 0.997 338 340 346 354 366 0.997 381 399 42 445 473 0.997 504 538 574 614 657 0.997 702 751 502 856 gi2 0.997 971 0.998 032 096 162 230 0.998 301 373 445 524 603 0.998 682 ae 547 931 0.999 O17 0.999 104 192 281 371 462 0.999 5 6 fk S Tonneiies Sy 04: 3 30 2 > 3 9 I.000 O15 20’ 0.997 338 341 347 356 368 0.997 384 403 425 450 478 0.997 599 544 581 621 664 0.997 710 759 SII 865 922 0.997 981 0.998 043 3 107 173 242 0.998 313 386 460 Sov 616 9.995 696 778 861 946 0.999 032 0.999 119 207 296 356 477 0.999 568 660 753 545 938 1.000 030 162 30’ 0.997 338 342 348 358 371 0.997 387 406 429 454 483 0.997 515 550 587 628 672 | 0.997 715 767 81g 874 931 0.997 991 0.998 053 118 185 254 0.998 325 398 473 550 629 0.998 709 79! 975 960 0.999 046 0.999 133 222 311 401 492 0.999 584 676 768 861 954 1.000 046 40’ 0.997 339 343 350 360 373 0.997 390 410 433 459 4858 0.997 520 556 594 635 679 0.997 726 776 $28 883 941 0.998 OOo! 064 129 196 265 0.998 337 4Io - 486 563 642 0.998 723 805 889 974 0.999 060 0.999 148 237 326 416 597 0.999 599 691 783 876 970 1.000 062 50’ 0.997 339 344 351 362 376 0.997 393 413 0.997 734 786 837 893 951 0.998 O11 074 140 207 277 0.998 349 423 499 576 656 0.998 737 819g 903 988 0.999 975 0.999 163 251 341 431 523 0.999 614 706 799 892 985 1.000 077 TABLE 58. RELATIVE ACCELERATION OF GRAVITY AT DIFFERENT LATITUDES. Ratio of the acceleration of gravity at sea level for each 10’ of latitude, to its acceleration at latitude 45°. 28 y= 0.002662 cos 2h £45 Latitude. 0’ 10’ 20’ 30/ 40’ 50/ 45° 1.000 000 1.000 O15 1.000 030 1,000 046 1.000 062 1.000 077 46 093 108 124 139 155 70} 47 186 201 217 232 247 202% 48 275 294 309 324 340 SOON 49 370 386 401 416 432 447 50 1.000 462 1.000 477 1.000 493 1.000 508 1.000 523 1.000 533 | 51 553 569 584 599 614 629 52 644 659 674 689 704 719 | 53 734 749 763 778 793 808 | 54 $23 837 852 867 881 $96 | 55 1.000 910 1.000 925 1.000 940 1.000 954 1.000 968 1.000 983, | 56 0 997 I O12 I 026 I O40 1 054 1069 | By 1 083 I 097 Tee 1125 I 139 1153 | 58 I 167 1 181 I 195 I 209 I 222 1236 | 59 I 250 I 263 1277 I 291 I 304 318: | 60 I.00I 331 I.001 344 I.001I 358 I.00I 371 I.0OL 384 1.001 397 61 I 4II I 424 I 437 I 450 I 463 1 476 62 I 489 I 501 I 514 I 527 I 540 1552 | 63 I 505 1577 I 590 I 602 I 614 I 627 | 64 I 639 I 651 I 663 1675 1 687 I 699 65 I.00I 711 T.00I 723 1.001 735 1.001 746 1.001 758 I.00I 770 66 I 781 I 793 1 S04 1815 1 $27 1 838 67 1 849 1 860 1 871 1 882 1 893 I 904 68 I 915 1926 | I 936 I 947 I 957 1968 | 69 1978 1 989 I 999 2 009 2 019 2029 | | 70 1.002 039 1.002 049 1.002 059 1.002 069 1.002 078 1.002088 | 71 2098 2 107 ZT 2 126 Q1a5 2144 7 2154 2 163 2B72 2 181 2189 2198 | 7a 2 207 2216 2 224 2232 2 241 2249 | 74 2 258 2 266 2 274 2 282 2 290 2298 | | ae) 1,002 305 1.002 313 1.002 321 1.002 328 1.002 336 1.002 343 | 76 2 350 2 358 2 365 DAUD 2 379 2 386 a7 2 393 2 399 2 406 2 413 2 419 2 426 78 2 432 2 438 2444 2450 2 456 2 462 fe. 79 2 468 2 474 2 480 2 485 2 491 2496 | | | 80 1.002 501 1.002 507 1.002 512 1.002 517 1.002 522 1.002 527 eet 2532 253 2 541 2 546 2 550 2555 | 82 2559 2 563 2 567 2571 2575 2579 3 2 583 2587 2590 2594 2597 2 601 | 84 2 604 2 607 2 610 2 613 2 616 2619 | 85 1.002 622 1.002 624 1.002 627 1.002 629 1.002 632 1.002 634 | 86 2 636 2 638 2 640 2 642 2 644 2 646 87 2 647 2 649 2 650 2 652 2 653 2 654 88 2655 2 656 2 657 2658 2 659 2660 | 89 2 660 2 661 2 661 2 662 2 662 2 662 | SMITHSONIAN TABLES. 163 TABLE 59. LENGTH OF ONE DEGREE OF THE MERIDIAN AT DIFFERENT LATITUDES. t 1 Latitude. Metres. Sears Comes. "| Latitude. a 1’ of the Eq. 0 110 568.5 68.703 ; 59.594 45° I 110 568.8 68.704 59.594 46 2 110 569.8 68.705 59.595 47 3 IIO571.5 68.706 59.596 48 4 110573.9 | 68.707 59-597 49 5 110577.0 68.709 59.598 50 6 110 580.7 68.711 59.600 51 7 I110585.1 68.714 59.603 52 8 110 590.2 68.717 59.606 53 9 110 595.9 68.721 59.609 54 110 602.3 68.725 59.612 55 Il 110 609.3 68.729 59.616 56 12 I10617.0 68.734 59.620 57 13 110 625.3 68.739 59.625 58 14 110 634.2 68.745 59.629 59 fen 110 643.7 68.751 59.634 60 | 16 110 653.8 68.757 59.640 61 17 110 664.5 68.763 59.646 62 [ieee 110 675.7 68.770 59.652 3, eee 110 687.5 68.778 59.658 64 20 110 699.9 68.786 59.665 65 21 110 712.8 68.794 59.672 66 22 110 726.2 68.802 59-679 7 23 110 740.1 68.810 59.686 68 | 24 110 754.4 68.819 59.694 69 | | 25 110 769.2 68.829 59.702 70 26 110784.5 | 68.838 59.710 71 27 110 800.2 68.848 59.719 2 28 110 816.3 68.858 59.727 73, 29 110 832.8 68.868 59-736 74 30 110 849.7 68.879 59-745 75 aI 110 866.9 68.889 59-755 7 32 110 884.4 68.900 59.764 Wi | a 110 902.3 68.911 59-774 78 |" 3, 110 920.4 68.923 59.794 79 35 110938.8 | 68.934 59-794 80 36 I110957.4 68.946 59.804 SI 37 110 976.3 65.957 59.514 82 38 110995.3 | 68.969 59.824 83 39 III O14.5 68.981 59.834 $4 | 40 III 033.9 68.993 59.845 85 | 4! III 053.4 69.005 59-855 86 | 42 III 073.0 69.017 59.866 87 43 I11092.6 | 69.029 59.876 88 44 III 112.4 69.042 59.887 89 | 45 Grr 13251 69.054 59.898 90 Metres. CEO e2ar TIL 151.9 TL O IIL 191.3 III 210.9 III 230.5 III 249.9 III 269.2 ITI 288.3 III 307.3 ILI 326.0 III 344.5 III 362.7 III 380.7 III 398.4 III 415.7 III 432.7 III 449.4 III 465.7 III 481.5 III 497.0 III 512.0 III 526.5 III 540.5 III 554.1 LIM 57a III 579.7 III 591.6 III 603.0 III 613.9 III 624.1 III 633.8 III 642.8 III 651.2 IIT 659.0 III 666.2 III 672.6 III 678.5 III 683.6 IrI 688.1 III 691.9 111 695.0 III 697.4 III 699.2 ILI 700.2 III 700.6 Statute Miles. 69.054 69.067 69.079 69.091 69.103 69.115 69.127 69.139 69.151 69.163 69.175 69.186 69.198 69.209 69.220 69.230 69. 241 69.251 69.261 69.271 69.281 69.290 69.299 69.308 69.316 69.324 69.332 69.340 69.347 69.354 69. 360 69.366 69.372 69.377 69. 382 69.386 69.390 69.394 69.397 69.400 69.402 69.404 69.405 69.407 69.407 69.407 Geographic Miles. 1’ of the Eq. 59-598 59.908 59-919 59-929 59-940 59.951 59.961 59-972 59.982 59-992 60.002 60.012 60.022 60.032 60.041 60.051 60.060 60.069 60.077 60.086 60.094 60. 102 60.110 60.118 60.125 60.132 60.139 60.145 60.151 60.157 60. 163 60.168 60.173 60.177 60.182 60. 186 60.189 60. 192 60.195 60.197 60.199 60.201 60.202 60.203 60.204 60.204 SMITHSONIAN TABLES. TABLE 60. LENGTH OF ONE DEGREE OF THE PARALLEL AT DIFFERENT | Latitude. ! oO OMNI OCI FwWnHO ° Metres. Tle 26 IIT 305.2 III 254.6 III 170.4 III 052.6 TIO QOI.2 110 716.2 110 497.7 I10 245.8 109 960.5 109 641.9 109 290. I 10S 905.2 108 487.3 108 036.6 107 §53-1 107 037.0 106 488.5 105 907.7 105 294.7 104 649.8 103 973-2 103 265.0 102 525.4 IOI 754.6 100 953.0 100 120.6 99 257.8 98 364.8 97 441.9 96 489.3 95 507.3 94 496.2 93 456.3 92 387.9 Statute Miles. 69.171 69.162 69.130 69.078 69.005 68.911 68.796 68.660 68.503 68.326 68.128 67.909 67.670 67.411 67.131 66.830 66.510 66.169 LATITUDES. Geographic Mt a Latitude. 1 of the Eq. 60.000 45° 59-991 46 59-964 47 59.918 45 59-855 49 59-773 50 59-673 51 59-556 52 59.420 53 59-266 54 59-095 55 58.905 56 58.697 57 58.472 55 58.229 59 57-969 60 57-690 61 57-395 62 57-082 63 56.751 64 56.404 65 56.039 66 55-657 67 55-259 68 54-843 69 54.411 70 53-963 71 53-495 72 53-016 73 52.519 74 52.006 75 51.476 76 50.931 77 50.371 78 49-795 79 49.204 80 48.598 SI 47-977 82 47-341 83 46.691 84 46.02 85 45-349 86 44.056 87 43-950 88 43-231 39 42.498 90 Metres. 78 850.0 77 466.5 76.059.2 74 628.5 73174-9 71 698.9 70 200.8 68 681.1 7 140.3 65 578.8 59 135-7 57 478.1 55 802.8 54 110.2 52 400.9 50 675.4 48 934.3 47 178.0 45 407.1 43 622.2 41 823.8 40 012.4 38 188.6 36 353-0 34 506.2 32 648.6 30 780.9 28 903.6 27 O17.4 25 122.8 23 220.4 21 310.8 19 394.6 17 472.4 15 544.7 Teion2-2 11 675.5 Statute Miles. 48.995 45.135 47.261 46.372 45.469 44.552 43.621 42.676 41.719 40.749 oO ~TI™I AND ne aH OO G2 G2 G2 G2 Go uw nm Dn NS Nw HH vf on G2 G2 G2 Go Go OH NwWL ho Od CO 7 .406 29.315 28.215 27.106 25.988 24.862 23-729 22.589 21.441 20.287 19.126 17.960 16.788 15.611 14.428 13.242 12.051 10.857 9.659 8.458 7-255 6.049 4.841 3.632 2.422 2 0.000 1 of the Eq. | Seas. | | 42.498 | 41.753 | 40.994 40.223 39.440 38.644 37-537 37.015 36.187 35-346 34-493 33.630 32-757 BY.072 39-979 30.076 29.164 28.243 27-313 26.374 SMITHSONIAN TABLES. 165 TABLE 61. DURATION OF Declination 0 the Sun. — 23° 27’ 20 Oo 20 — 13 20 20 20 SMITHSONIAN TABLES. NNN ONNS NNN ONIN OST SNS ON ONIN NNN SST ST ST STENT SO SST eS NSN™N Il Il acd | II era II | 11 II Il Il It If Il er Il It II iT jeu It It Lt It rf eT If II II Th Lt II tai TE II II II II : II Il Gent. TZ 12 14 LZ I2 50 50 50 SUNSHINE AT DIFFERENT LATITUDES. Il II 81 SE It Tet der rr Il It Il Il Il er Il uk 1h 1 LE eT It IT IT Il IT Il ok II It It It II ie II Dd II II Lt Tah rr Il II Il IT II ot Rs Il 5 G2 OG G2 GD Oo 3 BHO WN WN i Go G2 Go Nun O» G2 oxi II II II II If Te Il If er It or IT Il It Lr It It If IT It It II a: Il II 7 II II il IT Il Il Ta Il DT II Il II Il II If Il II Il II II Or II It IO § Io Io Io 10 It It LY. It It Il Il Il Il II IT Il IT IL Il Il IT Il If iL rt Lr Ly Il II It II II IT Il Il Il If II It IT II 2 LL If ee IT Il II NOM fw 28 30 IO IO IO IO IO IO 10 10 10 IO 10 IO IO 10 IO IO IO Io IO IT II LE IT II IT Il it It Il Il et Il Il rr II re II II If II Il er II Il it er I] Il 43 44 46 47 49 x 51 53 54 18 Ig 21 22 a 25 26 27 28 30 4 oO 32 34 35 36 37 10 Io IO 10 38 10 IO 42 10 44 10 46 10 48 IO 50 TON 52 10 IO IO II oO itty ie i Ti o6 Tis eo II II It Il me II IT II IO IO IO IO 20 23 25 28 10 30 IO 32 IO 35 IO 37 IO 40 IO 42 10 44 10 47 10 49 IO 52 10 10 56 10 iT 1) Lak 3 Ti 5 Tete Ta It II TABLE Gi. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. LATITUDE NORTH. Declination 0 the Sun. — 23°27’ — 23 20 —23 0 -22 40 pent ee) bea —21 40 —21 20 —2I oO —20 40 — 20 20 —20 0 40 20 oO 40 20 oO 40 20 Oo 40 20 O 40 20 oO 40 20 oO 40 20 oO 40 20 oO 40 IO 20 10 oO 10 40 | Io 20 10 Oo | A6 | 4| 10 40 A | : ror 20 5 / 10 oO 5 10 1O 40 5 IO 41} I0 20 55 10 44 | 10 oO 10 48| Io oom mmm mnwm non NNIN nbpp WNN MOwW Don Crom Onm@m ~ o Wn - me ON — DH DMM mon SC Or MNM ODDO OOO NNN NNN NNN e x Co MON NNN NNN NNN ONO mmm 0 © On ONN NNN NNN NNN DADA AVDA NO Oo W0 OOD OOM WKWY WWW WWW YOUN co co CO I Co C2 CO OO OOO OWOW OWOMO OOM OOO 0 NW Qe NI MMO ONIN NNN NNN NAD DDD AAA Onc HH 0OW OOO OOO OUWOUMO WOM”O 0 00 mH O0OOW OOW OWMD OOO OW” wowv ¢ 1 OWU OUWOW ODOM OUWOO OO wow OWOUW OWOUO OWOYW OOH HDHW moe AA OO BS www Www WWHD DWN H DHMH HHH SMITHSONIAN TABLES. 167 TABLE 61. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. ae LATITUDE NORTH. Bote 0 the Sun. SE NNN NwH NHK G2 G2 HHO NNN ONIN NTN STN NN SS ann app LH ane BBW WNHHN MONI Du NAHB WN H 7 5 7 6 7 6 7 6 7 6 7 7 7 7 Hf il NNN omN 0 OOM ONIN DO Ow dO eH Se is cui NIB PO oo NNN ONNTNT NINN HH 00 OMM 0 SIN™N SNS NnN™ “I SMITHSONIAN TABLES. 168 TABLE 61. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. Declination LATITUDE NORTH. 0 the Sun. hy m. esa h. m. hens h. m. h. m. h. m, isin h. m. Mi eiite II 58 | 10 53 | 10 48 | Io 43 | IO 36 | Io 30 | Io 21 | 10 57 | 10 52 | Io 46 | IO 40 | Io 34 | Io 26 | Io 50 | 10 44 | Io 38 | 10 31 | II 3] 10 59 | 10 54 | Io 48 | Io 42 | 10 35 | —6 40 II 21 | 11 17 |1II I4|II 1O|II 7 |I1II 2 | Io 58 | Io 52 | 10 47 | Io 4o | —6 20 pa 23k Le Oro eee aN | see Tis (pL) MO) |e Taney | Te IO 56 | 10 51 IO 45 | gy | 3B —7 40 Doe Ds LOp eer 5 L0 —7 20 Die lOn tetas |p ene eon etl —7 Oo PON LIers) ene | 01 sip x - a Oo i) ° on n —6 0 TON ele 2e |e On| ure to |e 137 |per II 5 |II ©] 10 55 | Io 50 —5 40 Teeess meas Tr 29) Tl) r9"| It, 16,) Fr 13.)0b 8 |) PR 4 | Mo 69 | 10°55 —5 20 RIGA | Lie 28. hk es te 22" rT TO.) Te 16 EL 1S, PIL On| ar. aay | TO —5 Oo Des I 59 Sele eTy |tees \iihe25.\ 1h 23,| Tr 19,) Tf 16°) TL 12 pat Spill ae 8 | —4 40 II 35 | 1 33 | It 31 | 11 28 | 11 26 | 1x 23 | 1X 20 | IL 16 | II 13] 11 | —4 20 EF 36 | 11°36 | 1 34) Pr 30 | If 29 |.11 26 | IT 23 | II-20 | 11 17 | It XG —4 oO tr 40 | Tr 38 | IT 37 |) LY 34° ; IL 32/11 30°) FL 27 | Il 24 | IP 21) Ir te 3 20 EW AS (et AS sbi 42 | 01 40 | 21 38) ) 10°37" |. 11-35 | £232) Fe 30°) Tla2z | ee) Il 47 | TI 46 | 11 45 | II 43 | 11 42 | 11 40 | 11 38 | It 36 | II 34 | IT 32 | m2 40 II 50 |11l 49 | Il 47 | II 46 | 11 45 | Il 44 II 42 | 11 40/11 2 Gm plaiera 7 | —2 20 PE S2 | TLest | 1150: |/T A9 || EL 48) IT 47 |i11.46 | TE 44 0 AS | ae AL \ ee TGS Supe S45 lee Soule 52) Mb 52) | Tresor) Pe4g: Pix 48 | Il 47 | 11 46 —I 40 TX 57 | IL 56 | IL 55 | LL 55 | 11 55 | 12 54 | II 53 | 11 52 4,11 G1] It 50 | —0 40 12) A. | 02) 4s) 12 94 | 12 A p12) 44 i2 «4 |1264-) 1294 ta. Ae te 4 | —o 20 ee lowers eyelet oy 7 ieee 7) icy a Le Oey La S| a Sal i aG +0 0 GoeOy| 02.0 2, Tonle TO |i2 TO. 12) PT na) EE 2 2. Lee 1S tk | oO 20 Teele | oT Oe TD eo Nero eeeah i 2 eA ie NS) eos Te EL 2 TO pee a7 es oS oO 40 12 I4 | 12 14 | 12 15 | 12-16 | 12 17 | 12 17 | 12 19 |) 12 20) 12 21 | 12 25 1 0 12 16 | 12 17 | 12-18 | 12 19 | 12 20 | 12 21 | 12 22.|12 24 | 12 25 | 12 27 | I 20 12 19 | 12 20 | 12 20 | 12 22 | 12 23 | 12 25 | 12 26 | 12 28 | 12 29 | 12 32 | 2 “y a I 40 12 2% | 12 22 | 12 23 | 12 25 |/12' 26 | 12 28 | 12 30 | 12 32 | 12 34 | 12 37 200 T2e2 2m lene) 254 T2026) 2) 25) el2e20 1230 oi T2340 Le 36 | mm 38 | 12 4T | 2 20 12 26) | F228, 12) 29 | 1203% | 02/32 | 12 35-| 12 37 | 12.40.) 12 43 | 12 46 | 2 40 T2 28 | 12 30 | 12 32 | 12 34 | 12 36 | 12.38 | I2 41 | 12 44 | 12 47 | 12 950 | Se On at2 3h | 12°32) 71235 | 12 37° | 1239) 12 4r | 12 44 | 12 AS 02) 502355 BuzO 12 33 | 12 35 | 12 37 | 12 40 | 12 42 |.12 45 | 12 40 | 12 52 | 12 55 | 13 © 3 40 I2 35 | 12 38 | 12 40 | 12 43 | 12 46 | 12 49 | 12 52 | I2 56 | 13 9/33 4 4 0 12 38 | 12 40 | 12 43 | 12 46 | I2 49 | 12 52 | 12 56/13 9/13 4)13 9 | 4 20 12 40 | 12 43 | 12 46 | 12 49 | 12 52 | 12 55 | 12 59 |13 4/13 8113 14) 4 4o 12 43 | 12 46 | 12 49 | 12 52 | 12 55 |12 59 |13 3 |13 8 | 13 13 | 13 19) | 5 0 12) 45.962 45) sroes ir | 12 55 | 12 BS ne 2) eo 7 | eee sen tS: 235) 5 20 2.47 | C2e5n | F25AG) arse | 13, 2 |.13, 6 |. 53. 11] BLOM alae zou Lanz 5 40 12 50.| 12 53 |12 57113 1|13 5113 10 | 13 14 | 13 20 | 13 26 | 13 33 | 6 0 12953 \'12 56)| r2 56 13 4 |13 > 8 [03 13 TZ IS j1g 241 03.3, | 13 38 6 20 12 55 |1259|13 2/13 7 |13 11 | 13 16 | 13 22 | 13 28 | 13 35 | 13 43 | 6 40 12 58|13 I|13 5|13 10|13 14 |13 20/13 26 |13 32 | 13 39 | 13 47 | Meer 13,0 | 13 4 |.13 8 |g 13) 13 18 | 13 23 | 13°29 | 13. 36)| 13 44 | 13 52 7 20 ray 2) | 13° 7 | 13 ty. |-23, 16-| 03. 20 | 13 27 |,29°33 |1s.40 |13 49 | 13°57 7 40 TZ 5/13 9/13 14 |13 19 | 13 25 | 13 31 13 37 |213 44 | 13/53.) 14° 2 | Reet 7.) a 124) Pa n7" \\Ts.29F | 12°28) F335 ne os aN 4 oa aS oe _ wo wn x a aS ; nN SMITHSONIAN TABLES. TABLE 6i. DURATION OF SUNSHING AT DIFFERENT LATITUDES. Beceanen [ | 0 the Sun. | | | | Heer. h. m. heme Heei: h. m, h. m, h, m. | h, m, | +8° 0/ 12? 7 |.%2 13; | 12-58 4) Sore4 | verse 02 138) elon en ore Ta 3 8 20 12> 7) | 12°13) ||) 1219 see S mle a2 eee som mona eon 23 38 8 40 12) 7 || 12°13) | 1219) 12°268)| 29335 |e Ao | ee AS eer 2esr Wey ts) 9 0 [2 7 | 12 13 | %2)20)} 12) 26) "52 34) 12. Ar.) 2 5072 5G temo g 20 12) 7 3) |) 12 20) S227 eras aes alee 520m ieee ate g 40 7; 2 14 | T2920 ~ | 12925) 912 336" 24412 53 3) 3 care 10 0 12 7 | 12:14 | Tae |) 2297129378 eteeAs yi are. 55) 1) cms ee IO 20 12) 37) 1| a2 AN 222 eee 12/33) | 2047; | 12.56) | orawa 3 19 IO 40 12°77 )| 2 S04) 2522 | ees On) M2 es Om ieet On| ons 379m 1ae22 | it 0 D2 7 | £2705 || 25237) i273) hea s4 OF ere 4 Os em25o) s\n mre eee 20 7 \\ L205 2528 | S12 22 en Aa RO Ey age || mectarcy, Ihesiey Ae | II 40 I2) 7 | 32°15 | 12024 | T2032" || F2 Aat | re e238) 2 J) as ee ee 1/20 I2.7 | 12 15 | l2 24 |02'g3s| 12 4a) ress | 1a) 4 cna ee I2 20 227 | et sO |mt2e25 2°34 |) T2744) 912 55.513) 8On | reSTom ame mer I2 40 12) 87 | 12°16") 12525) 12) 35) 12:45. |W sou Preres | eter seems 1320 12). 7 || 12.16 | 129264), 12.35) | 12).466) 227574) se" Bo 1) waar ame ase 3 20 12) 97) | I2e16 ee 26e sro es Gell eA7 alee 5S Bp LE, |) 3 2 5aqe An | 3 40 127 |PI 22079 S252 7 Tena 7 TO TASe lee) BO Belen eks eo 3 43 14 0 [2 7° | T2017 | ¥2)27 "| 32.38.) 12 Ao) ae | See ow oonaeto 14 20 IZ. Y | 12°27 | 122871 L2).39),) 12.50") ae 24a tor lore sar sereeatsS I4 40 [2 7 | 22.27 | 22°28) |) 12"40.4| Tee5no)) 13" 4M) senza eo eros 150 127 |||, 12 1S 9) i2e2om | a2 Aon I 2e5om | eiemes BP 10) | 13.2 5a meen 15 20 12°97 (| T2-1S 12529: | T2s4t | 1253. 813 27, | seen || ie eo re eee 15 40 [2 7 | 12°15" | 12:30 12 -4r >| 12) 54513) 8 eae 289 a a5 3 58 16 O 12) 7) | 12919) | 662030) 29425225 5a eam enews 25 Aisa 16 20 L277, ||| 12009 |5L20 30 1274s sei 2 256) cos ets) 26% eres eo lela 16 40 IZ 7 || 12-19) L230 | r2944qy) 2953 43) 201328) As a eA i720 12) 7 | 2510 P2632 5 eee Aan e256 3/13) | 13520) | ete) Aza I7 20 12) 07.) 12 20 5 Ri2s2oR Moe AG | ars) ois) roms 3.32 3550 alee rt 17 40 I2 (7 | 12°20 |. 12533-1246 | 13) 2 |-03 16") 13 aah) ee og ee 18 O 125 47-Al 12220) 525s eee |e ee 3 27) 3, 350 354 erAeno 18 20 I2 7 | 12.20 | 12.34 || 12.48 | 13,3 | 13 19 113 37 | 13/56 eideiG 18 40 12) 7 le 20 Ie eA er2EAG 3 4) | 13) 20 | 23,38 || ts) 58e eee 19 O I2 7 | 12 21 | 12 35 | 12 50 | 13 5 | 13 22 | 13 40 | 14 oO | 14 24 Ig 20 l2 7, 2°20 || T2035) i250) | 03) 16) | 130230 sed 2 aoe er eo6 Ig 40 I2 7 | 12 22 | 12°36 | 12 52° | 13 7 | 13 25 |-13° 44) \pad, So aa eo 20 0 12 7 |\12.22 | 12 36: | 12°52) 33 8 | 13926 | 13.460) cele 20 20 [2 7 | 12 22 | 12°37 | 12°53) | 13.10: |) 53 28. | 13947 ord TOP eras 20 40 [2 .7.| 12 22.) 12: 37°|/12 54 | 131k || 13/29 113.409) at Ten aaear, 21 0 [2° 7 | 12°23 | 12°38 || 12.55) 13 12) |) T3931 | 13 5r ra oar era 2I 20 12 7 | 12023 | 12,39 | 1256") 13 235] 03°32 1s Se Warsz des ans 21 490 I2, 7. | 12 23 | 12 39 | 12.56 | 13 14 | Ig 34 3 555d toe aa 22-0 12) 7) || 2) es || LaeAom anes 7, 3167] 13 35 | 135561) 14 20 aed 22, 20 [2 7 | 1224) | r254r | 2) 53) | 13 07) 13537 Nilsp Som mana line 22045 [2° 7. | 12 24 | 2gAL | i2550 1] a aton eres TA) 108) D4 25 ees 23 O 129 77 | el2e25) |e 3.0 | 13-49 | 23 40: | 14. 25) ora) 28 erases 2220) 27 | S22 el ae eA Si LT 3g) 20) igeAte | era a 20) eiSseao 2327, 2.7 9225 4 1243) 3 LS 20; || FeeAr eras ae Serene SMITHSONIAN TABLES. TABLE 61. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. poonatton 0 the Sun. veri ie. 13 13 28 Te 135g 13 13 34 13 13 38 13 13 41 13 13 44 13 13 48 13 44 | 13 51 13 ¢ 13 55 13 13 58 3 TAN a 13 T4 5 14 14 8 14 14 12 14 14 16 14 I4 19 14 14 22 14 14 26 14 I4 29 14 14 33 14 14 37 14 14 40 14 14 44 14 36 | 14 48 14 14 52 14 14 55 14 14 59 14 LOS 14 seh 14 I5 10 15 I5 14 15 15 18 15 8] 15 22 15 I5 26 T5 I5 30 T5 15 34 15 15 15 I5 42 15 15 46 I5 15 T5 LOK T5 15 15 16 15 16 15 16 oe NOW OWO SMITHSONIAN TABLES. TABLE 6i. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. LATITUDE NORTH. Declination 0 the Sun. -_ 5 ~ S ~ oo — 23° 27’ — 23 20 | —23 0 —22 40 | —22 20 —22 0 —21 40 —2I 20 —2I 0 40 20 Oo 40 20 oO 40 20 oO 40 20 oO 40 20 oO 40 20 oO 40 20 Oo 40 20 oO 40 ow moo bs of On & G nun N ONT G2 nou — Go Gw NR NOH OHH HN Now ° ° HOO NR Oond Ns] NON MM Go Go 2 ae Wh Aer CMON me OOo CO 0 DAW onw ono roe WNH afd nn MapwW CO rh em ne & CO.O ob Wwhrd xe nv WOH MN Ov. nN BN H + & BODO FATIH BOM > Ne) ADDN ANN AaMN KANN NUN + No Re eH ObR QNLK NOn FNO NED NWO ak fwWhd mOoor ST\O NOR nN WN Se Se _ Oo U1 Neo BW hd NRO NBO e fw HoH Nb H oO anf fp ond On WwW Noa NOR WHA tO on DNDN ANN ANN NN UMAR AHP C|WwW n & ne BW bo _ NST HWODONN NOH WAC OD DHAHNO WNATIH MOON NON NO ee | NSNN NN DD ADD ADA NNN vy neo Nor LAH HOW 9 CONN NNN NNN NAD ADD ADA num nM RW © NH Now ns 0 nae & NH HNL DOO co SNNNND DDD ADD UMNn NH NN™NONNN NNN ane Ww OR MO WNTIH NOD DOH NHR NOR “J OP Cc mn wn Ra NOR HAN OFND BOND ANN NINA DWN an BWW On OH £NO “I des on MOM MON NNN NNW NNID AAA ADA Dut | a | ~ oom Onin NINTNI eu Wh OwON UW oe eS mH Ne nv ano nw nb Cw mmo NADH NOW NHN OWN mon COnInN NINN NNW a abo ®WNN mH O nn Wb nan BBW Ow nm HEN ONM NO MaMmrh BWW Co 4 _p mon abe WHH Mmwn OM fm on CONNN NNN NN DD ADD ADAOW UN aAUNhf HAH RWW WhHbd = 0 0 > wo H H oO OC COmOO CON NNN NNN NDAD DDD ADU unn aL HPAL WW WN H oO 40 20 Oo 40 20 oO 40 20 O 40 see) O No a \o S Co Sw > oe COM ONIN NNN NNN DDD ADD an OMmMOo fOW NIN \o \o ONBW WN HH RN Hw NOn UCMO WAM na map Wl NNN “SI Ov “Ins OOO OOD OOO OO © ane BWN Nw H Or H awn Bw ow NDHDO foOow THAN OOO OOO WOW” WOOO OOO DHM NTN H oS) | SMITHSONIAN TABLES 172 TABLE 61. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. LATITUDE NORTH. Declination the’ Sn oe) 72° | 78° | Zak | 75° | 76e | 77°, 787) 78°. | BO" | h. m. | h. m. |] h.m. | bh. m. | bh. m. | bh. m, | bh. m. Teatien ||) Wert. lease | — 23°27’ | — 23 20 — 23 0 —22 40 | — 22 20 | —22 0 —21 40 — 21 20 —2I oO —20 40 — 20 20 —20 0 19) 40) (St 3 | — 19 20 I 50 —19 Oo 222 —18 40 DATEL 5 — 18 20 BOLO L 52 —18 o BEsOMzE25 —17 40 ByAGi\ w2e52.)|, i 0G —17 20 4 6) 3 14 F 55 me if. *O AG225 S300 |) 2.29 —1!6 40 AGS) SUE ANE 2-500 iit — 16 20 ACS? F4L2 |, 320) |, 1.58 aT) > O Be Gn | eAR2Gq|) 3 Ar 162 32 —15 40 Reg | 4) AA ACE le 3 Toh LTO aL 20 Reser Ae OOn Pag tou 6S 2a = ae eZ Ss) ae 5 44! 513] 4 36| 3 47 | 2 37 —14 40 BESO N) 527d 52 | cA False © [ag — 14 20 Gere 51 40th Sar yi 4020) lie Sas |) 2h. 5 SO 619| 552] 5 21| 443| 354] 2 42 —13 40 SL 2a ean Som 5eS5h le ons 414 io Ler Eds —13 20 Geto! 6 17 5d9clo 5) TO." 434 3.33") 2 10 —1I3 0 6511 629| 6 2| 531| 452| 4 2] 2 48 | —12 40 GOAN Omrsme5 459165) 9 47:23) |) 3) 29 1 18 —&2 20 711| 650| 627| 559] 525| 443| 3 46| 2 15 —12 0 OE WET EaletOV 9) nO es) a5) 47 | 5.0120) Ai TOW e295 —I! 40 PEI) fitz baG SE| O02) 5°50 95) FO) 24832 | geese | ak 28 —II 20 740| 7 23| 7°3| 638] 611| 5 38| 453] 355 | 2 20] =—0L oO EGY 7 494 wf Te POESLO| 0) 25 i S54 | Sp L3cle4e20) | a) =. Sao 1.7 59} 743 | 725| 7. 3) 634 | & 9] 5 30) 443) 5 35) 2 25 — 10 20 Se Sil) Jas Wego 7aesu) O52 tO 25.) 5 49 Se 0D) eo. | Seed —10 Oo Ser7 |) Se Bile pase 7 27 Je 45/0 O38 6 60 Se25) 4) oa le 3) 10 | — 9 40 8 26| 813] 756| 738| 717| 6 52| 6 22| 5 44 4 56 | 3 46 - 9 20 Bias |S 22) & Wala 50 | 7 29/70 | ergs | Os Rout v5. 29) [de 17 — 9 0 SrAda| 98) 30) (Sony |e Sa | a7sA4rsl e720 G5 6:20 5 40) A Aq P= 8 40 | 853| 8 4r| 8 27| 811] 753| 7 33) 7 8 6 38| 6 o| 5 I0 | — 8 20 Guile S500) 8.37) S22. 8 o> | 4G a7 22 6r5 50 mOntone5 34 7 0 910| 859| 8 47| 8 33'| 817| 759] 736) 7 12 | 6 38) 5 56 SMITHSONIAN TABLES. 173 TABLE 61. Declination LATITUDE NORTH. the Sane 6029) FO1o7 620 eke mc) is sant, 10 17 | IO 12 | 10 22 | 1017 IO 27 | 10 23 10; 10 28 DURATION OF SUNSHINE AT DIFFERENT LATITUDES. 2 G2 Oe o IO 37 | 10 33 | IO 10 38 IO 47 | 10 43 ab Cc | 10 52| 10 49 10 56 | 10 54 II 10 59 | 11 Il 4 | sr [ELIS TI II 14 nn mon oum CO re Cou II Il Et 26) |) rr | IX 31 | Ir NNN Le shi 32 1 I] II 45| 11 II 50|11 En 55) |) 11 11 II i I2 LZ / / ; EZ TZ RZ AD 2 ake? ‘ I2 TZ I2 I2 E2 Ondo NSN N™~ noe oe “SIN “I ITA DAO UUM LEP WWW HNN SMITHSONIAN TABLES. 174 . TABLE 61. DURATION OF SUNSHINE AT DIFFERENT LATITUDES. LATITUDE NORTH. Be eanon 0 the Sun. Ow vd - OO oO a! = COCONt Ny? NBO NH nn nNbe Wh mom Ne ONG NAO ROD DOA BAY — OH Ww bh Aw dO On Ny in OG Or CHW Ann CO H nN Gn Ure Cf ¢ MON Wun WwW nd — NN one Oo to Of OW Ooo — eS Re Ora GD Go No Re NH O HHH G2 G2 Go Nn f& NS NOR ON On a oS) WwW NN DN > NH OH SO MO WH UN WO AO Wnt wn “oe -— Se bE HEL a= NAO UNTO _— oe Oo ON Now COr.o Nv to CO tN + WwW on Dan on NW UN _— No nur “ION G2 No N On 0 SIDI DAO nM SRA wn in & now a SMITHSONIAN TABLES. TABLE 61. ‘ DURATION OF SUNSHINE AT DIFFERENT LATITUDES. LATITUDE NORTH. Declination 0 the Sun. + 8° 0/ 8 20 5 40 9 0 g 20 | 14 27] 14 32] 1439/14 46/ 1454/15 2/15 If | 15 21 | 15 32] 15 44] 15 57 9 40 | 1432| 14 38|1445|1452]15 0|15 9/15 18/15 28] 15 40|1552| 16 6 10 O |1437]1443]1450]1458]15 6/15 15] 15 25/15 35|1547|16 o| 1615 10 20 [1442] 1449]1456|15 4] 15 13| 15 22| 15 32/15 43/15 55/16 8 16 24 10 4o [1447] 1454/15 2] 15 10/15 19] 15 28/15 39|15 50/16 3] 1617] 16 33 18 O [1452/1459] 15 7] 15 16] 15 25] 15 35] 15 46/15 58] 16 11 | 16 26| 16 42 11 20 [1457/15 5|1513|15 22/15 31] 15 41/1553|16 5/16 19/ 16 34 16 52 Ir 40 [15 2] 15 10] 15 19] 15 28] 15 38/15 48/16 0} 16 13} 16 27/16 43} 17 1 12 O [15 8] 15 16| 15 25| 15 341] 15 441 15 55) 16 7} 16 21/ 16 35 | 1652) 17 15 12 20 | 1513] 15 21| 15 31] 15 40/15 50|16 2|1615|1629/1644|17 I| 17 21 12 40 [15 18] 15 27] 15 36| 15 46/15 57| 16 9] 16 22) 16 37 | 1653 | 17 11 | 17 31 13 “O° 115 23 | 15 33/15 42 || 25 53.96. 41) 16°06) 16 36) 16 45) 7 92) eo as 13 20 115 29| 15 39] 15 48| 15 59 | 16 11 | 16 23 | 16 37 | 16 53 | 17 10| 17 30| 17 52 13 40 11535115 4411555|16 5|1617| 1631 | 1645|17 1/17 19] 17 40} 18 3 | 14 0 [15 40|1550]16 1| 1612] 16 24 | 16 38 | 16 53 | 17 10/ 17 29| 17 50| 18 14 | 14 20 [15 46|15 56/16 7|1619| 16 31| 1646/17 1I|1719|17 38|)18 0 18 26 14 40 115 51/16 2] 1613] 16 25 | 16 38| 1653/17 9|17 28/17 48) 18 11 | 18 38 is O [1557/16 8| 1619] 1632|16 46/17 1| 1717] 17 37| 17 58| 18 22| 18 50 15 20 [16 2/1614] 16 26| 16 39| 1653/17 9|17 26/17 46|18 8] 1833] 19 3 15 4o 116 8| 16 20] 1632/16 46/17 1/17 17|17 35|1755|1818| 18 45| 19 16 16 O | 16 14| 16 26| 1639] 1653/17 8] 17 25|17 44/18 5| 18 29|/ 1857] I9 30 16 20 | 16 20| 16 32| 1646/17 O| 17 16| 17 33| 17 53| 18 15 | 18 40| 19 10] 19 45 16 40 | 16 26|1639]/1652/17 7/17 23/17 41/18 2] 18 25| 18 51| 19 23] 20 I 17. O 116 32| 16 45 | 16 59] 17 14] 17 31] 17 50| 18 11 | 18 35| 19 3] 19 36| 2017 17 20 116 38| 1652/17 6| 17 22| 17 39| 17 59| 18 21 | 18 46| 19 15 | 19 50| 20 35 17 40 |16 45| 1658] 1713] 17 29|1747|18 8] 1831 | 18 57 | 19 28| 20 6| 2055 18 O §165r/17 5°] 17 20] 17 37| 17 56| 1817) 18 41| 19 8] 19 41} 20 22) 21 17 18 20 |1658|17 12| 17 28/17 45/18 5| 18 26| 18 52| 19 20/ 19 55 | 20 40| 21 42 8 4o [17 4/1719] 17 35|1753| 1814] 18 36| 19 3] 19 33| 20 10| 20 59| 22 13 19 O [17 11| 17 26/17 43|18 2| 18 23] 18 46| 19 14] I9 46| 20 26 | 21 20) 22 58 19 20 [1717] 17 33] 17 51| 18 10 | 18 32| 18 56| 19 25| 20 O| 20 44 | 21 45 Ig 40 }17 24| 17 41} 1759]18 19}18 41) 19 7] 1937] 2014] 21 3] 22 16 20 O [17 31|17 48/18 7] 18 28] 18 51 | 19 Ig] 19 50] 20 30| 21 23 | 22 59 20 20 }17 38|1756|18 15 | 18 37| 19 I|19 30} 20 4| 20 47 | 24 47 20 40 117 45|18 4] 18 23] 18 46| 19 12| 19 42] 2019] 21 5] 22 17 21 O 11752] 14 11| 18 32 | 18 56| 19 23 | 19 25 | 20 34 | 21 26] 23 1 21 20 }18 o| 2820/18 41] 19 6] 19 34|20 8] 2050] 21 50 21 40 }18 8|18 28] 18 50] 19 16| 19 46| 20 22 21 8/ 22 19 22 O [1816] 1837|19 0] 19 27| 19 58) 20 37 | 21 29| 23 2 22 20 | 18 24] 18 46| 19 IO} 19 38 | 20 II | 20 53 | 21 52 22 40 | 18 32| 1855 | 19 20] 19 50| 20 25 | 21 II | 22 21 23 O {18 41|)I9 4]1931| 20 2] 2040| 21 31} 23 3 23 20 | 18 49| 19 13] 19 41 | 20 14 | 20 56| 21 54 23 27 |1852|1917|19 46|2019|2I 2/22 3 SMITHSONIAN TABLES, > = TABLE 61. TABLE 62. DURATION OF SUNSHINE AT DECLINATION OF THE SUN DIFFERENT LATITUDES. FOR THE YEAR 1894. LATITUDE NORTH. eee 0 the Sun. May. June. +15° 10’|-++22° 67|f Tose 3 22825 16 53 | 22 47 17 42 3 LO yey, 14 +19 IO 19 50 20 I5 20 49 21 21 49 mat = leet NOHOOHN who NO 1 Nw WYN bd hud Wb Own WNN NH oO» Ne) HOO Hin NdwoHNHH NH G2 G2 Ge G2 G2 Go SMITHSONIAN TABLES. 177 TABLE 63. RELATIVE INTENSITY OF SOLAR RADIATION. Mean vertical intensity for 24 hours of solar radiation / and the solar constant 4, in terms of the mean solar constant Al xs Date. Jan. Feb. | Mar. Apr. May | 16 | June July 1% 16 | Aug. V€GTi..5. Motion of the Sun in Longitude. a On Oo U1 4 59-14 73-93 89.70 104.49 119.29 134.05 149.82 164.60 179.39 194.13 209.94 224.73 3309.19 344.98 0.301 0.289 RELATIVE MEAN VERTICAL INTENSITY RIN, ° ( LATITUDE NORTH. 334 | -330 .322 | .310 261 | .225 236 | .194 211} .164 190 | .140 175 | .124 .167 | .115 0.268 |0.241 Q 216 231 291 .256 .220 ———] ss 1.0335 1.0324 1.0288 1.0235 1.0173 1.0096 1.0009 0.9923 0.9841 0.9772 0.9714 0.9679 0.9666 0.9674 0.9709 0.9760 | .300 28 .140 .043 0.9828 0.9909 .183 | .135 | -084 | .065 -147 | .097 | -047 | .O15 -114 | .063 | .o18 .089 | .o40 .072 | .024 .064 | .o16 0.209 eee 0.144 033) SMITHSONIAN TABLES. 178 0.9995 T.0080 1.0164 1.0235 1.0288 1.0323 0.126 CONVERSION OF LINEAR MEASURES. Inches into millimetres Millimetres into inches Feet into metres Metres into feet Miles into kilometres Kilometres into miles Interconversion of nautical and statute miles Continental measures of length with their metric and English equivalents 179 TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE 64 65 66 67 68 69 7O 7t TABLE -62- INCHES INTO MILLIMETRES. I inch — 25.40005 mm. .07 mim, . . . . . ° mm. 0.00 0.51 | ; 1.02 ; 1.52 1.78 5 2.29 2.54 : 3.05 A 3.56 : 4.06 4.32 : 4.83 5.08 ee 5.59 Roy 6.10 i 6.60 6.86 : 737, 7.62 7.8 8.13 3.38 8.64 : 9.14 9.40 : 9.91 10.16 : 10.67 | 10.92 | 11.18 : 11.68 | 11.94 2 12.45 12.70 195.) 13.22 || 13%469|\ "13.72 14.22 | 14.48 : 14.99 15.24 5. 15.75 | 16.00 | 16.26 : 16.76 | 17.02 : 17.53 17.78 5. 18.29 | 18.54 | 18.80 19.30 | 19.56 : 20.07 20.32 0:57 | 20/83 | 21-08) || 21-34 21.84 | 22.10 x 22.61 22.86 Bs 23.37 | 23.62 | 23.88 | 24.38 | 24.64 : 25.15 25.40 | .65 | 25.91 | 26:16 | 26:42 i 26.92 | 27.18 Me 27.69 27.94 28.45 | 28.70 | 28.96 29.46 | 29.72 ; 30.23 30.48 30.99) || 3.24 21.50 32.00 | 32.26 : B27, 33.02 33-53 | 33-78 | 34.04 34-54 | 34.80 [05 4ieg5-32 I9° 35.56 36:07 | 36.32 | 36.58 : 3700 37.34 ; 37.85 On Ge Pann CO 38.61 | 38.86 | 39.12] 3 39.62 | 39.88 513) |» 40:39 4I.15 | 41.40 | 41.66 42.16 | 42.42 2h 42.93 43-69 | 43-94 | 44.20 44.70 | 44.96 ; 45-47 , 46.23 | 46.48 | 46.74 47.24 | 47.50 7.75 | 48.01 48.77 | 49.02 | 49.28 49.78 | 50.04 ; 50.55 38.10 40.64 43.15 45-72 48.26 sfa le tS OS) &) G2 G Wb Coun RMI OU nob Mde 50.80 : 51.31 | 51.56 | 51.82 52.32 | 52.58 : 53-09 53-34 | 53: 53-85 | 54-10 | 54.36] 54.61 | 54.86 | 55.12 : 55-63 55.88 : 56.39 | 56.64 | 56.90] 57.15 | 57-40 | 57.66 | 57. 59.17 58.42 | 58. 58.93 | 59-18 | 59.44 | 59.69 | 59.94 | 60.20 60.71 | 60.96 | 61. 61.47 | 61.72 | 61.98 | 62.23 | 62.48 | 62.74 : 3.25 | 63.50 | 63.75 | 64.01 | 64.26 | 64.52 | 64.77 | 65.02 | 65.28 | 65. 65.79 66.04 ; 66.55 | 66.80 | 67.06 | 67.31 | 67.56 | 67.82 .07 | 68.33 | 68.58 3.8 69.09 | 69.34 | 69.60 | °69.85 | 70.10 | 70.36 | 70. 70.87 70.02 37 | 71.63 | 71.88 |. 72:14 i] 72220) “72.64. "| 72:90 3: 73-41 73-66 . 74.17 | 74.42 | 74.68 | 74.93 | 75.18 -| 75.44 75-95 76.20 | 76. 76.71 | 76.96 | 77-22 | 77.47 | 77-72 | 77-98 78.49 78.74 | 78. 79.25 | 79.50 | 79.76 | 80.01 | 80.26 | 80.52 : 81.03 | $1.28:| On. 81.79 | 82.04 | 82.30 | 82.55 | 82.80 | 83.06 ‘ 83.57 83.82 | 84.07 | 84.33 | 84.59 | 84.84] 85.09 | 85.34 | 85.60 P 86.11 | 86.36 | 86. 86.87 | 87.12 | 87.38 | 87.63 | 87.88 | 88.14 : 88.65 88.90 .15 | 89.41 | 89.66 | 89.92 | 90.17 | 90.42 | 90.68 : gI.19 91.44 ‘ 91.95 | 92.20] 92.46 | 92.71 | 92.96 | 93.22 : 93-73 93-98 |. 94-49 | 94-74 | 95.00 | 95.25 | 95-50 | 95.76 ; 96.27 96.52 é 97.03 | 97.28 | 97.54] 97-79 | 98.04 | 98.30 | 98.55 | 98.81 99.06 i 99-57 | 99.82 | 100.08 | 100.33 | 100.58 | 100.84 | IOI.0g | IOI.35 i i i i i 101.60 | 101.85 | 102.11 | 102.36 | 102.62 | 102.87 | 103.12 | 103.38 | 103.63 | 103.89 104.14 | 104.39 | 104.65 | 104.90 | 105.16 | 105.41 | 105.66 | 105.92 | 106.17 | 106.43 106.68 | 106.93 | 107.19 | 107.44 | 107.70 | 107.95 | 108.20 | 108.46 | 108.71 108.97 109.22 | 109.47 | 109.73 | 109.98 | 110.24 | 110.49 | 110.74 | III.0O | 111.25 | 111.51 T1II.76 | 112.01 | 112.27 | Lr2'52 | 11278 |) LT3.03) | 13-28 |. T13.54) | BI3-79) | LEALO5 114.30 | 114.55 | 114.81 | 115.06 | 115.32 ] 115.57 | 115.82 | 116.08 | 116.33 | 116.59 116.84 | 117.09 | 117.35 | 117.60 | 117.86 | 118.11 | 118.36 | 118.62 | 118.87 | 119.13 119.38 | 119.63 | 119.89 | 120.14 | 120.40 | 120.65 | 120.90 | 121.16 | 121.41 | 121.67 121.92 | 122.17 | 122.43 | 122.68 | 122.94 | 123.19 | 123.44 | 123.70 | 123.95 | 124.21 124.46 | 124.71 | 124.97 | 125.22 | 125.48 | 125.73 | 125.98 | 126.24 | 126.49 | 126.75 127.00 | 127.25 | 127.51 | 127. 128.02 |128.27 | 128.52 | 128.78 | 129.03 | 129.29 Inch. 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0,009 Proportional Parts. mm. 0.025 0.051 0.076 0.102 0.127 0.152 0.178 0.203 0.229 SMITHSONIAN TABLES, TABLE 64. INCHES INTO MILLIMETRES. I inch — 25.40005 mm, Inches. : F .02 | .03 | -04 3 .06 | .07 | .08 mm, mm, mm. . . mim, 127.00 ; 127.51 | 127.76 | 128.02 ns 128.52 | 128.78 129.54 : 130.05 | 130.30 | 130.56 : 131.06 | 131.32 132.08 ‘ 132.59 | 132.84 | 133.10 ; 133.60 | 133.86 134.62 .87 | 135.13 | 135-38 | 135.64 .89 | 136.14 | 136.40 137.16 .41 | 137.67 | 137.92 | 138.18 3. 138.68 | 138.94 139.70 ; 140.21 | 140.46 | 140.72 : 141.22 | 141.48 142.24 é 142.75 | 143.00 | 143.26 Be 143.76 | 144.02 144.78 : 145.29 | 145.54 | 145.80] 146. 146.30 | 146.56 147.32 | 147. 147.83 | 148.08 | 148.34 | 148. 148.84 | 149.10 149.86 ; 150.37 | 150.62 | 150.88 3 151.38 | 151.64 152.40 ‘ 152.91 | 153.16 | 153.42 on 153.92 | 154.18 154.94 | 155. 155-45 | 155-70 | 155.96 y 156.46 | 156.72 157.48 -73 | 157-99 | 158.24 | 158.50] 158. 159.00 | 159.26 160.02 .27 | 160.53 | 160.78 | 161.04 : 161.54 | 161.80 162.56 | 162. 163.07 | 163.32 | 163.58 : 164.08 | 164.34 165.10 : 165.61 | 165.86 | 166.12 : 166.62 | 166.88 167.64 .89 | 168.15 | 168.40 | 168.66 : 169.16 | 169.42 170.18 y 170.69 | 170.94 | 171.20} 171.2 171.70 | 171.96 172.72 207) (PL 7Ss23 1 173-40) 1730745 173: 174.24 | 174.50 175.26 : 175.77 | 176.02 | 176.28 53 | 176.78 | 177.04 177.80 : 178.31 | 178.56 | 178.82 | 179.07 | 179.32 | 179.58 180.34 : 180.85 | ISI.10 | 181.36 : 181.86 | 182.12 182.88 | 183. 183.39 | 183.64 | 183.90 A. 184.40 | 184.66 185.42 ; 185.93 | 186.18 | 186.44 : 186.94 | 187.20 187.96 sy 188.47 | 188.72 | 188.98 : 189.48 | 189.74 190.50 : IQI.OI | 191.26 | 191.52 ; 192.02 | 192.28 193.04 : 193.55 | 193.80 | 194.06 -31 | 194.56 | 194.82 195.58 5.83 | 196.09 | 196.34 | 196.60 .85 | 197.10 | 197.36 198.12 : 198.63 | 198.88 | 199.14 ; 199.64 | 199.90 200.66 , 201.17 | 201.42 | 201.68 : 202.18 | 202.44 ont ° is Tc yy 7° Te Te Ne) Oo°0 203.20 3.45 | 203.71 | 203.96 | 204.22 ‘ 204.72 | 204.98 205.74 : 206.25 | 206.50 | 206.76 re 207.26 | 207.52 208.28 : 208.79 | 209.04 | 209.30 .55 | 209.80 |} 210.06 2TO%$2 | 200. 250.33) 201.59) 201-84 2s 212.34 | 212.60 Dine > re) 213.36 : 213.87 | 214.12 | 214.38 f 214.88 sO NH © C0006 i) 4 on Ow an - 215.90 ; 216.41 | 216.66 | 216.92 218.44 : 218.95 | 219.20 | 219.46 220.98 : 221.49 222.00 223°5 2) 222°7 4. .28 | 224.54 226.06 | 226. : 226.82 | 227.08 sIQ 01 oo7S o~ ° 2 © % Ho WO ole 7 oO vw H NW NO NN HN HS RO NN NbN tO NHN Mur ° 228.60 231.14 233.68 236.22 238.76 241.30 243.84 246.38 248.92 251.46 2 2 2 SOMERS NE SHAG OS KA § OfWW DM HATO WN oONN NHN YNNNNDN 4 Oo Go G2 N NYNHHNN eH GW OnTO nN bwH Hb + G2 G2 G2 Go NO ( QD I WOMNHN DOU HNI 254.00 255-78 0.004 0.005 0.006 0.007 0.008 0.009 0.076 0.102 0.127 0.152 0.178 0.203 0,229 SMITHSONIAN TABLES. I8I TABLE 64. INCHES INTO MILLIMETRES. I inch = 25.40005 mm. Inches. Ol -02 .03 .04 .05 | .06 .07 | .08 .09 | mm. mm. mm. mm. mm. mm. mm, mm. mm. mm. 10.00 | 254.00 | 254.25 | 254.51 | 254.76 | 255.02 | 255.27 | 255.52 | 255-78 | 256.03 256.29 10.10 | 256.54 | 256.79 | 257-05 | 257.30 | 257-56 | 257-81 | 258.06 | 258.32 | 258.57 258.83 | 10.20 259.08 | 259.33 | 259-59 | 259-84 | 260. 10 | 260.35 | 260.60 | 260.86 | 261.11 | 261.37 | 10.30 | 261.62 | 261.87 | 262.1, | 262.38 | 262.64 | 262.89 | 263.14 | 263.40 | 263.65 | 263.91 | 10.40 | 264.16 264.41 | 264.67 264.92 | 265.18 | 265.43 | 265.68 | 265.94 | 266.19 | 266.45 10.50 | 266.70 | 266.95 | 267.21 | 267.46 | 267.72 | 267.97 | 268.22 | 268.48 268.73 | 268.99 10.60 | 269.24 | 269.49 | 269.75 | 270.00 | 270.26 | 270.51 | 270.76 | 271.02 | 271.27 | 271.53 10.70 | 271.78 | 272.03 | 272.29 | 272.54 | 272.80 | 273.05 | 273.30 | 273.56 273.81 | 274.07 | 10.80 | 274.32 | 274.57 | 274-93 275.08 | 275.34 | 275.59 | 275-84 | 276.10 | 276.35 | 276.61 | 10.90 | 276.86 | 277.11 | 277.37 | 277-62 | 277.88 | 278.13 | 278.38 278.64 | 278.89 | 279.15 11.00 | 279.40 | 279.65 | 279.91 | 280.16 | 280.42 | 280.67 | 280.92 | 281.18 | 281.43 | 281.69 11.1G | 281.94 | 282.19 | 282.45 | 282.70 | 282.96 | 283.21 | 283.46 | 283.72 | 283.97 | 284.23 11.20 | 284.48 | 284.73 | 284.99 | 285.24 | 285.50 | 285.75 | 286.00 | 286.26 | 286.51 | 286.77 11.30 | 287.02 | 287.27 | 287.53 | 287.78 | 288.04 | 288.29 | 288.54 | 288.80 | 289.05 | 289.31 11.40 | 289.56 | 289.81 | 290.07 | 290.32 | 290.58 | 290.83 | 291.08 | 291.34 | 291.59 | 291.85 11.50 | 292.10 | 292.35 | 292.61 | 292.86 | 293.12 | 293.37 | 293.62 | 293.88 | 294.13 | 294.39 11.60 °} 294.64 | 294.89 | 295.15 | 295.40 | 295.66 | 295.91 | 296.16 | 296.42 298-6 296.93 11.70 | 297.18 | 297.43 | 297-69 | 297.94 | 298.20 | 298.45 | 298.70 | 298.96 | 299.2f | 299.47 11.80 | 299.72 | 299.97 | 300.23 | 300.48 | 300.74 | 300.99 | 301.24 | 301.50 | 301.75 | 302.01 11.90 | 302.26 | 302.51 | 302.77 | 303.02 | 303.28 | 303.53 | 303-78 | 304.04 | 304.29 | 304-55 | £2.00 | 304.80 | 305.05 | 305.31 | 305.56 | 305.82 | 306.07 | 306.32 | 306.58 | 306.83 | 307.09 | 12.10 | 307.34 | 307.59 | 307-85 | 308.10 | 308.36 | 308.61 | 308.86 | 309.12 | 309.37 309.63 12.20 | 309.88 | 310.13 | 310.39 | 310.64 | 310.90 | 311.15 | 311.40 | 311.66 | 311.91 | 312.17 12.30 | 312.42 | 312.67 | 312.93 | 313.18 | 313.44 | 313.69 | 313-94 | 314.20 | 314.45 | 314.71 12.40 | 314.96 | 315.21 | 315-47 | 315-72 | 315-98 | 316.23 | 316.48 316.74 | 316.99 | 317.25 12.50 | 317.50 | 317.75 | 318.01 | 318.26 | 318.52 | 318.77 | 319.02 | 319.28 | 319.53 | 319.79 12.60 | 320.04 | 320.29 | 320.55 | 320.80 | 321.06 | 321.31 | 321.56 | 321.82 | 322.07 | 322.33 | 12.70 | 322.58 | 322.83 | 323.09 | 323.34 | 323-60 | 323.85 | 324.10 | 324.36 | 324.61 324.87 |} 12.80 | 325.12 | 325.37 | 325-63 | 325.88 | 326.14 | 326.39 326.64 | 326.90 | 327.15 | 327-41 | 12.90 | 327.66 | 327.91 | 328.17 | 328.42 | 328.68 | 328.93 | 329.18 | 329.44 329.69 | 329.95 13.00 | 330.20 | 330.45 | 330.71 | 330.96 | 331-22 | 331-47 | 331-72 | 331-98 | 332-23 | 332-49 13.10 | 332.74 | 332-99 | 333-25 | 333-50 | 333-76 | 334-01 | 334-26 | 334-52 | 334-77 | 335-03 13.20 | 335.28 | 335-53 | 335-79 | 336-04 | 336.30 | 336.55 | 336-80 | 337.06 | 337-31 | 337-57 13.30 | 337-82 | 338.07 | 338.33 | 338-58 | 338.84 | 339-09 | 339-34 | 339.60 | 339-85 | 340.11 3.40 | 340.36 | 340.61 | 340.87 | 341.12 | 341.38 | 341.63 | 341.88 | 342.14 | 342.39 342.65 | 13.50 | 342.90 | 343.15 | 343-41 | 343-66 | 343-92 | 344-17 | 344-42 | 344-68 | 344.93 | 345-19 13.60 | 345.44 | 345-69 | 345-95 | 346.20 | 346.46 | 346.71 | 346.96 | 347.22 | 347-47 | 347-73 13.70 | 347.98 | 348.23 | 348.49 | 348.74 | 349.00 | 349.25 | 349-59 | 349-76 | 350.01 | 350.27 13.80 ] 350.52 | 350.77 | 351-03 | 351-28 | 351-54 | 351-79 | 352-04 | 352-30 | 352-55 352.81 | 13-90 | 353.06 | 353-31 | 353-57 | 353-82 354-08 | 354-33 | 354-58 | 354-84 | 355-09 | 355-35 14.00 | 355.60 | 355.85 | 356.11 | 356.36 | 356.62 | 356.87 | 357-12 | 357-38 | 357-63 357.89 14.10 | 358.14 | 358.39 | 358.65 | 358.90 | 359-16 | 359.41 | 359-66 | 359-92 | 360.17 | 360.43 14.20 | 360.68 | 360.93 | 361.19 | 361.44 | 361.70 | 361.95 | 362.20 | 362.46 362.71 | 362.97 14.30 | 363.22 | 363.47 | 363-73 | 363.98 | 364.24 | 364.49 | 364.74 | 365-00 | 365.25 | 305.51 | 14.40 | 365.76 | 366.01 | 366.27 | 366.52 | 366.78 | 367.03 | 367.28 367.54 | 367.79 | 368.05 14.50 | 368.30 | 368.55 | 368.81 | 369.06 | 369.32 | 369.57 | 369.82 | 370.08 | 370.33 | 370.59 14.60 | 370.84 | 371.09 | 371.35 | 371.60 | 371.86 | 372.11 | 372.36 | 372.62 B72°87) (13 73-L3 14.70 | 373.38 | 373-63 | 373-89 | 374-14 | 374-40 | 374-65 | 374-90 | 375-16 | 375-41 | 375.67 14.80 | 375.92 | 376.17 | 376.43 | 376.68 | 376.94 | 377-19 | 377-44 | 377-79 | 377-95 | 378.21 14.90 | 378.46 | 378.71 | 378.97 | 379.22 | 379-48 | 379-73 | 379-98 | 380.24 | 380.49 | 380.75 15.00 | 351.00 381.51 | 381.76 | 382.02 | 382.27 | 382.52 | 382.78 | 383.03 383.29 7 Inch. 0.001 0.002 0.003 0.004 0.005 0,006 0.007 0.008 0.009 Esopartorias Baris: Mm, 0.025 0.051 0.076 0.102 0.127 0.152 0.178 0.203 0.229 SMITHBONIAN TABLES. 182 TABLE 64. i INCHES INTO MILLIMETRES. I inch = 25.40005 mm. 386.08 388.62 | 391.16 393-79 396. 24 398.78 401.32 403.86 406.40 408.94 411.48 414.02 416.56 419.10 421.64 424.18 426.72 429.26 431.80 434-34 436.88 439.42 441.96 444.50 447.04 449.58 452.12 454.66 457.20 459.74 462.28 464.82 467.36 469.90 472.44 474.98 477-52 480.06 482.60 485.14 487.68 490.22 492.76 495-30 497.84 500.38 502.92 505.46 Ol mm. 381.25 383-79 386.33 388.87 391.41 393-95 39.649 399-93 401.57 404.11 406.65 409.19 411.73 414.27 416.81 419.35 421.89 424.43 426.97 429.51 432.05 434-59 437-13 439.67 442.21 444.75 447.29 449.83 452.37 454-91 457-45 459-99 462.53 465.07 467.61 470.15 472.69 475.23 477-77 480.31 482.85 485.39 487.93 490.47 493.01 495-55 498.09 500.34 503.18 595-72 508.26 39.93 => 442.47 | 445.01 447.55 450.09 452.63 455-17 457-71 460.25 462.79 465.33 467.87 470.41 472.95 475-49 478.03 480.57 483.11 485.65 488.19 499.73 493-27 495.81 498.35 500.89 593-43 595-97 508.51 381.76 384.30 386.84 389.38 391.92 394.46 | 3 397-00 399-54 402.08 404.62 407.16 409.70 412.24 414.78 417.32 419.86 422.40 424.94 427.48 430.02 432.56 435-10 437.64 440.158 442.72 445. 26 447.80 459.34 452.88 455-42 457-96 460.50 463.04 - 465.58 468.12 470.66 473.20 475-74 478.28 480.82 483.36 485.90 488.44 490.98 493-52 496.06 498.60 501.14 503.68 506. 22 508.76 433-07 435-61 438.15 440.69 443.23 445-77 448.31 450.85 453-39 455-93 458.47 461.01 463.55 466.09 468.63 471.17 473-71 476.25 478.79 3 | 481.33 483.87 486.41 488.95 491.49 494.03 496.57 499.11 501.65 504.19 506.73 509.27 .06 mm, 382.52 385.06 387.60 390. 14 392.68 395.22 397-76 400.30 402.84 405.38 407.92 410.46 413.00 415.54 418.08 420.62 423.16 425.70 428.24 430.78 433-32 435.86 438.40 40.94 443.45 446.02 448.56 451.10 453-64 456.18 458.72 461.26 463.80 466.34 468.88 471.42 473-96 476.50 479.04 481.58 484.12 486.66 489.20 491.74 494.28 496.82 499. 36 501.91 504-45 506.99 999-53 .07 min, 382.78 385.32 387.86 390.40 392.94 395-48 398.02 400.56 403.10 405.64 408.18 410.72 413.26 415.80 418.34 420.88 423.42 425.96 428.50 431.04 433-58 436.12 438.66 441.20 443-74 446.28 448.82 451.36 453-99 456.44 458.98 461.52 464.06 466.60 469.14 471.68 474.22 476.76 479-39 481.84 484.38 486.92 489. 46 492.00 494.54 497.08 499.62 502.16 504.70 507.24 509.78 -08 mm, 353.03 385-57 388.11 390.65 393-19 395-73 398.27 400.81 403.35 405.89 408.43 410.97 413.51 416.05 418.59 421.13 423.67 426. 21 428.75 431.29 433-83 436.37 438.91 441.45 443-99 446.53 449.07 451.61 454.15 456.69 459.23 | 461.77 464.31 466.85 469.39 471.93 474.47 477.01 479-55 482.09 484.63 487.17 489.71 492.25 494.79 497-33 499.87 502.41 504.95 507-49 510.03 Ea | -09 mim, 383.29 385.83 388. 37 390.91 393-45 395-99 398.53 401.07 403.61 406.15 408.69 411.23 413.77 416.31 418.85 421.39 | 423.93 426.47 429.01 431.55 434-09 436.63 439-17 441.71 444.25 446.79 449-33 451.87 454.41 456.95 | 459-49 462.03 464.57 467.11 469.35 A719) 474.73 | 477-27 479.81 452.35 484.89 487.43 489.97 492.51 | 495-05 497-59 500.13 502.67 505.21 597-75 510.29 Inch. mm, 0.001 0.025 0.002 0.051 0,006 0.152 0.008 0.203 0.003, 0.076 0.004 0.102 0.005 0.127 0.007 0.178 0.009 0.229 Proportional Parts. SMITHSONIAN TABLES. 183 TABLE 64. INCHES INTO MILLIMETRES. I inch = 25.40005 mm. .02 ; . : .06 | .07 | -08 . mm. mm. ° s mm. mm. mm. mim, 20.00 F 508.51 | 508.76 ; 509.27 | 509.53 | 509.78 | 510.03 | 510.29 20.10 .80 | 511.05 | 511.30 : 511.8% | 512.07 | 512.32 | 512.57 | 512.83 20.20 -34 | 513.59 | 513-84 : 514.35 | 514.61 | 514.86 | 515.11 | 515.37 20.30 5.88 | 516.13 | 516.38 .64 | 516.89 | 517.15 | 517-40 | 517.65 | 517.91 20.40 | 518. 3. 518.67 | 518.92 ; 519.43 | 519.69 | 519.94 | 520.19 | 520.45 20.50 -70 | 520. 521.21 | 521.46 : 521.97 | 522.23 | 522.48 | 522.73 | 522.99 20.60 | 523.24 3.50 | 523-75 | 524.00 4. 524.51 | 524.77 | 525.02 | 525.27 | 525.53 20.70 -78 | 526. 526.29 | 526.54 5 526.95 | 527-31 | 527-50 | 527-81 | 528.07 20.80 28. 3.58 | 528.83 | 529.08 -34 | 529.59 | 529.85 | 530.10 | 530.35 | 530.61 20.90 8 512)| 53 037A 530.02 .88 | 532.13 | 532-39 | 532-64 | 532.89 | 533-15 21.00 -40 | 533-66 | 533-91 | 534-16 -42 | 534-67 | 534-93 | 535-18 | 535-43 | 535-69 21.10 .20 | 536.45 | 536.70 | 536.96 | 537-21 | 537-47 | 537-72 | 537-98 | 538.23 21.20 3.48 3.74 | 538.99 | 539.24 -50 | 539-75 | 540.01 | 540.26 | 540.51 | 540.77 21.30 . 41.28 | 541.53 | 541.78 | 542.04 | 542.29 | 542.55 | 542.80 | 543.05 | 543.31 |f 21.40 : .82 | 544.07 | 544.32 .58 | 544.83 | 545-09 | 545.34 | 545-59 | 545-85 21.50 46. 546.61 | 546.86 | 547. 547.37 | 547.63 | 547.88 | 548.13 | 548.39 21.60 | 548.64 | 548.90 | 549.15 | 549.40 | 549. 549.91 | 550.17 | 550.42 | 550.67 | 550.93 21.70 | 551.18 | 551.44 | 551-69 | 551.94 | 552-20 | 552.45 | 552-71 | 552-96 | 553-21 | 553-47 21.80 | 553-72 | 553-98 | 554-23 | 554-48 -74 | 554-99 | 555-25 | 555-50 | 555-75 | 556.01 21.90 6.26 | 556.52 | 556.77 | 557-02 -28 | 557-53 | 557-79 | 558.04 | 558.29 | 558.55 22.00 | 558. 559.06 | 559.31 | 559.56 .82 | 560.07 | 560.03 | 560.58 | 560.83 | 561.09 |f 22.10 .34 | 561.60 | 561.85 | 562.10 | 562. 562.61 | 562.87 | 563.12 | 563.37 | 563.63 |f 22.20 | 563.88 | 564.14 | 564.39 | 564.64 | 564. 565.15 | 565.41 | 565.66 | 565.91 | 566.17 22.30 | 566.42 | 566.68 | 566.93 | 567.18 | 567.44 | 567.69 | 567.95 | 568.20 | 568.45 | 568.71 22.40 8.96 | 569.22 | 569.47 | 569.72 | 569.98 | 570.23 | 570.49 | 570.74 | 579.99 | 571.25 22.50 .50 | 571.76 | 572.01 | 572.26 | 572.52 | 572-77 | 573-03 | 573-28 | 573-53 | 57379 22.60 | 574.04 | 574.30 | 574.55 | 574-80 | 575-06 | 575-31 | 575-57 | 575-82 | 576.07 | 576.33 22.70 | 576.58 | 576.84 | 577-09 | 577-34 | 577-60 | 577-95 | 578.11 | 578.36 | 578.61 | 578.87 22.80 |579. 579-38 | 579.63 | 579.88 | 580.14 | 580.39 | 580.65 | 580.90 | 581.15 | 581.41 22.90 | 581.66 | 581.92 | 582.17 | 582.42 | 582.68 | 582.93 | 583.19 | 583.44 | 583.69 | 583.95 23.00 | 584. 584.46 | 584.71 | 584.96 | 585. 585.47 | 585.73 | 585-98 | 586.23 | 586.49 2210.1 586; 587.00 | 587.25 | 587.50 | 587. 588.01 | 588.27 | 588.52 | 588.77 | 589.03 23.20 | 589.28 | 589.54 | 589.79 | 590.04 | 590.30 | 590.55 | 590.81 591.06 | 591.31 | 591.57 23.30 | 591.82 | 592.08 | 592.33 | 592.58 | 592.84 | 593-09 | 593.35 | 593-60 | 593.85 | 594-11 23.40 | 594.36 | 594.62 | 594.87 | 595.12 | 595-38 | 595-63 | 595.89 | 596.14 | 596.39 | 596.65 |f 23.50 ] 596.90 | 597.16 | 597.41 | 597-66 | 597-92 | 598.17 | 598.43 | 598.68 | 598.93 | 599-19 23.60 599.70 | 599.95 | 600.20 | 600.46 | 600.71 | 600.97 | 601.22 | 601.47 | 601.73 |f 23.70 | 601.98 | 602.24 | 602.49 | 602.74 | 603.00 | 603.25 | 603.51 | 603.76 | 604.01 | 604.27 23.80 | 604.52 | 604.78 | 605.03 | 605.28 | 605.54 | 605.79 | 606.05 | 606.30 | 606.55 | 606.81 23.90 | 607.06 | 607.32 | 607.57 | 607.82 | 608.08 | 608.33 | 608.59 | 608.84 | 609.09 | 609.35 | 24.00 | 609.60 | 609.86 | 610.11 | 610.36 | 610.62 | 610.87 | 611.13 | 611.38 | 611.63 | 611.89 24.10 | 612.14 | 612.40 | 612.65 | 612.90 | 613.16 | 613.41 | 613.67] 613.92 | 614.17 | 614.43 24.20 | 614.68 | 614.94 | 615.19 | 615.44 | 615.70 | 615.95 | 616.21 | 616.46 | 616.71 | 616.97 24.30 | 617.22 | 617.48 | 617.73 | 617.98 | 618.24 | 618.49 | 618.75 | 619.00 | 619.25 | 619.51 24.40 | 619.76 | 620.02 | 620.27 | 620.52 | 620.78 | 621.03 | 621.29 | 621.54 | 621.79 | 622.05 | 24.50 | 622.30 | 622.56 | 622.81 | 623.06 | 623.32 | 623.57 | 623.83 | 624.08 | 624.33 | 624.59 | 24.60 | 624.84 | 625.10 | 625.35 | 625.60 | 625.86 | 626.11 | 626.37 | 626.62 | 626.87 | 627.13 24.70 | 627.38 | 627.64 | 627.89 | 628.14 | 628.40 | 628.65 | 628.91 | 629.16 | 629.41 | 629.67 24.80 ] 629.92 | 630.18 | 630.43 | 630.68 | 630.94 | 631.19 | 631.45 | 631.70 | 631.95 | 632.21 24.90 | 632.46 | 632.72 | 632.97 | 633.22 | 633-48 | 633.73 | 633-99 | 634-24 | 634.49 | 634-75 25.00 | 635.00 | 635.26 | 635.51 | 635.76 | 636.02 | 636.27 | 636.53 | 636.78 | 637.03 | 637.29 Inch, 0,001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 Proportional Parts. Mm. 0.025 0.051 0.076 0.102 0.127 0.152 0.178 0,203 0.229 SMITHSONIAN TABLES, TABLE 64. INCHES INTO MILLIMETRES. I inch = 25.40005 mm. mim, . . < mm. mn. mm. mm. mm. 635.00 : 5. ae 636.02 | 636.27 | 636.53 | 636.78 | 637.03 637.54 | 637- OF .30 | 638.56 | 638.81 | 639.07 | 639.32 | 639.57 640.08 ie 4o. .84 | 641.10 | 641.35 | 641.61 | 641.86 | 642.11 642.62 | 642.38 : 643.64 | 643.89 | 644.15 | 644.40 | 644.65 645.16 . ‘ 645.92 | 646.18 | 646.43 | 646.69 | 646.94 | 647.19 647.70 : 48.21 | 648.46 | 648.72 | 648.97 | 649.23 | 649.48 | 649.73 650.24 : 75 | 651.00 | 651.26 | 651.51 | 651.77 | 652.02 | 654.27 652.78 | 653. ‘ 653-54 | 653-80 | 654.05 | 654.31 | 654.56 | 654.81 655.32 | 655. 5.83 | 656.08 | 656.34 | 656.59 | 656.85 | 657.10 | 657.35 657.86 : 58.37 | 658.62 | 658.88 | 659.13 | 659.39 | 659.64 | 659.89 660.40 : : 661.16 | 661.42 | 661.67 | 661.93 | 662.18 | 662.43 662.94 : 3.45 | 663.70 | 663.96 | 664.21 | 664.47 | 664.72 | 664.97 665.48 : 5. 666.24 | 666.50 | 666.75 | 667.01 | 667.26 | 667.51 668.02 : 53 | 668.78 | 669.04 | 669.29 | 669.55 | 669.80 | 670.05 670.56 8 : 671.32 | 671.58 | 671.83 | 672.09 | 672.34 | 672.59 .10 2 3.61 | 673.86 | 674.12 | 674.37 | 674.63 | 674.88 | 675.13 675.64 : 76. 676.40 | 676.66 | 676.91 | 677.17 | 677.42 | 677.67 678.18 A : 678.94 | 679.20 | 679.45 | 679.71 | 679.96 | 680.21 680.72 .98 | 681. 681.48 | 681.74 | 681.99 | 682.25 | 682.50 | 682.75 683.26 52 | 683. 684.02 | 684.28 | 684.53 | 684.79 | 685.04 | 685.29 685.80 ‘ 686.31 | 686.56 ! 686.82 | 687.07 | 687.33 | 687.58 | 687.83 688.34 | 688.60 | 688.85 | 689.10 | 689.36 | 689.61 | 689.87 | 690.12 | 690.37 690.88 .14 | 691.39 | 691.64 | 691.90 | 692.15 | 692.41 | 692.66 | 692.91 693.42 3.68 | 693.93 | 694.18 | 694.44 | 694.69 | 694.95 | 695.20 | 695.45 695.96 .22 | 696.47 | 696.72 | 696.98 | 697.23 | 697.49 | 697.74 | 697.99 698.50 | 698. 699.01 | 699.26 | 699.52 | 699.77 | 700.03 | 700.28 | 700.53 701.04. .30 | 701.55 | 701.80 | 702.06 } 702.21 | 702.57 | 702.82 | 703.07 703.58 .84 | 704.09 | 704.34 | 704.60 | 704.85 | 705.11 | 705.36 | 705.61 706.12 | 706.38 | 706.63 | 706.88 | 707.14 | 707.39 | 707-65 | 707.90 | 708.15 | 708.41 | 708.66 | 708. 799.17 | 709.42 | 709.68 | 709.93 | 710.19 | 710.44 | 710.69 | 710.95 711.20 : 711.71 | 711.96 | 712.22 | 712.47 | 712.73 | 712.98 | 713-23 | 713-49 |] 12.74 A. 714.2 14.50 | 714.76 | 715.01 | 715.2 15.52 | 715.77 | 716.03 |} 713-74 714.25 79} 7 (tS 22 3°92 | 725-77 | 719-03 716.28 -54 | 716.79 | 717-04 | 717-30 | 717-55 717.81 | 718.06 | 718.31 718.57 | 718.82 9.08 | 719.33 | 719.58 | 719.84 | 720.09 | 720.35 | 720.60 721.11 |f 721.3 722.1 2\\\7 22:39 1722.08 723.14 723.65 | 724.92 | 725.17 VE By 730.25 732-79 735-33 WSieor. 740.41 742.95 743-97 745-49 | 745. 9.00 | 746.25 | 746.51 748.03 | 748. 48.54 | 748.79 | 749.05 750-57 | 750-83 | 751.08 | 751.33 | 751-59 753 753°37 | 753- 753-87 | 754-13 755-91 | 756.16 | 756.41 | 756.67 758.45 | 758.70 | 758.95 | 759.21 760.99 | 761.24 | 761.49 | 761.75 763-53 | 763.78 | 764.03 | 764.29 . ©.00I 0,002 0.003 0.004 0.005 0.006 0.007 0.008 0,009 Proportional Parts. ~ S) © CO ou LS) re eS “I NSO won ~ DGS DQ COO OO ~sTIS7I“Is“I "I WOW byt INNN NN WD WoNNN Co DY rt DO ® WOa& nN o# Co Oo CON NTH WD WOM BNI OO NANIWO SIS NTN NST OS ON on ~J Oo “I af OH “IR Hs ~I SS al os Oo 0.025 0.051 0.076 0.102 0.127 0.152 0.178 0.203 0.229 SMITHSONIAN TABLES. 185 TABLE 64. Inches. 30.00 30.10 30.20 30.30 30.40 30.50 30.60 30.70 30.80 30.90 31.00 31.10 31.20 31.30 31.40 31.50 .60 fO .50 31.90 32.00 Proportional Parts. INCHES INTO MILLIMETRES. I inch —25.40005 mm. 787.40 789.94 792.48 795-02 797-5 S00. S02.€ $05.18 807.72 S10. 2 812.8c min. | 762.26 | 764.80 | 767.34 769.88 772-42 774-96 777-59 780.04 782.58 795. 787. Inch. mm. mm, 762.5) 765-05 767.59 779-13 772.67 SNS MMmOnINI nn vb ON UI ® MOnnT bd S1G2 0 OH 787.91 799-45 792-99 795-53 798.07 800.61 803.15 805.69 808.23 810.77 | | ®.00I 0.025 Soo0.86 503.40 505.94 808. 48 SII.02 0.002 0.051 SSSI SI OM MmxanI unr QD 803.91 806.45 $08.99 SII.53 0.094 0.005 0.102 0.127 0.006 0.152 0.007 0.178 764.03 766.57 769.11 771.65 774-19 776.73 779-27 781.81 784.35 786.89 789.43 791.97 794-51 797-05 799-59 802.13 804.67 807.21 $09.75 812.29 0.008 0.203 0.009 0.229 a a a SMITHSONIAN TABLES. TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. tee 0.0000 | 0.0394 | 0.0787 | 0.1181 | 0.1575] 0.1968 | 0.2362 0.2756} 0.3150 0.3543 | 0.3937 | 0.4331 | 0.4724| 0.5118] 0.5512] 0.5906 | 0.6299 0.6693 | 0.7087 | 0.7480 | 0.7874| 0.8268 | 0.8661 | 0.9055 | 0.9449] 0.9842 | 1.0236 1.0630] 1.1024] 1.1417 L.I811| 1.2205| 1.2598| 1.2992| 1.3386] 1.3780] 1.4173 | 1.4567 | 1.4961 | 1.5354 1.5748| 1.6142] 1.6535] 1.6929| 1.7323] 1.7716] 1.8110] 1.8504 1.8898 | 1.9291 1.9685 | 2.0079 | 2.0472| 2.0866] 2.1260] 2.1654] 2.2047| 2.2441 2.2835 | 2.3228 2.3622| 2.4016| 2.4409| 2.4803| 2.5197] 2.5590} 2.5984 2.6378 | 2.6772| 2.7165 7 2.7953 | 2.8346] 2.8740| 2.9134] 2.9528] 2.9921 | 3.0315 | 3-0709| 3.1102 3.1890 | 3.2283 | 3-2677| 3.3071| 3-3464| 3-3858| 3.4252 | 3.4646 | 3.5039 3.5828 | 3.6220| 3.6614] 3.7008] 3.7402 | 3.7795 | 3.8189 3.8583 | 3.8976 3.9764 | 4.0157| 4.0551 | 4.0945] 4.1338 | 4.1732| 4.2126] 4.2520] 4.2913 4.3701 | 4.4094| 4.4488] 4.4882] 4.5276 | 4.5669 | 4.6063 4.6457 | 4.6850 4.7638 | 4.8031 | 4.8425 | 4.8819] 4.9212| 4.9606] 5.0000 | 5.0394 5.0787 5.1575 | 5-1968]| 5.2362] 5.2756] 5-3150| 5-3543| 5-3937 | 5-4331 | 5.4724 5.5512| 5.5905| 5.6299| 5.6693] 5.7086] 5.7480] 5.7574 5.8268 | 5.8661 5.9449 | 5.9842| 6.0236| 6.0630] 6.1024 | 6.1417 | 6.1811 6.2205 | 6.2598 6.3386 | 6.3779| 6.4173 | 6.4567] 6.4960] 6.5354 | 6.5748 | 6.6142 6.6535 6.7323 | 6.7716] 6.8110] 6.8504} 6.8898 | 6.9291 | 6.9685 | 7.0079 | 7-0472 7.1260] 7.1653| 7.2047 | 7.2441] 7.2834| 7.3228] 7.3622 7.4016 | 7.4409 7-5197,| 7-559°| 7-5984| 7-6378| 7-6772| 7-7165 | 7-7559| 7-7953 | 7-8346 7.9134 | 7-9527| 7.9921 | 8.0315] 8.0708 | 8.1102 | 8.1496 8.1890 | 8.2283 8.3071 | 8.3464] 8.3858| 8.4252] 8.4646 | 8.5039| 8.5433 | 8.5827 8.6220 | 8.7008 | 8.7401 | 8.7795 | 8.8189] 8.8582 | 8.8976 | 8.9370 8.9764 | 9.0157 9.0945 | 9.1338 | 9.1732] 9.2126] 9.2520] 9.2913 | 9.3307 | 9.3701 | 9.4094 9.4882 | 9.5275 | 9.5669| 9.6063} 9.6456| 9.6850] 9.7244 9.7638 | 9.8031 9.8819 | 9.9212] 9.9606 |10.0000 }10.0394 |10.0787 |10.1 181 |10.1575 10.1968 | 10.2756 |10.3149 |10.3543 |10.3937 |L0.4330 |10.4724 |10.5118 |10.5512 |10.5905 10.6693 |10.7086 |10.7480 | 10.7874 ]10.8268 |10.8661 |10.9055 10.9449 |10.9842 11.0630 |LI.1023 |II.1417 |11.18F [11.2204 |£1.2598 | 11.2992 |11.3338 |11.3779 11.4568 |11.4960 [11.5354 |11.5748 ]I 1.6142 |11.6535 [11.6929 |11.7323 11.7716| 11.8504 |11.8897 |11.9291 |11.9685 |12.0078 |12.0472 |12.0866 12.1260 |12.1653 12.2441 |12.2834 |12.3228 |12.3622 |12.4016 |12.4409 12.4803 |12.5197 |12.5590 | 12.6378 |12.6771 |12.7165 |£2.7559 |12.7952 |12.8346 |12.8740 |12.9134 12.9527 | 13.0315 |13.0708 |13.1102 |13.1496 }13.1890 |13.2283 13.2677 |13.3071 |13-3464 | 13.4252 |13.4645 |13.5039 |13-5433 [13-5826 |13.6220 |13.6614 13.7008 |13.7401 | 13.8189 |13.8582 |13.8976 |13.9370 |13-9764 |14.0157 |14.0551 14.0945 |14.1338 | 32 |14.2126 |14.2519 |14.2913 |14.3307 [14.3700 |14.4094 14.4488 |14.4882 |14.5275 5669 |14.6063 |14.6456 |14.6850 |14.7244 |1 4.7638 |1 4.8031 |14.8425 14.8819 |14.9212 15.0000 |I5.0393 |15.0787 |15.L181 |15.1574 |15.1968 |15.2362 15.2756 |15.3149 | 15.3937 |15-4330 |15.4724 |15.5118 |15.5512 |15.5905 15.6299 15.6693 |15-7086 | | 15.7874 |15.8267 |15.8661 |15.9055 |15.9448 |15.9842 |16.0236 16.0630 |16.1023 | SMITHSONIAN TABLES. Tenths of a millimetre. 187 Hundredths of a millimetre. Inch. 0.0024 .0028 -0031 -0035 .0039 TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. . | 400 | 15.748 | 15.752 | 15.756 | 15.760 | 15.764 | 15.768 | 15.772 | 15.776 | 15.779 | 15.783 | 401 15.787 | 15-791 | 15-795 | 15-799 | 15.803 | 15.807 | 15.811 | 15.815 | 15.819 | 15.823 402 15.827 | 15.831 | 15.835 | 15.839 | 15.842 | 15.846 | 15.850 | 15.854 | 15.858 | 15.862 | 403 15.866 | 15.870 | 15.874 | 15.878 | 15.882 | 15.886 | 15.890 | 15.894 | 15.898 | 15.902 404 15-905 | 15-909 | 15-913 | 15-917 | 15.921 | 15.925 | 15.929 | 15.933 | 15-937 | 15.941 Inches. 406 15.994 | 15.988 | 15.992 | 15.996 | 16.000 | 16.004 | 16.008 | 16.012 | 16.016 | 16.020 407 16.024 | 16.028 | 16.031 | 16.035 | 16.039 | 16.043 | 16.047 | 16.051 | 16.055 | 16.059 408 16.063 | 16.067 | 16.071 | 16.075 | 16.079 | 16.083 | 16.087 | 16.091 | 16.094 | 16.098 409 | 16.102 | 16.106 | 16.110 | 16.114 | 16.118 | 16.122 | 16.126 | 16.130 | 16.134 | 16.138 | | | 405 | 15.945 | 15.949 | 15.953 | 15-957 | 15.961 | 15.965 | 15.968 | 15.972 | 15.976 | 15.980 | | | 410 | 16.142 | 16.146 | 16.150 | 16.154 | 16.157 | 16.161 | 16.165 | 16.169 | 16.173 | 16.177 411 16.181 | 16.185 | 16.189 | 16.193 | 16.197 | 16.201 | 16.205 | 16.209 | 16.213 | 16.217 412 16.220 | 16.224 | 16.228 | 16.232 | 16.236 | 16.240 | 16.244 | 16.248 | 16.252 | 16.256 413 16.260 | 16.264 | 16.268 | 16.272 | 16.276 | 16.279 | 16.283 | 16.287 | 16.291 | 16.295 414 | 16.299 | 16.303 | 16.307 | 16.311 | 16.315 | 16.319 | 16.323 | 16.327 | 16.331 | 16.335 | | | AIS 16.339 | 16.342 | 16.346 | 16.350 | 16.354 | 16.358 | 16.362 | 16.366 | 16.370 | 16.374 416 16.378 | 16.382 | 16.386 | 16.390 | 16.394 | 16.398 | 16.402 | 16.405 | 16.409 | 16.413 | 417 16.417 | 16.421 | 16.425 | 16.429 | 16.433 | 16.437 | 16.441 | 16.445 | 16.449 | 16.453 | } 418 16.457 | 16.461 | 16.465 | 16.468 | 16.472 | 16.476 | 16.480 | 16.484 | 16.488 | 16.492 "ATS 16.496 | 16.500 | 16.504 | 16.508 | 16.512 | 16.516 | 16.520 | 16.524 | 16.528 | 16.531 420 | 16.535 | 16.539 | 16.543 | 16.547 | 16.551 | 16.555 | 16.559 | 16.563 | 16.567 | 16.571 421 16.575 | 16.579 | 16.583 | 16.587 | 16.591 | 16.594 | 16.598 | 16.602 | 16.606 | 16.610 22 16.614 | 16.618 | 16.622 | 16.626 | 16.630 | 16.634 | 16.638 | 16.642 | 16.646 | 16.650 423 16.654 | 16.657 | 16.661 | 16.665 | 16.669 | 16.673 | 16.677 | 16.681 | 16.685 | 16.689 424 16.693 | 16.697 | 16.701 | 16.705 | 16.709 | 16.713 | 16.717 | 16.720 | 16.724 | 16.728 425 | 16.732 | 16.736 | 16.740 | 16.744 | 16.748 | 16.752 | 16.756 | 16.760 | 16.764 | 16.768 | 426 16.772 | 16.776 | 16.779 | 16.783 | 16.787 | 16.791 | 16.795 | 16.799 | 16.803 | 16.807 427 16.811 | 16.815 | 16.819 | 16.823 | 16.827 | 16.831 | 16.835 | 16.839 | 16.842 | 16.846 | 428 16.850 | 16.854 | 16.858 | 16.862 | 16.866 | 16.870 | 16.874 | 16.878 | 16.882 | 16.886 429 16.890 | 16.894 | 16.898 | 16.902 | 16.905 | 16.909 | 16.913 | 16.917 | 16.921 | 16.925 430 | 16.929] 16.933 | 16.937 | 16.941 | 16.945 | 16.949 | 16.953 | 16.957 | 16.964 | 16.965 431 16.968 | 16.972 | 16.976 | 16.980 | 16.984 | 16.988 | 16.992 | 16.996 | 17.000 | 17.004 432 17.008 | 17.012 | 17.016 | 17.020 | 17.024 | 17.028 | 17.031 | 17.035 | 17.039 | 17.043 | 433 17.047 | 17.051 | 17.055 | 17.059 | 17.063 | 17.067 | 17.071 | 17.075 | 17.079 | 17.083 | 434 17.087 | 17.091 | 17.094 | 17.098 | 17.102 | 17.106 | 17.110 | 17.114 | 17.118 | 17.122 |f 435 [17.126 | 17.130 | 17.134 | 17.138 | 17.142 | 17.146 | 17.150 | 17.154 | 17.157 | 17.161 |f 436 17.165 | 17.169 | 17.173 | 17.177 | 17-181 | 17.185 | 17.189 | 17.193 | 17.197 | 17.aOr | 437 17.205 | 17.209 | I7.213 | 17.217 | 17.220 | 17.224 | 17.228 | 17.232 | 17.236 | 17.240 || 438 17.244 | 17.248 | 17.252 | 17.256 | 17.260 | 17.264 | 17.268 | 17.272 | 17.276 | 17.279 |F 439 17.283 | 17.287 | 17.291 | 17.295 | 17.299 | 17.303 | 17.307 | 17.311 | 17.315 | 17.319 | | 440 | 17.323 | 17.327 | 17-331 | 17-335 | 17-339 | 17-342 | 17-346 | 17.350 | 17.354 | 17.358 | | 441 17.362 | 17.366 | 17.370 | 17.374 | 17.378 | 17.382 | 17.386 | 17.390 | 17.394 | 17.398 | | 442 17.402 | 17.405 | 17.409 | 17.413 | 17.417 | 17.421 | 17.425 | 17.429 | 17.433 | 17.437 | 443 | 17.441 | 17.445 | 17.449 | 17-453 | 17-457 | 17-461 | 17.465 | 17.468 | 17.472 | 17.476 | | 444 17.480 | 17.484 | 17.488 | 17.492 | 17.496 | 17.500 | 17.504 | 17.508 | 17.512 | 17.516 | | 445 | 17.520 | 17.524 | 17.528 | 17-531 | 17-535 | 17-539 | 17-543 | 17-547 | 17-551 | 17-555 446 |17.559 | 17.563 | 17.567 | 17.571 | 17-575 | 17-579 | 17-583 | 17-587 | 17.591 | 17.594 447 17.598 | 17.602 | 17.606 | 17.610 | 17.614 | 17.618 | 17.622 | 17.626 | 17.630 | 17.634 | 448 17.638 | 17.642 | 17.646 | 17.650 | 17.654 | 17.657 | 17.661 | 17.665 | 17.669 | 17.673 3 | 449 17.677 | 17.681 | 17.685 | 17.689 | 17.693 | 17.697 | 17.701 | 17.705 | 17.709 | 17.713 450 | 17.717 | 17.720 | 17.724 | 17.728 | 17:732'| 17.736'| 17-740 | 17.744) 17. 7A8,| 17.752 SMITHSONIAN TABLES. 188 , TABLE 65, MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres, Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches, Inches. 17.717 | 17.720 | 17.724 | 17.728 | 17.732 | 17-736 | 17-740 | 17-744 17.748 | 17.752 17.756 | 17.760 | 17.764 | 17.768 | 17.772 | 17.776 | 17.779 | 17-783 | 17-787 | 17-791 17.795 | 17.799 |. 17-803 | 17.807 | 17.811 | 17.815 | 17.519 PROS A LOS lly .OoL 17.835 | 17.839 | 17.842 | 17.846 | 17.850 | 17.854 | 17.858 | 17.862 17.866 | 17.870 17.874 | 17.878 | 17.882 | 17.886 | 17.890 | 17.894 | 17.898 | 17.902 | 17.905 | 17.909 17.913 | 17-917 | 17.921 | 17.925 | 17-929 | 17-933 | 17-937 | 17-941 | 17-945 | 17-949 7.953 | 17-957 | 17.961 | 17.965 | 17-968 | 17-972 | 17.976 | 17.980 | 17.984 17.988 17.992 | 17.996 | 18.000 | 18.004 | 18.008 | 18.012 | 18.016 | 18.020 | 18.024 18.028 18.031 | 18.035 | 18.039 | 18.043 | 18.047 | 18.051 | 18.055 | 18.059 18.063 .067 18.071 | 18.075 | 18.079 | 18.083 | 18.087 | 18.091 | 18.094 | 18.098 | 18. 102 3. 106 18.110 | 18.114 | 18.118 | 18.122 | 18.126 | 18.130 | 18.134 | 18.138 | 18.142 .146 18.150 | 18.154 | 18.157 | 18.161 | 18.165 | 18.169 | 18.173 | 18.177 | 18.181 3.185 18.189 | 18.193 | 18.197 | 18.201 | 18.205 | 18.209 | 18.213 | 18.216 | 18.220 | 18.224 18.228 | 18.232 | 18.236 | 18.240 | 18.244 | 18.248 | 18.252 | 18.256 | 18.260 | 18.264 18.268 | 18.272 | 18.276 | 18.279 | 18.283 | 18.287 | 18.291 | 18.295 | 18.299 -303 18.307 | 18.311 | 18.315 | 18.319 | 18.323 | 18.327 | 18.331 | 18.335 | 18.339 342 18.346 | 18.350 | 18.354 | 18.358 | 18.362 | 18.366 | 18.370 | 18.374 | 18.378 | 18.382 18.386 | 18.390 | 18.394 | 18.398 | 18.402 | 18.405 | 18.409 | 18.413 | 18.417 | 18.421 18.425 | 18.429 | 18.433 | 18.437 | 18.441 | 18.445 | 18.449 | 18.453 | 18.457 461 | 18.465 | 18.468 | 18.472 | 18.476 | 18.480 | 18.484 | 18.488 | 18.492 | 18.496 | 18.500 | 18.504 | 18.508 | 18.512 | 18.516 | 18.520] 18.524 | 18.528 | 18.531 | 18.535 539 | 18.543 | 18.547 | 18.551 | 18.555 | 18. 18.563 | 18.567 | 18.571 | 18.575 | 18.579 18.583 | 18.587 | 18.591 | 18.594 | 18.598 | 18.602 | 18.606 | 18.610 18.614 | 18.618 | 18.622 | 18.626 | 18.630 | 18.634 .638 | 18.642 | 18.646 | 18.650 | 18.654 | 18.657 18.661 | 18.665 | 18.669 | 18.673 | 18. 18.681 | 18.685 | 18.689 | 18.693 | 18.697 18.701 | 18.705 | 18.709 | 18.713 a7 18.720 | 18.724 | 18.728 | 18.732 | 18.736 18.740 | 18.744 | 18.748 | 18.752 : 18.760 | 18.764 | 18.768 | 18.772 | 18.77 18.779 | 18.783 | 18.787 | 18.791 .795 | 18.799 | 18.803 | 18.807 | 18.811 | 18.815 18.819 | 18.823 | 18.827 | 18.831 3 18.839 |'18.842 | 18.846 | 18.850 | 18.854 18.858 | 18.862 | 18.866 | 18.870 | 18. 18.878 | 18.882 | 18.886 | 18.890 | 18.894 18.898 | 18.902 | 18.905 | 18.909 : 18.917 | 18.921 | 18.925 | 18.929 | 18.933 | 18.937 | 18.941 | 18.945 | 18.949 .953 | 18.957 | 18.961 | 18.965 | 18.968 | 18.972 | 18.976 | 18.980 | 18.984 | 18.988 : 18.996 | 19.000 | 19.004 | 19.008 | 19.012 19.016 | 19.020 | 19.024 | 19.028 .031 | 19.035 | 19.039 | 19.043 | 19.047 | 19.051 19.055 | 19.059 | 19.063 | 19.067 : 19.075 | 19.079 | 19.083 | 19.087 | 19.091 19.094 | 19.098 | 19.102 | 19.106 | 19.110 114 | 19-118 | 19.122 | 19.126 | 19.130 | 19.134 | 19.138 | 19.142 | 19.146 | 19.150 .154 | 19.157 | 19.161 | 19.165 | 19.169 | 19.173 | 19.177 | 19.181 | 19.185 | 19.189 .193 | 19.197 | 19.201 | 19.205 | 19.209 19.213 | 19.216 | 19.220 | 19.224 | 19.228 : 19.236 | 19.240 | 19.244 | 19.248 19.252 | 19.256 | 19.260 | 19.264 | 19.268 2 19.276 | 19.279 | 19.283 | 19.287 19.291 | 19.295 | 19.299 | 19.303 | 19.307 ie 19.315 | 19.319 | 19.323 | 19.327 19.331 | 19.335 | 19.339 | 19.342 | 19.346 | 19.3: 19.354 | 19.358 | 19.362 19.366 | 19.370 | 19.374 | 19.378 | 19.382 | 19.386 .390 | 19.394 | 19.398 | 19.402 | 19.405 19.409 | 19.413 | 19.417 | 19.421 | 19.425 . 19.433 | 19-437 | 19-441 | 19.445 | 19.449 | 19.453 | 19.457 | 19.461 | 19.465 | 19.468 | 19.472 | 19.476 | 19.480 | 19.484 19.488 | 19.492 | 19.496 19.500 | 19.504 Be 19.512 | 19.516 | 19.520 19.528 19.531 | 19.535 | 19-539 | 19-543 -547 | 19.551 | 19.555 | 19.559 19.567 | 19.571 | 19.575 | 19.579 | 19.553 .587 | 19.591 | 19.594 | 19.598 19.606 | 19.610 | 19.614 | 19.618 | 19.622 .626 | 19.630 | 19.634 | 19.638 19.646 | 19.650 | 19.654 | 19.657 | 19.661 .665 | 19.669 | 19.673 | 19.677 19.685 | 19.689 | 19.693 | 19.697 | 19.701 } 19.705 | 19.709 BPRS | tO 1E0 SMITHSONIAN TABLES. 189 TABLE 65 MILLIMETRES INTO INCHES. I mm. == 0.03937 inches Milli- 0 A 2 metres. Inches. | Inches. | Inches. | Inches. | Inches. | Inches, | Inches. | Inches. | Inches, | Inches. 19.685 | 19.689 | 19.693 | 19.697 | 19.701 | 19.705 | 19.709 | 19.713 | 19.716 | 19.720 19.724 | 19.728 | 19.732 | 19.736 | 19.740 | 19.744 | 19.748 | 19.752 | 19.756 | 19.760 19.764 | 19.768 | 19.772 | 19.776 | 19.779 | 19.783 | 19.787 | 19.791 | 19.795 | 19.799 19.803 | 19.807 | 19.811 | 19.815 | 19.819 | 19.823 | 19.827 | 19.831 | 19.835 | 19.839 19.842 | 19.846 | 19.850 | 19.854 | 19.858 | 19.862 | 19.866 | 19.870 | 19.874 | 19.878: 19.882 | 19.886 | 19.890 | 19.894 | 19.898 | 19.902 | 19.905 | 19.909 | 19.913 | 19.917 19.921 | 19.925 | 19.929 | 19.933 | 19.937 | 19.941 | 19.945 | 19-949 | 19.953 | 19.957 19.961 | 19.965 | 19.968 | 19.972 | 19.976 | 19.980 | 19.984 | 19.988 | 19.992 | 19.996 20.000 | 20.004 | 20.008 | 20.012 | 20.016 | 20.029 | 20.024 | 20.028 | 20.031 | 20.035 20.039 | 20.043 | 20.047 | 20.051 | 20.055 | 20.059 | 20.063 | 20.067 | 20.071 | 20.075 20.079 | 20.083 | 20.087 | 20.091 | 20.094 | 20.098 | 20.102 | 20.106 | 20.110 | 20.114, 20.118 | 20.122 | 20.126 | 20.130 | 20.134 | 20.138 | 20.142 | 20.146 | 20.150 | 20.154 20.157 | 20.161 | 20.165 | 20.169 | 20.173 | 20.177 | 20.181 | 20.185 | 20.189 | 20.193 20.197 | 20.201 | 20.205 | 20.209 | 20.213 | 20.216 | 20.220 | 20.224 | 20.228 | 20.232 20.236 | 20.240 | 20.244 | 20.248 | 20.252 | 20.256 | 20.260 | 20.264 | 20.268 | 20.272 20.276 | 20.279 | 20.283 | 20.287 | 20.291 | 20.295 | 20.299 | 20.303 | 20.307 | 20.311 20.315 | 20.319 | 20.323 | 20.327 | 20.331 | 20.335 | 20.339 | 20.342 | 20.346 | 20.350 20.354 | 20.358 | 20.362 | 20.366 | 20.370 | 20.374 | 20.378 | 20.382 | 20.386 | 20.390 20.394 | 20.398 | 20.402 | 20.405 | 20.409 | 20.413 | 20.417 | 20.421 | 20.425 | 20.429 20.433 | 20.437 | 20.441 | 20.445 | 20.449 | 20.453 | 20.457 | 20.461 | 20.465 | 20.468 20.472 | 20.476 | 20.480 | 20.484 | 20.488 | 20.492 | 20.496 | 20.500 | 20.504 | 20.508 20.512 | 20.516 | 20.520 | 20.524 | 20.528 | 20.531 | 20.535 | 20.539 | 20.543 | 20.547 20.551 | 20.555 | 20.559 | 20.563 | 20.567 | 20.571 | 20.575 | 20.579 | 20.583 | 20.587 20.591 | 20.594 | 20.598 | 20.602 | 20.606 | 20.610 | 20.614 | 20.618 | 20.622 | 20.626 20.630 | 20.634 | 20.638 | 20.642 | 20.646 | 20.650 | 20.654 | 20.657 | 20.661 | 20.665 20.669 | 20.673 | 20.677 | 20.681 | 20.685 | 20.689 | 20.693 | 20.697 | 20.701 | 20.705 20.709 | 20.713 | 20.716 | 20.720 | 20.724 | 20.728 | 20.732 | 20.736 | 20.740 | 20.744 20.748 | 20.752 | 20.756 | 20.760 | 20.764 | 20.768 | 20.772 | 20.776 | 20.779 | 20.783 20.787 | 20.791 | 20.795 | 20.799 | 20.803 | 20.807 | 20.811 | 20.815 | 20.819 | 20.823 20.827 | 20.831 | 20.835 | 20.839 | 20.842 | 20.846 | 20.850 | 20.854 | 20.858 | 20.862 20.866 | 20.870 | 20.874 | 20.878 | 20.882 | 20.886 | 20.890 | 20.894 | 20.898 | 20.902 20.905 | 20.909 | 20.913 | 20.917 | 20.921 | 20.925 | 20.929 | 20.933 | 20.937 | 20.941 20.945 | 20.949 | 20.953 | 20.957 | 20.961 | 20.965 | 20.968 | 20.972 | 20.976 | 20.980 20.984 | 20.988 | 20.992 | 20.996 | 21.000 | 21.004 | 21.008 | 21.012 | 21.016 | 21.020 21.024 | 21.028 | 21.031 | 21.035 | 21.039 | 21.043 | 21.047 | 21.051 | 21.055 | 21.059 21.063 | 21.067 | 21.071 | 21.075 | 21.079 | 21.083 | 21.087 | 21.091 | 21.094 | 21.098 21.102 | 21.106 | 21.110 | 21.114 | 21.118 | 21.122 | 21.126 | 21.130 | 21.134 | 21.138 21.142 | 21.146 | 21.150 | 21.154 | 21.157 | 21.161 | 21.165 | 21.169 | 21.173 | 21.177 21.181 | 21.185 | 21.189 | 21.193 | 21.197 | 21.201 | 21.205 | 21.209 | 21.213 | 21.216 21.220 | 21.224 | 21.228 | 21.232 | 21.236 | 21.240 | 21.244 | 21.248 | 21.252 | 21.256 H _ 21.260 | 21.264 | 21.268 | 21.272 | 21.276 | 21.279 | 21.283 | 21.287 | 21.291 | 21.295 2 .303 | 21-307 || 21° 311!|' 21.315) 21.319)| 1215323) |. 20 e271 for sais 2neRs5 21.339 | 21.342 | 21.346 | 21.350 | 21.354 | 21.358 | 21.362 | 21.366 | 21.370 | 21.374 21.378 | 21.382 | 21.386 | 21.390 | 21.394 | 21.398 | 21.402 | 21.405 | 21.409 | 21.413 21.417 | 21.421 | 21.425 | 21.429 | 21.433 | 21.437 | 21.441 | 21.445 | 21.449 | 21.453 21.457 | 21.461 | 21.465 | 21.468 | 21.472 | 21.476 | 21.480 | 21.484 | 21.488 | 21.492 21.496 | 21.500 | 21.504 | 21.508 | 21.512 | 21.516 | 21.520 | 21.524 | 21.528 | 21.531 21.535 | 21.539 | 21.543 | 21.547 | 21.551 | 21.555 | 21-559 | 21-563 |'21.567 | 21.571 21.575 | 21.579 | 21.583 | 21.587 | 21.591 | 21.594 | 21.598 | 21.602 | 21.606 | 21.610 21.614 | 21.618 | 21.622 | 21.626 | 21.630 | 21.634 | 21.638 | 21.642 | 21.646 | 21.650 nN \O Ne} nN 21.654 | 21.657 | 21.661 | 21.665 | 21.66g | 21.673 | 21.677 | 21.681 | 21.685 | 21.689 SMITHSONIAN TABLES. 190 TABLE 65. MILLIMETRES INTO INCHES. I mm, = 0.03937 inches metres. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. 21.654 | 21.657 | 21.661 | 21.665 | 21.669 | 21.673 | 21.677 | 21.681 | 21.685 | 21.689 21.693 | 21.697 | 21.701 | 21.705 | 21.709 | 21.713 | 21.716 | 21.720 | 21.724 | 21.728 21.732 | 21.736 | 21.740 | 21.744 | 21.748 | 21.752 | 21.756 | 21.760 | 21.764 21.768 21.772 | 21.776 | 21.779 | 21.783 | 21.787 | 21.791 | 21.795 | 21.799 | 21.803 | 21.807 21.811 | 21.815 | 21.819 | 21.823 | 21.827 | 21.831 | 21.835 | 21.839 | 21.842 | 21.846 21.850 | 21.854 | 21.858 | 21.862 | 21.866 | 21.870 | 21.874 | 21.878 | 21.882 | 21.886 21.890 | 21.894 | 21.898 | 21.902 | 21.905 | 21.909 | 21.913 | 21.917 | 21.921 | 21.925 21.929 | 21.933 | 21.937 | 21.941 | 21.945 | 21.949 | 21.953 | 21.957 | 21.961 | 21.965 21.968 | 21.972 | 21.976 | 21.980 | 21.984 | 21.988 | 21.992 | 21.996 | 22.000 | 22.004 22.008 | 22.012 | 22.016 | 22.020 | 22.024 | 22.028 | 22.031 | 22.035 | 22.039 | 22.043 22.047 | 22.051 | 22.055 | 22.059 | 22.063 | 22.067 | 22.071 | 22.075 | 22.079 | 22.083 22.087 | 22.091 | 22.094 | 22.098 | 22.102 | 22.106 - 110 .1I4 .118 | 22.122 22.126 | 22.130 | 22.134 | 22.138 | 22.142 | 22.146 .150 .153 »157 | 22.100 22.165 | 22.169 | 22.173 | 22.177 | 22.181 | 22.185 .189 .193 .197 | 22.201 22.205 | 22.209 | 22.213 | 22.216 | 22.220 | 22.224 .228 £232 .236 | 22.240 22.244 | 22.248 | 22.252 | 22.256 | 22.260 | 22.264 .268 272 £276) || 22.270 22.283 | 22.287 | 22.291 | 22.295 | 22.299 | 22.303 | 22.307 SSD |, 22° 30591225310 22.323 | 22.327 | 22.331 | 22.335 | 22.339 | 22.342 | 22.346 350 | 22.354 358 22.362 | 22.366 | 22.370 | 22.374 | 22.378 | 22.382 | 22.386 .390 | 22.394 .398 22.402 | 22.405 | 22.409 | 22.413 | 22.417 | 22.421 | 22.425 | 22.429 | 22.433 437 22.441 | 22.445 | 22.449 | 22.453 | 22.457 | 22.461 | 22.465 .468 | 22.472 .476 22.480 | 22.484 | 22.488 | 22.492 | 22.496 | 22.500 | 22.504 .508 | 22.512 516 22.520 | 22.524 | 22.528 | 22.531 | 22.535 | 22.539 | 22.543 -547 | 22.551 555 22.559 | 22.563 | 22.567 | 22.571 | 22.575 | 22.579 | 22.583 .587 | 22.591 594 | 22.598 | 22.602 | 22.606 | 22.610 | 22.614 | 22.618 | 22.622 .626 | 22.630 .634 22.638 | 22.642 | 22.646 | 22.650 | 22.653 | 22.657 | 22.661 .665 | 22.669 .673 22.677 | 22.681 | 22.685 | 22.689 | 22.693 | 22.697 | 22.701 .705 | 22.709 | 22.713 22.716 | 22.720 | 22.724 | 22.728 | 22.732 | 22.736 | 22.740 -744 | 22.748 752 | 22.756 | 22.760 | 22.764 | 22.768 | 22.772 | 22.776 | 22.779 YI S322. 707, 791 | 22.795 | 22.799 | 22.803 | 22.807 | 22.811 | 22.815 | 22.819 .823 | 22.827 .831 22.835 | 22.839 | 22.842 | 22.846 | 22.850 | 22.854 | 22.858 .862 | 22.866 22.874 | 22.878 | 22.882 | 22.886 | 22.890 | 22.894 | 22.898 .902 | 22.905 22.913 | 22.917 | 22.921 | 22.925 | 22.929 | 22.933 | 22.937 | 22.941 | 22.945 22.953 |.22.957 | 22.961 | 22.965 | 22.968 | 22.972 | 22.976 | 22.980 | 22.984 22.992 | 22.996 | 23.000 | 23.004 | 23.008 | 23.012 | 23.016 | 23.020 | 23.024 .570 -909 “94 >Q NNNNN Ne) we eC @QNNNN .028 | O51 | 23.055 | 23.059 | 23.063 | 23.067 | .OQI | 23.094 | 23.098 .102 | 23.106 130 | 23.134 | 23.138 : 3.146 169 | 23.173 | 23.177 18 .185 5200) | 23.213, |'23.206 23.031 | 23.035 | 23.039 | 23.043 | 23.047 23.071 | 23.075 -079 | 23.083 | 23.087 23.110 | 23.114 <119) |/23.022)| 23.126 23.150 | 23.153 .157 | 23.161 | 23.165 23.189 | 23.193 .197 | 23.201 | 23.205 23.228 | 23.232 .236 | 23.240 | 23.244 .248 | 23.252 | 23.256 23.268 | 23.272 | 23.276 | 23.279 | 23.283 .287 | 23.291 | 23.295 23.307 | 23-311 | 23.315 | 23.319 | 23.323 +327 | 23-331 | 23-335 23.346 23.350 | 23.354 | 23.358 | 23.362 | 23.366 | 23.370 | 23.374 23.386 | 23.390 | 23.394 | 23.398 | 23.402 | 23.405 | 23.409 | 23.413 23-425 | 23.429 | 23.433 | 23-437 | 23-441 | 23-445 | 23-449 | 23.453 23.465 | 23.468 | 23.472 | 23.476 | 23.480 | 23.484 | 23.488 | 23.492 23.504 | 23.508 | 23.512 | 23.516 | 23.520 | 23.524 | 23.528 | 23.531 23.543 | 23-547 | 23-551 | 23-555 | 23-559 | 23-563 | 23-567 | 23-571 23.583 | 23.587 | 23.591 | 23.594 | 23.598 | 23.602 | 23.606 | 23.610 23.622 | 23.626 | 23.630 | 23.634 | 23.638 | 23.642 | 23.646 | 23.650 Ro wKNHH ND & G2 Go G WW SMITHSONIAN TABLES, IgI TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches | | Milli- | metres. Inches. | 600 | 23.622 }/ 601 23.661 | 602 23.701 | | 603 23.740 | 604 [23.779 | 605 23.819 | 606 23.858 | 607 23.898 | 608 23.937 609 23.976 610 24.016 611 24.055 612 24.094 613 24.134 614 BASITS | 615 24.213 616 24.252 617 24.291 ; 618 24.331 | 619 24.370 | 620 24.409 | a Ook 24.449 622 24.488 623 24.528 624 24.567 625 24.606 626 24.646 627 24.685 | 628 24.724 629 24.764 630 24.803 | 631 24.842 | 632 24.882 | 633 24.921 634 24.961 635 25.000 636 25.039 | 637 | 25-079 | 638 {25.118 | 639 | 25.157 640 25.197 | 641 251236 642 25.276 643 | 25-315 | 644 | 25-354 | 645 25.394 | 646 | 25.433 | 647 | 25.472 648 25.512 649 | 25.551 650 |} 25.591 SMITHSONIAN TABLES. Inches. | 24. 24. 24. 24. 24. Bae 24. 24. NO bw wb NHN nmin NNN NN NS JV WWwNN N On es fe G Oo mau wu 931 728 | 768 | 807 846 886 925 965 tS Gp Ce wun Mm RSID OO nN annn On ae) S LO No HH ND bd G2 Ga G2 Ga Oo to IUIDAD uns S102 0 U1 SI OO YNNHWWwWPH UMN bo vy wb BeSER SS 24.811 24.850 24.890 a) naomi Ow NHN bh Nb NN ND numno iy nr on ‘© or) Odo HW ND amon ; Inches. 634 -673 ate fe -791 bO NNN bd G2 G2 G) G2 Go 23.831 23.870 23.909 23-949 23.988 24.028 vo to Sse HHO of O OV OV Os! 2 to ae H co on to iS) Av N NNN by wn “IG Ob nm. oO tee NnokE om ono NO SeEee HESSS FEELS INI ADA Anns & Oman bv O PY ww NN 1020 On HAAN Bw HY Hb orn 1 U1 ow vnnNN bB&S HH NW NH ow o1gi 24.228 24.268 24.307 Pe heteee tent naanno Lenka oO STO2 0 OF Inches. 23.642 23.681 23.720 23.760 23-799 23.839 23.878 23-917 23-957 23.996 24.035 24.075 24.114 24.553 24.193 24.232 24.272 24.311 24.350 24.390 24.429 24.468 24.508 to mannan NNN NN wo vo bv Nob wooo LPOAa an I WwNN DN IOI LO U1 > u 492 NHNNHNN nm aon “SI Go ro nur _ .610 fF = LS ie © G2 SS Inches. 23.646 23.685 23.724 23.764 23.803 23.842 23.882 3.921 23.961 24.000 24.039 24.079 24.118 24.157 24.197 24.236 24.276 24.315 24.354 24.394 24.433 24.472 24.512 24.551 24.591 Inches. 23.650 23.689 23.728 23.768 23.807 23.846 23.886 23.925 23.965 24.004 24.043 24.083 24.122 24.161 24.201 24.240 24.279 24.319 24.358 24.398 24.437 24.476 24.516 24.555 24.594 24.634 24.673 24.713 24.752 24.791 24.831 24.870 24.909 24.949 24.958 25.028 25.007 .106 .146 .185 22 264 393 342 .382 2 25.461 Inches. 23.653 23.693 23.732 23.772 23.811 23.850 23.890 23.929 23.968 24.008 24.047 24.087 24.126 24.165 24.205 24.244 24.283 24.323 24.362 24.402 24.441 24.480 24.520 24-559 24.598 24.638 24.677 24.716 24.756 24.795 Inches. 23.657 23.697 23.736 23.776 23.815 23.854 23.894 23.933 23.972 24.012 24.051 24.091 24.130 24.169 24.209 24.248 24.287 24.327 24.366 24.405 24.445 24.484 24.524 24.563 24.602 24.642 24.681 24.720 24.760 24.799 24.839 24.878 24.917 24.957 24.996 25.035 25-075 25.114 25-153 25.193 25.232 25.272 25.311 25.350 25-390 | 25.429 |] 25.468 |§ 25.508 25-547 25.587 25.626 TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres. .| Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. 25.594 | 25.598 | 25.602 | 25.606 | 25.610 | 25.614 | 25.618 | 25.622 | 25.626 25.634 | 25.638 | 25.642 | 25.646 | 25.650 | 25.653 | 25.657 | 25.661 | 25.665 | 25.673 | 25.677 | 25.681 | 25.685 | 25.689 | 25.693 | 25.697 | 25.701 | 25.705 ares . 25.720 | 25.724 | 25.728 | 25.732 | 25.736 | 25.740 | 25.744 DT Re : 25.760 | 25.764 | 25.768 | 25.772 | 25.776 | 25.779 | 25.783 25.791 25.831 25.870 25.909 25.949 25.988 26.028 26.067 25.799 | 25.803 | 25.807 | 25.811 | 25.815 | 25.819 | 25.823 25.839 | 25.842 | 25.846 | 25.850 | 25.854 | 25.858 | 25.862 25.878 | 25.882 | 25.886 | 25.890 | 25.894 | 25.898 | 25.902 25-917 | 25-921 | 25-925 | 25-929 | 25-933 | 25-937 | 25-941 | 25.957 | 25.961 | 25.965 | 25.968 | 25.972 | 25.976 | 25.980 | 25.996 | 26.000 | 26.004 | 26.008 | 26.012 | 26.016 | 26.020 26.035 | 26.039 | 26.043 | 26.047 | 26.051 | 26.055 | 26.059 | 26.075 | 26.079 | 26.083 | 26.087 | 26.090 | 26.094 | 26.098 | Oo NNN N anu mon oo DORAN No On \O s) to ONONE ° eT H GO On eID LO No Onc O° eal 26.106 | 26.110 | 26.114 | 26,118 | 26.122 | 26.126 | 26.130 | 26.134 | 26.138 | 26.146 | 26.150 | 26.153 | 26.157 | 26.161 | 26.165 | 26.169 | 26.173 | 26.177 | 26.185 | 26.189 | 26.193 | 26.197 | 26.201 | 26.205 | 26.209 | 26.213 | 26.216 | 26.224 | 26.228 | 26.232 | 26.236 | 26.240 | 26.244 | 26.248 | 26.252 | 26.256 | 26.264 | 26.268 | 26.272 | 26.276 | 26.279 | 26.283 | 26.287 | 26.291 | 26.295 26.303 | 26.307 | 26.311 | 26.315 | 26.319 | 26.323 | 26.327 | 26.331 | 26.335 |I 26.342 | 26.346 | 26.350 | 26.354 | 26.358 | 26.362 | 26.366 | 26.370 | 26.374 | 26.382 | 26.386 | 26.390 | 26.394 | 26.398 | 26.402 | 26.405 | 26.409 | 26.413 26.421 | 26.425 | 26.429 | 26.433 | 26.437 | 26.441 | 26.445 | 26.449 | 26.453 26.461 | 26.465 | 26.468 | 26.472 | 26.476 | 26.480 | 26.484 | 26.488 | 26.492 26.500 | 26.504 | 26.508 | 26.512] 26.516 | 26.520 | 26.524 | 26.528 | 26.531 26.539 | 26.543 | 26.547 | 26.551 | 26.555 | 26.559 | 26.563 | 26.567 | 26.571 26.579 | 26.583 | 26.587 | 26.590] 26.594 | 26.598 | 26.602 | 26.606 | 26.610 |} 26.618 | 26.622 | 26.626 | 26.630] 26.634 | 26.638 | 26.642 | 26.646 | 26.650 26.657 | 26.661 | 26.665 | 26.669 | 26.673 | 26.677 | 26.681 | 26.685 | 26.689 26.697 | 26.701 | 26.705 | 26.709 | 26.713 | 26.716 | 26.720 | 26.724 | 26.728 26.736 | 26.740 | 26.744 | 26.748 | 26.752 | 26.756 | 26.760 | 26.764 | 26.768 26.776 | 26.779 | 26.783 | 26.787 | 26.791 | 26.795 | 26.799 | 26.803 | 26.807 26.815 | 26.819 | 26.823 | 26.827 | 26.831 | 26.835 | 26.838 | 26.842 | 26.846 | 26.854 | 26.858 | 26.862 | 26.866 | 26.870 | 26.874 | 26.878 | 26.882 | 26.886 26.894 | 26.898 | 26.902 | 26.905 | 26.909 | 26.913 | 26.917 | 26.921 | 26.925 || 26.933 | 26.937 | 26.941 | 26.945 | 26.949 | 26.953 | 26.957 | 26.961 | 26.965 26.972 | 26.976 | 26.980 | 26.984 | 26. 26.992 | 26.996 | 27.000 | 27.004 27.012 | 27.016 | 27.020 | 27.024 é 27.031 | 27.035 | 27-039 | 27.043 27.051 | 27.055 | 27.059 | 27.063 : 27.071 | 27.075 | 27-079 | 27.083 | 27.090 | 27.094 | 27.098 | 27.102 ‘ 27 -L1O)|) 27.ULAL 270k LO) | 2722 27.130 | 27.134 | 27.138 | 27.142 046) | 27.550) | 27.053) | 27-057 | 27.L0L 27 AMOS. Leal Sieh eile felow ; 27.189 | 27.193 | 27.197 | 27.201 27.209 | 27.213 | 27.216 | 27.220 | 27. 27.228 | 27.232 | 27.236 | 27.240 27.248 | 27.252 | 27.256 | 27.260 ; 27.268 | 27.272 | 27.276 | 27.279 27.287 | 27.291 | 27.295 | 27.299 | 27.303 | 27-307 | 27.311 | 27.315 | 27.319 27.327 | 27.331 | 27-335 | 27-339 | 27-342 | 27.346 | 27.350 | 27.354 | 27-358 27.366 | 27.370 | 27.374 | 27.378 | 27. 27.386 | 27.390 | 27.394 | 27.398 27.405 | 27.409 | 27.413 | 27.417 | 27. 27.425 | 27.429 | 27.433 | 27-437 27.445 | 27-449 | 27.453 | 27-457 | 27. 27.465 | 27.468 | 27.472 | 27.476 27.484 | 27.488 | 27.492 | 27.496 : 27.504 | 27.508 | 27.512 | 27.516 27.524 | 27.528 | 27.531 | 27-535 | 27- 27.543 | 27-547 | 27-551 | 27-555 27.563 | 27.567 | 27.571 | 27.575 | 27- 27.583 | 27.587 | 27.590 | 27-594 SMITHSONIAN TABLES, 193 TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres. . | Inches. | Inches. . | Inches. Inches. | Inches. | Inches. | Inches. 27.563 | 27.567 | 27. 27.575 27.583 | 27.587 | 27.590 | 27.594 7.602 | 27.606 : 27.614 27.622 | 27.626 | 27.630 | 27.634 .642 | 27.646 | 27.650 | 27.653 27.661 | 27.665 | 27.669 | 27.673 7.681 r. 27.693 27.7Ol |.272 705) 27.799) | Sues 7.720 7, : 27.732 36 | 27.740 | 27.744 | 27.748 | 27.752 27.772 27.779 | 27.783 | 27.787 | 27.791 27.811 27.819 | 27.823 | 27.827 | 27.831 | 27.850 27.858 | 27.862 | 27.866 | 27.870 27.890 8 27.898 : 27.905 | 27.909 | 27-929 27-937 | 27- 27-945 | 27.949 .760 -799 .839 .878 -917 ty No wNNN sss NnHNN ND NSNININ™SN NHNHN NHN SST STATS 27.968 7.976 .980 | 27.984 | 27.988 28.008 | 28. 8.016 : 28.024 | 28.028 28.047 | 2§ 8.055 | 28. | 28.063 | 28.067 28.087 36 8.094 | 28. 28.102 | 28.106 28.126 , 28.134 , 28.142 | 28.146 28.165 | 28. 28.173 ; 28.181 | 28.185 28.205 .209 | 28.213 | 28. 28.220 | 28.224 28.244 .248 | 28.252 28.260 | 28.264 28.283 .287 | 28.291 28.299 | 28.303 28.323 28.339 | 28.342 NO oO on 62 \0 U vo HNWOWwWH UU 28.307 28.346 28.386 28.425 28.465 28.504 28.378 | 28.382 28.417 | 28.421 28.457 | 28.461 28.496 | 28.500 28.535 | 28.539 28.575 | 28.579 28.614 | 28.618 28.653 | 28.657 28.693 | 28.697 28.732 | 28.736 NHNnowbh ADA! bo BS HN bh 00 So Co So Go nr & f Go oo mHNIO2\O U1 N bBo wow Hb ArmA A CAA MHG DM: WOOonrHNn bo Co on on =) I H 28.543 28.583 28.622 28.661 28.701 On abo S to on OUl No Ny wb bd Go $0 60 So Go So SIADAUUN > bo HoH HN bd Fi 28.772 | 28.776 28.811 | 28.815 28.850 | 28.854 28.858 | 28.8 28.890 | 28.894 28.898 28.929 | 28.933 28.937 | 28.9. 4 ; ‘ : : 28.968 | 28.972 28.976 : : : . : F 29.008 | 29.012 29.016 : ; : : .03 -043 | 29.047 | 29.051 29.055 : : : : : , 29.087 | 29.090 29.094 : ; ; : : , 29.126 | 29.130 29.134 : : bet ; : : 29.165 | 29.169 20.173, 7 18 : : E ; 29.205 | 29.209 29.213 : ; : : y : 29.244 | 29.248 29.252 : : : : : : 29.283 | 29.287 29.291 ' ; : : : ; 29.323 | 29.327 29.331 : : : : : 3 29.362 | 29.366 29.370 37 : : : ; : 29.402 | 29.405 29.409 ; z : : : : 29.441 | 29.445 29.449 : : : ; : ; 29.480 | 29.484 29.488 ; : ; : B ; 29.520 | 29.524 29.528 | 29. : : : 29.559 | 29-563 28.740 i 28.779 7 28.819 | 28.8 oO 6 Nb CO « NRA NHNHNHNND oO Om] NINN Gd G2 G2 Go NI ow HI —w On NSN snow BP WWW o Oo “I - = “I > Ww SMITHSONIAN TABLES. metres. 750 751 754 755 Inches. 29.528 29.567 29.606 29.646 29.685 29.724 29.764 29.803 29.842 29.882 29.921 29.961 30.000 39-039 30.079 30.118 30.157 30.197 30.236 30.276 30.315 30-354 309.394 39.433 30.472 30.512 30.551 30.590 30.630 30.669 39.799 30.748 30.787 30.827 30.866 30-905 30-945 30.984 31.024 31.063 .102 .142 -18I 31.220 .260 MILLIMETRES INTO ' Inches. 29.531 29.571 29.610 29.650 29.689 29.728 29.768 29.807 29.846 29.886 29-925 29.965 30.004 39-043 30.083 30.122 30. 161 30; 201 30.240 30.279 30.319 30.358 30.398 30.437 30.476 30.516 30.555 30.594 30.634 30.673 39.713 30.752 30.791 30.831 30.870 30-909 39.949 30.988 31.027 31.067 31.106 31.146 31.185 31.224 31.264 -299 31-339 31.378 31.417 31-457 31.496 SMITHSONIAN TABLES. 31.303 31.342 31.382 31.421 31.461 31.500 INCHES. I mm. = 0.03937 inches Inches. 29.535 29.575 29.614 29.653 29.693 29.732 29.772 29.811 29.850 29.890 29.929 29.968 30.008 39.047 30.087 30.126 30.165 30.205 30.244 30.283 30.323 30.362 30.402 30.441 30.480 30.520 30.559 30-598 30.638 30.677 30.716 30.756 30-795 30.835 30.874 39.913 39-953 30.992 31.031 Br.07% .IIO .150 .189 .228 .268 31.307 31.346 31.386 31.425 31.465 31.504 Inches. 29.539 29-579 29.618 29.657 29.696 29.736 29.77 29.815 29.854 29.894 29-933 29-972 30.012 30.051 30.090 30.130 30.169 30.209 30.248 30.287 30.327 30.366 30.405 30.445 30.484 30.524 30.563 30.602 30.642 30.681 30.720 30.760 30.799 30.839 30.878 30.917 30-957 30.996 31.035 31.075 31.114 31.153 31.193 31.232 Si272 31.311 31.350 31.390 31.429 31.468 31.508 Inches. 29-543 29.583 29.622 29.661 29.701 29.740 29-779 29.819 29.858 29.898 29-937 29.976 30.016 39.055 30.094 30-134 30.173 30.213 30.252 30.291 30.331 30.370 30.409 39-449 30.488 30.525 30.567 30.606 30.646 30.685 30.724 30.764 30.803 30.842 30.882 30.921 30.961 31.000 31.039 31.079 31.118 Bers 31.197 31.236 31.276 31.315 31.354 31.394 31.433 31.472 31.512 195 Inches. 29.547 29.587 29.626 29.665 29.795 29.744 29.783 29.823 29.862 29.902 29.941 29.980 30.020 30.059 30.098 30.138 39-177 30.216 30.256 30.295 30.335 30.374 30.413 30.453 30.492 30.531 30.571 30.610 30.650 30.689 30.728 30.768 30.807 30.846 30.886 30.925 30.965 31.004 31.043 31.083 £122 161 .201 .240 -279 31-319 -358 Inches. 29.551 29.590 29.630 29.669 29-709 29. 748 29.787 29.827 29.866 29.905 29.945 29.984 30.024 30.063 30.102 30.142 30.181 30.220 30.260 30-299 39-339 30.378 30.417 30.457 30.496 30-535 30-575 30.614 30.653 30.693 30.732 30.7,72 30.811 30.850 30.890 39-929 30.968 31.008 31.047 .087 .126 .165 31.520 Inches. 29.555 29.594 29.634 29.673 29.713 29.752 29.791 29.831 29.870 29.909 29.949 29.988 30.027 30.067 30. 106 30.146 30.185 30.224 30.264 39.303 39.342 30.382 30.421 30.461 30.500 39-539 30-579 30.618 30.657 30.697 30.736 30.776 30.815 30.854 30.894 39-933 30.972 31.012 31.051 31.090 31.130 31.169 31.209 31.248 31.287 31.327 31.366 31.405 31.445 31.484 31.524 TABLE 65. Inches, 29-559 29.598 29.638 29.677 29.716 29.756 29.795 29.835 29.874 29.913 29-953 29.992 30.031 30.071 30.110 30.150 30.189 30.228 30.268 30.307 30.346 30.386 30-425 30.465 30.504 39.543 30.583 30.622 30.661 30.701 30.740 30-779 30.819 30.858 30.898 39-937 30.976 31.016 31-055 31.094 31.134 rel 73 31.213 31.252 31.291 31.331 31-370 31.409 31.449 31.488 31.527 Inches. 29.563 29.602 29.642 29.681 29.720 29.760 29-799 29.839 29.878 29.917 29.957 29.996 30.035 30. 075 30.114 30.153 30.193 30.232 30.272 30.311 30.350 30.390 30.429 | 30.468 30.508 309-547 30.587 30.626 30.665 30-7095 39-744 30.783 30.823 30.862 30.902 30.941 30.980 31.020 31.059 31.098 31.135 31.177 31.216 31.256 31.295 31.335 31.374 31.413 31.453 31.492 31.531 TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres, Inches. | Inches. | Inches. | Inches. | Inches. ] Inches. | Inches. | Inches. | Inches. | Inches. 31.496 | 31.500 | 31.504 | 31.508 | 31.512 | 31.516 | 31.520 | 31.524 | 31.527 | 31.531 31-535 | 31-539 | 31-543 | 31-547 31.555 | 31-559 | 31.563 | 31.567 | 31.571 31.575 | 31-579 | 31-583 | 31-587 : 31.594 | 31.598 | 31.602 | 31.606 -610 31.614 | 31.618 | 31.622 | 31.626 .630 | 31.634 | 31.638 | 31.642 | 31.646 .650 31.653 | 31.657 | 31.661 | 31.665 : 31.673 | 31.677 | 31.681 | 31.685 .689 31.693 | 31.697 | 31.701 | 31. eile 7LSil 31-70 2720) poten -728 QT 31.736 | 31.740 | 31.744 | 31. -752 | 31.750 ) 31.760 | 31.764 .768 1.776 | 31.779 | 31. 31.78 -791 | 31-795 | 31-799 | 31.803 | 31.807 .815 | 31.819 | 31.823 | 31. .831 .835 | 31.839 | 31.842 .846 1.854 | 31.858 | 31.862 | 31. .870 .874 | 31.878 | 31.882 .856 2 Jur: G2 Go C WS 4 4 oO .898 937 .976 .O16 .055 .094 .134 a7 3 eT 252 594 -933 =972 4012) -O51 -go2 : -g09 913 -917 | 31-921 -925 941 -949 | 31-953 | 31-957 | 31-961 | 31.965 .980 ; 31.988 -992 .996 | 32.000 | 32.004 .020 | 32. 07 .035"| 32.039 | 32.043 059 32.067 32.075 | 32.079 | 32.083 | Ge G2 G2 G2 Go NN Ae a G2 G2 G2 Go Oo NN Ae Oe G2 G2 G2 Ga 2 NN RAR OD WW W G ON RRA .106 .146 .185 22 .264 -0gO .098 .138 77 .216 .256 LA | 225uToi eee. -153 | 32-157 | 32.161 | > DS 4 2 A a 32 3 29 3 = J G2 ©. [S} G2 &. 445 .484 .524 563 602 642 681 -720 .760 799 -839 .878 | 32.882 | 32.886 -917 | 32.921 | 32.925 32.957 | 32.961 | 32.965 32.996 | 33.000 | 33.004 33-935 | 33-039 | 33-943 33-075 | 33-079 | 33.083 22.114 | 33-1101 23.022 33-153 | 33-157 | 33-161 .508 | 32.512 | 32.516 *547 | 32-551 555 -587 | 32.590 | 32.594 .626 | 32.630 -634 .665 | 32.669 .673 DW WH G2 God RN NHN HN WW 2 GW GW NNNNbH 2 G2 G2 G2 OD NNNNN G2 G2 G2 G2 Gd NNNNDND G2 DR GG NNNNND WD Ge G2 G2 Go NNNNN oO nN eo tS .689 .724 .728 .764 .768 .803 | 32.807 .842 | 32.846 -705 | 32.709 713) -744 | 32.748 | 32.752 .703 |) Z2s707, | Sea Ou .823 | 32.827 | 32.831 2.862 | 32.866 | 32.870 nw ON nN Nt G2 G2 OG NN G GD nN G2 G2 G) GG NNNNN Go G2 CG Go Go NNNNN 32.902 | 32.905 | 32.909 32-941 | 32.945 | 32.949 32.980 | 32.984 | 32.988 33.020 | 33.024 | 33.027 33-059 | 33-063 | 33.067 33.098 | 33.102 | 33.106 33.138 33-142 33.146 33-177 | 33-181 | 33.185 33.193 197 | 33.201 33.216 | 33.220 | 33.224 B3.232 33.240 33.256 | 33.260 | 33.264 33-272 33-279 | 33: Bs. . 33-295 | 33-299 | 33-303 33-311 33-319 | 33-323 . 33-335 | 33-339 | 33-342 33-350 33-358 | 33-: : 33-374 | 33-378 | 33-382 33-390 33-398 | 33- . 33-413 | 33-417 | 33-421 33-429 33-437 | 33- : 33-453 | 33-457 | 33-461 33-468 | 33.472 | 33-476 | 33- 33-492 | 33-496 | 33-500 DH W OW WNNNN OG» Ga La Go Oo WONNN Oo = 2 DH WD WwW W KW G2 G2 Ge O» 2 G2 Gs Go OD WO WO DW GH GQ Ga Go G2 Go Ww Cr Go Oe i G G ¢ WW ® QW ( Hww®wWwW WS SMITHSONIAN TABLES. TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Inches. | Inches. | Inches. | Inches. Inches. | 33.484 | 33-488 | 33-492 | 33-496 | 33-500 | 33.524 | 33-527 | 33-531 | 33-535 | 33-539 33.563 | 33-597 | 33-571 | 33-575 | 33-579 33.602 | 33.606 33-610 | 33.614 33-618 | 33.642 | 33-646 | 33-650 | 33-653 | 33-657 | Inches. | Inches. | Inches. | Inches. | Inches. 33.464 | 33-468 | 33.472 | 33-476 | 33.480 33.504 | 33-508 | 33-512 | 33-516 | 33.520 33.543 | 33-547 | 33-551 | 33-555 | 33-559 33.583 | 33-597 | 33-590 | 33-594 | 33-598 33.622 | 33.626 33.630 | 33-634 | 33-638 33.661 | 33.665 | 33-669 | 33-673 | 33-677 | 33-68r | 33-685 | 33-689 | 33-693 33-697 33-701 | 33-705 | 33-709 | 33-713 | 33-716 | 33-720 | 33-724 | 33-728 | 33-732 33-736 33.740 | 33-744 | 33-748 | 33-752 | 33-756 | 33-760 | 33-764 | 33-768 | 33-772 | 33-77 33-779 | 33-783 | 33-787 | 33-79F | 33-795 | 33-799 | 33 803 | 33-807 | 33-811 | 33-815 33.819 | 33-823 | 33-827 | 33-831 | 33-835 | 33-839 | 33-842 | 33-846 | 33.850 33-854 | 33-858 33.862 | 33.866 | 33.870 | 33.874 | 33-878 33.882 | 33.886 | 33-890 | 33-894 33-898 | 33.902 | 33-905 | 33-909 | 33-913 | 33-917 | 33-921 | 33-925 | 33-929 | 33-933 33.937 | 33-941 | 33-945 | 33-949 | 33-953 | 33-957 | 33-961 | 33-964 | 33-968 | 33-972 33.976 | 33-980 | 33-984 | 33-988 | 33.992 | 33-996 | 34-000 | 34.004 | 34.008 | 34.012 | 34.016 | 34.020 | 34.024 | 34.027 | 34.031 | 34-035 | 34-039 | 34-043 | 34-047 | 34-051 | 34.055 | 34.059 | 34-063 | 34-067 | 34.071 | 34.075 | 34-079 | 34-083 | 34-087 | 34.090 34.694 | 34.098 | 34.102 | 34.106 | 34.110} 34.114 34.118 | 34.122 | 34.126 | 34.130 34.134 | 34.138 | 34-142 | 34.146 | 34.150 | 34.153 | 34-157 | 34-161 | 34-165 34. 169 | 34.173 | 34.177 | 34.181 | 34-185 | 34-189 ] 34-193 | 34-197 | 34-201 | 34-205 | 34.209 | 34.213 | 34.216 | 34.220 | 34.224 | 34.228 | 34.232 34.236 | 34.240 | 34.244 | 34.240 34.252 | 34.256 | 34.260 | 34.264 | 34.268 | 34.272 34.276 | 34-279 | 34.283 | 34-287 | 34.291 | 34.295 | 34.299 | 34-303 | 34-307 | 34-311 | 34-315 | 34-319 | 34.323 | 34-327 | 34.331 | 34-335 | 34-339 | 34-342 | 34-346 | 34-350 | 34-354 | 34-358 | 34.362 34-366 34.370 | 34.374 | 34.378 | 34-382 | 34-386 | 34-390 | 34-394 | 34.398 | 34.402 | 34.405 | 34.409 | 34.413 | 34.417 | 34-421 | 34.425 | 34-429 | 34-433 | 34-437 | 34-441 | 34-445 | 34.449 | 34.453 | 34.457 | 34-46r | 34.464 | 24.468 | 34.472 | 34-476 34.480 | 34.484 34.488 | 34.492 | 34.496 | 34-500 | 34.504 | 34.508 | 34.512 | 34.516 | 34.520 | 34.524 34.527 | 34.531 | 34-535 | 34-539 | 34-543 | 34-547 | 34-552 | 34-555 | 34-559 | 34-563 34.567 | 34.571 | 34-575 | 34-579 | 34-583 | 34-587 | 34-590 | 34-594 | 34-598 | 34-602 | 34.606 | 34.610 | 34.614 | 34.618 | 34.622 34.626 | 34.630 | 34.634 | 34.638 Seo 34.646 | 34.650 | 34.653 | 34-657 | 34-661 | 34.665 | 34-669 | 34-673 | 34-677 | 34-681 | 34.685 | 34.689 | 34-693 | 34-697 | 34-701 | 34-705 | 34-709 | 34-713 | 34-718 | 34.720 | 34.724 | 34.728 | 34-732 | 34-736 | 34-740 | 34-744 | 34-748 | 34-752 | 34-756 34.760 | 34.764 | 34.768 | 34.772 | 34-776 | 34-779 | 34-783 | 34-787 | 34-791 | 34-795 34-799 | 34.803 | 34.807 | 34.811 | 34.815 | 34-819 | 34-823 | 34-827 | 34-831 | 34-835 | 34-539 | 34.842 | 34.846 | 34.850 | 34.854 | 34-858 | 34-862 | 34.866 | 34.870 | 34.974 34.878 34.882 | 34.886 | 34.890 | 34.894 | 34-898 | 34.902 | 34.905 | 34-909 | 34-913 | 34-917 | 34.921 | 34.925 | 34.929 | 34-933 | 34-937 | 34-941 | 34-945 | 34-949 | 34-953 | 34-957 | 34.961 | 34.964 | 34.968 | 34.972 | 34.976 | 34.980 | 34.984 | 34-988 | 34-992 | 34-999 | 35.000 | 35.004 | 35.008 | 35.012 35.016 | 35.020 | 35-024 | 35-027 | 35-031 35-035 35.039 | 35-043 | 35-047 | 35-051 | 35-055 | 35-059 | 35-063 | 35-067 | 35-071 35.075 | 35-079 | 35-083 | 35-087 | 35-090 | 35-094 | 35.098 | 35-102 35-106 | 35.110 | 35-114 | 35.118 | 35-122 | 35-126 | 35-130 | 35-134 | 35-138 | 35-142 35-146 | 35.150 | 35-153 | 35.157 | 35-161 | 35-165 | 35-169 | 35-173 | 35-177 | 35-181 | 35-185 | 35-159 | 35-193 35.197 | 35.201 | 35.205 | 35.209 | 35-213 35.216 | 35.220 | 35.224 35.228 aed 35.236 | 35-240 | 35-244 | 35-248 | 35.252 | 35-256 35.260 | 35.264 | 35.268 | 35-272 35-276 | 35-279 | 35-283 | 35-287 | 35-291 | 35-295 | 35-299 | 35-303 | 35-307 | 35-311 | 35.315 | 35-319 | 35-323 | 35-327 | 35-332 | 35-335 | 35-339 | 35-342 | 35-346 | 35-359 | 35.354 | 35-358 | 35-362 | 35-306 | 35-370 | 35-374 | 35-378 | 35-382 | 35-386 | 35-399 | 35.30 | 35-398 | 35-402 | 35-405 | 35-409 | 35-413 | 35-417 | 35-421 | 35-425 | 35-429 | | 35-433 | 35-437 | 35-441 | 35-445 | 35-449 | 35-453 | 35-457 | 35-461 | 35-464 SMITHSONIAN TABLES. TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres. ‘ F ; . | Inches. | Inches. | Inches. |] Inches.| Inches.| Inches. | Inches. | Inches. 35-441 | 35-445 | 35-449 | 35-453 | 35-457 | 35-461 | 35.464 | 35.468 |f 35-480 | 35.454 | 35-488 | 35.492 | 35.496 | 35.500 | 35.504 | 35.508 |f 35-520 | 35-524 | 35-527 | 35-531 | 35-535 | 35-539 | 35-543 | 35-547 35-559 | 35-563 | 35-567 | 35-571 | 35-575 | 35-579 | 35-583 | 35-587 35-598 | 35.602 | 35.606 | 35.610 | 35.614 | 35.618 | 35.622 | 35.626 |f 35-638 | 35.642 | 35.646 | 35.650 | 35-653 | 35-657 | 35.661 | 35.665 35-677 | 35-681 | 35.685 | 35.689 | 35-693 | 35.697 | 35-701 | 35-705 35-716 | 35.720 | 35-724 | 35-728 | 35-732 | 35-736 | 35-740 | 35-744 35-756 | 35.760 | 35.764 | 35.768 | 35-772 | 35-776 | 35-779 | 35-783 35-795 | 35-799 | 35-803 | 35.807 | 35.811 | 35.815 | 35-819 | 35.823 { i ‘ ‘ : 35-835 | 35-839 | 35-842 | 35-846 | 35-850 | 35-854 | 35-858 | 35-862 35-874 | 35-878 | 35-882 | 35.886 | 35.890 | 35.894 | 35.898 | 35.902 35-913 | 35-917 | 35-921 | 35-925 | 35-929 | 35-933 | 35-937 | 35-941 35-953 | 35-957 | 35-961 | 35-964 | 35-968 | 35.972 | 35-976 | 35.980 |f 35-992 | 35.996 | 36.000 | 36.004 | 36.008 | 36.012 | 36.016 | 36.020 NAAM G2 G2 G2 Go Oo 36.031 | 36.035 | 36.039 36.043 36.047 | 36.051 | 36.055 36.059 36.063 : 36.071 | 36.075 | 36.079 | 36.083 | 36.087 | 36.090 | 36.094 | 36.098 36.102 : 36.110 | 36.114 | 36.118 | 36.122 | 36.126 | 36.130 | 36.134 | 36.138 36.142 : 36.150 | 36.153 | 36.157 | 36.161 | 36.165 | 36.169 | 36.173 | 36.177 36.181 : 36.189 | 36.193 | 36.197 | 36.201 | 36.205 | 36.209 | 36.213 | 36.216 36.220 5 36.228 | 36.232 | 36.236 | 36.240 | 36.244 | 36.248 | 36.252 | 36.256 36.260 .264 | 36.268 | 36.272 | 36.276 | 36.279 | 36.283 | 36.287 | 36.291 | 36.2905 36.299 | 36.303 | 36.307 | 36.311 | 36.315 | 36.319 | 36.323 | 36.327 | 36.331 | 36.335 36.339 | 36.342 | 36.346 | 36.350 | 36.354 36.362 | 36.366 | 36.370 | 36.374 36.378 : 36.386 | 36.390 | 36.394 36.402 | 36.405 | 36.409 | 36.413 |f 36.417 | 36. 36.425 | 36.429 | 36.433 | 36.- 36.441 | 36.445 | 36.449 | 36.453 36.457 | 36.2 36.464 | 36.468 | 36.472 : 36.480 | 36.484 | 36.488 | 36.492 36.496 90 | 36.504 | 36.508 | 36.512 : 36.520 | 36.524 | 36.527 | 36.531 36.535 36.543 | 36.547 | 36.551 | 36.555 | 36.559 | 36.563 | 36.567 | 36.571 36.575 36.583 | 36.587 | 36.590 | 36. 36.598 | 36.602 | 36.606 | 36.610 36.614 36.622 | 36.626 | 36.630 | 36.634 | 36.638 | 36.642 | 36.646 | 36.650 36.653 36.661 | 36.665 | 36.669 | 36. 36.677 | 36.681 | 36.685 | 36.689 36.693 36.701 | 36.705 | 36.709 | : 36.716 | 36.720 | 36.724 | 36.728 36.732 36.740 | 36.744 | 36.748 36.756 | 36.760 | 36.764 | 36.768 36.772 | 36.779 | 36.783 | 36.787 | ; 36.795 | 36.799 | 36.803 | 36.807 G2 G2 G) Go Od SINIDDOD UMN SIO O U1 ¢ NAAN CO sass wou me N 36.811 | 36.850 36.890 36.929 36.968 36.819 | 36.823 | 36.827 .831 | 36.835 | 36.839 | 36.842 | 36.846 36.858 | 36.862 | 36.866 | 36.870 | 36.874 | 36.875 | 36.882 | 36.886 36.898 | 36.902 | 36.905 | 36. 36.913 O17 : 36.925 36.937 | 36.941 | 36.945 | 36.949 | 36.953 | 36.957 | 36. 36.964 36.976 | 36.980 | 36.984 .988 | 36.992 : 6 37.004 37-043 37-083 37.122 37.161 37.201 |I GV. ON. OVIGV'GY (ON GNON OVO ONONON DW DW OS W Oo Wom COMOMO Nobu “102 00 OF 37-008 | 37. 37-016 | 37.020 | 37.024 | 37.027 | 37.031 37-047 7-055 | 37-059 | 37-063 | 37. 37-071 37.087 7.094 | 37.098 | 37.102 | 37.106 | 37.110 7.134 .138 | 37.142 | 37.146 | 37.150 as ao ~ a7 > > ioe > 27.073 .177 | 37.181 ‘ 37.189 3 3 im a 2 2 a Ose » non ®H G Go God G2 sSJIsSI“S SI“ Y ~ On a OC .212 252 .291 331 370 37.228 Re : 37.240 37.268 A : 37-279 37-307 | 37- . 37-319 37-339 37-346 | 37-35 37-358 37-378 37-386 | 37. 37-394 | 37-398 37-417 | 37-421 | 37-425 | 37- 37-433 | 37-437 37.220 37-260 37-299 O) DW OG O2 NSN™N™N SI WwWNN bo Cos ¢ NWO bo G Go G2 G SNS NI OG» G2 G2 Oo NSIN™NI™N™S DW GW ® SIN™NINI SI tO GG OO SINNNI™N t ¢, t nN Ww “NI > oO NO Ww “I 37-409 ow ey SMITHSONIAN TABLES. 198 ran TABLE 65. MILLIMETRES INTO INCHES. I mm. = 0.03937 inches Milli- metres. Inches. | Inches. | Inches. | Inches. | Inches. | Inches, | Inches. | Inches. | Inches. 37-402 | 37.405 | 37-409 | 37-413 | 37-417 | 37-421 | 37-425 | 37-429 | 37-433 37-441 | 37-445 | 37-449 | 37-453 | 37-457 | 37-461 | 37-464 | 37.468 | 37.472 37-480 | 37.484 | 37-488 | 37.492 | 37.496 | 37-500 | 37.504 | 37.508 | 37.512 37-520 | 37-524 | 37-527 | 37-531 | 37-535 | 37-539 | 37-543 | 37-547 | 37-551 37-559 | 37-563 | 37-567 | 37-571 | 37-575 | 37-579 | 37-583 | 37-587 | 37-590 | - 37-598 | 37.602 | 37-606 | 37.610 | 37.614 | 37.618 | 37.622 | 37.626 | 37.630 37-638 | 37-642 | 37.646 | 37.650 | 37.653 | 37.657 | 37.661 | 37.665 | 37.669 37-677 | 37-681 | 37-685 | 37.689 | 37.693 | 37-697 | 37-701 | 37-705 | 37-709 37-716 | 37-720 | 37-724 | 37.728 | 37-732 | 37-736 | 37-740 | 37-744 | 37.748 37-756 | 37-760 | 37-764 | 37-768 | 37.772 | 37-776 | 37-779 | 37-783 | 37-787 37-795 | 37-799 | 37-803 | 37-807 | 37.811 | 37-815 | 37.819 | 37.823 | 37.827 37-835 | 37-839 | 37-842 | 37-846 | 37.850 | 37.854 | 37.858 | 37.862 | 37.866 37-874 | 37-878 | 37.882 | 37.886 | 37.890 | 37.894 | 37.898 | 37.901 | 37.905 37-913 | 37-917 | 37-921 | 37-925 | 37-929 | 37-933 | 37-937 | 37-941 | 37-945 37-953 | 37-957 | 37-961 | 37-964 | 37.968 | 37.972 | 37.976 | 37.980 | 37.984 37-992 | 37-996 | 38.000 | 38.004 | 38.008 | 38.012 | 38.016 | 38.020 | 38.024 38.031 | 38.035 | 38.039 | 38.043 | 38.047 | 38.051 | 38.055 | 38.059 | 38.063 38.071 | 38.075 | 38.079 | 38.083 | 38.087 | 38.090 | 38.094 | 38.098 | 38.102 38.110 | 38.114 | 38.118 | 38.122 | 38.126 | 38.130 | 38.134 | 38.138 | 38.142 38.150 | 38.153 | 38-157 | 38.161 | 38.165 | 38.169 | 38.173 | 38.177 | 38.181 38.189 | 38.193 | 38.197 | 38.201 | 38.205 | 38.209 | 38.213 | 38.216 | 38.220 38.228 | 38.232 | 38.236 | 38.240 | 38.244 | 38.248 | 38.252 | 38.256 | 38.260 38.268 | 38.272 | 38.276 | 38.279 | 38.283 | 38.287 | 38.291 | 38.295 | 38.299 38.307 | 38.311 | 38.315 | 38.319 | 38.323 | 38.327 | 38.331 | 38.335 | 38.339 38.346 | 38.350 | 38.354 | 38.358 38.366 | 38.370 | 38.374 | 38.378 38.386 | 38.390 | 38.394 | 38.398 : 38.405 | 38.409 | 38.413 | 38.417 38.425 | 38.429 | 38.433 | 38.437 | 38.441 | 38.445 | 38.449 | 38.453 38.464 | 38.468 | 38.472 | 38.476 4 38.484 | 38.488 | 38.492 38.504 | 38.508 | 38.512 | 38.516 | 38. 38.524 | 38.527 | 38.531 38.543 | 38.547 | 38.551 | 38.555 | 38. 38.563 | 38.567 | 38.571 38.583 | 38.587 | 38.590 | 38.594 | 38.5 38.602 | 38.606 | 38.610 38.622 | 38.626 | 38.630 | 38.634 | 38.638 | 38.642 | 38.646 | 38.650 38.661 | 38.665 | 38.669 | 38.673 ‘ 38.681 | 38.685 | 38.689 38.701 | 38.705 | 38.709 | 38.713 | 38. 38.720 | 38.724 | 38.728 38.740 | 38.744 | 38.748 | 38.752 | 38. 38.760 | 38.764 | 38.768 UNA NTO2 00 On WN NY O26 Ll lanl 38.780 | 38.783 | 38.787 | 38.791 38.819 | 38.823 | 38.827 | 38.831 | 38.858 | 38.862 | 38.866 | 38.870 38.898 | 38.g0T | 38.905 | 38.909 38.937 | 38.941 | 38.945 | 38.949 38.976 | 38.980 | 38.984 | 38.988 39.016 | 39.020 | 39.024 | 39.027 39-055 | 39-059 | 39.063 | 39.067 | 39.094 | 39.098 | 39.102 | 39.106 39-134 | 39-138 | 39.142 | 39.146 7 | 39-181 | 39.185 | 39-220 | 39.222 39-264 | | 39-303 39-342 38.799 | 38.803 | 38.807 38.842 | 38.846 38.882 | 38.886 38.921 | 33.925 57 | 38.961 | 38.964 coc g ° WwW 2 W622 CO COMI oO oo © ° Go fo Go Go Go O&O O11 GK GG) G2 Go \O \O 39.000 | 39.004 39-939 | 39-043 39-051 | 39.079 | 39.083 39.090 | 39.118 | 39.122 39.130 39.157 | 39-161 39.169 39-197 | 39.236 | 39.276 39-315 39-354 39-394 ) 0 20 2 Go G2 Oo Oo ~ Oo 0 “SIO HHN 0 Oo - 39-209 | | 39.248 | 39-287 | 39-327 | 39.366 39-495 | O° G2 G2 G2 G2 Oo & NNN WOU RNs Rm HN Oo GW WWN ND WN HID 0 ORN NO O& G& G2 Od Od 0 ODODOO anwar O © DODO G2 G2 G2 Goa Go © POCO MO O OO Ww&oNnNN NbN we Ww x ° Oo Go oO e} Oo oO © ~~ SMITHSONIAN TABLES. 199 4 TABLE 66. Feet. 20 30 40 50 70 8o 10 8 | {00 200 300 400 500 600 700 800 goo 1000 IIoo 1200 1300 1400 1500 1600 1700 | 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2500 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 457.20 487.68 | 518. 16 | 548.64 579-12 609.60 640.08 670.56 7OI.04 731.52 762.00 792.48 $22.96 353-44 883.92 914.40 944.88 | 975-36 | 1005.84 1036.32 1066.80 1097.28 | 1127.76 | 1158.24 1188.72 1219.20 SMITHSONIAN TABLES. F 9 ° on H NO Ny IAA LHPHW W Wook OF ON NTO HOO S H NWO DW NIWO HO aS et coun NOS e DAAG REED oOpokf OLONM tO bd sf ~] Oo IO RW 2 OH O mn 02 CO jw on G G2 & b one Co oO pe ~ » \O 4 NI \O SOE NS \O 460.25 490.73 | 521.21 551.69 582.17 612.65 643.13 673.61 704.09 734-57 765.05 795-53 826.01 856.49 886.97 917-45 947-93 978.41 1008.89 1039-37 1069.85 1100.33 1130.81 1161.29 LIQI.77 1222.25 FEET INTO METRES. 1 foot — 0.3048006 metre. m. 0.610 3.658 6.706 9-754 12.802 15.850 18.898 21.946 24.994 28.042 20 36.58 67.06 97.54 128.02 158.50 188.98 219.46 249.94 280.42 310.90 341.38 371.86 402.34 432.82 463.30 493-78 524.26 554-74 585.22 615.70 646.18 676.66 797.14 737-62 768.10 798.58 829.06 859.54 890.02 920.50 950.98 981.46 IOTI.94 1042.42 1072.90 1103.38 1164.34 1194.82 1225.30 1133.86 | m. 0.914 3-962 7.010 10.058 13.106 16.154 Ig. 202 22.250 25.298 28. 346 30 39.62 70.10 100.58 131.06 161.54 192.02 222.50 252.98 283.46 313-94 | 3 344.42 374-90 405.38 435.56 466.34 | 496.52 | 499.87 527-31 | 539-35 557-79 | 560.83 588.27 | 591.31 618.75 | 621.79 649.23 | 652.27 79.71 | 682.75 FLOPTON 713.23 740.67 | 743-71 771.15 | 774.19 801.63 | 804.67 832.11 | 835.15 862.59 | 865.63 893.07 | 896.11 | 923-55 | 926.59 954-03 | 957-07 954.51 | 987.55 1014.99 1018.03 1045.47 |1048.51 1075.95 1078.99 1106.43 1109.47 1136.91 1139.95 1167.39 |1170.43 1197.87 1200.91 | 1228.35 |1231.39 200 m. 1.524 4.572 7.620 10.668 13.716 16.764 19.812 22.860 25.908 28.956 50 45-72 76.20 106.68 137.16 167.64 198.12 228.60 259.08 289.56 320.04 359.52 351.00 411.48 441.96 472.44 502.92 533-49 563.88 594-36 624.84 655.32 685.80 716.28 746.76 777-24 807.72 838.20 868.68 899.16 929.64 960. 12 990.60 1021.08 1051.56 1082.04 [112.52 1143.00 1173.48 1203.96 1234.44 48.77 79-25 109.73 140.21 170.69 201.17 231.65 262.13 292.61 323-09 353-57 354.05 414.53 445.01 475-49 595-97 536.45 566.93 597-41 627.89 658.37 688.85 719.33 749.81 780.29 810.77 841.25 871.73 go2.21 932.69 963.17 993-65 1024.13 1054.61 1085.09 TLS. 57; 1146.05 1176.53 1207.01 1237-49 51.82 $2.30 112.78 143.26 173-74 204.22 234.70 265.18 295.66 326.14 356.62 387.10 417.58 448.06 478.54 509.02 939-59 569.98 600.46 30.94 661.42 691.90 722.38 752.86 783-34 813.82 844.30 874.78 g05.26 935-74 966.22 996.70 1027.18 1057.66 1088.14 1118.62 1149.10 1179.58 1210.06 1240.54 m. 2.438 5.486 8.534 11.582 14.630 17.678 20.726 23-774 26.822 29.870 80 54.86 85.34 115.82 146.30 176.78 207.26 237-74 268.22 298.70 329.18 359-67 390.14 420.62 451.10 481.58 512.07 542-55 573-93 603.51 633-99 664.47 694.95 725-43 755-91 786.39 816.87 847.35 877.83 908. 31 938.79 969.27 999-75 1030.23 1060.71 I09I.1G 1121.67 1152.15 1182.63 T2030 1243-59 2.743 5-791 8.839 11.887 14.935 17.983 21.031 24.079 Diy, 30.175 90 57-91 88.39 118.87 149.35 179.83 210.31 240.79 27Te oy 301.75 332-23 | 362.71 393-19 423.67 454.55 484.63 515.11 545-59 576.07 606.55 637.03 667.51 697-99 728.47 758.95 789.43 819.91 850.39 880.87 QII.35 941.83 972.31 1002.79 1033.27 1063.75 1094.23 1124.71 1155.19 1185.67 1216.15 1246.63 TABLE 66. FEET INTO METRES. 1 foot = 0.3048006 metre. m. 1240.5 | 1243.6 | 1246.6 L271. M2740) | 27 70k 1295.4 | 1298.5 | 1301.5 | 1304.5 | 1307.6 1325.9 | 1328.9 | 1332.0 | 1335-0 | 1338.1 1356.4 | 1359.4 | 1362.5 | 1365.5 | 1368.6 1222.3 | 1225.3 | 1228.3 | 1231.4 1252.7 | 1255.8 | 1258.8 | 1261.9 1283.2 | 1286.3 1289.3 | 1292.4 1313.7 | 1316.7 | 1319.8 | 1322.8 1344.2 | 1347.2 | 1350-3 | 1353-3 1234.4 1264.9 | 1268.0 1386.8 | 1389.9 | 1392-9 | 1396.0 | 1399.0 1417.3 | 1420.4 | 1423.4 [ 1426.5 | 1429.5 1447.8 | 1450.9 | 1453.9 | 1456.9 | 1460.0 1478.3 | 1481.3 | 1484.4 | 1487.4 | 1490.5 1508.8 | 1511.8 | 1514.9 | 1517.9 | 1521.0 1374.7 | 1377-7 | 1380.7 | 1383.8 1405.1 | 1408.2 | I411.2 | 1414.3 1435.6 | 1438.7 | 1441.7 | 1444.8 x2 “7 1466.1 | 1469.1 | 1472 1475.2 1496.6 | 1499.6 | 1502 1505.7 1527.1 | 1530.1 | 1533-1 | 1536.2 | 1539-2 | 1542.3 | 1545.3 1548.4 | 1551.4 1557-5 | 1560.6 | 1563.6 | 1566.7 | 1569.7 | 1572.8 1575-8 | 1578-9 | 1581-9 | 1588.0 | 1591.1 | 1594.1 | 1597.2 | 1600.2 | 1603.3 | 1606.3 1609.3 | 1612. 1618.5 | 1621.5 | 1624.6 | 1627.6 | 1630.7 | 1633.7 | 1636.8 1639.8 | 1642.9 1649.0 | 1652.0 | 1655.1 | 1658.1 | 1661.2 | 1664.2 1667.3 | 1670.3 | 1673.4 1679.5 | 1682.5 | 1685.5 | 1688.6 | 1691.6 | 1694.7 1697.7 | 1700.8 | 1703.8 1709.9 | 1713.0 | 1716.0 | 1719.1 | 1722.1 | 1725.2 | 1728.2 | 1731.3 | 1734-3 | 1740.4 | 1743.5 | 1746.5 | 1749.6 | 1752.6 | 1755-7 1758.7 | 1761.7 | 1764.8 1770.9 | 1773.9 | 1777-0 | 1780.0 | 1783.1 1786.1 | 1789.2 | 1792.2 | 1795-3 | 1801.4 | 1804.4 | 1807.5 | 1810.5 | 1813.6 | 1816.6 | 1819.7 1822.7 | 1825.8 | 1828.8 | 1831.9 | 1834.9 | 1837.9 | 1841.0 | 1844.0 | 1847.1 | 1850.1 1853.2 | 1856.2 1859.3 | 1862.3 | 1865.4 | 1868.4 | 1871.5 | 1874.5 1877.6 | 1880.6 | 1883.7 | 1856.7 1889.8 | 1892.8 | 1895.9 | 1898.9 | 1902.0] 1905.0 | 1908.1 | IgII.I | 1914.1 | 1917.2 1920.2 | 1923.3 | 1926.3 | 1929.4 | 1932.4 | 1935-5 1938.5 | 1941.6 | 1944.6 | 1947.7 1950.7 | 1953.8 | 1956.8 | 1959.9 | 1962.9 | 1966.0 | 1969.0 | 1972.1 | 1975.1 1978.2 1996.4 | 1999.5 | 2002.5 | 2005.6 2008.6 2026.9 | 2030.0 | 2033.0 | 2036.1 | 2039.1 2057.4 | 2060.5 | 2063.5 | 2066.5 2069.6 2087.9 | 2090.9 | 2094.0 | 2097.0 | 2100.1 2118.4 | 2121.4 | 2124.5 | 2127.5 | 2130.6 | 6500 | 1981.2 | 1984.3 | 1987.3 | 1990.3 | 1993-4 6600 | 2011.7 | 2014.7 | 2017.8 | 2020.8 | 2023.9 6700 | 2042.2 | 2045.2 | 2048.3 | 2051.3 | 2054.4 | 6800 | 2072.6 | 2075.7 | 2078.7 | 2081.8 | 2084.8 6900 | 2103.1 | 2106.2 | 2109.2 | 2112.3 | 2115.3 7000 | 2133.6 | 2136.7 | 2139.7 | 2142.7 | 2145.8 7100 | 2164.1 | 2167.1 | 2170.2 | 2173.2 | 2176.3 ii 2148.8 | 2151.9 | 2154.9 | 2158.0 | 2161.0 2 7200 | 2194.6 | 2197.6 | 2200.7 | 2203.7 | 2206.8 2 7 2179.3 | 2182.4 | 2185.4 | 2188.5 | 2191.5 2209.8 | 2212.9 | 2215.9 | 2218.9 | 2222.0 2240.3 | 2243.3 | 2246.4 | 2249.4 | 2252. 2270.8 | 2273.8 | 2276.9 | 2279.9 | 2253.0 "7300 | 2225.0 | 2228.1 | 2231.1 | 2234.2 | 2237. 2255.5 | 2258.6 | 2261.6 | 2264.7 | 2267. “Ib 2286.0 | 2289.1 | 2292.1 | 2295.1 | 2298.2 } 2301.2 | 2304.3 | 2307.3 | 2310.4 2273-4 2316.5 | 2319.5 | 2322.6 | 2325.6 | 2328.7 | 2331-7 | 2334.8 | 2337.8 | 2340.9 | 2343.9 | 2347.0 | 2350.0 | 2353.1 | 2356.1 | 2359.2 2362.2 | 2365.3 | 2368.3 | 2371.3 | 2374-4 2377.4 | 2380.5 | 2383.5 | 2386.6 | 2389.6 | 2392.7 | 2395-7 2398.8 | 2401.8 | 2404.9 | 2407.9 | 2411.0 | 2414.0 | 2417.1 | 2420.1 | 2423.2 | 2426.2 | 2429.3 | 2432.3 2435-4 | 2438.4 | 2441.5 | 2444.5 | 2447.5 | 2450.6 | 2453.6 2456.7 | 2459.7 | 2462.8 | 2465.8 2468.9 | 2471.9 | 2475.0 | 2478.0 | 2481.1 2499.4 | 2502.4 | 2505.5 | 2508.5 | 2511.6 2529.8 | 2532.9 | 2535-9 | 2539-0 | 2542.0 2560.3 | 2563.4 | 2566.4 | 2569.5 | 2572.5 2484.1 | 2487.2 | 2490.2 | 2493. 2514.6 | 2517.7 | 2520.7 | 2523. 2545.1 | 2548.1 | 2551.2 | 2554. 2575.6 | 2578.6 | 2581.7 | 2584. “SI NNW to ou NO OV CO 2590.8 | 2593.9 | 2596.9 | 2599.9 | 2603.0 | 2606.0 2609.1 | 2612.1 | 2615.2 | 2618.2 2621.3 | 2624.3 | 2627.4 | 2630.4 | 2633.5 | 2636.5 | 2639.6 | 2642.6 2645.7 | 2648.7 2651.8 | 2654.8 | 2657.9 | 2660.9 | 2664.0 | 2667.0 | 2670.1 2673.1 | 2676.1 | 2679.2 2682.2 | 2685.3 | 2688.3 | 2691.4 | 2694.4 | 2697.5 | 2700.5 | 2703.6 2706.6 | 2709.7 2712.7 | 2715.8 | 2718.8 | 2721.9 | 2724.9 | 2728.0 | 2731.0 | 2734.1 | 2737-1 | 2740.2 2743.2 | 2746.3 | 2749.3 | 2752.3 | 2755.4 | 2758.4 | 2761.5 | 2764.5 2767.6 | 2770.6 SMITHSONIAN TABLES. 201 TABLE 67. METRES INTO FEET. I metre — 39.3700 inches — 3.280833 feet Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. 0 0.00 3.28 6.56 9.84 13.12] 16.40] (19.68) 22.97] 26:25) So552 10 32.81] 36.09] 39.37] 42-65] 45.93] 49.21] 52.49] 55-77| 59.05| 62.34 20 65.62] 68.90] 72.18} 75.46] 78.74] 82.02} 85.30] 88.58] 91.86] 95.14 30 98.42 | 101.71} 104.99] 108.27]| I1I.55| 114.83] 118.11} 121.39] 124.67] 127.95 4o 131.23] 134.51| 137-79| 141.08] 144.36] 147.64] 150.92] 154.20| 157.48] 160.76 50 164.04 | 167.32| 170.60] 173.88] 177.16] 180.45 | 183.73] 187.01] 190.29] 193.57 60 196.85 | 200.13| 203.41 | 206.69} 209.97] 213.25 | 216.53] 219.82] 223.10| 226.38 70 229.66} 232.94| 236.22} 239.50] 242.78] 246.06] 249.34] 252.62] 255.90] 259.19 So 262.47 | 265.75] 269.03] 272.31 | 275.59| 278.87] 282.15] 285.43] 288.71] 291.99 go 295.27 | 298.56] 301.84 | 305.12] 308.40] 311.68] 314.96] 318.24] 321.52] 324.80 100 | 328.08] 331.36] 334-64] 337-93 | 341-21] 344-49] 347-77| 351-05] 354.33| 357-61 IIo 360.89 | 364.17 | 367.45 | 370.73} 374-01] 377-30| 380.58] 383.86] 387.14] 390.42 120 393.70| 396.98} 400.26 | 403.54| 406.82] 410.10] 413.38] 416.67] 419.95] 423.23 130 | 426.51] 429.79] 433-07| 436.35| 439.63] 442.91 | 446.19] 449.47 | 452.75 | 456.04 140 459.32 | 462.60] 465.88] 469.16| 472.44] 475.72] 479.00| 482.28] 485.56] 488.84 150 492.12] 495.41 | 498.691 501.97 | 505.25] 508.53] 511.81! 515.09] 518.37! 521.65 160 | 524.93] 528.21] 531-49| 534.78] 538.06] 541.34] 544.62} 547.90] 551.18] 554.46 170 | 557-74.| 561.02] 564.30] 567.58} 570.86] 574.15 | 577-43 | 580.71 | 583.99| 587.27 180 590.55 | 593-83 | 597-11 | 600.39} 603.67] 606.95 | 610.23 | 613.52] 616.80] 620.08 190 623.36 | 626.64 629.92 | 633.20] 636.48] 639.76| 643.04 646.32] 649.60] 652.89 200 656.17 | 659.45 | 662.73 | 666.01 | 669.29] 672.57 | 675.85 | 679.13} 682.41 | 685.69 |f 210 688.97 | 692.26 | 695.54 698.82 | 702.10] 705.38] 708.66] 711.94] 715.22] 718.50 220 | 721.78) 725.06] 728.34 | 731-63| 734-91] 738.19] 741.47| 744-75] 748.03 | 751.31 230 754-59 | 757-87 | 761.15 | 764.43 | 767.71] 771.00] 774.28] 777.56| 780.84| 784.12 240 787.40 | 790.68 | 793.96| 797.24 | 800.52] 803.80] 807.08} 810.37 | 813.65 | 816.93 250 820.21 | 823.49 | 826.77 | 830.05 | 833.33] 836.61 | 839.89} 843.17] 846.45 | 849.74 260 853.02] 856.30] 859.58 | 862.86] 866.14] 869.42 | 872.70] 875.98] 879.26] 882.54 270 885.52] 889.11 | 892.39} 895.67 | 898.95] 902.23] 905.51} 908.79] 912.07] 915.35 280 918.63 | 921.91 | 925.19] 928.48] 931.76] 935.04 | 938.32] 941.60] 944.88] 948.16 | 290 951.44] 954-72| 958.00} 961.28} 964.56] 967.85 | 971.13] 974.41] 977.69] 980.97 300 984.25 | 987.53 | 990.81 | 994.09 | 997.37 |1000.65 {1003.93 |I007.22 |IOI0.50 |I013.78 | 310 = J LOI 7.06 {1020.34 |1023.62 |1026.90 |1030.18 }1033.46 |1036.74 |1040.02 |1043.30 |1046.59 |f | 320 1049.87 |1053.15 |1056.43 |1059.71 |1062.99 |1066.27 |1069.55 |1072.83 |1076.11 |1079.39 | 330 1082.67 [1085.96 |1089.24 |1092.52 |1095.80 |1099.08 |1 102.36 |1105.64 1109.92 |II12.20 | 340 |I115.48 [118.76 |1122.04 |1125.33 |1128.61 |1131.89 1135.17 {1138.45 |L141.73 |1145.01 | 350 = [1148.29 1151.57 |1154.85 |1158.13 |L 161.41 {1164.70 |1167.98 |1171.26 |1174.54 |1177.82 360 LISI.10 j1184.38 |1187.66 |1 190.94 |1194.22 |1197.50 |1200.78 |1 204.07 }1207.35 |I210.63 370 = | 1213.91 |I217.19 [1220.47 |1223.75 |1227.03 |1 230.31 |1233.59 |1236.87 |1240.15 |1243.44 | 380 = [1246.72 |1250.00 |1253.28 |1256.56 |1259.84 |1 263.12 |1266.40 |1269.68 |1272.96 |1276.24 | 390 1279.52 |1282.81 |1286.09 |1289.37 {1292.65 }1295.93 |1299.21 |1302.49 |1305.77 |1309.05 | .46 |1328.74 |1332.02 |1335.30 |1338.58 |1341.86 | 400 }1312.33 }1315.61 1318.89 |1- 5 8.26 |1361.55 |1364.83 }1368.11 |1371.39 |1374.67 I 3 13 I | 410 1345.14 |1345.42 |1351.70 |1354.98 |I | 420 —41377.95 [1351.23 1354.51 |1387.79 |1391.07 |1394.35 |I397-63 |1400.92 |1404.20 |1407.48 | 430 1410.76 |1414.04 |1417.32 |1420.60 |1423.88 |1427.16 |1430.44 |1433.72 |1437.00 |I440.29 I | 440 1443.57 1446.85 |1450.13 |1453.41 6.69 |1459.97 |1463.25 |1466.53 |1469.81 |1473.09 450 [1476.37 |1479.66 |1482.94 |1486.22 |1489.50|1492.78 |1496.06 |1499.34 |1502.62 |1505.90 460 {1509.18 |1512.46 |1515.74 |1519.03 |1522.31 |1525.59 [1528.87 |1532.15 |1535.43 |1538.71 479 = JL541.99 |1545.27 |1548.55 |1551.83 |1555-11 1559.40 [1561.68 |1564.96 [1568.24 |1571.52 | 480 11574.80 |1578.08 |1581.36 |1584.64 |1587.92 |I591.20 |1594.48 |1597.77 |1601.05 |1604.33 490 [1607.61 |1610.89 |1614.17 |1617.45 {1620.73 |1624.01 1627.29 |1630.57 |1633.85 |1637.14 pede oe 1650.26 |1653.54 |1656.82 |1660.10 |1663.38 |1666.66 |1669.94 500 = |1640.42 |1643.70 SMITHSONIAN TABLES. 202 TABLE 67. METRES INTO FEET. I metre — 39.3700 inches = 3.280833 feet 60 70 80 90 Feet. Feet. Feet. Feet. Feet. 1640.4] 1673.2| 1706.0] 1738.8] 1771.6 1968.5 | 2001.3 | 2034.1 | 2066.9 | 2099.7 2296.6| 2329.4] 2362.2] 2395.0| 2427.8 2624.7| 2657.5| 2690.3 | 2723.1] 2755-9 2952.7| 2985.6| 3018.4 | 3051.2| 3084.0 Feet. Feet. Feet. Feet. Feet. 1804.5 | 1837.3 | 1870.1] 1902.9] 1935-7 2132.5 | 2165.3 | 2198.2| 2231.0] 2263.8 2460.6 | 2493.4 | 2526.2| 2559.0] 2591.9 2788.7 | 2821.5 | 2854.3| 2887.1 | 2919.9 3116.8| 3149.6| 3182.4] 3215.2| 3248.0 ) 3444-9 | 3477-7| 3510.5| 3543-3} 3576-1 3608.9 | 3641.7 | 3674.5] 3707-3| 3740.1] 3773.0] 3805.8 3838.6 | 3871.4] 3904.2 3937-0] 3969.8 | 4002.6] 4035.4) 4068.2| 4101.0] 4133.8 4166.7 | 4199.5 | 4232.3 | 4265.1 | 4297-9] 4330.7 | 4363-5| 4396.3{ 4429-1| 4461.9| 4494.7| 4527-5 | 4560.4 4593.2| 4626.0] 4658.8} 4691.6] 4724.4] 4757.2 | 4790.0 4822.8 | 4855.6] 4888.4 3280.8 | 3313-6] 3346.4] 3379-3] 3412.1 4 4921.2| 4954.1} 4986.9] 5019.7 | 5052.5] 5085.3 | 5118.1 | 5150.9 5183.7 | 5216.5 | 5249.3| 5282.1 | 5314.9| 5347-8] 5380.6] 5413.4| 5446.2| 5479.0] 5511.8] 5544.6 5577-4| 5610.2] 5643.0| 5675.8| 5708.6] 5741.5 | 5774.3] 5807.1 | 5839-9 5872-7 5905.5 | 5938.3 | 5971-1 | 6003.9} 6036.7 | 6069.5 | 6102.3 6135.2 | 6168.0) 6200.8 6233.6| 6266.4 | 6299.2 | 6332.0] 6364.8] 6397.6| 6430.4 | 6463.2 6496.0 | 6528.9 6561.7 | 6594.5 | 6627.3 | 6660.1 | 6692.9| 6725.7 | 6758.5 | 6791.3 | 6824.1 6856.9 6889.7 | 6922.6} 6955.4| 6988.2] 7021.0] 7053.8| 7086.6] 7119.4| 7152.2 7185.0 7217.8| 7250.6| 7283.4] 7316.3| 7349.1| 7381-9 | 7414-7| 7447-5 | 7480.3 | 7513-1 45.9| 7578.7| 7611.5| 7644.3| 7677-1] 7710.0] 7742.8| 7775-6| 7808.4 | 7941.2 74.0| 7906.8} 7939.6| 7972.4] 8005.2] 8038.0} 8070.8 | 8103.7 8136.5 | 8169.3 8202.1 | 8234.9| 8267.7| $300.5 | 8333-3] $366.1 | 8398.9 | 8431-7 | 8464.5 8497-4 8530.2 | 8563.0] 8595.8} 8628.6] 8661.4] 8694.2 | 8727.0] 8759.8 8792.6 | 8825.4 8858.2| 8891.1 | 8923.9 | 8956.7| 8989.5] 9022.3 | 9055-1 | 9087.9 | 9120.7 | 9153-5 9186.3 | 9219.1 | 9251.9 9284.5 9317.6 9359-4 9383.2 | 9416.0| 9448.8] 9481.6 9514.4| 9547-2| 9580.0] 9612.8] 9645.6] 9678.5 | 9711.3] 9744-1 | 9776.9 | 9809-7 9842.5| 9875.3] 9908.1 | 9940.9] 9973.7 |10006.5 |10039.3 |10072.2 |I0105.0 10137.8 10170.6 |10203.4 |10236.2 |10269.0 |10301.8 |10334.6 |10367.4 |10400.2 |10433.0 10465.9 10498.7 |10531.5 |10564.3 |10597.1 |10629.9 |10662.7 |10695.5 10728.3 |10761.1 |10793.9 | 10826.7 |10859.6 |t0892.4 |10925.2 | [0958.0 |10990.8 |1 1023.6 |11056.4 |L 1089.2 |I 1122.0 L1154.8 |11187.6 |11220.4 |11253.3 |£1286.1 |[1318.9 |11351.7 |L1354.5 |11417.3 |11450.1 1482.9 |11515.7 |11548.5 |L1581.3 |I 1614.1 |11647.0 |11679.8 11712.6 |11745.4 }11778.2 L1S11.0 |£1843.8 |11876.6 |r1909.4 |11942.2 |L1975.0 |12007.8 |12040.7 |12073.5 |I2106.3 [2139.J |12171.9 |12204.7 |I2237.5 |12270.3 |12303.1 |12335-9 |12368.7 |12401.5 |12434.4 12467.2 |12500.0 |12532.8 |12565.6 |12598.4 |12631.2 |12664.0 |12696.8 |12729.6 12762.4 [2795.2 |12828.1 |12860.9 |12893.7 |12926.5 J12959.3 |12992.1 |13024.9 |13057-7 |13099.5 [3123.3 |13156.1 |13188.9 113221.8 |13254.6 13287.4 |13320.2 1133530 !13385.8 |13418.6 | [3451.4 |13484.2 |13517.0 |13549.8 |13582.6 |13615.5 |13648.3 |13681.1 ]13713.9 |13746.7 13779.5 |13812.3 |13845.1 |13877.9 |13910.7 |13943-5 13976.3 |14009.2 |14042.0 |14074.8 14107.6 |14140.4 I4173.2 |14206.0 |14238.8 |14271.6 |14304.4 |14337.2 |14370.0 14402.9| £4435-7 |14468.5 |14601.3 |14534-1 |14566.9 |14599-7 |14032.5 |14665.3 |14698.1 |14730.9 | 4763.7 |14796.6 |14829.4 |14862.2 |14895.0 |14927.5 14960.6 |14993.4 15026.2 |15059.0 | 5091.8 |15124.6 |15157.4 |I5190.3 |15223.1 |15255-9 |15288.7 |15321-5 |15354-3 15397.1 | 15419.9 |15452.7 |15485.5 |15518.3 |15551.1 15584.0 |15616.8 |15649.6 |15682.4 15715.2 | 5748.0 |15780.8 |15813.6 |15846.4 |15879.2 |15912.0 |15944.8 |15977-7 I6010.5 |16043.3 16076.1 |16108.9 |16141.7 |16174.5 |16207.3 |16240.1 |16272.9 |16305.7 |16338.5 16371 4 | 6404.2 |16437.0 16469.8 |16502.6 |16535.4 |16568.2 |16601.0 |16633.8 | 16666.6/16699.4 | | | Tenths of a metre. O.1 0.2 0.5 0.6 0.7 0.8 0.9 Feet. 0.328 0.656 0.984 2 2.9 + 312 1.640 1.968 2.297 SMITHSONIAN TABLES. TABLE 68. MILES INTO KILOMETRES. I mile — 1.609347 kilometres l 2 3 4 5 6 km. km. km, km. km. km. 2 3 5 6 8 10 18 19 21 23 24 26 3 35 37 39 40 42 50 51 53 55 56 58 66 68 69 71 72 74 82 84 85 87 89 90 98 100 IOI 103 105 106 114 116 117 119 121 122 130 132 134 135 137 135 146 148 150 I51 153 154 163 164 166 167 169 Li 179 180 182 183 185 187 195 196 198 200 201 203 211 212 214 216 217 219 227 229 230 232 233 235 243 245 246 248 249 251 259 261 262 264 266 267 275 207 278 280 282 283 291 293 295 296 | 298 299 307 309 311 312 314 315 323) 8325.1 327 1 ase) ees sON a Baa2 349 | 341 343 344 | 346 | 348 359% || =357 359 360 362 364 372 | 373 B/S 8), Gur eno ooo 383 | 389 391 393 | 394 | 396 4o4 406 407 409 AIO |e Are 420 422 23 425 426 428 436 | 438 439 441 443 444 452 454 455 457 459 460 468 470 472 473 475 476 484 | 486 | 488 | 489 | 4or 492 501 502 504 505 507 509 517 518 520 521 523 525 533 53 536 538 539 541 549 550 552 554 555 557 505... 560 |568: |. 670 a S70 Ul eo7g 581 553 584 586 587 589 597 599 600 602 604 605 613 | 615 616 618 620 621 631 632 634 636 637 645 647 649 650 652 653 661 663 665 666 668 669 678 679 681 682 634 686 694 | 695 697 | 698 | 7oo | 792 710 7iteL 753 715 716 718 726 | 727 | 729 | 731 | 732 | 734 742, | 744 | 745 | 747 | 748 | 750 758 760 761 763 764 766 774 | 776 | 778 | 779 | 781 | 782 799 | 792 | 793 | 795 | 797 | 798 806 808 S09 SrI 813 814 822 824 $26 827 $29 $30 838 840 842 843 845 847 855 856 858 859 S61 863 > 871 872 874 | 875 877 879 887 888 | 890 | 892 | 893 | 895 j SMITHSONIAN TABLES. Oo ran No) CO DUG) Oo oH SPB 6) WG Ww oO THU OWSTHMN Ap an On 480 on m4 \O nv OV x 528 544 560 576 592 608 624 641 657 673 689 795 721 VOI 753 769 785 Sor 818 834 850 866 882 898 km. 14 31 47 63 79 95 Iit Te, 143 159 175 192 208 224 240 256 22 288 304 320 336 352 369 385 4ol 417 433 449 465 481 497 513 52 546 562 578 594 610 626 MILES INTO KILOMETRES. TABLE 68. km. 855 gol 917 933 959 966 gS2 998 1014 1030 1046 1062 1078 1094 IIIO 1127 1143 1159 1175 I1gI 1207 1223 1239 1255 1271 1287 1304 1320 1336 1352 1368 1384 1400 1416 1432 1448 1464 1451 1497 1513 1529 1545 1561 1$77 1593 1609 Miles. {000 2000 3000 4000 5000 | | | km. 887 903 919 935 951 967 953 999 1OI5 1032 1048 1064 1080 1096 TS 1128 1144 I160 117 1193 1209 1225 I241 1257 1273 1289 1305 1321 1337 1353 379 386 1402 1418 1434 1450 1466 1482 1498 1514 1530 1547 1563 1579 1595 1611 kin. 1609 3219 4828 6437 8047 km. km. km. km. km. 888 890 892 893 895 go4 go6 gos gog gil g2t 922 924 925 927 937 | 938 | 940 | 941 943 953 | 954 | 956 | 958 | 959 969 | 970 | 972 | 974 | 975 955 987 985 999 991 1OOI 1003 1004 1006 1007 IO17 101g 1020 | 1022 1024 1033 1035 1036 | 1035 1040 1049 | IO5I 1053 1054 1056 1065 1067 1069 1070 1072 1081 1083 | 1085 | 1086 | 1088 1098 | 1099 | Ito! 1102 | 1104 III4 III5 Il17 1115 1120 LIGon | 131 Erase eEres: | ents 1146 | 1147 I14g | II51 1152 1162 1164 1165 | 1167 1168 1178 iatesyoy) |) aeateye 1183 1184 1194 | 1196 | 1197 }| I199 | 1201 T2TOM ||, L202 M203 ets 1217 1226 1228 | 1230 | 1231 1233 1242 1244 1246 1247 1249 1259 1260 1262 1263 1265 1275 1276 1278 1279 1281 1291 1292 1294 | 1296 | 1297 1307 1308 LILON |e Le 1313 1323 1324 1326 | 1328 1329 1339 | 1341 1342 | 1344 | 1345 1355 1357) 1358 | 1360 1362 7% | 1373) | 1374 || 1376 |) 1378 1387 | 1389 | 1390 | 1392 | 1394 1403 1405 1407 1405 1410 1419 1421 1423 1424 1426 1436 | 1437 | 1439 | 1440 | 1442 1452 | 1453 | 1455 | 1456 | 1458 1468 | 1469 | 1471 | 1473 | 1474 1484 | 1485 | 1487 | 1489 | 1490 1500 1502 1503 1505 1506 1516 1518 151g | 1521 1522 1532 1534 | 1535 | 1537 1539 E549 |) 1550] 1552) 1553 | 1555 1564 1566 1567 1569 1571 1580 1582 1594 1585 1587 1596 | 1598 | 1600 | I60I 1603 1613 1614 | 1616 | 1617 1619 Miles. km. Miles. km. 6000 | 9656 11000 | 17703 7000 | 11265 | 12000 | 19312 8000 | 12875 | 13000 | 20922 9000 | 14484 | 14000 | 22531 10000 24140 16093 15000 km, 896 gi2 929 945 961 977 993 1009 1025 1041 1057 1073 1090 T106 TI22 1138 1154 1170 1186 1202 1218 1234 1250 1267 1283 1299 1315 1331 1347 1363 1379 1395 I4II 1427 T444 1460 1476 1492 1508 1524 1540 1556 1572 1588 1605 1621 Miles. 16000 17000 18000 19000 | ae 32187 8 | 2 | km. km. | 898 goo | 914 | 916 | 930 ga5. | 946 | 948 | 962 964 | 978 g8o | 995 | 996 | IOI IOI2 1027 1028 1043 | 1044 1059 | I061 1075 1077 IOgt I093 1107 I10g 1123) | 2125 TEZO) | LAL Trs6 | TL57 | 1172 | 11Z3 1188 1189 | 1204 | 1205 | 1220 | | 1221 1236 1238 1252 | 1254 1268 | 1270 1284 | 1286 | 1300 1302 | 1316 | 13164 1333 | 133 1349 1350 1365 | 1366 1381 1352 1397 1399 1413 1415 1429 1431 1445 1447 1461 1463 1477 1479 1493 | 1495 1510 | I511 1526 | 1527 1542 1543 1558 | 1559 1574 | 1576 1590 | 1592 1606 | 1608 1622 1624 km. 25759 27359 28968 3957 pseeeeees| SMITHSONIAN TABLES. 205 TABLE 69. KILOMETRES INTO MILES. 1 kilometre — 0.621370 mile. Kilo- | metres. Miles. | Miles. Miles. : iles. | Miles. | Miles. | Miles. 0.0 6.2 12.4 18.6 24.9 al 3-7 4.3 5:0 9.9 10.6 Tie2 16.2 16.8 17.4 22.4 23.0 23.6 28.6 29.2 HONUD B = ‘Oo oH N HH DOW tO be ind Oo or = 35-4 41.6 47.8 54-1 60.3 66.5 C251 78.9 85. gl. 97- 103. 110.0 T16:2 122.4 128. 34. I4I. TAZ: 153. DOL WH NO WD HON UG oni & 02 SHAD HOS w COAL HO - Oita Nv WO & Oude HON \ ON >H WONTON Oy o aN OITA AML W Ww SyOre DIIA DUN OMAR NONUMY 2 Oo Ce a | ° MnnoWw THe Ob MHONIADN AN of OV APN O e HOH b Ny U1\0 Ww SI bo me 1 ON \O No} i OO HU H = ne Oo . Stak WO NI ONG bo ON Uw not Ov H WO NI ON Go COR an 0 MAL H BH HW HWW SON to t > HOH OO i by Oo Se RH eS eH 1 ONBwW bd u én Go HON wm HH COON or | 0D DANII DAAM NALPWwH bd So U0 GST H ODL bv ST U1 © 2~ oC eet Cou1itw HO Bown KH PN NO COAL WN O r > 261.0 | 267.2 273-4 279.6 285.8 292.0 298.3 304.5 310.7 316.9 B2351 329-3 335-5 DAWN wo HH HN NHN oO bw HN Wb WO WN 4 Oud Oo “I SMITHSONIAN TABLES. TABLE 69. KILOMETRES INTO MILES. Kilo- metres. Miles. a iles. | Miles. | Miles. . | Miles. iles. | Mile>. Miles. | 341.8 . 43-0 | 343.6 | 344.2 9 | 345-5 | 346.1 | 346.7 | 347-3 | 348.0 48. : 349.8 4 ; 351.7 eats (a2. 354-2 | 354. 55:4 | 356.0 | 356. 57-3 | 357-9 5 | 359.2 360. 4 : 362.3 : : 364.1 A. 365.4 366.6 : : 368.5 : ; 370.3 ; 371.6 372.8 379-0 385.2 391-5 374-7 | 375-: 5-9 | 376.6 -2 | 377.8 380.9 Sis 32. 382.8 , 384.0 387.1 Wie 388. 389.0 : 390.2 393-3 | 393. -6 | 395.2 | 395.8 | 396.4 397-7 399.5 | 400. : 4O1.4 : 402.6 403.9 405.8 : 407. 407.6 8. 408.9 410.1 : : 412.0 .2 | 413.8 | 414. 415. 416.3 : 417. 418.2 } 418.8 }| 419.4 | 420.0 . Aoyee 422.5 : 23: 424.4 | 425.0 25. 426. 427.! 428.7 | 429. : 430.6 | 431.2 ‘ 432. 433- 435-0 | 435. -2 | 436.8 | 437.4 439-6 441.2 | 441. 2-4 | 443-0 | 443-7 446. 447.4 49. . 449.3 | 449.9 452.4 453.6 54. 454.8 | 455.5 | 456.1 458. 459.8 EAy || : 461.7 | 462.3 464.8 | 466.0 2 467. 467.9 | 468.5 472.2 | 472. 473- 474.1 | 474.7 478.5 | 479. 79. 480.3 | 480.9 484.7 85.: 35. 486.5 | 487.2 490.9 | 491.5 | 492. 492.7 | 493-4 497.1 -7 | 498.3 | 499.0 | 499.6 503.3 | 503. : 505.2 | 505.8 509.5 : POMS Lie Asn | 52.0 515-7 : : BI7O) |) Lowe 522.0 : : 523.8 | 524.4 WO ONIN NOY — Aas &) G2 G2 G2) O2 Ure of nou O23 Ho C Go oO ow HON 471. O MAW H CARN nm 528.2 Ag : 530.0 | 530.6 534-4 | 535-0 |.535-6 | 536.2 | 536.9 540.6 -2 | 541.8 | 542.5 | 543.1 546.8 -4 | 548.0 | 548.7 | 549.3 553-0 | 553. -3 | 554-9 | 555-5 559.2 59. : 561.1 | 561.7 565.4 . -7 | 567.3 | 567.9 571.7 9 | 573-5 | 574-1 577-9 . -I | 579.7 | 580.4 554.1 A. : 586.0 | 586.6 590.3 : : 592.2 | 592.8 596.5 . -8 | 598.4 | 599.0 602.7 : A. 604.6 | 605.2 608.9 : : 610.8 | 611.4 615.2 =r || .4 | 617.0 | 617.6 621.4 : ; 623.2 | 623.9 On HD Nob Oo Con NS o> wo nN aS MOm~I~I AD MN 2 Far km. Miles. km. Miles. km. iles. ; Miles. 1000 | 621.4 6000 | 3728.2] 11000 : 9941.9 2000 | 1242.7 7000 | 4349.6] 12000 : 10563.3 3000 | 1864.1 8000 | 4971.0} 13000 : I11184.7 4000 | 2455.5 9000 | 5592.3} 14000 : 11806.0 5000 | 3106.8} 10000 | 6213.7} 15000 5 12427.4 SMITHSONIAN TABLES. 207 TABLE 70. INTERCONVERSION OF NAUTICAL AND STATUTE MILES. I nautical mile* — 6080.27 feet. Nautical Miles. Statute Miles. Statute Miles. O OI HDA HW NY me Nautical Miles. 0.8684 1.7368 2.6052 3-4736 4.3420 5.2104 6.0788 6.9472 7.8155 * As defined by the United States Coast Survey. TABLE 71. CONTINENTAL MEASURES OF LENGTH WITH THEIR METRIC AND ENGLISH EQUIVALENTS. The asterisk (*) indicates that the measure is obsolete or seldom used. Measure. Metric Equivalent. English Equivalent. El (Netherlands) metre. Fathom, Swedish Foot, Austrian* old French* Russian Rheinlandisch or Rhenish (Prussia%, Denmark, Norway*). Swedish * Spanish* 4 | *Klafter, Wiener (Vienna) *Tine, old French Mile, Austrian post* German sea Swedish Norwegian Netherlands (mijl) 36000 feet 36000 feet Prussian (law of 1868) Danish Palm, Netherlands *Rode, Danish *Ruthe, Prussian, Norwegian Sagene (Russian) *Toise, old French *Vara, Spanish Mexican 0.30480 0.31385 0.2969 0.2786 1.89648 0.22558 cm. 7.58594 km. 1.852 er 10.69 11.2986 I x 8 SINR OM ao Oo oO Ny XN - Ny yO 44 OQ oO Oa An Werst, or versta (Russian) = 500 sagene. . ae ce ce 0.0888 inch. 4.714 statute miles. 1. 500-0 wee ss 6.642 os 7.02 s 0.6214 4.660 ub 4.6804 ‘‘ 0.3281 feet. 125350 5uece 12356 7 ce 6.3943 2.7424 2.7293 3.500 SMITHSONIAN TABLES. 208 CONVERSION OF MEASURES OF TIME AND Arc into time . Time into arc. Days into decimals of a year and angle Hours, minutes and seconds into decimals of a day . Decimals of a day into hours, minutes and seconds . Minutes and seconds into decimals of an hour Mean time at apparent noon . Sidereal time into mean solar time Mean solar time into sidereal time . . . 209 ANGLE. TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE “I N ~I wn “I On ~ i | ~I 1 © CO ~I On oo ° TABLE 72. ARC INTO TIME. ° ——$<$<— | —— | ———— |] —————_—_—_' —___—_ | —___ 240] 16 0}|300 241| 16 4] 301 242|} 16 8] 302 243] 16 12] 303 244] 16 16} 304 245] 16 20}305 246] 16 24] 306 247| 16 28] 307 248] 16 32] 308 249] 16 36} 309 250] 16 4o| 310 251] 16 44] 311 252| 16 48} 312 253| 16 52] 313 254] 16 56| 314 255) 17 0; 315 256] 17 4] 316 25 7 de) Ono Ly 258] 17 12] 318] 27 259] 17 16} 319] 21 260) 17 20/320} 21 261) 17 24] 321} 21 262| 17 28] 322] 21 2031bt7. 32323 ote 264] 17 36} 324] 21 : 265] 17 40} 325) 21 266] 17 44 | 326] 21 267] 17 48 | 327] 21 268] 17 52] 328} 21 PUI DIB wWhy HO ( Ne) 1 ClO OI HOB W WHO SON | O on Al oon Bl oon oe OWN H ee 2 2 2 2 2 2 2 2 2 o Am | ¢ Av > Ow nd On HOS W DN 209 210 270] 18 0/330] 22 o 211| 14 18 4] 33 212 13) .0)] 332 213 185 12] 333 Io 16| 214 18 16] 334 10 20] 215 18 20] 335 10 24] 216 18 24 | 336 IO 28] 217 18 28] 337 10 32]{ 218 18 32} 338 10 36] 219 18 36| 339 10 40] 220 é 18 40 |340 10 44 18 44] 341 10 48 18 48] 342 10 52 18 52] 343 10 56 18 56] 344 Il oO 19 0] 345 II 4 19 4} 346 Lt 7S Ig 3] 347 II 12 | Ig 12] 348 II 16 19 16] 349 19 20] 350 19 24] 351 19 28] 352 19 32] 353 19 36] 354 19 40]355 II 4. 19 44 | 356 It 43} 237] 15 48] 297| 19 48] 357 LT ¢ 39] 15 52} 295) 19 52] 358 ) 15 56 9] 19 56 0} 16 o 2 " ~) NI “ 2 GG Oo SOON H Con? OV OTB Go Sy vH_NHNYpnne NwHNt YNvbv?t NINN Nas |JNNNNNNNNDHN \O t NjwSe wH HN Nvn vy vv n> WWWWWNNNHDN fet HDvoyndvnHNYnvnnn NNN YN WWwWwWwNN ¢ Aw’ | oO NR ow Oo OI nw bd II 20 it 2 11 Il 3 Tis II Z > ©) G2 G2 BW nb Nido) ew ° O|Dv OBO DDN OB] 1 lune Slen on nn wn CONT HOI Ww Oo HN ND N ol 3-733 3.800 3.867 J | 3-933 Ro HHH NON ON to w | to NHNHNHN ND wy Oo~wT OF DW GO G2 G2 OO GD G 1O0 en oF Ror ¢ \O JAM SH HwW bd ino pp RWW bv oN SINN™NINI Bl W G3 G2 G2 Go Go G2 lon lw ww wWwWo Db bbw D/Dd| SMITHSONIAN TABLES, TABLE 73. TIME INTO ARC. Hours into Arc. Arc. Time. Arc. com On won NNN Oo Minutes of Time into Arc. mrOO°0 nn HOOO wo on no hWH™= SINID OOD Dur un Oo mI OO! SW NO _ STANT ON ON ON Aunwwn N NH eH Nw See 2 7 2 7 3 8 3 8 a 8 WW hn Nd mm onnrni CA pPRARO na PRBRRW O0n0w on Hundredths of a Second of Time into Arc. Hundredths of aSec- | .00 Ol : .03 3 .05 .06 .07 ond of Time. ° oo 0.90 .40 3.90 5-40 6.90 X x 0.00 | 10 .20 | 30 | ae Oo naonww oi Ow non COO» SOE ND HY SST icteae, pes DAuiw vY Oo, Syuyn Onn STUB NR, to Oo SII bv Ay mamnnongi .40 ~ Oo 0.50 .60 ” = NHO N™NI ON bd awn 8.40 9.90 | II.40 12.90 14.40 cn on rH Hom oe eae oro our an Ut a On ovwonN COO COU» nour Ui Ut SMITHSONIAN TABLES, TABLE 74. DAYS INTO DECIMALS OF A YEAR AND ANGLE. Month. Day of Month. Decimal Day Decimal of = Saas of of a Year. Bissextile ||) Year. a Year, Common | Bissextile Year, Year. Year. 0.00000 ° Jan. 5I .13689 . 20\| Fe: .00274 52 .13963 21 -005458 53 - 14237 22 -00821 54 LI4511 23 55 .14784 24 56 .15058 25 57 | -15332 26 58 . 15606 27 59 . 15880 28 .02464 5 60 16153 .02738 61 .16427 .O3011 62 . 16701 .03285 5c | 63 . 16975 -03559 64 .17248 0.03833 48 5 i 65 | 0.17522 -O4107 / | 66 17796 04381 : i) 67.1) 4.18070 .04654 : 8 | 68 .18344 .04928 | 69 . 18617 .05202 70 | 0.18891 -05476 Fir - 19165 -05749 | 2 72 -19439 .06023 78 .19713 -06297 74 | .19986 . 20260 .20534 .20808 .21081 -21355 boH -O1095 .01369 .01643 -O1916 -02190 O ONDA PWN — NU fs Go nono uri Who Qn “I PIN NSW NH oO Ow \ NHHN HD wn Hw [So oO wHN 0.06571 .06845 | .O7118 | -07392 .07666 Om NUN wn RR 3 4 5 6 7 8 oO NN bd CONT Qn NHN WN NN wo \O NO HNHN YN Dui & Go KR wHHhH ND “I to oO \o ee) -O7940 .08214 .08487 05761 .09035 .21629 .21903 S22 77, > \O 62 G2 Ww G2 O2 O2 Oo NN WwW CG OG Go GQ wWwWwwWww W PWN © NnWwhN Ne + 09309 .09552 .09856 -IOI30 | - 10404 Com} GV OI Dur — W 5 O Nb ND WwW WWinw &W NI CO\O Oo WR WD WW Ww “I .10678 - 10951 .11225 -I1499 | 520773 Nv nO wo Nb woeu . 12047 . 12320 12594 26283 .12868 26557 STAD All v3 8 | iH .26831 NS . 26010 NO NN PI HDS WN 0.13415 8 18 | . 27105 © SMITHSONIAN TABLES. TABLE 74. DAYS INTO DECIMALS OF A YEAR AND ANGLE. Day of Month. Day of Month. Decimal | | Common | Bissextile | : : Common | Bissextile Year. Year. Year. Year. ° Apr. 0.41068 | 147°51/] May 31 May 30 | .41342 | 148 50 | June -41615 | 149 49 .41889 | 150 48 a) 8S 31 June 42437 | 152 46 5 -42710 | 153 45 42984 | 154 45 a -43258 | 155 44 8 -43532 | 156 43 9 -43806 | 157 42 oO -44079 | 158 -44353 | 159 -44627 | 160 : 2 9 -42163 | 151 47 4 6 I / I > a I I 12 13 oO» oO -44901 161 -45175 | 162 3 45448 | 163 .45722 | 164 -45996 | 165 .46270 | 166 -46543 | 167 .46817 | 168 -47091 | 169 -47365 | 170 no by by bd WWW GW WO) Go Gd HN®OWH MN AN CO -47639 | I71 3 247 O12) | 172 48186 | 173 .48460 | 174 -48734 | 175 .49008 | 176 -49281 Ty. -49555 | 178 .49829 | 179 .50103 | 180 Ny Go oOo 0 oN SI OU & Oo Le a) .50376 | 181 .50650 | 182 2 -50924 | 183 .51198 | 184 -51472 | 185 186 187 188 | 189 190 CONAN to Oo Nn HN pt WNH OW IgI 192 193 | 194 195 ann N®hYU noun unr on — 0.54483 SMITHSONIAN TABLES. TABLE 74. DAYS Day Decimal of of Year.| a Year. 201 | 0.54757 202 55031 203 | -55305 204 | -55575 205 | 0.55852 206 .56126 207 - 56400 208 | .56674 209 | -56947 210] 0.57221 211 57495 212 57769 213 58042 214 .58316 215 | 0.58590 216] .58864 217 -59138 218 -59411 219 -59085 220} 0.59959 221 .60233 222 | .60507 223 .60780 224 61054 225 | 0.61328 226 | .61602 227 .61875 225 -62149 229 .62423 230 | 0.62697 231 .62971 232 .63244 233 .63518 234 | -63792 235 | 0.64066 236} .64339 237 .64613 238 .64887 239 | .65161 240 | 0.65435 241 .65708 242 .65982 243 | .66256 | 244 | .66530 | 245 | 0.66804 246 | .67077 247 | .67351 248 .67625 | 249 | .67899 | 250] 0.68172 SMITHEONIAN TABLES, INTO DECIMALS OF A Angle. | =e 197 198 199 200 201 202 203 204 205 206 | 206 207 208 209 210 211 212 213 214 my Bo wBwHH bh G2 OG G2 WG Go wn Nob ann CoN! to wo wb DH GW Os \o NS > ~ 241 - 30 Day of Month. Common | Bissextile Year. | Year. 8/| July 20| July 19 df 21 20 6 22 | 21 5 23 22 4 24 23 3 25 24 2 26 25 I 27 26 I 28 27 oO 29 28 99 30 2 58 BL 30 57 Awl 31 56 2| dug. I 55 3 2 | 55 4 2) 54 5 4 53 6 5 52 7 6 51 8 7 90 9 8 49 Io 9 49 II 10 45 12 If 47 1 12 46 14 13 45 15 14 44 16 15 43 17 16 43 18 17 42 19 18 41 20 19 4o 21 206 39 22 21 38 23 22 37 24 3 36 2 24 36 26 25 35 27 26 34 28 27 33 29 28 32 30 29 31 31 30 30 | Sept. 1 31 2 SEDE. aol 29 3 2 28 4 3 27 5 4 25 7 6 | Year. wo bw bd INN Wd ty NN hb ND SST) Sa 294 295 298 299 300 YEAR AND ANGLE. Decimal O° “I G2 ON > CO ° -75017 -75291 75565 75838 -76112 0.76386 .76660 -76934 -77207 -77481 0.77755 -78029 -78303 -7857 -78850 0.79124 79398 -79671 -79945 .80219 0.80493 .80767 .S1O4O 81314 .81588 0.81862 Angle. 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 a O NNN NHN SNS ANI aN HWNH No HNN N STS ST NON wKNH HN CmMO on WOH A OW 284 285 286 287 288 289 290 291 292 293 294 24 23 22 21 20 19 18 17 17 16 15 14 13 12 Il Il Io \o OH NWH UMN ON © ow CO.O 10 5 nn am nan naannon - RnNwHN 50 49 48 47 46 46 45 44 43 42 Day of Month, Common Year. Oct. 9 10 Il 12 13 14 5 16 17 18 19 20 2I 22 23 24 25 26 27 28 29 30 I HOW ON An bv me be Bissextile Year. 246° 24’| Sedt. 8| Sept. OGE: 7 8 9 10 Il 12 3 14 15 16 Wy 18 1g 20 21 22 23 24 25 26 27 28 29 30 WO OND NALWDNH DAYS Decimal of a Year. 0.82136 .82409 .82683 -82957 .83231 -83504 8377 .54052 .84326 9.84600 .84873 .85147 .85421 85695 85969 .86242 .86516 .86790 .87064 87227 -97337 .S7611 .87885 .S8159 88433 .88706 .88980 .89254 .89528 .59802 ow wo o -90075 -90349 -90623 .90897 -9I170 W WOW Ww ao #F&NH -91444 -91715 .91992 .92266 -92539 .92813 -93087 -93361 -93634 -93908 -94182 94456 -94730 -95003 -95277 0.95551 “I OV’ OW W WOO 2 G2 Go Oct. 28 | Oct. nN G2 G2 G2 G2 Oo & Go Go OD CONDE WN HOW CO Wr Co G2 G2 OG) Ge hun ann GO?) G2 G2 G) G Oe \O Oe Day of Month. Common Year Year. on a9 30 31 ®WNHNHN Ow Oo» OO CONID NLPWNH On nur BWW HH Bissextile } No) ASI NO BWN — \o wWnNHOS = aS ag INTO DECIMALS OF A YEAR Decimal of a Year. 0.95825 -96099 .96372 .96646 0.96920 -97194 97407 -97741 -98015 0.98289 -98563 .98836 -99IIO -99334 0.99658 -99932 O.,OOIT4 126 0.00171 183 194 205 217 | 0.00228 | LS) WON N 5) 1 TABLE 74. AND ANGLE. Day of Month. | Angle. 344° 345 346 347 CO Epors G2 G2 Ne) Oo Common Year. 58/1 Dec. 57 56 on oO NR BNW pRUN NNN N ND on -& Oo ~unur minnow on Conversion for Dec. of Year. 0.00000 Bissextile Year. Dec. 16 17 18 19 | a) & NNHN Ou onl Minutes. / | Angle. | | | 0.04 Oo .08 I I 0.00001 | 0,OOOTT *» WO NNN MIO2 00 O71 % Cop WN on n SMITHSONIAN TABLES TABLE 75. HOURS, MINUTES AND SECONDS INTO DECIMALS OF A DAY. Day. .083 333 .166 667 0.205 333 -291 667 PINON WN — 0.416 667 -455 333 -500 O00 541 667 -Q a 593 333 0.625 000 .666 667 -708 333 -750 000 -791 667 2222 0.533 333 .575 000 -916 667 -958 333 I.000 OOO TABLE 76. 0.041 667 | .125 000 | +250 000 | 222222 | "IIS IIS +375 000 0.000 694 .OOT 359 .002 083 .002 775 0.003 472 .004 167 .004 861 005 556 .006 250 0.006 944 .007 639 .008 333 .009 028 .009 722 0.010 417 OLE ILE Ott 806 .O12 500 O13 194 0.013 889 O14 583 .O15 278 .O15 972 .016 667 0.017 361 .018 056 .O18 750 O19 444 .020 139 0.020 833 © oO oo 00 tow HK be Ono nn Ss we N WN HIN NN O 0.024 305 025 O00 .025 694 .026 389 .027 083 PMI VNDW LO bv =— DDH WD rio w W © 0.027 778 .028 472 .029 167 .029 861 .030 556 0.031 250 031 944 .032 639 033 333 .034 028 0.034 722 035 417 .036 III .036 806 037 90° 0.038 194 .038 889 .039 583 .040 278 | .040 972 0.041 667 0.000 O12 .000 023 .000 035 .000 046 0.000 058 .000 069 .000 OSI .000 093 .000 104. 0.000 116 .000 127 .000 139 .000 150 .000 162 0.000 174 .000 185 .000 197 .000 208 .000 220 0.000 289 .000 301 .000 313 .000 324 .000 336 0.000 347 Px DO LW YO me WD 0 2 2 W Ww Ww i HO Oo 0.000 359 .000 370 .000 382 -000 394 0,000 405 .000 417 .000 428 .000 440 | .000 451 0.000 463 .000 475 .000 456 .000 498 .000 509 | 0.000 521 | +000 532 .000 544 | .000 556 .000 567 | 0.000 579 .000 590 .000 602 .000 613 | .000 625 0.000 637 .000 648 .000 660 | .000 671 .000 683 .000 694 | DECIMALS OF A DAY INTO HOURS, MINUTES AND SECONDS. Hundredths of a Day. d. h. 0.01 -O2 .03 -O4 0.05 .06 107 .08 -O9 0.10 .20 -30 .40 0.50 8 .70 50 .9O SMITHSONIAN TABLES. i; 14 28 43 57 12 26 40 55 5 o) 48 I2 36 24 48 [2 36 Ss. 24 45 12 36 oO 24 48 12 36 d Ten Thousandths of a Day. 0.000! min. sec. $8.64 17.28 25.92 34-56 43.20 51.84 0.48 9.12 17.7 26.40 52.80 19.20 45.60 12.00 38.40 4.80 31.20 57.60 Millionths of a Day. d 0.000001 2 3 4 0.000005 6 i 8 9 0.000010 20 30 4o 0.000050 60 70 80 go sec, 0.09 0.17 0.26 0.35 0.43 0.52 0.60 0.69 0.78 0.86 Leg 2.59 3.46 4.32 5.18 6.05 6.91 7.78 — BONnNHO OONACSH LW b — iON hd bby NO 3 4 5 6 7 8 Oo nbd Sore MINUTES AND SECONDS Decimals of an hour, 0.016 667 22222 033 333 .183 333 -200 0OO 216 667 922222 8299 IIS .250 000 .266 667 .283 333 .300 000 .316 667 433 333 -450 000 .466 667 453 333 0.500 000 TABLE 77. INTO DECIMALS OF AN HOUR. Decimals of an hour. 0.516 667 533 333 +550 000 .566 667 0.583 333 - .600 000 616 667 633 333 .650 000 0.666 667 .683 333 -700 000 .716 667 -733 333 -750 000 -766 667 -793 333 .800 000 816 667 833 333 .850 000 .866 667 883 333 «JOO OOO 0.916 667 933 333 .950 000 .966 667 .983 333 I.000 000 ANID BWNH — \o Decimals of an hour. 0.000 278 .000 556 .000 833 .OOT III 0.001 359 .OOl 667 .OOI 944 .002 222 .002 500 0.002 778 .003, 056 003 333 .003 611 .003 889 0.004 167 004 444 .004 722 .005 000 .005 278 0.005 556 .005 833 .006 III .006 389 .006 667 0.006 944 .007 222 .007 500 .007 778 .008 056 0.008 333 SMITHSONIAN TABLES, Sec. WwW CPI Ag FW N — RWW Ww +P WwW tN Decimals of an hour. 0.008 611 .008 859 .009 167 009 444 0.009 722 -O10 OOO .O10 278 O10 556 O10 833 O.OIT ITI .OI1 389 .O1l 667 .OI1 944 O12 222 0.012 500 = 0 .012 778 013, 056 O13 333 O13 611 0.013 889 .O14 167 O14 444 O14 722 .OT5 000 0.015 278 O15 556 O15 833 .O16 III 016 389 0.016 667 TABLE 79. SIDEREAL TIME INTO MEAN SOLAR TIME. The tabular values are to be subtracted from a sidereal time interval. TABLE 80. a MEAN SOLAR TIME SIDEREAL TIME. The tabular values are to be added to a mean solar time interval. INTO Reduc- ; : Reduc- | Reduction Reduction to : : Hrs. to. Min Hrs. | Sidereal | Min. aoe Min, a Mean Time. Time. Tine: Time: | — | h. m. Ss: m. s. h. Teme Ss m. m. s. | I Oo 9.83 I 31 | 5.08 1} 0 9.86 ! 31] 5.09 2 | o 19.66 2 3045.20 2 On Lowa 2 204/526 3 | 9 29.49 3 33 | 5-41 Bi ON 29-57, s 33] 5-42 | 4 | 9 39.32 +f 34 | 5-57 | 4] 9 39-43 4 34} 5-59 | 5 | 0 49.15 | 5 35] 5-73 | 5 | 0 49.28 5 Soi 05:75 5 | 6 | 0 58.98 6 36 | 5.90 I. 167" On5osr4 6 26) 5.0104] 7 Ie 190-08 7 37 | 6.06 7 |) LF 9:00 7 37 | 6.08 8 1 18.64 8 BS .4|/ §Gr22 | Oh), De LSsd5 5 38} 6.24 | 9 | I 28.47 | 9 39 | 6.39 nO [aL e287) =o 39 | 6.41 110 | « 38.30 J 10] 1.64 [40] 6.55 80, caeS35 791 40| 6.57 1 I 48.13 | II E.80) fai. (6.72 DT ie d4oAe LI Al | 6.74 12 rE 57.96 | 12'| 1.97 2] 6.88 12) |e 5os20 mt ele 2| 6.90 arg. | 2) 7.75 1.53 | 2.53 glfAs i) 7205 Sel 2h OS) hel 3 43 | 7.06 tA re 2eT72OT. Wr 22.2 AAG F22¥ FA 82 17/00) | a4 AA 728 | | a | 15 2 QT AA NS | 2:46) PAS 737 ie tS, b- 227235 [5° 72.46 |} 45: eee tO a2. 37-27 1 16) 2:62 if 46 7.54 16)|) 2637.70 T6)1||1-262, eA Oils o 17 | 2 47.10 | 17 | 2.79 | 47 | 7-70 | EF) 2 AP SOIL 2.79) SPAT vere | 18 | 2 56.93 | 18 | 2.95 | 48] 7.86 | til a 57 2A0 IS} 2.96 | 48| 7.89 Re 3..°6:76) | 19 | 3.0r (1-40 3| "8:02 EO) || 3) ae LO) 3.02 49 | 8.05 | 20 | 3 16.59 | 20] 3.28 2013. Warayt2Ois: 20), | 50) Maz2r 2r | 3 26.42 | 21 | 3.44 | 2t | 3 26.09 | 21 | 3:45 | 52] 8.38 | 22 2) 30.25 22 3.60 22 | 3 36.84 2232261 52 o.54 | 23 | 3 46.08 | 23 | 3.77 | 23 | 3 46.70 | 23] 3-78 | 53| 8.71 | 24 | 3 55-91 | 24 | 3.93 | 24 | 3 56.56 | 24) 3-94 | 54] 8.87 | 25 | 4.10 | 55) | o:0r 25} 4.11 | 35] 9.04 | 26 | 4.26 | 56] 9.17 26)1|) 4:27, 56| 9.20 27 4.42 | 57 9.34 27| 4.43 57 |) 9:30 | 28 | 4.59 | 58} 9.50 28| 4.60 | 58] 9.53 | 29 | 4.75 | 59] 9.67 29| 4.76 | 59] 9.69 | ) | 30 | 4.92 | 60] 9.83 | 30] 4.93 | 60] 9.86 | | Reduction for Seconds—sidereal or mean solar. The tabular values are to be Sidereal |” or. I 2 5 Mean Time. Ss. SS De a a 0 0.00 0.00 0.01 0.01 IO E( 3 t 3 s¢ 3 O4 | 20 .06 .06 .06 .O7 | 30 05 .O9 .O9 <0 | 4o II aT 12 12 | | 50 0.14 0.14 0.14 0.15 | SMITHSONIAN TABLES. ( subtracted from a sidereal ) (added to a mean solar 0.02 05 .O7 10 ae 0.16 218 time interval. 0.03 O05 05 od abe MISCELLANEOUS TABLES. Density of air at different temperatures Fahrenheit . Density of air at different humidities and pressures— English measures. Term for humidity: auxiliary to Table 83 . P20. 876 29.921 29.921 Values of Density of air at different temperatures Centigrade Density of air at different humidities and pressures — Metric measures. Term for humidity: auxiliary to Table 86 Values of a = 6 — 0.378 e 760 760 Conversion of avoirdupois pounds and ounces into kilogrammes Conversion of kilogrammes into avoirdupois pounds and ounces Conversion of grains into grammes Conversion of grammes into grains Conversion of units of magnetic intensity . Quantity of water corresponding to given depths of rainfall . Dates of Dove’s pentades Division by 28 of numbers from 28 to 867972 Division by 29 of numbers from 29 to 898971 Division by 31 of numbers from 31 to 960969 Natural sines and cosines Natural tangents and cotangents . Logarithms of numbers LIST OF METEOROLOGICAL STATIONS TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE 8I 82 84 85 86 87 88 go gI 92 93 94 95 96 97 98 99 100 TABLE 81. DENSITY OF AIR AT DIFFERENT TEMPERATURES FAHRENHEIT. ss 0.00129305 ~~ T +0.0020389 (¢ — 32°) 1 cubic centimetre of dry air at the temperature 32° /. and pressure 760 mm., and under the standard value of gravity at latitude 45° and sea-level, weighs 0.00129305 gramme. 15339 15155 14977 14802 14631 0.00 14464 14395 14333 14269 14205 0.00 14142 14079 14017 13955 13894 0.00 ne 13533 13503 3773 13743 13713 0.00 13684 13654 13625 13596 13567 0.00 13538 13509 13480 13452 13423 0.00 13395 13367 Oo mn no! PwNnNHO aS oT] 2 2 © o a | GH GW &. ain 0M ~~ = ws NN b ty OnNwN oO to OrIH + + He He WW 2 WW ay urd 0.00 13118 13091 13064 13037 13010 SMITHSONIAN TASLES. -18579 . 18056 -17541 .17031 . 16527 . 16029 -15831 .15634 -15439 .15244 . 15050 .14856 . 14664 -14472 .14252 . 14092 -13997 - 13903 . 13508 -13714 362K -13527 -13434 - 13340 -13247 -13155 . 13062 .12970 3123877 .12785 7.12694 . 12602 -I12510 -12419 .12328 7022387 ~L2I47 . 12056 . 11966 .11876 -11786 . 11696 . 11606 -II517 -11425 ||Temper- ature. bt 0.00 12983 12957 12931 12904 12878 0.00 12852 12826 12800 12774 12749 0.00 12723 12695 12672 12647 12622 0.00 12597 12572 12547 12522 12497 0.00 12473 12448 12424 12400 7c 12375 0.00 12251 12327 12303 12280 12256 0,00 12232 12209 12185 12162 12138 0,00 12115 12092 12069 12046 12023 0.00 T2001 11978 11956 11933 7-11339 .11250 .IIT62 . 11073 . 10985 . 10897 . 10809 . 10721 -10633 . 10546 - 10459 .10372 .10285 - 10195 .IOII2 . 10025 “09939. -09853 .09767 .09682 7-09596 .O951I .09426 09341 .09256 7.09171 .09087 .09002 .08918 .08834 .0875V0 .08667 .08583 .08500 .08416 .08334 .08251 08168 .08085 .08003 7.07921 .07839 -07757 .07675 11888 11866 11844 11822 11800 0.00 11778 11756 T1734 L1713 L1691 0.00 11670 11648 11627 11605 11584 0.00 11563 11542 11521 11500 11479 0.00 11458 11438 11418 11397 11376 0.00 11356 11336 11315 11295 11275 0.00 11255 11235 T1215 11196 11176 0.00 II156 II117 11078 11040 TIOOL 0.00 10963 10870 10776 10686 10597 7.07512 -07430 -07349 .07268 .07187 .O7107 .07026 .06946 .06865 .06785 .06705 .06625 .06546 .06466 .06387 7.06307 .06228 .06149 .06070 -05992 .05913 -05835 -05757 .05678 .05600 7-95523 -05445 .05367 .05290 .05213 .05136 .05058 .04952 -04905 .04828 -04752 -04599 -O4447 .04296 -O4145 -03994 .03621 .03248 .02883 .02518 TABLE 82. DENSITY OF AIR AT DIFFERENT HUMIDITIES AND PRESSURES. ENGLISH MEASURES. Term for Humidity: Values of 0.378¢. Vapor pen Pressure. ll "é F. Inch. —40°, 0.0054 —39| .0058 —38| .0o61 — 37| -0065 — 36] .0069 — 35] 0.0073 — 34] .0077 — 33| .0082 — 32] .0087 — 31} .0092 | — 30) 0.0097 —29]| .o103 }— 28] .o109 |—27]| .O115 | — 26} .o12I | — 25) 0.0128 2a ee Ole | —23]| .O142 |—22]| .o150 | —a2r| .o158 | —20) 0.0167 |—19| .o176 —18}| .o185 —17| .0195 —16}| .0205 —15 | 0.0216 —14| .0227 |—13| -0239 | —12| .0251 —Ir| .0264 —10| 0.0277 — g} .0292 — 8] .0306 — 7| .0322 — 6} .0335 — 5} 0.0354 — 4| .0372 tonne OOo! — 2| .0409 — I| .0429 | @Q| 0.0449 |-+- I .O471 2| .0493 3| -9517 4| .0541 | 5 | 0.0567 SMITHSONIAN TABLES, 0.378é. Inch. 0.002 ¢ == Vapor pressure in inches. Vapor Dew- | Pres- Point. | sure. é. F. | Inch. 5°| 0.057 6 | .059 7 062 8 | .065 g | .068 10 | 0.071 Tene O74! I2 | .078 120 .0ok 14 | .085 15 | 0.088 16 092 177 |e OQO 18 IOL 19 105 20 | 0.110 21 II4 22 11g 23 124 24 | .130 25 | 0.135 26 | .I41 27 | «147 28 | .153 29 |) -259 30 | 0.166 31 173 32 180 33 | .187 34 | -195 35 | 0.203 36 QU 37 219 38 228 39 237 40 | 0.246 41 256 42 | .266 43 | .276 44 287 45 | 0.298 46 310 47 322 48 | .334 49 347 50 | 0.360 0.3782. Inch. | 0.021 2O22 .023 .025 .026 0.027 | .028 .029 .031 .032 0.033 | .035 .036 -035 .04o 0.042 | .043 1045 .O47 .049 0.051 -053 .056 | .058 | x .060 | 0.063 | .065 | .068 | O71 | -074 | 0.077 .080 .083 | .086 -O9O | 0.093 | 097 | IOI -105 | . 109 Dew- Point. Vapor Pres- sure. ° Co OV a HHH oO No} 4 a N CO m 0.3782. Inch. 0.136 -I41 .146 152 -158 0.163 .169 -076 > pitta) .189 0.195 | 203 >| -2TOm| 5207) | .225 iil 0.233 il -241 -250 -259 a207, || 01277, .286 .296 306 “SL7 Hy 0.327 -339 350 -362 -374 0.386 -399 .412 .426 -440 0.454 .469 | -484 .500 .516 Dew- Point. 95° 96 97 98 99 100 oI 102 103 104 105 106 107 108 109 110 a 112 113 II4 115 116 117 118 11g 120 121 122 123 124 125 126 127 128 129 130 131 ey 133 34 135 136 7 137 138 139 140 Auxiliary to Table 83. Vapor Fuge | o.a782. & Inches. | Inches. | 1.645 | 0.622 | 1.696 .641 | 1.749 | .661 | 1.803 .682 | 1.859 -703 | 1.916 | 0.724 | WO75e| 747 || 2.035 -769 | 2.097 793, | 2.160 .816 | 2.225 | 0.841 | 2.292 .566 | 2.360 | .892 |} 2.431 919 | 2.503 .946 | 2.576 | 0.974 2.652 | 1.002 27200 elo 2.810 | 1.062 2.591 | 1.093 2.975 | 1.125 31000 ||| 13057 3.148 | I.19g0 | 3220) |sL-224)| 323231 || 15259 3-425 | 1-295 ZEwy || Tiss keyt 3.621 | 1.369 | 3-723 | 1.407 | 3-827 | 1.447 | 3-933 | 1.487 | 4.042 | 1.528 | 4.154 | 1.570 | 4.268 | 1.613 4.385 | 1.658 | 4.504 | 1.703 4.627 | 1.749 4.752 | 1.796 4.880 | 1.844 5.011 | 1.894 5-145 | 1.945 5.282 | 1.997 5.422 | 2.050 5.565 | 2.104 5e7l2! 2.059 5.862 | 2.216 | TABLE 86. DENSITY OF AIR AT DIFFERENT HUMIDITIES AND PRESSURES. ENGLISH MEASURES. Values of tea . 29.921 4 — Barometric pressure in inches ; h __ 6 —0.378e 39.921. 29.921 é = Vapor pressure in inches. Inch’s. 10.0 LO: 1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 a o 10.9 h 29.921 G2 G2 G2 G2 Oe G2 Go G2 G) Go h t09 9.921. eG) 9.52402 -52835 . 53262 53686 .54106 9-54521 -54933 -55341 -55745 .56145 9.56542 -56935 -57324 -57710 -58093 9.58472 £59848 .59221 “59591 -59957 .60321 60681 .61038 -61393 -61745 9.62093 .62439 .62782 .63123 .63461 9.63797 .64130 .64460 .64788 65113 9.65436 -65756 .66074 .66390 .66704 wa 9.67015 -67324 .67631 -67936 .68239 9.68539 -68837 -69134 -69429 .69721 17.0 | 17.4 17.5 17.9 18.0 18.2 18.3 18.4 18.5 18.6 18.7 | 18.8 | 18.9 19.0 19.1 | 19.2 19.3 | 19.4 | 19.5 | 19.6 | 19.7 | 19.8 SMITHSONIAN TABLES, 19.9 5 8, ey ts ney 29.291 29.921 — Io 0.5013 9.70012 -5047 -70300 .5080 -70587 SLL -70871 -5147 -71154 0.5180 9.71435 .5214 7L7T5 +5247 -71992 -5281 -72268 -5314 +72542 0.5347 | 9.72814 -5381 -73085 -5414 +73354 -5448 -73621 .5481 -73887 0.5515 9-74151 -5548 -74413 5581 -74674 -5615 -74933 .5648 -75191 0.5682 | 9.75447 *5715 -75702 5748 -75955 -5782 -76207 -5815 -76457 0.5849 9.76706 .5882 -76954 -5916 -77200 -5949 -77444 .5982 -77687 0.6016 9.77930 .6049 -78170 .6083 -78410 -6116 -78648 .6149 -78884 0.6183 9.79120 .6216 -79354 .6250 -79587 .6283 -79818 .6317 .80049 0.6350 9.80278 .6383 .80506 .6417 .80733 .6450 .80958 .6484 .81183 0.6517 | 9.81406 .6551 .81628 .6584 .81849 .6617 .82069 .6651 .82288 h. Inches. 20.0 We2Ont | 20.2 20:3 20.4 20.5 20.6 | 20.7 20.8 20.9 21.0 21.1 2122 212.8 21.4 21.5 21.6 DT, | 21.8 | 21.9 22.0 22.1 22.2 22:8 22.4 | 22.5 22.6 22077 22.8 22.9 | 23.0 23.4 23.5 | 23-9 24.0 ae 29.921 0.6684 .6718 -6751 .6784 .6818 0.6851 .6885 .6918 .6952 .6985 0.7018 -7052 -7085 -7119 -7152 0.7186 -7219 252 .7286 -7319 0.7353 -7386 -7420 +7453 -7486 0.7520 *7553 +7587 .7620 -7653 0.7687 e720 7754 7787 -7821 0.7854 .7887 .7921 -7954 .7988 0.8021 .8054 .8088 .S121 .8155 0.8188 .8222 .8255 .8289 .8322 Log = 29.921 — 10 9.82505 .82722 .82938 .83152 -83365 9.83578 -83789 83999 .84209 84417 9.84624 .84831 .85036 .85240 85444 9.85646 .85848 .86048 .86248 86447 9.86645 .86842 .87038 87233 87427 9.87621 .87813 .88005 .88196 .88386 9.88575 .88764 .88951 .89138 .89324 9.89509 .89693 .89877 .90060 .90242 9.90424 .90604. .90784 .90963 -QII4L 9-91319 .91496 -91672 .91848 .92022 TABLE 86. DENSITY OF AIR AT DIFFERENT HUMIDITIES AND PRESSURES. ENGLISH MEASURES. Values of ees ce: h __ b=0.378e. ek 6, 29.921 29.921 6 = Barometric pressure in inches; ¢-— Vapor pressure in inches. | h. a Log —" | : Log a : ; — |Log c 29.921 29.921 |} 92 29.921 : 29.921 | Inches. — © ; —I10 . — 10 25.06} 0.8355 | 9.92196 é 9.95939 0.9859 9.99355 | 25.05 .8372 .92283 a3 .9124 .96019 .9876 .99458 25.10 .8389 -92370 mae -QI4I .96008 -9893 99532 | | 25-15 .8405 92456 . 9157 .96177 -9909 99605 © 25.20 .8422 .92542 ; -9174 .96256 .9926 .99678 | 125.25] 0.8439 9.92628 ; -GIQI 9.96336 .9943 9.99751 | | 25.30 .8456 -92714 : .9208 | .96414 -9960 .99824 | 25-35 | .8472 -92800 || 27. +9224 -96493 -9976 -99897 25.40 .8489 .92886 : -9241 .96572 -9993 -99970 | 25.45 .5506 -92971 : .9258 .96650 -OOTO 9.00042 | 25.50} 0.8522 9.93056 -9274 9.96728 | .0026 -OO1I5 | | 25-55 | -8539 | °.93141 |} 27. 9291 | .96807 SONS ae case | 25.60 .8556 .93226 | OF -9308 .96885 .0060 .00259 | 25.65 -8573 -93311 |] 27. -9325 -96963 .0076 .00331 25.70 8589 -93396 || 27. .9341 .97040 .0093 .00403 25.75] 0.8606 | 9.93480 || 28. 9358 | 9.97118 | .O1IO 00475 | 25.80 .8623 | .93564 | 28. -9375 -97195 | .O127 .00547 ee .8639 .93648 35 .9391 297273 30.3 .O143 .00618 25.90 .8656 | .93732 oe -9408 -97350 | .O160 -00690 | 25-95 .8673 .93816 | 3. -9425 -97427 I [O17 7; .00761 | | 26.00] 0.5690 | 9.93900 | 4 -9441 | 9.97504 | 0193 .00832 | 26.05 -8706 | .93983 || 28. -9458 -97591 .0210 .00903, | 26.10 | .8723 | .94066 || 28.35 4 .9475 | .97657 .0227 | .00975 26.15 .8740 -94149 28.2 -9492 -97734 | .0244 .OTO45 | | 26.20 .8756 .94233 : .9508 -97810 | .0260 .O1T16 | 26525;| -0:38772 9.94315 : .9525 9.97887 | 10277; .O1187 | 26.30 .5790 -94398 28.5 -9542 -97963 .0294 .O1257 26.35 .8806 -94480 28. -9558 .98039 .0310 .01328 | 26.40 | .8823 94563 3.6: .9575 98115 | .0327 01398 | 26.45 .8840 .94645 || 28. -9592 .9SIQI .0344 .01468 | 26.50| 0.8857 | 9.94727 | 28. .9609 | 9.98266 .036 0.01539 | 26.55 8873 | .94809 3.8 .9625 98342 || ; .037 01608 | 26.60 .8890 | .94891 || 28.8 .9642 -98417 : : .01678 | 26.65 .8907 | .94972 || 28. .9659 .98492 31.15 ; | .01748 | 26.70 .8924 .95054 .9F .9675 98567 | : : .o1818 | 26.75 | 0.8940 | 9.95135 || 29. .9692 | 9.98642 , 0.01887 |26.80 | .8957 95216 |) 29.c .9709 .98717 || 31.: ; 01957 | 26.85 .8974 | .95297 || 20. .9726 -98792 || 31.35 : .02026 | 26.90 .8990 | .95378 |i} 29.15 -9742 | .98866 | é .02095 | 26.95 -9007 | .95458 |] 29. -9759 | .98941 | ; .02164 127.00] 0.9024 | 9.95539 | : -9776 | 9.99015 | : 0.02233 27.05 -g040 | .95619 | M9 -9792 | .99089 |] - | .02302 |27-10 | .9057 | .95699 || 29.35 | -9809 | .99163 || 31. | 02371 27.15 -9074 95779 - 9826 | .99237 | 31. | 02439 27.20 -909I | .95859 45 .9843 | .99311 2170 ; .02508 |} SMITHSONIAN TABLES. 223 TABLE 84. DENSITY OF AIR AT DIFFERENT TEMPERATURES CENTIGRADE. al Ob 760 cubic metre of dry air at the temperature o° C. and pressure 760 mm., and under the 0.00129305 I + 0.003670 ¢ standard value of gravity at latitude 45° and sea level, weighs 1.29305 kilogramme. t. bt, 760 Cc. 0.00 oe 14774 — 33 14712 — 32 14651 eH 14590 0.00 — 30 14530 carn) 14471 — 28 I4412 ai) 14353 — 26 14295 0.00 — 25 14237 — 24 14179 — 23 14123 — 22 14066 — 21 T4010 0.00 | —20.0| 13955 = 19-5 13927 —19.0] 13900 — 18.5 13872 | — 18.0 13845 0.00 —17.5 13518 — 17.0 13791 — 16.5 13764 — 16.0 13737 — 15.5 13710 0.00 —15.0] 13684 —#4.5] 13657 — 14.0 13631 — 10.5 13449 0,00 —10.0] 13423 — 9.5} 13398 — 9.0} 13372 a5 13347 — 8.0 13322 0.00 — 7.5 13297 —= 7.0 13271 — 6.5 13246 — 6.0 13222 aLo-0 13197 0,00 SMITHSONIAN TABLES. Log bt, 760 ~ “J “I “I J “I say “I 7.16950 .16768 . 16587 . 16407 Fe 1O227 . 16049 .15871 -15693 -15517 -15341 .15166 -14991 .14818 14645 -14472 .14386 .14301 .14215 - 14130 14044 -13959 .13874 -13790 -13705 .13621 -13536 -13452 .13368 .13285 .13201 .13117 -13034 . 12951 .12868 -12785 .12703 . 12620 -12538 .12456 -12374 s12202 .12210 12128 -12047 - 11966 LO) 215 2.0 OM WAKA HEY OonNnongd non bt, 760 0.00 13148 13123 13099 13074 0.00 13050 13026 13002 12978 12954 0.00 12931 12907 12884 12860 12836 0.00 12813 12790 12766 12744 12720 0.00 12698 12675 12652 12629 12607 0.00 12584 12562 12539 12517 12495 0,00 12473 12451 12429 12407 12385 0.00 12363 12342 12320 12299 12277 0.00 12256 12235 12213 12192 12171 0,00 12150 224 | Log 8¢, 760 | — Io | 7.11885 - 11804 ew p28 . 11642 7.11562 -11481 . 11401 11320 - 11241 7.11162 . 11082 . 11006 . 10923 -10844 7.10765 . 10686 . 10607 . 10529 . 10450 7.10372 . 10294 . 10216 . 10138 . 10069 7.09214 9137 go61 8986 8910 7.08834 759 8683 8608 8533 7.08458 18°0 18.5 19.0 19.5 20.0 20.5 21.0 2725 22.0 22.5 23.0 2305 24.0 24.5 25.0 ~ 25-5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33-0 33-5 34.0 34.5 35.0 3595 36.0 36.5 2720 37.5 38.0 38.5 39-0 39-5 40.0 bt, 760 0.00 12129 12108 12088 12067 0.00 12046 12026 12005 11985 11965 0.00 11944 11924 11904 11884 11864 0.00 11844 11824 11804 11784 11765 0.00 T1745 11726 11706 11687 11667 0.00 11648 11629 11610 11591 11572 0.00 11553 11534 T1515 11496 11477 0.00 11459 11440 11421 11403 113985 0.00 11366 11348 11330 II311 11293 0.00 11275 7-07349 7276 7204 7131 7058 7.06986 6913 6841 6769 6697 7.06625 6554 6482 6411 6340 7.06268 6197 6126 6055 5954 7.05913 5843 5772 5702 5632 7.05562 5492 5422 5352 5282 7.05213 TABLE 84. DENSITY OF AIR AT DIFFERENT TEMPERATURES CENTIGRADE. 11028 10994 10960 Log bt, 760 iL) 7.05213 .05074 04936 .04798 .04660 7-04523 04387 -O4251 -O4115 .03980 0.00 10926 10892 10858 10825 10792 0.00 10759 10726 10694 10661 10629 DENSITY OF AIR AT Term for humidity: values of 0.378¢. (Continued. ) bt, 760 Log bt, 760 —10 7-03845 -03710 .03576 -03443 -03309 7-03177 -03044 .02912 .02780 .02649 C. 60° 61 62 63 64 65 66 bt, 760 0,00 10597 10565 10534 10502 10471 0.00 10440 10409 10379 10348 Log 5t, 760 | —10 7.02518 .02385 .02258 .02128 -O1999 7.01870 .O1742 .O1614 .O1486 | .01358 TABLE 85. DIFFERENT HUMIDITIES AND PRESSURES. METRIC MEASURES. Auxiliary to Table 86. ¢@ == vapor pressure in mm. Vapor \— 3.16 3.41 3-67 3-95 4.25 SMITHSONIAN TABLES. Pressure. 0.378 e c | — 20 0.94 O 19 1.03 18 el 7 We22 16 1.32 —15 1.44 Oo 14 1.56 13 1.69 12 1.84 Il 1.99 OI .88 2.15 Oo 2.33 2.51 2172 I 2.93 I Vapor Pressure. 0.378 € e mn. mm. 4.57 1.73 4.91 1.86 Se 1.99 5.66 2.14 6.07 2.29 6.51 2.46 6.97 2.63 7.47 2.82 7-99 3.02 8.55 Be23 9.14 3-45 9-77 3.69 10.43 3-94 II.14 4.21 11.88 4.49 12.67 4.79 13.51 5.11 14.40 5.44 15-33 5-79 16.32 6507, 17.36 6.56 18.47 6.98 19.63 7.42 20.86 7.59 22.15 8.37 Pressure. é mm. STS 33-37 35-32 37-37 39-52 41.78 44.16 46.65 49.26 52.00 54.87 57-87 61.02 64.31 ae ae 36 a: 07 79- 83.19 87.49 g1.98 96.66 IOI.55 106.65 111.97 117.52 123.29 129.31 135.59 142.10 mm. II.QI 12.61 13.35 14.13 14.94 15-79 16.69 17.63 18.62 19.66 20.74 21.86 23.06 24.31 25.61 26.97 28.40 29.89 31-45 33-07 34-77 36.54 38.39 40.31 TABLE 86. DENSITY OF AIR AT DIFFERENT HUMIDITIES AND PRESSURES. METRIC MEASURES. WD Ww > &» > OV ww on Tes 374 376 378 380 382 384 386 388 390 392 | 394 | 396 | 398 h Values of 760° h 760 - 0.3947 -3974 . 4000 -4026 -4053 0.4079 -4105 -4132 -4158 -4184 0.42TI +4237 4263 -4289 -4316 0.4342 -4368 +4395 4421 -4447 0.4474 «4500 -4526 ©4553 -4579 0.4605 -4632 -4658 .4684 4711 0.4737 +4763 “4789 -4816 .4542 0.4868 -4895 -4921 -4947 -4974 0.5000 .5026 +5053 -5079 »5105 0.5132 -5158 -5184 -5211 +5237 SMITHSONIAN TABLES, 8 8, h __ 6—0.378e 7 7607; 760 6 = Barometric pressure in mm.; e = Vapor pressure in mm. h Log ——- 760 LO 9.59631 “59919 .60206 .60491 .60774 9.61055 61334 61612 .61887 -62161 9.62434 .62704 -62973 .63240 -63506 9.63770 .64032 .64293 -64552 64510 9.65066 .65321 -65574 .65526 .66076 9.66325 66573 .66819 .67064 .67307 9-67549 .67790 .68029 .68267 .68503 9.63739 -68973 .69206 -69437 .69668 9.69897 -70125 +79352 -79577 -70802 9.71025 -71247 -71465 -71688 -71907 mim. 400 4ol 402 493 404 405 406 407 408 409 410 4II 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 445 449 760 0.5263 -5276 .5289 -5303 -5316 0.5329 5342 5355 5369 5382 0.5395 -5408 -5421 -5434 -5447 0.5461 -5474 5487 -5500 -5533 0.5526 .5540 5553 5566 -5579 0.5592 .5605 .5618 .5632 5645 0.5658 .5671 .5084 -5697 -5711 0.5724 °5737 .5750 -5763 -5776 0.5790 -5903 .5316 25929 .5942 0.5355 .5868 .5582 -5895 -5908 h 8 760 — 10 9.72125 72233 -72341 -72449 *72557 9.72664 7 2U aL -72878 -72985 -73091 9-73197 WwW on I a Si ek ee ste “INININI NININI -74140 9.74244 -74347 74450 -74553 -74655 9-74758. -74860 -74961 -75063 75164 9.75265 75366 -75467 75567 -75668 9.75768 -758607 -75967 -76066 -76165 9.76264 .76362 -76461 -76559 -76657 9.76755 -76852 -76949 -77046 -77143 464 465 0.5921 +5934 -5947 -5961 -5974 0.5987 .6000 .6013 .6026 .6040 0.6053 .6066 .6079 .6092 -6105 0.6118 .6132 -6145 .6158 {617 0.6184 .6197 .6210 .6224 .6237 0.6250 .6263 .627 .6289 .6303 0.6316 .6329 .6342 -6355 .6368 0.6382 -6395 .6408 -6421 6434 0.6447 .6461 -6474 .6487 .6500 0.6513 .6526 .6540 -6553 .6566 226 h Logh=—— : 760 ea 60 6— Barometric pressure in mm.; e=— Vapor pressure in mm. —Io |] mm. 9.81816 || 550 9.85955 9.89734 .81902 551 ‘ .86034 .89806 .81989 552 Sie .S6112 .89878 .82075 553 : .S6191 .89950 .82162 554 qe .86270 .90022 9.82248 555 7.30: 9.86348 9.90094. -82334 556 : .86426 -90166 .82419 557 : .86504 -90238 | .82505 || 558 SHE. .86582 -90309 .82590 559 -7355 .86660 -90380 9.82676 560 ; 9.86737 9.90452 .82761 561 wie .S6815 .90523 .82846 562 aya .86892 -90594 .82930 || 563 fe .56969 -90665 .83015 || 564 : .87046 -90735 9.83099 565 : 9.87123 9.90806 .83184 566 -7447 .87200 -90877 .83268 567 72 SO 27i7) -90947 .83352 568 : .87353 -QIOI7 | .83435 569 -748 .87430 -91088 | 9.83519 570 : 9.87506 9.91158 .83602 571 : .87582 . -91228 .83686 572 ‘ .87658 ; -91298 .83769 573 . 87734 . -91367 .83852 574 : .87810 : -91437 9.83934 575 : 9.87885 : 9.91507 .84017 576 ; .87961 : -91576 .84100 577 ; .88036 : -91645 .84182 || 578 : .S8III : -91715 .84264 579 : 3 .88186 ; -91784 9.84346 580 763 9.88261 : 9.91853 .84428 581 7645 .88336 : .91922 .84510 582 765 .S8411 2 -91990 .84591 583 a7 .88486 | ‘ .92059 .84673 FOAM .88 : .92128 9.84754 585 -76¢ .88634 | : 9.92196 -84835 586 : .88708 | : -92264 .84916. || 587 eT .8878 37 : -92332 .84997 588 ; .888 5 . .92401 .85078 || 589 . : i 92469 9.85158 || 590 776% : . 9-92537 85238 || 591 ; 8 : .92604 5 Hl ©6592 -778 -S9I5I | : .92672 593 -7903 . : .92740 594 78 8 | : .92807 595 -782 .8937 : 9.92875 596 785 : : -92942 597 -7°595 “o : -93009 598 ; } : 8: -93076 -93143 SMITHSONIAN TABLES. TABLE 86. DENSITY OF AIR AT DIFFERENT HUMIDITIES AND PRESSURES. METRIC MEASURES. 6 — Barometric pressure in mm.; h Values of 760° mm. 650 “I ¢ to 679 680 681 682 683 684 685 686 687 688 689 690 691 | 692 693 | 694 695 | 696 | 697 698 | 699 oO. h es 8553 .8566 ° -8579 .8592 .8605 8618 .8632 .8645 .8658 .8671 .8684 .8697 .8711 .8724 -8737 .8750 .8763 .8776 .8790 .8803 oO. 8816 .8829 .8842 .8855 .8569 ° 8882 .8595 .8908 .8921 -5934 .8947 .5960 .8974 .8987 .gOOO .9013 .9026 -9039 .9053 : g066 .9079 -9O92 .9105 .G118 -9132 -9145 -9158 -9I7I -9184 -9197 SMITHSONIAN TABLES, 9.93210 -93277 -93341 -93410 -93476 9.93543 .93609 -93675 -93741 -93807 9.93873 93939 94004 -94070 94135 9.94201 .94266 -94331 94396 -94461 9.94526 94591 .94556 -94720 94785 9.94549 “94913 -94978 -95042 .95106 9.95170 -95233 -95297 -95361 95424 9.95458 -95551 .95614 95977 -95740 9.95804 -95866 -95929 -95992 .96054 9.96117 .96180 .96242 96304 .96366 re bas x" | 7 |; 0.9211 9224 9237 +9250 .9263 0.9276 .9289 +9303 -9316 -9329 0.9342 -9355 .9368 .9382 9395, 0.9408 -9421 -9434 -9447 -9461 0.9474 -9487 -9500 9513 .9526 0.9539 -9553 .9566 -9579 +9592 0.9605 .9618 .9632 9645 .9658 0.9671 .9684 -9697 -Q71I .9724 0.9737 +9759 -9763 -9776 .9789 0.9803 9516 .9829 .9542 -9955 228 8 3. e — Vapor pressure in mm. 9.96738 -96799 .96360 .96922 .96983 9.97044 -97 106 97167 .97228 .97288 9-97349 -97410 -97470 .97531 .97592 9.97652 -97712 -97772 -97832 .97892 9-97952 .98012 .98072 .98132 .9SIGI 9.98250 .98310 .98370 .98429 .98488 9.98547 .98606 .98665 -98724 -98783 9.98842 .98900 -98959 .99018 .99076 9.99134 -99192 -9925I1 -99309 -99367 b—0.378e 760 nee 760 0.9868 -9882 -9895 -9908 .9921 0.9934 9947 -9961 9974 -9987 1.0000 -OOT3 .0026 .0039 +0053 .0066 .0079 .00G2 .O105 .O118 H HH .0132 .O145 .O158 .OI71 .O184 .O197 .O2TI .0224 .0237 -0250 4 coal .0263 .0276 .0289 .0303 .0316 4 +0329 .0342 +0355 .0368 .0382 -0395 .0408 .0421 -0434 -O447 .O461 .OA74 .0487 .0500 -0513 I H ie —-- A 760 — LO 9-99425 -99483 -99540 -99598 .99656 9-99713 -99771 .99828 .99886 -99943 0.00000 .00057 .OOIT4 -OO171 .00228 0.00285 .00342 .00398 -00455 .OO51I | 0.00568 .00624 .00680 .007 36 -00793 0.00849 .00905 .00961 .O1O17 .O1072 .O1128 -OT184 .O1239 -O1295 | -01350 | 0.01406 .O1461 -O1516 .OI571 .01626 O1681 .01736 -O1791 -O1846 -O19OI 0.01955 .O2010 .02064 -O2119 .02173 a Y O AVOIRDUPOIS POUNDS AND OUNCES I avoirdupois pound — 0.4535924 kilogramme. Pounds. kg. 0.0000 0.4536 0.9072 1.3608 1.8144 2.2680 2.7216 3-175! 3.6287 4.0823 “OO oI mwWNHH OS Oo I avoirdupois ounce 0.0454 0.4990 0.9525 1.4061 1.8597 2.3133 .7669 .2205 3-6741 4.1277 0.0028 .0312 -O595 .0579 ~rl62 0.1446 .1729 .2013 .2296 | .2580 0.2863 -3147 +3430 -3714 -3997 .4281 | kg. 0.0907 0.5443 | 0.9979 | T.4515 1.9051 2.3587 2.5123 3.2659 3-7195 4.1731 kg. 0.1361 0.5897 1.0433 1.4969 1.9504 2.4040 2.8576 BxsbL2 3.7648 4.2184 0.1814 0.6350 1.0886 1.5422 1.9958 2.4494 2.9030 3-3566 3.5102 4.2638 kg. O.O1T3 -0397 .0680 .0964 .1247 -1531 .1814 -2098 .2381 .2665 .2948 Bo2R2 *3515 -3799 .4082 .4366 0.2268 0.6804 1.1340 1.5876 2.0412 2.4948 2.9454 3.4019 3-8555 4.3091 SMTHSONIAN TABLES. 229 TABLE 87. INTO KILOGRAMMES. 0.0283495 kilogramme. I I 2 2 ° os oo ©» oe Oo kg. 0.2722 0.7257 -1793 .6329 .0865 .5401 2.9937 3-4473 3-9009 4.3545 | 0.0170 .0454 -0737 . 1021 .1304 0.1588 . 1871 2155 -2438 52722. 2.5855 3-0391 3-4927 3.9463 4.3998 kg. 0.3629 0.8165 1.2691 7237, PWG 9 2.6308 3.0844 3.5300 | 3-9916 4.4452 kg. 0.4082 0.8618 | 1.3154 1.7690 2.2226 2.6762 | 3.1298 | 3-5834 4.0370 4.4906 TABLE 88. KILOGRAMMES INTO AVOIRDUPOIS POUNDS AND OUNCES. 1 kilogramme = 2.204622 avoirdupois pounds. Kilo- grammes. 0.0 | Av. lbs. 0.000 2.205 4.409 6.614 8.818 11.023 13.228 15.432 17.637 19.842 0 I 2 3 4 5 6 7 8 9 TABLE 89. 0.1 Av. lbs. 0.220 2.425 4.630 6.834 9-039 11.244 13.448 15.653 17.857 20.062 Oz. 02 | 03 | Av. lbs. 0.441 2.646 4.850 7-055 9-259 11.464 13.669 15.873 18.078 20.283 | Av. Ibs. 0.661 2.866 5.071 7-275 9.480 11.684 13.889 16.094. 18.298 20.503 kg. oO. Av. Ibs. 0.882 3.086 5.291 7-496 9.700 11.905 14.110 16.314 18.519 20.723 Tenths of a Kilogramme into Ounces. Oz. 21.1644 24.6918 28.2192 31.7466 35-2740 kg. lav. Ibs. . | Av. Ibs. 1.543 3-748 5-952 8.157 10.362 12.566 14.771 16.976 19.180 21.3985 Hundredths of a Kilogramme into Decimals of a Pound and Ounces. 0.022 = 0. .044 = 0. Oz. 35 71 .066 = 1.06 .088 = 1.41 -II0 = I. GRAINS INTO GRAMMES. I grain —0,06479892 gramme. 76 O:132)—= 2512 +154 = 2.47 176 = 2.82 198 = 3.17 -220 = 3.53 gram's. 0.0000 0.6489 1.2960 1.9440 2.5920 32399 3.8879 4.5359 5.1839 5.8319 Grain. O.1 gram’s. 0.0648 0.7128 1.3608 2.0088 2.6568 3-3047 3-9527 4.6007 5.2487 5.8967 gram’s. 0.1296 0.7776 1.4256 2.0736 2.7216 3.3695 4.0175 4.6655 5.3135 5.9615 gram’s. 0.1944 0.8424 1.4904 2.1384 2.7864 3-4343 4.0823 4.7393 5-3783 6.0263 Tenths of a Grain. gramme, 0.0065 .0130 -O194 -0259 -0324 I Gr gram’s. 0.2592 0.9072 1.5552 2.2032 2.8512 3-4991 4.1471 4.7951 59-4431 6.0911 ain. gramme. 0.6 7 8 9 Re) 0.0389 +0454 .0518 -0583 -0648 gram’s. 0.3240 0.9720 1.6200 2.2680 2.9160 3-5639 4.2119 4.8599 5.5079 6.1559 Grain, 0,01 .02 .03 -04 .05 gram’s. 0.3888 1.0368 1.6848 2.3328 2.9808 3.6287 4.2767 4.9247 5-5727 6.2207 gram’s, 0.4536 I. 1016 1.7496 2.3976 3.0456 3.6935 4.3415 4.9895 5.6375 6.2855 gram’s. | gram's, 0.5184 | 0.5832 1.1664 | 1.2312 |} | 1.8144 | 1.8792 |f 2.4624 | 2.5272 || 3.1103 | 3.1751 3-7583 | 3-8231 4.4063 | 4.4711 || 5.0543 | 5-119T |f 5.7023 | 5.7671 || 6.3503 | 6.4151 Hundredths of a Grain. gramme. Grain, 0.0006 .0013 .0019 -0026 -0032 0.06 -07 -08 .09 .10 SMITHSONIAN TABLES, 230 gramme. 0.0039 .0045 -0052 .0058 .0065 . GRAMMES INTO GRAINS. PRBke 30: I gramme = 15.43235!1 grains. Grammes.} : a ee ; | i, ; a Or | a ee Grains. | Grains. | Grains. | Grains. | Grains. Grains. | Grains. | Grains, | Graims. 0.00 1.54} 3-09] 4.63 6.17 9.26} 10.80] 12.35] 13.89 15.43] 16.98] 18.52! 20.06] 21.61 24.69 || 26.24'| 27:78 | 29:32 30.86 | 32.41} 33. eee 35-49 | 37-04 40.12} 41.67] 43.21] 44.75 50.93 | 52.47 55-56| 57-10] 58.64] 60.19 66.36 | 67.90 79.99 | 72.53| 74.08] 75.62 81.79 | 83.33 86.42 | 87.96] 89.51] 91.05 97.22] 98.77 TOI.85 | 103.40 | 104.94 | 106.48 112.66 | 114.20 117.29 | 118.83 | 120.37 | 121.92 128.09 | 129.63 132272) T24.26) "035. o0"Mmerea5 143.52 | 145.06 148.15 | 149.69 | 151.24 | 152.78 46.30} 47.84] 49.38 61.73 | 63.27| 64.82 77.16} 78.71 | 80.25 92.59} 94.14] 95.68 108.03 | 109.57 | III.11I 123.46 | 125.00 | 126.55 138.89 | 140.43 | 141.98 OMIDGTARWNHO 9 4 . | Grains, | Grains. | Grains. | Grains, 92.59 | 108.03 | 123.46] 138.89 246.92 | 262.35 | 277.78] 293.21 401.24] 416.67] 432.11] 447.54 555-50| 571.00] 586.43 | 601.56 799.89 | 725-32| 740.75| 756.19 864.21 | 879.64} 895.08 | 910.51 1018.54 |1033.97 |1049.40 |1064.83 1172.86 |1188.29 |1203.72 |1219.16 1327.18 |1342.62 |1358.05 |1373.48 1481.51 |1496.94 |1512.37 |1527.80 Grains. | Grains, | Grains. | Grains. | Grains. 0.00] 15.43] 30.86] 46.30} 61.73 154.32] 169.76] 185.19] 200.62] 216.05 308.65 | 324.08 | 339-51 | 354-94] 370.38 462.97 | 478.40] 493.84 509.27 | 524.70 617.29| 632.73] 648.16| 663.59| 679.02 771.62} 787.05 | 802.48} 817.91 025.94] 941.37 | 956.81 | 972.24 . 1080.26 |1095.70 |III1.13 |1126.56 |1I4I.99 1234.59 |1250.02 |1265.45 |1280.89 |1296.32 1388.91 |1404.34 |I419.78 gramme. rain. gramme.| Grain. gramme. Grain. gramme.| Grain. 0.154 y 0.926 0.001 0.015 0.006 0.093 -309 : 1.080 .002 -031 .007 -108 -463 : 1.235 -003 -046 .008 23 -617 z 1.389 -004 .062 -009 «139 1.543 -005 -077 -O10 -154 TABLE 91. CONVERSION OF UNITS OF MAGNETIC !NTENSITY. | English Units. Dynes. 7 English Units. }| 2.168 82 4.337 64 6.506 46 8.675 28 oO = COON ADAT hob = 0.046 108 .092 216 138 324 184 432 0.230 540 .276 648 .322 756 368 864 -414 972 10.844 10 13.012 92 15.181 74 17.350 56 19.519 38 | 2 5 4 5 6 7 8 g The English unit of magnetic intensity is the force which acting for 1 second on a unit of magnetism, associated with a mass of 1 grain, produces a velocity of 1 foot per second. The C. G. S. unit of magnetic intensity is the dyze—the force which, acting on one gramme for one second, generates a velocity of 1 centimetre per second, The dimensions of magnetic intensity are [ot ea] 23% TABLE 92. QUANTITY OF RAINFALL CORRESPONDING TO GIVEN DEPTHS. i inch of rainfall = 22624.0417 imperial gallons per acre. = 226613.713 lbs. per acre. 1 inch of rainfall = 113.3068 tons per acre. 2516.3878 tons per sq. mile, Depth | imperial Tons | Depth | imperial Tons | Depth Imperial Tons of |Gallons| persquare || 0 allons| per square | of allons per equare Rainfall.) per acre. ile. | Rainfall. per acre. Mile. | Rainfall.) per acre. Mile. Inches. | Inches Inches. 0.00 —— | 0.20 | 4524.80) 14503.27 || 0.40 9049.61) 29006.55 OI 226.24 725.16 | .21 | 4751.04) 15228.44 | .41 | 9275-85| 2973-71 02 452.48] 1450.32 || .22 | 4977-28] 15953.60 || .42 9502.09} 30456.88 03 | 678.72] 2175.49 || +23 | 5203.52] 16678.76 | .43 9728.33] 31182.04 -04 | 904.96) 2900.65 | +24 | 5429-77) 17403-93 | +44 9954-57| 31907.21 0.05 | 1131.20] 3625.81 || 0.25 | 5656.01] 18129.09 || 0.45 | 10180.81| 32632.3 -06 | 1357-44] 4350.98 | 2 5882.25) 18854.26 -46 10407.05| 33357-53 07 | 1583.68) 5076.14 || .27 | 6108.49) 19579.42 47 10633-29| 34082.70 -08 | 1809.92] 5801.31 | 28 | 6334.73] 20304.58 -48 10859.53| 34807.86 .09 | 2036.16] 6526.47 | 2 6560.97| 21029.75 || -.49 LOSS G7) se 55Ss.Os 0.10 | 2262.40} 7251.63 || 0.30 | 6787.21] 21754.91 || 0.50 | 11312.02] 36258.19 -Ir | 2488.64] 7976.80 | 31 | 7013-45] 22480.08 -60 13574-42] 43509.83 -12 | 2714.88] 8701.96 2 | 7239.69] 23205.24 -70 15836.82] 50761.47 +12) | 2941.02 9427.03 33 | 7465-93] 23930.40 .80 18099.23] 58013.11 14° "| 3167.36) TO152)29 -34 | 7692.17) 24655.57 -gO 20361.63} 65264 74 0.15 | 3393-60) 10877.45 | 0.35 | 7918.41) 25380.73 | 1.00 | 22624.04| 72516.38 -16 | 3619.84| 11602.62 -36 | 8144.65} 26105.89 || 2.00 45248.08] 145032.7 -17 | 3846.08] 12327.78 | 37 | 8370.89! 26831.06 | 3.00 | 67872.12] 217549.16 -18 | 4072.32] 13052.94 38 | 8597.13] 27556.22 || 4.00 g0496.16) 290065 .55 -Ig | 4298.56] 13778.11 39 | 8823.37] 28281.39 I} 5.CO | 113120.20) 362581.93 0.20 | 4524.80] 14503.27 || 0.40 | 9049.61) 29006.55 || 6.00 | 135744.24| 435098. 32 TABLE 93. Feb. Mar. Mar. San. Feb. I Zo 6 II 16 21 to 26 Biel ev: o IO 20 25 Mar. 15 fo | No. No. No. |_of Epoch of the of Epoch of the of | Pen- ear, Pen- Year. en- tade. itade tade IO || 20 6 10 Hi] 38 15 jl] 21 II 15 | 39 20 || 22 16 20 |j| 40 25/23} Apr.21 to 25 | 41 30 II] 22 26 30 |i 42 4 i] 25 | Way 1 5 43 9 || 26 6 10 Hi] 44 14 |) 27 1 15 jh 45 May t6to 20} 46 24 Ill 29 21 25 |ll 47 I || 30 26 30 || 48 6 Il 31 31 June 4\\\ 49 TI 32 | June 5 9 || 50 16 |) 33 | Juze 10 to 14 jj 51 21 Hl 32 15 19 |] 52 26 Ill 35 20 24 11 53 31 il} 36 25 29 Ill 54 232 5} 19 | Apr. 1 fo 5 || 37 PENTADES Epoch of the Year. Sune 30 to July July § IO 15 14 9 14 19 July 20 to 24 25 29 30 Aug. 3 Aug.- 4 8 5 13 Aug.14 to 18 19 23 24 28 29 Séepi: 2 Sept. 3 7 Sept. 8 to 12 13 17 18 22 23 27 *In the bissextile year the 12th pentade contains six days. No. of Pen- 55 |.Sept. 28 to Oct. 2 || Epoch of the 56 | Oct. 59 | Oct. 62 |Nov. 64 | Nov. 68 | Dec. Year. 8 13 18 fo 23 28 Nov 2 12 fo 16 17 21 22 26 D7 DEC aN 2 6 a II 12 16 17 21 22 26 27 an ae 7 12 17 22 27 ; TABLE 94, DIVISION BY 28 OF NUMBERS FROM 28 TO 867972. 300 400| 500 | 600 700 800 > 196 wou OOS wOsioVes 197 SOs OVO DIO HO OUIO BIO KIOD | 105 106 | 3 | 246 107 : 247 108 ie 248 | | 81 | Tog | 249 | 82 TIO | 8§ | 250 | | Peose|. 105 || 136 7 223 251 | 279 00° “200, 300 | 800 | 900 Retasaciaars 233 | SMITHSONIAN TABLES. — TABLE 95. 0 | 100 Oo 29 I 30 Z 3l 3| 32 33 5 | 34 6} 35 77130 8 | 37 9} 38 10 | 39 II 40 12 4I 13 42 14 43, | 0 | 100 15 | 44, 16 | 45 17 46 18 | 47 19} 48 20} 49 21 50 22 51 23 52 24| 53 25 | 54 26 | 55 | 27 | 56 0 | 100) SMITHSONIAN TABLES. DIVISION BY 29 OF NUMBERS FROM 29 TO 898971. 200 | 300 58 | 87 59 | 88 60 | 89g 61 | go 62 | 9gI 63 | 92 64 | 93 65 | 94 66 | 95 67 | 96 68 | 97 69 | 98 79 | 99 71 | 100 72 | Iol 200 | 300 73, | 102 74 | 103 75 | 104 76 | 105 77 | 106 78 | 107 79 | 108 80 | 10g SI | I10 82 | III 83 | 112 84 | 113 85 lrg 200 300 500 145 146 147 148 149 165 166 167 168 169 184 185 186 700 217 242 243 244 245 900 261 600 | 700 | 800 | 900 199 200 201 202 600 218 231 700 | 800 260 234 286 287 288 289 900 QO. _ 4 00 00 16 04 03 07 1g | 06 14 22 18 09 21 25 25 12 28 28 32 I5 35 02 38 42 05 45 21 49 08 52 56 er 59 27 63 14 66 OL 69 17 73 04 76 80 07 83 23 87 IO 90 26 94 13 97 29 ol 45 05 32 08 48 12 35 15 51 19 22 54 26 4I 29 57 33 44 36 si 39 47 43 46 50 50 37 53 53 57 4o 60 56 64 43 67 30 70 46 74 33 77 49 sl 36 84 52 88 39 91 55 95 42 98 87 03 go 10 93 17 96 24 99 3l 89 41 435 406 | a7 TABLE 96. DIVISION BY 31 OF NUMBERS FROM 31 TO 960969. 100 | 200 | 300 500 600 | 700 800 900 62 | 93 186 | 217 | 248 63 | 94 187 3 | 249 64] 95 188 250 65 | 96 189 66 | 97 67 | 98 68 | 99 69 | 100 79 80 SI 82 83 145 84 146 85 147 86 148 87 3 | 149 | 180 88 150 | I81 89 151 | 182 go 152 | 183 OVO UIO VIO LIOY ODIO TO UIOY OO BIO MOYO NOK OU OHO UO HO! — ~ | BO! gI 153 | 184 92 154 | 185 200 | 300 | 400| 500 SMITHSONIAN TABLES. TABLE 97. _—)———————qu“ce i 0° | .0000 00 I .O174 52| 2 -0349 O | 3 +0523 4 4 .0697 6 5 .0871 6 6 -1045 3 7 .1218 7 8 .1392 9 .1564 10 .1736 II .1908 eae .2079 13 .2250 14 .2419 15 -2588 16 .2756 17 .2924 18 - 3090 19 .3256 20 -3420 21 .3584 22 -3746 23 -3997 24 .4067 25 .4226 26 -4384 27 -4540 25 .4695 29 -4848 30 .5000 31 .5 150 32 -5299 I 33 -5446 ly 34 | -5592 | | 35 | .5736 k 3 .5878 37 .6018 38 .6157 39 | -6293 40 -6428 | 41 F501 al 42 | .6691 43 .6820 | 44 6947 | 45 7071 | 60’ | NATURAL SINES AND COSINES. Natural Sines. 10’ .09OO 5 .1074 2 .12476 .1421 -1593 .1765 -1937 .2108 .2278 - 2447 .2616 .2784 .2952 .3118 3283 3448 3611 25752 "9/19 -3934 -4094 +4253 -4410 .4566 -4720 -4574 -5025 »5175 -5324 -5471 -5616 .5760 -5901 6041 6180 .6316 .6450 .6583 6713 6841 .6967 - 7092 .0029 09} .0058 .0203 6 .0375 I -0552 4 .0726 6 20’ 30’ 18} .0087 27 .02327 | .02618 .0407 I .0436 2 .0581 4 | .06105 .07556] .07846 09295 | .0958 5 = LLOSA || ees 20 -£276)4)) |). 120583 -1449 .1478 . 1622 1650 .1794 .1822 -1965 1994 2136 2164 -2306 33 .2476 2504 .2644 .2672 | .2812 2840 -2979 - 3007 -3145 -3173 -3311 -3338 -3475 -3502 3638 3665 . 3800 3827 -3961 3987 -4120 4147 -4279 -4395 | .4436 -4462 | .4592 .4617 -4746 4772 -4899 -4924 -5050 | -5075 5200 | .5225 -5345 5373 +5495 5519 .5640 5664 -5783 -5807 -5925 -5948 .6065 .6088 .6202 .6225 .6338 .6361 .6472 6494 .6604 .6626 | 6734) 36756" | | .6862 .6884 | .6988 | .7009 | .7112 | .7133 L aor 40’ .O116 35 .0290 8 -0465 3 -0639 5 .0813 6 .0987 4 . 11609 -1334 .1507 .1679 -1851 .2022 .2193 2363 -2582 .2700 .2868 »3035 .3201 3365 3529 -3692 -3854 .4014 -4173 -4331 .4488 4643 -4797 -4950 -5100 -5250 5398 5544 -5688 5931 »5972 6ITI .6248 .6383 .6517 .6648 6777 -6905 - 7030 -7153 20’ | 30’ -0319 9 +0494 3 .0668 5 .0842 6 .1016 4 .1189 8 .1363 .1536 .1708 . 1880 .205[ 2221 2391 .2560 .2728 .2896 3062 3228 -3393 -3557 -3719 -3881 -4041 .4200 -4358 .4514 .4669 .4823 -4975 SSS -5275 .5422 -5508 25702 -5854 -5995 .6134 .6271 .6406 6539 .6670 -0799 .6926 -7050 -7173 Proportional arts. 29 | 28 2.9} 2.8 5.8] 5.6 8.7| 8.4 11.6 | 11.2 14.0 17.4 | 16.8 20.3 | 19.6 23.2 | 22.4 26.1 | 25.2 OMIA PWNHH AD | > un BI AMNABWNH ~ ow n _ ow ° 0 Ss = ow to w p CON ANRWNHH ~ H nN n b NS ° © N dN ¢ Ears to m Oa WO WI AMNAPWNHH ~ ~ ur ONUNWwWH OAL WN AAFP NO WAL HD OV I He RH 2ielme0 ||" 2:0 2] 4.0 3] 6.0 4| 8.0 10.0 12.6 | 12.0 14.7 | 14.0 16.8 | 16.0 18.9 | 18.0 WO OI AMNHWNHH ~ i) ° On Natural Cosines. 236 NATURAL SINES AND COSINES. Natural Sines. 0’ 10’ 20’ 30’ 40’ 507 7071 .7092 72 Ay fick) -7153 a7 7193 +7214 +7234 -7254 +7274 -7294 7314 -7333 -7353 -7373 -7392 7412 7431 -7451 -7479 -7499 -7509 +7528 7547 -7566 +7585 -7604 -7623 .7642 -7660 7679 -7698 -7716 -7735 7753 TAL 7799 .7808 -7826 -7844 -7862 .7880 7898 -7916 -7934 -7951 -7969 -7986 8004 .8021 .8039 .8056 .8073 .Sogo S107 .S124 .SI4I .8158 .8175 S1g2 8208 .8225 S241 .8258 .8274 8290 -8307 .8323 .8339 -8355 .8371 8387 8403 .8418 .8434 .8450 .8465 .8480 $496 .S5II .5526 .8542 .8557 8572 | .8587 .S601 .S616 .8631 .8646 .S660 | .8675 .8689 8704 .8718 .8732 .8746 | .8760 .8774 8788 .8802 .8816 .8829 .8543 .8857 8870 .8854 ,8897 .Sg1O .8923 .5936 .8949 .8962 .8975 .8988 goo .9O13 .9026 .9038 .9051 .9063 9075 .9088 gI0o -Q1I2 | .9124 .9135 -9147 -9159 gI7I .9182 .9194 -9205 -9216 .9228 9239 .9250 .9261 -9272 9283 -9293 9304 +9315 +9325 -9336 9346 -9356 9367 -9377 -9387 -9397 -9407 -9417 +9426 -9436 -9446 9455 9465 -9474 9453 9492 9502 -9511 9520 -9528 -9537 -9546 -9555 -9563 9572 -9580 .9588 -9596 -9605 -9613 .9621 -9628 .9636 .9644 | .9652 .9659 | .9667 .9674 .g681 .9689 .9696 -9703 | -9710 -9717 -9724 -9730 9737 ‘9744 | -9750 -9757 9763 9769 :9775 9781 | .9787 9793 | -9799 -9805 -QSTI 9816 | .9822 .9827 .9833 .9838 .9543 .9848 | 9553 .9858 .9863 .9868 .9872 -9877 9881 .9886 .9890 .9894 | .9899 -9903 .9907 .gQII -9914 .9918 | .9922 -9925 -9929 +9932 -9936 -9939 -9942 -9945 9948 -9951 -9954 -9957 | -9959 .9962 | .9964 | .9967 | .9969 | .9971 | -9974 -9976 -9978 -9980 -9931 -9983 | -9995 .9986 9985 .9989 .9990 | .9992 -9993 9994 | -9995 | -9996 | .9997 | -9997 -9998 -9998 | .9999 | -9999 1.0000 1.0000 I 0000 | | 50’ | 40’ | 30 20/ 10’ SMITHSONIAN TABLES. Natural Cosines. 237 Angle. 44° 43 42 41 4o 39 38 36 30 34 33 32 30 29 28 NN bw wm an! N Nw NHN N Oo on ani NW TABLE 97. Proportional arts. 21 19 1) ee, ai Ae | 3:5 2 6:30) 527 4| 8.4] 7.6 5} 10.5] 9-5 6| 12.6] 11.4 7 | 14.7 | 13.3 8 | 16.8 | 15.2 g | 18.9] 17.1 PAS aloe | Tall Mies) okey 2| 3-6] 34 3] 5-4] 5-1 4: | °7-2:]) 16:8 5} 9.0] 8.5 6 | 10.8 | 10.2 7 | 12.6 11.9 8 | 14.4 | 13.6 9 | 16.2} 15.3 e ‘| 16 ; 15 1] 1.6] 1.5 PBN ic 1) 3/ 4.8] 4.5 4] 6.4} 6.0 5 | 8.0) 7.5 6 | g.6| 9.0 7|11.2|)105 8 | 12.8 | 12.0 9! 14.4} 13-5 r| 14 7 13 Te Ted etes 2} 2 8 | 2.6 3| 4:2) 3:9 4; 5-6] 5.2 5 | 7-0 | 6.5 6 | oe 7.8 7\| 9.8] 91 8 | 11.2] 10.4 9 | 12.6 | 11.7 r| 12 1 Deke |) bar 2|\\2.4 | 2.2 3} 3-6] 3.3 4} 4.5] 4.4 5| 6.0] 5.5 OV) 752) 16:6 7| 8.4| 7-7 8 9.6 8.8 9)108]}| 9.9 TABLE 98. NATURAL TANGENTS AND COTANGENTS. Natural Tangents. Ta aa el 10’ 20’ 30’ | 40’ | 50’ | Angle: Prop. Farts] ° .00291I} .00582| .00873 | .o1164] .01455]| . 89° .02036| .02328| .02619] .02910] .03201] . 88 .0378 3 | .04075| .04366]| .04658| .04949/] . 87 .05533| -.05824| .06116 | .06408] .06700| . 86 .07285| .07578]| .07870]| .08163] .08456 | .0874 85 hwnH OO | 0904 2| .09335| .09629] .09923] .10216| . 84 .10805| .11099| .11394| .11688)| .11983] . 83 .12574| .12869] .13165] .1346 1376 : 82 -1435 | -1465 -1495 1524 1554 .158 SI 1614 .1644 1673 .1703 1733 : 80 Peers Oo00MWM0 1793 1823 1853 .1883 -IQI4 -1974 .2004 .2035 .2065 -2095 .2156 | .2186 2217, .2247 .2278 2339 .2370 -2401 2432 -2462 2524 2555 .2586 .2617 .2648 i 69 G9 69 & me HOO 227 TT 2742 2773) .2805 .2836 .2899 2931 .2962 -2994 3026 3089 ||| .312u 3153 3185 Bony, 3281 3314 -3346 3378 3411 -3476 | .3508 -3541 +3574 .3607 2 bo Go WOWNNNA -3673 | 3706 -3739 -3772 -3805 .3872 | .3906 -3939 -3973 .4006 .4074 .4108 4142 4176 .4210 4279 | .4314 -4348 -4383 -4417 4487 | .4522 4557 -4592 .4628 OD 2 GO) G2 Oo 4699 | -4734 -4770 .4806 4841 -4913 | .4950 -4986 .5022 -5059 5132 5169 .5206 5243 .5280 5354 | -5392 .5430 5467 +5505 5581 | .5619 5658 5696 5735 DON AA aAnp Bw WO yo 5912 5951 : 5930 5969 .6048 6088 4 6168 .6208 .6289 | .6330 : .6412 6453 6536 | .6577 : .6661 .6703 .6787 .6830 : .6916 .6959 SERRY wWnr OW) WWW wh -7046 -7089 : JU77 7220 *7310 -7355 : -7445 -7499 7581 -7627 ‘ -7720 -7766 -7860 -7907 é .8002 .8050 3146 S195 : 5292 .8342 WWwWwWw Ww CN ang \O BREESE ON AUS 8441 | .8491 : .8591 .8642 8744 8796 : 8899 .8952 -9057 -Ql10 : -9217 -9271 9380 9435 : 9545 .9601 9713 | -9770 : 9854 9942 AANA SION WN O 40’ 10’ Natural Cotangents 238 NATURAL TANGENTS AND COTANGENTS. 0’ | 10’ 20’ 1.0000 | 1.0058] I.O117 1.0355 | 1.0416] 1.0477 1.0724] 1.0786] 1.0850 TLIO) ieuezn || 1.2237 1.1504| I.1571] 1.1640 1.1918} 1.1988] 1.2059 I.2349| 1.2423] 1.2497 1.2799 | 1.2876] 1.2954 Ge327O |aoss5L || 1.3432 1.3764 | 1.3848] 1.3934 1.4281 | 1.4370] 1.4460 1.4826] 1.4919] I.5013 1.5399} 1.5497) 1-5597 1.6003 | 1.6107] 1.6212 1.6643 | 1.6753| 1.6864 1.7321 | 1.7437] 1.7556 1.8040 | 1.8165] 1.8291 1.8807 | 1.8940] 1.9074 1.9626| 1.9768] I.9912 2.0503 | 2.0655! 2.0809 2.1445 | 2.1609] 2.1775 2.2460 | 2.2637| 2.2817 2.3559 | 2-3759|] 2-3945 2.4751 | 2.4960| 2.5172 2.6051 | 2.6279] 2.6511 2.7475 | 2.7725 | 2.7980 2.9042 | 2.9319] 2.9600 3-0777 | 3-1084| 3.1397 3.2709} 3.3052] 3.3402 3-4874 | 3.5261 | 3.5656 3.7321 | 3.7760| 3.8208 4.0108 | 4.0611 | 4.1126 4.3315 | 4.3897] 4.4494 4.7046 | 4.7729| 4.8430 5-1446| 5.2257] 5.3093 5-6713 | 5-7694| 5.8708 6.3138 | 6.4348 | 6.5606 7.1154) 7.2687| 7.4287 8.1443 | 8.3450] 8.5555 9.5144 9.7882 | 10.0780 II.4301 | 11.8262 | 12.2505 14.3007 | 14.9244 | 15.6048 19.0811 | 20.2056 | 21.4704 28.6363 | 31.2416 | 34.3678 57.2900 | 68.7501 | 85.9398 60’ 50/ 40’ Natural Tangents. 30’ 40’ 50’ 1.0176 1.0235 1.0295 1.0538 1.0599 1.0661 1.0913 1.0977 1.1041 1.1303 1.1369 1.1436 1.1708 1.1778 1.1847 I.2131 1.2203 1.2276 1.2572 1.2647 1.2722 1.3032 WernL 1.3190 1.3514 1.3597 1.3680 1.4019 1.4106 1.4193 1.4550] 1.4641] 1.4733 1.5108 1.5204 1.5301 1.5697| 1.5798} 1.5900 1.6319 1.6426 1.6534 1.6977 1.7090] 1.7205 1.7675 | 1.7796) 1.7917 1.8418 1.8546 1.8676 1.9210 1.9347 1.9486 2.0057 2.0204 2.0353 2.0965 2.1123 2.1283 2.1943 22012, 2.2286 2.2998 2.3183 2.3369 2.4142 2.4342 2.4545 2.5356 2.5605 2.5826 2.6746 2.6985 2.7228 2.8239 2.8502 2.8770 2.9887 3.0178 3.0475 3.1716 3.2041 3.2371 3-3759 3-4124 3-4495 3.6059 3.6470 3.6891 3.8667 3.9136 3.9617 4.1653] 4.2193] 4.2747 4.5107 4.5736 4.6382 4.9152| 4.9894} 5.0658 5-3955| 5-4845] 5.5764 5.9758 6.0844 6.1970 6.6912 6.8269 6.9682 7-5958| 7-7704| 7-9530 8.7769 | 9.0098] 9.2553 10.3854| 10.7119} I1.0594 12.7062 | 13.1969] 13.7267 16.3499 | 17.1693] 18.0750 22.9038 | 24.5418] 26.4316 38.1885 | 42.9641] 49.1039 114.5887 | 171.8854 | 343-7737 30’ 20’ 10’ SE 1.4826 1.5399 1.6003 1.6643 1.7321 1.8040 1.8807 1.9626 2.0503 2.1445 2.2460 2.3559 2.4751 2.6051 2.7475 14.3007 19.0811 28.6363 57-2900 co 0’ TABLE 98. Angle. Pies te CNSNONONEN OW AR HO co com AnNnwouhd = et FV OROXE SS One OH 8 ° 12.8 Or NW wm ani Oo QS = a o Natural Cotangents. 239 TABLE 99. LOGARITHMS OF NUMBERS. Nf 0. 4002 Ora) SAS) 6G are oe Prop. Parts. Overs. 0000 3010 4771 6021 | 6990 7782 8451 9031 9542 1 | 0000 0414 0792 1139 1461 | 1761 2041 2304 2553 2788 2 | 3010 3222 3424 3617 3802 | 3979 4150 4314 4472 4624 3 | 4771 4914 5051 5185 5315 | 5441 5563 5682 5798 5911 naa | ee eel te 4 | 6021 6128 6232 6335 6435 | 6532 6628 6721 6812 6902 2] 8,6] 8,4] 8,2] 8,0 5 | 6990 7076 7160 7243 7324 | 7404 7482 7559 7634 7709 3 a72 | 188 |36 | 1610 | 6 | 7782 7853 7924 7993 S062 | 5129 8195 8261 8325 8388 5 | 21,5 | 21,0 | 20,5 | 20,0 7 | 8451 8513 8573 8633 S692 | 8751 8808 8865 8921 8976 pte ae ne eae 8 | 9031 9085 9138 9I9I 9243 | 9294 9345 9395 9445 9494 8 | 34.4 | 33,6 | 32,8 | 32,0 9 | 9542 9590 9638 9685 9731 | 9777 9523 9868 9912 9956 9 | 38,7 | 37,8 | 36,9 | 36,0 10 | 0000 0043 0086 0128 O170 | 0212 0253 0294 0334 0374 | 41 11 | 0414 0453 0492 0531 0569 | 0607 0645 0682 0719 0755 | 38 12 | 0792 0828 0864 0899 0934 | 0969 1004 1038 1072 1106 | 35 39 | 38) 37) 36 13 | 1139 1173 1206 1239 1271 | 1303 1335 1367 1399 1430 | 32] 1] 3.9} 3:8) 37) 3:6 14 | 1461 1492 1523 1553 1584] 1614 1644 1673 1703 1732 | 30| 3]xf7| ata | aa | 1098 15 | 1761 1790 1818 1847 1875 | 1903 1931 1959 1987 2014 | 28] 4] 15,6| 15,2 | 14,8 | 14,4 16 | 2041 2068 2095 2122 2148 | 2175 2201 2227 2253 2279 | 26| 3 ae ae ase ae 17 | 2304 2330 2355 2380 2405 | 2430 2455 2480 2504 2529 | 25 | 7] 27,3| 26.6 | 25.9 | 25.2 18 | 2553 2577 2001 2625 2648 | 2672 2695 2718 2742 2765 | 24 8 | 31,2 | 304 | 29,6 | 28,8 19 | 2788 2810 2833 2856 2878 | 2900 2923 2945 2967 2989 | 22 9) 35,7 I) Soe Sosa 20 | 3010 3032 3054 3075 3096 | 3118 3139 3160 3181 3201 | 21 ar | 3222 3243 3263 3284 3304 | 3324 3345 3365 3385 3404 | 20 | 22 | 3424 3444 3464 3483 3502 | 3522 3541 3560 3579 3598 | 19 35 | 34] 33] 32 23 | 3617 3636 3655 3674 3692 | 3711 3729 3747 3766 3784 | 18 | 1| 35) 34) 3:3) 32 > > 5QnQ nQ nQ 2 - 2] 7,0] 6,8] 6,6] 6,4 24 | 3802 3820 3838 3856 3874 | 3892 3909 3927 3945 3962 | 18 | 3} 10,5} 10,2] 9,9] 96 25 | 3979 3997 4014 4031 4048 | 4065 4082 4099 4116 4133 | 17 | 4) M0) 13:6) 13,2 12,8 96 | 4150 4106 4183 4200 4216 | 4232 4249 4265 4281 4298 | 16] 3] 37° a oe ae 27 | 4314 4330 4346 4362 4378 | 4393 4409 4425 4440 4456 | 16 | 7) 245 23,8 | 2350 12238 | 28 | 4472 4487 4502 4518 4533 | 4548 4564 4579 4594 4609 | 15 | ara aoe lectr ieee | 29 | 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 | 15 : 30 | 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 | 14 | 31 | 4914 4928 4942 4955 4969 | 4983 4997 5011 5024 5038 | 14 | 32 | 5051 5065 5079 5092 5105 | 5119 5132 5145 5159 5172 | 13] , Ai elec p cs: | 33 | 5185 5198 5211 5224 5237 | 5250 5263 5276 5289 5302 | 13} 2| 62| d0 Ba Ec | 34 | 5315 5328 5340 5353 5366 | 5378 5391 5403 5416 5428 | 13 | 3) 9:3) 90 rie ee | 35 5441 5453 5465 5478 5490 | 5502 5514 5527 5539 5551 | 12] 5145's | 15,0| 14,5 | 14,0 | 36 | 5563 5575 5587 5599 5611 | 5623 5635 5647 5658 5670 | 12} 6) 186 | 18,0) 17,4 | 16,8 37 | 5682 5694 5705 5717 5729 | 5740 5752 5763 5775 5786 | 12} 8) 24'S | 24'0| 23.2 | 2ac4 38 | 5798 5809 5821 5832 5843 | 5855 5866 5877 5888 5899 | IT | 91 27,91 27,01 26,1 | 25,2 39 | 5911 5922 5933 5944 5955 | 5966 5977 5988 5999 G60I0 | II | 6021 6031 6042 6053 6064 | 6075 6085 6096 6107 6117 | II | 41 | 6128 6138 6149 6160 6170 | 6180 6191 6201 6212 6222 | Io 27 | 26) 25) 24 6232 6243 6253 6263 6274 | 6284 6294 6304 6314 6325 | Io] 1] 27| 2.6) 25 a4 335 6345 6355 6365 6375 | 6385 6395 6405 6415 6425 | 10} 3] st] F3| S'S] 712 | 6435 6444 6454 6464 6474 | 6484 6493 6503 6513 6522 | 10 | 4] 10,8} 10,4] 10,0| 9.6 | 6532 6542 6551 6561 6571 | 6580 6590 6599 6609 6618 | I0 ele ote ae ae | 6628 6637 6646 6656 6665 | 6675 6684 6693 6702 6712 | 9] 7| 18,9] 18,2] 17,5 | 16.8 6721 6730 6739 6749 6758 | 6767 6776 6785 6794 6803 | 9] 8|24’s| 23°4| 22's | 26 6812 6821 6830 6839 6848 | 6857 6866 6875 6884 6893 | 9 eh = 6902 6911 6920 6928 6937 | 6946 6955 6964 6972 6981 | 9 6990 6998 7007 7016 7024 | 7033 7042 7050 7059 7067 | 9 Ai On eed a ee ee 5 6° sr 8 49d: Prop. Parts. a AW See Pi Sloth SMITHEONIAN TABLES. 240 6990 6998 7007 7076 7084 7093 7160 7168 7177 7243 7251 7259 7324 7332 7340 7404 7412 7419 7482 7490 7497 7559 7566 7574 7634 7642 7649 7709 7716 7723 7782 7789 7796 7853 7860 7868 7924 7931 7938 7993 8000 8007 8062 8069 8075 8129 8136 8142 8195 8202 8209 8261 8267 8274 | 8325 8331 8338 8388 8395 8401 8457 8463 8519 8525 8579 8585 8639 8645 8698 8704 8756 8762 $814 8820 8871 8876 8927 8932 8982 8987 8451 8513 8573 8633 8692 8751 8808 8865 8921 8976 9036 9042 9090 9096 9143 9149 g196 9201 9248 9253 9299 9359 9400 9450 9499 9031 9085 9138 grgl 9243 9294 9345 9395 9445 9494 9355 9405 9455 9504 9304. 9309 LOGARITHMS OF NUMBERS. 7016 7024 7101 7185 7267 7348 7427 7505 7582 7657 7731 7803 7875 7945 Sor4 8082 S089 8149 8156 8215 8222 8280 8287 8344 8351 8407 8414 8470 8476 8531 8537 8591 8597 8651 8657 8710 8716 8768 8774 8825 8831 8882 8887 8938 8943 8993 8998 9047 9053 QIOI 9106 9154 9159 9206 9212 9258 9263 9315 9360 9365 9410 9415 9460 9465 9599 9513 7110 7193 7275 7356 7435 7513 7589 7664 7738 7810 7882 7952 $021 7933 7118 7202 7284 7364 7443 7520 7597 7672 7745 7818 7889 7959 8028 8096 8162 8228 8293 8357 $420 8482 8543 8603 8663 8722 8779 8837 7042 7126 7210 7292 7372 7451 7528 7604 7679 7825 7896 7966 8035 8102 $169 8235 8299 8363 8426 8488 8549 8609 8669 8727 8785 8842 8893 8899 8949 8954 9004. 9009 9058 9063 QII2 9117 9165 9170 9217 9222 9269 9274 9320 9325 9379 9375 9420 9425 9469 9474 9518 9523 9542 9547 9552 9557 9562 9566 9571 9600 9647 9694 9741 9786 9832 9877 9921 9965 0009 9590 9638 9655 9731 9777 9823 9868 ggi2 9956 0000 9595 9643 9689 9736 9782 9827 9872 9917 9961 0004 Oo 1 2 g605 9609 9652 9657 9699 9703 9745 9750 9791 9795 9836 9841 g881 9886 9926 9930 9969 9974 OOI3 OOI7 3 at 9614 9619 9661 9666 9708 9713 9754 9759 g800 9805 9845 9850 9890 9894 9934 9939 9978 9983 0022 0026 ey AS SMITHSONIAN TABLES. 7752 SerurS 7059 7067 7143 7152 7226 7235 7308 7316 7388 7396 7466 7474 7543 7551 7619 7627 7694 7701 7760 7767 7774 7832 7993 7973 8041 8109 8176 8241 8306 8370 8432 8494 8555 8615 8675 8733 791 7059 7135 7218 7300 7380 7459 7536 7612 7686 7839 7846 7910 7917 7980 7987 8048 8055 8116 8122 8182 8189 8248 8254 8312 8319 8376 8382 8439 8445 8500 8506 8561 8567 8621 8627 8681 8686 8739 8745 797 8802 8848 8854 8859 8904 8910 8915 8960 8965 8971 9015 9020 9025 9069 9074 9079 9122 9128 9133 9175 9180 9186 9227 9232 9238 9279 9284 9289 933° 9335 9340 9380 9385 9390 9439 9435 9440 9479 9484 9489 9528 9533 9538 9576 9581 9586 9624 9628 9633 9671 9675 9680 9717 9722 9727 9763 9768 9773 9809 9814 9818 9854 9859 9863 9899 9903 9908 9943 9948 9952 9987 9991 9996 0039 0035 9039 Cue Sins o2 cogspo cabico ani) oe pals SHH un unin la erreren nnn euler er DAN AAD ae o| DAANNN NNN | N TABLE 99. Prop. Parts. 10,0] 9, 12,0] 11,4 14,0/ 13,3 16,0|15,2 18,0] 17,1 17,6| 16,8 19,8/ 18,9 OW OI ANLPW DH & NF AWOO NF OC 10,2 ; II,9]1I,2| 10,5 13,6] 12,8} 12,0 1553)1454) 13,5 4 | 9,8 | 11,2 12,6 WO ON ANA WH meee AF YN OONNG —_ — 0009 HO arin © to “I 0 DUI AUD WH ST OUE S 0000 nos oo A OH WO OI ANA DH @ ° ES 0 DI ANHW NH 2 ° oo H oe ~ Nf AWO NE AO OAPPO HN HO & DO WE DHRT NANPRONDHO © OI ANLWNH 241 te Me Se a eg pay-A Ne Rt me ti 7 > te : . ; é : ” ; yor LIST OF METEOROLOGICAL STATIONS. Nortu AMERICA — Canscaeeeek, 2 a | eee nee Gan shy PAGE 244 Genthalesanernicas 2 >. Se wh ae pe GS 244 Gipceml aitcer es tes Gate 9 i Oe a ee: ota etc § 244 iN corel cn = OIG, - Pas A un tain oa alate nor Mae 244 Tet eCMRSEateS@mne Uiccecuea ls fie coc ures ee, oak, cad ok ee 245 Nilestaeiieliesmm © 6 cal fe. On eee oe 8 ge 244 SOmmEe Aw RICA Eh oy Slee Ae ee BIN oa a fey ssf) ME AGH 2A EuROPE — MGStcOrkMineary: 7) i tae, OM Sa Ge al ye ees AGHA Ses gE Me tinsel he “ety Vale tk ae A ae eh ee ger eco ge 248 EE ttSSleSt we Per tree BPS! Boake es yy eds Sep ue’ 248 cnet tne ee are oo | Pers eye Be a. as cle Raat it 249 irae meme ey bea hk Ra |e nies We Seer a erin res aye te 249 Sree ame a ah ee FA re Gorey SO My ta Girne or ae 250 Grececme ta See oles tent Mi Gey an, Jorp vot be 248 ERR Ner acl eats te Rk So A BRS WS itr, ary - Sina, oye Oe aes 248 ileal hy ae ee Pe ne nee oe ee on ae a 251 AN OTaUy Vac eRe eee fe Pte 25 aed: at, UE Sgaae ae, Pre ce 249 | EO GET ctl mer ater rte mee O RAs Ps 4 Sa Gel Picea. sm eh oe 253 PROUT ATI Aha ee et ee Ge a A ee a a 248 [RED SSE IGE, Glume ge RE Re le eas 251 ater ae eee MNRT gl cn Sees ep ee te wt he os. 253 See Crm Re CMR ne: Co | pois. iw) Pid osler uy 3s 249 Seite ee Eo ne i sk a: Sets. SS 25a Slecitixen Sea Wes te eens as ee A es are eet ay cent 248 PST AM Gs sted Slee eee ee eee de. My 2. Soh ude wn Pt) Se AGhEOhe UNS US TACUINGS ga eR") ER, De ae me SMT PAGE 256 IAPRICA AND NEIGHBORING ISLANDS. . . . .+=« . « > PAGE 256 INTERNATIONAL POLAR STATIONS. <3. ~. «9. s . i. . . PAGE 257 RUSCHEBANEOUS ISLANDS «) os.) 3° Gian 6. te Be, ees oe oe AGH 257 243 TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) NORTH AM ERICA. CANADA. Father Point ... “RT COChICEtOlaene) ae eee ee ni | *Halifax....... ANAT SStOM se) a ee MON trealiw san me Parry, Sound 2": Ona ppelley a... SOneDeC wpm =Saint Jonn. 2)... A SVGNCYi-a-aace wees ACOLONtOm yo encu *Winnepeg 3.94... | * Woodstock. .... CENTRAL AM | Godthaab ..... Pe vAketity esto cee | UU perniviky #3 so. “Westminster... . steer nev eeioee nome ERICA. (See MEXICO.) GREENLAND. MEXICO, CENTRAL AMERICA, WEST INDIES, £T7C. Guanajuato, Mexico Mazatlan, Mexico . Mexicol, chala se | *Nassau, Bahamas . New Castle, Jamaice Pabellon, Mexico . Leon, Mexico ..- . % Bermuda, West Indies....... “Habatia, Cuba cw es occ. Gece eee Kingston, West Indies....... ay os ots) "eee ee Rome Port aw. Prince, Haiti. (yaaa Puebla, Mexico . . St: Thomas, West Indies. =. ... Saltillo, Mexico. . San wis Potosi, Mexico...... San Salvador, Centr Santiago, Cuba . . | Tacubaya, Mexico. Vera Cruz, Mexico Zacatecas, Mexico SMITHGONIAN TABLES. al America. . Latitude. 48° 31/N. AO, 44 39 44 14 45 30 45 19 59 44 46 48 45 17 46 8 43 29 49 12 49 51 43 8 64 11 N. 61 12 72 47 32S ON: 2 iO 3 8 7 yO i Gi 22) a1 1g 26 25 «5 18 6 22a) 18 34 19m 52 18 20 2525 22) 820 13 44 TQ 55 Ig 24 ie) 307) 22 47 244 Longitude from Greenwich. 68° 28/ W. 66 38 63 36 76 29 (SeaS 80 oO 103 42 Zee tes) 66°73 60 I0 79 23 122) 453 Damen. 80 47 51 46 W. 48 II Sof 09 64 47 W. IOL 15 1OPTSS 76 48 IOI 41 106 25 99 8 77° (21 70) wA2 102 I2 7221 98 II 64 56 100 638 100 58 89 9 Td, 282 99 12 96 8 I0O 15 Height above Sea-level. Feet. m. 20 6 164 50 122 37 307 94 187 57 641 195 293 59 116 35 37 Il 350 107 33 IO 758 231 980 299 36 IT 16 5 39 I2 151 46 6759 2060 62 19 10 3 5899 1798 249 a 7487 2282 44 13 3800 1158 6312 1924 118 36 7119 2170 131 4o 5358 1633 6201 1890 2156 657 21 6 7621 2323 23 7 8189 2496 TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude Latitude. from Greenwich. Height above Sea-level. WEST INDIES. (See MEXICO.) Feet. UNITED STATES. * Abilene, Texas * Albany, New York * Alpena, Michigan * Atlanta, Georgia * Augusta, Georgia * Bismarck, North Dakota * Blue Hill, Massachusetts * Boston, Massachusetts * Buffalo, New York * Chicago, Illinois * Cincinnati, Ohio | *Cleveland, Ohio _* Columbus, Ohio | * Davenport, Iowa *Denver, Colorado _* Des Moines, Iowa | * Detroit, Michigan * Dodge City, Kansas _* Duluth, Minnesota _* Eastport, Maine * El Paso, Texas * Fort Assiniboine, Montana * Galveston, Texas ; * Hamilton, Mount, California... . feweelena- Montana; sie. ./2-3 5 2 : * Huron, South Dakota | * Indianapolis, Indiana | *Jacksonville, Florida * Kansas City, Missouri *Keeler, California. ......... | *Key West, Florida | * Knoxville, Tennessee | * Lynchburg, Virginia * Manistee, Michigan * Marquette, Michigan * Memphis, Tennessee | * Milwaukee, Wisconsin | * Moorhead, Minnesota * Nantucket, Massachusetts | * Nashville, Tennessee | * New Orleans, Louisiana | * New York City, (Weather Bureau) . | * New York, (Central Park) | * Norfolk, Virginia SMITHSONIAN TABLES. TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude i Latitude. ia Helghi abby : Greenwich. UNITED STATES. Feet. (Continued.) | *Olympia, Washington ; 44 * Omaha, Nebraska * Philadelphia, (Girard College) | * Philadelphia, (Weather Bureau) . * Pike’s Peak, Colorado * Pittsburg, Pennsylvania * Portland, Oregon * Rochester, New York * Roseburg, Oregon | *St. Louis, Missouri *St. Paul, Minnesota * Salt Lake City, Utah * San Diego, California | *San Francisco, California | * Santa Fé, New Mexico * Sault de Ste. Marie, Michigan . . . * Savannah, Georgia Sitka, Alaska * Spokane, Washington *Tampa, Florida * Toledo, Ohio Unalaska, Alaska * Vicksburg, Mississippi * Washington City, (Weather Bureau) * Washington City, (aval Obs’ v’y) . Washington, Mount, N. H * Wilmington, North Carolina... . *Yuma, Arizona ro qo ye SY) NT ES) “NO? ON_CO) CO NHN N OO DW WN H - SOUTH AMERICA. Bahia-Blanca, Argentine Republic . Bogota, United States of Columbia . 3uenos Ayres, Argentine Republic . Caldera, Chile Caracas, Venezuela Catamarca, Argentine Republic. . Cayenne, French Guiana Concordia, Argentine Republic. . Coquimbo, Chile Cordoba, Argentine Republic. ... Corrientes, Argentine Republic. . Georgetown, British Guiana . Iquique, Chile La Plata, Argentine Republic... SMITHSONIAN TABLES TABLE 100. LIST OF METECROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude Latitude. from Greenwich, Height above Sea-level. SOUTH AMERICA. (Continued.) Lima, Peru S. 7 Rai. Matanzas, Argentine Republic... 58 37 Montevidio, Uruguay 3 56 15 Natal, Brazil ud Paramaribo, Dutch Guiana : 55 22 Parana, Argentine Republic... . ‘ 60 16 Potosi, Bolivia 3 65 35 70 54 Quito, Equador 78 45 Rio de Janeiro, Brazil 43 10 Rioja, Argentine Republic 67 10 Santa Cruz de la Sierra, Bolivia . . 63 O Santiago, Chile 70 4I Sao Paulo, Brazil 46 40 Valdivia, Chile 73 16 Valparaiso, Chile E 712g Villa Formoza, Argentine Republic 58 6 EUROPE. AUSTRO-HUNGARY. * Agram, (Zégrab) * Barzdorf Bregenz Brinn | * Budapest PIOZerMOWILZ «ete a set eho ct coe. | *Fiume Gleichenberg Gorz Gries Krakow Kremsmaiinster Lemberg Lesina Lienz He on &® U1 or © on tS on Ownr od lO W | * Salzburg | | h Ee SMITHSONIAN TABLES. a TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) ¥ Longitude Hei Latitude. from eight above Greenwich. Sea-level. AUSTRO-HUNGARY. = (Continued.) Feet. mi. Sem aiene ta a ccsoay es 2 ee eee 47° 47/N. 13° 26’E. 5827 1776 Soniblickarmer sau inion i-arvar eins ATi ae I2 57 10154 3095 WeesIIeSt een aeule e Reree ee cece 45 39 13 46 85 26 % Wien ee ae ests rata tetteiatsiiefalaihnt i= eer ante 48 Tey 16 oii 663 202 Zagrab (see Agram) 2.2. =. «+: GREECE, ROUMANIA, TURKEY. SMITHSONIAN TABLES. 248 | Athens, Greece .....:...-- 37 58 N. 23, A5)) BD: | Bagdad, AsiaticTurkey.......- ey ads) 44 26 Betnitphurkeyy eon me cee we 33 54 35 28 112 34 *Bucarest, Roumania......... 44 25 26700 285 87 Constantinople, furkey 7. ea. = - AL 32 28 59 Samsoun, Asiatic Turkey ...... 41 18 36 19 26 8 Sinaia ROumaniauee- es met cle ASmi2i 25 34 2822 860 Sinope; Burke ya ta weet er 42 eT 35 19 49 15 | @SulinasRoumaniag tessa Ae 45 9 29 40 7 2 | Trebizond, Asiatic Turkéy ....:.-{ 41 I 39 45 92 28 | BELGIUM AND HOLLAND. | (ACI On mb el Sime we eee ee 49 40 N. 5 48 E. 1286 392 leebruxelles pBeloaurny pete ot mene: 50 51 4 22 177 54 Murnes, Below. tee ee ed 2 40 10 3 |'* Groningen,, Holland =~ 2x27." Bor 1s 6 34 49 15 ‘ pelder, Hollands y. 20. ayaa ere 52 57 4 45 oO oO AT Aeges Belgie fig ey team Means 50 37 od 200 61 Maeseyck, Beloim ~ 9.2 Gams: nO 5 48 115 35 Maestricht, Holland......... 50 51 5 4I 164 50 | *Ostende, Belgium. ..-.--....- 51 14 2 55 16 fF *Titrecht: tevolllamd' 7: ee eee eee i OnmeS en 43 13 BRITISH ISLES. tr Aberdeen::5-) Ps «tet eee 57 sto. N, 2 6 W. 88 oF Armagh Foose. US one 54 21 6 39 196 60 | *Ben’ Nevis 407.8 |< Gist ee ees 56 48 5 8 4406 1343 Dublin: ..u. eee oe eee Gey 2 Gr 2i 155 47 Dundee 6. 2-36 fect uence 56 28 2 56 160 49 | Edinburoch*\..83... s+ .2 00 beeen: 55 56 31 | almonth ..-..5 0.) +: 2 Avera veers 509 reed 183 56 iG lascOw co 3 loss. e Wms means 55 53 4 18 180 55 PACE! Ue lee rsa aeiee, oN ihsL 2) coe eM me 51 28 Oo 19 34 10 |) londonderry ... =... .- 1. 1955 5 0 7 AIG) 220 67 avai kree’ Castle ae rte fii ae 54 It 8 27 122 37 Wen@xtordra ke .., Sian Cusse act use eae 51 46 I 20 212 65 | *Richmond, (Greenwich Observat’y) | 51 29 Ono 159 48 | TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude | Latitude. from Greenwich. Height above Sca-level. BRITISH ISLES. : (Continued.) Feet. Southampton : 24/ W. 78 Southbourne 48 295 * Stonyhurst 28 375 | * Valencia 18 23 5 167 | DENMARK, NORWAY, SWEDEN. Bodo, Norway _ Carlshamn, Sweden | * Christiania, Norway Christiansund, Norway Dovre, Norway Fano, Denmark Floro, Norway Haparanda, Sweden Hernosand, Sweden Kjébenhavn, Denmark Skagen, Denmark Skudesues, Norway Stockholm, Sweden * Upsal, Sweden _*Vandrup, Denmark FRANCE. Bagnéres-de-Biggorre Besancon Bordeaux Oki Cherbourg Dunkerque mnnxHPt OM O wo ¢ Langres ° 466 299 75 Ig00 4I 340 NY WY NH DH WH WH Ww AG NI * Lyon * Marseille ieNont Ventoux. = = a). ses = = oe Nantes NS on GW CO * Paris, (Parc de Saint-Maur) .... * Paris, (Zour Ezffel) Paris, ((Zontsourts) * Perpignan * Pic-du-Midi Puy-de-Dome, (/lazne) * Puy-de-Dome, (Somme?) * Saint-Martin -de-Hinx * Toulouse oOo HW Se WH . Oo CO on Oo UMN OF NW NNNN NN H ow U1 ~ han nnd & Go SMITHSONIAN TABLES. TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Latitude. GERMANY. Bambero. Bavaria’ s-6)- 2 2 49° 54/N. Berlin sPrussia’ ean tess screen 52 Bont PriSsialeacgs ee eee ee 53) 35 Bremen & 2-5 S se gee ee eee 53. 51 Breslatt ee rissia) eee eae Teen Brom bere rUSSiale eee eee eee eye) es Chemnitz, Saxony eae 50 50 IBFnvAted IGN! 5/55 Socios a eed & 54 21 lpeeDresden Saxony ates nen aie len a2 | Bichberg,) Pruissiaye 2) ee 50 55 |. Breibero, Saxony 05 facie «coe 50 55 Friedrichshafen, Wurttemberg ...] 47 39 Gottingen, Prussia. 2 -(.-) -%.2.4- - Bie 632 alleserussiay eects awe ale 51 29 he Elam Urs). ci eo Pens) 2) ee ts Hai28 Heidelberg;;Badents)-)-9 6.) epee rene 49 25 | elirschibere, Bavaria, Gass) a 47 40 Hohenpeissenberg, Bavaria ..... 47 48 ee) Sta axO Tye nope presi aarmtee ston elite 50 56 | *Kaiserslautern, Bavaria ....... AQ 27 Karisruhie, Baden... 2-7... 49° I Kassel Prussialeanaiey eee eee eon 51 19 Pertti we ruSSlamn cy ieee eneme sient. 54 54 | Kael OP russia mn peacpees Pts. none ee 54 20 | Leipzig,Saxony............ 51 20 ('** Magdeburg, Prussia © 72. 4 2s 1: 52 8 | Mannheim, Baden ..... 20... 49 29 maVemeleserussiaues me cae cee) cate Bends | Metz, Woraine a. 284, ee eee net AQ 7 Mulhausen, Alsace .......... 47 45 | * Munchen Bavaria a. atc sens) 48 9 | * Neufahrwasser, Prussia. ....... 54 24 INutnbers, Bavariar oo. sb). oe 49 27 Regensburg, Bavaria......... 49 1 Rostock, Mecklenburg 3. 25. -0-- Pas Rugenwaldermtinde, Prussia... . 54 26 Schneekoppe; Prussia). 55 2). -/-- 50 44 Strassburg, Alsace she Seat ase caer 48 35 Stuttgart, Wurttemberg ....... 48 47 ASwinemunde,, ErtisStavs aus eee 53 56 Wendelstein, Bavaria......... 47 42 Wilhelmshaven, Oldenburg 53 32 Warzburce, Bavariay 7. es ees 49 48 | * Wustrow, Mecklenburg ....... 54 21 HOLLAND. (See BELGIUM.) SMITHSONIAN TABLES. Longitude from Greenwich. Io” 53’ E. ey 2) 6 40 8 48 17; a2 18 I2 55 18 4o 13 44 15 48 ey 9 28 9 56 ie 38 9 58 8 42 Te B42 ee Il 35 7 46 8 25 9 30 8 22 10 9g 1223 It) 38 8 28 Ta) 6 10 7 20 re 30 18 40 Gh 4! 12 6 2 nay 16, 23 15 44 7 45 g 10 14 16 [2a 8 9 9 56 12) 24) Height above Sea-level. Feet. m. 817 249 161 49 33 Io 13 4 482 147 138 42 1037 316 7D 22 390 11g T1145 349 1335 407 1335 407 492 150 364 III 85 26 394 120 4954 T510 3261 994 525 160 794 242 407 124 669 204 3 9 154 47 390 119 177 54 367 ToL 13 4 600 183 787 240 1736 529 13 4 1033 315 Ln75 358 72 22 13 4 5259 1603 472 144 879 268 3 10 5606 72 26 8 587 179 23 il TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude i Latitude. for iar i Greenwich. Feet. mi. Agnone 41° 48/N. TAw 227; 2644 806 Allessandria 44 54 838 322 _ 98 Bologna 44 30 Il 279 85 Catania, Sicily 371 5 14 55 102 Cosenza 16 840 Firenze eee 240 Genova d 8 55 Te Milano : 9 482 Modena g IO 210 Moncalieri 7 846 Napolitano 14 (e LS7, Palermo } 13 33 10 295 15 46 12 164 Siracusa 15 72 | * Torino 7 go2 Venezia d 12 69 Verona II 217 NORWAY. (See DENMARK.) PORTUGAL. (See SPAIN.) ROUMANIA. (See GREECE.) RUSSIA. Alexandrowka, Siberia Astrachan Baranowo Barnaul, Siberia . on On OV vO Oo nw Or 0 ¢ Bogoslowsk Brest-Litowsk IAT AES Rag) os PA wes) oo) eye 8 day SUSE Dorpat Elissawetgrad Enisseisk, Siberia | Eriwan | Gudaur | * Helsingfors, Finland | *Irkutsk, Siberia Kaluga Kargopol mona on ¢ = 1m OW bd Noo Troan n > ul y Oo NO oH N OO Gees OQ HH eH AO b ” SMITHSONIAN TABLES. bo on = TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude Latitude. from Greenwich. Height above Sea-level. RUSSIA. (Continued.) ° nnunn f& oOo nw Oo OV ty O92 2 me Oo O Oo OD Hw Oo Mm wn oO’ 4 Lugan Malyj-Usen Marchinskae, Siberia > nm n Oa oO to ° Pou Hw Ww Ww On Now Oo - Gee fa 2 We ~~ A won > eh & Oo 0 NW wna _ MO On a7 Oo on won oO Ow on An 4- ap Now fe OV ss mou to Oo fe ° £ on MO wv Omsk, Siberia Orenburg * Pawlowsk on on ~1 Oo ho ° eo Ht fm fe oo OO f= ° to ve) on ou - GO” to i Oo ° oO | Ow WN me Oo to OV Pjatigorsk + on DH Ov to ° OV Polibino to Oo on Rostow, a. Rykowskoe, Siberia © St. Petersburg ‘© Oo f= On Oo on to dm GO UO eH eA w ee HUI tv _ nur on AG GY sofijskij Priisk, Siberia olowezkij-Kloster Staro-Ssidorowa, Siberia 1 + ans YY on oo - ou em OV SMITHSONIAN TABLES ty on LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) RUSSIA. (Continued.) Tjumen, Siberia Tobolsk, Siberia Tomsk, Siberia Tunka, Siberia Uralsk Urjupinskaja Ust-Ssyssolsk Walaam, Finland Warschau Wernyj, Siberia Wilna Wjatka Wladikawkas. . Wologda Wyschnij-Wolotschek Barcelona, Spain Cadiz, Spain * Coimbra, Portugal | Gibralter | * Lisboa, Portugal Madrid, Spain Oporto, Portugal Oviedo, Spain : San Fernando, Spain Valencia, Spain SWEDEN. (See DENMARK.) SWITZERLAND. Altstatten Altdorf * Bern | Castasegna Chaumont Gabris Lugano Neuenburg Rigi-Kulm ..° * St. Bernhard SMITHSONIAN TABLES, SPAIN AND PORTUGAL, *Sierra da Estrella, Portugal .... Latitude. Longue rom Greenwich. aan cw won on OM 32. 14 58 33 13 22 oO 51 OF 2 53 18 4I 41 53 34 WwW & WwW oOo ex Ou Oo WwW bd no uw Oo CO un “I I mH OG x O-™ TABLE 100. Height above Sea-level. Feet. 272 171 305 2434 735 98 302 413 I41 390 2402 348 587 2244 387 545 69 TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) - Long tude Latitude. from Greenwich. Height above Sea-level. SWITZERLAND. (Comtinued.) Silos Weartar co-ed os ty a eee ee ZaTIChy 2 Ree aaron ee ee TURKEY. (See GREECE.) ACS ILAS. [Zhe Stations are in India unless otherwise indicated. For Stberian stations, see Russra.] AdensAtrabiay eae ions ae eee ANIC e Seeae ede ee en ee ee Nf on 2 \O Nv CO pe au On Bangalore Beleanim 3 piven oe oer agen Bellary.) tos sacs ean eee eae Benares 4) sole ch eee es oe ee Betham pores. s 24 47 67 4 49 15 PeLGAOLCree erty a akeccid aye series cy alas Ate reA: 74 20 702 214 HGS Keen emer Wr teae irs oof is) «: fol¥ei ey oko GeYie. « 24 TO 77 AZ 11503 3506 NICK O We atte er cre tay 2 Gc eks, eh ane a 26 50 Sito 369 112 IWR dT aS Mate se veterans) Srl, egh 1 4 80 14 22 7 Wraridallaygeepater | s/o eure cits ces 21 59 96 «(8 Wart ralOvempeees yttce series = I2 52 74 54 26 8 IRS eel Se 2 ce er 12 Si 98 38 96 29 IM (oo bas (Sybase ey Se, 2 16 29 97. 40 94 29 | IMI SSOOLGE RM ee Saisie fecessctemon se 2OmE2S 7 Omen 6881 2097 | WaASasaA KT ApAM ss srs sie so es 32 44 129 52 190 58 | NRO Uren bar sisi fe) am: eae res 215 G Siew 1025 312 | IN GTIe TROUT reese) step iey aa, ce 439520 145 35 89 Di INE een UA soars ke rein! ch eyes S755 139 3 85 26 Byicay papal = Sy .iate cc) sh eee foul sey 238 203 iene 26 8 at ae eee re oe eee, 25ST 85 14 183 56 Peli omi@ hina. i) pele se, tl 39 57 116 28 125 38 RBeshawatareoen et scnta 6 icheckouae sq Fie wT 1110 338 | I OOTLAMMEI TE Fe oes. soi ss ss aha, seh ccnp salons 18 28 74 10 1840 | 561 @Quetta; Beluchistan: .2 #2. 04. . 30) IT 67 3 5502 | 1677 | Pea as GPS, 1 Sk eae SA ae, 2I 15 81 41 960 293 | | RATIO tiey see aie achat whe ta seat aes be 22 7, 70 52 429 3 Teen | RATIO OOM Seas ose a 4st ss 16 46 96 12 41 12 | We SA AIeR Ap atieees (22. A oc tiss cacao 35. 433 133) yr 7 nl 2 S2ucorelcolande seu cvaneseta cs eee 21 39 88 5 | oe. | 8 | SiGH ate sees Cee Sch othe ee 24 49 2. 150 104 | 32 | Stitt aa | eae: een: eer 5: 3m 6 Tele 7048 2148 Si-wan-tse; Chinal...). % S146. 2 4o 59 115 18 3904 1190 ee SoulsiCorea. erie eh te) eet ree 37 35 127° 7 118 36 Soy as. |ADAL, M7!) oh engh tee wren eiee 45 31 I4I 55 79 24 | Mesure |. 3% 2 we oho ee om 113 72 46 AG: 1 eae feeelerice @hinta:,. (yc fee 4 38 59 II7 40 33 Io | PREZ Tee oof s, on esi te! tas Ge ah ease ae 26 36 92 50 251 76 ROKION [APAN s «+, 2/1 +1. epeneeen eee 35 «41 139 45 69 21 SPGICHINO POLY: -s crc: din as Myon kets ee I0 50 78 44 255 78 cherie USA je. x5 col ws, bette eee AAs aos TLL Lo | RG rea S/o. e ore) 2 ellvicet 47 55 106 50 3773 T1I50 WAZA AP AUANTIP S 1. <. 3! 10a uc, le) fattelle tiers ite te: Sou 22 31 oy PAMENSAM COLCA oo, 10,12 iene dele let 39 10 e225 | * Zi-Ka-Wei, China . ar Ie tig 6 23 7 | | SMITHBONIAN TABLES. 255 TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order. ) Longitude Latitude. from Greenwich. Height above Sea-level. AUSTRALASIA. Adelaide, South Australia 36 : 138° 35’ E. Albany, West Australia 117 54 88 Alice Springs, South Australia... ays ay 2100 | Auckland, New Zealand 174 51 | * Batavia, Java 106 50 26 * Boulia, Queensland 139 38 Bourke, New South Wales 145 58 * Brisbane, Queensland 153. 6 | *Burketown, Queensland 139 34 * Cooktown, Queensland 145 17 Derby, West Australia 122/529 Eucla, South Australia 128 58 Hobart, Tasmania 147 20 * Mackay, Queensland 149 13 Malacca, Straits Settlements... . TO2 wid * Manila, Philippine Islands 120 58 Melbourne; Victoria). 2 344s one 145 oO Penang, Straits Settlement 100 20 Perth, West Australia II5 52 Port Darwin, South Australia .. . 130 51 Province Wellesley, Straits Settle- 100 30 ment. 51 | Singapore, Straits Settlement .. . * Sydney, New South Wales 12 |*Thargomindah, Queensland ... . 43 |*Thursday Island, Queensland .. . I2 Wellington, New Zealand 47 Feet. N. N. S. N. Ss. Ss. N. N. Ss. Ss. Ss. Ss. | AFRICA AND NEIGHBOR- | ING ISLANDS. Alexandria, Egypt Assab, Abyssinia Alger, Algeria 3iskra, Algeria 3izerte, Tunis Cairo, Egypt Cape Town, Cape Colony Ceres, Cape Colony Constantine, Algeria Cradock, Cape Colony Fort Napier, Natal Fort National, Algeria Gabeshunis: 29.) ue eee Ghardaia, Algeria Grahamstown, Cape Colony Ismailia, Egypt Kimberley, Cape Colony SMITHSONIAN TABLES. TABLE 100. LIST OF METEOROLOGICAL STATIONS. (The asterisk * designates stations of the first order.) Longitude Latitude. from Greenwich. AFRICA AND NEIGHBOR- |————_|_—>_"—————__—_——"——_- ING ISLANDS. Feet. m. (Continued.) if Height above Sea-level. | Laghouat, Algeria Memours, Algeria Oran, Algeria Port Elizabeth, Cape Colony .... Port-Said, Egypt Queenstown, Cape Golony *St. Paul de Loando, Angolo Sierra Leone, Senegambia Sidi-Bel-Abbés, Algeria Suez, Egypt Tamatave, Madagascar Tananarive, Madagascar Tripoli Vivi, Congo aN Co ~“ Z oO ° 2454 13 197 181 20 3500 awriaont SON Su se os bo hone wn Own ow | INTERNATIONAL POLAR STATIONS. _Bossekop, (Vorway) Fort Rae, (Great Britain) Godthaab, (Denmark) Jan Mayen, (Austria) Kingua-Fjord, Cumberland Sound, (Germany). Lady Franklin Bay, (United States) Nowaja Semlja, (Russia) Orange Baie, Cape Horn, (france) . Point Barrow, (Unzted States) ... Sagastyr, Lena River, (Azssia) Sodankyla, (Fizland) Spitzbergen, (Szweden) Sud-Georgien, (Germany) MISCELLANEOUS ISLANDS. Barbados Honolulu, Hawaiian Islands... . La Canée, Créte Wasiealmas, Canaries 5 2.2.7): Malta, Mediterranean Massaua, Red Sea * Port Louis, Mauritius *St. Helena Sainte-Croix, Teneriffe Stykkisholm, Iceland Thorshaven, Férvé Island wow a oO al on ° om WN Od oo ann On FW we na No HOH HN © ND Oo boon oow mn db &® NW NO HOWnNT HN O AS OV tS aS Sy SMITHSONIAN TABLES. APPEN BASS CONSTANTS. Numerical Constants. Base of natural (Naperian) logarithms, Log e, modulus of common logarithms, Circumference of circle in degrees, s 6 Ee in minntes, in seconds, Circumference of circle, diameter unity, «ce cas «ec Number. Logarithm. am = 6.2831853 0.798799 = = 1.0471976 0.0200286 = = 0.3183099 —-9.5028501 — Io m2 —= 9.8696044 0.9942997 The arc of a circle equal to its radius is in degrees, Pp? = 180/7r in minutes, p’ = 60 P® in seconds, p’” = 60 p’ For a circle of unit radius, the arc of 1° =1/p° arc of) 1/— pe arc (or sine) of 1/7 =1/p/” Geodetical Constants. 8 | 1/7 Vie Vr V2 Number. 2.7182818 0.4342945 360 21 600 I 296 000 = 3.14159265 0. 1013212 1.7724539 0.5641896 ll || 3 | 2 | | I 1.4142136 V/3 1.7320508 57-2957 3 437-7468” 206 264.8// ll i ll 0.017 4533 0.000 2909 0.000 00485 Logarithm. 0.4342945 9.6377843 — 10 2.5563025 4.3344538 6.1126050 0.4971499 9.0057003 — 10 0.2485749 G.7514251 — 10 0.1505150 0.2385607 1.7581226 3-5362739 5.3144251 8.2418774 — Io 6.4637261 — Io 4.6855749 — 10 Dimensions of the earth (Clarke’s spheroid, 1866) and derived quantities : Equatorial semi-axis in feet, in miles, Polar semi-axis in feet, in miles, a2— b2 (Eccentricity)? = a Flattening = = Perimeter of meridian ellipse, Circumference of equator, Area of earth’s surface, Mean density of the earth (HARKNESS) Surface density ‘“ « sf Acceleration of gravity (HARKNESS) : @ == 20926062. a— 3963.3 6 = 20855121. b= 3949.8 €2 = 0.00676866 & = 1/294.9784 = 24859.76 = 24901.96 = 196 940 400 = 5.576+0.016. == 2/56 -=10.10. 7.3206875 3-5980536 7.3192127 3-5965788 7.8305030 — IO miles. «ec square miles. gs (cm. per second) = 980.60 (1 — 0.002662 cos 2 $) for latitude ¢ and sea level. &, at equator = 977.99 ; g, at poles = 983.21; Length of the seconds pendulum (HARKNESS) : Z = 39.,012540 + 0.208268 sin? inches == 981.17; g, at Washington = 980.07; g, at Paris = 980.94. g, at Greenwich 0.990910 + 0.005290 sin? d metres. SMITHSONIAN TABLES. 258 APPENDIX. CONSTANTS.— Continued. Astronomical Constants (HARKNESS). Sidereal year = 365.256 357 8 mean solar days. Tropical year = 365.2422 d. Sidereal day = 23% 56” 4.1005 mean solar time. Mean solar day = 24% 3” 56.5465 sidereal time. Mean distance of the earth from the sun = 92800000 miles. Physical Constants. Velocity of light (HARKNESS) = 186 337 miles per second = 299878 km. per second. Velocity of sound through dry air = 1090 /1+0.00367 2° C. feet per second. Weight of distilled water, free from air, barometer 30 inches; Weight in grains. Weight in grammes. Volume, 62° F. AG 62° F. 4°'C. 1 cubic inch (determination of 1890) 252.286 252.568 16.3479 16.3662 1 cubic centimetre (1890) 15.3953 15-4125 0.9976 0.9987 I cubic foot (1890) at 62° /. 62.2786 lbs. A standard atmosphere is the pressure of a vertical column of pure mercury | whose height is 760mm. and temperature o° C,, under standard gravity at latitude 45° and at sea level. 1 standard atmosphere — 1033 gtammes per sq. cm. = 14.7 pounds per sq. inch. Pressure of mercurial column I inch high = 34.5 grammes per sq. cm. — 0.491 pounds per sq. inch. Weight of dry air (containing 0.0004 of its weight of carbonic acid) ; I cubic centimetre at temperature 32° /. and pressure 760 mm. and under the standard value of gravity weighs 0.00129305 grammie. Density of mercury at o°? C. (compared with water of maximum density under atmospheric pressure) = 13.5956. Freezing point of mercury = —38°5 C. (REGNAULT, 1862.) Coefficient of expansion of air (at const. pressure of 760”) for 1° C. (Do.): 0.003670. Coefficient of expansion of mercury for Centigrade temperatures (BROCH) : A = A, (1— 0.000 181 792 # — 0.000 000 000 175 #2 — .000 000 000 035 1162). Coefficient of linear expansion of brass for 1° C., B= 0.0000174 to 0.000 0190. Coefficient of cubical expansion of glass for 1° C., Y=0.000021 to 0.000 028. Ordinary glass (RECKNAGEL); at 10° C., Y = 0.0000255; at 100°, Y = 0.000 0276, | Specific heat of dry air compared with an equal weight of water : at constant pressure, Ay = 0.2374 (from 0° to 100° C., REGNAULT). at constant volume, Ay = 0.1689. | Ratio of the two specific heats of air (RONTGEN): Kp / Ku = 1.4053. | Thermal conductivity of air (GRAETZ): & = 0.000048 4 (1 +0.001 85 # C) ae : [The quantity of heat that passes in unit time through unit area of a plate of unit thick- ness, when its opposite faces differ in temperature by one degree. ] Latent heat of liquefaction of ice (BUNSEN) = 80.025 mass-degrees, C. Latent heat of vaporization of water = 606.5 — 0.695 2° C. Absolute zero of temperature (THOMSON, Heat, Lncyc. Brit.): —273°0 C. = —459°4 F. | Mechanical equivalent of heat*: | 1 pound-degree, / (the British thermal unit) = about 778 foot-pounds. 1 pound-degree, C. = 1400 foot-pounds. 1 calorie or kilogramme-degree, C. = 3087 foot-pounds = 426.8 kilogram- | metres = 4187 joules (for g = 981 cm.). * Based on Prof. Rowland’s determinations. (Proc. Am. Acad. Arts and Sci’; 1880.) SMITHSONIAN TABLES: 259 APPENDIX. SYNOPTIC CONVERSION OF ENGLISH AND METRIC UNITS. English to Metric. Metric equivalents. Logarithms. Units of length, 1 inch. 2.54000 centimetres. 0.404 835 1 foot. 0.304801 metre. 9.484 016 — ro yard. 0.914402 se g.961 137 — 10 mile. 1.60935 kilometres. 0.206 650 Units of area. square inch. 6.4516. square centimetres. 0.809 669 square foot. 929.034 = s 2.968 032 square yard. 0.83613 square metre. 9.922 274 — 10 acre. 0.404687 hectares. 9.607 120 — 10 square mile. 2.5900 square kilometres. 0.413 300 ss ss 259 hectares. 2.41% 300 Units of volume. cubic inch. 16.3872 cubic centimetres. I.214 504 cubic foot. 0.028317 cubic metres or steres. 8.452 047 — Lo cubic yard. 0.76456 cubic metres or steres. 9.883 41I — Io Units of capacity. gallon (U. S.) = 231 cubic inches. 3.78544 litres. 0.578 116 quart (U. S.) 0.94636 litres. 9.976 056 — 10 Imperial gallon (British), 4.5468 litres. 0.657 709 277.463 cubic inches (1890). bushe] (U. S.) = 2150.42 cubic inches. 35.2393 litres. 1.547 027 bushel (British). 36.3477 litres. 1.560 477 Units of mass. ’ grain. 64.7989 milligramumes. 1.811 568 pound avoirdupois. 0.4535924 kilogrammes. 9.656 666 — 10 ounce avoirdupois. 28.3495 grammes. 1.452 546 ounce troy. 31.1035 grammes. 1.492 809 ton (2240 lbs.). 1.01605 tonnes. 0.006 914 Units of velocity. foot per sec. (0.6818 miles per hr.) = 0.30480 metres per sec. = 1.0973 km. per hr. mile per hr. (1.46667 feet per sec.) = 0.44704 metres per sec. = 1.6093 km. per hr. Units of force. I poundal. 13825.5 dynes. 4.140 682 Weight of 1 grain (for g = 981 cm.). 63.57 dynes. 1.803 237 Weight of 1 pound av. (for g—=981em.). 4.45 X Io” dynes. 5-648 335 Units of stress—in gravitation measure. pound per square inch == 70.307 grammes per sq. centimetre. 1.846 997 pound per square foot = 4.8824 kilogrammes per sq. metre. 0.688 634 Units of work—in absolute measure. foot-poundal. 421 403 ergs. 5.624 697 —in gravitation measure. foot-pound (for g = 981 cm.) = 1356.3 X Io* ergs = 0.138255 kilogram-metres. Units of activity (rate of doing work). foot-pound per minute (for g = 981 cm.) = 0.022605 watts. horse-power (33 000 foot-pounds per min.) = 746 watts = 1.01387 force de cheval. Units of heat. pound-degree, /. — 252 small calories or gramme-degrees, C. pound-degree, C. — 1.8 pound-degrees, SMITHSONIAN TABLES, APPENDIX. SYNOPTIC CONVERSION OF ENGLISH AND METRIC UNITS. Metric to English. English equivalents. Logarithms. Units of length. I metre (10° microns). 39.3700 ‘inches. 1.595 165 cs 3.28083 feet. 0.515 984 a 1.09361 yards, 0.038 863 1 kilometre. 0.62137 + miles. 9-793 350 — IO Units of area. I square centimetre. 0.15500 square inches, g. 190 33I — 10 I square metre. 10.7639 square feet. 1.031 968 ue amc 1.19599 square yards. 0.077 726 I hectare. 2.47104 acres. 0.392 880 I square kilometre. 0.38610 square miles. , 9.586 700 — 10 Units of volume. I cubic centimetre. 0.0610234 cubic inches. 8.785 496 — Io I cubic metre or stere. 35-3145 cubic feet. 1.547 953 cs aS cs 1.30794 cubic yards. 0.116 589 Units of capacity. 1 litre (61.023 cubic inches). 0.26417 gallons (U. S.). 9.421 884 — 10 “ 1.05668 quarts (U. S.). 0.023 944 “e 0.21993 Imp. gallons (British). 9.342 291 — 10 t hectolitre. 2.83774 bushels (U. S.). 0.452 973 ce 2.7512 bushels (British). 0.439 523 Units of mass. I gramme. 15.4324 grains. 1.188 432 1 kilogramme. 2.20462 pounds avoirdupois. 0.343 334 ss 35.274 ounces avoirdupois. 1.547 454 ee 32.1507 ounces troy. 1.507 I9I 1 tonne. 0.98421 tons (2240 lbs.). 9.993 086 — Io Units of velocity, 1 metre per second. 3.2808 feet per second. 0.515 984 a es ‘s 2.2369 «miles per hour. 0.349 653 t km. per hr. (0.2778 m. persec.) 0.62137 miles per hour. 9.793 350 — IU Units of force. I dyne (weight of (981) grammes, for g = 981 cm.) = 7.2330 X 10 poundals. Units of stress—in gravitation measure. I gramme per square centimetre. 1 kilogramme per square metre. t standard atmosphere. 0.014223 pounds per sq. inch. 0.20482 pounds per sq. foot. 14.7 pounds per sq. inch. Units of work—in absolute measure. (See def. p. 259.) I erg. é 2.3730 X 10° foot-poundals. I megalerg = 108 ergs; I joule = Io’ ergs. —in gravitation measure. 1 kilogram-metre (for g = 98i1cm.) = 981 X I0° ergs = 7.2330 foot-pounds. Units of activity (rate of doing work). I watt. 4 44.2385 foot-pounds per minute, for ¢ = 981 cm. 1 watt — 1 joule per sec. — 0.10194 kilogram-metre per sec., for g = 981 cm. 1 force de cheval = 75 kilogram-metres per sec. = 735} watts = 0.98632 horse-power. Units of heat. 1 calorie or kilogramme-degree = 3.968 pound-degrees, /, = 2.2046 pound-degrees, C. 1 small calorie or therm, or gramme-degree = 0.001 calorie or kilogramme-degree. SMITHSONIAN TABLES. 261 APPENDIX. DIMENSIONS OF PHYSICAL QUANTITIES. L=length; M—mass; IT —time. Quantity. Dimensions. Quantity. Ares. [12] Momentum. Volume. [Ls] Moment of Inertia. Mass. [M] Force. Density. [M I] Stress (per unit area). Velocity. eye Work or Energy. Acceleration. Beats] Rate of Working. Angle. [0] Heat. Angular Velocity,” (fi ] Thermal Conductivity. In Electrostatics. Symbol. Quantity of Electricity. e Surface Density: quantity per unit area. o Difference of Potential: quantity of work required E to move a quantity of electricity ; (work done) + (quan- tity moved). Electric Force, or Electro-motive Intensity: F (quantity ) + (distance’). Capacity of an accumulator: e+ Z. C org Specific Inductive Capacity. k In Magnetics. Quantity of Magnetism, or Strength of Pole. m Strength or Intensity of Field: SS (quantity) + (distance’). Magnetic Force. H Magnetic Moment; (quantity) x (length). ml Intensity of Magnetization: magnetic moment per If unit volume. Magnetic Potential: work done in moving aquantity VorQ of magnetism ; (work done) + (quantity moved). Magnetic Inductive Capacity. be : Dimensions in In Electro-magnetics. Symbol. electro-magnetic system. Intensity of Current. z (L? M2 aT] Quantity of Electricity conveyed by cur- é (1? M4] rent; (intensity) x (time). Potential, or difference of potential ; (work E (L? M? ‘Dall done) + quantity of electricity upon which work is done. Electric Force: the mechanical force act- 3 [13 M2 aml ing on electro-magnetic unit of quantity ; (mechanical force) + (quantity). Resistance of a conductor: # +17. R [tea Capacity: quantity of electricity stored up q ileal] per unit potential-difference produced by it. Specific Conductivity; the intensity of femal current passing across unit area under the action of unit electric force. Specific Resistance: the reciprocal of vr fe =] specific conductivity. SMITHSONIAN TABLES, electrostatic system. Dimensions. [lL MT} [M I] [LM T?] [LMT] [2 M T=] [l? M TS] [L? M T2] [L-! M T-"] Dimensions in [L? mM? T] (LM? tT] (2 M? T+) [U3 mM? T] [1] [0] Dimensions in electro-magnetic system. [L? Mi Tt] (LM? TJ (LU? M? Ty [L424 Mi tT) cL? M? Tj [L? M? T“] [0] Name of practical unit. Ampere. | Coulomb, Volt. Ohm. Farad. Smithsonian Miscellaneous Collections 854 SMITHSONIAN GEOGRAPHICAL TABLES PREPARED BY R. S. WOODWARD CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTITUTION 1894 The Riverside Press, Cambridge, Mass., U.S.A. Electrotyped and Printed by H. O. Houghton & Co. eee ADVERTISEMENT. In connection with the system of meteorological observations established by the Smithsonian Institution about 1850, a series of meteorological tables was compiled by Dr. Arnold Guyot, at the request of Secretary Henry, and was pub- lished in 1852 as a volume of the Miscellaneous Collections. A second edition was published in 1857, and a third edition, with further amendments, in 1859. Though primarily designed for meteorological observers reporting to the Smithsonian Institution, the tables were so widely used by meteorologists and physicists that, after twenty-five years of valuable service, the work was again re- vised, and a fourth edition was published in 1884. In a few years the demand for the tables exhausted the edition, and it appeared to me desirable to recast the work entirely, rather than to undertake its revision again. After careful consideration I decided to publish the new work in three parts: Meteorological Tables, Geographical Tables, and Physical Tables, each representative of the latest knowledge in its field, and independent of the others ; but the three forming a homogeneous series. Although thus historically related to Doctor Guyot’s Tables, the present work is so entirely changed with respect to material, arrangement, and presentation, that it is not a fifth edition of the older tables, but essentially a new publication. The first volume of the new series of Smithsonian Tables (the Meteorological Tables) appeared in 1893. The present volume, forming the second of the series, the Geographical Tables, has been prepared by Professor R.S. Woodward, formerly of the United States Coast and Geodetic Survey, but now of Columbia College, New York, who has brought to the work a very wide experience both in field work and in the reduction of extensive geodetic observations. S. P. LancuLey, Secretary. PREFACE. In the preparation of the following work two difficulties of quite different kinds presented themselves. The first of these was to make a judicious selec- tion of matter suited to the needs of the average geographer, and at the same time to keep the volume within prescribed limits. Of the vast amount of material available, much must be omitted from any work of limited dimen- sions, and it was essential to adopt some rule of discrimination. The rule adopted and adhered to, so far as practicable, was to incorporate little material already accessible in good form elsewhere. Accordingly, while numerous ref- erences are made in the volume to such accessible material, an attempt has been made wherever feasible to introduce new matter, or matter not hitherto generally available. The second difficulty arose from the present uncertainty in the relation of the British and metric units of length, or rather from the absence of any generally adopted ratio of the British yard to the metre. The dimensions of the earth adopted for the tables are those of General Clarke, published in 1866, and now most commonly used in geodesy. These dimensions are expressed in English feet, and in order to convert them into metres it is necessary to adopt a ratio of the foot to the metre. The ratio used by General Clarke, and hitherto gener- ally used, is now known to be erroneous by about one one hundred thousandth part. The ratio used in this volume is that adopted provisionally by the Office of Standard Weights and Measures of the United States and legalized by Act of Congress in 1866. But inasmuch as a precise determination of this ratio is now in progress under the auspices of the International Bureau of Weights and Measures, and inasmuch as the value for the ratio found by this Bureau will doubtless be generally adopted, it has been thought best in the present edition to restrict quantities expressed in metric measures to limits which will require no change from the uncertainty in question. In conformity with this decision the dimensions of the earth are given in feet only, and, with a few unimportant exceptions, to which attention is called in the proper places, tables giving quan- tities in metres are limited to such a number of figures as are definitely known. vl PREFACE. It is a matter of regret that, owing to the cause just stated, less prominence has been given in the tables to metric than to British units of length. On the other hand, it seems probable that the more general use of British units will meet the approval of the majority of those for whose use the volume is designed. The introductory part of the volume is divided into seven sections under the heads, Useful Formulas, Mensuration, Units, Geodesy, Astronomy, Theory of Errors, and Explanation of Source and Use of Tables, respectively. In pre- senting the subjects embraced under the first six of these headings an attempt was made to give only those features leading directly to practical applications of the principles involved. It is hoped, however, that enough has been given of each subject to render the work of value in a broader sense to those who may desire to go beyond mere applications. The most of the calculations required in the preparation of the tables were made by Mr. Charles H. Kummell and Mr. B. C. Washington, Jr. Their work was done with skill and fidelity, and it is believed that the systematic checks applied by them have rendered the tables they computed entirely trustworthy. Mention of the particular tables computed by each of them is made in the Explanation of Source and Use of Tables, where full credit is given also for data not specially prepared for the volume. The Appendix to the present volume is that prepared by Mr. George E. Cur- tis for the Meteorological Tables. Its usefulness to the geographer is no less obvious and general than to the meteorologist. The proofs have been read independently by Mr. Charles H. Kummell and the editor. The plate proofs, also, have been read by the editor ; and while it is difficult to avoid errors in a first edition of a work containing many formulas and figures, it is believed that few, if any, important errata remain in this volume. R. S. Woopwarp. CoLuMBIA COLLEGE, New York, N. Y., June 15, 1894 CONTENTS. USEFUL FORMULAS. Te OE GRERATONIBORMULAS 6.0 6 ee cg et mat, yal ed, a. Arithmetic and geometric means. . .... - BewAnthmetic propression . 3 3 ss wv ewe GeGeometnG PrOcression. = “os ewe ke as d: sumsiot special’ series <= |, . : e. The binomial series and quniioaions f. Exponential and logarithmic series . . . oe ee . Relations of natural logarithms to other fear 3: Te cic BGRIMUEAS) Pipi l dee te O20 ste tory, or oc a. Signs of trigonometric functions. . . . .. . b. Values of functions for special angles. . . . . c. Fundamental formulas . . . . : : d. Formulas involving two angles . . .... .» Formulas involving multiple angles. . . ae f. Exponential values. Moivre’s formula. : : D Values of tunctions.In SerieS| «|. «6 : 3. FORMULAS FOR SOLUTION OF PLANE TRIANGLES . 4. FORMULAS FOR SOLUTION OF SPHERICAL TRIANGLES Right angled spherical triangles. . . . by Oblique angled triangles. - . . 2... 5. ELEMENTARY DIFFERENTIAL FORMULAS Se AISCMEAIG. OW ittyn on Seen exe. we oe b. Trigonometric and inverse trigonometric . 6. TAYLOR’S AND MACLAURIN’S SERIES... . Ao PAVIOGS SCWUCS as sehen Sankyo Oe G by Maclauriinsrsemess 55 “is ss ce. Exaniple of Vaylors Series...) 75 (2.2 +) d. Example of Maclaurin’s series . .. . 7. ELEMENTARY FORMULAS FOR INTEGRATION. . a. Indefinite integrals b. Definite integration . . . .. MENSURATION. EN ES ge P Pare. Sie ero, ome eae eee a. In a circle bein resular polypon’ 2. sl: *5)4. a 4s PAPEL OSC os 15 ds one ace ce ha ce h. Conversion of arcs into angles and angles into arcs PAGE xiii xill xii Xill xili Xiv Xiv XV XV XV XV XV XV1 XV1 xvi XVil Xxvil XViil xk XXxi Xxli XXli Xxli Xxil XXiil Xxill XXIll Xxvi XXViil XXViil XXViil KDE vill 2. 3. ae Ny TAN BPW TT. Zs CONTENTS. AREAS. 0% 38 fs hea ee ee ee a a. ‘Area of plane triangle... 4/05) ). (. 2 eee ee b. Area of trapezpids, J. 2k Ga), = c. Aréa of regular polyson:: a <4: | Ae eee eee ee d. Ared of circle, circular,annulus, ete: “<)ceoe) ene eee e. Area ofellipse*s. 2 ss Js) cba ee ee f--Surtace:Ob Sphere, ete. vs, a et ee g. Surface of right cylinder . .... . ho surface of riphticoneé= <2 =. 5) aa eae i, ‘surface of spheroid: eee VOLUMES. 5 (2. he ebee Ue eee een Mn ee) a.:/Volumexof prisms’... 22) 7) cana ee eee ee b. Volumesot:pyramid) -)2.) ees eee c. Volume of right circular cylinder . . é d. Volume of right cone with circular base . . ..... . e. Volume of sphere and spherical segments . ..... ., f. Volume (of ellipsoids: 5. see eens eee ne UNITS. STANDARDS OF LENGTH AND Mass .......... BRITish .MEASURESLAND: WEIGHTS. 2) 2.255) 2) Gaon (ee ee a. JHIN eal AMCASUTES> oo, iey a) os or hin ee b. Surfaceyorisquare measures... “2. ean ee c. Measures of capacity. . . ds. Measures of weiphtye.. ssh. 6. 9) ) ee METRIC MEASURES’ AND, WEIGHTS 3 2). (7. ee) ue ae Fae C.GrSOJSvstem OF UNITS.) 20.) ee ee GEODESY. ForM OF THE EarTH. THE EARTH’S SPHEROID. THE GEOID. . ADOPTED DIMENSIONS OF EARTH’S SPHEROID. . ..... + AUXILIARY ‘OUANTITIESS” “£0 GC. desde: ee ae ey eer ae EQUATIONS TO GENERATING ELLIPSE OF Guana ee ls ales a LATITUDES, USED IN GEODESY; ) 2, bynes oe aa oO et ee Rapil OF CURVATURE .. . : : «aS LENGTHS OF ARCS OF Meer AND Baers OF aan : a. Ares.of mendian: <..i:c ue tee nn) svc nae en ae b. -Ares-of parallel sic. 2 ee se ae bi Sp ae on Rapius-VECTOR OF EARTH’S SPHEROID . . . Meera. AREAS OF ZONES AND QUADRILATERALS OF THE Parnes SURFACE SPHERES OF EQUAL VOLUME AND EQUAL SURFACE WITH EARTH’S SPHEROID..9'i0) alates eoiee a one PEt Reale eles CO-ORDINATES FOR THE Poreeone Pee merion OF Mee mee LINES ON A SPHEROID . Je De, Mi ee oc area eT a. Characteristic property of curves of vertical section . . . b, (Characteristic property. of: seodesic line ae. aye an ene, aie XXIx ExIx XXix xKx XXX XXX xxx KET XXX Kee XXXil XXXxli XXxii 2M XXXli XXxii XXxiil XXXIV XXXVI XXXVI XXXVili XXXVili XXX1X xl xlii xiii xliii xlili xliv xliv xlv xlvi xlvi xlix lii liii lvi lvi lvii 4 _ 13. 14. ES: 16. 17. Gs 4. CONTENTS. SOLUTION OF SPHEROIDAL TRIANGLES . . + «© «© «© © « «© « a. Spherical or spheroidal excess . ... . Baty, tet ere, GEODETIC DIFFERENCES OF LATITUDE, LONGITUDE, AND AZIMUTH aw Prmmany thianpulation: «9S is Ok ee es be secondary triangtilation . “) Gee ey TRIGONOMETRIC LEVELING .. . aeeree ys ‘ahah a. Computation of heights from aheeed zenith mernees nee, ie b. Mochieients OL retraction <. f. Paar ie eases tee wee c. Dip and distance of sea horizon. . . . MISCELLANEOUS FORMULAS . . ere Not es Correction to observed angle for ecrertne position of instrument a. b. Reduction of measured base to sealevel. . . . . «=. e. The three-point'problem .. . 2s te 8 em ws SALIENT Facts oF PHysicaAL GEODESY ... .- . i a. Area of earth’s surface, areas of continents, area bi oceans . b. Average heights of continents and depths of oceans . . . . c. Volume, surface density, mean density, and mass of earth d. Principal moments of inertia and energy of rotation of earth . ASTRONOMY. THE CELESTIAL SPHERE. PLANES AND CIRCLES OF REFERENCE . MPrERCAL CO-ORDINATES 6, of 04 Seas - am) be ee os a, Notation +. %. 3 : erase Ry ac ia ce ean b. Altitude and pe math in terms tae decinatian and hour angle . c. Declination and hour angle in terms of altitude and azimuth d. Hour angle and azimuth in terms of zenith distance . . . .- e. Formulas for parallactic angle . ..... . Be aay se f. Hour angle, azimuth, and zenith distance of a star at pleneanod g. Hour angle, zenith distance, and parallactic angle for transit of a star across prime vertical . . . . in es h. Hour angle and azimuth of a star when in hae neneont or at the time of rising or setting... . . i, Differentialformulas. . . . re Peet Se cone . RELATIONS OF DIFFERENT KINDS OF fiers USED IN he onouns : a, Che siderealand solar.days: ... 2. «= | = -. © « % © @ b. Relation of apparent and meantime . . . ees c. Relation of sidereal and mean solar intervals on tIME 70 ee d. Interconversion of sidereal and mean solar time . ... . e. Relation of sidereal time to the right ascension and hour angle foyik Bele: hae a a Re PRN ree MEO ES Mn, MET AD cv DETERMINATION OF “UIME... 5) Seas oa. ee en, open ew ts a. By meridian transits. . . ooh Sr Ae ee ew b. By a single observed altitude ae a (Starsh Ver ue ete el by euudl altitudes Of. a Stak. i Sin 4, (4@+6"=> @ +2 a ————— a'-2 3 n(n — 1) (w —2) be te ees ae oe For << a, (1 t2"—r1ine fe spa n(n De 2) See ee =1—-“*4+2°—2?+44-... Fe ee a ae Goap St teetse tat tsatt... GQ+aji=r1+he—f0°4 yo — shyt... (a ie) Dg I apap Side bt eat iy ot I Goapmitietie tat wet +... f. Exponential and logarithmic series. For — o x—1\7 EO * apa PA ears) PAG ea) stot (acres OR | TS07 270° 360° | 30° 45° 60° a a | BEG 5. Heme wey Me ° +1 Oo — 1 Oo t 1/2 | a/3 cosine ...j|—+1 O° — I Oo +1 | 47/3 | iW2 i. tangent . ... ° Co ° oo ° 1/3 I V3 | eGrangvent «.. <. eo foe re) ° | oo /3 I iW/3 | c. Fundamental formulas. sin? a + cos? a = 1, tan aycot aT, €0S a’ SeC a == Tt, sin a cosec a = 1, sin a cos a NC) = CoOL. — ; cos a sin a 1 + tan? a = “7 == sec? a 1+ cot?4=— “y= cosec? a cos? a , sin? a ’ versed sin a = 1 — cosa. xvi USEFUL FORMULAS. d. Formulas involving two angles. sin (a + 8) = sinacos B + cos asin B, cos (a + 8) = cos a cos P Fsin a sin B. tan (a + 8) = (tan a + tan f)/(1 F tan a tan f), cot (a + 8) = (cot a cot B F 1)/(cot a + cot B). sin a + sin B = 2 sin $(a + B) cos }(a — B), sin a — sin B = 2 cos }(a + £) sin }(a — f). cos a + cos B = 2 cos }(a+ f) cos }(a — B), cos a — cos 8B = — 2 sin }(a + £) sin }(a — £). sin (a + B) cos a cos f sin (B + a) sin a sin B 2 sin a sin B = cos (a — f£) — cos (a + f), 2cosacos B = cos (a — B) + cos (a + f), 2 sin a cos B = sin (a — f£) + sin (a f). eee = tan }(a + £) cot }(a — f), COS COs 0 ame cosa—cosB” cot $(a ++ f) cot $(a — f). fan’ oa. -— tan 3. CORO ie CObyiaa— e. Formulas involving multiple angles. sin 2a == 2 SIN @-COS.a, sin 3 a =3 sin a cos* a — sin® a, — 2 nz oe 2372 — 2 cos 2 a = cos’ a — SIN’ a =—=T1 — 2 SIN" a = 2 COS” a—I, cos 3 a = cos* a — 3 sin’ a Cos a. " sina | t1—cosa_ (1 — cosa\i tang — 5 eos a Sina a Ne icoskay 2 tana : cot? a — 1 n2a—— 2? COZ {OG — aaa HS I — tan?a 2 cota a 2tanda Aisi ean aaa Oa a eT) Ea ae — F x 1+ tan? da 1+ tan?da 2 Sin* a, =r — COS 2.0, 2 cos? a = 1 -+ cos 2 4, 4 sin? a = 3 sin a — sin 3 4, 4 cos® a = 3 coSa-+ COS 3 a. f. Exponential values. Moivre’s formula. e = base of natural logarithms, A/S, Br, ee cos x=} (¢*+e-*), sin ar (Coa), cos x =} (e-7 + &), sin, 7 4, (en (cos x +2 sin x)"= cos mx +7 sin mx. USEFUL FORMULAS. Xvli g. Values of functions in series. For x in arc the following series hold within the limits indicated. x ines 6 tae eet I20 6 _ x cos 4 = 1 pete — ocx 4, B < 90° and but one value results. When dé > a, 8 has two values. y | y= 180? — (a+ A). C ¢ =asin y/sin a. A A=taésin y. a, a, B b 6 = asin B/sin a. y | y= 180° — (a+ f). c c =a sin y/sin a =a sin (a + P)/sin a. A | A=}tadbsiny=}a’sin B sin y/sin a. @ sin 6Y, a, b, y a tan oe gees y a, 8 | § (a+ f)=90° — by, ae 1 Cae) ey OLY | c= (a+ 0? — 2 ab cos y)', = {(a +4) — 4a bcos? } 7}, = {(a — 4+ 44d sin? § op}, = (a — b)/cos ¢, where tan ¢ = 2 Ya sin } y/(a — 4), | =a sin y/sin a. A |A=tsabsiny. USEFUL FORMULAS. 4. FoRMULAS FOR SOLUTION OF SPHERICAL TRIANGLES. a. Right angled spherical triangles. a, b, c= sides of triangle, ¢ being the hypotenuse, a, 8, y = angles opposite to a, 4, ¢, respectively, arn ° y— 907 sin a = sin ¢ sin a, sin 6= sinc sin B, tan a = tan ¢cos B£, tan d= tan ¢ cosa, = sin) tan a, = Sinia tal os cos a = cos a sin B, cos B= cos ésin a; COS ¢ = c0s'2 Cos) = cota. coup. b. Oblique angled triangles. a, 6, c= sides of triangle, a, 8, y = angles opposite to a, 8, ¢, respectively, s=h(a+5+0, o=3(a+ f+ »), e=a-+ 6+ y — 180° = spherical excess, S' = surface of triangle on sphere of radius ». sin @ sin 6) -sim.¢ > —) ee) ’ Sina sySines wi sin -y cos @ = cos 6 cos¢ + sin 6 sin ¢ cos a, — cos o cos (o — a) cos (« — 8) cos (« — y) in ke eee in2 — : : 2 ca : : a sin B sin y i econ ia sin B sin y — cos o cos (o — a tan? i a= ( ) . 2 cos (o — B) cos (o — y) . sin (s — 6) sin (s —c sin s sin (s—a Sin. 6 SS nee) cos" ..4a Se Se) 2 sin @ sin ¢ 2 sin 6 sin ¢ sin'(s — 1) isini(@— 4 tan?...4— —— es ) ert a) Z sin s sin (s —@) cots acot} dé cos cot 4 « = ———_ tetas HE, sin tan? «= tan 3s tan 3 (s — a) tan } (s — BJ) tan 3 (s — 0). € SS == are 180° © NVapier’s analogies. sit(a— inl(a— tan § (a + 4) = SPD tan 3 tan} (@— ) = SET tan be cos } (a — db) sin 4 (a — 0) tan 4 oie) ee 1 (a +6) cot 4 Y tan 4 — 8) = sin g (a8) cot hy. USEFUL FORMULAS. Xxi Gauss’s formulas. cos } (a + B) cos }¢= cos $ (a+ 4) sin} y, sin } (a + f) cos } c= cos $ (a — 4) cosh y, cos } (a — f) sin }e¢ = sin} (a+ 4)sin}y, sin i (a — 8) sin} c =sin } (@ — 4) cosh y. 5. ELEMENTARY DIFFERENTIAL FORMULAS. a. Algebraic. U, U, W, ... == variables subject to differentiation, a, b, ¢,... = constants. da+u)=du, dau)=adu, dutovtw+..j)=du+dv+du-..., du v)=udv-+v du, a a a duow..)=(S4 E+ Oti)urwi., a(;) _ vdu—udv __ ad __udv 2 Saami OR U U Vv uv et) = Ge hAtgu} (Atguy CE dn Ue a0, Wo = aus: 2 Ju da — a log 2 dv; ae —— 6 ae (e = base of natural logarithms), d log v = av/v. OF 3 9 AF(u,v, WwW...) = dt do to dw +... “~ Ou b. Trigonometric and inverse trigonometric. “asin % — cos @ ax, dcos x = — sin x ax, dtan x = sec? x dx, dcot x = — cosec? x dx, dsecx == sec? x sinx dx, dcosec x = — cosec’ x cos x dx. dlog sin x = cot x dx, -dlog cos x = — tan x dx. . ax ax fac sa — darc cos x = + = Vi — + Vr — x ax ax darc tan x = — gare cot + = —— ipa pa Xxli USEFUL FORMULAS. 6. TAyLor’s AND MACLAURIN’S SERIES. a. Taylor’s series. If «~=/(x-+ 4%), any finite and continuous function of « + 4%, # being an arbitrary increment to x; and if du/dx, d*u/dx*, . . . are finite and deter- minate, v=SO+D=LOAS AES ODES oat where f(x), /’ (x), f” (x), . . - are the values of f(x + %), du/dx, d*ufdx*, when 4 =o. This is Taylor’s series or theorem. The remainder after the first m terms in Z is expressed by the definite integral h I —————— n+1 n peer os (wh — 2) 2 de. ) b. Maclaurin’s series. If in Taylor’s series we make x = 0, and 4 = x, the ee is M=SM=SOTSOF+O DH Aste, where / (0), 7’ (0), f” (0), - . . are the values of f(x), du/dx, d*u/dx?,. . . when x==o. This is Maclaurin’s series or theorem. The remainder after the first 7 terms in x is expressed by the definite integral x I Ts 28 i JT @ — 8) aa Ot 6) ei tie o c. Example of Taylor’s series. uf (« + hk) = log («+ A). S (x) = log x, du I : we eee. J’ (4) = + 2, au I : de eee a) re a ge =t+ Garp J" (%)=+2 «7%, Hence for common logarithms, » being the modulus, log (a +h) =logx+ p(x th—tx?H+ tx hi—...), and the sum of the remaining terms is h Sh ay eee Nena ee ° USEFUL FORMULAS. Xxlil Since x is the least value of (x + / — z) within the limits of this integral, the sum of the remaining terms is negative, and numerically < (=) If, for example, (#/x) = 1/100, the remainder in question is less than 1 X 0.434 X 107%, or about one unit in the ninth place of decimals. d. Example of Maclaurin’s series. 47, (0) — Sas LON c, x = cos x, (Oat = =-—sin x, hi (0)—=0, oe — — cos XK; if (C= 1 Hence : . : a Z le oe es aaa es and the sum of the remaining terms is as I . ss ass (x — 2) 2° dz. ° If g is the greatest value of sin (x — z) within the limits of this integral the remainder in question is negative and numerically <= x aT If, for example, x = 7/6 (the arc of 30°), g = 3, and the remainder is numeri- cally less than 0.00001 43. 7. ELEMENTARY FORMULAS FOR INTEGRATION. a. Indefinite integrals. fade =a eg G {7@ de + fe (x) dx ={Vv@ + ¢ (x)} de. If «= ¢$(y), and dx = ¢' (y) ay, SF @) ae = [7 fb } # ) & ete ne jae XXiv USEFUL FORMULAS. Since d(uv) = udv + vdu, f udv = uv — | vdu; and if “z= f(x) and v= ¢ (2), fre Be ax == f)ige () —fe (x) DO) ce, * fi ax ue Ax, 9) ty = hi dy ip Ix, 9) dx. fa I(x) dx = x | f@) dx — | af(x) dx. n ey estan = hia T+ C, ax =n as ae +C, pain [G4 bay de =e @+ns + a. fGavsett+o ax aa etG Jess “= Tete te ax a be —— me log (a -- bx). ae — ax fess tan x + C, JaGaex cot x + C. ax 1+ ax x— 1 fee 10: I sag ES fear tite Vi Iz 7ilw= = (ab)—} arc tan (6/a)! x + C, for a and d both positive, = (ab)~* are cot (4/a)' x + C, for a and d both negative (— ab): — = 3 (— ab)“ log (a a ee C, for ad negative. ax b+ cx a en ay ee ene ae Ae a5 ES (ac — 6*)~? are tan Gar i+ C, for ac—b?> 0, (8? — ac)’ —b — ex = (07 — acy} MOE (= aeopeace woe —ac>o. fo fe ae Ue == Ae (a -- x) -+ 1a log {x + (a -|- x*)t} + Gc f@ — x*\)t dx =} x (a? — x’)! + 3.’ arc sin ~ + C. fi (a + bx) de = 3 (a + bx)i/b + C. * This is the formula for integration by parts t Natural logarithms are used in this and the following integrals. For relation of natural to common logarithms see section I, g. USEFUL FORMULAS. XXV Slap 2 bx + ext dv = 4 0 + ex) (a $2 bx + exile 4k (ac — Bc ( (at 2 bx + ext} dx + C. f (a + bx)-* dx = 2 (a+ ba)b +. SH Ba) (@ + bx} ds = 33 ab — 2 aB + Bods) (a+ day'/P + C. f (a? — x2} dv = t arc sin= + CG, et arc cos + ¢, v x\t == 2are tan (2) + C. fet debs E+E bAIEAG x + (a+ 2°) 3 log x — (a + x) i I fe + 2 bx + 6x?) dx = va log {+ ex + (ac bex + 2x*)'}-+- C, for ¢ > 0, I . b= o& ——— vane Grtcani + G fore (6 @) ae SB Ga), a a formula useful in determining approximate values of integrals. See,e. g., section 6, d. b i Se (x) ax, a du a S=-4@, G=t®. am ax Sees at ° I f Tee a Ge ee ee ra 27 ° I a ax ax ae Fa = }7/V (ad), / Va? 2 USEFUL FORMULAS. XXVli 60 oo fe —=3 dy —} Az, ee an) AV (x/a?). ° ° «o eet 9 Oe Tks eine Wen (2 a) ~ et Az, ° oO ufige 2 at dx = WV (n/a). Oo ake Tv fain mx sin ax dx = | cos mx cos mx dx = 0. Oo ° when 7 and z are unequal integers. T Jfsin mx COS 1x ax —= — for m and 7 integers and m — 7 odd, ° =o, for m and 7 integers and m — 7 even. T T f sin? mx dx —= | cos* mx dx = 4 7, for m an integer. ° ° ker be sin” x ax se ff C3sh a fa == C= ae, ° ° ° oO. 0 Se =f Qe a = Vf). o ° Ca 00 fsin x? dx = (cos x? dx = 4 V(x/2). fo) fe) co Ne cos 26x dx — 4 e—@/a)3 V(x /a). oO oO ilies 74 sin’ 20% 2L—=0. ° MENSURATION. 1. LINES. a. In a circle: 7 == radius of circle, ¢ = length of any chord, § = arc subtended by ¢, a = angle corresponding to s, h = height of are s above ¢, or perpendicular distance from middle point of arc to chord. Circumference = 2 77, m == 3-14159265, log r= 0.49714987, 2 i= 0.20315 530, = OP 2im—— 0.7 Ooty 05 7 C= 277 Sino, S = Fuge Length of perpendicular from center on chord 97 1COS yi od (Ge —j} cA) =r{.-1(5)-1(2)-a h—=r(1—cos $a) == 27,sin? 4a =r—(r—}2) —lr ; ()'+ os (5) +145 (Z)'+... Y s—czyAs(a?—PW att...) — s{i+a(F)+... i. b. In regular polygon. ry = radius of inscribed circle, #& = radius of circumscribed circle, == number of sides, s = length of any side, f& = angle subtended by s, p = perimeter of polygon. 7 | MENSURATION. Xxix B = 360°/n, ¥ S.== 2/4 tals BP — 2 sin $B, P= ns S=2netan B= 22 sin't Bp. See table under c, below. cy In elivnse: @ = semi-axis major, 6 = semi-axis minor, é = eccentricity = (1 — 6?/a*)!, / = perimeter of ellipse, n = (a —d)/(a+ 8) Pea Vr vet ees 5a, a ena a Shon 1 ae Distance from centre to focus = ae, Distance from focus to extremity of major axis = a (1 — é), Distance from focus to extremity of minor axis = a. PH=ra+d)ativ+yAwttsewt.., = 7 (a -+ 4) g, say, where g stands for the series in z. The values of g cor- responding to a few values of z are : — 72 gd | 2 gd ° 1.0000 || 0.5 1.0635 O.1 1.0025 | 0.6 1.0922 0.2 [.Or6o || 0:7 1.1267 0.3 1.0226 0.8 1.1077 0.4 1.0404 | 0.9 | 1.2155 ll Pis0 1.27392 2. AREAS. a. Area of plane triangle. (See table on p. xix.) b. Area of Trapezoid. 5, = upper base of trapezoid, 6, = lower base of trapezoid, a = altitude of trapezoid, or perpendicular distance between bases. Area = } (4, + &) a. MENSURATION. c. Area of regular polygon. ‘== Ared, x, R = radii of inscribed and circumscribed circles, s = length of any side, zz == number of sides, 8 = angle subtended by s = 360°/z. A=nr'tan} B=}2 Ff’? sn B=} 251 cot £.f. TABLE OF VALUES. mn | B | A A | R s 3 L20y 0.4330 S* 1.2990 R*) 0.5774 S LF Quite, 4 go 1.0000 2.0000 | 0.7071 1.4142 5 72 17205 2.2770 0.8507 1.1750 6 60 2.5981 | S22508r 1.0900 1.0000 a 512 3-6339 2.7364 1.1524 0.8678 8 45 5.8284 2.8284 1.3066 0.7654 9 40 6.1818 2.8925 1.4619 0.6840 10 36 7.6942 2.9389 1.6180 0.6180 II 3217 9:3656 | 2.9735 1.7747 0.5635 12 30 11.1962 | 3.0000 1.9319 0.5176 13 28495 13-1858 3.0207 2.0893 0.4786 14 257 15-3345 | 3:0372 2.2470 0.4450 1G 24 17.6424 3.0505 2.4049 0.4158 16 224 | 20.1094 | *3.e6z5 | 2.5629 0.3902 d. Area of circle, circular annulus, etc. 7 = Yadius,of:circle; d@ = diameter, a. = angle of any sector, 7, % == smaller and greater radii of an annulus. Area of circle = 7 2 =1 x a, wT = 3.14159265, log r= 0.49 714987. Area of sector = a 7”, for a in arc, = 7 7* (a/360), for a in degrees. Area of annulus = z (7? — 7). e. Area ofellipse: a, 6 = semi axes respectively e = eccentricity = (a? — 4”)#/a = {@ + 4) @—4)}}/a. MENSURATION. XXXi Area of ellipse = = a J, =a V1 = e = 7 a’ cos 4, if e= sin ¢. f. Surface of sphere, etc. yr = radius of sphere, 1, $y = latitudes of parallels bounding a zone, ¢ = spherical excess of a spherical triangle — sum of spherical angles less 180°, Total surface = 4 7 7. Surface of zone = 2 z 7*(sin ¢. — sin )), = 4 7 7° cos § (fo + 1) sin } (2 — Fr) Surface of spherical triangle = 7” «, for in arc, = 7* «/p", for « in seconds, p == 206 264.5:, log p” = 5.31 442 553. g. Surface of right cylinder. y = radius of bases of cylinder, h = altitude of cylinder. Area cylindrical surface = 2 7 7 4. Total surface = 277 (7 + 4%). h. Surface of right cone. yr = radius of base, A— altitude, s = slant height. Conical surface = rrs =r (hK? + 7°), Total surface —==ar(s-+7). i. Surface of spheroid. a, 6 = SEMI axes, e = eccentricity = {(¢ + 4) a — b)/a. tog (E=E2) ie enn —y4¢—7,c—...). Surface of oblate spheroid = 2 7 a are sin @ M J —4rab(1—-}—-We ee as * The logarithm in this formula refers to the natural or “ Napierian” system. For areas of zones and quadrilaterals of an oblate spheroid, see pp. 1-lii. Surface of prolate spheroid = 2 7ad / (a — e+ XXXil MENSURATION. 3. VOLUMES. a. Volume of prism. A = area of base, 4=altitude, V= volume. CSA: For an oblique triangular prism whose edges a, 4, ¢ are inclined at an angle a to the base, V=} (¢a+6+9) A sina. b. Volume of pyramid. A = area of base, 4 —altitude, MV= volume. V=AEeAL For a truncated pyramid whose parallel upper and lower bases have areas 4, and A, respectively and whose distance apart is 4, V=34h(4,+ VA, 4,+ 4). The volume of a wedge and obelisk may be expressed by means of the volumes of pyramids and prisms. c. Volume of right circular cylinder. xy = radius of base, “4 = altitude, V= volume. V=T eh == 3.14050 205, losm— 0.49774. 957. For an obliquely truncated cylinder (having a circular base) whose shortest and longest elements are 4, and /, respectively, —_— 3 T r (hy = hy). For a hollow cylinder the radii of whose inner and outer surfaces are 7, and 72 respectively, and whose altitude is 4, V=7h (73 — 79) d. Volume of right cone with circular base. 7 = radius of base, #4 = altitude, VY = volume. rh: For a right truncated cone the radii of whose upper and lower parallel bases are 7, and 7, respectively, and whose altitude is 4, V=hi7hA(r§3+~"4+7}). e. Volume of sphere and spherical segments. ———— r = radius of sphere, #4 = altitude of segment, V = volume. eee MENSURATION. XXXiii For the entire sphere V = $7 7? = 4.1888 7* approximately. (For m and log m see c above.) For a spherical segment of height % V=7h? (r—th). For a zone, or difference in volume of two segments whose altitudes are /, and Ay, respectively Vour(— A —37@—A* =t7TA43n7+37+ 4, where 7 and 7 are the radii of the bases of the zone and A = A, — hy. f. Volume of ellipsoid. a, 6, ¢ == semi axes, Y= volume. PE en OO For an ellipsoid of revolution about the a-axis, V= 47a 5%, the d-axis, V= 4 7 a? B, UNIS: 1. STANDARDS OF LENGTH AND Mass. THE only systems of units used extensively at the present day are the British and metric. The fundamental units in these systems are those of time, length, and mass. From these all other units are derived. The unit of time, the mean solar second, is common to both systems. The standard unit of length in the British system is the Imperial Yard, which is defined to be the distance between two marks on a metallic bar, kept in the Tower of London, when the temperature of the bar is 60° F. The standard unit of mass in the British system is the Imperial Pound Avoirdu- pois. It is a cylindrical mass of platinum marked “ P. S. 1844, 1 lb.,” preserved in the office of the Exchequer at Westminster. In the metric system the standard unit of length is the Metre, now represented by numerous platinum iridium Prototypes prepared by the International Bureau of Weights and Measures. The standard of mass in the metric system is the Kilogramme, now represented by numerous platinum iridium Prototypes prepared by the International Bureau ~ of Weights and Measures. Both systems of units have been legalized by the United States. Virtually, how- ever, the material standards of length and mass of the United States are cer- tain Prototype Metres and certain Prototype Kilogrammes. ‘The present status of the two systems of units so far as it relates to the United States is set forth in the following statement from the Superintendent of Standard Weights and Measures, bearing the date April 5, 1893. FUNDAMENTAL STANDARDS OF LENGTH AND Mass.* “While the Constitution of the United States authorizes Congress to ‘ fix the standard of weights and measures,’ this power has never been definitely exer- cised, and but little legislation has been enacted upon the subject. Washington regarded the matter of sufficient importance to justify a special reference to it in his first annual message to Congress (January, 1790), and Jefferson, while Secre- tary of State, prepared a report at the request of the House of Representatives, in which he proposed (July, 1790) ‘to reduce every branch to the decimal ratio already established for coins, and thus bring the calculation of the principal affairs of life within the arithmetic of every man who can multiply and divide.’ The consideration of the subject being again urged by Washington, a committee * Bulletin 26, U.S. Coast and Geodetic Survey. Washington: Government Printing Office, 1893. Published here by permission of Dr. T. C. Mendenhall, Superintendent Coast and Geo- detic Survey. UNITS. XXXV of Congress reported in favor of Jefferson’s plan, but no legislation followed. In the mean time the executive branch of the Government found it necessary to procure standards for use in the collection of revenue and other operations in which weights and measures were required, and the Troughton 82-inch brass scale was obtained for the Coast and Geodetic Survey in 1814, a platinum kilo- gramme and metre, by Gallatin, in 1821, and a Troy pound from London in 1827, also by Gallatin. In 1828 the latter was, by act of Congress, made the standard of mass for the Mint of the United States, and although totally unfit for such pur- pose it has since remained the standard for coinage purposes. “In 1830 the Secretary of the Treasury was directed to cause a comparison to be made of the standards of weight and measure used at the principal custom- houses, as a result of which large discrepancies were disclosed in the weights and measures in use. The Treasury Department, being obliged to execute the consti- tutional provision that all duties, imposts, and excises shall be uniform throughout the United States, adopted the Troughton scale as the standard of length; the avoirdupois pound to be derived from the Troy pound of the Mint as the unit of mass. At the same time the Department adopted the wine gallon of 231 cubic inches for liquid measure and the Winchester bushel of 2150-42 cubic inches for dry measure. In 1836 the Secretary of the Treasury was authorized to cause a complete set of all weights and measures, adopted as standards by the Depart- ment for the use of custom-houses and for other purposes, to be delivered to the Governor of each State in the Union for the use of the States respectively, the object being to encourage uniformity of weights and measures throughout the Union. At this time several States had adopted standards differing from those used in the Treasury Department, but after a time these were rejected, and finally nearly all the States formally adopted by act of legislature the standards which had been put in their hands by the National Government. Thus a good degree of uniformity was secured, although Congress had not adopted a standard of mass or of length other than for coinage purposes as already described. “The next and in many respects the most important legislation upon the subject was the Act of July 28, 1866, making the use of the metric system lawful through- out the United States, and defining the weights and measures in common use in terms of the units of this system. This was the first genera/ legislation upon the subject, and the metric system was thus the first, and thus far the only system made generally legal throughout the country. “In 1875 an International Metric Convention was agreed upon by seventeen governments, including the United States, at which it was undertaken to establish and maintain at common expense a permanent International Bureau of Weights and Measures, the first object of which should be the preparation of a new inter- national standard metre and a new international standard kilogramme, copies of which should be made for distribution among the contributing governments. Since the organization of the Bureau, the United States has regularly contributed to its support, and in 1889 the copies of the new international prototypes were ready for distribution. This was effected by lot, and the United States received metres Nos. 21 and 27, and kilogrammes Nos. 4 and 20. The metres and kilo- grammes are made from the same material, which is an alloy of platinum with ten per cent of iridium. XXXvi UNITS. “On January 2, 1890, the seals which had been placed on metre No. 27 and kilogramme No. 20, at the International Bureau of Weights and Measures near Paris, were broken in the Cabinet room of the Executive Mansion by the Presi- dent of the United States, in the presence of the Secretary of State and the Secretary of the Treasury, together with a number of invited guests. They were thus adopted as the National Prototype Metre and Kilogramme. “The Troughton scale, which in the early part of the century had been tenta- tively adopted as a standard of length, has long been recognized as quite un- suitable for such use, owing to its faulty construction and the inferiority of its graduation. For many years, in standardizing length measures, recourse to copies of the imperial yard of Great Britain had been necessary, and to the copies of the metre of the archives in the Office of Weights and Measures. The standard of mass originally selected was likewise unfit for use for similar reasons, and had been practically ignored. “The recent receipt of the very accurate copies of the International Metric Standards, which are constructed in accord with the most advanced conceptions of modern metrology, enables comparisons to be made directly with those stand- ards, as the equations of the National Prototypes are accurately known. It has seemed, therefore, that greater stability in weights and measures, as well as much higher accuracy in their comparison, can be secured by accepting the international prototypes as the fundamental standards of length and mass. It was doubtless the intention of Congress that this should be done when the International Metric Convention was entered into in 1875; otherwise there would be nothing gained from the annual contributions to its support which the Government has con- stantly made. Such action will also have the great advantage of putting us in direct relation in our weights and measures with all civilized nations, most of which have adopted the metric system for exclusive use. The practical effect upon our customary weights and measures is, of course, nothing. The most care- ful study of the relation of the yard and the metre has failed thus far to show that the relation as defined by Congress in the Act of 1866 is in error. The pound as there defined, in its relation to the kilogramme, differs from the impe- rial pound of Great Britain by not more than one part in one hundred thousand, an error, if it be so called, which utterly vanishes in comparison with the allow- ances in all ordinary transactions. Only the most refined scientific research will demand a closer approximation, and in scientific work the kilogramme itself is now universally used, both in this country and in England.* * Note. — Reference to the Act of 1866 results in the establishment of the following :— Lquations. 3600 . 1 yard = °—~ metre 3937 lavoirdupois = ——— kil 1 pound avoirdupois = 57576 kilo. A more precise value of the English pound avoirdupois is 320462 kilo., differing from the above by about one part in one hundred thousand, but the equation established by law is sufficiently accurate for all ordinary conversions. As already stated, in work of high precision the kilogramme is now all but universally used, and no conversion is required. — UNITS. XXXVii “In view of these facts, and the absence of any material normal standards of customary weights and measures, the Office of Weights and Measures, with the approval of the Secretary of the Treasury, will in the future regard the Interna- tional Prototype Metre and Kilogramme as fundamental standards, and the cus- tomary units, the yard and the pound, will be derived therefrom in accordance with the Act of July 28, 1866. Indeed, this course has been practically forced upon this office for several years, but it is considered desirable to make this for- mal announcement for the information of all interested in the science of metrology or in measurements of precision. T. C. MENDENHALL, Superintendent of Standard Weights and Measures. “ Approved : je Ga CARLISLE, Secretary of the Treasury. April 5, 1893.” No ratios of the yard to the metre and of the pound to the kilogramme have as yet been adopted by international agreement; but precise values of these ratios wil] doubtless be determined and adopted within a few years by the International Bureau of Weights and Measures. In the mean time, it will suffice for most pur- poses to use the values of the ratios adopted provisionally by the Office of Stand- ard Weights and Measures of the United States. These values are — 1 yard = $§99 metres, or 1 metre = 3237 yards, 1 pound = 33998 kilogrammes, or 1 kilogramme = 72°48 pounds. These ratios were legalized by Act of Congress in 1866. Expressed decimally these values are * — I yard = 0.914 402 metres, 1 metre = 1.093 611 yards, 1 pound = 0.45 359 kilogrammes, 1 kilogramme = 2.20462 pounds. The above values of the relations of the standards of the British and Metric systems of units are adopted in this work. Tables 1 and 2 give the equivalents of multiples of the standard units and also equivalents of multiples of the derived units of surface and volume. These tables are published by the Office of Stand- ard Weights and Measures of the United States, and are here republished by per- mission of the Superintendent of that Office. 2. British MEASURES AND WEIGHTS. a. Linear measures. The unit of linear measure is the yard. Its principal sub-multiples and multi- ples are the inch; the foot; the rod, perch, or pole; the furlong ; and the mile. The following table exhibits the relations among these measures : — * The actual error of the relation of the yard to the metre may be as great as 1/200 oooth part, and the actual error of the relation of the pound to the kilogramme as great as 1/100 oooth part. XXXVIii UNITS. Inches, Feet. Yards. Furlongs. Miles. re 0.083 0.028 0.00505 0.00012626 0.0000157828 12 r. 0:633 0.06060 O.OOI51515 0.00018939 36 3. $2 0.1818 0.004545 0.00056818 198 16.5 5.5 us 0.025 0.003125 7920 660. 220. 40. I. O:125 63360 | 5280. 1760. 320. 8. Ta Other measures are the — Surveyor’s or Gunter’s chain = 4 rods = 66 feet = 100 links of 7.92 inches each. Fathom = 6 feet; Cable length = 120 fathoms. Hand = 4 inches; Palm = 3 inches; Span = g inches. b. Surface or square measures. The unit of square measure is the square yard. Its relations to the principal derived units in use are shown in the following table : — Gigs feet. | Sq. yards. Sq. rods. Roods. Acres. | Sq. miles. Is O.IIII 0.00367 309 0.000091827 0.000022957 9. Tr 0.0330579 0.000826448 0.000206612 272.25 30.25 I. 0.025 0.00625 10890. 210. 40. i 0.25 43500. 4840. 160. 4. I. 27878400 3097600. 102400. 2560. 640. 0 c. Measures of capacity. The unit of capacity for dry measure is the bushel (2150.4 cubic inches about). The units of capacity for liquid measure are the British gallon (of 277.3 cubic inches about) and the wine gallon (of 231 cubic inches, nominally). The latter gallon is most commonly used in the United States. The following table shows the relations of the sub-multiples and multiples of the bushel and gallon : — UNITS. XXXiX Dry Measures. Liquids. Pint = g; bushel. || Gill = 5 gall. Quart = 2 pints = 7, “ Pint = 4 gills wee ae Peck = 8 quarts = end latitudes of arc. Formula (4) will suffice for the calculation of any portion or the whole of a quadrant. The length of a quadrant is the value of the first term of (4) when ¢ = 45° and Ad = 90°, since all of the remaining terms vanish. Numerical examples. — 1°. Suppose d, = 0° and ¢. = 45°. Then api AG. Ad = 45°. log. cons’t 5-5618284 45 1.6532125 ist term + 16 407 443 feet ist term 7.2150409 cos 2h =.9.8 494850 — Io sin Ap 9.8 494850 — 10 cons’t 5.0269880 2d term — 53 205.7 feet 2dterm 4.7259580 The third term of the series vanishes by reason of the factor cos 4 ¢ = cos 90° —o. The sum of the first two terms, or length of a meridional arc from the equator to the parallel of 45°, is 16 354 237 feet. 2°. Suppose fi Sy ANG aehy —= Gore Then 2h: wens Ad = ABe. The numerical values of the terms will be the same as in the previous example, but the sign of the second term will be p/ws. Hence the length of the meridional arc between the parallel of 45° and the adjacent pole is 16 460649 feet. The sum of these two computed distances, or the length of a quadrant, is 32 814 886 TEEE. GEODESY. xlix This agrees as it should with the length given by (4) when 2¢ = go° and Ad ==90.” b. Arcs of parallel. The radius of any parallel of latitude is equal to the product of the radius of curvature of the normal section for the same latitude by the cosine of that lati- tude. That is, see Fic. 1, ~ being the radius of the parallel — + = Pn COS F, and the entire length of the parallel is — 27 — 2p, COS G: Designate the portion of a parallel lying between meridians whose longitudes are A, and A, by AP, and call the difference of longitude Ay — A,, AA, Then — Arc of parallel A? in feet. __2 7 Pn COS P= AX (in seconds), 1296000 a 2 = fe 05 AA (in minutes), (1) 27 py COS b f Secs AX (in degrees). log (2 z/1296000) = 4.6855749 — 10, log (2 7/21600) = 6.4637261 — Io, log (2 7/360) = 8.2418774 — 10. A,, A., = end longitudes of arc, AA =A,—A,, pn = radius of curvature of normal section for latitude of parallel; for log pr see Table 11. Numerical Example. — Suppose ¢ = 35°, and AX = 72°. Then from the third of (9) log. cons’t 8.2418774 — 10 Table 11, Pu 73221716 cos ¢ 9.9133645 — 10 AX 1.8573325 AP — 25264 S27 feet. AP 4.3325460 * The best formula for computing the entire length of a meridian curve is this: m(a+é6)(1t+42+ant+...), in which a, 6, and 2 are the same as defined in section 2. For the values here adopted — log. (1+ 222+...) 0.0000003 (a + d) 7.6209807 ™ 0.4971499 length 8.1181 309 The length of the perimeter of the generating ellipse, or the meridian circumference of the earth, is, therefore — 131 259 550 feet = 24 859.76 miles. ] GEODESY. The values of AP for intervals of 10”, 20” . . . 60”, and for 10’, 20’... are given in Table 18 for each degree of latitude from 0° to go°. 8. Rapius-VEcTOR OF EARTH’s SPHEROID. p = radius-vector =a(1 — 2¢ sin? ¢ + é& sin? 6)! (1 — é sin? ¢)-?. LC) erty 2 + p (m — n) cos 2h log p = log — tp (m? — n*) cos 4h +14 (m'® — n*) cos 66 For the adopted spheroid log (p in feet) = 7.3199520 + [3.86769] cos 2h — [1.2737] cos 44, the logarithms for the terms in ¢ corresponding to units of the seventh decimal place. Thus, for ¢6=o, log p = 7.3199520 aie a EOTGre — 18.8 =—= 7.32006 75,—0Pra, 9. AREAS OF ZONES AND QUADRILATERALS OF THE EARTH’S SURFACE. An expression for the area of a zone of the earth’s surface or of a quadrilateral bounded by meridians and parallels may be found in the following manner : — The area of an elementary zone ¢@7Z, whose middle latitude is ¢ and whose width is p,, dp, 1s (see Fic. 1), aZ —=27F pm ah == 2p iPaCOS Pile, By means of the relations in section 6 this becomes cos } a aL = 29 a CS) Ge Sea Si ae (1) 1—e ad(esin®d) Di EN ee = ae e (1 —e’sin® ¢)? The integral of this between limits corresponding to q¢, and ¢», or the area of a zone bounded by parallels whose latitudes are ¢, and ¢, respectively, is | ésin dy e sin ¢, ‘ I — é* sin? dy 1 — é’ sin? dy, I—é Z—=r a’ ake (2) | + 4 No. ee (x + esin d.) (1 — esin gy) 5 (i —esin ¢,) (1 +e sin 4) GEODESY. li To get the area of the entire surface of the spheroid, make ¢;= — 4 7 and ¢, =-+ 47in(2). The result is aod Ce é Surface of spheroid = 2 7 a? [ +- - ae Nap. log ( *) (3) For numerical applications it is most advantageous to express (3) in a series of powers of e. Thus, by Maclaurin’s theorem, 2 4 6 Surface of spheroid = 4 7 a ( ee eae =a iy (4) For the calculation of areas of zones and quadrilaterals it is also most advan- tageous to expand (2) in a series of powers of ¢ sin ¢, and ¢ sin ¢y and express the result in terms of multiples of the half sum and half difference of ¢, and ¢2. Thus, (2) readily assumes the form Z=27 a (1 — &) [ (sin gy — sin 4) re 2 (sin? d. — sin? ¢) +.. 4 From this, by substitution and reduction, there results Pre eg ete er aay ) eae aa) Ceeos sa sin § Ag — - (5 wherein b = (do + 41); Ad = $2 — d1, 2 4 6 Gao (1— —- 2-5 y) C= 2 canna (6) 2—=2a°\— ieee tose ee : se é a=re@Be+ly...), If Q be the area of a quadrilateral bounded by the parallels whose latitudes are ¢, and ¢, and by meridians whose difference of longitude is AA, Ar Oo 27 Z. Hence, using the English mile as unit of length, (5) and (6) give for the adopted spheroid — Area of quadrilateral in square miles. me he q cos ¢ sin } Ad — & cos 3¢ sin $ Ad ) Q = Ad (in degrees) id eoswasm Ad =... \ log a* = 5.7375398; (7) log ¢ == 2.79173, log ¢; = 9-976 — Io. ¢=4(¢.+ >); Ad = $, — ,, $,, ~, = latitudes of bounding parallels, Ad = difference of longitude of bounding meridians. * ¢,, Cy, ¢; are obtained from C,, C,, C, respectively by dividing the latter by the number of degrees in the radius, viz: 57.29578. ii ; GEODESY. Numerical examples. —1°. Suppose ¢, = 0, $2 = go° and AA = 360°. Then (7) should give the area of a hemispheroid. The calculation runs thus : log. log. log. 4 5-7375398 C2 2.79173 és 9.976 — 10 cos ¢ 9.8494850 — 10 cos3 ¢ 9.84948,— 10 cos5¢ 9.849, — 10 sin } Ad 9.8494850 — 10 sin 3 Ad 9.84949 — 10 sin § Ad 9.848, — 10 360 2.5563025 360 2.55630 360 2.556 Sum 7.9928123 5-04700, 2.229 Hence — ist term = + 98358591 2d term=-+ 111429 3d term = + 169 C= sum = 98470189 Twice this is the area of the spheroidal surface of the earth; 2 ¢., 196 940 378 square miles. ° 2°, The last result may be checked by (4). Thus, ee e (= + 7 +... ) = 0.00225928 e log (: aie ) = 9.9990177 log a? == 7.190072 log 4 7 = 1.0992099 log (196940407) = 8.2943348 This number agrees with the number derived above as closely as 7-place logarithms will permit, the discrepancy between the two values being about soodooo Part of the area. Hence, with a precision somewhat greater than the precision of the elements of the adopted spheroid warrants, Area earth’s surface = 196 940 400 square miles. The areas of quadrilaterals of the earth’s surface bounded by meridians and parallels of 1°, 30’, 15’, and 10’ extent respectively, in latitude and longitude, are given in Tables 25 to 29. 10. SPHERES OF EquaL VoLUME AND EQUAL SURFACE WITH EarTH’s SPHEROID. 7, = radius of sphere having same volume as the earth’s spheroid, 7%, = radius of sphere having same surface as that spheroid. 8/92 r, = V/a*b —= 2 —12°-—Wwae rege oe —-..). GEODESY. liii ( ou ee éé )} 1% —2 nee eee eee : 5 eo 5 = a(t — fe — why ef — shh oo — .-.). a—n7=— jaf i+ Wwe+...) 0.00173 a, about. %, — 1, = zy ae* +... == 0.000001 a, about. II. CO-ORDINATES FOR THE PoLyconic PROJECTION oF Maps. In the polyconic system of map projection every parallel of latitude appears on the map as the developed circumference of the base of a right cone tangent to the spheroid along that parallel. Thus the parallel #/ (Fic. 2) will appear in projection as the arc of a circle LOF (Fic. 3) whose radius OG = is equal to the slant height of the tangent cone ZG (Fic. 2). Evidently one meridian and only one will appear as a straight line. This meridian is generally made the central meridian of the area tral meridian between consecutive parallels are made equal (on the scale of the map) to the real A distances along the surface of the spheroid. The circles in which the parallels are developed are not concentric, but their centres all lie on the central meridian. The meridians are concave a toward the central meridian, and, except near the corners of maps showing large areas, they cross the paral- lels at angles differing little from right angles. In the practical work of map making, the meridians and parallels are most ad- vantageously defined by the co-ordinates of their points of intersection. These co- ordinates may be expressed in the following manner: For any parallel, as HOF (Fic. 3), take the origin O at the intersection with the central meridian, and let the rectangular axes of Y (OG) and X (OQ) be re- spectively coincident with and perpendicular to this meridian. Call the interval in longitude between the central meridian and the next adjacent one AA, and - denote the angle at the centre: G subtended by the developed arc OP by a. liv GEODESY. Then from Fic. 3 it appears that C2 Sie y = 2 /sin?* ha. But from Fics. 2 and 3, = p, cot ¢, fa, 7 AX —— po Anicosi, whence a = Ad sin ¢. Hence, in terms of known quantities there result x = p, cot ¢ sin (AA sin ¢), Jy = 2 p, cot ¢ sin? } (Ad sin ¢). (1) Numerical example. — Suppose ¢ = 40° and AX = 25° = goooo”. Then log goooo” = 4.9542425, log sin 40° = 9.8080675 — Io, log578c0."83) == 4,7623100' AX sind = 16° 04’ 10.”88, 4 (AA sind) = 8° 02’ 05,44. log. log. sin (AX sin d) 9.4421760 — 10 sin } (AX sin #) 9.1454305 — 10 cot ¢ 0.0761865 sin 4 (AX sin #) 9.1454305 — 10 Pn lable 11 7.3212956 cot ¢ 0.0761865 Pn Table 11 7.3212956 2 0.3010300 x 6.8396581 vy 5-9893731 x = 6 912 865 feet y= 975 826 feet. The equations (1) are exact expressions for the co-ordinates. But when AX is small, one may use the first terms in the expansions of sin (AA sin ¢) and sin? }(AX sin @) and reach results of a much simpler form. Thus, sin (AA sind?) =AdAsingd — A(Arsingd)F+..., . sin? 3(A¢ sin ¢) = }(AA sin f)? — ~g(AA sin d)*+...; whence, to terms of the second order, x = p, AA cos $ [1 — ¥(AX sin ¢)?], Y =p, (Ad)? sin 2¢ [1 — Py(AA sing)? ]. If the terms of the second order in these equations be neglected, the value of x will be too great by an amount somewhat less than }(AA sin ¢)?. x, and the value of y will be too great by an amount somewhat less than y4(AQ sin ¢)?. y. An idea of the magnitudes of these fractions of « and y may be gained from the following table, which gives the values of }(AX sin ¢)* for a few values of the arguments AX and ¢. (2) GEODESY. lv Values of ¥(AX sin $)*. $ AX 20° | 40 I 1/168000 1/47700 2 1/42000 1/11g0b 3 1/18700 1/5300 It appears from this table that the first terms of (2) will suffice in computing the co-ordinates for projection of all maps on ordinary scales, and of less extent in longitude than 2° from the middle meridian. For example, the value of x for AX = 2°, and ¢ = 40°, and for a scale of two miles to one inch (1/126720), is 53.063 inches less 1/11900 part, or about 0.004 inch, which may properly be . regarded as a vanishing quantity in map construction. For the computation of the co-ordinates given in the tables 19 to 24, where AA does not exceed 1°, it is amply sufficient, therefore, to use Xx = Pn AX cos d, ( ) y = p, (AA)? sin 2¢. 2 In these formulas and in (2), if AA is expressed in seconds, minutes, or degrees, it must be divided by the number of seconds, minutes, or degrees in the radius. The logarithms of the reciprocals of these numbers are given on p. xlvi. In the construction of tables like 19 to 24, it is most convenient, when English units are used, to express AX in minutes and x and yininches. For this purpose, sup- posing log p, to be taken from Table 11, if s be the scale of the map, or scale factor, equations (3) become — Co-ordinates x and y in inches for scale s. I2 a ee ey ace O—Haaqqey Sonat S ote: — ed a (AA) SI 2 Y= Gagr-rary OS OY sin ag, AX in minutes ; (4) log (12/3437-747) == 7.54291 — 10, log (3/(3437-747)') = 3-4046 — ro. Tables 19 to 24 give the values of x and _y for various scales and for the zone of the earth’s surface lying between o° and 80°. Numerical example. — Suppose ¢ = 40° and AX = 15’; and let the scale of the map be one mile to the inch, or s = 1/63360. Then the calculation by (4) runs thus : lvi GEODESY. log. log. cons't 7.54291 — 10 cons’t 3.4046 — Io Pn 732130 Pn 7-3213 S 5-19818 — 10 s 5.1982 — 10 15 1.17609 (75)? 23522 cos ¢ 9.88425 — Io sin 2¢ 9.9934 — 10 os 1.122472 y 8.2697 — 10 In. In. 113-206 == /O;0186r. These values of x and y, it will be observed, agree with those corresponding to the same arguments in Table 22. When many values for the same scale are to be computed, log s should, of course, be combined with the constant logarithms of (4). Moreover, since in (4) x varies as AX and y as (AX)*, when several pairs of co-ordinates are to be com- puted for the same latitude, it will be most advantageous to compute the pair cor- responding to the greatest common divisor of the several values of AA and derive the other pairs by direct multiplication. 12. LINES ON A SPHEROID. The most important lines on a spheroid used in geodesy are (a) the curve of a vertical section ; (4) the geodesic line ; and (¢) the alignment curve. Imagine two points in the surface of a spheroid, and denote them by /, and P, respectively. The vertical plane at /, containing /, and the vertical plane at ?, containing *, give vertical section curves or lines. The curves cut out by these two planes coincide only when /, and /, are in a meridian plane. The geodesic line is the shortest line joining /, and /,, and lying in the surface of the spheroid. The alignment curve on a spheroid is a curve whose vertical tangent plane at every point of its length contains the terminal points “, and A. The curve (2) lies wholly in one plane, while (4) and (c) are curves of double curvature. In the case of a triangle formed by joining three points on a spheroid by lines lying in its surface, the curves of class (a) give two distinct sets of triangle sides, while the curves of classes (4) and (c) give but one set of sides each. For all intervisible points on the surface of the earth, these different lines differ immaterially in length; the only appreciable differences they present are in their azimuths (see formula under b below). Of the three classes of curves the first two only are of special importance. a. Characteristic property of curves of vertical section. Let 4,2 = azimuth of vertical section at /, through P,, a2, —= azimuth of vertical section at /, through /,, 6,, 6, = reduced latitudes of /, and P, respectively, 6, 6, = angles of depression at /, and P, respectively of the chord joining these points. Then the characteristic property of the vertical section curve joining /, and /, is Sin a2 cos 6, cos 6, = sin (a,,; — 180°) cos & cos 6. GEODESY. lvii The azimuths a, and a,,, it will be observed, are the astronomical azimuths, or the azimuths which would be determined astronomically by means of an alti- tude and azimuth instrument. b. Characteristic property of geodesic line. Let a’). == azimuth of geodesic line at /,, a’,,; == azimuth of geodesic line at /, 6,, 6. = reduced latitudes of /, and /, respectively. Then the characteristic property of the geodesic line is sin a, cos 6; = sin (180°—ay,) cos 6 = cos A, where @ is the reduced latitude of the point where the geodesic through /, and P, is at right angles to a meridian plane. The difference between the astronomical azimuth a,, and the geodesic azimuth a';» is expressed by the following formula: 2 . S. ° Cp Q15 (in seconds) — ys p" e? (;) cos? @ sin 20) 99 a where s = length of geodesic line P, P,, @ = major semi-axis of spheroid, e= eccentricity of spheroid, pr == 206204.'8: = astronomical latitude of P,, a, == azimuth (astronomical or geodesic) of P; P,, 2 log ys p” ({) = 7.4244 — 20, for a in feet. Thus, for ¢ =o and a,.,= 45°, for which cos? ¢ sin 2a;, = 1, the above for- mula gives Q1.9 — @ 19 = 0."074, for s = 100 miles, —G290, for 5 = 200 miles; ee so that for most geodetic work this difference is of little if any importance. 13. SOLUTION OF SPHEROIDAL TRIANGLES. . The data for solution of a spheroidal triangle ordinarily presented are the measured angles and the length of one side. ‘This latter may be either a geodesic line or a vertical section curve, since their lengths are in general sensibly equal. Such triangles are most conveniently solved in accordance with the rule afforded by Legendre’s theorem, which asserts that the sides of a spheroidal triangle (of any measurable size on the earth) are sensibly equal to the sides of a plane triangle having a base of the same length and angles equal respectively to the spheroidal angles diminished each by one third of the excess of the spheroidal triangle. In other words, the computation of spheroidal triangles is thus made to depend on the computation of plane triangles. lviii GEODESY. a. Spherical or spheroidal excess. The excess of a spheroidal triangle of ordinary extent on the earth is given by ; — yi « (in seconds) = p one where .S is the area of the spheroidal or corresponding plane triangle; p,, p, are the principal radii of curvature for the mean latitude of the vertices of the tri- angle ; and p” = 206 264."8. For a sphere, pm, == p, = radius of the sphere, Denote the angles of the spheroidal triangle by 4, B, C, respectively ; the cor- responding angles of the plane triangle by a, B, y (as on p. xviii); and the sides common to the two triangles by a, 6,¢. Then S=tabsny=—}bcesna=taasin B. a=A—te B=B—ie y= C—te Tables 13 and 14 give the values of log (p’/2p,,p,) for intervals of 1° of astro- nomical or geographical latitude.* 14. GEroDETIC DIFFERENCES OF LATITUDE, LONGITUDE, AND AZIMUTH. a. Primary triangulation. Denote two points on the surface of the earth’s spheroid by /, and /, respec- tively. Let s = length of geodesic line joining /, and /,, ¢, $2 = astronomical latitudes of 7; and P,, Ay, Ay = longitudes of /, and /,, AA = A.—A,, a). = azimuth of FP, P, (s) at A, 02, == azimuth of P, F, (s) at A, e = eccentricity of spheroid, Pms Pn == principal (meridian and normal) radii of curvature at the point /,. Then for the longest sides of measurable triangles on the earth the following formulas will give dy, As, and ag; in terms of qj, Aj, a2, and s. The azimuths are astronomical, and are reckoned from the south by way of the west through 360°. a’ = 180° — ayo, and ay; = 180° + a”, for a5 <180° I a’ = a,,— 180°, and a); = 180° —a", fOr Gyy Se 10Os " 1 +4 a (°) ‘cos ¢h, Cos” ak (2) Pn t "Te" Np, : ‘ aie c=4 < 2 cos? ¢, sin 2a! (3) * For the solution of very large triangles and for a full treatment of the theory thereof, consult Die Mathematischen und Physikalischen Theoricen der Hoheren Geoddsie, von Dr. F. R. Helmert. Leipzig, 1880, 1884. GEODESY. lix 1 ° tial AN pe CUS sO g) tan 3(a + +é cos 1(go° = am =- ”) cot x o ae (4) ur sin » oO —, — ’ tan $(a” — AA + 0) = nie cot ha __s sin }(a” —a +0) P aM ; ee cde ag ae rn co hey ee > G) To express », & and ¢,— ¢; in seconds of arc we must multiply the right hand sides of (2), (3), and (5) by p” = 206 264.”8. For logarithmic compution of 1’ and @”, or and ¢ in seconds, we may write with an accuracy generally sufficient log 4” = log (p"s/pn) 4+ $ — (=) cos” ¢, Cos? a’, (6) fh e " : ' log ¢” = log } G—)_p" + log {(7’")? cos? ¢, sin 2 a’}, (7) where in (6) is the modulus of common logarithms, For units of the 7th deci- mal place of log 7” we have for the adopted spheroid e” BB 7 a= 3-69309. 1 log g Also e (1 — e*)p’ Similarly, for the computation of the logarithm of the last factor in (5) we have = 1.91697 — Io. bl log log {1 + rz 9° cos? 3(a” — a’)} = log {1 + aa (7'")” cos* 3(a” — a')}. Putting for brevity i 1 ' = aa" (7)? cos? 3(a” — a’) the logarithm of the desired logarithm is given to terms of the second order inclusive in g by log log (1 + 4) = logpg— 3g. For the adopted spheroid log —" . —= 4.92 — 10 D> Toa") 9 975 for units of the seventh decimal place. For a line 200 miles (about 320 kilometres) long, the maximum value of the second term in (6) is but 12.6 units in the 7th place of log 7’. For the same length of line, the maximum value of &” is 0.895, and the maximum value of the logarithm of the last factor in (5), or log (1 +g), is less than g22 units in the seventh place of decimals. For computing differences of latitude, longitude, and azimuth in primary triangulation whose sides are 1° (about 70 miles, or roo kilometres) or less in length, the most convenient means are formulas giving ¢y— q), A, — Ay, and Ix GEODESY. a), — (180° — a,9), in series proceeding according to powers of the distance s. Formulas of this kind with convenient tables for facilitating the computations are given in the Reports of the U. S. Coast and Geodetic Survey.* b. Secondary triangulation. For secondary triangulation, wherein the sides are 12 miles (20 kilometres) or less in length, and wherein differences of latitude and longitude are needed to the nearest hundredth of a second only, the following formulas may suffice. Using the same notation as in the preceding section, the formulas are : — oo = $1 es Ad, Ay =A, + Ad, (1) ay, = 180° + ayy = Aa, Ad = — @ S$ COS a9 — ay S* Sin? ayo, Ad = + 4b sec ¢, 5 sin ay. — dy Ss? sin a1. COS ay, (2) Aa = — ¢ tan ¢) 5 Sin ayy+ G s* sin a5 COS ay». The constants entering the latter equations are defined by the following expressions, wherein p,, and p, are the principal radii of curvature of the spheroid at the point whose latitude is ¢, and p” = 206 264.8: p” pl Qs — —; 4=4=>-, Pm Pn pee p” tan ¢, pos p”’ sec d, tan ¢, a p' (1+ 2 tan? d)) a eo en os ca eee 2 Pm Pn Pro a Pr The logarithms of the factors a, 3), 4, @2, d, ¢, are given in Table 1s for the English foot as unit, and in Table 16 for the metre as unit, the argument being the initial latitude ¢, for all of them. When all of the differences given by (2) are computed, they may be checked by the formula sin 3(¢, + 4) = = (3) For convenience of reference in numerical applications of the above formulas, (2) may be written thus: Ad A, + A,, A\ = &,+ B,, Aa — G -- Co in which, for example, 4, and A, are the first and second terms respectively of A¢, due regard being paid to the signs of the functions of a». Numerical example. The following example will serve to illustrate the use of formulas (1) to (3). The value of log s is for s in English feet, s being in this case about 12.3 miles. fi, 38° 54’ 08."38 , 88° 03’ 24."15 a. 43° o1' 46."29 Ap = —07' 50."21 AX +009! 20."22 Aa —os5! 51./32 do 38° 46'18."17 Ag 88° 12’ 44."39 a, 222° 55’ 5 4."97 £ ($2 $i) 38° 50! 13."27 * See Appendix 7, Report of 1884, for latest edition of these tables. GEODESY. lxi log log log log S§ 4.81308 S$ 4.81308 § SIN a,9 4.647 S$ SIN a,9 4.647 COS a9 9.86392 SiN ay 9.83402 § SiN a9 4.647 $ COS 9 4.677 @ 7.99495 sec ¢, 0.10890 az 0.279 b, 0.688 b, 7.99316 630.733 A, 2.67195 By, 2.74916 Ay 9.573 By 0,012 sin $1 9-79795 Cz 0.057 C, 2.54711 log A, — 469.84 B, + 561. i C, — 352.46 Aa 2.54570 A,— 0."37 B,— 1."03 G+ 1./14 AX 2.74836 Ag — 470.21 AX + 560."22 Aa — 351."32 sin $(¢2 + $1) 9-79734 15. IRIGONOMETRIC LEVELING. a. Computation of heights from observed zenith distances. Let s = sea level distance between two points /, and P,, f7,, H, = heights above sea level of /, and F,, 2, = observed zenith distance of /, from 7, Z, = observed zenith distance of P, from /,, p = radius of curvature of vertical section at /, through /,, or at 2, through /,, the curvature being sensibly the same for both for this purpose, C = angle at centre of curvature subtended by s, M,, Mm, = coefficients of refraction at P, and f,, Az,, Az, = angles of refraction at A, and F,. Then, the fundamental relations are s — a Az —==7,6, Az, = mC, 2 + % + Az, + Az = 180° + C, ae (1) ea When the zenith distances z, and z, are simultaneous, or when Az, and Az, are assumed to be equal, (2) becomes ff, — H,=s tan }(z + Az, — 2, — Az) (: + Hore as et ate) & For the case of a single observed zenith distance 2, say, and a known or assumed value of # = m, = m, the following formula may be applied : 2m fT, — H, = s cot z, +} —— — et ae cot? z 2). (4) The coefficient of refraction m varies very greatly under different atmospheric conditions. Its average value for land lines is about 0.07. The following table gives the values of log 3(1 — 2 m) and log (1 — m) for values of m ranging from 0.05 too.10o. It is taken from Appendix 18, Report of U. S. Coast and Geodetic Ixii GEODESY. Survey for 1876. Table 12 taken from the same source gives values of log p needed for use in (3) and (4). Zable of values of log (1 — 2 m) and log (1 — my). mm log (1 — 2m). | log (1 — m). m log #(1 —2m). | log (1 — m). | 0.050 9-65321 9.978 0.075 9.62839 9.966 51 65225 77 76 62737 66 52 65128 TT 77 62634 65 3 65031 76 78 62531 65 54 64933 76 79 62428 64 0.055 9.64836 9-975 0.080 9.62325 9.964. 56 64738 nS 81 62221 63 Ey 64640 75 82 62118 63 58 64542 74, 83 62014 62 59 64444 74 84 61910 62 0.060 9.64345 9-973 0.085 9.61805 9.961 61 64246 73 86 61700 61 62 64147 2 87 61595 60 63 64048 72 88 61490 60 64 63949 7a 89 61384 60 0.065 9.63849 9.971 0.090 9:61278 9.959 66 63749 7° gt 61172 59 67 63649 70 g2 61066 58 68 63548 - 69 93 60959 58 69 63448 69 94 60853 57 0.070 9-63347 9-968 0-095 9-607 46 9-957 71 63246 68 96 60638 56 72 63144 68 97 60531 56 73 63043 67 98 60423 55 74 62941 67 99 60315 55 0.100 9.60206 9-954 For less precise work one may use equation (4) in the form ff, — H,=s cot 2, + ¢ s?, (5) wherein, if we make 7 = 0.07 and use for p its average value, or ¥ p,, p,, for a latitude 45°, log ¢ = 2.313 — 10 for s in feet, = 2.829 — to for s in metres. - Thus, for a distance (s) of 10 miles the value of the term ¢s? in (s) is 57.3 feet. If altitudes o,, say, are observed in the place of zenith distances 2, it is most convenient to write (5) thus : — | i, — M,=+5 tang +s’, (6) GEODESY. Ixiii where the upper sign is used when a is an angle of elevation and the lower sign when a, is an angle of depression. b. Coefficients of refraction. When 2; and 2, are both observed for a given line, a coefficient of refraction may be computed from the assumption of equality of coefficients at the two ends of the line. Thus, equations (1) give Az, + Az, = 180° + C — (@, + %), or s oy ar aw (m, + my) as 180° + aa (a, + %), whence my + my, = 1 — (2 + 2, — 180°). Assuming mm, = m, = m, and supposing 2 ++ 2% — 180° expressed in seconds of arc, ( p °7 m=t51-—-——ae 2, — 180 : eat sp” ‘ a ) p’= 206264. 8, log p == 5-31 44261. c. Dip and distance of sea horizon. Let h = height of eye above sea level, 5 = dip or angle of depression of horizon, s == distance of horizon from observer. Then 8 (in seconds) = 58.82 y/ in feet, = 106.54 ¥/ in metres. s (in miles) = 1.317 Vz in feet, s (in kilometres) = 3.839 V4 in metres. The above formulas take account of curvature and refraction. They depend on the value 0.0784 for the coefficient of refraction, and are quite as accurate as the uncertainties in such data justify. For convenience of memory, and for an accuracy amply sufficient in most cases, the coefficients of the radicals in the last two formulas may be written 4 and 1 respectively. 16. MuiIscELLANEOUS FORMULAS. a. Correction to observed angle for eccentric position of instrument Let C’ be the eccentric position of the instrument, and Cy the observed value of the angle at that point between two other points 4 and 2. Let C denote the central point as well as the angle ACA desired. Call the distance CC’ ~ and denote the angle ACC’ by 6. Denote the lines BC and AC, which are as- sumed to be sensibly the same as BC’ and AC’, by a and 4 respectively. Then lxiv GEODESY. we = Ae fs C— C, (in seconds) = eee ae = oe p” = 206 264."8, log pir st AAare. Attention must be paid to the signs of sin (@ —C,) and sin @, and to the fact that angles are counted from 4 towards & through 360°. A diagram drawn in accordance with the above specifications will elucidate any special case. b. Reduction of measured base to sea level. Let 7 be the length of the bar, tape or other unit used in measuring the base. Let 7, be the corresponding length reduced to sea level for a height %, this latter being the observed height of 2. Then if p denote the radius of curvature of the earth’s surface in the direction of the base, _ Nao 2 i Rae 4 —_— p -e h a (: ss p + eee )e with sufficient accuracy. Hence, for the whole length of the base, I SS) If Z denote the total measured length, Z, the corresponding total sea level length, and // the mean value of the heights /, the above equation gives Tiel eee p c. The three-point problem. In this problem the positions of three points 4, 2, C, and hence the elements of the triangle they form, are given together with the two angles APC and BPC at a point P whose position is required. Denote the angles and the sides of the known triangle by 4, B, C, and a, 4, ¢, respectively. Also put AFC=B, BPC—a, PACH a, PRC ==. Then the sum of the angles in the quadrilateral PACB is a+ B+ «+ y+ C= 360°, Ma ++ 9) = 180° — H(a-+ B+ C). (1) Compute an auxiliary angle z from the equation whence asin Bp, tanz=73no? (2) Then tan $(* — y) = tan (2 — 45°) tan $(x + 9). (3) These three equations give all the data essential to a complete determination of the position of . Any special case should be elucidated by a diagram drawn in accordance with the specifications given above. GEODESY. lxv When the positions of the points 4, 4, C are given on a map, the position of FP on the same map may be found graphically by drawing lines making angles with each other equal to the given angles a and £ from a point on a piece of tracing paper, and then placing this tracing on the mapso as to meet the required conditions. This ready method of solving the problem is often sufficient. 17. SALIENT Facts or PuysicaAL GEODESY. a. Area of earth’s surface, areas of continents, area of oceans.* Square miles. Potalarea of earth's surface). . = 4% <, .« 196:940.000 Breacontinent of Furope.. 6 essa) %s 3 820 000 ¢ as ASIA 2p) s) cud eee jae Se Pay 22 010CR a ATTICA ss he: eae ee de TACO OOS a +h Australia’. 6.0 see vhs 3 406 000 = a AMET CAT sia ek fe) a 4s ES GROIGOO (otal area Of continents ©.) = 2 «9. 4 < “52886 cco “otal akea Of OCGans’ 4.7. 4. "ss i. = TAR ehgoc0 b. Average heights of continents and depths of oceans.f Feet. Metres. Average height of continent of Europe . . . . 980 300 = < a INSIAy cow hee) a, een LOA 500 “ - AGPiCa 5 pos" %, = |) LAO 500 oh Be << UStrAliaae cn

    g0°, or when the declination (8) of the star is negative. c. By equal altitudes of a star. By this method, when a fixed star is observed first east of the meridian and then west of the meridian at the same altitude, the direction of the meridian will * In precise work the computed azimuth requires the following correction for daily aberration, namely :— where A is to be reckoned from the south by way of the west through 360°. Ixxxii ASTRONOMY. obviously be given by the mean of the azimuth circle readings for the two observed directions. ‘This process will thus give the direction of the meridian free from the effect of any instrumental errors common to the equal altitudes observed. Neither does it require any knowledge of the star’s position (right ascension and declination). It is therefore available to one provided with no- thing but an instrument for measuring altitudes and azimuths, and is susceptible of considerable precision when a series of such equal altitudes is carefully referred to a terrestrial mark. When the sun is observed, it is essential to take account of its change in declination between the first and the second observation. Let 4, and A, be the true azimuths counted from the meridian toward the east and west respectively at the times 4 and 4, of the two observations. Also, let Ad be the increase in declination of the sun in the interval (4— 4). Then Ad Ap — ‘ "~~ cos $ sin 3(% — 4) Calling the azimuth circle readings for the east and west observations A, and FR», respectively, the resulting azimuths are A; = $(Re —- ke) ai }(A, “Be A,), A, = }(R, — Ry) + (A, — Ai). References. Many excellent treatises on spherical and practical astronomy are available. Among these the most complete are the following : — “A Manual of Spherical and Practical Astronomy,” by William Chauvenet. Philadelphia: J. B. Lippincott & Co., 2 vols., 8vo, 5th ed., 1887. “A Treatise on Practical Astronomy, as applied to Astronomy and Geodesy,” by C. L. Doo- little. New York: John Wiley & Sons, 8vo, 2d ed., 1888. ‘Lehrbuch der Spharischen Astronomie,” von F. Briinnow. Berlin: Fred. Dumler, 8vo, 1851. “ Spherical Astronomy,” by F. Briinnow. ‘Translated by the author from the second German edition. London: Asher & Co., 8vo, 1865. THEORY OF ERRORS. 1. Laws oF ERROR. Tue theory of errors is that branch of mathematical science which considers the nature and extent of errors in derived quantities due to errors in the data on which such quantities depend. A law of error is a relation between the magni- tude of an error and the probability of its occurrence. ‘The simplest case of a law of error is that in which all possible errors (in the system of errors) are equally likely to occur. An example of such a case is had in the errors of tabular logarithms, natural trigonometric functions, etc. ; all errors from zero to a half unit in the last tabular place being equally likely to occur. When quantities subject to errors following simple laws are combined in any manner, the law of error of the quantity resulting from the combination is in general more complex than that of either component. Let « denote the magnitude of any error in a system of errors whose law of error is defined by ¢(c). Then if « vary continuously the probability of its occurrence will be expressed by ¢(e)de. If ¢ vary continuously between equal positive and negative limits whose magnitude is @, the sum of all the probabili- ties (<)de must be unity, or +a fs de— is For the case of tabular logarithms, etc., alluded to above, («) = ¢, a constant whose value is 1/(2 @) = 1, since a = 0.5. For the case of a logarithm interpolated between two consecutive tabular values, by the formula v =z, + (v, — 7) f= 7 (1 — 7) + % 4, where 2, and v» are the tabular values, and ¢ the interval between v, and the derived value v, #(e) has the following remarkable forms when the extra decimals (practically the first of them) in (v, — 7) ¢ are retained : — 1 p(<) = es for values of « between — 4 and — (4 — 4), = — for values of « between — (4 — ¢) and+ (4 — 4), (1) $ — ae for values of « between + (4 — #) and-+ }. Ixxxiv THEORY OF ERRORS. It thus appears that ¢(c) in this case is represented by the upper base and the two sides of a trapezoid. When, as is usually the practice, the quantity (v7, — 7) ¢ is rounded to the nearest unit of the last tabular place, ¢(€) becomes more complex, but is still represented by a series of straight lines. It is worthy of remark that the latter species of interpolated value is considerably less precise than the former, wherein an additional figure beyond the last tabular place is retained. When an infinite number of infinitesimal errors, each subject to the law of con- stant probability and each as likely to be positive as negative, are combined by addition, the law of the resultant error is of remarkable simplicity and generality. It is expressed by Be ohne : ear (2) where ¢ is the Napierian base, 7 = 3.14159 +, and / is a constant dependent on the relative magnitude of the errors in the system. ‘This is the law of error of least squares. It is the law followed more or less closely by most species of observational errors. Its general use is justified by experience rather than by mathematical deduction. a. Probable, mean, and average errors. For the purposes of comparison of different systems of errors following the same law, three different terms are in use. These are the probable error,* or that error in the system which is as likely to be exceeded as not; the mean error, or that error which is the square root of the mean of the squares of all errors in the system; and the average error, which is the average, regardless of sign, of all errors in the system. Denote these errors by €, €n. €a, respectively. Then in all systems in which positive and negative errors of equal magnitude are equally likely to occur, and in which the limits of error are denoted by — a and -+} a, the analytical definitions of the probable, mean, and average errors are : — =< 0 + ¢ 4a fH de= [HJ de= [HO d= [HOe=}, i Hy : a 3) Cn= (HO ed, a= fo ede mene * The reader should observe that the word probable is here used in a specially technical sense. Thus, the probable error is not “the most probable error,” nor “the most probable value of the actual error,” etc., as commonly interpreted. THEORY OF ERRORS. Ixxxv b. Probable, mean, average, and maximum actual errors of interpo- lated logarithms, trigonometric functions, etc. When values of logarithms, etc., are interpolated from numerical tables by means of first differences, as explained above, the probable and other errors depend on the magnitude of the interpolating factor. Thus, the interpolated value is v= y+ (%— un) ¢ where 7, and 7 are consecutive tabular values and ¢ is the interpolating factor. For the species of interpolated value wherein the quantity (v2 — v%) ¢ is not rounded to the nearest unit of the last tabular place (or wherein the next figure beyond that place is retained) the maximum possible actual error is 0.5 of a unit of the last tabular place, and formulas (1) and (3) show that the probable, mean, and average errors are given by the following expressions : — - =+t(1—2) for ¢ between o and }, =}-4 A/2t (1—7) for ¢ between } and 3, = Gs for ¢ between 3 and tr. eae (1 — 2 ft )t 7 96 (1 —A)z¢ 1 — (1 — 27) = a= 2 F for ¢ between o and }, 1 — (2¢—1)8 ra aA Nz for ¢ between } and r. It thus appears that the probable error of an interpolated value of the species under consideration decreases from 0.25 to 0.15 of a unit of the last tabular place as ¢ increases from o to o.s. Hence such interpolated values are more precise than tabular values. For the species of interpolated values ordinarily used, wherein (v2 — %}) ¢ is rounded to the nearest unit of the last tabular place, the probable, mean, and average errors are greater than the corresponding errors for tabular values. The laws of error for this ordinary species of interpolated value are similar to but in general more complex than those defined by equations (1). It must suffice here to give the practical results which flow from these laws for special values of the interpolating factor 7* The following table gives the probable, mean, average, and maximum actual error of such interpolated values for = 1, 4, 3,... py It will be observed that ¢= 1 corresponds to a tabular value. * For the theory of the errors of this species of interpolated values see Annals of Mathematics, vol. ii. pp. 54-59. Ixxxvi THEORY OF ERRORS. Characteristic Errors of Interpolated Logarithms, ete. Interpolating o Probable Mean Average factor error error error Maximum actual z | é, ‘e e error | I 0.250 0.289 0.250 4 4 .292 408 233 I 3 .256 347 .287 é $ -276 382 3313 I 4 .268 .370 303 5 $ 277 385 Pas I : 274 380 311 i | $ 279 389 318 I | $ 278 386 316 te po 281 392 320 I 2. THe Metuop or LEAstT SQUARES. a. General statement of method. When the errors to which observed quantities are subject follow the law ex- pressed by d(e) = — ze el . a unique method results for the computation of the most probable values of the observed quantities and of quantities dependent on the observed quantities. The method requires that the sum of the weighted squares of the corrections to the observed quantities shall be a minimum,* subject to whatever theoretical condi- tions the corrections must satisfy. These conditions are of two kinds, namely, those expressing relations between the corrections only, and those expressing relations between the corrections and other unknown quantities whose values are disposable in determining the minimum. A familiar illustration of the first class of conditions is presented by the case of a triangle each of whose angles is mea- sured, the condition being that the sum of the corrections is a constant. An equally familiar illustration of the second class of conditions is found in the case where the sum and difference of two unknown quantities are separately observed ; in this case the two unknowns are to be found along with the corrections. Mathematically, the general problem of least squares may be stated in two * Hence the term least squares. t THEORY OF ERRORS. Ixxxvii equations. Thus, let x, y,2,.. . be the observed quantities with weights 4, g, r,.... Let the corrections to the observed quantities be denoted by Ax, Ay, Az, ...; so that the corrected quantities are x + Ax, y+ Ay, z+ Az,.... Let the disposable quantities whose values are to be determined along with the correc- tions be denoted by & 7, ¢,.... Then, the theoretical conditions which must be satisfied by « + Ax, y + Ay, 2 + Az,...and by é, y, @ ... may be symbolized by F, (1, 6..." + Ax, y + Ay, z+ Az...) =o. (4) Subject to the conditions specified by the 7 equations (4), we must also have p (Ax)? + g (Av + 7 (42)? +... =a minimum (5) == Saye Equations (4) and (5) contain the solution of every problem of adjustment by the method of least squares. Two examples may suffice to illustrate their use. First, take the case of the observed angles of a triangle alluded to above. Calling the observed angles x, , 2, we have a+ Ax + y+ Ay + 2-+ Az = 180° + spherical excess, Ax + Ay + Az = 180° + spherical excess — (* + y + 2) == Say. or This is the only condition of the form (4). The problem is completely stated, then, in the two equations Ax + Ay+ Az =c « p (Ax)? + g (Ay)? + 7 (Az)? =a min. = wu. To solve this problem the simplest mode of procedure is to eliminate one of the corrections by means of the first equation and then make wa minimum. Thus, eliminating Az, there results “= p (Ax)? + ¢g (Ay)? + 7 (¢ — Ax — Ay)? The conditions for a minimum of z are : — Ou Sag et) Ax + rAy — 76 =09, Sap F) A) — to —— 0), and these give, in connection with the value Az = ¢ — Ax — Ay, Ree AG a e WN — Q 2 q r where Cc 7 So a i g+Et When the weights are equal, or when # = g =”, the corrections are — ag Ayia) en Ixxxviii THEORY OF ERRORS, Secondly, take the case, also alluded to above, of the observed sum and the observed difference of two numbers. Denote the numbers by é and 7, the latter being the smaller. Let the observed values of the sum (¢ + 7) be denoted by 2%, %,-..%m and their weights 2, J, ..- Pm respectively. Likewise, call the observed values of the difference (€— 7), j1, Yo... Vn, and their weights Jy J2+++9, respectively. Then there will be #- ” equations of the type (4), namely : — £-- 9 — Gi ax) 16, E--.9 — (4 - Ax) =9, é + Oars (fm—-+ Aa) os E—y—(n+An) =o, f—9y—(O2+ An) =0, &— 4 — On+ Arn) =0; and the minimum equation is wu = py (Axy)” + pz (Axr)” +... + m1 (An)? + 9 (Ay)? +... =a min. (b) The equations of group (a) give Ax, =é+7n-—-%, Ax, = €+ 7 — x (a) ens (c) Ayn =f—-—yn-y, Ay, =E— 7 — Jy, - and these values in (b) give UPS aia Aa)” hee of tt Che ee) oie (d) Thus it appears that all conditions will be satisfied if € and y are so determined as to make wz in (d) a minimum. Hence, using square brackets to denote sum- mation of like quantities, the values of € and 7 must be found from S=letolétle—ala— leet a=, ©) Sale - dit let a—Le — gy) =o. Equations (e) give ¢ and », and these substituted in (c) will give the corrections to the observed quantities. b. Relation of probable, mean, and average errors. The introduction of the law of error (2) in equations (3) furnishes the following relations, when it is assumed that the limits of possible error are —o and +o: €5 == 0.0745 6 — 00403 (6) THEORY OF ERRORS. Ixxxix c. Case of a single unknown quantity. The case of a single unknown quantity whose observed values are of equal or unequal weight is comprised in the following formulas : — X1, Xx, . . » Xj, == observed values of unknown quantity, Piy Pay 2 «Pm — the weights of x, 45... V3) Voy « » « Um = Most probable corrections to x, %, .. - x == most probable value of the unknown quantity, m == the number of éndependent observations. Then the conditional equations (4) are See tee ean mnt 5 xX — Xp = Um5 the minimum equation (5) is Dw + pov2? ai ee [p27] as [A(x an x;)"| = min., Mnete¢—— 1, 2,...7, and = Pr + Poxy + a

    Mean error of x = €n Vay, Mean error of vy = én VBo, Mean error of z = €, V¥35 ee where a, B2, ys, +. . are defined by equations (c) and (d) above. e. Case of functions of several observed quantities x, y, Z,.... This case is that in which the conditional equations (4) contain no disposable quantities & 7, ¢,.... It is the opposite extreme to that represented by the case of the preceding section.* It finds its most important and extensive application in the adjustment of triangulation, wherein the observed quantities are the angles and bases of the triangulation, and the conditions (4) arise from the geometrical relations which the observed quantities f#/wvs their respective corrections must satisfy. An outline of the general method of procedure in this case is the following : — The first step consists in stating the conditional equations and in reducing them to the linear form if they are not originally so. The form in which they present themselves is (4) with & 7, % . . . suppressed, or F (4, + Ax, % + A x, x3 + Aw...) =0, wherein x, y, z,...o0f (4) are replaced by x, %, x3... for the purpose of sim- plicity in the sequel. If this equation is not linear, Taylor’s series gives ; FF (Hy, Xa, Xg-.. +5 Ax + a e700, since the method supposes that the squares, products, etc., of Ax, Ax)... may be neglected. The last equation is then linear with respect to the corrections Ax,, Ax, ... which it is desired to find. For brevity put F (21). Xo) X3... ) =, a known quantity, OF oF oF AL — et eee — By - «oe Oxy ly Ox. 2 Ox, 3 Then the conditional equations will be of the type QAx, a AAX, — a,AX5 a ew oe q = se f * The middle ground between these extremes has been little explored ; indeed, most practical applications fall at one or the other of the extremes. XCiV THEORY OF ERRORS. There will be as many equations of this type as there are independent relations which the quantities x, + Ax, «, -+ Ax, ... must satisfy. Suppose there are & such relations, and let the differential coefficients I/O, IF/dx, ... for the sec- ond relation be denoted by 4, 2,, d;,... ; for the third relation by 4, ¢, &, . . etc. Then all of the conditional equations may be written thus: a@Ax, + aAx, + a,Ax,+... +9,=09, b, a by a bs ++ eee + G2 — O, (a) a +6 + 6 +... + 9,=0, id, foe the number of these equations being &. Call the weights of the observed quantities x, x, ...f), f..... Then, sub- ject to the conditions (2) we must have (in accordance with (5)) u = p(n)! + pdm) +... = [p(Ax)’] () a minimum. Equations (a) and (4) contain the solution of all problems falling under the present case. Obviously, the number of conditions (a2) must be less than the number of observed quantities x, or less than the number of Ax’s in (0); in other words, if # denote the number of observed quantities, # > 4, for if m = & the minimum equation (4) has no meaning. The question presented by (a) and (4) is one of elimination only. Two methods, the one direct and the other indirect, are available. Thus, by the direct method one finds from (a) as many Ax’s as there are equations (a), or & such values, and substitutes them in (4). The remaining (# — &) values of Ax in (2) may then be treated as independent and the differential coefficients of « with respect to each of them placed equal to zero. Thus all of the corrections Ax become known. By the indirect process, one multiplies the first of equations (a) by a factor Q,, the second by Q,, the third by Q;, ... and subtracts the differential (with respect to the Ax’s) of the sum of these products from half the differential of (6). The result of these operations is 4 du= {p Ax, — (4Q+40+420; +.. .)} dAxy a {Podx, — (42.0, + bQ2 + @Q;+...)} dAx Aa ike ae (Qn ?; +. On Q; ao Gn Qs -|- athe -)} MNXmn Now we may choose the factors Q,, Q:,... Q, in such a way as to make & of the coefficients of the differentials in this equation disappear; and after thus elimi- nating & of these differentials we are at liberty to place the coefficients of the remaining (# — ) differentials equal to zero. Thus all conditions are satisfied by making aQ; aa b,Q, oe o,Q3 al s) (0/8 — pAx, — oO, a +h +a +...—pAxm =0, Qin + Om + Gn + os Nelo pal PnrAXm —odO; and the values of the corrections will be given by these equations when the fac- tors Q,, Q,,... are known. To find the latter it suffices to substitute the values () ' THEORY OF ERRORS. XCV - of Ax, Ax, ... from (c) in (a), whereby there will result £ equations containing the Q,, Q,... Q, alone as unknowns. ‘The result of this substitution is =] at[F] a+{+] Q+...+m=9, fm] +f] +E] toters F] +E) Ee] + t0e These equations (@) are derived directly from (¢) in the following manner: multi- ply the first of (c) by me the second by ze etc., sum the products, and compare the 1 2 sum with the first of (a). The first of (¢) is then evident ; the others are obtained in a similar way. The mean error of an observed quantity of weight unity is in this case given by the formula ae / [2ax)) m Wi where & is the number of conditions (2); and the mean error of any observed value of weight # is Em Ve f. Computation of mean and probable errors of functions of observed quantities. Let V denote any function of one or more independently observed quantities eae eg os Chat 1s, let v= pee -)s A question of frequent occurrence with respect to such functions is, What is the mean * error of V in terms of the mean errors of x, y, z,...? The answer to this question given by the method of least squares assumes that the actual errors (whatever they may be) of x, y, z,... are so small that the actual error of Visa linear function of the errors of x, y,z. In other words, if ¢@,, ¢,, ¢.,... denote the actual errors of x, 7, z,..., and AV denote the corresponding actual error of V, the method assumes that ) V )V ) V c Co c ON ice in lia enc? (2) wherein the squares, products, etc., of ¢,, ¢, ¢,... are omitted. This condition being fulfilled, let ¢ eee the mean error of V, and «¢,, €,, €,... denote those of x, y, 2z,... respectively. Then the law of error of least squares | . | requires that ee (Ret (yer (Gyert-. (2) cx * Since the probable error is 0.6745 times the mean error the latter only need be considered. xcvi THEORY OF ERRORS. This equation includes all cases. Its analogy with (a) should be noted, since the step from (a) to (4) is clear when the correct form of (a) is known. Mistakes in the application of (2) are most likely to arise from a lack of knowledge of the independently observed quantities x, y, 2,... or from a lack of knowledge of the true form of (a2). Hence,* in deriving probable errors of functions of observed quantities attention should be given first to the construction of the expression for the actual error (a). A few examples may serve to illustrate the use of (a) and (4). (1.) Suppose ; V=f (x,y, %..)=a(e—y+o(y+2) +¢e—1?). aoV OV OV isha iee Sy ee Bp = OS AV=ae,+ (6—aje + (6+ Oe, 2 = are? + (6 — a)? + (6 + 0/7. Then (2.) Suppose a y VF (69; Bre eee Then a ae: aV_}b OW ce oi) 52 by, Oa Pe. Nae oy. 2 oz gone A= = ee fg ee pe 2 Bae bry? a = e+ A 7 oe : 2 eZ. (3.) Suppose V=a log x-+ 6sin y + ¢ log tan 2. Then aV apt Lar OV cu xe Se Oz Sinz cosz ox x oy i ap . 9 2 2 Cm 2 ae (*) 4 at (00S) irae fr 2 :) = (4.) Suppose the case of a single triangle all of whose angles are observed. What is the mean error, 1st, of an observed angle; 2d, of the correction to an observed angle ; and 34, of the corrected or adjusted angle ? Let x, y, z denote the observed angles, , g, 7 their weights, and Aw, Ay, Az the corresponding corrections. Then, as shown on p. Ixxxvil, Ax + Ay + Az = c= 180° + sph. excess — (x + + 2) = error of closure of triangle, and G Cee oo ae La e Nye Az = gq: Pp q r * As remarked by Sir George Airy in his Theory of Errors. Tt # = modulus of common logarithms. THEORY OF ERRORS. xCVil For brevity, put g = 180° + spherical excess, 4= mala P QH=hg-—*#—y—nD= KM, Qi) Then he Bam ae a de =F(e—2—y— 2) +H with similar expressions for the other two angles. Now by the formula on p. xcv the square of the mean error of an observed angle of weight unity is (since there is but one condition to which Ax, Ay, Az are subject), pdx) + ar) + (a2 = © ae Hence, the squares of the mean errors of the observed angles «, y, 2, their weights being /, g, 7 respectively, are hc? he? hc* ? ? pe q r respectively. To get the mean error of a correction, Ax for example, formula (a) gives AV = A(Ax) =— 5 Bees) and the corresponding expressions for the actual errors of Ay and Az are found from this by replacing ~ by g and + respectively. Thus by (4), observing that the mean errors of x, y, z are given above, there result Square of mean error of Ax = (/c/p)’, “6 “c “é Ay a (hc/9)’, sé “c “6 Az = (Ac/r)?. Likewise, the formula for the actual error of « + Ax is h h h AV = AG Ax) — (: —5)e = -— oe and the corresponding expressions for the actual errors of y + Ay and z + Az are found by interchange of gand 7 with g. Thus the squares of the mean errors of the adjusted angles are : — hc? h for (x + Ax), a (: — 3) (x + Ax) 2 3 hc? h for (vy + Ay), 2 (-7 ( ) q Z, hc? h Az = =p Ne for (z + Az), : (: *) xcvill THEORY OF ERRORS. In case the weights are equal, or in case /=g—=7, h=}, and there result, — Square of mean error of observed angle = 14 dapat « —_“ correction to observed angle = } c’, he eee ees “« “ adjusted angle ea where ¢ is the error of closure of the triangle ; so that in this case of equal weights the three mean errors are to one another as 373, 4, and 32. References. The literature of the theory of errors, especially as exemplified by the method of least squares, is very extensive. Amongst the best treatises the following are worthy of special mention: Method of Least Squares, Appendix to vol. ii. of Chauvenet’s “ Spherical and Practical Astronomy.” Philadelphia: J. B. Lippin- cott & Co., 8vo, 5th ed., 1887. ‘‘ A Treatise on the Adjustment of Observations, with Applications to Geodetic Work and Other Measures of Precision,” by T. W. Wright. New York: D. Van Nostrand, 8vo, 1884. ‘On the Algebraical and Numerical Theory of Errors of Observation and on the Combination of Observa- tions,” by Sir George Biddle Airy. London: Macmillan & Co., 12mo, 2d ed., 1875. ‘ Die Ausgleichungsrechnung nach der Methode der Kleinsten Quadrate, mit Anwendungen auf die Geodasie und die Theorie der Messinstrumente,” von F. R. Helmert. Leipzig: B. G. Teubner, 8vo, 1872. PXPLANATION OF SOURCE AND USE OF THE TARE ES: TABLES 1 and 2 are copies of tables issued by the Office of Standard Weights and Measures of the United States, edition of November, 1891. Table 3 is derived from standard tables giving such data. The arrangement is that given in “ Des Ingenieurs Taschenbuch, herausgegeben von dem Verein ‘ Hiitte’” * (11th edition, 1877). The numbers have been compared with those given in the latter work, and also with those in Barlow’s “Tables.” The loga- rithms have been checked by comparison with Vega’s 7-place tables. Table 4 is abridged from a similar table in the Taschenbuch just referred to. Tables 5 and 6 are copies of standard forms for such table. They have been checked by comparison with standard higher-place tables. The mode of using these tables will be evident from the following examples : — (x.) To find the logarithm of any number, as 0.06944, we look in Table 5 in the column headed N for the first two significant figures of the number, which are in this case 69. In the same horizontal line with 69 we now look for the number in the column headed with the next figure of the given number, which is in the present case 4. We thus find .8414 for the mantissa of the logarithm of the number 694. To get the increase due to the additional figure 4, we look in the same horizontal line under Prop. Parts in the column headed 4 and find the number 2, which is the amount in units of the fourth place to be added to the part of the mantissa previously found. Thus the mantissa of log (0.06944) is 8416. The characteristic for the logarithm in question is —2—=8—10. Hence log (0.06944) = 8.8416— 10. (2.) To find the number corresponding to any logarithm, as 8.8416—10, we look in Table 6 in the column headed L for the first two figures of the mantissa, which are in this case 84. In the same horizontal line with 84 we now look for the number in the column headed by the next figure of the mantissa, which is in this case 1. We thus find 6394 for the number corresponding to the mantissa 8410. To get the increase due to the additional figure 6, we look in the same horizontal line under Prop. Parts in the column headed 6 and find ro, which is the amount in units of the fourth place to be added to the number previously found. Thus the significant figures of the number are 6944, and since the char- acteristic of the logarithm is 8—10== —2, the required number is 0.06944. * Berlin: Verlag von Ernst & Korn. This work is an invaluable one to the engineer, archi- tect, geographer, etc. c EXPLANATION OF SOURCE AND USE OF TABLES. Tables 7 and 8 are taken from “Smithsonian Meteorological Tables ” (the first volume of this series). Their mode of use will be apparent from the follow- ing example: Required the sine and tangent for 28° 17’. sine 28° x0’, Table'7.-. ... . . 0.4720. Tabular difference = 26. Proportional part for 7’ as Seo on eae 18, SIPC 2O0e1 7" ce alee 4° eee oP ed [ie as OR Ree tangent 28° 10’, Table8 . . . . . 0.5354. Difference for 1’= 3.8. Encrease for 7)(7 23-8) 1 er eee ay tangent.23° ay! /i7 Oe) ee ae os eae Table g is a copy of a similar table published in “ Professional Papers, Corps Engineers,” U.S. A., No. 12. It has been checked by comparison with other tables in general use. This table is useful in computing latitudes and departures in traverse surveys wherein the bearings of the lines are observed to the nearest quarter of a degree, and in other work where multiples of sines and cosines are required. Thus, if Z denote the length and Z the bearing from the meridian of any line, the latitude and departure of the line are given by LcosB and JZsinB respectively; the “latitude ” being the distance approximately between the paral- lels of latitude at the ends of the line, and the “departure” being the distance approximately between the meridians at the ends of the line. As an example, let it be required to compute the latitude and departure for Z = 4837, in any unit, and B= 36° 15’. The computation runs thus :— Latitude. Departure. For 4000. 2) ger 2 fw eg 922 5077 2365.23 So wes atc hee. oa OG EO 473-05 Oy a0 Poy eS ee ee 24.19 17.74 WA “maretetn Me: xen let ey a 5-63 4-14 4837 .- ». . « . LeosB=3900.77 LsinB = 2860.16 Tables ro and 11 give the logarithms of the principal radii of curvature of the earth’s spheroid. They were computed by Mr. B. C. Washington, Jr., and care- fully checked by differences. They depend on the elements of Clarke’s spheroid of 1866. The use of these tables is sufficiently explained on p. xlv—xlix. Table 12 gives logarithms of radii of curvature of the earth’s spheroid in sec- tions inclined to the meridian sections. It is abridged to 5 places from a 6-place table published in the “Report of the U. S. Coast and Geodetic Survey for 1876.” Its use is explained on pp. lxi-Ixiv. Tables 13 and 14 give logarithms of factors needed to compute the spheroidal excess of triangles on the earth’s spheroid. No. 13 is constructed for the Eng- lish foot as unit, and No. 14 for the metre. These tables were computed by Mr. EXPLANATION OF SOURCE AND USE OF TABLES, ci Charles H. Kummell. Their use is explained on p. lviii. The following example will illustrate their use : — Latitude of vertex 4 of triangle 48° 08’ “ “ce B “ 47 52 “ee “ec GC “ 47 04 Mean latitude 47 41 Angle C= 51° 22’ 55” logsin C 9.89283 — 10 log a (feet) 5.64401 log & (feet) 5.58681 log factor, Table 13, for 47° 41’ 0.37176 Spheroidal excess = 31.”290, log 1.49541 Tables 15 and 16 give logarithms of factors for computing differences of lati- tude, longitude, and azimuth in secondary triangulation whose lines are 12 miles (20 kilometres) or less in length. These tables were computed by Mr. Charles H.Kummell. Table 15 gives factors for the English foot as unit, and Table 16 for the metre as unit. The use of these tables is illustrated by a numerical exam- ple given on pp. Ix and Ixi. For lines not exceeding the length mentioned, the tables will give differences of latitude and longitude to the nearest hundredth of a second of arc, using 5-place logarithms of the lengths of the lines, Table 17 gives lengths of terrestrial arcs of meridians corresponding to lati- tude intervals of 10”, 20”,... 60”, and 10’, 20',... 60’, or lengths corresponding to arcs less than 1°. The unit of length is the English foot. The table was computed by Mr. B. C. Washington, Jr. The length corresponding to any latitude interval is the distance along the meridian between parallels whose latitudes are less and greater respectively than the given latitude by half the interval. Thus, for example, the length corre- sponding to the interval 30’ and latitude 37° (182047.3 feet) is the distance along the meridian from latitude 36° 4s’ to latitude 37° 15’. By interpolation, we may get from this table the meridional distance corre- sponding to any interval. The following example illustrates this use: Required the distance between latitude 41° 28’ 17.8 and latitude Ate 3Q) 6c ete difference of these latitudes is 11’ 35.6, and their mean is 41° 34’ 05."6. The computation runs thus : — Latitude 41°. Tabular difference. 10’ 60724.60 feet 10.70 feet 1’ 6072.46 “ TOyy os: 30" 3036.23 “* 54 “ a 506.04 “ee 09 “cc 0.6 C072 ie ‘or er ei AS Fon % sum, 12.41 “ Distance = 70407.10 When the degree of precision required is as great as that of the example just cil EXPLANATION OF SOURCE AND USE OF TABLES. given, it will be more convenient to use formulas (2) on p. xlvi. Thus, in this example, — log. Ad = 695.6 2.8423596 o = 41° 34 05."6, p,m (Table 10) 7.3196820 cons’t 4.6855749 Length = 70407.10 feet 4.8476165 Table 18 gives lengths of terrestrial arcs of parallels corresponding to longi- tude intervals of 10”, 20”, ... 60”, and 10, 20’,... 60’, or lengths corresponding to arcs less than 1°. The unit is the English foot. This table was computed by Mr. B. C. Washington, Jr. The method of using this table is similar to that applicable to Table 17 explained above. For the computation of long arcs it will in general be less laborious to use the formulas (1) on p. xlix than to resort to interpolation from Table 18. Tables 19-24 give the rectangular co-ordinates for the projection of maps, in accordance with the polyconic system explained on pp. liii-lvi, for the following scales respectively : — 1 Table 19, scale 250000 “ “ce 1 20 JOR) ° . e . pape Lee : } unit == English inch. 21, uen (2 miles to 1 inch) oY 22, i (rmile tome anehy i) “c “ 1 23; anos | . “1: ie iz ; unit = millimetre. 24 a , was J These tables were computed by Mr. B. C. Washington, Jr. The use of these tables and their application in the construction of maps may be best explained by an example. Suppose it is required to draw meridians and parallels for a map of an area of 1° extent in longitude, lying between the paral- lels of 34° and 35°. Let the scale of the map be one mile to the inch, or 1/63360, and let the meridians and parallels be 10’ apart respectively. Draw on the pro- jection paper an indefinite straight line 42, Fig. 4, to represent the middle me- ridian of the map. ‘Take any convenient point, as C, on this line for the latitude 34°, and lay off from this point the meridional distances CD, CZ, C#,... C/, given in the second column of Table 22, p. 114.* Through the points D, 2, £; . I, thus found, draw indefinite straight lines perpendicular to 42. By means of these lines and the tabular co-ordinates, points on the developed parallels and meridians are readily found. Thus, for example, the abscissas for points ten minutes apart on the parallel 34° 20’ are 9.53, 19.06, and 28.59 inches. ‘These distances are to be laid off on V4’ in both directions from 4%. At the points L, M, N, L’, M', N', so determined, erect perpendiculars to VV’ equal in length, respectively, to the ordinates corresponding to the longitude intervals * The meridional distances and the abscissas of the points on the developed parallels in Fig. 4 are one twentieth of the true or tabular values. The ordinates of points on the developed paral- lels are the tabular values. EXPLANATION OF SOURCE AND USE OF TABLES. cili 10’, 20’, 30. Thecurved line joining the extremities of these perpendiculars is the parallel required. It may be drawn by means of a flexible ruler. The other parallels are constructed in the same manner. They are all concave towards the north or south according as the map shows a portion of the northern or southern hemisphere. The meridians are drawn in a similar manner through the points (c.g, P, Q, M, R, S, 7, Vin Fig. 4) having the same longitude relative to the middle meridian. All meridians are concave towards the middle meridian. A test of the graphical work which should always be applied is the approxima- tion to equality of corresponding diagonals in the various quadrilaterals formed. Thus in Fig. 4, VX should be equal to WY, CV to CN’, EV to EW, etc.* Fig A. Tables 25-29 give areas of quadrilaterals, bounded by meridians and parallels, of the earth’s surface. They are taken from “ Bulletin 50, U. S. Geological Sur- vey.” The unit of length used is the English mile, and the areas are thus given in square miles. The method of using these tables is obvious. Table 30 gives data for the computation of heights, from barometric meas- ures, in accordance with the formula of Babinet.t This table is taken from the “Smithsonian Meteorological Tables” (the first volume of this series). The manner of using it is explained in connection with the table. * It should be noted that Cis not equal to ZV, Vand V referring here to points on the developed parallels. + Comptes Rendus, Paris, 1850, vol. xxv. p. 309. Civ EXPLANATION OF SOURCE AND USE OF TABLES. Table 31 gives the mean astronomical refraction in terms of the apparent alti- tude of a star or other object outside the earth’s atmosphere. It is taken from Vega’s 7-place table of logarithms. Its use will be evident from the following example : — Apparent altitude of star —— Arye T te Refraction = 1’ 24."3 — 5 X 1./1 = I 24.1 True altitude of star 194) 15 45.0 Tables 32 and 33 facilitate the interconversion of arc and time. They are taken from the “Smithsonian Meteorological Tables” (the first volume of this. series). The following examples illustrate their use :— (1.) To convert 68° 29’ 48.8 into time we have from Table 32 — 68° =—_ 4° om 008 20 1 56 1c B20 O..o=— 0S Equivalent in time = 4 33 59.25 (2.) To convert 5" 43™ 28.°8 into arc we have from Table 33 — E75 (00 00) 43, i——"104 45100 oa 7 00 075 '—— 12 Equivalent in arc = 85 52 12 Tables 34 and 35 facilitate the interconversion of mean solar and sidereal time intervals. They are taken from Vega’s 7-place table of logarithms. The mode of using them is explained in the tables themselves. Tables 36 and 37 give the lengths of degrees of terrestrial arcs of meridians and parallels expressed in metres,* statute miles (English), and geographic miles (distance corresponding to 1’ on the earth’s equator). These tables are taken from the “Smithsonian Meteorological Tables” (the first volume of this series). Table 38 facilitates the interconversion of statute (English) miles and nautical miles. ‘The nautical mile used is that defined by the U. S. Coast and Geodetic Survey, namely: the length of a minute of arc of a great circle of the sphere whose surface equals that of the earth (Clarke’s spheroid of 1866). For formula for radius of such sphere see p. lii. ‘This table is taken from the “ Smithsonian Meteorological Tables ” (the first volume of this series). Table 39 gives the English and metric equivalents of other standards of length still in use or obsolescent. It is taken from the “Smithsonian Meteoro- logical Tables ” (the first volume of this series). Table 40 gives values of the acceleration (g) of gravity, log g, log (1/2g), log V2 8, * It should be observed that the metric values given in these tables depend on Clarke’s value of the ratio of the yard to the metre, which is now known to be erroneous by about the 1/100000th part. ge JZ EXPLANATION OF SOURCE AND USE OF TABLES. CV and (g/z*) or the length of a seconds pendulum, for intervals of 5° of geograph- ical latitude. It was computed by the editor, and is based on the formula for g given by Professor William Harkness in his memoir “ On the Solar Parallax and its Related Constants.” * Table 41 gives the linear expansions of the principal metals. It was compiled by the editor from various sources. The values given for the expansion per degree Centigrade have been rounded (with one exception) to the nearest unit in the millionths place, or to the nearest micron, since different specimens of the same metal vary more or less in the ten-millionths place. Table 42 gives the fractional changes in numbers corresponding to changes in the 4th, 5th,...7th place of their logarithms. These fractions are often con- venient in showing the approximate error in a number due to a given error in its logarithm, or the converse. ‘Thus, for example, referring to the remark in a foot-note under explanation of Tables 36 and 37 above, the error in the loga- rithm of Clarke’s ratio of the yard to the metre is about 4 units in the sixth place of decimals ; the Table 42 shows, then, that the metric equivalents in Tables 36 and 37 are erroneous by about 1/100 oooth part. * Washington, Government Printing Office, 1891. GEOGRAPHICAL TABLES TABLE 1. FOR CONVERTING U. S. WEIGHTS AND MEASURES.* CUSTOMARY TO METRIC. LINEAR. CAPACITY. Fluid Inches to : drams to | Fluid milli- Feet to | Yards to | Miles to millilitres | ounces to | Quarts to| Gallons to pee metres. metres. | kilometres. or cubic milli- litres. litres. centi- litres. metres. 3°70 29°57 | 0°94630| 3'78543 Hao, 59°15 | 189272] 7757087 I1‘09 88°72 | 2°83908] 11°35630 14°79 118°29 | 3°75543] 15°14174 18°48 | 147°87 | 4°73179| 15°92717 22°18 177°44 | 5°67815| 2271261 25°88 207°02 | 6°62451 | 26749804 29°57 | 236'59 | 7°57087 | 30°28348 33°27 206°16 | 851723] 34°00891 25°4001| 0°304801| 0°914402] 1°60935 50°8001| 0°609601) 1°828804] 3721869 76°2002] 0°91 4402| 2°743205| 4°82804 IOI*6002] 1°219202! 3°657607] 6'43739 127°0003] 1°524003| 4°572009] 804674 152°4003] 1°828804) 5°486411| 9°65608 1778004] 2°133604] 6'4008 13] 11°26543 203°2004] 2°438405| 7°315215| 12°87478 228°6005| 2°743205| 8229616] 14°48412 He Oo SI AnifW DN He OO ONIONS) WN SQUARE. WEIGHT. Avoirdu- Avoirdu- ae pois Troy pee pounds to| ounces to ounces . cee kilo- grammes. Square Square inches to feet to square square centi- deci- metres. metres. Square yards to Acres to square hectares. metres. Grains to milli- grammes. grammes. 64.7989] 28°3495| 0745359] 3110348 129°5978] 56°6991| 0°90719| 62°20696 194°3968] 85'0486) 1°36078 | 93°31044 259°1957| 113°398t| 1°81437 |124°41392 323°9946| 141°7476| 2°26796 |155°51740 388°7935| 170°0972| 2°72156 |186°62088 453°5924| 198°4467| 3°17515 |217°72437 518°3914| 226°7962| 3°62874 |248°82785 §83°1903} 2551457] 4°08233 |279°93133 6°452 9.290 | 0'836 12°903 | 18°581 1°672 19'355 | 27871 | 2°508 25307 | 37161 | 3°344 32°258 | 46452 | 4181 38°710 | 55°742 | S017 45161 | 657032 | 5853 5613 | 747323 | 6639 58°065 | 83°13 | 7°525 I 3 4 5 6 7. 8 0 ON ANnfW Nw I ae \o Cubic 5 . Cubic inches to |Cubic feet yards to | Bushels to cubic to cubic cubic hectolitres. centi- é . metres. metres. 0°35239 1 Gunter’s chain == 201168 metres. 0°70479 I sq. statute mile == 259'000 hectares. 105718 1 fathom == | 1'820)) “metres: O°11327 : 1°40957 I nautical mile == 18'53'25 metres. o'14158 : 1°76196 1 foot = 0.304801 metre, 94840158 log. 0" 16990 "58 2°11436 I avoir. pound = 453°5924277 gram. 0°19822 2°46675 || 15432°35639 grains = 1 kilogramme. 131°097 | 0°22654 'r16 | 281914 147°484 | 0°25485 8 317154 The only authorized material standard of customary length is the Troughton scale belonging to this office, whose length at 59°.62 Fahr. conforms to the British standard. The yard in use in the United States is therefore equal to the British yard. The only authorized material standard of customary weight is the Troy pound of the Mint. It is of brass of unknown density, and therefore not suitable for a standard of mass. It was derived from the British standard Troy pound of 1758 by direct comparison. The British Avoirdupois pound was also derived from the latter, and contains 7,000 grains Troy. The grain Troy is therefore the same as the grain Avoirdupois, and the pound Avoirdupois in use in the United States is equal to the British pound Avoirdupois. The British gallon = 4.54346 litres. The British bushel = 36.3477 litres. The length of the nautical mile given above and adopted by the U. S. Coast and Geodetic Survey many years ago is defined as that of a minute of arc of a great circle of a sphere whose surface equals that of the earth (Clarke’s Spheroid of 1866). * Issued by U. S. Office of Standard Weights and Measures, and republished here by permission of Superintendent of Coast and Geodetic Survey. SMITHSONIAN TABLES. 2 FOR CONVERTING U. S. WEIGHTS AND MEASURES. ©” ** METRIC TO CUSTOMARY. LINEAR. CAPACITY. Millilitres . or cubic | Centi- Metres to| Metres to |Metres to a a centi- litres to | Litres to inches. feet. yards. rate fluid quarts. Deca- Hecto- litres to litres to meee gallons. | bushels. miles. to fluid | ounces. drams. 39°3700| 3.28083] 1°093611| 0°62137 75°7400| 6°56167| 2°187222| 1°24274 1181100] 9754250] 3°280833} 186411 157°4800| 13°12333| 4°374444] 2748548 196°S500} 1640417] 5°468056) 3710685 236°2200] 19°68500) 6°561667) 3°72822 275°5900| 22°96583) 7°055278| 4°34959 3149600] 26°24667} 8748889] 4°97096 354°3300| 29752750] 9.842500] 5759233 0°338 | 10567 | 2°6417| 2°8377 0°676 | 2°1134 | 5°2834] 5°6755 rol1g4 | 3°1700 | 779251] 8'5132 1°353 | 4°2267 | 1075668] 11°3510 1691 5°2834 | 13°2085| 14°1887 2°029 | 6°3401 | 15°8502| 17°0265 2°367 | 7°3968 | 184919] 19°8642 2°705. | 8°4535 | 21°1336] 22°7019 31043) | OS LOK 162357753)" 455397 ON Quit bh | et Oo ONT Quiros DN © SQUARE. WEIGHT. Square Hecto- Kilo- centi- Bauer Bonar rece Milli- Kilo- grammes grammes metres to}. square | to square| to acres grammes to| grammes to] to ounces to pounds square feet yards 7 grains. grains. avoirdu- avoirdu- inches. 3 pois. pois. 0701543 | 1543236] 375274 2°20462 0°03086 30864°71 770548 4°40924 0°04630 46297°07} 1075822 6°61387 0°06173 61729°43| 14°1096 8°81849 0°07716 77161°78| 17°6370 1102311 0109259 92594714] 21°1644 13°22773 010803 | 108026'49| 24°6918 15°43236 0°12346 | 123458°85| 28:2192 17763698 0°13889 | 138891°21] 31°7466 19°84160 01550 | 10°764 | 1°196 o°3100 | 21°528 | 2°392 0°4650 | 32°292 | 37588 0.6200 | 43°055 | 4°784 0°7750 | 53°819 | 5°980 0.9300 | 64°583 | 77176 170850 | 75°347 | 8°372 12400 | 86111 | 97568 1°3950 | 96°875 | 10°764 Oo ON DUI OD NH WU WWE TE EAT 0 ON DANPW DN A WL WUE EE WEIGHT — (continued). Cubic Cubic centi- deci- metres to} metres to cubic cubic inches. | inches. Cubic Cubic metres | metres to Quintals to to cubic cubic pounds av. feet. yards. Milliers or Kilogrammes tonnes to to ounces pounds av. Troy. o0610 | 617023] 35°314 0°1220 | 122°047| 70°629 0°1831 | 1837070] 105°943 0'2441 | 244°094| 141°258 0°3051 | 305°117| 176°572 0°3661 | 366°140| 211°887 0°4272 | 427°164| 247°201 0°4882 | 488°187 | 282°516 0°5492 | 549°210| 317°830 220°46 ; 32°1507 440°92 : 64°3015 661°39 3 96"4522 $81°85 518*5 128-6030 1102°31 : 160°7537 B39 2257/7; i 192°9044 1543°24 : 2250554 1763°70 7637" 257°2059 1984°16 : 289°3567 NE Que: 8H cour NO DU BRON HO DNoonkt aM ON OU DH o rH we HU UE TE WE TE at a et Oo ONT Dn fW DN .o By the concurrent action of the principal governments of the world an International Bureau of Weights and Measures has been established near Paris. Under the direction of the International Committee, two ingots were cast of pure platinum-iridium in the proportion of 9 parts of the former to 1 of the latter metal. From one of these a cer- tain number of kilogrammes were prepared, from the other a definite number of metre bars. These standards of weight and length were intercompared, without preference, and certain ones were selected as International prototype stand- ards. The others were distributed by lot, in September, 1889, to the different governments and are called National prototype standards. Those apportioned to the United States were received in 1890 and are in the keeping of this office. The metric system was legalized in the United States in 1866. The International Standard Metre is derived from the Métre des Archives, and its length is defined by the dis- tance between two lines at 0° Centigrade, on a platinum-iridium bar deposited at the International Bureau of Weights and Measures. The International Standard Kilogramme is a mass of platinum-iridium deposited at the same place, and its weight in vacuo is the same as that of the Kilogramme des Archives. The litre is equal to a cubic decimetre, and it is measured by the quantity of distilled water which, at its maximum density, will counterpoise the standard kilogramme in a vacuum, the volume of such a quantity of water being, as nearly as has been ascertained, equal to a cubic decimetre. SmITHSONIAN TABLES. 3 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCARITHMS OF NATURAL NUMBERS. 1000.000 500.000 333-333 250.000 200.000 166.667 142.857 125.000 III.111 WOON QAM fH 100.000 : : 1.00000 90.9091 3331 ; 1224 1.04139 83.3333 1728 : 2.28 1.07918 76.9231 2197 : : 1.11394 71.4286 2744 : Ze 1.14613 66.6667 3375 ; s 1.17609 62.5000 4096 : : 1.20412 58.8235 4913 : . 1.23045 55-5556 5832 1242 62 1.25527 52.6316 6859 350 : 1.27875 50.0000 8000 : : 1.30103 47.6190 4 9261 582 -758 1.32222 45-4545 3 10648 : 802 1.34242 43-4783 12167 : ; 1.36173 41.6667 13824 : : 1.38021 40.0000 15625 : 22 1.39794 38.4615 17576 ; ‘ 1.41497 37-0370 19083 -1962 : 1.43136 35-7143 21952 : : 1.44716 34.4823 24389 : ; 1.46240 33-3333 27000 . , 1.47712 32.2581 20791 : : 1.49136 31.2500 32768 : : 1.50515 30.3030 35937 : : I.51851 29.4118 39304 : : 1.53148 28.5714 42875 : : 1.54407 27.7778 460650 7 : 1.55630 27.0270 50653 .082 : 1.56820 26.3158 54872 : : 1.57978 25-0410 59319 2 : 1.59106 25.0000 64000 Baz 42 1.60206 24.3902 68921 : : 1.61278 23-8095 74088 .48 : 1.62325 23-2555 79507 3 1.03347 22.7273 85184 .0332 : 1.64345 QI125 7082 : 1.65321 21.7391 97330 : unoE 1.66276 21.2766 103823 8 ; 1.67210 20.8333 110592 9282 .6342 1.608124 20.4082 117049 : : 1.69020 20.0000 125000 : , 1.69897 19.6078 132651 , 708 1.70757 19.2308 2 140608 52 f 1.71600 18.8679 148877 ; ; 1.72428 18.5185 157464 : ; 1.73239 SMITHSONIAN TABLES. VALUES OF RECIPROCALS, SQUARES, CUBES GARITHMS OF N ROOTS, AND COMMON LO 14.2857 14.0845 13.8889 13.6986 13-5135 13-3333 13-1579 12.9870 12.8205 12.6582 12.5000 12.3457 12.1951 12.0482 11.9048 11.7647 11.6279 11.4943 11.3636 11.2360 TU-DIIE 10.9890 10.8696 10.7527 10.6383 10.5263 10.4167 10.3093 10.2041 10.1010 10.0000 9-90099 9.80392 9-70874 9.61538 9.52381 9.43396 9-34579 9.25926 9.17431 343000 357911 373248 389017 405224 421875 438976 450533 474552 493039 512000 531441 551368 571787 592704 614125 636056 658503 681472 704969 729000 753571 778088 804357 830554 857375 834736 912673 941192 970299 1000000 1030301 1061208 1092727 1124864 1157625 11gto16 1225043 1259712 1295029 8.1240 8.1854 $.2462 8.3066 8.3666 8.4261 8.4853 8.5440 8.6023 8.6603 8.7178 8.7750 8.8318 8.8882 8.9443 9.0000 90554 g.1104 g.1652 9-2195 9.2730 9-3274 9.3808 9.4340 9.4868 9-5394 9.5917 9.6437 9.6954 9.7468 9.7980 9.8489 9.8995 9.9499 10.0000 10.0499 10.0995 10.1489 10.1980 10.2470 10.2956 10.3441 10.3923 10.4403 TaBLeE 3. SQUARE ROOTS, CUBE ATURAL NUMBERS. 1.80618 1.81291 1.81954 1.82607 1.83251 1.83885 1.84510 1.85126 1.85733 1.86332 1.86923 1.87506 1.88081 1.88649 1.89209 1.89763 1.90309 1.90849 1.91381 1.91908 1.92428 1.92942 1.93450 1.93952 1.94448 1.94939 1.95424 1.95904 1.90379 1.96848 1.97313 1.97772 1.98227 1.98677 1.99123 1.99564 2.00000 2.00432 2.00860 2.01284 2.01703 2.02119 2.02531 2.02938 2.03342 2.03743 TABLE 3S. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCARITHMS OF NATURAL NUMBERS. 1 © 1000. | \ log. 9.09091 1331000 10.4881 : 2.04139 9.00901 1367631 10.5357 : 2.04532 8.92857 ! 1404928 10.5530 .82 2.04922 8.84956 1442897 10.6301 83 2.05308 8.77193 1451544 10.6771 : 2.05690 1520875 10.7238 : 2.06070 1560896 10.7703 8 2.06446 1001613 10.8167 : 2.00819 1643032 10.8625 ; 2.07188 1685159 10.9057 7 2.07555 1728000 10.9545 . 2.07918 1771561 11.0000 Q 2.08279 1815848 11.0454 i 2.08636 1860867 11.0905 7 2.08991 1906624 11.1355 : 2.09342 1953125 11.1803 : 2.09691 2000376 11.2250 : 2.10037 2048383 11.2694 .02 2.10380 2097152 T3137 : 2.10721 7-7 5194 2146089 11.3578 : 2.11059 7.69231 2197000 11.4018 : 2.11394 7-63359 2248001 11.4455 s 2.11727 7-57576 2299968 11.4891 : 2.12057 7.51880 2352637 11.5326 : 2.12385 7.46269 2406104 11.5758 ; 2.12710 2460375 11.6190 : 2.13033 2515450 11.6619 2 -13354 2571353 11.7047 : -13672 2628072 11.7473 ; -13988 2685619 11.7898 : -14301 2744000 11.8322 ; 14613 2803221 11.8743 -202 14922 2863288 11.9164 ; 2.1522 2924207 11.9583 o22 15534 2985984 12.0000 2d 2.15836 3048625 12.0416 H 16137 3112136 12.0830 16435 3176523 12.1244 16732 3241792 12.1655 17026 3307949 12.2006 17319 -17609 17898 18184 .18469 .187 52 NS NNN 337 5000 12.2474 3442051 12.2882 3511808 12.3288 3581577 12.3693 3052264. 12.4097 NON N HN 3723875 12.4499 : 3790416 12.4900 6.36943 3869893 12.5300 6.32911 2 3944312 12.5098 6.28931 28 4019079 12.6095 .19033 19312 19590 -19866 -20140 NNN NN 6.25000 4096000 12.6491 : 2.20412 6.21118 4173281 12.0886 y. 2.20683 6.17284 4251528 12.7279 f 2.20952 6.13497 265 4330747 12.7671 3 2.21219 6.097 56 4410944 12.8062 : 2.21484 SMITHSONIAN TABLES. 1 1000.) 166 6.02410 167 5.98802 168 5-95238 5-91716 170 588235 171 5.84795 172 5.81395 173 5-78035 174 574713 iS 5-71429 176 5.68182 177 5-64972 178 5-61798 179 5.58659 180 5-55550 181 5.52486 182 5-4945E 183 5-46448 184 5.43478 185 5-40541 186 5.37634 187 5-347 59 188 5-319015 189 5.29101 190 5-26316 IgI 5-23500 192 5-20833 193 5.18135 194 5-15464 195 5.12821 196 5-10204 197 5.07614 198 5.05051 5.02513 165 6.06061 29241 29584 29929 30276 30625 30976 31329 31084 32041 32400 32761 33124 33489 33856 34225 34596 34969 35344 35721 36100 36481 30864 37249 37636 38025 38416 38809 39204 39601 4492125 4574290 4657463 4741632 4826809 491 3000 5000211 5088445 SI77717 5268024 5359375 5451776 5545233 56397 52 5735339 5832000 5929741 6028 568 6128487 6229504 6331625 64348 56 6539203 6644672 67 51269 68 59000 6967871 7077888 7189057 7301354 7414875 752953 7645373 7762392 7880599 200 5.00000 201 4.97 512 202 4.95050 203 4.92611 204 4.90196 205 4.87805 206 4.85437 207 4.83092 208 4.80769 209 4.78469 40000 40401 40804 41209 41616 42025 42436 42849 43264 43681 8000000 8120601 8242408 8365427 8489664 8615125 8741816 8869743 8g98912 9129329 210 4.76190 aut 4-73934 212 4.71698 213 4-69484 214 4.67 290 215 4.65116 216 4.62963 217 4.60829 218 4.58716 219 4.56621 44100 44521 44944 45309 45796 46225 460656 47089 4752 47901 SMITHSONIAN TABLES. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, AND COMMON LOCARITHMS OF NATURAL 12.8452 12.8841 12.9228 12.9615 13-0000 TABLE 3. ROOTS, CUBE NUMBER — wa eee/e 13.0384 13.0767 13-1149 13-1529 13-1909 13.2288 13-2665 13-3041 E5347 13;3/791 13.4164 13-4530 13-4907 13-5277 13-5647 13-601 5 13.6382 13.6748 13.7113 13-7477 13.7840 13.8203 13-8564 13.8924 13.9284 13-9642 14.0000 14-0357 14.0712 14.1067 14.1421 14.1774 14.2127 14.2478 14.2829 14.3178 14.3527 14.3875 14.4222 14.4568 PPD NNNNN > “i \o N NNNNN tb ty Bx nN 875 103 Noh NNN Now wb WN CO 00 CO CON Ww Oo ° NNNNN Lo Go Gd WO Nw NWN bo Go Go WO 9261000 9393931 9525128 9663597 9800344 9938375 10077696 10218313 10360232 10503459 14-4914 14.5258 14.5602 14-5945 14.6287 14.6629 14.6969 14.7309 14.7648 14.7986 2 a yocee 428 NNN ty Go Ga Ga G Ga” GN NN co Ww oo by ydybvd Go Od nd WD On Go ON ag ON TABLE 3S. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCARITHMS OF NATURAL NUMBERS. 1 : ° § 1000.;, log. 2 > ~ 4.54545 10648000 14.8324 ; 2.34242 4.52489 10793861 14.8061 : 2.34439 4.50450 10941048 14.8997 0: 2.34635 4.48431 11089567 14.9332 : 2.34830 4.46429 6 11239424 14.9606 .O7 2.35025 i) tN BONA O NNN HN NWN lo 4.44444 11390625 15.0000 : 2.35218 4.42478 11543176 15-0333 .OQI2 2.35411 4.40529 11697083 15.0005 ; 2.35603 4.38596 11852352 15.0997 2.35793 4.306081 12008989 15.1327 : 2.35984 nN N db wW LH N Nw Oo ON AG NO @ oS 4.34783 12167000 15.1658 : 2.36173 4.32900 12326391 15-1957 : 2.36361 4.31034 12487168 15-2315 : 2.30549 4.29185 12649337 15-2643 : 2.36736 4.27 350 12812904 15.2971 162 2.30922 Go Ga G2 2 BON RN HLH wo w 2a Ge Go Oo Oo ON AG 4.25532 12977875 15.3297 2.37107 4.23729 13144256 15.3623 179 2.37291 4.21941 13312053 15-3948 : 2.37475 4.20168 13481272 15.4272 .1972 2.37658 4.18410 13651919 15-4596 ; 2.37840 NNN N nN ne oO 4.16667 13824000 15-4919 2.38021 4.14938 ‘ 13997 521 15-5242 : 2.38202 4.1322 14172488 15-5503 .2 2.38382 4.11523 14348907 15.5885 : 2.38561 4.09830 14520784 15.6205 | .2488 2.38739 NNN BRR Wn = NO i i a + 4.08163 14706125 15-6525 : 2.38917 4.06504 14886936 15-6844 ; 2.39094. 4.04558 15069223 15-7162 227 2 2.39270 4.03226 15252992 15-7480 : 2.39445 4.01606 15438249 15-7797 : 2.396020 4.00000 15625000 15.8114 : 2.39794 3-98406 15813251 15.8430 : 2.39967 3.96825 16003008 15.8745 5 2.40140 3-95257 16194277 15-9060 7 2.40312 3-93701 16387064 15.9374 . 2.40483 3-921 57 16581375 15.9687 : 2.40654 3-90625 16777216 16.0000 ; 2.40824 3.89105 16974593 16.0312 ; 2.40993 3.87597 17173512 16.0624 ; 2.41162 3.86100 17373979 16.0935 : 2.41330 3.8461 5 17576000 16.1245 382 2.41497 383142 17779581 16.1555 3.81679 17984728 16.1864 3.80228 18191447 16.2173 3.78788 18399744 16.2481 3-77358 18609625 16.2788 3-75940 18821096 16.3095 3:74532 2 19034163 16.3401 3:73134 19248832 16.3707 S717 47 19465109 16.4012 mR NNN Pep fpAHK 3.70370 19683000 16.4317 3.69004. 19902511 16.4621 3.67647 E 20123048 16.4924 3.66300 20346417 16.5227 3.64964 20570824 16.5529 ems Be SMITHSONIAN TABLES. a tit me { TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOGARITHMS OF NATURAL NUMBERS. 20796875 16.5831 21024570 16.61 32 21253933 16.6433 1454952 16.6733 16.7033 952000 16.7332 > I 2188041 16.7631 242 10.7929 2 5 16.8226 2 16.8523 Nw wHh hb 16.8819 16.9115 16.9411 16.9706 24137509 17.0000 NN HNN to 24389000 17.0294 24642171 17.0587 24897088 17.0880 25153757 ° 17.1172 25412184 17.1464 NNNL Ne Ov 0 1 25672375 17.1756 25934330 17.2047 2019807 3 1732337, 26463592 17.2627 267 30899 17.2916 NNNNN fsb > SST ST Gy Wk by BO Ans vy “SI OW WN 27000000 17.3205 27270901 17-3494 27543008 17.3781 27818127 17.4009 28094404 17.4350 NNNNN 28372625 17.4642 28652616 17.4929 28934443 17.5214 29218112 17.5499 29503629 17.5784 29791000 17.6068 30080231 17-6352 30371328 17.6635 30664297 17.6918 30959144 17-7200 SNI™NI NI 31255875 17.7482 3-16456 5 31554496 17.7704 3-1 5457 100489 31855013 17.8045 3.14465 LOLI 24 32157432 17.8326 3.13480 101761 32461759 17.8606 17.8885 17.9165 17-9444 17.9722 18.0000 3.12500 102400 S527 103041 310559 103684 3:09598 104329 3.08642 104976 DAD ADAAKH AAADH Wo G2 Wd Go 3.07692 105625 34328125 18.0278 3.06748 106276 34645970 18.0555 3.05810 106929 34905783 18.0331 3.04878 107584 35287552 18.1108 3-03951 108241 35611289 18.1384 SmitHSONIAN TABLES. TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOGARITHMS OF NATURAL NUMBERS. 3.03030 35937000 2 6.9104 2.51851 3.02115 30264691 5. 6.9174 2.51983 3.01205 22 30594308 .22 6.9244 2.52114 3-00300 30926037 ; 6.9313 2.52244 2.99401 37259704 2 6.9382 2.52375 2.98507 37595375 : 6.9451 2.52504 2.97619 2 37933056 ; 6.9521 2.52634 2.967 36 38272753 : 576 6.9589 2.52763 2.95858 22 38614472 18.3548 6.9658 2.52892 2.94985 38958219 18.4120 6.9727 2.53020 2.94118 39304000 18.4391 6.9795 2.53148 2.93255 2 39051821 18.4662 6.9864 2.92395 40001688 18.4932 6.9932 2.91545 40353607 18.5203 7.0000 2.90698 40707 584 18.5472 7.0068 ppp nin Woo Qu mt OV 2.89855 41063625 18.5742 7.01 36 2.89017 41421730 18.6011 7.0203 41781923 18.6279 7.0271 42144192 18.6548 7.0338 42508549 18.6815 7.0400 122500 4287 5000 18.7083 7.0473 123201 43243551 18.7350 7:0540 123904 43614208 18.7617 7.0007 124609 43986977 18.7883 7.0674 125316 443601864 18.8149 7.0740 126025 4473887 5 18.8414 7.0807 1267306 45118016 18.8680 7.0873 127449 45499293 18.8944 7-0940 128164 45982712 18.9209 7.1000 128881 460268279 18.9473 7.1072 129600 46656000 18.97 37 7.1138 130321 47045881 19.0000 7.1204 131044 47437928 19.0263 7.1269 131769 47832147 19.0520 7-1335 132496 48228544 19.0788 7.1400 PP Ypp 133225 48627125 19.1050 7.1466 133956 49027896 19.1311 7.1531 134059 49430863 19.1572 7-1596 135424 498 36032 19.1833 7.1001 130161 50243409 19.2094 7.1726 NNNNN NIN™N™N™NI N™NNIN™N 2.70270 136900 50653000 19.2354 2.69542 137641 51004811 19.2014 2.68517 138384 51478848 19.2873 2.68097 139129 51895117 19.3132 2.67 380 139876 19.3391 140625 d 19.3649 14137 Cys 19.3907 ae 326 19.4165 142884 19.4422 143641 19.4679 f «| Ppt to LX NNN 144400 19.4936 145161 55300341 19.5192 145924 55742968 19.5448 146689 56181887 19.5704 147450 56623104 19.5959 font Sule es No oHNN R HN HN pian SVS Vey Se SMITHSONIAN TABLES. Io TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON’ LOGARITHMS OF NATURAL NUMBERS. n ye 148225 57066625 19.6214 148996 57512450 19.6469 149769 57960603 19.6723 150544 58411072 19.6977 151321 58863869 19.7231 > Co “ a to dO bo io N oN 4 152100 59319000 19.7484 152551 59776471 19.77 37 153064 60236288 19.7990 154449 60698457. 19.8242 155230 61162984 19.8494 QAYHs4O WO MON G2 Gd GW G3 Go 156025 61629875 19.8746 156816 620991 36 19.8997 157609 62570773 19.9249 158404 63044792 19.9499 159201 63521199 19.9750 160000 64000000 20.0000 160801 64481201 20.0250 161604 64964808 20.0499 162409 65450827 20.0749 163216 65939264 20.0998 WO G2 Wd NNNNN py Pps 164025 66430125 20.1246 164836 66923416 20.1494 165649 67419143 166464 67917312 167281 68417929 NN NN nN 168100 68921000 168921 69426531 169744 69934528 170569 70444997 171396 79957944 NwNN bd PES99 Go oe NWN wb NN HN HN 172225 71473375 173056 71991296 173889 72511713 174724 73034632 175561 73500059 NN NNN YNNNN 176400 74088000 20.4939 177241 74018461 20.5183 178084 75151448 20.5426 178929 75086967 20.5670 179776 76225024 20.5913 VRHOHVHNN Quin & Go So N tN iS) ts G3 G2 WW WwW dd Ne Cn “I 180625 76765625 20.6155 181476 77 3087 76 20.6398 182329 77854483 20.6040 183184 784027 52 20.6882 184041 78953589 20.7123 NNN HN te Ga Ga Ga Ga Oo 2 184900 79507000 20.7364 185761 80062901 20.7005 186624 80621 568 20.7846 187489 81182737 20.8087 188356 81746504 20.8327 NNNNN BRO GO 18922 82312875 20.8567 190096 82881856 20.8806 190969 83453453 20.9045 191844 84027672 20.9284 192721 84604519 20.9523 NNNNN bbRRK SMITHSONIAN TABLES. EE TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCARITHMS OF NATURAL NUMBERS. 1000.— nm 23 yz Ye log. 2 2.27273 193600 85184000 20.9762 7.6059 2.64345 2.267 57 194481 85766121 21.0000 7.6117 2.64444 2.26244 195304 80350888 21.0238 7.0174 2.64542 2.25734 196249 86938307 21.0476 7.6232 2.64640 2.25225 197136 87528384 21.0713 7.6289 2.647 38 2.24719 198025 88121125 21.0950 7.6346 2.64836 2.24215 198916 88716536 21.1187 7-6403 2.64933 2.23714 199809 89314623 21.142 7.6460 2.65031 2.23214 200704 8991 5392 21.1660 7.0517 2.65128 2.22717 201601 90518849 21.1896 7-6574 2.6522 2.22222 202500 QI 125000 21.2132 7.6631 2.65321 2.21730 203401 917339851 21.2368 7-6638 2.65418 2.21239 204304 92345408 21.2003 7.0744 2.65514 2.207 51 205209 92959677 21.2838 7.0801 2.65010 2.20264 200116 93570664 21.3073 7.0857 2.65706 2.19780 207025 94196375 21.3307 7.6914 2.65801 4 2.19298 207936 94818816 21.3542 7-6970 2.65896 2.18818 208849 95443993 21.3776 7.7026 2.65992 [ 2.18341 209764 96071912 21.4009 7.7082 2.66087 | 2.17865 210681 96702579 21.4243 7.7138 2.60181 h 2.17391 211600 97336000 21.4476 7.7194 2.66276 2.16920 212521 97972181 21.4709 7.7250 2.66370 2.16450 213444 98611128 21.4942 7.7306 2.66464 2.15983 214309 99252847 21.5174 7-7362 2.66558 2.15517 215296 99897 344 21.5407 7.7418 2.66652 2.15054 216225 100544625 21.5639 7.7473 2.66745 , 2.14592 217156 101194696 21.5870 7-7529 2.66839 2.14133 218089 101847 563 21.0102 77-7584 2.66932 } 2.13675 21902 102503232 21.6333 7.7639 2.67025 Y 2.13220 219961 103161709 21.6504 7.7695 2.67117 [ e 2.12766 220900 103823000 21.6795 7.7750 2.67210 . 2.12314 221841 104487111 21.7025 7.7805 2.67 302 . 2.11564 222784 105154048 21.7250 7.7860 2.67 394 ' 2.11416 22372 105823817 21.7486 7-795 2.67486 © 5 2.10970 224677 106496424 21-7705 7.7970 2.67578 7 2.10526 22562 107171875 21.7945 7.8025 2.67669 , 2.10084 226576 107850176 21.8174 7.8079 2.67761 a 2.09644 22752 108531333 21.8403 78134 2.67852 2.09205 228484 109215352 21.8632 7.8188 2.67943 i 2.08763 229441 109902239 21.8861 7.8243 2.68034 A 2.08333 230400 110592000 21.9089 7.8297 2.6812 ; 2.07900 231361 T11284641 21.9317 7.8352 2.68215 ‘ 2.07469 23232 Ir1980168 21.9545 7-3406 2.68305 2.07039 233289 112678587 21.9773 7.8460 2.68395 2.06612 234256 113379904 22.0000 7.8514 2.68485 2.06186 235225 114084125 22.0227 7.55608 2.68574 2.05761 236196 114791256 22.0454 7.8622 2.68664. 2.05339 237169 115501303 22.0081 7.8676 2.687 53 2.04918 238144 116214272 22.0907 7.8730 2.68842 2.04499 239121 116930169 22.1133 7.8734 2.68931 2.04082 240100 117649000 22.1359 7.8837 2.69020 2.03666 241081 118370771 22.1585 7-8891 2.69108 2.03252 242004 119095488 22.1511 78944 2.69197 2.02840 243049 119823157 22.2036 7.8998 2.69285 2.02429 244036 120553754 22.2201 7-9OSI 2.69373 SMITHSONIAN TABLES. I2 TABLE 3. UARE ROOTS ae CUBE ALS, SQUARES, CUBES, S eee Gare OF RECIPROC Q ts aT TE NUMBE »y AND COMMON "LOGARITHMS OF 1 1000.;- 2.02020 2.01613 2.01207 2.00803 2.00401 2.00000 1.99601 1.99203 1.98807 1.95413 1.98020 1.97628 1.97239 1.96850 1.96404 1.96078 1.95695 iE east 1.94932 1.94553 1.94175 1.93798 1.93424 1.93050 1.92678 1.92308 1.91939 1.91571 1.91205 1.90840 1.90476 I.QO114 1.89753 1.89304 1.89036 1.88679 1.88324 1.87970 1.87617 1.87266 1.86916 1.86567 1.86220 1.85874 1.85529 1.85185 1.84843 1.84502 1.84162 1.83824 1.83486 1.83150 1.82815 1.82482 1.82149 SMITHSONIAN TABLES. 2 u- 245025 246016 247009 248004 249001 250000 251001 252004 253009 254016 255025 256036 257049 258064. 259081 260100 261121 262144 2631609 264196 265225 266256 267289 268324 269361 270400 271441 272484 273529 274576 27 5625 276676 277729 278784 279841 280900 281961 283024 284089 285156 286225 287296 288369 289444 290521 291600 292681 293764 294549 295936 297025 298116 299209 300304 301401 ns 121287375 122023930 122763473 123505992 124251499 I 25000000 125751501 126506008 127263527 128024064 128787625 129554216 130323543 131090512 13187222 132651000 133432831 134217728 135005697 135799744 13659087 5 137 388096 138188413 138991832 139798359 140608000 141420761 142236648 143055667 143877824 144703125 145531576 146303183 147197952 148035559 148877000 149721291 150568768 151419437 152273304 53130375 183090050 154554153 155720872 156590819 157404000 158340421 159220088 160103007 160989184 161878625 1627713306 163667323 164566592 165499149 NWN Nb NNN HN NNHNN NH NNN NW ay oe. 239) eee ry aes ao aes 22 “< 3 3 3 3 4 4 4 4 4 5 5 5 5 6 6 6 6 6 a yi 7 7 8 82 is iS ic oo Ww N NNN HN NNN NN N&R NNN tM weN HN tN w%wwKHN NNNNN tN \O OV 0 fe} Coo “Sin nas Wun NdNHN NH WQNNNN Oo NH HHL WO Ow WN LN to Ww oo & BG Go SNH Nb WO 2 GG Go Oo N Yn 7-9105 7-9158 7.9211 7-9264 7-9317 7-9370 7-9420 7-9476 7.9528 7.9581 7-9034. 7.9036 7-9739 7-9791 7-9343 7.9896 7-9948 8.0000 8.0052 8.0104 8.0156 8.0208 8.0260 8.0311 8.0363 8.0415 8.0466 8.0517 8.0569 8.0620 8.0671 8.0723 8.0774 8.0825 8.0876 8.0927 8.0978 Oo ° Ww dN Cour COLD Nw KS eS On) COU Go Gs Go log. 2 2.69461 2.69548 2.69636 2.69723 2.69810 2.69897 2.69934 2.70070 2.70157 2.70243 2.70329 2.70415 2.70501 2.70586 2.7007 2 2.707 57 2.70842 2.70927 NNNNN NNN NH i) t Syed SST N™N™N™NI™N NR dw bh wR NHN YN NO ty NO vyvbv Ss Woh db 0 N NNN N NSNINININ G2 Ga GW G2 Go 1S) NNN nN NNNINNI BAA 13 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON’ LOGARITHMS OF NATURAL NUMBERS. 1 2 . P 1000.— log. 2 1.81818 5 16637 5000 1.81488 167284151 1.81159 168190608 1.808 32 8 169112377 1.80505 5 170031464 2.74030 2.74115 2.74194 2.74273 2-74351 RNHN Wh 25889 = Ww Hor Cu Ore &e NY 1.80180 170953875 1.79856 3 171879616 1.79533 d 172808693 1.79211 173741112 1.78891 , 174676879 2.74429 2.74507 2.74586 2.74063 2.74741 NNN HN bo Gi NN N ywb © =WAin QO NN OO O 1.78571 17 5616000 1.78253 d 170558481 1.77930 34. 177504328 1.77620 178453547 1.77305 179400144 2.74819 2.74896 2.74974 2.7 5051 2.75128 Nw NN NNN DN ty 9000009000 9000000000 90. 00.09000.00 QOun & NN YON bd 180362125 -7697 2 2.75205 181321490 -7908 -2719 2.75282 182284263 22: 27 2.75358 183250432 | 23.832 . 2.75435 184220009 8 32 2.75511 1.76991 1.76678 1.76367 1.76056 1.75747 1.75439 1.75131 1.74825 1.74520 1.74216 185193000 872 : 2.75587 18616941 I : -2962. 2.75004 187149248 ; : 2.75740 188132517 189119224 Nv WwW Wd OH OD 02 GO) GG) G2 "1.73913 190109375 1.73611 191102976 1.73310 2 192100033 1.73010 193100552 1.72712 2 194104539 1.72414 195112000 1.72017 196122941 1.71821 197137308 1.71527 38 198155287 1.71233 4105 199176704 1.70940 2 200201625 1.70648 201230056 24.2074 1.70358 69 2028RO0G 24.2281 1.70068 203297472 24.2487 1.69779 204330469 | 24.2693 1.69492 } 205379000 24.2899 1.69205 20642507 1 1.68919 5 207474688 1.68634 d 208527857 1.68350 2 209584554 1.68067 21064487 5 mph 21 ORS. -07 504 212770173 1.67224 5 213847192 1.60945 214921799 1.66667 216000000 : : 2.77815 1.66389 217081801 : ; 2.77887 1.66113 362 218167208 53! . 2.77960 1.65837 21925622 ; 3.448 2.78032 1.65503 220348864 | 24. 453 2.78104 SmitHsonian TABLes. 14 634 635 640 645 649 650 654 655 656 657 658 659 1 1000.;- 1.65289 1.65017 1.64745 1.64474 1.64204 1.63934 1.63006 1.63399 1.63132 1.62806 1.62602 1.62338 1.6207 5 1.61812 1.61551 1.61290 1.61031 1.60772 1.60514 1.60256 1.60000 1.59744 1.59490 1.59230 1.58983 1.58730 1.58479 1.58228 1.57978 1.57729 1.57480 ESI 33 1.56986 1.56740 1.56495 1.56250 1.56006 1.55763 1.55521 1.55280 1.55039 1.54799 1.54560 1.54321 1.54083 1.53846 1.53010 1.53374 1.53139 1.52905 1.52672 1.52439 1.52207 1.51976 1.51745 SMITHSONIAN TABLES. 9 m* 306025 367236 308449 309664. 370881 372100 373321 374544 375769 376996 378225 379450 380689 381924 383161 384400 385641 380884 388129 389376 390625 391876 393129 394384 395041 396900 398161 399424 400089 401956 403225 404496 405769 407044 408321 409600 410881 412164 413449 414736 416025 417316 418609 419904 421201 422500 23801 425104 426409 427716 429025 430330 431649 432964 434281 n> 221445125 2545010 645543 NNN = G2 wOdwoWN Het 229220928 30346397 3147 5544 2608375 3744596 34885113 230029032 237176059 byt OO 238328000 239483061 240041848 241804367 242970024 244140625 245314376 246491883 247673152 248855189 250047000 251239591 252435968 2536361 37 254840104 256047875 257250456 258474853 259694072 260917119 262144000 263374721 264609288 265847707 267089984 268336125 2695861 36 270840023 272097792 27 3359449 274625000 275894451 277167808 278445077 279720264 281011375 282300416 283593393 284590312 286191179 Now Nb PLLA H oO Ke Ni f 24.7992 24.8193 24.5395 24.8596 24.5797 24.8998 24-9199 24-9399 24.9600 24.9800 25.0000 25-0200 25.0400 25-0599 25-0799 25.0998 25.1197 25.1396 25-1595 25-1794 25.1992 25-2190 25-2389 25.2587 25.2784 25-2982 25.3180 25-3377 25:3574 Doe Wd tb -3969 a ON mn bow WN bL WMA +. in mn Ch ‘4755 5-495! wal _ MN “5343 5539 "5/34 .5930 2 3 .6320 6515 .6710 NHN Nb Wun = S] “ Mmmm uitn wm Nw HN WL Muu 5544 Wiad Aun Oo mo OV - Oo onI™N as bp Nn oO ON nN C0900 00 00 HOM MM MMM ~O CO Mum ut TABLE 3S. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCARITHMS OF NATURAL NUMBERS. 2.79239 2.79309 2.79379 2.79449 2.79518 2.79934 2.79657 2.79727 2.79796 2.79865 2.79934 2.80003 2.80072 2.80140 2.80209 2.80277 2.80346 2.80414 2.80482 2.80550 2.80618 2.80686 2.807 54 2.80821 2.80889 2.80956 2.81023 2.81090 2.81158 2.81224 2.81291 2.81358 2.81425 2.81491 2.81558 2.81624 2.81690 mS TABLE 3. VALUES OF RECIPR ROOTS, AND 1.51515 1.51286 1.51057 1.50830 1.50602 1.50376 1.50150 1.49925 1.49701 1.49477 1.49254 1.49031 1.48810 1.48588 1.48368 1.48148 1.47929 1.47710 1.47493 1.47275 1.47059 1.46843 1.46628 1.46413 1.46199 1.45985 1.45773 1.45560 1.45349 1.45138 1.44928 1.44718 1.44509 1.44300 1.44092 1.43885 1.43678 1.43472 1.43266 1.43062 1.42857 1.42653 1.42450 1.42248 1.42045 1.41844 1.41643 1.41443 1.41243 1.41044 1.40845 1.40647 1.40449 1.40252 1.40056 430921 435244 439569 440896 44222 443556 444589 446224 447561 448900 450241 451584 452929 454276 455625 456976 458329 459084 401041 462400 463761 465124 466489 467856 46922 470596 471969 473344 474721 476100 477481 478864 480249 451636 483025 484416 485809 487 204 488601 490000 491401 492804 494209 495616 497025 498430 499849 501264 502681 504100 505521 506944 508369 509796 287496000 288804781 290117528 291434247 292754944 294079625 295408296 296740963 298077632 299418309 300763000 302111711 303464448 304821217 306182024 30754687 5 308915776 310288733 3116657 52 313040839 314432000 315821241 317214508 318611987 32001 3504 321419125 3228288 56 324242703 6) Od Gd Wd OD WWwwh vd 335792375 337153536 33860887 3 340068 392 341532099 343000000 344472101 345948408 347428927 34891 3064 350402625 351895816 353393243 354594912 350400529 35791 T0000 359425431 360944128 362467097 363994344 SMITHSONIAN TABLES. 16 8457 8650 tt NNN 8844 -9037 .9230 .9422 5.9615 25.9808 26.0000 26.0192 26.0384 26.0576 26.0768 26.0960 26.1151 26.1343 26.1534 wWNN NN 26.1725 26.1916 26.2107 26.2298 26.2488 26.2679 26.2869 26.3059 26.3249 26.3439 26.3629 26.3818 26.4008 26.4197 26.4386 26.4575 26.4764 26.4953 26.5141 26.5330 NNHHNON 2.82475 2.82543 2.82607 2.82672 2.82737 2.82802 2.82866 2.82930 2.82995 2.83059 2.83123 2.83187 2.83251 2.8331 2.8337 2.83442 2.83506 2.83569 2.83032 2.83696 2.837 59 2.83822 2.83885 2.83948 2.84011 2.84073 2.84136 2.84198 2.84261 2.84323 2.84386 2.84448 2.84510 2.84572 2.84034 2.84696 2.84757 2.84819 2.84880 2.84942 2.85003 2.85065 2.85126 2.85187 2.85248 2.85309 2.85370 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LO ARITHMS OF NATURAL NUMBERS. 365525875 942 2.85431 367061696 .7 582 : 2.85401 308601813 : ; 2.85552 370146232 : 95 2.85612 516961 371694959 S142 2.85673 518400 37 3248000 26.832 962 2.85733 519841 374805361 ; 3. 2.85794 521284 376367048 5 z 2.85554 522729 377933067 26.8887 9752 2.85914 524176 379593424 26.9072 . 2.85974 525625 381078125 26.9258 ; 2.86034 527076 382657176 26.9444 ; 2.86094 528529 384240583 26.9629 : 2.86153 529984 385828352 26.9815 : 2.86213 531441 387420489 27.0000 : 2.86273 532900 389017000 27.0185 i 2.86332 534361 390617891 27.0370 : 2.86392 535024 392223168 27.0555 ; 2.86451 537289 393832837 27.0740 ; 2.86510 538756 395446904 | 27.0924 2.86570 540225 397008375 27.1109 .024 2.86629 541696 398688256 27.1293 .028 2.86688 543169 400315553 | 27-1477 2.86747 544644 401947272 27.1662 i 2.86806 546121 403583419 27.1846 ; 2.86864 547600 405224000 27.2029 : 2.86923 549081 406869021 27.2213 : 2.86982 550504 408518485 27-2397 . 2.87040 552049 410172407 27.2580 : 2.87099 553536 411830784 | 27.2764 2.87157 555025 413493625 550516 415160936 558009 416832723 559504 418508992 561001 420189749 NNNNN 562500 421875000 564001 423564751 565504 425259008 567009 426957777 568516 428661064 2.87622 2.87679 2.87737 NNN NH 2.87795 2.878 52 2.87910 2.87967 2.88024 570025 43036887 5 571530 432081216 573049 433798093 574504 435519512 576081 437245479 Nw HNL 2.88081 2.881 38 2.88195 2.88252 2.88 309 88366 88423 -88480 577600 438976000 579121 440711081 580644 4424507 28 582169 444194947 583696 445943744 NOH HHN NSINN™N SJ 585225 447697125 5867 56 449455096 588289 451217063 589824 4529848 32 591361 4547 56609 NNHNN NNN Hh ees ET) Say SeT ST SMITHSONIAN TABLES. 17 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCGARITHMS OF NATURAL NUMBERS. 03 450533000 458314011 460099648 461889917 463684824 ~ “NI ° nu Nw HN bd yy bwbHH % d%o& 2 G0 60 oes oO 465484375 467288576 469097433 470910952 472729139 ow wN bh 474552000 476379541 478211768 480048687 481890304 4837 36625 485587656 487 443403 489303372 491169069 493039000 494913671 496793088 498677257 500566154 wR NN dN ad Nm wWKN be 632025 502459875 | 28.1957 633616 504358330 28.2135 635209 506261573 28.2312 636804 508169592 28.2489 638401 510082399 28.2066 Ro NN HN 640000 512000000 28.2843 641601 513922401 28.3019 643204. 515849608 28.3196 644809 517781627 28.3373 640416 519718404 | 28.3549 bRHKKA .2422¢ 648025 521660125 28.3725 649636 523606616 28.3901 651249 525557943 | 28.4077 652864 527514112 28.4253 654481 529475129 | 28.4429 656100 531441000 657721 533411731 659344 535387 328 660969 537 367797 662596 539353144 Nb t 664225 541343375 665856 543339490 667459 545338513 669124 547 343432 670761 549353259 NRHN bw Wb 672400 551308000 28.6356 674041 553397661 28.6531 67 5684 555412248 28.6705 677329 557441767 28.6880 678976 55947622 28.7054 2.91593 SmitHSONIAN TABLES. | 18 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOGARITHMS OF NATURAL NUMBERS. 1 2 $ ! 1000.;~ nn log. 2 1.21212 680625 561515625 : .378 2.91645 1.21065 682276 563559970 ' .38 2.91698 1.20919 683929 565609283 3. : 2.91751 1.20773 685584 507663552 : 30 2.91803 1.20627 687241 569722789 .20482 688900 571787000 -20337 690561 573856191 -20192 69222 $7 5930368 .20048 693889 575009537 “19904 695556 580093704 .19760 697225 582182875 -19617 698896 584277050 -19474 700569 586376253 -19332 702244 588480472 “19190 703921 590589719 .19048 705600 592704000 -18906 707281 594823321 18765 708964 596947685 .18624 710649 599077 107 .18483 712336 601211584 bY wVN 18343 714025 603351125 -18203 715716 605495736 .18064 717409 607645423 17925 719104 609800192 17786 720801 611960049 bdyyyn 17647 722500 614125000 17509 724201 616295051 0737.1 725904 618470208 7233 727609 620650477 17090 729316 622835864. NNNHNN 16959 731025 625026375 16822 732730 627222016 .16686 42 629422793 16550 631628712 16414 633839779 NNNNN 16279 6360 56000 16144 2 638277381 .16009 , 640503928 -15875 642735047 -15741 644972544 NO NHN bd .15607 22¢ 647214625 -15473 7499! 649461896 -15340 5168 651714363 15207 3424 653972032 -15075 5 656234909 byw nvbd um rs ON & 14943 756900 658503000 -I4501 758041 660776311 14679 760384 663054548 -14548 762129 665338617 -14416 763876 667627624 in wm ° _ NNN NN .14286 765625 669921875 14155 767376 672221376 14025 769129 674526133 13895 770884 676336152 -13766 772641 679151439 Ryn NN SMITHSONIAN TABLES. 19 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOGARITHMS OF NATURAL NUMBERS. 774400 681472000 776161 683797841 777924 686128968 779089 688465387 781450 690807 104 RY wHHAN 783225 693154125 784996 695506456 786769 697864103 788544 700227072 790321 702595369 792100 704969000 : : 2.94939 793881 797347971 2.94988 795064 7097 32288 866. y 2.95036 797449 712121957 : 799236 714516954 NNN b bv OOGOGS 801025 716917375 802816 719323130 804609 721734273 806404 724150792 808201 726572699 ppppy 810000 729000000 811801 731432701 813604. 733870808 815409 730314327 817216 738763264 30.0066 819025 741217625 30.08 32 8208 36 743077416 30.0998 822649 740142643 30.1164 824464 748613312 30.1330 826281 751089429 30.1496 828100 753571000 30.1662 : 2.95904 829921 7506058031 30.1828 : 2.95952 831744 758550528 | 30.1993 2.95999 833509 761048497 | 30.2159 . 2.96047 835390 703551944 | 30.2324 2.96095 1.09290 83722 76606087 5 30.2490 4 2.96142 1.09170 839056 768575296 30-2655 : 2.96190 1.09051 840889 771095213 30.2820 : 2.962337 1.08932 842724 77 3620632 30.2985 718 2.96284 1.08814 844561 770151559 30.3150 Wee 2.96332 1.08696 846400 778688000 30.3315 : 2.96379 1.08578 848241 781229961 30.3480 : 2.96426 1.08460 850084 783777448 30.3045 722 2.96473 1.08342 851929 789330467 30.3809 : 2.90520 1.08225 853776 788859024 30.3974 } 2.90507 1.08108 855625 791453125 30.4138 k 2.90614 1.07991 857476 794022776 30.4302 : 2.90061 1.07875 859329 796597983 | 30.4467 2.96708 1.07759 861184 7991787 52 30.4631 ; 2.96755 1.07643 863041 801765089 30.4795 ; 2.90802 1.07527 864900 804357000 30.4959 , 2.96848 1.07411 866761 806954491 30.5123 . 2.96895 1.07296 868624 809557568 30. 5287 768 2.96942 1.07181 870489 812166237 30.5450 : 2.96988 1.07066 872356 814780504 30.5014 . 2.97035 SMITHSONIAN TABLES. 20 VALUES OF RECIPR ROOTS, AND C 1.06952 1.06838 1.06724 1.06610 1.06496 1.06383 1.06270 1.061 57 1.00045 1.05932 1.05820 1.05708 1.05597 1.05485 1.05374 1.05263 1.05152 1.05042 1.04932 1.04522 1.04712 1.04603 1.04493 1.04384 1.04275 1.04167 1.04058 1.03950 1.03832 1.03734 1.03627 1.03520 1.03413 1.03306 1.03199 1.03093 1.02987 1.02881 1.02775 1.02669 1.02564 1.02459 1.02354 1.02249 1.02145 1.02041 1.01937 1.01833 1.01729 1.01626 1.01523 1.01420 1.01317 1.01215 1.01112 SMITHSONIAN TABLES. ° go2500 904401 906304 908209 QIO116 912025 913930 915849 917764 919681 921600 23521 925444 927369 929296 93122 933156 935009 937024 938961 940900 942841 944784 946729 948676 950625 952576 954529 956484 958441 960400 962361 964324 966289 968256 970225 972196 974169 976144 978121 817400375 820025856 822656953 825293072 827930019 $30584000 833237621 835896888 835561807 841232384 843908625 846590536 849278123 851971392 854670349 85737 5000 86008 5351 862801 408 865523177 868250664 70983875 873722816 876467493 879217912 881974079 8847 36000 887 503681 890277128 893056347 895841344 898632125 901428696 904231063 907039232 9098 53209 91267 3000 QI5498011 918330048 921167317 924010424 926859375 929714176 932574833 935441352 938313739 941192000 944076141 946966168 949862087 952763904 955671625 958585256 961 504803 964430272 967 301669 21 eee. 30.0105 30.6268 30.6431 30-6594 30-67 57 30.6920 30.7083 30.7246 30-7409 39-7572 39-7734 30.7896 30.8058 30.8221 30.8383 30-5545 30.8707 30.8869 30.9031 30.9192 30-9354 30.9516 30-9677 30.9839 31.0000 31.0161 31.0322 31.0483 31.0644 31.0805 31.0966 aU Li27 31.1288 1448 -1609 .1769 .1929 2090 2250 2410 2570 .2730 .2890 31.3050 31.3209 31-3369 31.3528 31.3088 31.3847 31.4006 31.4166 oh A325 31-4484 9.8132 9.8167 g.8201 9.8236 9.8270 9-8305 9.8339 9.8374 9.8408 9.8443 9.8477 9.8511 9.8546 9.8580 9.8614 9.8648 9.8683 9.8717 9.8751 9.8785 9.9329 9.9363 9.9396 9.9430 9.9464 NN NN Nr NNNNN N NNN to PHP Pp Oo _ wn WwW Oo PHP Pp ‘9 0 000 0 COCO C0 CO mCOnnmnnnm Om On~I I ON Quin & NN NNN 2.0.00 2.99344 2.99388 2.99432 2.99476 TABLE 3. VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND COMMON LOCARITHMS OF NATURAL NUMBERS. = 2 : 3) 1000. 2 log. 2 1.01010 980100 970299000 : 2.99564 1.00908 982081 97 3242271 7 2.99007 1.00806 984064 976191488 . 2.99051 1.00705 986049 979146657 2.99695 1.00604 988036 982107754 ’ 2.99739 1.00503 990025 9 1.00402 992016 9 1.00301 994009 9 3 307487 5 ; 2.99782 85047930 7 2.99826 9102697 3 : 2.99870 1.00200 996004 99401 1992 99: 2.99913 1.00100 998001 997002999 99k 2.99957 1.00000 1000000 1000000000 10.0000 3-00000 SMITHSONIAN TABLES. 22 ~~ TABLE 4. CIRCUMFERENCE nr eet OF CIRCLE IN TERMS OF 3848.45 3959-19 4071.50 4185-39 4300.54 4417.86 n> tN 4536-46 4656.63 4778.36 4901.67 5026.55 5153-00 5281.02 5410.61 5542-77 NN tv 5674-50 5808.80 5944-68 6082.12 6221.14 6361.73 6503.88 6647.61 3 4 5 6 No WN o0noMm N WHN 2 Wd Qn = 3216.99 3318.31 3421.19 G2 2 Go On SMITHSONIAN TABLES. TABLE 5. LOCGARITHMS OF NUMBERS. Prop. Parts. 23) 45°56) 77889 Ot2 17 21 25 zo eepy, 8 II 151923 26 30 34 710 141721 24 28 31 610 131619 23 2629 6 9 121518 21 24 27 0086 0128 0170 | 0212 0253 0334 0374 0492 0531 0569 0645 0719 0755 25 0864 0899 0934 | oc 1004. 1072 1106 1200 1239 1271 | 1303 1335 1399 1430 1523 1553 1584 | 1614 1644 1703 1732 Il. 14.07 .20°22)25 111316 18 21 24 IO) 1295) Lzeeoee 91214 16109 21 91113 1618 20 1818 1847 1875 1931 1987 2014 2095 2122 2148 | 2 2201 2253 2279 2355 2380 2405 | 2430 2455 2504 2529 2601 2625 2648 | 2672 2695 2742 2765 2833 2856 2878 | 2 2923 2907 2989 NNKHWW WHWWAL HE 3054 3096 3139 3181 3201 3203 3304 3345 3385 3404 3464 3483 3502 | 3522 3541 3500 3579 3598 3055 3692 | 3711 3729 3766 3784 3838 3856 3874 3909 3945 3962 ID 13) 0s 7ATg IOI2 141618 IOI2 141517 gt) wih is 407) TT een mmo HRPARAR BUUUHA NN HNN SJ 4014 4031 4048 4082 4116 4133 4183 4200 4216 4249 4281 4298 4346 4362 4378 | « 4409 4440 4456 4502 4518 4533 5 4564 4594 4609 4954 4069 4053 4713 4742 4757 12 14 ity ate: II 13 I2 me NNN bd buOninu MaAANADH G2 Ga G2 OG OD NOmDmMmMO wow 4800 4814 4829 | « 4857 4886 4900 3 4942 4955 4969 33. 4997 5024 5038 5 5079 5092 5105 5132 5159 5172 9 $211 5224 5237 50 5263 5289 5302 28 5340 5353 5306 5391 5416 5465 5478 5490 | 5502 5514 5539 5587 5599 S611 23 5035 5647 5058 5705 5717 5729 | 5749 5752 5763 5775 §021 5832 5843 355 §866 5877 5888 2 5933 5944 5955 5977 5988 5999 6042 6053 6064 6085 6096 6107 6149 6160 6170 80 6191 6201 6212 6253 6263 6274 84 6294 6304 6314 6355 6365 6375 | 6385 6395 6405 6415 6454 6464 6474 6493 6503 6513 _— MRAMNO OOWODO I I I I I Ga GW G2 G2 Go O22 Go & HARE Pe Nw WK Wb et NKNNHN HN Wo Ga Ga Ga G2 6551 6561 6571 6590 6599 6609 6646 6656 6665 6084 6693 6702 6739 6749 6755 | 6767 6776 6785 6794 6830 6839 6348 | 6857 6866 63875 68384 6920 6928 6937 | 6946 6955 6964 6972 OY Rw WHN NN G2 Ga Gd Ga G2 7007 7016 7024 | 7033 7042 7050 7059 7067 7093 7IOI 7110 | 7115 7126 7135 7143 7152 3.7177 F185 7193 '|-7202,7210 7215 7220 7235 7259 7207 7275 | 7284 7292 7300 7308 7316 734° 7348 7350 | 7364 7372 7380 7388 7396 Nd NWUY W a GG) G2 AAPA H AALAALHL hun UN aAD ANANN APRA AL &AUMN Umm WADDAGA QAONNN ANMMn WN AD ADAnNDAD NNNN = NRwN NHN SMITHSONIAN TABLES. ~ TABLE 5. LOCGARITHMS OF NUMBERS. Prop. Parts. » WNW AHL OO 7404 7412 7419 7427 7435 | 7443 7451 7459 7406 7474 7482 7490 7497 7505 7513 | 7520 7528 7530 7543 7551 7559 7506 7574 7582 7589 | 7597 7604 7612 7619 7627 7634 7642 7649 7657 7664 | 7672 7679 7686 7694 7701 7709 7716 7723 773! 7739 | 7745 7752 7760 7767 7774 Pe ie helo eennn N VNONNLN &Z G2 C2 Ga Ga G2 7782 7789 7796 7803 7810 | 7818 7825 7832 7839 7846 7853 7860 7868 7875 7882 | 7889 7896 7903 7910 7917 7924 7931 7938 7945 7952 | 7959 7966 7973 7980 7987 7993 8000 8007 8014 8021 | 8028 8035 8041 8048 $055 8062 8069 8075 8082 8089 | 8096 8102 8109 $116 8122 os — NNN WN 8129 8136 $142 8149 8156 | 8162 8169 8176 8182 8189 8195 8202 8209 8215 8222 | $228 8235 8241 8248 8254 8261 8267 8274 8280 8287 | 8293 8299 8306 8312 8319 8325 8331 8338 8344 8351 | 8357 8363 8370 8376 8382 $388 8395 S4o1 8407 8414 | 8420 $426 8432 8439 8445 by G2 G2 Ga Go Ka Ga Ga G2 G2 — — Oe NNN NN 8451 8457 8463 8470 8476 | 8482 8488 8404 8500 8506 8513 8519 8525 8531 8537 | 8543 8549 8555 8561 8567 8573 8579 8585 8591 8597 | 8603 8609 8615 8621 8627 8533 8639 8645 8651 8657 | 8663 8669 8675 8681 8686 8692 8698 8704 8710 8716 | 8722 8727 8733 8739 8745 Se ee ee i el NNN HW NNN HNN 8751 8756 8762 8768 8774 | 8779 8785 8791 8797 8802 8808 8814 8820 8825 8831 | 8837 8842 8348 8854 8859 8865 8871 8876 8882 8887 | 8893 8899 8904 8910 8915 =— = = eS eR i NNN WN RN N NW 8921 8927 8932 8938 $943 8949 8954 8960 8965 8971 WWW OW a pH HL RBH FHUIMIMN G QQ Od G2 G2 OD WD G2 G2 G2 G2 WW WG Gd 8976 8982 8987 8993 8995 | 9004 9009 9OI5 9020 9025 9031 9036 9042 9047 9053 | 9058 9063 9069 9074 9079 go85 gogo 9096 QIOI 9106 | OII2 OII7 9122 9128 9133 9133 9143 9149 9154 9159 | 9165 9170 9175 gI80 9156 QIOI 9196 9201 9206 9212 | 9217 922 9238 9243 9248 9253 9258 9263 | 9209 - = = oe i RN NHNN NNN NN G2 G2 Ga G2 G2 Go Go Ga G2 Go 9294 9299 9304 9309 9315 | 9320 9345 9350 9355 9360 9365 9395 9400 9405 9410 9415 | 9420 9425 9430 9435 9440 9445 9450 9455 9460 9465 | 9469 9474 9479 9484 9489 9494 9499 9504 9509 9513 | 9518 9523 9528 9533 9538 9542 9547 9552 9557 9562 | 9566 9571 9576 9581 9586 9590 9595 9000 9605 9609 | 9614 9OIg 9624 9628 9633 9638 9643 9647 9652 9657 | 9661 9666 9671 9675 9650 9685 9689 9694 9699 9703 | 9708 9713 9717 9722 9727 | 9731 9736 9741 9745 9750 | 9754 9759 9763 9768 9773 se Wh bw wR WN NO WwW ty GIG ooo, SS SS WWutkf hAHLH AL hALAHAL pAPRPLH bhp Minin Muu ss] ooo 00 sa Ss = Se es Ss eS NNN N Nb NKHNN G2 Ga G2 OG) OD bo GW G2 W G2 ty 2 G2 G2 G2 G2 tl 9777 9782 9786 9791 9795 | 9800 9805 9809 9814 9818 9823 9827 9832 9836 9841 | 9845 9850 9854 9859 9563 9868 9872 9877 9881 9886 | 9890 9894 9899 9903 9908 9912 9917 9921 9926 9930 | 9934 9939 9943 9948 9952 9956 9961 9965 9969 9974 | 9978 9983 9987 9991 9996 o0o0o0°0 = = = eS eR NwHNN Nw WN NWN SS ee ware ARR hAHAA LP AhAAA LH hRBRUnN WU Mminiuiinin UM AADN ADAQanndd © AAPDAA AAHLAR AEREUN UUUUNH UNUNW WMD DADA ANDAADA NNNNN O Wd G2 G2 G2 G2 Go Ga Go o o SMiTHSONIAN TABLES. TABLE 6. ANTILOCARITHMS. Prop. Parts. He HR Ree OL oa IOI4 1038 1062 1086 I1I2 Oo0O0000 ae mee OD = eee Ne eee YNvYNNDN AJ YNNHnNHb OO bdo bwHNnN O 1138 1164 IIQI 1219 1247 dh oo0o0°0 so ot ee! ee oe NNN NN NdodoHN Noh 1276 1306 1337 1308 1400 oo0000 = a — = et Nw NN a wNwONNN NwNH HN 1432 1406 1500 1535 1570 oo0o0o0°0 =x = St wb NHNN NwNHNN —~— 1607 1644 1683 1722 1762 o0o000 = = NoYON HA NwNNYN NNNNDHN bo G2 G2 WG 2 Ga G2 Go Go WWwNhKN G2 G2 OG WG WNNNL 1803 1845 1883 1932 1977 OF OO; O80 wWNN NL No NN HN 2023 2070 2 2118 2 2168 2218 -O000 Nw eRe RN wWKHNN WNNNN = aise OWN +O NNN HN WV SHwWNn bd NNN NbN Ss = Se NNN HN NOnvw NN ON ce) 2 2518 2576 2636 2 2698 2761 3 2559 2 2618 262 2679 2742 2 2805 2 Nw HN WN | NwNNN 3 2825 2 2838 2 2871 2891 2904 2924 2 2938 2958 2 2972 3006 3027 3041 2 3069 3076 3097 3141 3148 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 aA A LD HHA DH QO Wo Oa Gd Wa 2 G2 U2 WWW dv DADmnNn UNUMNMinN UNMPHHAHL AHHH BOW PRWWW WHWWWWH WHWwww = = = eS RNNNN MnAMnn HBHPSAH SHPHAAH HWOWWH WHWWW WWW WWwN Nb » a o © SMITHSONIAN TABLES. TABLE 6. ANTILOCARITHMS. Prop. Parts. 6 » ANDNDADND DAOiunMN Nunn MAPLE HHH A 3162 3170 3177 3184 3199 3206 3214 3221 3228 3236 3243 3251 3258 3273 3281 3289 3296 3304 3311 3319 3327 42 | 3350 3357 3365 3373 3381 3388 3396 3404 3428 3436 3443 3451 3459 3467 3475 3483 3508 3516 3524 3532 3540 ee | nNNHNeA WN YnNHvHKHN W ANDAAD OE 3548 3556 3565 3573 3589 3597 3606 3614 3622 3031 3639 3045 3073 3081 3690 3698 3707 3715 3724 3733 3741 375° | 3758 3767 3776 3784 3793 3802 3811 3319 3828 3846 3855 3564 3873 3882 3890 3899 3908 3917 3936 3945 3954 3963 3972 3981 3990 3999 4009 4027 4036 4046 4055 4064 4074 4083 4093 4102 412I 4130 4140 4150 4159 4169 4178 4188 4198 4217 4227 4236 4246 4256 4266 4276 4285 4295 4305 | 4315 4325 4335 4345 4355 4305 4375 4385 4395 4406 | 4416 4426 44360 4446 4457 — = NNNNN WWW WWW d WOD00D CO ADHOON NNNNN CO NNN NW Oe 4467 4477 4487 4498 4508 | 4519 4529 4539 4550 4560 4571 4581 4592 4603 4613 | 4624 4634 4645 4656 4667 4677 4088 4699 4710 4721 | 4732 4742 4753 4704 4775 4786 4797 4808 4819 4831 | 4542 4853 4864 4875 4887 4898 4909 4920 4932 4943 | 4955 4966 4977 4989 5000 Noh WOnowno ae mmcn§ on NNNNI™N et NNN 5012 5023 5035 5047 5058 | 5070 5082 5003 5105 5129 5140 5152 5164 5176 | 5188 5200 5212 522 5248 5260 5272 5284 5297 | 5309 5321 5333 5346 5370 5383 5395 5408 5420 | 5433 5445 5458 5470 5495 5505 5521 5534 5546 | 5559 5572 5555 5598 5623 5636 5649 5662 5675 | 5689 5702 5715 5728 5754 5768 5781 5794 5808 | 5821 5834 5845 5861 5858 5916 5929 5943 | 5957 5979 5984 5998 6026 6053 6067 6081 | 6095 O109g 6124 6138 6166 6180 6194 6209 6223 | 6237 6252 6266 6281 ee ee | KW NW oo WOOO MDH DRHONN NNNN QQ ADADDAGDA DAdNinim ay SS = = ee O20) Wa Ga Ga 6310 6324 6339 6353 6368 | 6383 6397 6412 6427 6457 6486 6501 6516 | 6531 6546 6561 6577 6607 6622 6637 6653 6068 | 6633 6699 6714 6730 6761 6792 6808 6823 | 6839 6855 6871 6857 6918 6950 6966 6982 | 6998 7015 7031 7047 DNADAD DAOUnN NANUMNn NAPAHLA PERAHRPR HRHhWWW WWWWW OWOOWO OW COMO oOOoOnNN™N NNN OO DANDADA NMUMnn Mmununn > NNNNHe OW Gd) G2 G2 No 7079 7112 7129 7145 | 7161 7178 7194 7211 7244 7278 7295 7311 | 7328 7345 7362 7379 7 7413 7430 7447 7464 7482 | 7499 7516 7534 7551 7586 7603 7621 7638 7656 | 7674 7691 7709 7727 7 7762 7798 7816 7834 | 7852 7870 7889 7907 7 NN NN NNN NS 13 14 1315 13.15 I4 15 14 16 14 1618 7943 7980 7998 8017 | 8035 8054 8072 8091 8 8128 8 8166 8155 8204 | 8222 8241 8260 8279 82 8318 8337 8356 8375 8395 | 8414 8433 8453 8472 8 8511 8551 8570 8590 | 8610 8630 8650 8670 8710 8730 8750 8770 8790 | 8810 8831 8851 8872 8 Co0OMDO OOO NM mmomoni NNNNIN NNNN WN mon on — Se 8913 8933 8954 8974 8995 | 9016 9036 9057 9078 9120 9141 9162 9183 9204 | 9226 9247 9208 9290 9333 9354 9376 9397 9419 | 9441 9462 9484 9506 9550 9572 9594 9616 9638 | 9661 9683 9705 9727 9772 9795 9817 9840 9863 | 9886 9903 9931 9954 I5 17 19 15 17 19 15 17 20 16 18 20 16 18 20 won ne -— SS aH O 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 7 if 7 mnt PARR f& BO) Go) G2 NN WN be SMITHSONIAN TABLES. TABLE 7. NATURAL SINES AND COSINES. Natural Sines. 60° ° .0000 00] . : .0087 27] .o11635| . 41 .0174 52 0174 52] .020-° 0232 02618 | .o2908 | . 03490 03490 | .0378 z .04362 | .04653 | .0402 0523 4 05234 | - .058 06105 | .06395 | .0668 .0097 6 .00976] . : 07846 | .08136] .o842 .0871 6 PP 08716] . : 09585 | .09874] . 1045 3 104531). : “LT32/05|) -LTOOO|e. 1218 7 12187 “2 : -13053 |] -1334 . -1392 LBO2 ; ; 1478 : 15 +1564 1504 : 162 1650 : -1708 -1736 yyy WOON AM BwWnHO 1736 17 . 1822 : .188 .1908 -1908 : ; -1994 ae. : -2079 2079 -2108 ; 2164 f .222 -2250 -2250 .22 : +2334 : .239 2419 2419 2 : +2504 : : 2588 NNNHNN 2588 2 -2 .2672 27 2 -2756 -2756 a2 2812 -2840 2 : 2924 -2924 2952 . +3007 ; +3062 3090 -3090 3 : ‘3173 : : 3250 -3256 -32 : +3330 : : 3420 pNP 3420 7 34 3502 : : 3594 3594 : -3638 -3065 : : -3746 -3746 : . -3827 : : -3907 +3907 =f : 3987 : : -4067 -4067 : 412 -4147 : : -4226 ppp 4226 : E «4305 433 : -4384 4384 ; ; -4462 5 -4540 : . 4017 “4998 : ; 4772 484 . -4924 NNNNN . 5000 : , .5075 -5150 : 52 ~522 -5299 : 3 “5073 “5446 . . “5519 5592 ; : 5064 9 9 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 7 7 7 7 7 7 6 6 6 6 5 °5 oe) 5 4 4 NN ww 5736 : ; -5807 5878 , : 5948 6018 : : -6088 -O157 : -6202 6225 6293 E d 6361 pep WwW Woo .6428 : : 6494 6561 : : 6626 6691 : : .67 56 .6820 . : -6854 -6947 ; : -7009 NNNNN sem NN YN 30’ SMITHSONIAN TABLES. 2 Natural Cosines. ¢ 28 i) TABLE 7. NATURAL SINES AND COSINES. Natural Sines. — ~ etl oes Milas Bin ie 6 6 6 5 5 4 4 4 3 3 SMITHSONIAN TABLES. Natural Cosines. 29 NATURAL TANCENTS AND COTANCENTS. Natural Tangents. Prop. Parts Angie. for 1. PPP ph COO0DD WVUUUYO see OO Ww nN inGs =\ONT fe ON me QW WU 2 2. 3: 3: 3: 3: 3: 3: 3: 3: 3: 3: 3: 3: 3: NNN SO Nd RN NN NO Oo ON OQ MON AD UNSW WdKHHA WYwwW WWW Q o .6168 6412 6661 .6916 22 OO Wh = -7177 7445 7720 -8002 5292 ON Quis Wns Ow 85901 .8599 .9217 9545 RUC CC Eastcote erecta oe Nuk Oo SMITHSONIAN TABLES. Natural Cotangents, 30 TABLE 8. Prop. Parts : for 1’. NATURAL TANCENTS AND COTANCENTS. Natural Tangents. MOI DADA AvnOnhd Oo AF HO OnI es SS eS et MANO AWA WH QAd™ 2.0 2.8 3.6 4.6 57. 6.9 8.3 9-9 1.7 37 bd YB OOO Cn NNNNN I I I 2 2 ~ Ok NI ° OonNnNN AH BRO WWW NO Af NO I ON “SI 4.4494 4.8430 5.3093 5-8708 6.5606 7.4287 8.5555 10.0780 | 10.3854 11.4301 12.2505] 12.7062 14.3007 | 14.9244] 15.6048| 16.3499 19.0811 | 20.2056] 21.4704] 22.9038 28.6363 | 31-2416] 34.3678 | 38.1885 | 42.9641 57-2900 | 68.7501 | 85.9398 |114.5887 |171.8854 |3 | 60’ 50’ 40’ 30’ 20° s if . MITHGONIAN 1 ABLES Natural Cotangents. 31 ee TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE. Minutes Distance. Lat. | Dep. Lat. Dep. Lat. Dep. 1.00000 0.00000 | 0.99984 0.01745 0.99939 0.03490 2.00000 0.00000 1.99969 0.03490 1.99578 0.06980 300000 0.00000 2.99954 0.05235 2.99817 0.10470 4.00000 0.00000 3-99939 0.00950 | 3.99756 0.13960 5.00000 0.00000 4.99923 0.08726 4.99695 0.17450 6.00000 0.00000 5-99905 0.10471 5-99634 0.20940 7.00000 0.00000 6.99893 0.12216 6.99573 0.24430 8.00000 0.00000 7.99878 0.13961 7-99512 0.27920 9.00000 0.00000 8.99862 0.15707 8.99451 0.31410 Oo ON ANAW db oN oO 0.99999 0.00436 0.99976 0.02181 0.99922 0.03925 1.99998 0.00872 1.99952 0.04363 1.99845 0.07851 2.99997 | 0.01308 | 2.99928 | 0.06544 | 2.99763 | 0.11777 399996 | 0.01745 3-99904 0.08725 3-99691 0.15703 4.99995 | 0.02181 4.99881 0.10907 4.99014 0.19629 5.99994 | 0.02617 | 5.99857 | 0.13089 | 5.99537 | 0.23555 6.99993 0.03054 6.99833 0.15270 6.99460 0.27431 7-99992 0.03490 7-99809 0.17452 7:99333 0.31407 3.99991 0.03926 8.99785 0.19633 8.99306 0.35333 Oo ON Quthw bd Ee > Mm 0.99996 0.00872 0.99965 0.02617 0.99904 0.04361 1.99992 0.01745 1.99931 0.05235 1.99809 0.08723 2.99988 0.02617 2.99897 0.07853 2.99714 0.13085 3-99984 | 0.03490 | 3.99862 | 0.10470 | 3.99619 | 0.17447 4.99981 0.04363 4.99828 0.13088 4.99524 0.21809 5.99977 | 9.05235 | 5-99794 | 0.15706 | 5.99428 | 0.26171 6.99973 0.06108 6.99760 0.18323 6.99333 0.30533 7.99969 0.0698 I 7.99725 0.20941 7-99238 0.34895 8.99905 | 0.07853 | 8.99691 | 0.23559 | 8.99143 | 0.39257 w oO © ON QAuhWw bd 0.99991 0.01308 0.99953 0.03053 | 0.99884 0.04797 1.99982 0.02617 1.99906 0.06107 1.99769 0.09595 2.99974 0.03926 2.99860 0.09161 2.99654 0.14393 3.99995 0.05235 3-99813 0.12215 399539 9.19191 4-99957 | 0.00544 | 4.99766 | 0.15269 | 4.99424 | 0.23989 5.99948 0.07553 5-99720 0.18323 5.99309 0.28786 6.99940 0.09162 6.99673 0.21376 6.99193 0.33584 7.99931 0.10471 7.99626 0.24430 7.99078 0.38382 8.99922 0.11780 8.99580 0.27484 8.98963 0.43180 10 ONY ONAW bd ~_ wm Dep. Lat. Dep. , Dep. Lat. ‘a0uej}sIq | © OY OQNnAW db HE © OY QupwW nw O ON QUAW WE © ON QANAW db | Distance. "SONU ‘g0uejsIq SMITHSONIAN TABLES. 32 ) TABLE 9. TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE. —ConrTINUED. Minutes Distance. Distance. Minutes. Lat. Dep. Lat. Dep. Dep. 0.99863 0.05233 0.997 56 0.06975 0.99619 0.08715 1.99726 0.10467 1.99512 0.13951 1.99238 0.17431 2.99589 0.15700 2.99269 0.20926 2.98858 0.26146 3-99452 0.20934 3-99025 0.27902 3:95477 0.34862 4.99315 | 0.26163 | 4.98782 | 0.34878 | 4.98097 | 0.43577 5-99178 0.31401 5-98 538 0.41853 5:97716 0.52293 6.99041 0.36635 6.98294 0.48829 6.97330 0.61008 7:98904 0.41868 7-98051 0.55805 7-96955 0.697 24. 8.98767 0.47102 8.97807 0.62780 8.96575 0.78440 0 ON Quiftics ty OW ONI QuishwWb 0.99839 | 0.05669 | 0.99725 | 0.07410 | 0.99580 | 0.09150 1.99678 0.11338 1.99450 0.14821 1.99160 0.18300 2.99517 0.17007 2.99175 | 0.22232 | 2.98741 0.27450 3-99356 0.22677 3-98900 0.29643 3-98321 0.36600 4.99195 | 0.28346 | 4.98625 | 0.37054 | 4.97902 | 0.45750 5:99035 | 0.34015 5-98350 | 0.44465 5-97482 | 0.54900 6.98874. 0.39684 6.9807 5 0.51875 6.97063 0.64051 7.98713 0.45354 | 7-97800 | 0.59286 | 7.96643 0.73201 8.98552 0.51023 8.97525 0.66697 8.9622 0.82351 OW ON Qufhw bd al 3 4 5 6 7 8 9 0.99813 | 0.06104 | 0.99691 0.07845 } 0.99539 | 0.09584 1.99626 0.12209 1.99383 0.15691 1.99079 0.19169 2.99440 0.18314 2.9907 5 0.23537 2.98618 0.28753 3.99253 0.24419 3.98766 0.31383 3.98158 0.38338 4.99067 | 0.30524 | 4.95458 | 0.39229 | 4.97698 | 0.47922 5.98880 0.36629 5.98150 0.47075 5.97237 0.57507 6.98694 0.42733 6.97842 0.54921 6.96777 0.67092 7.98507 0.48838 | 7.97533 0.62767 7.96316 | 0.76676 8.98321 0.54943 | 8.97225 0.70613 | 8.95856 | 0.86261 © ON Qufu nr OW ON Qustw nd 0.99785 0.06540 | 0.99656 | 0.08280 }| 0.99496 | 0.10018 1.99571 0.13080 1.99313 0.16561 1.98993 0.20037 2.99357 0.19620 2.98969 0.24842 2.98490 0.30056 3-99143 0.26161 3-98626 0.33123 397987 0.4007 5 4.98929 0.32701 4.98282 0.41404 4.97484 0.50094 5-98715 0.39241 5.97939 0.49684 5.96981 0.60112 6.98501 0.45782 6.97595 0.57965 6.96477 0.70131 7.98287 0.52322 7.97252 0.66246 7-95974 0.80150 8.98073 0.58362 8.96908 0.74527 8.95471 0.90169 O ON QUhW bd O ON Auf W tb Dep. : Dep. Lat. Dep. ‘g0ursIC] ‘g0uvysIq *SoNUIT, SMITHSONIAN TABLES. 33 TAPCEASE TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE.-—ConrtiNnueb. Minutes Distance. Distance. Minutes Yat. Dep. Lat. Dep. Lat. Dep. 0.99452 | 0.10452 }| 0.99254 | 0.12186 | 0.99026 | 0.13917 1.93904 0.20905 1.98509 0.24373 1.98053 0.27834 2.98356 0.31358 2.97703 0.36560 2.97080 0.41751 3.97808 0.41811 3.97018 0.48747 3-96107 0.55069 4.97261 0.52264 4.96273 0.60934 4.95134 0.69586 5.96713 0.62717 5-95519 0.73121 5-94160 0.83503 6.96165 0.73169 | 6.94782 0.85308 } 6.93187 0.97421 7-95617 0.83622 7.94038 0.97495 7-92214 1.11338 8.95069 0.94075 | 8.932901 1.09682 8.91241 1.25255 0 ON Qusw np OW ON QubwW vb 0.99405 0.10886 0.99200 0.12619 0.98965 0.14349 1.98811 0.21773 1.98400 0.25239 1.97930 0.28698 2.98216 0.32660 2.97601 0.37859 2.90895 0.43047 3-97622 | 0.43546 | 3.96801 | 0.50479 | 3.95860 | 0.57307 4.97028 0.54433 4.96002 0.63099 4.94825 0.71746 5-96433 | 0.65320 | 5.95202 | 0.75719 | 5.93790 | 0.86095 6.95839 -762 6.94403 | 0.85339 | 6.92755 | 1.00444 7:95245 7-93603 | 1.00959 | 7.91721 | 1.14794 8.94650 9798 8.92804 1.13579 | 8.90686 1.29143 OW ON Qufhwn Zz 3 4 5 6 7 8 9 0.99357 0.11320 | 0.99144 0.13052 0.98901 0.14780 1.98714 0.22040 1.98288 0.26105 1.97803 0.29561 2.98071 | 0.33960 | 2.97433 | 0.39157 | 2.96704 | 0.44342 3.97428 0.45281 3.96577 0.52210 3-95606 0.59123 4.96786 0.56601 4.95722 0.65263 4.94508 0.73904 5.90143 0.67921 5:94866 0.78315 5-93409 0.8368 5 6.95500 0.79242 6.94011 0.91 365 6.92311 1.03466 7.94357 0.90562 7.93155 1.04420 7.91212 1.18247 8.94214 1.01882 8.92300 1.17473 8.90114 1.33028 O ON QuAwW db 0 ON Quifhu vn 0.99306 0.11753 0.99086 0.13485 0.988 36 0.15212 1.98613 0.23507 1.98173 0.26970 1.97672 0.30424 2.97920 35261 2.97259 0.40455 2.96508 0.45637 3-97227 | 0.47014 | 3.96346 | 0.53940 | 3-95344 | 0.60849 4.96534 | 0.58768 | 4.95432 0.67425 | 4.94180 | 0.76061 5-95541 0.70522 5-94519 0.80910 5.93016 0.91274 6.95147 0.82276 6.93606 0.94395 6.91853 1.06486 7.94454 0.94029 7.92092 1.07880 7.90689 1.21698 8.93761 1.05783 8.91779 1.21305 8.89525 1.36911 0 ON Qudw wn O ON Qutpw v Dep. Lat. Dep. ‘SoINUT]Y ‘g0ur}sI(] *20Ue}SICL soqnuUlyy SMITHSONIAN TaBLEs. 34 TABL e TRAVERSE TABLE. =e DIFFERENCES OF LATITUDE AND DEPARTURE. — ConrtTINueED. Distance. Distance. Minutes Lat. Dep. Lat. Dep. Lat. Dep. 0.98768 0.15643 0.98480 0.17364 | 0.98162 0.19081 1.97 537 0.31286 1.96961 0.34729 1.96325 0.38162 2.96306 0.46930 2.95442 0.52094 2.94485 0.57243 3-95075 | 0.62573 | 3.93923 | 0.69459 | 3:92650 | 0.76324 4.93844 0.78217 4.92403 | 0.86824 4.90813 0.95405 5.92612 0.93860 5-90884 1.04188 5.88976 1.14486 6.91381 1.09504 6.89365 1.21553 6.87139 1.33566 7-QOI50 1.25147 7.87540 1.38918 7.85301 1.52048 8.88919 1.40791 8.86327 1.56283 8.83464 1.71729 OW ONI QubhWw wv LO ON QAnuAW bd 0.98699 0.16074 0.98404 0.17794 | 0.98078 0.19509 1.97399 0.32148 1.96808 0.35588 1.96157 0.39018 2.96098 0.48222 2.95212 0.53393 2.94235 0.58527 3-94798 0.64297 3-93616 0.71177 3.92314 0.78036 4.93498 0.80371 4.92020 0.88971 4.90392 0.97545 5.92197 0.96445 5-90424 1.06766 5-88471 1.17054 6.90897 1.12519 6.88828 1.24560 | 6.86549 1.36563 7.89597 1.28594 | 7.87232 1.42354 | 7.84628 1.56072 8.88296 1.44668 8.85636 1.60149 | 8.82706 1.75591 O ON Qupw bv al 5 4 5 6 7 8 9 0.98628 0.16504 | 0.98325 0.18223 0.97992 0.19936 1.97257 | 0.33009 | 1.96650 | 0.36447 | 1.95984 | 0.39873 2.95885 0.49514 2.94976 0.54670 2.93977 0.59810 3:94514 | 0.66019 | 3.93301 | 0.72894 | 3.91969 | 0.79747 4.93142 0.82523 4.91627 O.QI117 4.89962 0.99683 5-91771 0.99028 5.89952 1.09341 5:87954 1.19620 6.90399 | 1.15533 | 6.88278 | 1.27564 | 6.85947 | 1.39557 7.89028 1.32038 7.86603 1.45788 7.83939 1.59494 8.87657 1.48542 | 8.84929 1.64011 8.81932 1.79431 t © ON Qufhuw hn O ON QubwW db 0.16935 0.98245 0.18652 0.97904 0.20364 0.3 3870 1.96490 0.37 304. 1.95809 0.40728 0.50805 2.94735 0.55957 2.93713 0.61092 0.67740 3-92980 0.74609 3-91618 0.81456 0.8467 5 4.91225 0.93262 4.89522 1.01820 1.01610 5.89470 1.11914 5.87427 1.22185 1.18545 | 6.87715 1.30566 | 6.85331 1.42549 1.35480 | 7.85960 1.49219 7.83230 1.62913 1.52415 8.84205 1.67871 8.81140 1.83277 0.98555 1.97111 2.95666 3:94222 4.92778 5-91333 6.895389 7-88444 8.87000 0 ON Qupw bv 0 ON Qupw bp eH Dep. Lat. Dep. Lat. Dep. Lat. std "SONU *20uv ‘g0ueISIC SMITHSONIAN TABLES. 35 TABLE Q. TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE.—ConrTINUED. Minutes Distance. ats 2p. Lat. 0.97814 0.20791 0.97437 0.22495 0.97029 0.24192 1.95629 0.41582 1.94574 0.44990 1.94059 0.48384 2.93444 0.62373 2.92311 0.67485 2.91088 | 0.72576 3.91259 0.83164 3.89748 0.89980 3.88118 0.96768 4.89073 1.03955 4.87185 1.12475 4.85147 1.20961 5-86885 1.24747 5.84622 1.34970 582177 | 1.45153 6.84703 1.45538 6.52059 1.57405 6.79206 | 1.69345 7.82518 1.66329 7.79496 1.79960 7-76236 1.93537 8.80332 1.87120 8.76933 2.02455 8.73206 2.17729 OW ONIONS by 0.97723 0.21217 0.97 337 0.22920 0.96923 0.24615 1.95446 0.42435 0.45540 1.93846 0.49230 2.931609 0.63653 2 0.68760 2.90769 | 0.73845 3.90892 0.84871 38 0.91680 3.87692 0.98461 4.88615 1.06088 : 1.14600 4.84615 1.23076 5.86338 1.27306 : 1.37520 5.81539 1.47091 6.84061 1.48524 k 1.60440 1.72307 7.81784 1.697 42 78 1.83360 7-7 538 1.96922 8.79507 1.90959 7002 2.06280 3. 2.21537 © ONIOUNAW db 0.97629 0.21644 : 0.23344 : 0.25038 1.95259 | 0.43288 9447 0.46689 : 0.50076 2.928388 0.64932 Zi 0.70033 2. 0.75114 3.90518 | 0.86576 88 0.93378 8 | 1.00152 4.88148 1.08220 8618 1.16722 84073 1.25190 5:95777 1.29864 5.8342 1.40007 : 1.50228 6.83407 1.51508 8 1.63411 E f 1.75266 781036 1.73152 778 1.86756 : 3 2.00304 8.75666 1.94796 : : 2.10100 : 2 2.25342 OW ON QuswW dv 0.97 534 0.22069 .Q71° 0.23768 : 0.25460 1.95008 0.44139 942 0.47 537 AC 0.50920 2.92602 0.66209 QI 402 0.71305 2 0.76380 3-90136 0.88278 885; 0.95074. : 1.01540 4.87671 1.10348 4.8 1.18843 4.83523 1.27301 5:35205 1.32418 828 1.42611 5.80227 1.52761 6.82739 1.54488 799% 1.66350 6.76932 1.78221 7.80273 1.76557 . 3 1.90148 7.73030 2.03081 8.77808 1.98627 ; 2.13917 8.70341 2.29141 O CONI OANFW vb | Dep. Lat. : Lat. Dep. g g a AQ aT: 3 4 5 6 oi 8 eS 1 3 4 5 6 Z 8 9 1 3 4 5 6 7 8 9 1 3 4 5 6 7 8 9 g S 8 ‘soynUry ‘Q0uRISIC *soqnUIyL SMITHSONIAN TABLES. 36 TABLE 9. TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE.— CONTINUED. Minutes Distance. Distance. Minutes. Dep. | | | 0.25881 0.961 26 sey 0.95630 0.29237 0.51763 1.92252 . 1.91260 0.58474 0.77645 2.88378 826 2.80891 0.57711 1.03527 3-84504 , 3:82 521 1.16948 1.29409 4.80630 : 5 4.78152 1.46185 579555 | 1-55291 | 5-76757 65382 | 5-73752 | 1-75423 6.76145 1.91173 6.72883 1.92946 6.69413 2.04660 7:72740 2.07055 7-69009 2.20509 7-65043 2.33897 8.69333 2.32937 8.65135 2.48073 | 8.60674 2.03134 © ON ONO by OW ON QAubw bd 0.96478 0.26303 0.96005 0.27982 0.95502 0.29654 1.92957 0.52606 1.92010 0.55965 1.91004 0.59308 2.89436 0.78909 2.8801 5 0.53948 2.86506 0.88962 3.85914 1.05212 3.84020 1.11931 3.82008 1.18616 4.82393 1.31515 4.80025 1.39914 4.77510 3 5-78872 1.57518 5.76030 1.67897 5-7 3012 6.75351 I.S4121 6.72035 1.95880 6.68514 7.71829 2.10424 7.68040 2.23863 7.64016 8.68308 2.36728 | 8.64045 2.51846 | 8.59518 O ON Qubwn Oo ON Aufhw bd 0.96363 | 0.26723 | 0.95882 | 0.28401 0.95371 1.92726 0.53447 1.91764 0.56803 1.90743 2.89089 0.80171 2.87646 0.85204 2.86115 3.85452 1.06895 | 3.83528 1.13606 }| 3.81486 4.81815 1.33619 4.79410 1.42007 4.76858 5-78178 1.60343 5:7 5292 1.70409 Sees 6.74541 1.87066 6.71174 1.98810 6.67601 7.70904 2.13790 7.67056 2.27212 7-62973 8.67267 2.40514 | 8.62938 2.55013 | 8.58345 OW ON Aubhw bv lt 3 4 5 6 7 8 9 0.96245 0.27144 | 0.95757 0.28819 | 0.95239 1.92491 0.54258 1.91514 0.57639 1.90479 0.81432 2.87271 0.86458 2.85718 1.08576 3.83028 1.15278 3.80958 1.35720 4.78785 1.44098 4.76197 1.62864 5:74542 1.72917 5.71437 1.90008 0.70299 2.01737 6.66677 2.17152 7.66057 2.30557 7-61916 2.44296 | 8.61814 2.59376 8.57156 O MHI ANUS W wv WO ON OAnLW dv & Dep. Lat. Dep. *20UL}SICT *soINUI] *90UL}SICT SMITHSONIAN TABLES. 37 E 9. TaP TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE.—Conrinuep. Minutes Distance. Distance. Dep. : Dep. 0.94551 0.32556 | 0.93969 0.34202 1.89103 0.65113 1.87938 0.08404 2.83655 0.97670 2.81907 1.02606 3.78207 1.30227 BOTT, 1.36808 4.72759 1.62784 4.69846 1.71010 5-67311 1.95340 5-63815 6.61863 2.27897 6.57784 7-56414 | 2.60454 | 7-51754 8.50966 2.93011 8.45723 NENED SAE OsOLO On t \“ 0 ON Quihw dv OW ON Quthw bv 0.94408 0.32969 | 0.93819 1.88817 0.65938 1.87638 2.8322 0.98907 2.81457 3:77635 | 1.31876 | 3.75276 4.72044 | 1.64845 | 4.69095 5:66453 1.97814 5-62914 6.60862 2.30783 6.56733 7:55271 | 2.63752 | 7.50553 8.49680 2.90721 8.44372 pNNAmMMO00 0 CON Qusbwn O ON Qutbw bd 0.94264 | 0.33380 | 0.93667 1.88528 0.66761 1.87334 2.82792 1.00142 2.81001 3-77056 1.33522 3-74668 4.71320 1.66903 | 4.68336 5 2.00284 5:62003 2.336064 6.55070 2.67045 | 7-49337 300426 8.43004. NIN TN ER EOLOKO Cn NOM NWO ADL 0 ON Quhw bv aL 3 4 5 6 7 3 9 0.33791 0.93513 »35429 0.67 583 1.87027 0.70858 1.01375 2.80540 1.06287 1.35166 3-74054 1.41716 1.68958 4.67 507 1.77145 2.02750 5-61081 2.12574 2.36541 6.54594 2.48003 2.70333 7.48108 2.83432 3.04125 8.41621 3.18861 0 ON Quhwn 0 ON Qui2rw wv | Dep. Lat. soyNUlyYy ‘aourysiq *20uv}sSIq soyNUry SMITHSONIAN TABLES. 38 TRAVERSE TABLE. et DIFFERENCES OF LATITUDE AND DEPARTURE. —ConrTINuUED. Distance. Distance. Minutes. Lat. : Lat. Dep. . Dep. | | 0.93358 | 0.35836 | 0.92718 0.37460 ; 0.39073 1.50716 0.71673 1.85436 0.74921 84 0.78146 2.80074 1.07 510 2.78155 1.12381 ; 1.17219 3-73432 1.43347 3-70873 1.49842 : 1.56292 4.06790 1.79183 4.63591 1.87303 5-60148 2.15020 5.50310 2.24763 6.53506 2.50857 6.49028 5 7-40864 2.86694 7-41747 .40222 3-22531 8.34465 337145 0 ON QuitwW tv 0 ON Quihw bv 0.93200 0.36243 0.92554 0.37864 i 0.39474 1.80401 0.72487 1.85108 0.75729 8 5 0.78948 2.79602 1.08731 2.77662 1.13594 7563 1.18423 3.72803 4 3.70216 1.51459 i 1.57897 4.66004 ; 4.6277 1.89324 59: 1.97372 5.59204 : 5-55324 | 2.27189 3 2.30846 6.52405 2. 6.47878 2.05054 ec 2.76320 7-45606 8 7.40432 3.02918 -3503 3.15795 8.38807 : 8.32986 3.40783 26912 3.552609 © ON QufwW vd © ON QAUAW bd 0.93041 i 0.92388 | 0.38268 : 0.39874 1.86083 : 1.84776 0.76536 83412 0.79749 2.79125 : 2.77164 1.14805 : 1.19624 3-72167 4 3-69552 | 1.53073 6682 1.59499 4.65208 832 4.61940 1.91341 . 1.99374 5.58250 : 5.54328 2.29610 : 2.39249 6.51292 2: 6.46716 2.67878 : 2 2.79124 7-44334 7-39104 | 3.06146 -33648 | 3.18999 8.37375 2 8.31492 | 3-44415 | 8.25354 | 3.58874 0 ON Qubwn L 3 4 5 6 7 8 9 0.92881 0.37055 922 0.38671 0.91531 0.40274 1.85762 O.74111 : 0.77 342 1.53062 0.80549 2.78643 1.11167 : 1.16013 2.74593 B.7 LCA 1.48222 : 1.54684 3-661 24 4.04405 | 1.85278 1.93355 5-57286 2.22334 53% 2.32026 6.50167 : 45 5¢ 2.70697 7-43048 : : 3.09368 8.35929 3-48039 OW ON QAupwW bv s0urysiq | O ONIOUPW bd ‘SONU ‘90URISICT SMITHSONIAN TABLES. 39 TABLE 9. TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE.—ConrTinueb. vi 9 24° ae = um = Q Lat. 1 0.91354 0.4067 3 2 1.82709 0.81347 | 3 2.74003 1.22020 4 3.65418 1.62694 ° 5 4.56772 2.03308 6 5.48127 2.44041 7 6.39481 2.84715 8 7.30836 3.25389 9 8.22190 3-66062 aL 0.91176 0.41071 2 1.82352 0.82143 3 2.73528 1.23215 4 3-64704 1.64287 15 5 | 4-55881 | 2.05359 6 5.47057 2.40431 7 6.38233 2.87 503 8 | 7.29409 | 3.28575 9 } 8.20585 | 3-69647 1 0.90996 0.41469 2 1.81992 0.82938 3 2.72988 1.24407 4 | 3.63984 | 1.65877 30 5 4.54980 | 2.07346 6 5.45976 2.48815 7 6.36972 2.90285 8 7-27909 | 3-31754 9 8.18965 3'7.3223 1 0.90814 0.41866 2 1.81628 0.83732 3 2.72442 1.25598 4 | 3.63257 | 1.67464 45 5 4.54071 2.09339 6 5-44885 2.51196 7 6.35700 2.93062 8 7.20514 3.34928 9 | 817328 | 3.76794 i o Dep Lat. ~y n e | 8 oO ~ " @ 65° SMITHSONIAN TABLES. 0.90069 1.80139 2.70209 3.60279 4.50349 5.40418 6.30488 7.20558 8.10628 Dep. 0.42261 0.84523 1.26785 1.69047 2.11309 2-53 ae 2.95832 3-38094 3-80356 0.42656 0.85313 1.27970 1.70027 2.13284 2759042 2.98598 SAt254 3.83911 0.43051 0.86102 29153 72204 15255 2.58306 3-01357 3-44405 387459 ~ YN 0.43444 0.80889 1.30333 1.73778 207/222 2.60667 3.04111 3-47 556 3-91000 at: 0.89879 1.79758 2.69638 3°59517 4-49397 5.39276 6.290155 7:19035 8.08914 0.89687 1.79374 2.69061 3-58749 4.48436 5.35123 6.27310 7-17498 8.07185 0.89493 1.78986 2.68480 3-57973 4-47 467 5.30960 6.26454 7-15947 8.05440 0.89297 1.78595 2.67893 3-57191 4.40489 5.35787 6.25085 7-14383 8.03081 Dep. 0.43837 0.87674 1.31511 1.75348 2.19185 2.63022 3.00859 3.50096 3-94533 0.44228 0.88457 1.32686 1.76915 2.21144 2.65373 3.09602 3-53830 3-98059 0.44619 0.89239 1.33359 1.75479 2.23098 2.67718 3-12338 3.56958 4.01578 0.45009 0.90019 1.35029 1.80039 2.25049 2.70059 3.15008 3-60078 4.05088 Distance. © ON QNAW bd OW ON Qusfw hd 0 ON Quhw wv © ON Qutbw bd FH Minutes. 45 30 15 Dep. 40 Lat. Dep. at: a0ur4siq *soINUIY an eT ale i TRAVERSE TABLE. TAPES DIFFERENCES OF LATITUDE AND DEPARTURE. —COonrTINUED. Distance. Distance. Minutes. eat, | | 0.88294 0.87462 1.76589 1.74924 2.64884 : 2.62386 3-53179 3-49848 4-41473 4.37310 5.29763 ; 5:24772 6.18063 : 6.12234 7.06358 5 6.99696 7.94052 : 7.57156 OW ON Quthw hn 0 ON Quifw rn 0.88089 0.47332 0.87249 1.76178 0.94664 1.74499 2.64267 1.41996 2.61748 3-52356 3.48998 4.40445 3 4.36248 5.25534 | 2.53992 | 5.23497 6.16623 a 6.10747 7:04712 : 6.97996 7.92801 735246 | 4.39759 0 ON OQUuitwn O ON QNUAW dS 0.87881 0.87035 0.49242 1.75763 | 0.95431 ] 1.74071, | 0.98454 2.63045 1.43147 2.61106 1.47727 3.51526 1.90863 3.48142 1.96969 4-39408 | 2.38579 | 4:35177 | 2.46211 5-27 290 2.86295 5.22213 2.95454 6.15171 3.34011 6.09248 3.44696 7.03053 3.81727 6.96254 5 7-90935 | 4:29442 | 7.93320 OO ON QUPW bd EH 7 3 4 5 6 1 8 9 0.87672 0.48098 0.86819 1.75345 | 0.96197 | 1.73639 2.63018 1.442096 2.60459 3-50690 | 1.92395 | 3-47279 4.38363 wf 4.34099 2.48108 5-26036 88 5.20919 2.97729 6.13708 .36692 | 6.07739 | 3.4735! 7-01 381 8479 6.94559 | 3-96973 7-89054 32 7-81378 | 4.40594 0 ON QUAPW dv 0 ON Qudw bh H | | Dep. Lat. ‘g0ue}siqy ‘g0uv}SIC] SMITHSONIAN TABLES. 41 TABLE Q. TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE. -—ConrTINuUED. Minutes. Distance. Distance. Dep. Lat. Dep. Lat. Dep. 0.50000 0.85716 | 0.51503 | 0.84804 | 0.52991 1.00000 1.71433 1.03007 1.69609 1.05983 I.50000 | 2.57150 1.54511 2.54414 1.58975 2.00000 | 3.42866 2.06015 | 3.39219 2.11967 2.50000 | 4.28583 2.57519 | 4.24024 2.64959 3.00000 | 5.14300 | 3.09022 5-088 28 3.17951 3.50000 6.00017 3.60526 5-93633 3-70943 4.00000 | 6.85733 | 4.12030 | 6.78438 4.23935 4-50000 } 7.71450 | 4.63534 | 7-03243 | 4-70927 0 OI OUupuw nh © ON ANnpwW bd 0.50377 0.85491 0.51877 0.84572 0.53361 1.70982 1.037 54. 1.69145 1.06722 2.56473 1.55631 2.53718 1.60084 3.41964 2.07 509 3.38291 2.13445 4.27456 2.59386 4.22863 .60807 5.12947 3.11263 5-07430 5.98438 3.63141 5-92009 6.83929 4.15018 6.76582 7.69420 4.66895 761155 OW ON Qushw bv FH 1 3 4 5 6 7 8 S 0.50753 | 0.85264 | 0.52249 | 0.84339 1.01507 1.70528 1.04499 1.68678 1.07400 1.52261 2.55792 1.56749 2.53017 1.61190 2.0301 5 3.41056 2.08999 3.37350 2.14920 2.53769 4.26320 2.61249 4.21695 2.68650 3:04523 Gaui 584 3.13499 5.06034 -22380 3-55276 | 5.96048 | 3.65749 | 5-90373 | 3-76110 4.06030 6.82112 4.17998 6.74713 4.29840 4.56754 | 7-67376 | 4.70248 | 7.59052 | 4.83570 0 ON QudpwW db & 0 ON Quhwn 0.51129 | 0.85035 0.52621 0.84103 0.54097 1.02258 1.70070 1.05242 1.68207 1.08194 1.53397 2.55105 1.57864 2.52311 1.62292 2.04517 3.40140 2.10485 3.30415 2.16389 2.55046 | 4.25176 2.63107 4.20519 2.70487 3.00775 5.10211 3.15728 5-04623 3.24584 3:57995 | 5-95246 | 3.65349 | 5.88827 | 3.78682 4.09034 6.80281 4.20971 6.72831 4.32779 4.60163 | 7.65316 | 4.73592 | 7-56035 | 4.56877 OW ON QuAwW pb © ON Quhw wv | | | Lat. Dep. Lat. Dep. Lat. *SoNUTTA ‘dduUv}SIC, ‘g0uvISIC SaqnuUly SMITHSONIAN TABLES. 42 TRAVERSE TABLE. Tape ge DIFFERENCES OF LATITUDE AND DEPARTURE. —Conrtinueb. Minutes. Distance. Distance. Minutes Lat. : s Dep. Lat. Dep. | | 0.83867 ; f 0.82903 0.55919 | 0.81915 0.57357 1.67734 .0892 1.65807 1.11838 1.63830 1.14715 2.51601 -633¢ 2.49711 1.67757 2.45745 1.72072 3.35468 ; 3-31615 2.23677 3-27660 2.29430 4-19335 2.72316 4.14515 2.79590 4.09576 2.86788 5.03202 2 4.97422 3.35515 4-91 491 3-44145 587069 812. 580326 | 3.91435 5:73406 | 4.01503 6.70936 ; 6.63230 4.47354 6.55321 4.58561 7.54803 2 7.46133 5:03273 7.372306 5.16218 OW ON OUubW wv O ON Quhwn 0.83628 : 0.82659 0.56280 0.81664 0.57714 1.67257 : 3 1.12560 1.63328 1.15429 2.5088 5 ; wd 1.68541 2.44992 1.73143 334514 : .30636 2.25121 3-26656 2.30858 4.18143 : 132 2.81402 4.08320 2.88572 5.01771 .2 : 3.37682 4.89984 3.46287 5-85400 8 -756 3.93963 5.71649 4.04001 6.69028 : ‘ 4.50243 6.53313 4.61716 7.52657 s : 5.06524 | 7-34977 5.19430 OW ONY QubwW vb 10 OI QAuthwW bd 0.83388 0.55193 82412 0.56640 | o.814II 0.58070 1.66777 1.10387 : 1.13281 1.62823 1.16140 2.50165 1.65581 ; 1.69921 2.44234 1.74210 3.33554 2.20774 .296 2.26562 | 3.25046 4.16942 2.75968 ; 2.83203 4.07057 5.00331 3-3" 162 9447 3.39843 4.88469 5.83720 | 3.86355 : 3.96484 5-69880 6.67108 4.41549 ; 4.53124 6.51292 7-50497 | 4-96743 5.09765 | 7-32703 O ON QubwW db T 3 4 5 6 7 8 9 0.83147 | 0.55557 82 5.56999 | 0.81157 1.66294 I.IT114 : 1.13999 1.62314 2.49441 1.6667 1 2.462 1.70999 2.43472 3.32588 2 ue, 2.27998 3-24629 ples -10823 | 2.84998 | 4.05787 4.95852 3.41998 | 4.86944 5-52029 58399 rf 3.98997 5.68101 6.65176 : ; 4.55907 6.49260 7.48323 : -39¢ 5-12997 7.30416 0 ON Quhw vo 0 ON Qutpwn | | Dep. *soqnuryl g0uvjSI(] ‘Q0Uur}SIC] sonUly SMITHSONIAN TABLES. 43 TABLE 9. TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE. —CONTINUED. Minutes. Distance. | Minutes. 0.80901 5% H : 0.78801 1.61803 : -597 : 1.57602 2.42705 y Zs 8 2.36403 3:23606 : : 2.4072 3-15204 4.04505 : s : 3-94005 4.85410 : 7918 : 4.72806 5-66311 : .5904 S202 5-51607 6.47213 .70228 38 812 6.30408 7.28115 : 18 : 7.09209 O ON QUubW b © ON AubwW vb 0.80644 ; ! ; 1.78531 1.61288 -18 : ; 1.57003 38 2.35595 3.14126 3-92658 4.71190 5-49721 6.28253 5.44704 | 7-060785 WO ON AubhwW bv OW ON ANnAW bd 0.79335 | 0.60876 | 0.78260 1.18964 1.58670 1.21752 1.56521 1.78446 2.38005 1.82628 2.34782 2:37929 | 317342 2-43504 | 3-13043 2.97411 3.96676 | 3.04380 | 3.91304 3.56893 4.760011 3-65256 | 4.69564 4.10375 | 5-55347 | 4.26132 | 5.47525 4-75858 | 6.34682 4.87009 | 6.26086 5.35340 | 7-14017 | 5.47885 | 7-04347 OW ON Qufw bv © ON Qufbwnhd eH 0.59832 | 0.79068 0.61221 0.77988 1.19664 1.58137 1.22443 1.55940 1.79497 2.37206 1.83665 2.33905 2.39329 3.16275 2.44886 3-11953 2.99162 3-95344 3.06108 3.89942 3.58994 | 4-74413 | 3-67330 | 4-67930 4.18327 5-53482 4.28552 5-45919 4-78659 | 6.32551 | 4.89773 } 6.23907 5.38492 7-11620 5-50995 7.01896 OW ON QUubwW bd Dep. *SOPNUTT “90ue ISIC | OW ON Auf wn ‘g0ue}SICT SMITHSONIAN TABLES. 44 —— T ; TRAVERSE TABLE. ioe bi DIFFERENCES OF LATITUDE AND DEPARTURE. -— ConrTINUED. Minutes. Dep. » Distance. Minutes | 0 OY OupW vb | Distance. 0.77714 .62932 0.75470 0.65605 1.55429 255 1.50941 Eeoueun 2.33143 85796 ‘ 2.20412 1.90817 3.10855 51728 3.01883 2.62423 388573 377354 | 3-28029 4.66287 7756 4.52825 3.93035 5.44002 .405: : 5.28296 4.59241 6.21716 : 6.03767 5.24847 6.99431 6638 6.79238 | 5-90453 O ON Quidhw vb 0.77439 63 0.75184 | 0.65934 1.54878 2 1.50368 1.31869 2.32317 898 2.25552 1.97803 3.09757 | 2. 3.00736 | 2.63738 3.87196 10% 3.7 5920 3.29672 4.64635 -7902 4.51104 | 3-95607 5-42074 42 5-26288 4.61542 6.19514 s 5 6.01472 5.27476 6.96953 : 6.76656 5-93411 OW ON Qufhu wv O MONI QufW bd 0.77162 : : 0.74895 0.66262 1.54324 : 52 1.49791 1.32524 2.31487 .9082 ‘ 2.24686 1.98786 3.08649 2.5% .0< 2.99582 2.65048 3.85812 I : 3:74477 3.31310 4.62974 . 5624 4.49373 | 3-97572 5-401 37 45 : 5.24268 4.63834 d 2 : 5-99164 530096 6.74060 5-96358 OW ON Qufwd els 3 4 5 6 7 8 9 0.66588 1.33176 1.99764 2.66352 3.32940 3:99529 4.00117 532795 6.81808 | 5.87484 | 6.714 5-99293 0 OI QNuswW b O ON Qufuw nd & Dep. ‘Sonu *9OULISI(T ‘a0uvySI(] ‘soqnUry SMITHSONIAN TABLES. 45 ABLE 9. = F TRAVERSE TABLE. DIFFERENCES OF LATITUDE AND DEPARTURE. —ConrTINUED. Minutes Distance. Distance. | Minntes. | 0.73135 0.68199 719 0.69465 1.46270 1.36399 of 1.38931 2.220/ 2.0073 2.19406 2.04599 : 2.08397 7 ‘ 2.92541 2.72799 : 2.77803 3-65676 | 3.40999 3-47329 4.35812 4.09199 i 4.16795 5-11947 4.77398 : 4.86260 5.85082 5-45598 : 5-55726 6.58218 6.13798 a 6.25192 O OI ANnAW bv 0.72837 0.68518 716° 0.69779 1.45674 1.37036 432 1.39558 2.18511 2.05554 ; 2.09337 2.91348 2.74073 2.8652 2.791 16 3-64185 | 3.42591 5 3.48895 4.37022 4.11109 .2978 4.18674 5.09859 | 4-79628 . 4.88453 5-82696 5.48146 : 5§-58232 6.55533 6.16064 : 6.28011 aE 3 4 5 6 7 8 9 0.72537 0.68835 : 0.70090 1.45074 1.37670 : 1.40181 2.06506 : 2.10272 2.75341 : 2.80363 3:377 . 3:44177 . 3:50454 4.05354 -3522¢ 4.13012 “2 4.20545 4.72913 ‘ 4.81848 : 4.90036 5.40472 : 5.50083 ; 5.60727 6.08031 ; 6.19519 5 6.30815 OW ON QNUAW bn 0.73432 0.67880 ; 0.691 51 ; 0.70401 1.460864 1.35760 , 1.38302 ; 1.40802 2.20296 2.03040 7 2.07453 aXe 2.11204 2.93729 2.71520 .88 2.76005 2: 2.81605 3-671 61 3.39400 61182 3.45750 ; 3.52007 4.40593 4.07280 -334 4.14907 Ke 4.22408 5.14025 4-7 5160 ; 4.84059 : 4.92810 5:87455 5.43040 77 5.53210 3 5.63211 6.60890 6.10920 : 6.22361 , 6.33613 10 ON OQUutpwW bd | | Dep. Lat. "sounUlyy ‘20Ue}SIC | O OI AnAW bv OW ON Quhwn © ON QufpwW dv 0 ON Qutpun eH "sayNUl *Q0UL}SICT SMITHSONIAN TABLES. 46 TRAVERSE TABLE. TABLE 9. DIFFERENCES OF LATITUDE AND DEPARTURE. —ConrtTiNueb. SMITHSONIAN TABLES. Distance. Distance. = to 3 4 5 6 7 8 9 0.70710 1.41421 2.12132 2.82842 3°53553 4.24264 4-94974 5.65685 6.36396 0.70710 1.41421 2.12132 4.24264 4.9497 4 5-65685 6.36396 *QOUvISI(CT Dep. | Lat. 45° 47 g0ueqSIC] TABLE 10. LOGARITHMS OF MERIDIAN RADIUS OF CURVATURE pp, IN ENCLISH 7.317 | 7.817 | 7.817 | 7.817 | 7.817 | 7.317 | 7.817 | 7.3817 | 7.817 | 7.317 | 7.3817 7392 7433 7500 7593 7392 7434 é 7595 7393 7435 7597 7394 7436 7599 7394 | 7437 7600 7395 7438 7602 7395 7438 7604 7396 7439 7606 7396 7440 7608 7397 7441 7397 7442 7612 7398 7443 7614 7398 7444 7616 7399 7445 7618 7399 7446 7619 7400 7447 7621 7401 7448 22 7623 7408 7449 5 7625 7402 7450 7627 7402 7451 7403 | 7452 7404 | 7453 7404 | 7454 7495 | 7455 7495 7456 7406 | 7458 7497 7459 7497 7460 7408 7461 7408 7462 409 7463 7543 7659 7410 7464 7545 7652 7410 7465 7546 7654 7411 7466 7548 7656 7412 7467 7549 7658 7413 7469 7551 7661 7413 7470 7553 7663 7414 747% 7554 7665 7415 7472 7550 7667 7415 7473 7557 7669 7673 7418 7476 7675 7418 7478 7677 7419 7479 7679 7420 7480 7682 7421 7482 7684 7422 7483 7686 7422 7484 7688 7424 7487 7692 7425 7488 57% 7694 7426 7489 7696 7427 7490 7699 7428 7491 7701 7429 7493 7703 7429 7494 7795 7430 7496 58! 7707 7431 7497 7710 7392 7433 7500 7593 7714 SMITHSONIAN TABLES. 7416 7474 767 7423 7486 7690 7432 7498 7712 REET [Derivation of table explained on p. xlv.] 7714 7716 7719 7721 7723 7726 7728 7730 7732 7735 7737 7739 7742 7744 7746 7749 775% 7753 7755 7861 7864 7866 7869 7872 7875 7877 7880 7883 7885 7858 7891 7894 7896 7899 7902 7905 7908 7910 8034 8037 8040 8043 8046 8050 8053 8056 8059 8062 8065 8068 8071 8075 8078 So81r 8084 8087 Sogr 8094 8097 8100 8104 8107 8110 8114 8117 8120 8123 8127 8130 8133 8137 8140 8144 8147 8150 8154 8157 8161 8164 8167 8171 8174 8178 8181 8184 8188 8191 8195 8198 8201 8205 8208 8212 8215 8219 8222 8226 8233 8233 8237 8240 8244 8247 8251 8255 8258 8262 $265 8269 8273 8276 8280 8283 8287 8291 8294 8208 8301 8305 8309 8312 8316 8320 8324 $327 8331 8335 8338 8342 8346 8350 8353 8357 8361 8365 8369 8372 8376 8380 8384 8388 8392 8396 8400 8403 8407 841 8415 8458 8462 8466 8470 8474 8478 8482 8486 8490 8494 8498 &502 8506 $510 8514 8518 $523 8527 8531 8535 8539 8543 8547 8551 8555 8559 8564 8568 8572 8576 8580 8584 8588 8593 8597 8601 8605 8609 8614 8618 8622 8626 8631 8635 8639 8643 8648 8652 2656 8661 8419 8423 8427 8431 8435 8439 8442 8446 8450 8665 8669 8674 8678 8683 8687 8691 8696 8700 8705 8709 8709 $713 8718 8722 8727 8731 8735 8740 8744 8749 8753 8758 8762 8767 8771 $776 8780 8785 8789 8794 8798 8803 8807 8812 8816 8821 8826 8830 8835 8839 8844 8849 $853 8858 8862 8867 8872 8876 8881 8885 88g0 8895 8899 8904 8909 8014 8918 8923 8928 8932 8937 8942 8947 8951 8956 8961 8966 8971 8975 8980 8985 TaBLe 10. LOCARITHMS OF MERIDIAN RADIUS OF CURVATURE p,, IN ENGLISH FEET. (Derivation of table explained on p. xlv-] 2 9966 0340 9972 © 346 0744 9978 | 0353 0750 9984 0359 0757 9990 03606 0764 9996 0372 0771 *o002 0379 0778 *ooo8 0385 0784 *oo14 0392 OW ON DU WHNHH *o020 0398 *0026 0404 *0032 o4tl *0039 0418 *o045 0424 *oo51 0430 *0057 | 0437 *0063 0443 *0070 0450 *o0076 *o082 *oo88 *o094 *o101 *0107 ¥o113 *o11g *or25 *o132 ¥*o138 *or44 *o150 *o156 *o163 *o169 *o175 *or81 *o187 *o194 *0200 *o0206 *o212 *o219 *o0225 *o231 *0238 *o244 *o250 *0256 *0263 *0269 *0275 *o282 *0288 *0295 *o0301 *0307 *o314 *0320 *0327 *0333 SMITHSONIAN TABLES. TABLE 10. LOGARITHMS OF MERIDIAN oe CURVATURE p,, IN ENCLISH [Derivation of table explained on p. xlv.] e 0 ONY Ant Wh wa b °o SMITHSONIAN TABLES. TABLE 10. LOCARITHMS OF MERIDIAN ecco CURVATURE pp, IN ENGLISH {Derivation of table explained on p. xlv.] 7.318 | 7.318 | 7.319 | 7.319 | 7.319 | 7.319 | 7.319 | 7.319 | 7.319 | 7.319 oO’ 9086 9773 0472 1182 1902 2631 3369 4114 4866 5623 9098 9785 0484 1194 1914 2643 3381 4126 4878 5636 9109 9796 0495 1206 1926 2656 3394 4139 4891 5649 g120 9807 0507 1218 1938 2668 3406 4151 4904 5661 9132 9819 0519 1230 1950 2680 3418 4164 4916 5674 9143 9831 0531 1241 1962 2692 3431 4176 4929 5687 9154 9843 0542 1253 1974 2705 3443 4189 4941 5699 9166 9854 0554 1265 1986 2717 3455 4201 4954 5712 9177 9866 0566 1277 1999 2729 3468 4214 4966 5725 9189 9877 0577 1259 2011 2741 3480 4226 4979 5737 O ON BUI WNH 9200 9889 0590 1301 2753 3492 4239 4992 5750 g211 9900 o6o1 1313 35 2766 3505 4251 5004 5763 9223 ggi2 0613 1325 2778 3517 4264 5017 5775 9234 9924 0625 1337 279° 3530 4276 5029 5788 9245 | 9935 | 0637 1349 7 2803 3542 4289 5042 58or 9257 9947 0648 1361 2 2815 3554 4301 5055 5813 9268 9958 0660 1373 2827 3567 4314 5067 5826 : 9280 | 9970 | 0672 1385 2839 | 3579 | 4326 | 5080 | 5839 9291 9982 0684 1397 2852 3592 4339 5092 5851 0696 2 2864 3604 4351 5105 5864 5118 2888 2901 5143 2913 5156 2925 5168 2938 5181 2950 5193 2962 5206 2974 5219 2987 5231 2999 5244 3011 5256 3024 5269 3036 5282 3048 5294 3060 z s 5307 3973 5320 3085 5332 3°97 5345 6156 6169 6582 6195 6207 5459 6220 5471 6233 5484 6245 *0355 5497 6258 ¥0366 1075 5 5509 6271 *0378 1087 8 5 4 5522 6284 *0390 1098 5535 | 6296 40402 1110 8 5! 5547 6309 (0413 1122 3 57 ; 5560 6322 *o425 1134 8 5573 | 6335 *0437 1146 é 5585 | 6347 *0449 1158 ‘ 3344 8 5598 6360 *o0460 1170 2 8 56rr 6373 *0472 1182 § 5623 6385 SMITHSONIAN TABLES. TABLE 10. LOCARITHMS OF MERIDIAN ee OF CURVATURE p,, IN ENCLISH [Derivation of table explained on p. xlv.] 8692 9464 0236 1007 3704 9476 0248 8717 9489 0261 1033 8730 9502 0274 1045 8743 9555 0287 1058 8756 9528 0300 1071 8769 9541 0313 1084 8782 9554 0326 1097 8794 9566 0338 I1Io 8807 9579 0351 1122 8820 9592 0364 1135 8833 9605 0377 1148 8846 9618 0390 1161 8859 9631 0403 1174 8872 9644 0416 1187 8834 9057 0429 1199 8897 9669 0441 1212 8910 9682 0454 122 8923 9695 0467 1238 8936 9708 0480 1251 1264 1276 5 1289 6679 7 398 1302 NNN 6692 322 go00 7 1315 6704 : 42 9013 5 1328 6717 325 9026 1341 6730 4 3 9039 5 1353 6743 328) 9052 5 5 1366 6755 é 2 9065 8 1379 NNN Ane WN H ao 28 29 6768 5 9°77 5 1392 6781 gogo 3 1405 6794 9103 9875 1418 6806 9116 9888 1430 6819 9129 ggor 1443 6832 8 3 9142 9914 0686 1456 6844 338 9155 9927 0699 1469 6858 7626 9168 9940 o7II 1482 6870 7638 3 g180 9953 0724 1494 6883 795% 22 9193 9965 0737 6896 7664 : 9206 9978 0750 1520 6909 7677 9219 999% 0763 1533 6921 7690 9232 | *ooo4 0776 1546 6934 7702 9245 | *oo17 0788 1559 6947 7715 9258 | *oo30 o8o1 1571 6960 7728 9270 | *o043 o814 15384 6973 7741 9283 | *oo55 0827 1597 6985 7754 5 9296 | *o068 0840 1610 6998 7767 9309 | *oo8r 0853 1623 7OLL 7779 35 9322 | *oo94 0866 1635 7024 7792 3 9335 | *oro7 0878 1648 7036 7805 357 9348 | *or20 0891 1661 7049 7818 35§ 9361 | *o133 0904 1674 7062 7831 2 9373 | *or46 0917 1687 7°75 7344 ‘ 9386 | *o1s8 | 0930 1699 7088 7856 9399 | *o1r71 0943 1712 7100 7869 9412 | *or84 0955 1725 7113 7382 9425 | *or97 0968 1738 7126 7895 8666 9438 | *o2z10 0981 1751 7139 7908 8679 9451 | *o223 0994 1763 7152 7921 8692 9464 | *o236 | 1007 | 1776 2543 | 3306 SMITHSONIAN TABLES. ss TasB_e 10. LOGARITHMS OF MERIDIAN eens OF CURVATURE p, IN ENCLISH 2 0 ON OUMNS WHH 5203 5216 5228 5241 5253 5266 5278 5291 5393 SMITHSONIAN TABLES. 5564 5576 5589 5601 5613 5625 5638 5650 5662 5675 5687 5699 5712 5724 5737 5749 5761 5774 5786 5799 5811 5823 5836 5848 5860 5872 5885 5897 5909 5922 5934 5946 5959 5971 5983 5995 6008 6020 6032 6045 6057 6069 6082 6094 6106 6118 6131 6143 6155 6168 6180 6192 6205 6217 622 6241 6254 6266 6278 6291 6303 (Derivation of table explained on p. xlv.] 6315 6327 6340 6352 6364 6376 6388 6401 6413 6425 6437 6449 6462 6474 6486 6498 6510 6523 6535 6547 6559 6571 6584 6596 6608 6620 6632 6645 6657 6669 6681 6693 6706 6718 6730 6742 6754 6767 6779 6791 6803 6815 6828 6840 6852 6864 6876 6889 6901 6913 6925 6937 6949 6961 6973 6986 6998 7o1o 7022 7934 | Fue 7323 7335 7348 7360 7372 7384 7396 7408 7420 7432 7444 7456 7468 7480 7492 7504 7516 7528 7549 7552 7564 7576 7588 7600 7612 7624 7636 7648 7660 7672 7684 7696 7708 7720 7732 7744 7756 7750 77608 7780 7792 7804 7815 7827 7839 7851 7863 7875 7887 7899 7goiL 7923 7934 7946 7958 7970 7982 7994 8006 8018 8030 8042 8053 8065 8077 8089 8101 8113 8125 8137 8148 8160 8172 8184 8196 8207 8219 8231 $243 8255 8266 8278 8290 8302 8314 8325 8337 8349 8361 8373 8384 8396 8408 8420 8432 8443 8455 8467 7.320 | 7.320 | 7.320 | 7.321 8467 8479 8491 8502 8514 8526 8538 8550 8561 8573 8585 8597 8608 8620 8632 8643 8655 8667 8679 8690 8702 8714 8725 8737 8749 8760 45> 8772 8784 8796 8807 8819 8831 8842 8854 <2 9168 9180 gt9r 9203 9214 9226 9238 9249 9261 9272 9284 9295 9397 9318 9330 9341 9353 9364 9376 9387 9399 9410 9422 9433 9445 9456 9468 9479 9491 9502 9514 9525 9537 9548 9560 9571 9583 9594 9606 9617 9629 9640 9652 9663 9675 9686 9697 9709 9720 9732 9743 9754 9766 9777 9789 g800 9811 9823 9834 9846 9857 9868 9880 9891 9993 9914 9925 9937 9948 9960 997% 9982 9994 (0005 *o016 *0027 *0039 *oo050 *oo61 *0073 *o084 *0095 *o107 *¥o118 *o129 *o140 *o152 *o0163 *o174 *o186 *o107 ¥*0208 *o219 *0231 *o242 *0253 *0264 *0275 *0287 ¥*o298 *o0309 *0320 ¥*0332 *0343 ¥0354 *0305 *0377 ¥0388 *0399 *o4rt ¥0422 *0433 *o444 *o0456 *0467 ¥*0478 *o48Q *o500 ¥o512 *0523 *0534 0534 0545 0550 0567 0578 0589 o6o1 o612 0623 0634 0656 0667 0678 0689 0701 0712 0723 0734 0745 0750 0767 0778 0789 0800 o812 0823 0834 0845 0856 0867 0878 0889 0goo ogit 0g22 0933 0944 0955 0966 0977 0988 0999 1010 1021 1032 1043 1054 1065 1076 1087 1098 1109 1120 1131 1142 1153 1164 1175 1186 1197 0645 TABLE 10. LOCGARITHMS OF MERIDIAN Seles OF CURVATURE p,, IN ENGLISH [Derivation of table explained on p. xlv.] t N oO 3097 3698 4282 4848 5396 5924 6432 on 000 3107 | 3708 | 4292 | 4857 5405 5933 6440 3117 | 3718 | 430% 4807 | 5414 | 5941 6448 3127 3728 | 4311 4876 5423 5950 | 6457 3137 | 3738 | 4320 | 4885 | 5432 | sosS | 6465 3147 3747 4330 4894 5440 5967 6473 3158 3757 4340 4904 5449 5976 6481 3168 | 3767 | 4349 | 4913 5458 | 5984 | 6489 3178 3777 4359 4922 5407 5993 6498 3188 3787 4368 4932 5476 6oo1 6506 3198 3797 4378 4941 5485 6o10 6514 NNN NNN Mun UU Utne ” OuNntR WN © ON NNN 3208 3807 4387 4950 5494 6018 6522 3218 3817 4397 4959 5503 6027 6530 3228 | 3826 | 4406 4969 5512 6035 6539 3238 | 3836 | 4416 4978 5521 6044 6547 3248 3846 4425 4987 5529 6052 6555 3259 3856 4435 4996 5538 6061 6563 3269 3866 4444 5005 5547 6069 6571 3279 3875 4454 5015 5556 6078 6580 3289 3885 4463 | 5024 5565 6086 6588 3299 3895 4473 5033 5574 6095 6596 3309 3905 4482 5042 5583 6103 6604 3319 3915 4492 505! 5592 6112 6612 3329 3924 4501 5060 5600 6120 | 6621 3339 3934 4511 5069 5609 6129 6629 2111 3349 3944 4520 5078 5618 6137 6637 2122 3360 3954 4530 5088 5627 6146 6645 2132 3370 3964 4539 5097 5636 6154 6653 2143 3380 3973 4549 5106 5044 6163 6662 2153 3390 3983 4558 5115 5653 6171 6670 2164 2790 3400 3993 4508 5124 5662 6180 6678 2175 2800 3410 4003 4577 5133 5671 6188 6686 2185 2811 3420 4012 4587 5142 5680 6197 6694 2196 2821 3430 4022 4590 5151 5688 6205 6702 2206 2831 3440 4032 4606 5160 5697 6214 6710 2217 2841 3450 404t 4015 5169 5706 6222 6718 2228 2852 3460 4051 4024 5179 5715 6230 6727 2238 2862 3470 4061 4034 5188 5724 6239 6735 2249 2872 3480 4071 4643 5197 5732 6247 6743 2259 2883 3490 4080 | 4653 52 5741 6256 6751 2270 2893 3500 4002, 4062 5215 5750 6264 6759 2280 2903 3510 4100 4671 522 5759 6272 6767 2291 2913 3520 4109 4681 5233 5707 6281 6775 2301 2924 3530 4119 4690 5242 5776 6289 6783 2312 2934 3540 | 4128 | 4699 5251 5785 6298 | 6791 2322 2944 3549 4138 4708 5260 5793 6306 6799 2333 2954 3559 4148 4718 5270 5802 6314 6807 2343 2964 3569 4157 4727 5279 58r1 6323 6815 2354 2975 3579 4167 4736 5288 5820 6331 6823 2364 2985 3589 4176 aaa 5297 5828 6340 6831 2375 2995 3599 ance 4755 5306 5837 6348 6839 1749 2385 3005 3609 4196 1759 2396 3015 3619 4205 1770 2406 3026 3629 4215 4764 5315 5846 6356 6847 4774 5324 5854 6365 6855 4783 5333 5863 | 6373 | 6863 1781 2417 3036 3639 4224 4792 5342 5872 6382 6871 1791 2427 3046 3648 4234 4801 5351 5880 63990 6879 1802 2437 3056 3658 4244 4811 5300 5889 6398 6887 1813 2448 3066 3668 4253 4820 5369 5898 6407 6895 1524 2458 3077 3678 4263 4829 5378 5907 6415 6903 1834 2409 3087 3688 4272 4839 5387 5915 6424 6911 4848 5396 5924 6432 6919 1845 2479 3097 | 3698 4282 SMITHSONIAN TABLES. 54 TABLE 10. LOCARITHMS OF MERIDIAN ees OF CURVATURE pp, IN ENCLISH (Derivation of table explained on p. xlv.] 7.821 | 7.321 | 7.321 | 7.321 | 7.321 | 7.821 | 7.321 | 7.321 | 7.322 | 7.322 o ~ ~ ” wn 8650 9025 9377 9704 0007 0284 7836 7843 7851 7858 7865 7872 7879 7887 7894 8656 903r 9383 9709 oo12 0288 8663 9037 9388 9714 0017 0293 8669 9043 9394 9720 0021 0297 8676 9049 9399 9725 0026 0302 8682 9°55 9405 9730 0031 0306 8688 go6r g4It 9735 0036 0310 8695 9067 9416 9749 0041 0315 87or 9073 9422 9746 0045 0319 8708 9°79 9427 975% 0050 0324 NN N Ou Com nua aM @w mann te Co y o oS COON DNs WHH Ww = 0 Sn ao oo ow _ © 790% 8714 9085 9433 9756 0055 0328 7908 8720 9091 9435 9761 0060 0332 7915 8727 9097 9444 9766 0064 0337 7922 8733 9103 9449 977% 0069 0341 7929 8346 8739 g109 9455 9776 0074 0345 7936 8353 8745 9115 9460 | 978t 0078 0349 7944 8359 8752 gi2t 9466 9787 0083 0354 795% 8366 8758 | 9127 9471 9792 0088 0358 7958 8373 8764 9133 9477 9797 0093 0362 7965 8379 8771 9139 9482 g8o02 0097 0367 moo wWHw Wwry ond 7972 8386 8777 9145 9488 9807 o102 0371 7979 8393 8783 91st 9493 9812 o107 0375 7986 8399 8790 9157 9499 9817 Orr 0379 7993 8406 8796 9163 9504 9822 o116 0384 8000 8413 8802 9169 9510 9827 0120 0388 8007 8419 8808 9174 9515 9832 0125 0392 8014 8426 8815 g180 9521 9838 0130 0396 8021 8433 8821 9186 9526 9843 0134 0400 8028 8440 8827 gi92 9532 9848 0139 0405 8035 8446 8834 9198 9537 9853 0143 0409 8042 8453 8840 | 9204 9543 9858 | o148 0413 8049 8460 8846 g210 9548 9863 0153 0417 8056 8466 8852 g216 9554 9868 O157 0421 8063 8473 8859 g221 9559 9873 o162 0426 8070 8479 8865 9227 9565 9878 0166 0430 8077 8486 8871 9233 957° 9883 o1r7t 0434 8084 8493 8877 9239 9575 9888 | 0176 | 0438 8091 8499 8883 9245 9581 9893 o180 0442 8098 8506 8890 9250 9586 9898 o185 0447 8105 8512 8896 9256 9592 9993, o189 O45. S112 8519 Sgo2 9262 9597 9908 | 0455 8119 | 8526 | 8908 | 9268 | g602 | 9913 | org 0459 8126 8532 8914 9274 9608 gg918 : 0463 $133 Sg21 9279 | 9613 9923 208 0467 8140 8927 285 9619 9928 0471 8147 8933 9291 9624 9933 OATS 8154 8939 9297 9629 9938 0480 8161 565 8945 9303 9635 9943 0484 8168 3 8952 9308 9640 9948 : 0488 8175 8958 | 9314 9646 9953 0492 8182 8964 9320 9651 9958 0496 7763 8189 8970 9326 9656 9963 0500 7324 7771 8196 ‘ 8976 9331 9662 9968 0504 7332 7778 | 8203 : 8982 9337 9667 | 9973 0508 7339 7785 8210 8988 9343 9672 9978 5 o512 7347 7792 8216 9348 9677 9982 0516 7355 7800 $223 2 9354 9683 9987 0520 7362 7807 8230 3 9360 9688 9992 0524 737° 7814 8237 9366 9693 9997 0528 7377 7822 8244 9371 9699 | *ooo2 0532 7385 | 7829 | 8251 9377 | 9704 | *0007 SMITHSONIAN TABLES. 55 TABLE 10. LOCARITHMS OF MERIDIAN RADIUS OF CURVATURE p,, IN ENGLISH FEET. [Derivation of table explained on p. xlv.] 2 1504 1505 1506 1611 1507 1611 1509 1611 1510 1612 1511 1612 1613 O ON ANP WHH 1613 1613 1614 1614 1615 1615 1615 1616 1616 1617 1617 1617 1617 1618 1618 1618 1618 1618 1619 1619 1619 1619 1619 1620 1620 1620 1620 xm NNN 1620 1621 NNN 0690 0694 0697 0701 0705 0708 0712 0716 0720 0723 0932 3 5 1622 0935 : 6 2 5 1622 0938 F 1622 0941 8 3 1622 0944 1622 0947 1622 ogst 1623 0954 R 1623 0957 G 2° 1623 0960 35 5 5 1568 1623 0963 3 1569 1623 SmitHsonian TABLEs. TABLE 11. LOGARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION pn IN ENGLISH FEET. [Derivation of table explained on p. xlv.] x 2 3 4 5 6 7 8 9 7277 7279 7280 7282 7283 7284 7286 7287 7289 7291 7293 7294 7296 7297 7298 7300 7301 7303 7304 7305 7397 7308 7310 7311 7313 7314 7316 7317 7319 | 741% SMITHSONIAN TABLES. TABLE 11. LOCARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION p, IN ENCLISH FEET. [Derivation of table explained on p. xlv.] ee | be 7.320 | 7.320 | 7.320 7411 7511 7619 7736 7860 7992 8132 2 7413 7513 7621 7738 7862 7994 8134 7414 7514 7623 774° 7864 7997 8137 7416 7516 7625 7742 7867 7999 8139 7417 7518 7627 7744 7869 | 8001 8142 7419 7519 7628 7746 7871 8003 8144 7421 7521 7630 7748 7873 8006 8146 7422 7523 7632 7750 7875 S008 8149 7424 7525 7034 7752 7878 | 8010 | 8151 7425 7526 7636 7754 7880 8013 8154 © ON AuA WH H 7427 7528 7638 7756 7882 8015 8156 7429 7530 7640 7758 7884 8017 8158 7430 7532 7642 7760 7886 8020 8161 7432 7533 7644 7762 7888 | 8022 8163 7433 7535 7646 7764 7890 8024 8166 7435 7537 7647 7766 7892 8026 8168 7437 7539 7649 7768 7895 8029 8170 7438 754% 7651 7770 7897 8031 8173 7449 7542 7653 7772 7899 8033 8175 7441 7544 7655 7774 7901 8036 8178 7443 7546 7657 7776 7903 8038 8180 7445 7548 7659 7778 7905 8040 8182 7446 7550 7661 7780 7907 8043 8185 7448 755% 7663 7782 7910 | 8045 8187 7450 7553 7665 7734 7912 8047 8190 745% 7555 7666 7786 7914 8049 8192 7453 7557 7668 7789 7916 | 8052 8195 7455 7559 7670 7791 7918 8054 7457 7560 7672 7793 7921 8056 7458 7562 7674 7795 7923 8059 7460 7564 7676 7797 7925 8061 7462 7566 | 7678 | 7799 | 7927 | 8063 7463 7508 7680 7801 7929 8066 7465 7569 7682 7803 7932 8068 7466 757% 7684 7805 7934 8071 7468 | 7573 | 7686 | 7807 | 7936 | 8073 7479 7575 7688 7810 7938 8075 7471 7577 7690 7812 7940 8078 7473 7578 7692 7814 7943 8080 7580 7094 7816 7945 8083 7582 7696 7318 7947 8085 7554 7698 7820 7949 8087 7586 7700 7822 7952 8090 7588 7702 7824 7954 8092 759° 7704 7826 7956 8094 7591 7706 7828 7958 8096 7593 7708 7831 7961 8099 7595 7710 7833 7963 Sror 7597 7712 7835 7965 8103 7599 | 7714 | 7837 | 7968 | 8106 7493 7601 7716 7839 7970 8108 7495 7603 7718 7841 7972 8110 7497 7605 7720 7843 7974 8113 7493 7606 7722 7845 7977 8115 7500 7608 7724 7347 7979 $118 7502 7610 7726 7849 7981 8120 7504 7612 7728 7852 7983 8122 7506 7614 | 7730 7854 7985 8125 7507 7615 7732 7856 7988 8127 7509 7617 7734 7258 7990 8130 7511 7619 7736 7860 7992 8132 SMITHSONIAN TABLES. a ge eas ee — RN ae ia rs fee TABLE 11. LOCARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION pn IN ENCLISH FEET. [Derivation of table explained on p. xlv.] 7.320 | 7.320 | 7.3820 | 7.320 | 7.3820 | 7.320 | 7.320 | 7.321 | 7.321 | 7.321 8763 8939 9120 9308 9502 9701 9997 o1n7 0332 0553 2 8766 8942 9123 9311 9505 9795 9910 o121 0336 0556 8769 8945 g126 9314 9508 9708 9913 O124 0340 0560 8772 8948 9129 9318 9512 9712 9917 0128 0343 0564 8775 8951 9132 9321 9515 9715 9920 O13T 0347 0567 8778 8953 9136 9324 9518 9718 9924 0135 0351 0571 8780 8956 9139 9327 9521 9722 9927 0138 0354 0575 8784 8959 9142 9330 9525 9725 993% o142 0358 0579 8786 8962 9145 9333 9528 9728 9934 0145 0361 0582 0586 COON ANNs WN 059° 0594 9346 0597 9349 5 o6or 9353 0605 9356 0608 9359 0612 9362 : 0616 9365 y 0620 9368 0623 9372 ; 0627 9375 : 0631 9378 5 0635 9381 0638 9384 0642 9388 0646 9391 0649 9394 C of 0653 9398 *ooo. 35 0657 9401 8 r 36 0661 9404 g6o1 0224 0664 9032 9407 9604 0668 8856 9035 Q4it g608 0231 0672 8859 9038 9414 grr ‘ 22 0235 0676 8862 go41 9417 9614 é f 0238 0679 8865 9044 2 9420 9618 3 *oo2 0242 0683 8868 9047 9424 g621 3 0246 0687 8871 9050 9427 9624 ¢ 0249 0691 8874 9053 9430 9628 0253 0694 8877 9056 9433 963 ; 0256 0698 8879 9°59 9437 9634 3 0260 0702 8882 go62 944° 9638 0264 82 0706 8885 9065 I 9443 9641 8 ’ 0267 8 0710 8888 go068 9446 9644 § 0271 9 0713 8891 9071 9450 9648 8 0274 g 0717 8894 9°74 9453 9651 ’ 0278 0721 9077 9456 9654 35 6 0282 5 0725 go8o 9459 9658 ' 0285 0728 9083 9463 9661 9865 | * 0289 508 0732 9086 9466 9664 9869 | 7 3 0293 5 0736 9671 9875 *oo8 0300 051 0743 9674 9879 ‘oo 0303 : 0747 9678 9882 *oog2 0307 2 0751 9681 9886 *o0c O3I1 0755 9685 9889 | * 0314 9759 9638 9893 0318 0762 9691 9896 0322 0766 9695 ggoo | * 0325 0770 9698 9903 | *or1: 0329 0774 9093 9279 9472 go96 | 9283 9476 9099 9286 9479 gio2 9289 9482 g105 9292 9455 g108 9295 9489 gir 9298 9492 gri4 9302 9495 9117 9395 9498 go89 9469 9668 9872 *oo82 0296 0740 gizo | 9308 | 9502 | 9701 | 9907 7 posse °777 SmitHsonian TABLEs. 59 TABLE 11. LOGARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION Px IN ENCLISH FEET. [Derivation of table explained on p. xlv.] ae 7.321 | 7.321 | 7.321 | 7.321 | 7.321 | 7.321 | 7.321 | 7.321 2 0777 1006 1239 1476 1716 1959 2205 2453 0785 1014 1247 1484 1724 1967 2213 2462 0789 1018 1251 1488 1728 1971 2217 2466 0793 1022 1255 1492 1732 1975 2221 2470 0796 1026 1259 1496 1736 1979 2226 2474 0800 1029 1263 1500 1740 1983 2230 2478 1504 1744 1988 2234 2482 1508 1748 1992 2238 2487 1512 1752 1996 2242 2491 0804 1033 1267 0808 1037 1271 o8ir O41 1275 Oo ON AUh WNW 10 o815 1045 1279 II o819 1049 1282 12 0823 1053 1286 13 0827 1057 1290 14 0830 1060 1294 15 0834 1064 1298 16 0838 1068 1302 17 0842 1072 1306 18 0846 1076 1310 0781 1010 1243 1480 1720 1963 2209 2457 19 0849 1080 1314 20 0853 1084 1318 1556 1797 2041 2287 2537 1087 1322 1560 1801 2045 2292 2541 1091 1326 1564 1805 2049 2296 2545 1095 1330 1568 1809 2053 2300 2549 1099 1334 1572 1813 2057 2304 2553 1103 1337 1576 1817 2061 2308 2557 1107 1341 1580 1821 2065 2312 2562 III 1345 1584 1825 2069 2316 2566 IIIS 1349 1588 1829 2073 2321 2570 1118 1353 1592 1833 2077 2325 2574 30 o891 1122 1357 1596 1837 2082 2329 2578 2830 1126 1361 1600 1841 2086 2333 2583 2834 3087 1130 1365 1604 1845 2090 2337 2587 2838 3092 1134 1369 1608 1849 2094 2341 2591 2843 3096 1138 1373 1612 1853 2098 2345 2595 2847 3100 1142 1377 1616 1857 2102 2350 2599 2851 3104 1146 1381 1620 1861 2106 2354 2603 2855 3109 1150 1385 1624 1865 2110 2358 2608 2859 3113 1153 1389 1628 1870 2114 2362 2612 2864 3117 1157 1393 1632 1874 2119 2366 2616 2868 3121 1161 1397 1636 1878 2123 2370 2620 2872 3126 1165 1401 1640 1882 2127 2374 2624 2876 3130 1169 1405 1644 1886 2131 2379 2629 2880 3134 1173 1409 1648 1890 2135 2383 2633 2885 3138 1177 1412 1652 1894 2139 2387 2637 2889 3143 1181 1416 1656 1898 2143 2391 2641 2893 3147 1185 1420 1660 1902 2147 2395 2645 2897 3151 1189 1424 1664 1906 2151 2399 2649 2902 3155 30 1192 1428 1668 1910 2156 2403 2654 2906 3160 40 1196 1432 1672 1914 2160 2408 2658 2910 3164 50 4r | 0933 42 | 0937 43 | 0941 44 0945 45 0949 46 0953 47 | 0956 48 0960 49 0964 60 0968 1200 1436 1676 1918 2164 2412 2662 2914 3168 51 0972 1204 1440 1680 1922 2168 2416 2666 2918 3172 1208 1444 1684 1926 2172 2420 2670 2923 3177 53 0979 1212 1448 1688 1931 2176 2424 2675 2927 3181 54 0983 1216 1452 1692 1935 2180 2428 2679 2931 3185 59 0987 1220 1456 1696 1939 2184 2433 2683 2935 3189 56 0991 122 1460 1700 1943 2188 2437 2687 2940 3193 57 0995 1228 1464 1704 1947 2193 2441 2691 2944 3198 58 0999 1231 1468 1708 1951 2197 2445 2696 2948 3202 59 1003 1235 1472 1712 1955 2201 2449 2700 2952 3206 60 1006 1239 | 1476 | 1716 | 1959 | 2205 2453 2704 | 2956 3210 SMITHSONIAN TABLES. gt ER Pe ES a TABLE 11. LOCARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION IN ENCLISH FEET. (Derivation of table explained on p. xlv.] Pn 7.321 | 7.3821 | 7.3821 | 7.321 | 7.321 | 7.321 | 7.321 | 7.321 | 7.321 | 7.321 O/ | 3210 3466 I 3215 3470 2 3219 3474 3 3223 3479 4 3227 3483 5 3232 3487 6 3236 3491 7 3240 3496 8 | 3244 | 3500 9 3249 3504 10 3253 3508 xr 3257 3513 12 3261 3517 13 3266 3521 14 3270 3526 15 3274 3530 16 3278 3534 17 3283 3538 18 3287 3543 19 3291 3547 3722 3726 373! 3735 3739 3744 3748 3752 3756 3761 3765 3769 3774 3778 3782 3786 3791 3795 3799 3803 3979 3983 3988 3992 3996 4001 4005 4009 4013 4018 4022 4026 4031 4035 4939 4043 4048 4052 4056 4061 4236 4494 4241 4498 4245 4502 4249 4507 4254 450r 4258 4515 4262 4520 4267 4524 4271 4528 4275 4532 4279 4537 4751 4755 4760 4764 4768 4772 4777 4781 4785 4789 4794 4798 4802 4807 4811 4815 4819 4824 4828 4832 5007 5263 5517 5012 5016 5020 5024 5029 5033 5037 5042 5046 5050 5054 5959 5063 5067 5071 5076 5080 5084 5088 5267 5271 5276 5280 5284 5288 5293 5297 5301 5305 5310 5314 5318 5322 5327 5331 5335 5339 5344 5522 5526 5530 5534 5538 5543 5547 5551 5555 5560 5564 5568 5572 5576 5581 5585 5589 5593 5598 SMITHSONIAN TABLES. 4194 4198 4202 4206 4211 4215 4219 422. 4228 4232 4230 4284 4541 4288 4545 4292 4550 4297 4554 4301 4558 4305 4562 4309 | 4567 4314 4571 4318 4575 4322 4580 4327 45384 4331 4588 4335 4592 4339 4597 4344 4601 4348 4605 4352 4610 4357 4614 4361 4618 4365 4622 4369 4627 4374 4631 4378 4635 4382 4640 4387 4644 4391 4648 4395 4652 4399 4657 4404 4661 4408 4665 4412 4070 4417 4674 4421 4678 442 4682 4430 4687 4434 4691 4438 4695 4442 4700 4447 4704 4451 4708 4455 4712 4460 4717 4464 4721 4468 4725 4472 4730 4477 4734 4494 4751 5263 5395 5399 5493 5407 5412 5416 5420 5424 5428 5433 5437 5441 5445 5450 5454 5458 5462 5467 5471 5475 5479 5484 5488 5492 5496 §500 5505 5509 5513 5517 5732 5737 5741 5745 5749 5753 5758 §762 5766 5779 10 20 30 40 50 TABLE 11. LOCGARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION 5938 5942 5946 5951 5955 5959 5963 5967 5972 5976 5980 5934 5988 5992 5996 6000 Goos | 6009 6013 6021 7.321 | 7.321 6021 6025 6029 6034 6038 6042 6046 6050 6055 6059 6063 6067 6071 6075 6079 6083 6088 6092 6096 6100 6104 6108 6112 6117 6121 6125 6129 6133 6138 6142 6146 6150 6154 6158 6162 6166 6171 6175 6179 6183 6187 6191 6195 6200 6204 6208 6212 6216 6221 6225 6229 6233 6237 6241 6245 6249 6254 6258 6262 6266 6270 SMITHSONIAN TABLES. p, IN ENCLISH FEET. [Derivation of table explained on p. xlv.] 6517 6521 6525 6529 6533 6537 6541 6545 6549 6553 6557 6561 6565 6569 6573 6577 6582 6586 6590 6594 6598 6602 6606 6610 6614 6618 6623 6627 6631 6635 6639 6643 6647 6651 6655 6659 6663 6667 6671 6675 6679 6683 6687 6691 6695 6699 6704 708 6712 6716 6720 6724 6728 6732 6736 6740 6744 6748 6752 6756 6760 6881 6885 6889 6893 6897 6901 6905 6909 6913 6917 6921 6925 6929 6933 6937 6941 6945 6949 6953 6957 6961 6965 6969 6973 6977 6981 6985 6989 6993 6997 7OO1 7120 7124 7128 7132 7136 7139 7143 7147 71S1 7155 7159 7163 7167 7171 7175 7179 7183 7187 7191 7195 7199 7203 7207 7211 7215 7218 7222 7226 7230 7234 7238 62 7246 7250 7254 7257 72601 7265 7269 7273 7277 7281 7285 7289 7293 7296 7300 7304 7308 7312 737% 7374 7378 7382 7386 7390 7394 7398 7402 7406 7410 7413 7417 7421 7425 7429 7437 7441 7445 7449 7452 7456 7460 7404 7468 7472 7433 7652 7655 7659 7663 7667 7671 7974 7678 7682 7686 7690 7693 7697 77oO1 7927 8016 8019 8023 8027 8031 8034 8038 8042 8045 8049 8053 8056 8060 8064 8068 8071 8075 8079 8082 8086 8089 8093 8097 8100 8104 8107 Sri 8115 8118 8122 8126 8129 8133 8137 8141 8144 8148 TABLE 11. LOGARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION p, IN ENCLISH FEET. [Derivation of table explained on p. xlv.] 7.321 | 7.321 | 7.321 | 7.321 | 7.321 | 7.821 | 7.321 | 7.321 | 7.821 | 7.321 S 8148 | 8364 8575 8781 8982 9176 | 9365 9548 9724 9893 8152 $368 | 8578 8784 8985 9179 | 9368 9551 9727 9896 8155 | 8371 8582 | 8788 | 8989 | 9182 | 937% 9554 | 9730 | 9898 8159 | 8375 | 8585 | 8791 8992 | 9186 | 9374 | 9557 | 9732 | 990% 8162 8378 8589 8795 8995 9189 9377 9560 9735 9904 8166 8382 8592 8798 8998 gig2 9380 9562 9738 9906 8170 | 8386 | 8596 | 8801 gooz | 9195 | 9384 | 9565 | 974% 9999 8173 8389 8599 | 8805 goos 9198 9387 9568 9744 ggi2 8177 | 8393 8603 8808 | goo8 | 9202 | 9390 | 9571 9746 | 9915 8180 | 8396 | 8606 8812 gor2z 9205 9393 9574 9749 9917 OON Out® WH 8184 8400 8610 8815 gors g208 9396 9577 9752 9920 8188 8403 8613 8818 go18 g211 9399 9580 9755 9923 8191 8407 8617 8822 go2r 214 9402 9583 9758 9926 8195 8410 8620 8825 go25 g218 9405 9586 9761 9928 8198 8414 8624 8829 9028 g221 9408 9589 9764 993 8202 8417 8627 8832 go3t 9224 9411 9592 9766 9934 8206 8421 8631 8835 9034 9227 9415 9595 9769 9937 8209 | 8424 8634 8839 9°37 9230 | 9418 9598 9772 9940 8213 8428 8638 8842 go4t 9234 9421 g6or 9775 9942 8216 8431 8641 8846 9044 9237 9424 9604 9778 9945 8220 | 8435 8645 8849 9047 9240 | 9427 9607 978 9948 $224 8648 8852 go50 9243 9430 9610 9784 995" 8227 8652 8856 9054 | 9246 9433 9613 9787 9953 8231 8655 8859 9°57 9250 | 9436 9616 | 9789 9956 $235 8659 8862 go60 9253 9439 9619 9792 9959 8238 2 8662 8865 9063 9256 9442 9621 9795 9961 8242 8665 8869 9067 9259 9445 9624 9798 9964 8246 8669 8872 g070 9262 9448 9627 g8o1 9967 8250 8672 8875 9073 9266 9451 9630 9803 9970 8253 8676 8879 9°77 9269 9454 9633 g806 9972 8679 | 8882 | 9080 | 9272 | 9457 | 9636 | 9809 | 9975 8682 8885 9083 9275 9460 9639 9812 9978 8686 8889 go86 9278 9463 9642 9815 gg8o 8689 8892 gogo g281 9466 9645 9817 4983 8693 8896 9093 9284 9469 9648 9820 | 9986 8696 8899 gog6 9287 9472 9651 9823 g988 8699 8902 9099 9291 9475 9654 9826 9991 8703 | 8906 | g102z2 | 9294 | 9478 | 9657 | 9829 | 9994 8706 8909 g106 9297 9481 9660 983! 9997 8710 8913 9109 9300 | 9484 9663 9834 9999 8713 8916 gii2 9303 9487 9666 9837 | *ooo2 8716 8919 gis 9306 949° 9669 9840 | *o005 8720 8923 g118 9309 9493 9672 9843 | *oo07 8723 8926 gi22 9312 9496 9675 9845 *oo10 8727 8929 | 9125 9315 9499 9678 9848 | *oor3 8730 8932 g128 9318 9502 9680 9851 *oo15 8733 8936 9131 9322 9506 9683 9854 | *oo18 8737 8939 9134 9325 9509 9686 9857 | *oo2x 8740 | 8942 9138 9328 9512 9689 9859 | *oo24 8744 8946 9141 9331 | 9515 9692 | 9862 | *oo26 8747 8949 9144 9334 | 9518 9695 9865 | *oo29 8750 8952 9147 9337 9521 9698 9868 | *o032 8754 8956 9150 9340 9524 9701 9871 | *o034 8757 8959 9154 9343 9527 9704 9873 | *0037 8761 8962 9157 9346 9530 9797 9876 | *o039 8764 8965 g160 9349 9533 9709 9879 | *oo42 8767 8969 9163 9353 9536 9712 9882 | *oo45 8771 8972 9166 9356 9539 9715 9885 | *o047 8774 8975 9170 9359 9542 9718 9887 | *ooso 8778 8979 9173 | 9362 9545 9721 9890 | *oo52 8781 | 8982 | 9176 | 9365 | 9548 9893 SMITHSONIAN TABLES. 63 TABLE 11. LOCARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION 2 WON Auk WNHH e o 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 41 43 44 45 46 47 49 50 SI 52 53 54 55 57 58 59 60 0085, 0087 00go 0092 0095 0098 o100 0103 O105 o108 Olir O1l3 o116 o118 O121 OI24 0126 o129 O131 0134 0137 0139 O142 0144 0147 o15o O152 0155 o160 o162 0165 0167 0170 o172 O175 0177 o180 0182 0185 0187 o1go oO1g2 orgs 0197 0200 0202 0205 0207 O157 7.322 o210 0213 0238 0241 0243 0246 0248 0251 0253 0256 0258 0261 0263 0266 0268 0271 0273 0276 0278 0281 0283 0286 0288 0291 0293 0296 0298 0300 0303 0305 0308 0310 0312 0315 0317 0320 0322 0324 0327 0329 0332 0334 0336 0339 0341 0344 0346 9349 0351 0354 0356 pn IN ENGLISH FEET. [Derivation of table explained on p. xlv.] 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 9359 0361 0364 0366 0369 0371 0373 0376 0378 0381 0383 0385 0388 0390 0392 0394 0397 0399 O401 0404 0406 0408 O4II 0413 0416 0418 0420 0423 0425 0428 0430 0432 0435 0437 0439 0441 0444 0446 0448 0451 0453 0455 0458 0460 0462 0464 0467 0469 O471 ©0474 0476 0478 o481 0483 0485 0487 0490 0492 0494 0497 2499 SMITHSONIAN TABLES. 0499 0632 oO501 0634 0504 0636 0506 0639 0508 0641 0510 0643 0513 0645 0515 0647 O517 0650 0520 0652 0522 0654 0524 0656 0526 0658 0529 0660 0531 0662 0533 0664 0535 0667 0537 0669 0540 0671 0542 0673 0544 0675 0546 0677 0549 0679 o551 0681 0553 0683 0555 0685 0558 0688 0560 o6g0 0562 0692 0565 0694 0567 0696 0569 0698 0571 0700 0574 0702 0576 0704 0578 0706 0580 0708 0582 0710 0585 0712 0587 o714 0589 0716 os5gt 0718 0593 0720 0596 0722 0598 0724 0600 0726 0602 0729 0604 0731 0607 0733 0609 0735 o611 0737 0613 0739 0615 o741 0617 0743 0619 0745 o621 0747 0624 0749 0626 0751 0628 0753 0630 0755 0632 0757 0757 0759 0761 0763 0765 0767 0769 0771 °773 9775 °777 °779 0781 0783 0785 0787 0789 0791 °793 °795 9797 °799 o8or 0803 0805 0807 0809 o811 0813 0815 0817 0819 o821 0823 0825 0826 0828 0830 0832 0834 0836 0838 0340 0842 0844 0846 0848 0850 0852 0854 0875 0877 0879 0880 0882 0884 0886 0888 0889 o891 0893 0895 0897 0899 ogor o0go2 0904 0906 0908 og1o ogi2 ogI4 0916 0917 ogI9 og2r 0923 0925 0926 0928 09390 0932 0934 0935 0937 0939 0941 0943 0944 0946 0948 0950 0952 0953 0955 0957 2959 0961 0962 096 4 0984 0986 0987 0989 oggt o0gg92 0994 0996 0998 0999 1001 1003 1004 1006 1008 1009 IOII 1013 IOIS 1016 1018 1020 1021 1023 1025 1026 1028 1030 1032 1033 1035 1037 1038 1040 1042 1043 1045 1047 1049 1050 1052 1054 1055 1057 1058 1060 1062 1063 1065 1066 0856 0858 0860 0862 0864 0865 0867 0869 o871 0873 0966 0968 0970 0971 2973 0975 °977 °979 og8o0 0982 0984 1068 1070 1071 1073 1075 1076 1078 1080 1082 1083 1085 1085 1177 1087 1178 1088 1180 1090 1181 109! 1183 1093 1184 1095 1186 1096 1187 1098 1189 1099 1190 1101 1192 1102 1193 1104 1195 I105 1196 1107 1198 1108 1199 1110 1200 TITE 1202 III3 1203 1114 1205 1116 1206 1118 1207 1119 1209 1121 1210 1122 1212 1124 1213 1126 1214 1127 1216 1129 1217 1130 1219 1132 1220 1133 1221 1135 1223 1136 1224 1138 1226 1139 1227 1141 1228 1142 1230 1144 1231 1145 1233 1147 1234 1148 1235 1150 1237 1151 1238 1153 1240 1154 1241 1156 1242 1157 1244 1159 1245 1160 1247 1162 1248 1163 1249 1165 1251 1166 1252 1168 1253 1169 1254 II7t 1256 1172 1257 1174 1258 1175 1260 1177 1261 cs ao eae > ee eee { = TABLE 11. LOGARITHMS OF RADIUS OF CURVATURE OF NORMAL SECTION p, IN ENCLISH FEET. [Derivation of table explained on p. xlv.] 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 | 7.322 0’ 1261 1337 1403 1461 I511 1551 1583 1605 1619 I 1262 1338 1404 1462 1512 1552 1583 1605 1619 2 1264 1339 1405 1463 1512 1552 1584 1606 1619 3 1265 1340 1406 1404 1513 1553 1584 1606 1619 4 1266 1341 1407 1465 1514 1553 1585 1606 1619 5 1267 1342 1408 1465 1514 1554 1585 1606 1619 6 1269 1344 1410 1466 1515 1555 1585 1607 1620 7 1270 1345 I4it 1467 1516 1555 1586 1607 1620 8 1271 1346 1412 1468 1517 1556 1586 1607 1620 9 1556 1587 1608 1620 15g SMITHSONIAN TABLES. 1568 1569 1569 1570 1570 1571 157t 1572 1572 1312 1382 1443 1495 1539 1573 1599 41 1313 1383 1444 1496 1540 1573 1599 42 1315 1384 1445 1497 1540 1574 1600 43 1316 1385 1446 1497 1541 1574 1600 44 1317 1386 1447 1498 1541 1575 1600 45 1318 1387 1447 1499 1542 1575 1600 46 1320 1389 1448 1500 1543 157 1601 47 1321 139° 1449 1501 1543 1576 1601 48 1322 1450 1501 1544 1577 1601 1577 1578 1578 1602 52 1327 1395 1454 1505 1546 1579 1603 53 1329 1396 1455 1505 1547 1579 1603 54 1330 1397 1456 1506 1547 1580 1603 55 1331 1398 1456 1507 1548 1580 1603 56 1332 1399 1457 1508 1549 1581 1604 57 1333 1400 1458 1509 1549 rg8r 1604 58 1335 1401 1459 1509 5 1582 1604 1582 1583 15g! 1591 1592 1592 1593 1593 1593 1594 1594 1595 1602 1602 1605 1605 TABLE 12. LOGARITHMS OF RADIUS OF CURVATURE fa (IN METRES) OF SECTION OF EARTH’S SURFACE INCLINED TO MERIDIAN AT AZIMUTH a. [Formula for pa given on p. xlv.] LATITUDE. Azimuth. DBO | 230 24° 250 26° 29° 25> 29° 30° gi” | a | See | eee 0° | 6.80237, 6.80242 6.80248) 6.80254| 6.80260) 6.80266] 6.80272) 6.80279} 6.8028 5] 6.80292 5 239) 244 250 256 262 268 274 280 287 204 10 244 250 255 261 267 272 279 285 292 298 15 254 259 264 270) 276 282 288 204 300 306 20 266 271 277 282 288 293 299 305 311 B07, 2 282 287 292 297 302 308 313 319 325 331 30 300 3°95 309 314 319 324 339 335 340 346 35 320] 324) «= 320) S333] «= 338] S343} «= 348] «= 353] «= 358) 363 40 341] 345] «= 350) 354) = 358] 9 362] 367] 9 372] = 377} =~ 382 - 45 364} 36 371) 375| += 379] ~—s 383} = 287} = 391] += 396) += 400 50 386 = 389) += 392] +3 396) 3S 399] +3 403] Ss 407] = ATT] = 415] 419 55 407 410, 413} 416} 420) 423} 426} 430] 434) 437 60 427 430| 432 435} 438) — 442 445 448} 451 455 65 445, 448 450] 453] «4551 «= 458] = 461) 9 464, 46 470 70 461 463) 465) 468; = 470) = 473} 475 478| 481 484 75 473 476) 478 480| = 482 434 487 489 492 494 80 4831 485} 487} = 480) = 491} 493} 495] += 498} = 500] S502 85 489} 490| 492) 494 496} = 498} So 503} 505} 507 go 490; 492 494, 490, = 498 500 502 504 507 509 LATITUDE. Azimuth. B27) if See BP |. B57 236" | Laz | Ba) heaos teen i 0° | 6.80299} 6.80306] 6.80313] 6.80320] 6.80327] 6.80335) 6.80342] 6.80350] 6.80357| 6.80365 5 300, = 307/314) = 322] «= 320] «= 336 S344} = 351] «= 350} += 366 10 305} 312} 319} 326} = 333} «= 340}. «3S 348] = 355) ~=— 303} 370 15 313] 320) «3 326} = 333}, 3S 340). «Ss 348} = 355] += 302] = 369) «3 3:76 20 324, 330 ~=- 337}. S343] «= 350] «= 357) += 364, 3S 371] 3 378} = 385 25 337| 343] «= 349], «= 355] = 362] «S 368) 375] 3 382) 9 388} 395 30 352] 358} = 364) 370] 3S 376, 3 382} 3 388) 394, = 401] = 407 35 369 374 380 385 391 397 402 408 414 420 40 386, 392 397 402| 407 412 418) 423} 429) 434 45 405, 410) 414) 9419) = 24} 420) 434 = 439] 32 4441 449 50 423 428) 432 436) 441 445 450|} 454, 459) 464 55 441 445 449 453 457 461 465 409] = 474 478 458 462 405 409 472 476 480 484 487 491 65 473 476 480 483 486 489} 493 496 500 503 70 486} 489) 492) 495] = 498] = So], = S04} 9 507} 2S 510] 514 75 497 500 502 505 508 510 513 516 519 22 80 505 507 510 GI2 515 517 520 523 525 528 85 510 512 514) 517 519 22 524 SI 52 poe 528, 531] 533 go 511 514 516 518 521 52 526 SMITHSONIAN TABLES. 66 TABLE 12. LOGARITHMS OF RADIUS OF CURVATURE Pa (IN METRES) OF SECTION OF EARTH’S SURFACE INCLINED TO MERIDIAN AT AZIMUTH a. [Formula for pa given on p. xlv.] LATITUDE. 46° ©° | 6.80373] 6.80380] 6.80388] 6.80396) 6.80404) 6.80411) 6.80419} 6.80426 6.80434] 6.80442 5 374, 382] + 380] = 397) 404] 42] 420) 428} 435] 443 10 378] 385} = 393). «= 400 S408] 4s} = 423} = 430] 438) 445 15 384, 391 399] 406) 413} = 420) S428] 2 435] = 442) 450 20 392 399 406} = 413}, = 420) 427 434 441 448 455 2 402} 408} 415 22} 429) 436] 442} 449] 456) = 463 30 413} 420, 426 4331 43901 446 452| 458) 405) 471 35 426} 432) 438] 444} 4501 = 456] = 462] = 468] = 474) = 480 40 440 446 451 457 462 468 474 479 485 490 45 454] 4501 464, 470/ 475, 480) 485; 490] 495 500 50 468} 473} += 478} = 482} = 487} 9 492/496} 501 506} 510 55 482} 486, 490} 495 499] 503) 508} = 5512/ = 16) 520 60 495, 499|° 502} soo} «= sto], rq) 518} = 522} 9 526) 830 65 go7] sto «= salt} = 520]. S524] «= 528] 531] 9 534, 538 70 517} 520] S52 526, 52g = 532}. S536) «= 539} 542) 545 525, 5281 530] 534, 530, 539 542 545, 548} 9552 531 534 536 539 542 544 547 550 553 55 534 537 540 542 545 548 550 553 555 55 536 538 541 544 546] °549 551 554 556 559 LATITUDE. 6.80449 | 6.80457 | 6.80464 | 6.80471 | 6.80479 | 6.80486 | 6.80493 | 6.80500 6.80506 450 458 465 472 479 486 493 500 507 453 460 497 474 481 488 495 502 509 457 464 471 478 485 492 498 505 Sil 20 462 469 476 453 489 496 502 509 515 25 . 469 476 482 489 495 Sol 505 514 520 477 484 490 490 502 508 514 519 525 486 492 498 503 509 515 520 525 531 40 490 Sor 506 S12; 517 22 527 532 537 45 505 nS 525 ae 575 53° 534 539 543 50 515 520 524 528 533 537 542 546 550 55 524 528 533 537 541 545 548 552 556 60 533 537 541 544 548 552 555 558 502 65 541 545 548 551 555 558 561 564 567 70 548 551 554 557 560 503 566 569 572 75 554 557 559 562 565 565 570 573 575 So 558 561 563 566) 568 571 573 576 578 85 560 563 566 568 570 573 575 578 580 ge 561 564 S00: )) | 509), 7s 574 576 578 580 SmitHsonian Tastes. 67 TABLE 13. 7 LOCARITHMS OF FACTORS =-;-FOR COMPUTING SPHEROIDAL EXCESS OF TRIANGLES. UNIT=THE ENGLISH FOOT. (Derivation and use of table explained on p. Iviii.] log. factor and log. factor and log. factor and log. factor and change per change per change per change per minute. minute. minute. minute. 0.37498 : 40° 0.37255 60° 0.37056 — 0.00 : —o.18 : 498 244 — 0.02 : — 0.17 497 234 — 0.02 ; — 0.17 490 22 — 0.02 ; — 0.17 495 ee — 0.03 7 — 0.18 203 —0.17 193 — 0.17 133 — 0.17 173 —o.18 162 — 0.17 152 — 0.17 142 — 0.17 132 — 0.17 122 — 0.17 112 — 0.15 103 —0.17 093 — 0.17 083 074 — 0.15 065 056 SMITHSONIAN TABLES. 68 TABLE 14. at LOCARITHMS OF FACTORS=;.>, FOR COMPUTING SPHEROIDAL EXCESS OF TRIANCLES. UNIT=THE METRE. [Derivation and use of table explained on p. lviii.] log. factor and change per change per change per minute. log. factor and log. factor and log. factor and change per minute. minute. minute. 1.40695 1.40626 40° 1.40452 : — 0.00 — 0.12 —o.! 619 441 — 0.12 — 0.17 612 431 —0.12 —o. 605 421 — 0.13 —o. 597 411 —o0.12 —o.18 59° 400 — 0.17 SMITHSONIAN TABLES. 69 TABLE 15. LOGARITHMS OF FACTORS FOR COMPUTING DIFFERENCES OF LATI- TUDE, LONCITUDE, AND AZIMUTH IN SECONDARY TRIANGULATION. UNIT=THE ENGLISH FOOT, (Derivation and use of table explained on p. lx.] ? y= ° baal 7- 7.99669 | 7-99374 ee 669 669 669 669 669 668 668 6638 668 668 668 668 668 668 668 668 667 667 667 667 667 667 666 666 666 666 666 665 665 665 665 664 664 664 664 663 663 663 5) 662 662 662 662 661 661 661 660 660 659 6 59 659 658 658 657 657 657 656 656 655 SMITHSONIAN TABLES. 374 374 374 374 374 374 374 374 374 374 374 374 373 373 373 313 373 373 373 3/3") S75 Bis a7s 373 373 | 373 | 373 3/3 373 373 373 372 372 372 | 372 | 372 372 372 372 372 372 372 371 371 | 371 371 | 371 371 371 371 371 379 | 370 | 370 379 37° | 379 be —_—C 8.137 8.438 8.614 8.739 8.336 8.915 8.982 9.040 9.091 9-137 9-179 9.216 9.251 9.283 9.314 9-342 9.368 9-393 9-417 9-439 9.460 9.481 9.500 9.519 91597 O:594 9-579 9.586 9.602 9-617 8 | 9.903 9-910 | | 9.918 | 91926) 0.372 0.372 0.372 0.372 0.372 0.372 0.372 0.372 0.372 0:3/5 9.373 0.373 0.373 0:373 0.373 0.374 0-374 0-374 0.374 0-375 0:375 0.375 0.376 0.376 0.376 O37 7 0-377 0.377 9.378 0.378 0-379 9.63 I | 0.379 9-645 | 0.379 0.380 0.380 0.381 0.381 0.382 0.383 0.383 0.384 0.384 0.385 0.386 0.386 | 0.387 | 0.387 0.388 0.389 0.389 0.390 0.391 0.392 | 0.392 0.393 0.394 0.395 lo. 396 0.396 0.397 0.398 ay | 7. 99855 7: 99369 55 654 654 654 a8 = 652 651 ae 650 650 649 649 648 648 647 646 646 645 645 644 644 643 642 bg 9.926 9-933 9-941 9.948 9-955 9.963 9-979 9-977 9-983 9.999 9-997 0.003 0.010 0.016 0.023 0.029 0.035 0.041 0.048 0.054 0.060 0.065 0.071 0.077 0.08 0.08 0.094 0.100 0.105 O.III 0.116 0.121 0.127 0.132 0.137 o.1 42 0.147 | 0.15 0.15 0.163 0.1 65 | 0.173 0.178 0.182 0.187 0.192 0.197 0.202 0.206 O.211 0,216 0.220 0.225 0.22 0.234 0.239 0.243 0.248 0.252 0.256 0.261 c 0.398 0.399 0.400 0.401 0.402 0.403 0.404 0.404 0.405 0.406 0.407 0.408 0.409 0.410 0.412 0.413 0.414 0.415 0.416 0.417 0.418 0.419 0.420 0.422 0.423 0.424 0.425 0.426 0.428 0.429 0.430 0.431 0.433 0.434 0-435 0-437 | 0.438 0.439 0.441 0.442 0.443 (0.445 0.446 0.448 0.449 0.4.50 0.452 0.453 0.455 0.450 0.458 0.459 0.4601 0.463 0.464 0.466 0.467 0.469 0.470 0.472 0.474 i - hy y , ; . ny, TABLE 15. LOGARITHMS OF FACTORS FOR COMPUTING DIFFERENCES OF LATI- TUDE, LONCITUDE, AND AZIMUTH IN SECONDARY TRIANCULATION. UNIT=THE ENGLISH FOOT. [Derivation and use of table explained on p. Ix.] bg a by = Ce ~ 2 20°00’) 7.99617 | 7.99357 | 9-935) 0.261 30°00"| 7.99558 | 7-99337 | 0-135] 0.496 | 0.593 IO 616 356 | 9.939| 0.265 10 557 337 0.500 | 0.59 350 | 9. 0.270 20 556 336 | 0. 0.503 | 0.59 356 | 9.947 | 0.274 30 555 330 | o. 0.507 | 0.600 355 | 9: 0.27 40 554 335 | ©: 0.511 | 0.603 0.282 50 553 335 | ©. 0.514 | 0.605 0.287 552 335 | ©. 0.518 | 0.607 355 | 9- 0.291 10 550 3344) 0: 0.522 | 0.610 0.295 20 549 334 | 0. 0.525 | 0.612 0.299 30 548 433)| 0: 0.529 | 0.615 354 | 9: 0-304, 40 547 S5Si ace 0.532 | 0-617 0.308 50 546 333 11.0. 0.536 | 0-619 31 | 0.312 545 2324) 0: 0.540 | 0.622 353 | 9-984| 0.316 10 544 332 1/0: 0.543 | 0-624 : 0.320 20 542 332 | 0. 0.547 | 0.627 0.324 30 541 331 | ©. 0.550 | 0.629 0.328 40 540 331 | 0. 0.554 | 0-632 0.332 50 539 330 | O- 0.558 | 0.634 0.336 330 | ©. 0.561 | 0.637 0.340 10 330 | 0.188 | 0.565 | 0.639 0.344. 329 | ©. 0.568 | 0.642 0.348 329 | ©. 0.572 | 0.644 0.352 328 | 0. 0.575 | 0-647 0.356 328 | 0.199) 0.579 | 0.650 0.360 328 | 0. 0.583 | 0.652 0.364 32750: 0.586 | 0.655 0.368 327 | 0. 0.590 | 0.657 0.372 326 | 0.210 0.593 | 0.660 0.376 326 | 0.213] 0.597 | 0.663 0.380 326 | 0.216} 0.600 | 0.665 0.384 325 | 0.218 | 0.604 | 0.668 0.388 325 | 0. 0.608 | 0.671 0.392 324 | 0.224! 0.611 | 0.673 0.396 2 .226 0.615 | 0.676 0.399 | 0. 2 .229 | 0.618 | 0.679 0.403 .232 | 0.622 | 0.681 0.407 0.625 | 0.684 0.411 0.629 | 0.687 0.415 0.632 | 0.689 0.418 0.636 | 0.692 0.422 | 0.640 0-695 0.426 0.643 | 0.69 0.430 Y 0.647 | 0.700 O455 2 . 0.650 | 0.703 0.437 2 : 0.654 | 0.706 0.441 .258 | 0.657 | 0.709 0.445 | 0. : | 0.661 | 0.712 0.448 .263 0.665 | 0.715 0.452 12 0.668 | 0.717 0.456 : 0.672 | 0.720 | 0.460 : | 0.675 | 0.723 3 | 0.463 : 0.679 | 0.726 0.467 : 0.683 | 0.729 0.471 .278 | 0.686 | 0.732 0.474 Ms 0.690 | 0.735 0.478 .284 | 0.693 | 0.738 23| 0.482 Ke 0.697 | 0.741 26| 0.485 30 | 2 0.701 | 0.744 0.489 | 0.588 5 0.704 | 0.747 0.493 c 0.294 | 0.708 | 0.750 0.135 | 0.496 3 0.296 | 0.711 | 0.753 | | — 7 NNN NNN Be N NNO SMITHSONIAN TABLES. TABLE 15. LOGARITHMS OF FACTORS FOR COMPUTINC DIFFERENCES OF LATI- TUDE, LONGITUDE, AND AZIMUTH IN SECONDARY TRIANCULATION. UNIT=THE ENGLISH FOOT. [Derivation and use of table explained on p. Ix.] ¢ j= 2 2 a hc 40°00"| 7.99486 | 7.99313 50°00'| 7.99409 | 7.99287 10 | 485 312 10 408 287 484 20 407 ee 312 30 406 481 . 40 404 480 311 50 403 479 oo 402 477 fe) 401 476 20 399 475 30 398 473 4° 397 472 59. 396 471 00 394 470 10 393 468 20 392 467 30 391 466 40 389 464 50 388 453 387 462 oO 386 461 384 459 383 45 3¢ 2 457 381 455 379 454 378 453 377 452 376 450 Sip 449 373 448 372 446 I 371 445 37° 444 369 367 306 365 364 363 361 360 359 % 57 356 354 353 352 35! 35° 349 347 346 345 344 343 342 341 339 338 337 - ~ NN NNN ~ ee ee ee ee ee el . ae elas oes) awe 1s Snes eve Slsiare wis Seen ee ee ee SMITHSONIAN TABLES. 72 TABLE 15. LOCARITHMS OF FACTORS FOR COMPUTINC DIFFERENCES OF LATI- TUDE, LONGITUDE, AND AZIMUTH IN SECONDARY TRIANGULATION. UNIT=THE ENGLISH FOOT. [Derivation and use of table explained on p. Ix.] 9 b= 2 a ay bg C2 60°00" 7.99337 | 7-99263 10 336 263 335 263 334 262 333 262 332 201 261 261 260 260 260 259 259 259 258 258 257 257 257 256 250 256 255 255 255 254 254 254 253 253 253 252 252 252 251 251 251 250 250 250 249 249 249 249 248 248 248 247 247 247 246 246 246 246 245 245 245 244 244 244 244 70°00'| 7.99278 | 7.99244 | 0.809] 1.575 1.576 oO 277 243 | 0.813] 1.583 | 1.584 20 277 243 | 0.817] 1.590] 1.591 276 243 | 0.821] 1.598] 1.599 275 242 | 0.825 | 1.605 | 1.606 274 242 | 0.829| 1.613 | 1.614 273 242 | 0.833| 1.621 | 1.621 273 242 | 0.837 | 1.629] 1.629 272 241 | 0.841} 1.636] 1.637 271 241 | 0.845] 1.644] 1.645 270 241 | 0.849) 1.652] 1.653 2609 241 | 0.854] 1.660] 1.661 269 0.858 | 1.669 | 1.669 268 0.862 | 1.677 | 1.677 267 0.866 | 1.685 | 1.686 266 0.871 | 1.694 | 1.694 266 0.875 | 1.702 | 1.702 265 0.880 | 1.710] 1.711 264 0.884} 1.719] 1.720 264 0.889 | 1.728 | 1.728 263 3 | 0.893] 1.737 | 1-737 262 0.898 | 1.745 | 1-746 261 0.903} 1.754] 1-755 261 3 | 0.907 | 1.763 | 1.764 260 0.912 | 1.772] 1.773 259 0.917 | 1.782 | 1.782 259 0.922 | I.791 | 1.791 258 0.927 | 1.800 | 1.801 257 0.931 | 1.810] 1.810 257 0.936 | 1.820 | 1.820 256 0.941 | 1.829] 1.830 255 0.946 | 1.839 | 1.839 255 0.952! 1.849] 1.849 0.957 | 1.859] 1.859 0.962 | 1.869 | 1.869 0.967 | 1.879 | 1.880 0.973| 1.890 | 1.890 0.978 | 1.900 | 1.901 0.984} 1.911 | 1.911 0.989 } 1.922} 1.922 0.995} 1-933 1-933 1.000} 1.944 } 1.944 1.006} 1.955] 1-955 I.012| 1.966] 1.966 1.018 | 1.978 | 1.978 1.024] 1.989 | 1.989 1.030 | 2.001 | 2.001 1.036] 2.013 | 2.013 1.042] 2.025 | 2.025 1.048 | 2.037 | 2.037 1.054] 2.050] 2.050 1.061 | 2.062 | 2.062 1.067 | 2. 2.075 1.074] 2. 2.088 1.081 -IOI 1.087 -II4 1.094 128 1.101 142 1.108 .156 1.116 .170 1.123] 2.184 | 2.184 — ay fee 8 God N ee ~ _ 7 G2 Go Gs db we Qs HO - = oe it to te ano Wnt © Cn NON & OO a on™ in 2 er bob PDHKR VHKBHNNVKHNVNVDN me NWN BOW a LS) 3 Rw d&o NNN WN G2 Wd G2 dG) GIO GO oO etme ttt Owo roto WWwWw Gb InN Ww ee O bo C2 Ga Oe Go Ga Go t & & ON MO W RARA ARARA ROG NH A WO WWW GI WWW O30) 2 WOW WWW WOW OOWHPRRBRABR ONO DA ADAG ANN NN OC Bee ew NN NNN NOH GH NNN NN Nn NNKR NNN I. I. I. I I. I. I I I I I. I I. I. I. I I I I I.4 I.2 I. I. I. I. I. I. I. I. I. I. I. I. LS I. I. I. YDNNNKN NNN NNN NNK NNN NNN NNN HNN NNN NNN bY H NNN WK G2 Od Gd GI OI Gd CI G2 Gd Wn Gs G2 - SMITHSONIAN TABLES. qs TABLE 16. LOCARITHMS OF FACTORS FOR COMPUTING DIFFERENCES OF LATI- TUDE, LONCITUDE, AND AZIMUTH IN SECONDARY TRIANGULATION. UNIT=THE METRE. [Derivation and use of table explained on p. Ix.] ay 4=c 8.51268 | 8.50973 | —0o | 1.404 268 973 | 8. 9.169 | 1.404 268 973 | 9. 9-470 | 1.404 268 973 | 9. 9-646 | 1.404 268 973 | 9. 9-771 | 1.404 268 973 | 9. 9.868 | 1.404 267 973 | 9-049 | 9.947 | 1.404 267 973 | 9. 0.014 | 1.404 267 973 | 9. 0.072 | 1.404 267 973 | 9. 0.123 | 1.405 267 973 | 9. 0.169 | 1.405 267 973 | 9.912] 0.211 | 1.405 267 972 | 9. 0.248 | 1.405 267 972 985 | 0.283] 1.405 267 972 | oO. 0.315 | 1-405 266 972 | 0. 0.346 | 1.406 266 972 | o. 0.374 | 1.406 266 972 | ©. 0.400 | 1.406 266 972 | ©. 0.425 | 1.406 266 972 | ©. 0.449 | 1.407 266 972 | ©. 0.471 | 1.407 266 972 | 0. 0.492 | 1.407 266 972 | 0.214] 0.513] 1.408 266 972 | o. 0.532 | 1.408 265 972 | 0.252] 0.551 | 1.408 265 972 | ©. 0.509 | 1.409 265 972 | 0.2 0.586 | 1.409 265 972 | ©. 0.602 | 1.409 265 972 | oO. 0.618 | 1.410 264 972 | ©. 0.634 | 1.410 264 972 | ©. 0.649 | 1.411 264 971 | o. 0.663 | 1.411 264 971 | oO. 0.677 | 1.411 264 O71; 0: 0.691 | 1.412 263 971 od 0.704 | I.412 263 971 : 0.717 | 1.413 971 | 0. 0.729 | 1.413 971 | o. 0.741 | 1.414 971 | oO. 0.753 | 1-415 O71) ||. (0: 0.764] 1.415 971 ; 0.776| 1.416 971 | 0.485] 0.787 | 1.416 979 | 0.4 0.797 | 1.417 970 | o. 0.808 | 1.417 970 | 0. 0.818 | 1.418 970 | 0.526] 0.828 | 1.419 970 | o. 0.838 | 1.419 970 | ©. 0.848 | 1.420 970 | ©. 0.857 | 1.421 970 | ©. 0.806 | 1.421 970 | ©. 0.875 | 1.422 969 | o. 0.884 | 1.423 969 | o. 0.893 | 1.424 969 598 | 0.902 | 1.424 969 | o. 0.910 | 1.425 969 | o.€ 0.918 | 1.426 969 | o. 0.927 | 1.427 969 | o. 0.935 | 1.428 969 .638 | 0.942 | 1.428 968 | o. 0.950 | 1.429 all .653| 0-958 | 1.430 Non Gow QW ~] ) t t w = NN 2 NR YN KH bw YL AN MMO 0K NWW RUN AN OO OO O NN NNKNHK NN — YN NHON NNN NNN NNN HNN NNN ~ SMITHSONIAN TABLES. TABLE 16. LOGARITHMS OF FACTORS FOR COMPUTING DIFFERENCES OF LATI- TUDE, LONCITUDE, AND AZIMUTH IN SECONDARY TRIANCULATION, UNIT=THE METRE. (Derivation and use of table explained on p. Ix.] ay ral 8.51157 | 8.50936 : a 930 155 935 154 935 153 934 152 934 Ist 934 149 933 148 933 147 933 146 932 145 144 143 141 140 139 138 137 a6 134 133 132 131 130 128 127 126 125 124 122 121 120 119 118 116 IIS 114 113 III IIo 109 108 106 105 104 103 102 100 099 098 097 095 094 093 ? 090 089 088 086 085 & \o oO Qo 2 a NI Ww Net Go ae °o aw Ww Own nn OAnN © ww no Oe Ce nn a ee ee ee ee el Sabi eah teeta oh Peleg ten te hicoh ats Cig Seniesa ers Mec ow 5 Go ON ww NI to ty tN WN N 2 2 2 2 2 2 -2 2 2 2 2 2 2 2 2 2 2 2 2 2 NE FO DSK HO QW OO CH N ONS HO DW SSN DD DOM HHH WWW Do cee OO ee OO ee oe ee SMITHSONIAN TABLES. . TABLE 16. LOGARITHMS OF FACTORS FOR COMPUTING DIFFERENCES OF LATI- TUDE, LONGITUDE, AND AZIMUTH IN SECONDARY TRIANGULATION. UNIT=THE METRE. (Derivation and use of table explained on p. 1x.] ay by —C, ‘| 8.51085 | 8.50912 | 1. : : °00'| 8. . ee 1.971 | 1.987 084 QIr | I. : : 10 007 886 | I. 1.975 | 1.990 083 gir | I. : ; 885 | I. 1.980 oS OL er : 793 885 | I. 1.934 080 gio | I. ; : 885 | I. 1.988 079 gio | I. 762 | 1.8 884 | I. 1.992 078 909 | I. a 8 884 | I. 1.996 909g | I. : 8 883 | 1.498] 2.000 075 gos | I. é 8 ; 883 | I. 2.004 gos | I. : 812 882 | I. 2.008 go08 | I. .780 | 1.8 6 882 | I. 2.013 907 | I. 783 | 1.818 oy 882 | 1.508] 2.017 907 | I. : 82 881 | I. 2.021 go6 | tI. : 82 38 . 2.025 906 | I. : 828 5 : 2.030 gos | I. 7 83 ; 2.034 905 | I. 802 | I. z 2.038 905 | 1.3 : : : 2.042 904 | 1.372 3 1.8 ) : 2.047 904 | I. : : : 2.051 9033/1: 3 8. ; 2.055 | 2 903 | 1.3 : ; 82 . 2.060 go2 | I. 824 | 1.853 : 2.064 go2 | I. : : 8 : 2.008 go2 | 1.3% 832 | 1.8 : 2.073] 2 gol | I. : : : 2.077 gor | 1.3 =e 8 6 : 2.081 goo | 1.3 8 : 2.086 900 5 899 o 2. 2. 2. 2 2. 2. 2. 2. 2. 2. 2. Y NN NNN No N NNN NNN NNN POW Nh NN ON N NNN NY NN bd SMITHSONIAN TABLES. TABLE 16. LOGARITHMS OF FACTORS FOR COMPUTING DIFFERENCES OF LATI- TUDE, LONGITUDE, AND AZIMUTH IN SECONDARY TRIANGULATION, UNIT=THE METRE. [Derivation and use of table explained on p. 1x.] j= 60°00’) 8.50936 | 8.50862 a 70°00"| 8.50877 | 5.50842 | I. 2.607 842 | I. 2.615 842 | I. 2.622 842 | I. 2.630 841 | I. 2.637 841 4 2.645 OAT | at. 2.653 | 2 841 | 1.869] 2.661 840 | I. 2.668 840 | I. 2.676 840 | I. 2.684 84o | 1.8 2.692 839 | I. 2.701 839 | 1.8 839 839 838 838 838 838 837 837 837 837 836 836 836 836 836 835 835 835 835 834 834 834 834 834 833 833 833 833 833 832 832 $32 832 $32 832 831 831 831 831 831 $31 | 2. 3.133 830 | 2. 3.146 830 | 2. 3-160 830 : 3-174 Z 830 | 2. 3.188 | 3.18 830 | 2.148 | 3.202 | 3.202 830 | 2. 3-216 | 3-216 bn NN NN NNN a | ° ~ NNH NNH WN 3 Ww G2 G2 Go WWW WWW A&W WbWNnN NNN NNN NN wR NNHN NNN NNN No N N N N NN N NN N No N MH HHH HHOOOO0OO OOK UDO OOD UONR Sau GSS SSE BE A 8 0 WO ON OO dn WEB™ ON 00 oN fu ON © NW Ww mo nnn noo a4 Ys BW Ne OB MHD A OHWNAMN OF DUNN Aer ONO BROW KU SAW N mmm MDOmONININ 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2 2 2. 2. 2. 2. 2. 2. 2 2 2. 2. 2. 2 2. 2. 2. Ob RRO OOM ONIN DONUNSWWNN = =O 00 © COIN DOV BRBERBKR Bord BOO DOH HOW OHH WHW®YNYNH NNN VL OO ONAN bo Nyy bv & kA f Anu —& Oo ANF ON OO in BON = OW OC WOOD DOO OO & & OV SIS ONL WWN NHS FSR DN Bx? S 00 MWe Oo SIUnW = O ON QU WNN SHR See me BON Wm PON FO ONION fWN | 020000 000 Woy wy m= OO90 Now aD ON A NO moO bw OVO nin intinta nin Minn nin ff n Sane ons > CO. NON iS) N NNN NNN NNN NNN N 8 SMITHSONIAN TABLES. TABLE 17. LENGTHS OF TERRESTRIAL ARCS OF MERIDIAN. [Derivation of table explained on p. xlvi.] Latitude | Latitude. Interval. o? Feet. 1007.66 2015.31 3022.97 4030.63 5038.28 6045.94 60459.4 120918.8 181378.3 241837.7 302297.1 362756.5 ce 1007.73 2015.47 3023.20 4030.94 5038.67 6046.41 60464.1 120928.2 181392.3 241856.4 302320.5 362784.6 Too 1007.97 2015.93 3023.90 4031.86 5039-83 6047.80 60478.0 120955-9 181433.9 241911.8 302389.8 362867.8 Gs 1008.34 2016.69 3025.03 4933-37 5041.72 6050.06 60500.6 I21001.2 181501.7 242002.3 302502.9 363003.5 20° 1008.86 2017.71 3026.56 4035-42 5044.28 6053.13 60531.3 121062.6 181593.9 242125.2 302656.5 363 187.8 Latitude. 1° Feet. 1007.66 2015-32 3022.98 4030.64 5038.30 6045.96 60459.6 120919.2 181378.8 241838.4 302298.0 362757.6 6° 1007.77 2015-54 3023.31 4031.08 5038.84 6046.61 60466.1 120932.3 181398.4 241864.6 302330.7 362796.8 Tie 1008.03 2016.06 3024.09 4032.12 5040.15 6048.18 60481.8 120963.6 181445.4 241927.2 302409.0 362890.8 16° 1008.44 2016.87 3025.30 4933-74 5042.18 6050.61 60506. 1 I21012.2 181518.3 242024.4 302539.5 363036.6 21 1008.97 2017.95 3026.92 4035.89 5044.86 6053.84 60538.4 121076.8 181615.1 242153.5 302691.9 363230.3 SMITHSONIAN TaABLEs. Latitude. 2° Feet. 1007.67 2015.34 3023.01 4030.68 5038.35 6046.02 60460.2 120920.4 181380.6 241840.8 302301.0 362761.2 70 1007.81 2015.62 3023-43 4031.24 5039.04 6046.85 60468.5 120937-I 181405.6 241874.2 302342-7 362811.2 127 1008.10 2016.20 3024.30 4032.40 5040.50 6048.60 60486.0 120972.0 181458.0 241944.0 302430.0 362916.0 re 1008.53 2017.06 3025.60 4034-13 5042.66 6051.19 60511.9 121023.8 181535.8 242047.7 302559.6 363071-5 222 1009. 10 2018.19 3027.28 4030.38 5045-48 6054.57 60545-7 I210Q1.4 181637.1 242182.8 302728.5 363274.2 Latitude, 3 Feet. 1007.68 2015.37 3023.06 4039.74 5038.42 6046.11 60461.1 120922.2 181383.3 241844.4 302395-5 362766.6 8° 1007.86 2015-71 3023.56 4031.42 5039.28 6047-15 60471.3 120942.6 181413.9 241885.2 3023 56.5 362827.8 Ta 1008.18 2016.35 3024-52 4032.70 5040.88 6049.05 60490.5 120981.0 181471.5 241962.0 302452.5 362943.0 18° 1008.63 2017.27 3025.90 4034.54 5043.18 6051.81 60518.1 121036.2 181554.3 242072.4 302590.5 363108.6 1009.22 2018.44 3027.66 4036.88 5046.10 6055-33 60553-3 121106.5 181659.8 242213.0 302766.3 363319.6 Latitude. 4° Feet. 1007.71 2015.41 3023.12 4030.83 5038.54 6046.24 60462.4 120924.8 181387.3 241849-7 302312.1 362774-5 1007.91 2015.82 3023.72 4031.63 5039-54 6047-45 60474.5 120949.0 181423.4 241897.9 302372.4 362846.9 1008.26 2016.51 3024.77 4033.02 5041.28 6049.54 60495-4 120990.7 181486.1 241981.4 302476.8 362972.2 19° 1008.74 2017.48 3026.23 4034.97 5043-71 6052.45 60524.5 121049.0 181573.6 242098.1 302622.6 363147.1 1009.35 2018.70 3028.06 4037-41 5046.76 6056.11 60561.1 I21122.2 181683.4 242244.5 302805.6 363366.7 TABLE 17. LENCTHS OF TERRESTRIAL ARCS OF MERIDIAN, [Derivation of table explained on p. xlvi.] Latitude Interval. SMITHSONIAN TABLES. Latitude. Zhe Feet. 1009.49 2018.97 3028.46 4037-95 5047.44 6056.92 60569.2 121138.5 181707.7 242276.9 302846.1 363415.4 30° 1010.22 2020.44 3030.66 4040.88 5051.10 6061.32 60613.2 121226.4 181839.7 242452.9 303066.1 363679-3 35° IOTL.03 2022.06 3033-10 4044-13 5055.16 6066. 19 60661.9 121323.9 181985.8 242647.8 303309-7 363971-7 ° 4c IOII.go 2023.80 3035-70 4047.60 5059-50 6071.39 60713.9 121427.9 182141.8 242855.8 303569.7 364283.7 45° Latitude. oO 20 Feet. 1009.63 2019.25 3028.88 4038.51 5048.13 6057.76 60577.6 I21155.2 181732.7 242310.3 302887.9 363465-5 Latitude. 2yG Feet. 1009.77 2019.54 3029.31 4039.08 5048.85 6058.62 60586.2 I21172.3 181758.5 242344-7 302930.9 363517.1 Latitude. 250 Feet. 1009.92 2019.83 3029-75 4039-67 5049.58 6059.50 60595.0 121190.0 181785.0 242379.9 302974-9 363569.9 Latitude. 29° Feet. 1010.07 2020.13 3030.20 4040.27 $050.33 6060.40 60604.0 121208.0 181812.0 242416.0 303019.9 363623.9 at 1010.38 2020.75 3031.13 4041-51 5051.89 6062.26 60622.6 121245.3 181867.9 242490-5 303113.2 363735-8 30° IOII.20 2022.40 3033.61 4044.81 5056.01 6067.21 60672.1 121344.3 182016.4 242688.5 303360.6 364032.8 41° 1012.08 2024.15 3036.23 4048.31 5060.38 6072.46 60724.6 121449.2 182173-8 242898.4 303623.0 364347-6 46° 32° IOI0.54 2021.07 3031-61 4042.15 5052.68 6063.22 60632.2 121264.4 181896.6 242528.8 303161.1 363793-3 IO1I.37 2022.75 3034-12 4045-50 5056.87 6068.24 60682.4 121364.9 182047.2 242729-7 303 412.2 364094.6 42° 1012.25 2024.51 3036.77 4049.02 5061.28 6073.53 60735.3 121470.6 182206.0 242941.3 303676.6 364411.9 47° 1012.79 2025.59 3038.38 4051.18 5063.97 6076.77 60767.7 121535+3 182303.0 243070.6 303838.3 364606.0 1012.97 2025.95 3038.92 4051.go 5064.87 6077.85 60778.5 121556.9 182335-4 243113.9 303892.4 364670.8 1013.15 2026.31 3039.46 4052.62 5065-77 6078.93 60789.3 121578.5 182367.8 243157.0 303946.3 3647355 79 49° JO 1010.70 2021.40 3032.10 4042.80 5053-50 6064.20 60642.0 121283.9 181925.9 242567.9 303209.9 363851.8 38° IOII.55 2023.09 3034.64 4046.19 5057-74 6069.29 60692.9 121385.7 182078.6 242771-4 303464.3 364157.1 40 43 1012.43 2024.87 3037-30 4949-74 5062.17 6074.61 60746.1 121492.2 182238.2 242984.3 393730.4 364476.5 48° 1013.33 2026.67 3040.00 4953-34 5066.67 6080.00 60800.0 121600.1 182400.1 243200.1 304000, I 364800,2 1010.86 2021.73 3032-59 4043.46 5054-32 6065.19 60651.9 121303.8 181955-7 242607.6 303259.4 363911.3 39° IO1I.72 2023.44 3035-17 4046.89 5058.61 6070.34 60703.4 121406.7 182110.1 242813.-4 303516.8 364220.2 ° 44 1012.61 2025.23 3037.84 4050.46 5063.07 6075.69 60756.9 I21513.7 182270.6 243027.4 303784.3 364541.2 49° 1013.51 2027.02 3040.54 4054-05 5067.56 6081.08 608 10.8 121621.5 182432.3 243243.0 304053.8 364864.5 TABLE 17. LENCTHS OF TERRESTRIAL ARCS OF MERIDIAN. [Derivation of table explained on p. xlvi.] Latitude | Latitude. Latitude. Latitude. Latitude. Latitude. Latitude. Interval. 2. 0 ° Feet. 1014.04 1014.22 1014.39 1014.56 2028.09 2028.44 2028.78 2029.12 3041.07 2 3042.13 3042.65 3043.17 3043.68 4054.76 4955-47 4056.17 4056.87 4057.56 4058.24 5068.46 5069.34 5070.22 5071.09 5071.96 5072.80 6082.15 6083.21 6084.26 6085.31 6086.35 6087.37 60821.5 60832. 608 42.6 60853.1 60863.5 60873.7 121642.9 121664.2 121685.2 121706.2 121726.9 121747-3 182464.4 182496.2 182527.7 182559.2 182590.4 182621.0 243285.8 243328.3 243370.3 243412.3 243453-8 243494.6 304107.3 304160.4 304212.9 304265.4 304317.3 304368.3 364992.5 365055.5 365118.5 365180.8 365242.0 1014.73 1014.90 1015.06 1015.22 1065.38 1015.53 2029.46 2029.79 2030.12 2030.44 2030.76 2031.07 3044.19 3044.69 3045.18 3045.66 3046.14 3046.60 4058.92 4059.58 4060.24 4060.88 4001.52 4062.14 5073-65 5074.48 5075-30 5076.10 5076.90 5077-67 6088.38 6089.38 6090.36 6091.33 6092.27 6093.20 60883.8 60893.8 60903.6 60913.3 60922.7 60932.0 121767.6 121787.5 121807.2 121826.5 121845-5 121864.1 182651.4 182681.3 182710.8 182739.8 182768.2 182796.1 243535-2 243575-0 243614.4 243653.0 243691.0 243728.2 304419.0 304518.0 304660.2 365421.6 1015.69 1015.83 1015.98 1016.12 1016.26 1016.39 2031.37 2031.67 2031.96 2032.24 2032.51 2032.75 3047.06 3047.50 3047-94 3048.36 3048.77 3049-16 4062.74 4063.34 4063.92 4064.48 4065.02 4065.55 5078.43 5079.17 5079.90 5080.60 5081.28 5081.94 6094.12 6095.00 6095.87 6096.71 6097.54 6098.33 60941.2 60950.0 60958.7 60967.1 60975.4 60983.3 121882.3 121900.1 121917.5 121934.3 121950.7 121966.6 182823.5 182850.1 182876.2 182901.4 182926.1 182949.8 243764.6 243800.2 243835.0 243868.6 243901.4 243933.1 304705.8 304750.2 304793-7 304835.7 304916.4 365647.0 365700.2 365752.4 365802.8 365899.7 1016.87 2033-03 : : 2033-75 3049-55 ; : 3050.62 4066.07 i 4067.49 5082.58 A : 5084.36 6099.10 ; f 6101.24 A 6102.52 60991.0 ‘ 61012.4 61025.2 121982.0 121996.8 ; 122024.8 122037.8 122050.3 182973.1 182995.2 3016. 183037.1 183056.8 183075-5 243964.1 243993-6 244022.2 244049.5 244075.7 244100.6 304955-1 304992.0 305027.7 305061.9 305094.6 305125.8 365940.1 365990.4 366033.2 366074.3 366113.5 360151.0 7a 75 76° We. Joe 79° 1017.18 . 1017.28 1017.37 1017.45 1017.53 1017.60 2034.37 2034.56 2034.73 2034.90 2035.05 2035.19 3051.56 3051.84 3052.10 3052.35 3052.58 3052.79 4068.74 4069.12 4069.46 4069.80 4070.10 4070.38 5085.92 5086.40 5086.83 5087.24 5087.63 5087.98 6103.11 6103.67 6104.20 6104.69 6105.16 6105.58 61031.1 61036.7 61042.0 61046.9 61051.6 61055.8 122062.2 122073.5 122083.9 122093.9 122103.1 I22111.5 183093.3 183110.2 183125.9 183140.8 183154.7 183 167.3 244124.4 244147.0 244167.8 244187.8 244206.2 244223.0 305155.5 305183.7 305209.8 305234.7 305257-8 305278.8 366186.6 366220.4 366251.8 366281.6 366309.4 366334.6 SMITHSONIAN TABLES. 80 TABLE 18. LENCTHS OF TERRESTRIAL ARCS OF PARALLEL. (Derivation of table explained on p. xlix.] Longitude| Latitude. Interval. 0° IOI4.52 2029.05 3043-57 4058.10 5072.62 6087.14 60871.4 121742.9 182614.3 243485.8 304357.2 365228.6 4042.76 5053-45 6064.14 60641.4 121282.8 181924.2 242565.6 303207.0 363848.4 299763.9 359716.7 1960.35 2949.53 3920.71 4900.88 5881.06 58810.6 117621.2 176431-9 235242.5 294053-1 352863.7 1907.44 2861.15 3814.87 4768.59 5722.31 57223. 1144460.2 171669.2 228892.3 286115.4 343338.5 SMITHSONIAN TABLES. Latitude. 1° 1014.37 2028.74 3043-11 4057-48 5071.86 6086.23 60862.3 121724.5 182586.8 243449.0 304311.3 2018.01 3027.01 4036.02 5045.02 6054.02 605 40.2 121080,5 181620.7 242161.0 302701.2 363241.4 179281.3 239041.7 298802. 1 358562.5 175585-3 234113.8 292642.2 Latitude. 72 1013.91 2027.82 3041-73 4055-64 5069.55 6083.46 6083 4.6 121669.2 182503.8 243338.4 304173.0 365007.6 1007.01 2014.03 3021 04 4028.05 5035.06 6042.08 60420.8 120841.6 181262.3 241683.1 302103.9 362524.7 59550.0 I19100.0 178650.0 238200.0 297750.0 357300.0 116457.0 174635.5 232914.0 2911 42.5 349371.0 Latitude. ‘° 1013.14 2026.29 3939-43 4952 57 5065.72 6078.86 60788.6 121577.2 182365.7 243154-3 303942.9 364731-5 1004.72 2009.43 3014.15 4018.87 5023.58 6028.30 60283.0 120566.0 180849.1 241132. ZO01415.1 59321-5 118642.9 177964-4 237285.8 296607.3 3860.73 4825-91 5791-09 57910-9 115821.8 173732.8 231643-7 289554.6 347495-5 Latitude. 4° 1012.07 2024.14 3036.21 4048.28 5060.35 6072.42 60724.2 121448.4 182172.6 242896.8 303621.0 364345-2 1002, 12 2004.23 3006.35 4008.47 5010.58 6012.70 60127.0 120254.0 180381.1 240508. 1 300635.1 59975-0 118150.4 177225. 236300.2 295375-2 354450-2 1895.10 2842.66 3790-21 4737-76 5685.31 56853.1 113706.2 170559-4 227412.5 284265.6 341118.7 56465.8 II2931-5 169397-3 225863.0 282328.8 338794.6 81 1868.71 2803.07 3737-43 4671.78 5606.14 56061.4 112122.8 168184.3 224245.7 280307.1 336368.5 3799-33 4636.66 5564.00 55640.0 111280.0 166919.9 222559.9 278199.9 333839.9 TABLE 18. LENCTHS OF TERRESTRIAL ARCS OF PARALLEL. Longitude Interval. [Derivation of table explained on p. xlix.] Latitude. 250 Feet. 920.03 1840.05 2760.08 3680.11 4600.14 5520.17 55201.7 110403.3 165605.0 220806.6 3517-39 4399-74 5276.09 52760.9 105521.8 158282.6 211043.5 263804.4 316565.3 249592.9 299511.5 3891.30 4069.56 46695.6 93391.2 140086.7 186782.3 233477-9 280173.5 1437-19 2155.78 2874.38 3592-97 4311.56 43115.6 86231.3 129346.9 172462.5 215578.2 258693.8 Latitude. 2737-33 3649.77 4562.21 5474-65 54746.5 109493.0 164239.5 2189386.1 273732.6 4939-37 49303-7 98607.4 147911.2 197214.9 246518.6 295822. 4600.73 46007.3 92014.7 138022.0 184029.3 230036.7 276044.0 795-99 1411.97 2117.96 2823.94 3529.93 4235-91 42359-1 84718.2 127077.3 169436.5 211795-6 254154-7 SMITHSONIAN TABLEs. Latitude. 904.58 1809.16 2713-74 3618.32 4522.89 5427-47 54274-7 108549.5 162824.2 217099.0 271373-7 1722.37 2583-55 3444-74 4305.92 5167.10 51671.0 1033 42.1 155013.1 206684.2 258355-2 194695.2 243369.0 292042.8 2265.25 3020. 33 3775-42 4530.50 45395.0 g90610.0 135915.0 181220.0 226525.0 207947-9 249537-5 82 Latitude. ° 215145-7 268932.2 322718.6 51102.4 102204.8 153397-3 204409.7 192116.0 240145.0 288174.0 2972-59 3715-73 4458.88 44588.8 89177.6 133766.4 178355-2 222944.0 267532.8 2720.49 3400.61 4080.73 40807.3 $1614.6 122421.9 163229.2 204036.4 244843-7 106563.5 159845.3 213127.1 266408.8 2525.91 3367.88 4209.85 5051.82 50518.2 101036.4 151554-6 202072.8 252591.0 3157-97 3947-46 4736.95 47369-5 94739-1 142108.6 189478.2 236847.7 284217.2 175435-3 219294.7 263153.6 1333-75 2000.62 2667.50 3334-37 4001.25 40012.5 0024.9 120037.4 160049.9 200062.3 240074.8 TABLE 18. LENCTHS OF TERRESTRIAL ARCS OF PARALLEL. (Derivation of table explained on p. xlix.] Longitude | Latitude. Interval. 39205.4 78410.8 117616.1 156821.5 196026.9 235232-3 Latitude. 639-77 1279-54 1919.31 2559.08 3198.85 3838.62 38386.2 76772.4 115158.6 153544.8 I91931-0 230317.2 Latitude. 1877-76 2503.68 3129.60 3755-52 37555-2 75110.4 112665.6 150220.8 187776.0 34118.3 68236.7 102355.0 136473-4 170591-7 204710.0 62° 477-55 955-10 1432.66 1910.21 2387.76 2865.31 28653.1 57306.2 85959-4 114612.5 143265.6 171918.7 45739-0 68608.4 91477-9 114347-4 137216.9 1402.60 1683.11 16831.4 33662.3 50493-4 67324.6 84155-7 100986.8 SMITHSONIAN TABLES. 33232.2 66464.4 99696.6 132928.8 166161.0 199393-2 63° 461.83 923.65 1385.48 1847.31 2309-14 2770.96 27709.6 55419-2 83128.9 110838.5 1093-95 1458.60 1823.25 2187.90 21879.0 43758.0 65637.0 87516.0 1093950 131274.0 15804.7 31609.3 47414.0 63218.6 79023-3 94828.0 2694.64 3233-57 32335-7 64671.5 970907.2 129343.0 161678.7 194014.4 64° 445-96 891.92 1337-88 1783.84 2229.80 2675-75 26757-5 53515-1 80272.6 107030.2 133787.7 1044.09 1392.12 1740.14 2088.17 20881.7 41763-5 62645.2 83527.0 104408.7 125290.4 246.22 492-44 738.66 984.88 1231.10 1477-33 14773-3 29540.5 44319.8 59093-9 73866. 3 88639.6 Latitude. 611.88 1223.76 1835.63 2447-51 3959-39 3671.27 36712.7 73425+4 110138.0 146850.7 183 563.4 1571.47 2095.29 2619.12 3142.94 31429-4 62858.8 94288.1 125717.5 157146.9 188576.3 65° 429-95 859-91 1289.86 1719.81 2149.76 2579-72 25797-2 51594-4 77391-5 103188.7 128985.9 1656.50 1987.81 19878.1 39750-1 59634-2 79512.2 99399-3 119268.4 Latitude. 1792.94 2390.59 2988.28 3585-89 35858-9 71717.8 107576.6 143435-5 179294-4 215153-3 395 13-3 61026.6 91539-9 122053.2 152566.5 183079.8 66° 413.82 827.63 1241.44 1655.26 2069.08 2482.89 24828.9 49057-8 74486.7 99315-6 1241 44.5 148973-4 1257-88 1572.34 1886.81 18868. 1 37736.3 56604.4 75472-6 94340-7 113208.8 Latitude. 583.23 1166.47 1749-79 2332.93 2916.16 3499-49 34994-0 69988.0 104981.9 139975-9 174969.9 209963.9 59175-5 88763.2 118351.0 147938.7 177526.4 67° 397-55 795-10 1192.64 1599. 19 1987-74 2385.29 23852.9 47705.8 71558.6 9541165 119264.4 143117.3 17852.3 357094-7 53557-0 7 1409.4 89261.7 457-91 686.86 915-82 1144.78 1373-73 13737-3 27474.6 4I211.9 54949- 68686. 63485.4 76182.5 23305.8 34958.7 46611.6 58264.5 69917-4 TABLE 19. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE a2,500: (Derivation of table explained on pp. liii—lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR — rom Meridiona tances parallels 15/ longitude. 30/ longitude. 45/ longitude. 1° longitude. Latitude of parallel Inches. | Inches. | Inches. - | Inches. | Inches. | Inches. | Inches. 4.383 .000 8.766 : 13.148 | . 17.531 .000 4.383 000 8.766 : 13.148 : 17.531 .OO1 4.383 000 8.765 : 13.148 | 17.53 -0O1 4.382 -000 8.765 : 13.147 : 17.530 002 4.382 .000 8.764 : 13-146 : 17.528 13.145 .002 U7sce7 13.144 : 17.525 13.142 .003 17.523 13.141 : E7527 13.138 : 17.518 13.336 : 17.514 13.133 ; 17.511 Ww “NI 17.507 17-503 17.493 17-494 17.488 WO) Oo “SINS Win OO ww MI to 17.483 17.478 17.472 GC) G2 Go DAaNT ao = 4. 4. 4. 4. 4. 4. 4- 4. 4. 4 4. 4. vo ON ON 17.465 a ow Oo _ 17.458 17.451 17-443 17-435 17.428 17.419 17-410 oo Ww ON ww 17.401 17.392 17.382 17.372 17.362 17.351 17-340 17.328 17.316 17.305 17.292 17.280 17.266 SMITHSONIAN TABLES. 84 TABLE 19, CO-ORDINATES FOR PROJECTION OF MAPS. SCALE azyho0- t » we = 82 o.. Gee es | e588 it eyve 2 co = Sa ora ao eKa>s - Yeon . = > (Derivation of table explained on pp. liii—lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 15/ longitude. y 30’ longitude. x y 45/ longitude. x i 1° longitude. a | | a | Se Inches. 4-317 4-313 4.310 4.306 Inches. 4-303 4.299 4-295 4.292 4.288 4.284 4.280 4-275 4.271 woth oO +O bow NN CS) Kote) Inches. +002 -002 -002 -002 -002 -002 -002 002 .003 .003 .003 Inches. §.633 8.626 8.620 8.613 8.606 8.598 8.591 8.583 8.575 8.567 8.559 8.551 8.542 8.534 8.525 8.516 8.507 8.498 8.488 8.479 8.469 8.459 8.449 8.439 8.428 Inches. .009 .009 009 009 O10 -O10 -O10 O10 -O10 OIL .OIL -OIT OI -OIT Inches. 12.950 12.940 12.930 12.919 12.908 12.897 12.886 12.875 12.863 12.851 12.839 12.826 12.813 12.800 12.707, 12.774 12.760 12.746 125732 12.718 12.703 12.688 12.673 12.058 12.642 12.626 12.610 12.594 12.577 12.561 12.544 12.526 12.509 12.491 12.473 12.455 12.436 12.418 12.309 12.380 Inches. O15 O15 .O1S -O16 .O16 _ 016 O17 .O17 O17 018 018 O19 .O19 O19 .020 .020 -020 0 0600 0 OO/0 N NNN tN NNN > OW ww NNN 00 nN as 025 027 .027 .028 x y, Inches. Inches. 17.266 .026 17.253 .027 17.240 .027 17-2201 |\) 025 17.211 .029 17.196 .029 17.182 -030 17.166 | .031 17.150 .031 17.134 032 17.118 032 17.102 033 17.084 034 17.067 034 17-050 035 17.032 035 17.013 | .036 16.995 036 16.976 037 10.957 038 16.938 .038 16.918 03 16.898 039 16.877 .040 16.856 O41 16.835 O41 16.814 042 16.792 042 16.770 043 16.748 043 16.725 044 16.702 044 16.679 045 16.655 | -045 16.631 .046 16.606 .046 16.582 .047 16.557 .048 16.532 048 16.506 048 16.480 .049 SMITHSONIAN TABLEs. TABLE 19. ‘ CO-ORDINATES FOR PROJECTION OF MAPS. SCALE azphos- [Derivation of table explained on pp. liii-lvi.] b Sey CO-ORDINATES OF DEVELOPED PARALLEL FOR— mae gE bs 34 a $a 15/ longitude. 30/ longitude. 45/ longitude. 1° longitude. aries Begs ————— 4 s Soa x y x y x y x y Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 20200) | nareieiat wo ° mn > SMITHSONIAN TABLES. TABLE 20. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE js2500- {Derivation of table explained on pp. liii— lvi.] ABSCISSAS OF DEVELOPED PARALLEL. 3 ORDINATES OF : DEVELOPED 3° PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. / 5 10° 15 20 25 Latitude of parallel. Meridional dis- tances from even degree parallels. Inches. Inches. Inches. Inches. N 5.844 8.765 | 11.687 | 14.609 5-843 | 8.765 | 11.687 | 14.608 5-843 | 8.765 | 11.686 | 14.608 5-343 | 8.765 | 11.686 | 14.608 5-843 8.764 | 11.686 | 14.608 5343 8.764 | 11.686 | 14.607 Longitude interval Inches. 0.000 -O0O0 -O00O0 +000 -000 +000 NN HNvN mW NHK NHN be HN NNNN WODOODOO OODDODOHN OKoOKUoUULYD N 5-843 8.764 | 17.685 | 14.606 5.842 8.763 11.684 | 14.606 5.842 8.763 | 11.684 | 14.604 5-341 8.762 | 11.683 | 14.604 5-341 8.761 11.682 | 14.602 5.840 8.761 11.681 | 14.601 NNN NN Nw NN Wb bo OOF FS ee _ = in NNN NH a nobhuN —~ ~ SMITHSONIAN TABLES. 94 TABLE 20: CO-ORDINATES FOR PROJECTION OF MAPS. SCALE T2e000° (Derivation of table explained on pp. liii-lvi.] ———————— ABSCISSAS OF DEVELUPED PARALLEL. ORDINATES OF , , DEVELOPED 5 Tse 20 25 30 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. ¢ ¢ 10 Latitude of parallel. Meridional dis- tances from even degree parallels. Inches Inches. ' Inches. Inches. inches. 10.683 | 13-354 | 16.024 5-814 | 2.667 eae : 10.669 | 13.336 | 16.003 11.628 | 2.664 ‘ : 10.655 | 13-319 | 15.982 17.442 | 2.660 : 98 10.641 | 13.301 | 15-961 2.657 : : 10.627 | 13-284 | 15.940 2.653 ; .960 | 10.613 | 13.266 | 15.919 Longitude interval Inches.\ Inches. O.OOI 0.OOI .003 .007 013 -020 2.650 2.646 2.642 2.639 2.635 2.631 10.599 | 13-249 | 15.898 10.584 | 13-231 | 15-877 10.570 | 13.212 | 15-854 10.555 | 13-194 | 15.833 10.540 | 13-176 | 15.811 10.526 | 13-157 | 15-788 AnI™N HOO NN NW WN 10.511 | 13-139 | 15-767 10.496 | 13.120 | 15-744 10.481 | 13-101 | 15-721 10.466 | 13.082 | 15.698 10.451 | 13-063 | 15-676 10.436 | 13-045 | 15-654 2.624 2.620 2.616 2.613 2.609 CnwoMmn Wd SGmnOo RwHHHANDN ebook Rin 2.605 : : 10.421 | 13.026 | 15.631 10.405 | 13-006 | 15.608 10.390 | 12.987 | 15-584 10.3°4 | 12.967 | 15.560 10.358 | 12.947 | 15-537 10.342 | 12.928 | 15.514 10.327 | 12.909 | 15-490 10.311 | 12.889 | 15-466 10.294 | 12.8638 | 15.442 10.278 | 12.848 | 15.418 10.262 | 12.828 | 15.394 10.246 | 12.808 | 15.369 10.230 | 12.788 | 15.345 10.213 | 12.767 | 15-320 10.197 | 12.746 | 15.295 10.180 | 12.725 | 15-270 10.163 | 12.704 | 15-245 Cane: lesen 10.146 | 12.683 | 15.220 1004 004 008 O15 023 034 30 OnMN MOw 10.130 | 12.662 | 15.195 10.113 | 12.641 | 15.169 10.099 | 12.620 | 15-14 10.078 | 12.598 | 15.118 10.061 | 12.577 | 15.092 10.044 | 12.555 | 15.006 Oo mann ncn ou fku™N WwW AOnUN® wn iS) ° 10.027 | 12.534 | 15.040 10.009 | 12.512 | 15.014 9.992 | 12.490 | 14.987 9.974 | 12.467 | 14.960 9.950 | 12.445 | 14.934 9.938 | 12.423 |] 14.908 9.921 | 12.401 | 14.881 SMITHSONIAN TABLES. 95 TaBLeE 20. / CO-ORDINATES FOR PROJECTION OF MAPS. SCALE jis¢5o0- [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF , : ; , ‘ ; DEVELOPED 5 10 15 20 25 30 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. tances from even degree Latitude of parallel Meridional dis- parallels. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 3 rnd aie x) B27 OO cciecrarseie 2.480 4.960 7.441 9.921 12.401 | 14.881 22 3? 10 5-821 | 2.476 4.951 7.427 9.903 | 12.379 | 14.854 | 47 20' (|. sLP.642)|\" 2:47 4.942 7.413 9.884 | 12.355 | 14.827 30 | 17.462 | 2.467 4.933 7-400 9.866 | 12.333 | 14.800 Tithes ike 40 | 23.283 | 2.462 4.924 | 7.386 | 9.848 | 12.310 | 14.772 5’| oor | 0.001 50 | 29.104 | 2.458 4-915 7.373 9.830 | 12.288 | 14.745 | 16 1004 I ; BZ OOU laetee ero 2.453 4.906 7.359 9.812) | 12-265 | 14.717 2 ore 10 5.822 | 2.445 | 4.806 | 7.345 | 9.793 | 12.241 | 14.689 | 5 ae 20 | 11.643 | 2.444 4.887 72330 9.774 | 12.218 | 14.661 30 | .034 30 | 17-465] 2.439 | 4.878 | 7.316 | 9.755 | 12-194 | 14.633 40 | 23.287 | 2.434 | 4.868 7.302 9-730 | 12.171 | 14.605 5° | 29.109 | 2.429 4.859 7.288 O71Si | el2.047 4) 14.570) || ——— ° ZA OOM aerators 2.425 4.850 7.274 9.699 | 12.124] 14.549 34 10 5.82 2.420 4.840 7.260 9.680 | 12.100] 14.520 |—— 20 | 11.645 | 2-415 4.830 7.246 9.661 12.076 | 14.491 5 | 0.001 30))|, 17-468:;,| <2:410 4.821 7231 9-642 | 12.052 | 14.462 | 10] .004 40 | 23.291 2.406 4.811 Feo, 9.622 12.028 | 14.434 | 15 | .009 50 | 29.113 ] 2.401 4-802 7.203 9.604 | 12.004 | 14.405 | 20 | .o16 2 02 SLi lpoenodar 2.396 3 9 7-188 | 9.584 | 11.980 | 14.376 | 30 "eae 4-792 10 5.82 2.391 4.782 7.174 9.565 | 11.956 | 14.347 20 | 11.647 2.386 4-773 7.159 9-545 | 11.932 | 14.318 30) 17.4714 || 22-301 4.763 7-144 | 9.526 | 11.907 | 14.288 40 | 23.294 | 2-377 4-753 7-130 9.506 | 11.88 14.259 36° 50: ii) -20:118) ||" (23372 4-743 7S 9.486 | 11.85 14.230) |e SOOO M|tetecia cise 2.367 4.733 7.099 9.466 | 11.833 | 14.200 | 5 | 0.001 10 5-824 | 2.362 4-72 7.085 9-446 | 11.808 | 14.170 | 10 | .004 20 | 11.649] 2.357 4.713 7.070 9-426 | 11.783 | 14.139 | 15 | -009 30 | 17-473 | 2-351 | 4.703 | 7.055 | 9.406 | 11.757 | 14.109 | 20] .o16 40 | 23.297 | 2.346 4.693 7.039 9.386 | 11.732 | 14.078 | 2 02 50 | 29.122 | 2.341 4.083 7.024 9.366 | 11.707 | 14.048 | 30] .036 37. 00/\ Soe 2.336 4.673 7.009 9.345 | 11.682 | 14.018 |__ 10 5.826 | 2.331 4.662 6.994 9-325 | 11.656 | 13.987 “ 20 | 11.651 | 2.326 4.652 6.978 9.304 | 11.630 | 13.956 38 30 |. 17.477 2.321 4.642 6.963 9.284 | 11.605 13.925 | —— 40 | 23.302 | 2.316 4-031 6.947 9.263 | 11.579 | 13-894 5 | 0.001 50 | 29.128 | 2.311 4.621 6.932 9.242 | 11-553 | 13-864 | 15 :004 15 | .009 R500) leew eee 2.305 4.611 6.916 9.222 | 11.527 | 13:532 10 5.82 2.300 4.600 6.900 9.200 | I ree eas oe ae 20 | I 1.653 2.295 4-590 6.884 9-179 | 11.474 | 13.769 30 037 30 | 17.480 | 2.290 4.579 6.569 9.158 11.448 | 13.737 F 40 | 23.306 | 2.284 4.508 6.853 9.137 11.421 | 13.705 50) 620.133 |) "23270 4.555 6.837 OFT 6 | 53950 |)613-075 5 aaa o? BOi00 || iwe so «'s 2.274 4.548 6.821 9.095 | 11.369 | 13.642 5 10 5.828 | 2.268 4-537 6.805" || 9.073) ||| 1153425), 13.610) || 20 | 11.655 | 2.263 4-526 6.789 9.052) ||| re3r5 | ersth77 5 | 0.001 30 | 17.483 | 2.258 4-515 6.773 9.030 | 11.288 | 13.545 | 10} .004 40° ||*23:310 | 2.252 4.504 6.756 0:008) "|| UTT-261 || Sg hs 4/5 1.009 50 | 29.138 | 2.247 4-493 6.740 | 8.987 | 11.234 | 13-480 | 20 ee 2 .02 AO OO aliietes’e eles 2.241 4-483 6.724 8.965 | 11.207 | 13.448 | 30] .038 SMITHSONIAN TABLES. TaBLe 20. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE rene: (Derivation of table explained on pp. liii-lvi.J ABSCISSAS OF DEVELOPED PARALLEL. gree S. ORDINATES OF DEVELOPED , 5 10’ af i PARALLEL. longitude. | longitude. | longitude. enjeitaties longitude. | longitude. tances from Meridional dis- even de parallel Latitude of parallel Inches. Inches. Inches. Inches. Inches. ° 4.483 6.724 8.965 | 11.207 | 13.448 a 4.472 6.707 8.943 | 11.179 | 13-415 4.461 6.691 8.921 | 11.152 | 13.382 4-450 6.674 8.599 11.124 | 13-349 Trches 4-439 6.658 8.877 | 11.097 | 13.316 O.ccl 4-428 | 6.641 8.855 | 11.069 | 13-283 004 .0 4-417 6.625 8.834 | I1.042 | 13.250 oe 4.406 6.603 8.811 TT-O14 |) 13-217 ince 4.394 6.591 8.788 10.98 5 13.183 1038 4-383 | 6.575 8.766 | 10.958 | 13.149 4.372 6.553 8.744 | 10.929 | 13.115 4.360 | 6.541 8.721 | 10.901 | 13.081 interval. Longitude | 4-349 6.524 8.698 | 10.873 | 13.048 4.338 6.507 8.676 | 10.844 | 13.013 4.326 6.490 8.653 10.316 12.979 0.001 | 0.001 4.315 6.472 8.630 | 10.787 | 12.945 004 | .004 4-303 | 6.455 | 8.607 | 10.759 | 12.910 010 | .010 6.435 8.584 | 10.730 | 12.876 017 | .017 026 | .027 6.421 : 10.702 | 12.842 .038 038 6.403 : 10.672 | 12.807 6.386 ; 10.643 | 12.772 6.368 : 10.614 | 12.737 6.351 : 10.585 | 12.701 44° 6.333 : 10.556 | 12.667 6.316 7 10.526 | 12.631 6.298 f 10.496 | 12.596 6.280 : 10.467 | 12.560 6.262 : 10.437 | 12.524 6.244 32 10.407 | 12.489 6.22 : 10.378 | 12.453 6.209 : 10.348 | 12.417 6.191 2 10.317 | 12.381 6.172 : 10.288 | 12.345 6.154 32 10.257 | 12.308 6.136 5: 10.226 | 12.272 6.118 , 10.197 | 12.236 6.100 313: 10.166 | 12.199 6.081 108 | 10.136 | 12.163 10.104 | 12.125 10.074 | 12.089 10.043 | 12.052 10.013 | 12.015 9.981 | 11.978 9-951 | 11.941 9.919 | 11.903 9.3888 | 11.866 9.357 9.826 9-794 SMITHSONIAN TABLES. TABLE 20. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE pata [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF r F : DEVELOPED 5 10° rs 20 25 30 PARALLEL, longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Meridional dis- tances from L ititude of parallel, even depree parallels. Inches. 3 Inches. % Inches. Inches. 5-876 : 9-794 | 11.752 1.952 2 5.857 8 9.762 | 11.714 1.946 2S 5-838 ; 9.730 | 11.677 ate 1.940 : 5.819 . 9.699 I 1.638 Inches. | Inches. 1.933 3 5.800 . 9.667 | 11.600 0.001 | 0.001 1.927 5.781 . 9.635 | 11-562 004 | .004 010 | .oro 5.762 . 9.603 | 11-523 | 2 017 | .017 5.743 | 7: 9-571 | 11.485 026 | .026 5-723 : 9-539 | 11-446 .038 | .038 5.704 | 7. 9-507 5-654 57 9-474 5-665 7 9.442 48° 49° Longitude ii terval 1.921 1.914 1.908 1.9o! 1.895 1.888 NSN ODOO co ne Wn NOK Ga NOOO = 1.882 1.875 1.869 1.562 1.856 1.849 5-646 : 9.409 5-626 ; 9.376 Dae 9.311 9.278 9255 PEWQQn POQmmg cw NOt OV DArfbhN Of Or Ce 1.842 1.836 1.829 1.823 1.516 1.809 9.212 9-179 9.146 9.113 9.080 9.046 RMrywwn Sper lite lige aes fees Je | “sI™M bb & ROO DAADADDAA GNA AUS =—Wwhu™N © Cnn 1.893 1.790 1.789 1.782 1.776 1.769 9.013 8.980 8.946 8.912 8.878 8.844 WEWOOG WWW wy an Mma OV CMOrm Cnn Git DIO O 1.762 8.811 1.755 8.777 1.748 ‘ s 8.742 1.742 .48 : ; 8.708 1.735 : .2 : 8.674 1.725 : 18 O12 8.640 i) 1.721 ‘ : 8.606 1.714 wd ; 8.572 1.707 : : 8.537 1.700 rf «802 8.502 1.694 ; ; 8.468 1.687 3 ; 8.433 1.680 1.673 1.666 1.659 1.652 1.645 SMITHSONIAN TABLES. TaBLe 20. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE rxe000- (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF , , DEVELOPED 5 10 15 20 25 30 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude | longitude. Latitude of parallel. Meridional dis- tances from even degree parallels. Inches. Inches. % Inches. Inches. Inches. 1.638 I 631 1.624 1.616 1.609 1.602 Oo 4.913 | 65st | 8188 | 9826 Sen cae 4.892 : : 9.784 ae7c -49- . aS 4.049 . : 9-09 Inches. 4.828 ; . 9.656 0.001 4.807 : 9.013 .004 .009 9-571 016 9-527, .02 9-485 ose 9.442 9.398 9.356 235 9.269 9.226 9.182 ot39 9:095 9.052 9.008 8.963 8.920 8.876 8.831 8.788 8.743 8.699 8.654 8.610 8.566 Longitude interval NN WW HK NN GG WG Gao oO 1.595 4.785 1.585 : 4.764 1.581 : 4.742 1.574 : 4.721 1.566 ; 4.699 1.559 ; 4.678 NN NO W AON NNOUWU ODO NOALWN 1 COMO 00 WwW AOL IY An CH O 58° 3 1.552 : 4.656 1.54 4-634 1.53 4.613 1.530 : 4.591 T5239 : 4-509 1.516 E 4-547 ADADAN DANA no. OOnr—-F WN NO Hus O Mm ADOAN A So-um On I 509 A 4.526 1.501 Bt 4-504 1.494 4.482 1.487 4.460 1.479 4.438 1.472 4.416 Woot hON DOWN Of ODWNWODW OWN to 1.465 1.457 1.450 1.442 1.435 1.428 4-394 4.372 4-349 4-327 4-305 4.283 Go NNNNNN NUU MDM DNDODO © mm NN NOOO Wn ah ON mn~rI CO mn OwMmods Mun NO QW 4.261 : ‘ 8.521 4-238 8.476 4.216 8.431 4.193 8.386 4.571 5.342 4 148 8.297 1.420 1.413 1.405 1.398 1.390 I. NCO rN Arn 0Mnod NNNNNN WOO nN 8.252 8.207 8.161 8.116 8.071 8.026 4.126 4.103 4.081 4.058 4-035 4.013 ow ANT Cun NY vYNNN QAannN 0 NUN momnod a« WWwhkRARA ANAaAD Gs Ga G2 Ga CC in COrb~I O G00 m= Go un Cn 16 7.980 7-934 7-839 7343 7-797 7-751 3-990 3-967 3-944 3 g2I 3-899 3.876 msm NN NO GQ MMNMANAn Nanna WOU as, NUWO moo 3-853 ~ Ww Q SMITHSONIAN TABLES. 99 TABLE 20. CO-ORDINATES FOR PROJECTION OF MAPS. (Derivation of table explained on pp. liii-lvi.] SCALE iaeho0° ABSCISSAS OF DEVELOPED PARALLEL. 7 5 Latitude of parallel Meridional dis- tances from even degree parallels, Inches. Inches. 1.277 1.269 1.261 1.254 1.246 1.238 1.231 1.22 1.215 1.207 1.200 1.192 1.184 1.176 1.168 161 153 longitude. / Io longitude. | longitude. | longitude. | longitude. | longitude. Inches. 2.569 27599 2.538 2.523 2.507 2.492 2.477 2.461 2.446 2.430 2.415 2.399 2.384 2.368 2.352 2-397, 2.321 2.305 2.290 2.274 2.258 2.243 25227 2.211 2.195 2.180 2.164 2.148 2.132 2.116 2.100 2.084 2.068 2.052 2.037 2.021 2.005 1.989 1.972 1.956 1.940 1.924 1.908 1.892 1.876 1.860 1.844 1.828 1.811 15 WHWHOWNQN WHWHWWY hHAUAMNUNH in OV MmOoO yun 5 Mnmo nn \O bt , 20 Inches. 5-137 5-106 5.076 5-045 5.014 4-984 4-953 4.922 4.891 4.860 4.829 4-798 4.767 4-736 4.705 4.673 4.642 4.611 4.580 4-548 4-517 4-485 4-454 4.422 4-391 4-359 4.328 4.296 ee 4.232 4.201 4.169 4-137 4.105 4-073 4.041 4.009 3:977 3-945 3-913 3.881 3.848 3.816 3-784 3:7 52 3:729 3-687 3-055 3.623 SMITHSONIAN TABLES. 100 Inches. 6.422 6.383 6.345 6.307 6.268 6.230 6.192 6.153 6.114 6.075 6.037 5-998 5.959 5-920 5.581 5.842 5.803 5-764 Inches. ORDINATES OF DEVELOPED PARALLEL. Longitude interval. £ Oo “A ° Inches. 0.00! .003 .008 013 O21 .030 TABLE 20. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE jzeyoo- (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED Li 10° nee PARALLEL. longitude. | Jongitude. | longitude. | longitude. | longitude. | longitude. tances from even degree parallels. parallel. Meridional dis- Latitude of Inches. Inches. Inches. Inches. Inches. 1.811 : 3-623 | 4.529 5-434 1.795 : 3-590 4.488 5.306 1.779 . 3-558 | 4-447 | 5-336 7a 1.763 : 3-525 4-407 5.288 Inches.| Inches. 1.746 x ' 4.366 | 5-239 | 5’| o.001 | 0.001 Bio s £3250 h) oa4 97 11 -t0 | © .0098 | seco I5 | .006 005 4-285 S-F4i"|'36'| so1o |) sore 4.244 Jen 2 016 | .O15 4-205 : oO} .02 .021 4-162 | 4-994 : 3 4-121 4-945 4.081 4.897 Longitude interval 1.714 1.697 1.681 1.66 1.64 1.632 Ww Go NY YOwouwt 1.616 ; : 4.040 4.847 1.599 . . 3-999 | 4-798 160 | 3-957 | 4-748 3-916 | 4-699 3875 | 4-650 3.834 4.601 3-793 | 4-552 3-752 | 4-502 3-711 | 4-453 3-669 | 4.403 3-628 | 4.354 3-587 | 4-304 3-546 3-504 3-463 3-421 3.380 3-339 3.256 .214 3.172 3.131 3.089 N&WWO Sh SIOW™N OW Of OH hw NNN NNN HAR HOG Oo Om Om Ui SmitHsonian TaBLes. Io! TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE jraya5- (Derivation of table explained on pp. liii-lvi.] 15/ longitude. Meridional dis- tances from even degree Latitude of parallels, parallel. Inches. Inches. 8.647 .000 8.646 -000 8.646 .000 8.646 8.645 8.644 8.643 8.642 8.641 30! longitude. Inches. 17-293 17.293 17.292 17.291 17-291 17.289 17.287 17.285 na 7-203 17.279 17.276 17.273 17.270 17.265 17.260 17.250 T7251 17.245 17.240 17.234 17.228 17.221 17213 17.206 17-199 17.191 17.182 17-174 17.165 17-155 17-145 P7130 17.126 17.015 17.104 17-093 17.082 17.069 17.057 17-045 17.032 Inches. -000 -OOI -OOI -OOI 45/ longitude. Inches. Inches. 25.940 000 25.939 -OO1 25-938 -OOI -002 .003 .003 004 005 CO-ORDINATES OF DEVELOPED PARALLEL FOR— 1° longitude. Inches. 34-586 34-585 34-584 34-582 34-581 34-577 34-573 34-569 34-565 34-559 34-552 34-546 34-539 34-530 34-521 34-512 34-502 34-491 34-479 34-467 34-456 34-441 34-427 34-412 34-398 34.381 34-304 34-347 34-330 34-310 34-291 34-272 34-252 34-230 34.208 34-186 34-163 34-138 34-114 34.089 34.064 SMITHSONIAN TABLES. 102 TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE gzairz5- (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR — even degree tances from parallels. 15/ longitude. 30/ longitude. 45/ longitude. 1° longitude. parallel. Meridional dis- Latitude of Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 8.516 .003 17.032 013 25.548 029 | 34.064 : 8.509 .003 17.019 | .013 25.528 030 | 34.037 17.181 | 8.502 .003 17.005 013 25.507 .031 34.010 25.772 | 8.496 003 16.991 O14 25.487 032 33-982 34.363 | 8.489 004 16.977 O14 25.466 | .032 33-955 8.591 | 8.481 .004 16.962 : : : 33-925 17.183 | 8.474 .004 16.947 O15 : 033 33-895 25-774 | 8.466 : 16.933 | -O15 ; : 33-865 34-365 | 8.459 | - 16.918 33835 33.803 33-779 33-738 34.368 | 8.426 : 16.853 : 25. : 33-706 8.592 | 8.451 : 16.901 17.184 | 8.443 002 16.885 25.776 | 8.434 : 16.869 nonin wn G29 Ga Non hy 8.592 | 8.418 : 16.83 : 2 : 671 17.18 8.409 : 16.818 : 25.22 : see 25-778 | 8.400 : 16.800 : : : 33-601 34.370 | 8.301 s 16.783} - : 33-566 8.593 8.382 F 16.764 : 25. : 33.528 17.186 2 : 16.745 2 ; : 33-490 25-780 : ‘ T6720") 7 : 33-453 34-373 : : 16.708 : : : 33-415 8.594 ; : 16.688 Z : : 3-37 17.188 : : 16.668 ; : : ae 25.782 : : 16.647 : : : 33-205 16.627 . | < 33-255 16.606 | . : : 33-212 16.585 : 8 : 33-170 16.564 s 8 : 35.027 16.542 ; : 33-084 16.520 021 : : 33-039 16.497 02 24. : 32-994 16.475 .022 712 : 32-949 16.452 : : : 32.904 16.428 .022 2 ; 32.856 16.404 02 24. A 32.809 16.381 : 24. z 32.761 16.357 5 : 32.714 16.332 : .4C : 32.664 16.307 022 uc : 32.614 16.282 .02¢ 422 : 32.563 16.257 : 24.3% : 32.513 | SMITHSONIAN TABLES. 103 TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE is¢ysz: [Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 15/ longitude. 3° longitude. 45/ longitude. 1° longitude. even degree Latitude of parallel. Meridional dis- tances from parallels. Inches. Inches. Inches. Inches. 16.257 024 24.385 055 32.513 16.230 024 24.346 050 32-461 16.204 | .025 24.306 | .056 | 32.408 16.178 .025 24.267 .057 32.356 21 00 34-394 : : 16.152 025 24.227 057 32.303 8.599 : : 16.124) |) 24.186 | .058 | 32.248 17-199 : : 16.097 026 24.145 058 32.193 25.798 : : 16.069 | .026 | 24.104] .059 | 32.138 34.398 : : 16.042 : 24.062 059 | 32.083 15 8.600 ; : 16.013 : 24.019 .060 | 32.026 30 17.201 : : 15-984 02 23-976 .060 31.968 45 25.801 : : 15-955 : 23-933 O61 31.911 23 00 34.402 : : 15-927 . 23.890 | .o61 31.853 15 8.602 é . 15-897 30 17.203 : : 15.867 45 25.804 : : 15-837 Co f 062 31-794 .062 31.734 063 31.674 NNN Wow ga “IO mo ano to Wag 24 00 34.406 : : 15-807 063 31.614 ~“ I ~ IS 8.603 . ‘ 15.776 30 17.205 : 3 : 15-745 45 25.808 : : 15-713 31.552 .064 31.489 31.427 .065 31.365 31.300 060 31.235 .067 31.170 2 2 2 nad “SI = OO) Oona nN 25 00 34.410 : : 15-682 8.604 82 : 15.650 17.207 : : 15-617 25.811 ; : 15.585 34-415 , : 15.553 : .067 31.106 8.605 : : 15.519 ; : 31.039 17.210 TAG : 15.486 : .068 30.972 25.814 ; : 15-452 : ; 30.905 34.419 : : T5sAL Ou) lees .069 | 30.838 WOW a 1S) NN WN 8.606 : : 15-384 : 069 30.769 17.202 : : 15-350 : 070 30.699 25.818 65 : 15-315 : : 30.630 34.424 : : Hi5-2004| ee : 30.560 8.607 : ‘ 15.244 : : 30.489 17-205 : -00! 15-208 : : 30.417 25.822 : : 15-173 z : 30.345 29 00 34-430 a5 6 : P5s37, : : : 30.274 I5 8.609 5! : 15.100 : : : 30.200 30 172217 eG: 2 15.063 : ; 5 30.125 45 25.826 : : 15.026 , : : 30.051 30 00 34-435 : : 14.989 : : E 29.978 SMITHSONIAN TABLES. 104 TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE Tera: (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— ces from even degree parailels. 15/ longitude. 30/ longitude. 45/ longitude. 1° longitude. Latitude of parallel Meridional dis- tar Inches. Inches. Inches. Inches. . Inches. Inches. .008 14-989 033 : 074 29.978 -131 7-475 008 14.951 033 : .074 29.902 “IgE 7-450 008 14.913 033 : 074 29.825 2032 7.437 .008 14.874 033 : .075 29.749 -133 7.418 .008 14.836 033 ; 075 29.672 133 7-3 : 14.797 033 7.379 .008 14.758 034 7-359 | - 14.718 | .034 075 29-594 -134 .076 29.515 ray .076 29.437 135 Nw hy NNN OH 7.340 : 14.679 034 23 .076 29.358 .136 7.319 : 14-639 034 : .077 29.278 -136 7.299 : 14.598 | .034 : .077 29.197 a7 7-279 s 14.558 034 : 077 7.259 : 14.518 .034 : .078 : .138 7.238 : 14.476 | .035 ; .078 ; 138 7.217 : 14.435 035 : .078 : 139 7-197 | - 14.393 | -035 : 078 7.176 : 14.352 035 : 079 ; -140 7.154 : 14.309 035 7.133 : 14.266 035 : 079 533 141 7eUL2 : 14.224 035 42 7-091 : 14.181 7.069 : 14.138 7-047 -006 14.094 7-025 : 14.050 7.003 : 14.007 6.981 : 13.962 6.959 y 13.917 6.936 : 13.873 6.914 : 13.828 6.891 : 13.782 6.868 : 13.736 6.845 : 13-690 6.822 : 13-645 6.799 | - 13.598 6.775 z TSe6Cr 6.752 ; 13.504 6.729 | - 13.457 6.705 : I 3-409 6.681 : 13-361 6.657 : 13.314 6.633 E 13.266 SMITHSONIAN TABLES. 105 TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE jz¢ya5: [Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— ces from even degree parallels. 15/ longitude. 30’ longitude. 45/ longitude. 1° longitude. Latitude of parallel. Meridional dis- tar Inches. shes. Inches. inches. Inches. Inches. Inches. 6.633 : 13.266 037 19.899 08 4 26.532 6.608 : 13.217 037 19.825 .084 26.434 6.584 : 13.168 -037 19.7 52 -084 26.336 6.560 : 13-119 | .037 19.679 | .084 26.238 6.535 : 13.070 037 19.605 | .084 26.140 6.510 E 13.020 037 19.530 -084 26.041 6.485 , 12.970 .037 19.456 .084 25.941 6.460 : 12.920 037 19.381 084 25.841 6.435 : 12.871 037 19.306 | .085 25.741 -150 6.410 ‘ 12.820 | .037 19.230 | .085 | 25.640} .150 6.385 : 12.769 | .038 19.154 | .085 25.539 .)| se SI 6.359 : 12.718 .038 19.077 085 25.436; 15! 6.334 . 12.667 .038 19.001 085 | 25-335 | -I5I 6.308 : 12.615 .038 18.923 | .085 25.231 -IS1 6.282 : 12.563 038 18.845 085 25.127 «151 6.256 : 12.512 .038 18.767 085 25.023 ISI 6.230 : 12.460 | .038 18.689 | .085 | 24.919] «151 6.203 : 12.407 .038 18.610 : 24.814 ISI 6.177 7 12.354 038 18.531 085 24.708 ISI 6.151 7 12.301 : 18.452 : 24.603 UST 6.124 7 ; ; 18.373 : 24.497 -IS1 6.097 E : 18.292 : 24.390 151 6.071 : : 18.212 : 24.283 | -151 6.044 : Z 18.131 : 24.175) SUSY 6.017 : : 18.051 : 24.068 | .151 5.990 s : 17.969 |. 23-959 | -I5I 5-962 7 : 17.887 : 23.849 | «ISI 5-935 : ; 17.805 < 23-740 | 151 5-908 : : U7 723i ws 23.631 ISI 5-380 7 : E7GAO ll ye 23-520 IS] 5.352 : : 17 550 : 23.408 15 5-324 5 : 17-473 : 23-297 ISI 5-796 E : 17.389 : 23-186 150 5.768 , : 17.305 : 23:07.3 14, e150 5-740 : : 17.220 : 22.960 -150 571Z : : 17.135 : 22.847 150 5-684 2 : 17.051 : 22.734 -150 5-655 ‘ d 16.965 : -150 5-626 : Rok 16.879 : : .150 5-598 : : 16.793 : : -150 5.5609 d : 16.707 Z : -150 SMITHSONIAN TABLES. TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE jyyeyz5- [Derivation of table explained on pp. liii-lvi.] Inches. 10.905 10.669 10.430 9.942 4.846 .009 9-693 4.720 .009 9.441 4.593 009 9.186 4.464 .008 8.929 SMITHSONIAN TABLES. 107 037 8.669 | Inches. 037 Inches. 16.358 16.004 15-734 15.645 14.912 14.539 14.162 083 Inches. .080 .080 -079 .078 .076 :075 a .148 145 a des CO-ORDINATES OF DEVELOPED PARALLEL FOR— c 6| ee Rs ts gocs 15/ longitude. 30/ longitude. 45/ longitude. 1° longitude. ye moo —_ qd | osc - a x y x y x y x y RQLO08 ncieaie irs 5-569 009 I 1.138 .037 16.707 .084 22.276 150 15 8.640 | 5-540 009 11.080 .037 16.620 .084 22.160 149 30 17.279 | 5-511 -009 11.022 037 16.532 084 22.043 149 45 25-919 | 5-482 009 10.963 037 16.445 083 21.927 149 A 10.846 .037 16.269 083 692 148 30 17.282 | 5-394 009 10.787 037 16.181 .083 21.574 148 : 10.728 -037 16.092 .083 21.456 147 147 3 , : 10.609 .036 15.914 .082 21.218 146 30 17.28 3 5-275 009 10.549 C36 15-824 082 21.099 -146 10.490 .082 ' 145 . 10.369 .036 15.554 .082 20.738 145 30 17.288 | 5.154 009 10.309 036 15-463 081 20.617 -144 Zee 10.248 MiG 372 O81 20.496 144 10.187 15.281 081 20.374 | .144 15 8.646 | 5.063 009 10.126 .036 15.189 081 20.252 143 30 17.291 5-032 009 10.064 036 15.097 .080 20.12 143 45 25.937 | 5-002 009 10.003 036 15.004 080 20.006 142 142 4-940 009 9.879 | .035 | 14.819 19.759 | -14I 30 17-294 4-909 009 9.817 035 14.726 079 19.634 -14I 45 | 25-941 | 4.878 009 9-755 | -035 | 14.633 | -079 | 19.510 | -140 -140 15 8.648 | 4.815 .009 9.630 035 14.445 .079 19.260 140 30 | 17-297 | 4-784 | 009 9.567 | 035 | 14.351 | 078 | 19.134 | 139 45 | 25:946| 4.752 .009 9-504 035 14.256 .078 19.008 139 15 8.650 | 4.689 .009 9-377 035 14.066 077 18.754 138 30 17.300 | 4.657 .009 9.314 034 13.970 -077 18.62 sey) 45 25.950 | 4.625 .009 9.250 034 13-875 .077 18.500 a7, a 8.651 | 4-561 .008 9.122 .034 13-683 .076 18.244 035 30 17-303 | 4-52 .008 9.058 034 13.586 .076 18.115 135 45 | 25.954] 4-497 | .008 8.993 | 034 | 13-490] .075 | 17.980] .134 15 8.653 | 4-432 .008 8.864 033 13.296 075 17.728 133 30 17.305 | 4-399 .008 8.799 033 13.198 075 17-597 -133 45 25.955 | 4-367 .008 8.734 033 13-100 074 17.467 132 : 4 TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE 13ers: (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR — 15/ longitude. 30’ longitude. 45/ longitude. 1° longitude. even degree tances from parallels. Latitude of parallel Meridional dis- Inches. ‘ Inches. Inches. Inches. Inches. : 8.669 033 13.003 074 17.337 4.301 : 8.603 032 12.904 074 17.206 17.308 | 4.269 : 8.537 032 12.806 073 17.074 25.962 | 4.236 : 8.471 .032 12.707 073 16.943 34.616 | 4.203 : 8.406 .032 12.608 .072 16.811 8.655 | 4.170 z 8.339 : 12.509 2 16.679 17.311 | 4.136 : 8.273 .032 12.410 .072 16.546 25-966 | 4.103 : 8.207 .031 12.310 .071 16.413 34.621 | 4.070 : 8.140 : 12.210 : 16.280 8.657 | 4.036 : 8.073 ; : 16.146 17-313 | 4.003 : 8.006 : : 16.012 25.970 | 3.970 : 7-939 : : 15.878 34-626 | 3.936 : 7.872 . ; 15-744 8.658 | 3.902 : 7.804 s : 15.609 17.316 3.868 : 78737 ; : 15-474 25-974 | 3-835 | 00; 7.669 | - . 15.338 34.632 | 3.801 7 7-602 z : 15-203 8.659 | 3-767 : 7.533 : : 15.067 17.318 3733 ; 7.405 : ; 14.930 25-977 | 3-69 7-397 | 02 . 14-794 34-636 | 3.664 : 7.329 .02 . 14.658 8.660 | 3.630 ; 7.260 : : 14.520 17.321 | 3.506 : 7-191 02 : 14.383 25-981 | 3.561 : 7.123 : : 14.245 34-641 | 3.527 ; 7.054 : : 14.108 8.661 | 3.492 : 6.984 : : 13.969 17-323 | 3-458 : 6.915 5 -062 13.830 25.984 | 3-423 : 6.846 : : 13.692 34.646 | 3.388 ; 6.776 2 z 13.553 8.663 | 3.353 : 6.706 .027 : 13.413 17.325 | 3.318 : 6.637 02 : 133273 25.985 | 3.283 : 6.567 .02 ; 13.134 34.650 | 3.248 2 6.497 : : 12.994 8.664 | 3.21 : 6.427 02 : 12.854 17.3275) 3.17% ‘ 6.356 : : 12.713 25.991 | 3.143 : 6.286 025 : 12.572 34-655 | 3-108 ; 6,216 : : 12.431 8.665 | 3.072 : 6.145 028 c 12.290 17.329 | 3-037 : 6.074 : ; 7 12.148 25-994 | 3.002 . 6.003 0 : 12.006 34.659 | 2.966 : : : : 11.865 SMITHSONIAN TABLES. TABLE 21. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE ja¢ra0- [Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR — 1s/ longitude. 30/ longitude. 45/ longitude. 1° longitude. a g 3 g Latitude of parallel. Meridional dis- tances from even degree paraliels. x yi x y x y x y Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 2.966 .006 5-932 024 8.899 055 11.865 097 2.930 006 5-361 024 8.792 055 11.722 .096 2.895 006 5-790 023 8.685 054 11.580 095 2.859 .006 5-718 023 8.575 053 11.437 094 2.824 .006 5-647 : 8.471 .052 11.294 | .093 2.788 006 5.576 .02 8.363 052 II.1S1 092 2.752 .006 5-504. .02 8.256 O51 11.008 Og! 2.716 .006 5-432 .022 8.148 O51 10.864 2.680 : 5.360 : 8.040 .050 10.720 | .089 2.644 : 5.288 : 7.932 050 10.576 : 2.608 : 5-216 : 7.524 049 10.432 .087 2.572 : 5-144 : 7.716 -049 10.288 2.536 : 5.072 : 7.608 : 10.144 2.500 | - 4.999 | - 7-499 | .048 9.998 2.463 | - 4-927 . 7-390 | -047 9-854 2.427 : 4.854 : 7.281 .046 9.708 2.391 : 4.782 : mel : 9.563 2.354 : 4-709 : 7.063 : 9.417 2.318 : 4.636 019 6.954 : 9.272 2.281 : 4-503 Z 6.544 5 9.126 2.245 : 4.490 O19 6.735 : 8.980 2.208 : 4.417 : 6.625 : 8.834 2a 72 : 4.343 018 6.515 : 8.687 2.135 ' 4.270 , 6.405 Roy 8.540 2.098 : 4.197 018 6.296 F 8.394 2.062 2 4.123 .o18 6.185 : 8.247 2.025 : 4.050 O17 6.075 : 8.100 1.988 3-976 , 5.904 : 7.952 1.951 . 3-903 O17 5.854 : 7.805 1.914 : 3.829 O17 5-743 : 7.658 1.877 : : O16 5-632 : 7.510 1.840 : .68 O16 5.522 : 7.362 1.804 : : O15 5.411 E 7.214 1.766 ; : .O15 5-300 . 7.066 1.729 : .45 O15 5-188 ; 6.918 1.692 z 38 O14 5-077 : 6.769 1.655 : ; O14 4.966 : 6.621 1.618 : We O14 4.854 ; 6.472 1.581 : ; 013 4.742 é 6.323 1.544 ; ; O13 4.631 ‘ 6.174 1.506 : ; 013 4.519 : 6.026 SMITHSONIAN TABLES. 109 TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE gs}av: (Derivation of table explained on pp. liii-Ivi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF . , : DEVELOPED 5 10 15 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Latitude of Meridional dis- tances from even degree parallels. parallel. Inches. Inches. Inches. Longitude interval % Re rs ee 11.529 | 17-293 5-764 11.528 | 17.293 5-764 II.528 | 17.292 . 20.02 : Inches. 7 OAU MeL. 528ml 17.262 s 3: 58 Altea 5-764 | 11.528] 17.201 28.8 58 - ican 5.704) | 15278)" 17-200 : . "re | 0S teOeo 20 | .000 5-764 | 11.527 | 17.291 : ; 4. am en 5.708) |) DIss26.101072280 052 34-579 JO eee 5-703) | Lt.525ul W7e2eo ‘ 28.813 | 34-576 5-762 11524) |, 17-207 : 28.811 | 34-573 5-762 11.524 | 17.285 d : 34-571 5-768 || 0.523 )|| 47:204 : : 34-568 5-7OUe || 52287-2538 ‘ 28. 34-565 5-760 | 11.520] 17.281 | 23. : 34.561 5-759 | 11.519 | 17.278 5 . 34.556 5-759 | 11-517 | 17.276 : 794 | 34-552 5-758 | 11.516] 17.274 : s 34-548 CST. aL 5Ldet) 72720) 23.02 7 34-543 5-750:.|| (EX513°| 17.2704] 123.02 : 34-539 5-750) | DESL) | 27.267) v23.022 : 34-533 5:754 | 11.509 | 17.264 5 5-753 | 11-507 | 17.260 C7 Sem lcSOSs| 17-257, 5:95 11-503°| 17-254 E7SOM WISOl #| T7265 5:749 | 11.498 | 17.247 5-748 11.496 | 17.243 5-746 | 11.493 | 17.240 5:745 T'1-490 5-744 11.485 NNNN NN NNN YN W 68.708 | 5.743 | 11.485 11-452 | 5-741. |] 11-482 22.903 52732) a1) hIeA79. 34-355 | 5-738 | 11.476 45-806 | 5.736 | 11.472 57-253 | 5.735 | 11.469 11.466 . . . . N 0.0 2 o ton WN wn bv 68.710 to tN ve Ni ou w YNYHNNN t NOHNONHN tt Co MOOO 0 \o 11.462 11.458 11.455 11.451 11.447 SJ NTS NN NOW O™MN 0 = | NS + Wo nan “I to i) Nv N 11.443 | 17.165 SMITHSONIAN TaBLEs. Ilo TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE axhao: [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. d Ee Seg o.. | SE es ORDINATES OF aS S gus : : : F ; i DEVELOPED = s E = g = 5 10 15 20 25 3° PARALLEL. s “ee . . . . oe aoe longitude. | longitude. | longitude. | longitude. longitude. | longitude. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 3 a if = > ° 8° 68.712 | 5.722 | 11.443 | 17-165 | 22.887 | 28.609 | 34.330] & 2 7 (ee — — 11.452 | 5.720 | 11.439 | 17.159 | 22.878 | 28 598 34-317 4am aa een 22.905 | §.717 | 11-435 | 17-152 | 22.869 | 28.587 | 34-304 Inches.| Inches. 34-355 | 5-715 | 11-430 17.146 22.861 28.576 | 34-291 5’| 0.000 | 0.001 45810 | 5.713 | 11.426 | 17.139 | 22.552 28.565 | 34-278 | 16 002 002 57-202.) 5.712 11.422 | 17.132 | 22.843 | 28.554 | 34-265 15 005 005 68.715 | 5.709 | 11.417 | 17.126 | 22.834 | 28.543 | 34-252 | 2 013 ‘O14 11.453 | 5-706 | 11.412 | 17.119 | 22.825 | 28.531 | 34-237 22.900 | 5.704 | 11.407 | 17.111 | 22.815 | 28.519 | 34.222 SER es 5.701 | 11.403 | 17-104 | 22.805 | 28.507 | 34.208 45.812 | 5.699 | 11.398 | 17.096 | 22.795 | 28.494 | 34-193 57.265 | 5.696 | 11.393] 17.089 | 22.780 | 28.452 | 34.178 68.718 | 5.694 | 11.388 | 17.082 | 22.776 | 28.470 34-163 9° 10° 11.454 | 5-691 11.382 | 17.073 | 22.764 | 28.456 | 34-147 a 22.907 | 5.688 | 11.377 | 17-065 | 22.754 | 28.442 | 34-130 5 | 0.001 | 0.001 33-361 5.686 | 11.371 | 17.057 | 22.742 | 28.428 | 34-114 10 | .003 | -003 45.814 | 5.683 | 11.366 | 17.049 | 22.732 | 28.415 | 34-097 15 | .006 | .006 57-268 | 5.680 | 11.360 | 17.040] 22.720 | 28.401 2#OS1. | S0g le son> Mee ore 2 16 | .o18 5.677 | 11.355 | 17.032 | 22.710 | 28.387 34.064 | 301) 4-02 .026 68.722 11.454 | 5.674 | 11.349 | 17.023 | 22.698 | 28.372 34.046 22. 5-671 11.343 | 17.014 | 22.685 | 28.357 34.028 34-263 | 5.668 | 11.337 | 17.005 | 22.673 | 28.342 | 34.010 45.817 | 5.665 | 11.331 | 16.996 | 22.661 | 28.327 | 33-992 | — 57-272 | 5.662 | 11.324 | 16.987 | 22.649 | 28.311 | 33-973 ' 68.726 | 5.659 | 11.318 | 16.978 | 22.637 | 28.296 | 33-955 |——|- .OOI | 0.001 (1.455 | 5.656 | 11.312 | 16.968 | 22.624 | 28 280 | 33-935 = pee Bao 22.910 | 5.652 | 11.305 | 16.958 | 22.610 | 28.263 | 33-915 1s | .007 | .008 34.365 | 5-649 | 11.298 | 16.948 | 22.597 28.246 | 33595 | 451 .o1 3 | 014 45-820 5-646 11.292 | 16.938 | 22.584 | 28.230 33:87 Sule 020 021 5.642 | 11.285 | 16.928 | 22.570 | 28.213 33-555 30 | .028 | .031 271 | 16.907 | 22.5 78 | 33-314 5-63 64 | 16.896 | 22.528 | 28.160 | 33-792 5.628 | 11.257 | 16.885 | 22.514 | 28.142 | 33-770 |—__ 5-625 | 11.250 | 16.87 22.499 | 28.12 33-749 12° 14° 5-621 11.242 | 16.864 | 22.485 | 28.106 | 33-727 | 5-618 | 11.235 | 16.853 | 22.470 | 28.088 | 33-706] 5 | 0.001 } 0.001 5.614 | 11.227 | 16.841 | 22.455 | 28.069 33.682 | 15 | .008 | .009 5-610 | 11.220 | 16.82 22.439 | 28.049 | 33-659 | 20] .o15 | 016 5.606 | 11.212 | 16.818 | 22.424 28.030 | 33-635 | 25 1023 || ).02 5-602 | I1.204 | 16.806 | 22.408 | 28.010 | 33-612 | 30 | -033 | -035 5.598 | 11-196, 16.794 | 22.392 | 27-991 33-589 5.594 | 11.188 | 16.783 | 22.377 | 27-971 | 33-565 SMITHSONIAN TABLES. Li TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE gsten- {Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF . DEVELOPED % 10 15 20° ane PARALLEL. longitude. | longitude.| longitude.| longitude.| longitude.| longitude. Latitude of parallel. Meridional dis tances from even degree parallels. Inches. Inches. Inches. Inches. Inches. Y Inches. 14°00’ | 68.740] 5.594 | 11.188 | 16.783 | 22.377 ; 33-505 Io | 11.458 | 5.590 -180 | 16.770 | 22.360 ; 33-540 20 | 22.915 | 5.586 -172 | 16.758 | 22.344 : 33-515 34-373 | 5-582 LOZ a TO:7455|)22:327 : 33-490 45.530 5-578 155) | 180.7330 22-3100 | moze 33-465 57-288 | 5-573 -147 | 16.720 | 22.294 : 33-440 Longitude interval. _ > ° - nn ° 68.746 | 5.569 138 | 16.708 2: 2 33-415 11.459 | 5.565 16.694 33-389 22.917 | 5.560 7 16.031 33-362 34-376 | 5-556 16.667 33-335 45.834 | 5-551 . 16.654 33-308 57-293 | 5-547 16.641 33-282 68.752 | 5.542 16.628 f : 33-255 11.460 | 5.538 16.613 33-227 22.919 | 5.533 16.599 33-198 34-379 | §.525 16.585 33-170 45-838 | 5.524 16.571 33-142 57-298 | 5-519 16.556 33-113 NR NNN N NNNN NH NN NHN N NNYNNN 68.758 | 5.514 16.542 : : 33-085 11.46t | 5.509 ¥6:527° ||) 2223 7 33-055 22.921 5-504 TO.STZuii22: : 33.025 34-382 | 5-499 16.497 | 21. . 32-994 45.843 5-494 16.482 E 4 32.964 57-304 | 5-489 16.467 | 21. 32-934 68.764 | 5.484 16.452 : : 32.904 11.462 | 5.479 16.436 d ; 32.872 | 5 | 0.001 22.924 5-473 16.420 | 21. 3 32.840 | 10 .005 34.386 | 5.468 16.404 : 3 32.809 | 15 | .o1r 45-548 | 5.463 16.389 | 21.852 32:777 | 20 | .020 57-310 | 5-458 16.373 ; : 32-746 | 25 | .o31 39 | -044 68.771 | 5.452 16.357 . 27. 32.714 11.463 | 5.447 16.340 : : 32.680 22.926 | 5-441 16.324 | 21. 27.2 32.647 34-390 | 5-436 16.307 : : 32.614 45.553 | 5-430 16.290 | 21.72 : 32.580 57-316 | 5-424 16.274 . . 32-547 68.779 | 5.419 16.257 : : 22.513 se 5 | 0.001 11.464 | §.413 16.239 : } 32.478 | 10 | .005 22.929 | 5.407 16.222 .62 y 32.443 | 15 | -O12 34-394 | 5-401 16.204 : ; 32.408 | 20 | .022 45-558 | 5.396 16.187 : : 32.373 | 25 | -034 57-322 | 5-390 16.169 | 21. 206. 32.338 | 39 | -049 68.787 | 5.384 16.151 2 7 32.303 SMITHSONIAN TABLES. II2 TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE ashen (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF y . r . ? DEVELOPED 5 10 15 20 25 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Latitude of parallel Meridional dis- tances from even degree parallels. Inches. Inches. Inches. Inches. Inches. i inches. Longitude interval 68.787 | 5.384 | 10.768 | 16.151 | 21.535 ; 32.303 11.466 | 5.378 | 10.755 | 16.133 | 21-511 : 32.266 22.932 | 5-372 | 10.743 | 16.115 | 21.486 : 32.230 34-397 | 5-366 10.731 16.097 | 21.462 | 26.82 32.193 Bere eae 45.863 | 5-359 | 10.719 | 16.078 | 21.438 | 26. 32.150 ae he | 57-329 10.707 | 16.060 | 21.413 : 32.120 15 | ‘org 013 > Deltas peor ZONnOz2 .023 | 68.795 10.694 | 16.042 | 21.389 7 32.083 25 | 2036 036 11.467 ; 10.682 | 16.022 | 21.363 ; S25 cae ‘O52 22.934 : 10.669 | 16.003 | 21.338 : 32.006 34-401 : 10.656 | 15.984 | 21.312 45.568 : 10.643 | 15.965 | 21.287 57-330 : 10.631 | 15-946 | 21.261 68.803 10.618 | 15-927 .236 Ga 3 0 10.604 | 15.907 | 21. 10.591 | 15.887 | 21.182 10.578 | 15.867 | 21.156 10.565 | 15.847 | 21.12 10.551 | 15.027 | 21.102 11.469 22.937 34-406 45.874 57-343 68.812 bb b WO “I OOO O Ano Av ty 2 10.538 | 15-807 10.526 | 15.789 10.512 | 15-767 10.498 | 15-746 10.483 | 15-725 10.469 | 15-704 11.470 22.940 34-410 45-880 Ve Sz-35° 68.821 : 10.455 | 15-682 NNN HNN Wwe eu OO WM nwo QU 2° 11.472 ao 10.441 | 15.661 ; 0.002 22.943 ; 10.426 | 15.639 : .006 34-415 : 10.412 | 15.618 26.02 : .O14 | 45.886 , 10.397 | 15-596 -993 : .026 57-350 7 10.383 | 15-575 66 : : .040 .058 10.369 | 15-553 10.354 | 15-53! 10.339 | 15-508 10.324 | 15.486 10.309 | 15.463 10.294 | 15-441 NS 10.279 | 15.419 10.264 | 15-396 10.248 | 15.373 10.233 | 15-349 10.218 | 15.326 10.202 ] 15-303 N NH NN 10.187 | 15.280 SMITHSONIAN TABLES. 113 TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE gszstaz- [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED PARALLEL. ¢ a 10 ros 20 Meridional dis- tances from even depree Latitude of parallel parallels, longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Inches. : Inches. 10.187 ; 25.467 Longitude interval 10.171 : 25-427 10.155 S222 25.387 . Inches. 10.139 : . . 0.002 10.123 : . : .007 10.107 . . Oe 016 10.091 : : +22 . ee .043 10.075 s083 10.058 10.042 10.025 10.009 9.995 4.988 | 9.976 4979 | 9-959 4-971 | 9.942 4.962 9.92 4-954 | 9.90 4.945 | 9.891 4-937 | 9873 4.928 | 9.356 4-919 9.838 4.910 9.821 4.902 9.804 4.893 | 9.786 4.884 9.768 4.875 9:750 4.866 9-732 4.857 | 9-714 4.548 9.696 4.839 | 9.679 4.830 9.660 4.821 9.642 4.812 9.623 4.802 9.605 4:793 | 9.586 4-784 9.568 “—s 9-549 | 14.323 9-530 | 14.295 9.511 14.267 9.492 | 14.238 9.473 | 14.210 QOnWN > 45-949 57-437 SN Whur Qn pb #hSHs | 9-454 14.181 “SI nN ™~N 68.924 SMITHSONIAN TABLES. 114 TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sateoe (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED 5 10° ry PARALLEL, longitude. | longitude. | longitude. | longitude. i .| longitude. Latitude of parallel. Meridional dis- tances from even degree parallels. Inches. Inches. Inches. Inches. Inches. Inches. Inches. > ° 6° ‘| 68.924] 4.727 | 9.454 | 14.181 | 18.908 | 23.636 | 28.363 35 3 Longitude interval. oo N 28.305 28.246 28.188 28.130 28.072 11.489 . 9.435 | 14.152 | 18.870 22.978 2 9.415 | 14.123 | 18.831 34-468 .698 9.396 | 14.094 | 18.792 45-957 | 4- 9-377 | 14.065 | 18.753 57-446 | 4. 9-357 | 14.036 | 18.714 Go Oo Inches. | Inches. 0.002 cos 018 : .032 68.935 : 9.338 | 14.007 | 18.676 | 23. : ; te NNN N bv Ud G2 9 Wtihnun Oo no 11.491 | 4. 9.318 | 13.977 | 18.636 te 22.983 : 9.298 | 13-947 | 18.596 34-474 d 9.278 | 13-917 18.556 45-965 : 9.258 | 13.887 | 18.517 57-457 : 9.238 | 13-858 | 18.477 68.948 : 9.219 | 13-828 |: 18.437 9.198 | 13.797 | 18.396 9.178 | 13-767 | 18.356 9-157 | 13-736 | 18.315 9-137 | 13-706 | 18.274 9.117 | 13-675 | 18.234 9.096 | 13-645 | 18.193 9.076 | 13.613 | 18.151 9.055 | 13-582 | 18.109 9.034 | 13-551 | 18.068 9.013 | 13-520 | 18.026 8.992 | 13-488 | 17-984 No HHN NH NNH NN 8.971 | 13-457 | 17-943 8.950 | 13-425 | 17-900 8.929 | 13-393 | 17-858 8.908 | 13-361 | 17.815 8.886 | 13-330 | 17-773 8.865 | 13-298 | 17.730 8.844 54266, 17.688 8.822 | 13.233 | 17-644 8.800 | 13.201 | 17.601 8.779 | 13.168 | 17.557 8.757 | 13-135 | 17-514 8.735 | 13-103 | 17-470 8.713 | 13-070 | 17.427 8.691 | 13.037 | 17-383 8.669 | 13-004 | 17.338 8.647 12.971 | 17.294 8.625 | 12.937 | 17-250 8.603 | 12.904 | 17.205 8.581 12.871 | 17.161 SMITHSONIAN TABLES. TIS TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE az}55: (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF ; ; ; , : DEVELOPED 5 10 15 20 25 30 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Meridional dis- tances from even degree Latitude of parallel parallels. Inches. Inches. Inches. interval. 12.871 | 17.16% | 21.451 Longitude 12.837 | 17.116 | 21.395 12.803 | 17.071 21-338 Inches. | Inches. 12.769 | 17.025 | 21.252 0.002 | 0.002 12.735 | 16.980 | 21.22 .008 | .008 12.701 | 16.935 | 21.169 .019 12.667 | 16.890 ; ee :075 | 12.633 | 16.844 12.598 | 16.798 12.564 | 16.751 12.529 | 16.705 12.494 | 16.659 12.460 | 16.613 44° 45° 12.425 | 16.566 :O49) Alpe 12.390 | 16.519 . 5 | 0.002 12.354 | 16.473 24-709 | 10 | .008 008 12.319 | 16.426 6: ES |, O19 || Gong 12.284 | 16.379 24. 20 | . 034 2 : 053 16.332 : 30 ; 11.509 : 16.284 23.018 7 16.236 34.528 ; 16.188 40.037 f ; 16.141 57-546 : 16.093 16.045 11.511 : 15-997 : 5 | 0.002 23.023 .98 15.948 .922 | 10 | .008 34-534 : 15-899 8 15] .o19 40.045 A 15-351 ; 20] .034 672557 : 15.802 ; 2 053 30 | .076 69.068 : 15-754 11.513 ; 15.704 23-027 . 15.655 34.540 : : 15.606 46.053 | 3.8 15-556 57-567 : 15.507 69.080 : 15-457 eee 008 15.407 : 15-357 po 15-307 15.257 15-206 15.156 SMITHSONIAN TABLES. 116 TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE antes: {Derivation of table explained on pp. liii-lvi.J ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF ; 2 : : DEVELOPED 5 10 15 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. ; oo cv me < c 2 7 & 3 cs Inches. Inches. Inches. Inches. Inches. Inches. 49°00’ | 69.093 | 3-789 11.367 | 15.156 | 18.945 | 22.734 tances from even degree Latitude of parallels. parallel. Longitude interval. LO) |) AeSU zal S770 : 15.105 | 18.882 | 22.658 20 | 23.035 | 3-764 : 15.054 | 18.818 I 30 | 34-552] 3-751 : 15.003 | 18.754 40 | 46.070} 3.738 : 14.952 | 18.690 50 | 57-587 | 3-725 , 14.901 | 18.627 Nv iS mn Inches. 5| 0.002 Io 15 20 25 30° vd . . N un no wn NN NN 5000 | 69.105 | 3.713 : 14.850 | 18.563 Io | I1.520 | 3-700 .099 | 14.799 | 18.499 20 | 23.039 | 3-687 : 14.747 | 18.434 34-555 : : 14.695 | 18.369 46.078 b : 14.644 | 18.305 57-598 c : 14.592 | 18.240 NHN NN = mw LN 69.117 z : 14.540 | 18.176 II.520 Q : 14.488 | 18.110 23.043 : 82 14.430 | 18.045 34-564 | 3- 14.383 | 17-979 40.086 58 2748: | 14.330 | 17-913 57-607 ; : 14.278 | 17.848 69.128 : i 14.226 | 17.782 1.523 : 14.172 | 17.716 23.047 s ; 14.119 | 17.649 34-570 ; : 14.066 | 17.583 460.094 : : : 14.013 | 17.516 57-617 ; : 13.960 | 17.450 13.906 | 17.383 13.852 | 17.316 13-798 | 17.248 13.745 | 17.181 13.691 | 17-114 13.637 | 17.046 13-583 | 16.979 13.528 | 16.910 13-474 | 16.842 13-419 | 16.774 13.364 | 16.706 13.310 | 16.637 16.569 16.500 16.431 16.362 16.293 16.22 16.155 SMITHSONIAN TABLES. TABLE 22. ; CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sxtat: [Derivation of table explained on pp. liii-lvi.] e ABSCISSAS OF DEVELOPED PARALLEL. we 3. | 8 be ORDINATES OF ge | Seve ; ; , , . DEVELOPED Be | 22s 5 10 15 20 25 30° PARALLEL. aS Vers a a = Oe longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Inches. Inches. Inches. Inches. Inches. Inches. 231 6.462 } 9.693 | 12.924] 16.155 | 19.385 56° 57° Longitude interval 3.217 6 434 | 9.651 | 12.868 | 16.085 | 19.301 3.203 6.406 9.609 | 12.812 | 16.015 | 19.217 Tuches \reenes ee 6.378 9.567 12.756 | 15.945 | 19.134 &"| o.cos |Motee 3 161 6.350 | 9.525 | 12.700 | 15.875 | 19-050 | 15] 6081 .oo8 6.322 | 9.483 | 12.644 | 15.805 | 18.906 15] .o18 1017 20:| J i 3-147 6.294 | 9.441 | 12.588 | 15.735 | 18.882 | 5 cu oe 3-133 | 6.266 | 9.398 | 12.531 | 15.664 |] 18.797 oP eel sc09 3.119 | 6.237 9.356 12.475 | 15-504 | 15.712 3-104 6.209 | 9.314 | 12.418 | 15.523 | 18.627 3-090 6.181 9.271 12.362 15.452 | 18.542 3.076 6.152 9.22 12.305 | 15.381 | 18.457 3.062 6.124 9.186 | 12.248 | 15.311 | 18.373 58° 59° 3.048 | 6.096 | 9.143 | 12.191 | 15.239 | 18.287 |——| 3.034 6.067 g.101 12.134 | 15.108 | 18.201 5 | 0.002 | 0.002 3-019 6.038 9.058 | 12.077 | 15.096 | 18.115 | 10] .008 007 3.005 6.010 9.015 12.020 | 15.025 | 18.029 | 15] .o17 .O17 2.991 | 5.981 | 8.972 | 11.962 | 14.953 | 17-944 | 20] .030] .030 2.976 5-953 8.929 | 11.905} 14.882 | 17.858 | 30 68 067 2.962 5-924 8.885 ||) “11-847 "|| 114.000) |) e777 2.947 5.895 8.842 | 11.790 | 14.737 | 17.684 2.933 5-866 | 8.799 | 11.732 | 14.665 | 17.597 2.918 5-837 8.755 | 11.674 | 14.592 | 17.510 2.904 5-808 8.712 | 11-616 | 14.520) | 17.424 2.890 | 5.779 | 8.669 | 11.558 | 14.448 | 17.337 2.875 5-750. | 8.625 | 11.500 | 14.375 | 17.249 | 5 | 9.002 | a.co2 2.860 5-721 8.581 11.441 | 14.302 | 17.162 | 10 | .007 007 2.846 5-691 S537 1isosel 14-22 17.074 | 15 | .0r6 016 2.831 5-662 8.493 | 11.324 | 14.156 | 16.987 | 20] .029 029 2.816 5-633 8.450 | 11.266 |} 14.083 | 16.899 | 25] -045 045 30 | .065 .064 2.802 5.604 8.406 | 11.208 | 14.010] 16.811 2.787 5-574 8.361 11.148 | 13.936 | 16.723 2.772 5-545 8.317 I1.090 | 13.862 | 16.634 2.758 S115 8:273 |) 11.030"]) 13'785)|) 16ss4Ou|= 2.743 5-486 8.229 10.972 | 13-715 | 16.457 Bc 2.728 5-456 | 8.184 | 10.912 | 13.641 | 16.369 62 2.713 5-427 8.140 | 10.854 | 13-567 | 16.280 5 | 0.002 | 0.002 2 699 5-397 8.096 | 10.794 | 13-493 | 16.191 ie ae pa e 2.684 5-307 8.051 10.734) 13:418: | 1OsT02))|" = a 30 | 34.626 | 2.669 5.397 8.006 | 10.675 13.344 16.012 oe oe 2), 40 | 46.168 | 2.654 5-308 7.961 10615 | 13.269 | 15.923 | 25 ey cee 50 | 57-710 | 2.639 5-278 7-917 TO.S567| 03-195 /lemg oases ‘ ‘ 6300 | 69.253 | 2.62 5-248 7.972 10.496 | 13.120] 15.744 SMITHSONIAN TABLES. 118 TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE eahan: (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF : * DEVELOPED 5 10 The PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. Latitude of parallel Meridional dis- tances from even degree parallels. Inches. Inches. Inches. Inches. Inches. Inches. 63° Longitude interval 69.253 5.248 7.872 | 10.496 | 13.120 | 15.744 11.544 5-218 7.827 | 10.436 | 13.045 | 15-654 23.087 5-188 7.782 10.376 | 12.970 | 15-564 Trches. 34-631 | 2. 5-158 | 7.737 | 10.316 | 12.895 | 15-473 | 6’! 0.002 40.175 6 5-128 | 7.692 | 10.256 | 12.820 | 15.383 1007 57-718 5.098 7.647 10.196 | 12.745 | 15-293 O15 .027 043 .O61 69.262 5.068 7.602 | 10.136 | 12.670 | 15-203 11.545 5-037 7.556 | 10.075 | 12.594 | 15-112 23-091 5 5-007 7.511 | 10.014 | 12.518 | 15-022 34-036 4.977 | 7-465 | 9-954 | 12-442 | 14-930 46.152 4.947 | 7.420 9.893 | 12.367 | 14.840 57-727 4.916 7.374 9.832 | 12.291 | 14.749 4.886 | 7.329 9.772 | 12.215 | 14.658 4.855 7.283 9.711 | 12.139 | 14.566 4.825 ey) 9.650 | 12.062 | 14.474 4-794 7.191 9.588 | 11.986 | 14.383 4-764 7.145 9.527 | 11-909 | 14.291 4.733 7.100 9.466 | 11.833 | 14-199 4.702 7.054 9.405 | 11.756 | 14.107 4.672 7.007 9.343 | 11-679 | 14.015 4-041 6.961 9.282 | 11.602 | 13.922 4.010 6.915 9.220 | 11.525 | 13.830 4.579 | 6.869 9.158 | 11.448 | 13.738 4.548 6.823 9.097 | 11-371 | 13-645 4-518 | 6.776 | 9.035 | 11.294 | 13-553 4.487 6.730 8.973 13.460 4-455 6.683 8.911 13.3606 4.424 6.637 8.849 13-273 4.393 6.590 8.787 13-180 4.362 6.543 8.724 13.087 Nb yd NbN se NND ne v2 CO =eNN 4.331 6.497 8.662 12.994 4.300 6.450 8.600 12.900 4.269 | 6.403 8.538 12.806 4.237 6.356 8.475 12.712 4.206 6.309 8.412 12.619 4.175 6.263 8.350 12.525 4.144 6.216 8.288 4.112 6.169 8.22 4.081 6.121 8.162 4.049 6.074 8.099 4.018 6.027 8.036 3-986 | 5.980 | 7-973 3-955 5-932 7-910 SMITHSONIAN TABLES. 11g TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE osha [Derivation of table explained on p. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. —_—_—_—__—————— ORDINATES OF ; DEVELOPED 30 PARALLEL. longitude.| longitude.| longitude.| longitude. | longitude. | longitude. ¢ 7 5 10° 15 20 25 Latitude of parailel. Meridionel dis- tances from even degree parallels, Inches. Inches. Inches. Inches. Inches. Inches. 69.317 | 1.977 | 3-955 | 5.932 | 7-910 11.865 11.554 | 1.962 | 3.923 | 5.885 | 7.846 ' 11.770 23-109 1.946 3.892 5.837 7.783 11.675 M7gerhes: 34-663 | 1.930 | 3.860 5:790 | | 7.720 : 11.579 46.217 | 1.914 3.828 5-742 7.656 ; 11.485 Fee Longitude interval. NI ee “N ~ ° 57-772 | 1.898 | 3-796 | 5.695 | 7-503 ; 11.389 é ‘O12 69.326 | 1.882 | 3.765 | 5.647 | 7-530 11.294 | a0] one 11.556 | 1.866 3-733 5.600 od . II.199 af 23-111 1.850 3-701 5-552 . E II.103 34-667 | 1.835 3-669 5-504 238 : 11.008 40.222 | 1.819 3-637 5-450 , : 10.912 57:778 | 1.803 3.605 5-408 : ; 10.516 69.334 | 1.787 3-574 5-360 Bi ! 10.721 11.557 | 1-771 3-542 5-312 : : aes 23-114 | 1.755 3-509 5-264 : 774 10.52 34-670 | 1.739 | 3-477 5-216 C : 10.432 46.227 1.723 3-445 5-168 é 612 10.336 57-784 | 1-707 3-413 : : 10.240 1.691 3.381 : : 10.144 1.674 3-349 : : 10.047 1.658 3.317 : ‘ ; 9.950 1.642 3.284 9 ; 2 9.853 TeO26.m's 33/252 : ; : 9-757 1.610 | 3.220 8 : 9.660 1.594 3.188 : 4 9.563 1.578 3-155 73 : 9.466 1.562 3.123 : 2 808 9.369 1.545 3.091 ; : 9.272 1.529 3.058 ; : 9-175 1.513 3.026 . : 9.077 1.497 2.993 .4C : 8.980 1.480 2.961 ; 5 ‘ 8.882 1.464 2.928 : : 8.785 1.448 2.896 : ie 8.687 1.432 2.863 : : : 8.590 1.415 2.831 ‘ ; 8.492 1.399 | 2.798 8.304 -383 2.765 ; 8.296 -360 73 ; i 8.198 .350 2 4 7 8.099 1.334 : : 8.002 L3t7 1.301 SMITHSONIAN TABLES. TABLE 22. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE eaten (Derivation of table explained on p. liii-lvi.] ABSCISSAS OF DEVELOPED PARALEL. ORDINATES OF : , : : DEVELOPED 5 10 15 PARALLEL. longitude. | longitude. | longitude. | longitude.| longitude. | longitude. Latitude of parallel. Meridional dis- tances from even degree parallels. Inches. Inches. Inches. Inches. Inches. ° ° 1.301 4 3-903 6.505 7.805 7 sh Longitude interval 1.284 : 3.854 : 6.423 7.707 1.268 530 3.804 : 6.341 7.609 1.252 : 3-755 : 6.258 7.510 5 3-700 : 6.176 Inches. \ Inches. 0.OoI 0.001 IO | .004 003 3.650 CN 15| .008 | .008 20 | .o15 O14 25] .023 O21 3-558 Bogos lia yates |e coal) ade 3-508 5.847 3-459 5-765 3-410 5-683 3-360 5-600 3-607 6.012 3.311 5.518 3-261 5-435 3.211 5-352 3.162 5-270 3.112 5-187 3-062 5-104 3.013 5.022 SMITHSONIAN TABLES. I21I TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE az¢00° (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10! longitude.| 20/ longitude.| 30/ longitude.| 40’ longitude.| 50/ longitude.| 1° longitude. Latitude of parallel. Meridional dis- tances from even degree Wm. mi. nm. mm. Wn, Wm. Wm. . . mm. 185.5 278.3 403.8 185.5 278.3 463.8 185.5 278.3 463.8 185.5 278.3 463.5 185.5 278.3 463.8 185.5 278.3 463.7 185.5 185.5 185.5 185.5 185.4 185.4 S = 000000 *#00000 000000 000000 W000 10 0 YNNNNNN 463.7 463-7 463-7 463-7 403.6 463.6 463.6 463-5 403.4 403-4 403-3 463.2 NUNN DnnnowH to x ~ Go 000000 000000 400000 WWwowowrs NY WK NN LO 000000 RN NN be Go G0 G0 0 Ge NRK HNN bem ST SSN 185.4 185.4 185.4 185.3 185.3 185.3 185.3 185.2 185.2 185.2 185.1 185.1 WOO owm”s NNYVY NW 000000 000000 NN NNN bo NNN Go oe Go O0 00 Ge OOOH He HO0000 OO ete bbawham bbkhbKKHKLH 463.2 t NN SN OO 2 ™N Ni CO CO to t 7 7 7 7 Zk 7 6 6 6 6 6 6 000000 000000 to ™N NS fa hs te he bbbRHKHL 10.10.00 00 YPNNNNN mw ot No 185.1 185.0 185.0 185.0 184.9 184.9 184.8 184.8 184.7 184.7 184.6 184.6 Ny to ty NS™N™N N™N it CNG a3 WKHNRNVNVN 000000 000000 by wh bol bet bat dtd bRHRAKKHbL WMMODO0O SST ues WOOO O0 YPNNNHHN 000000 mH HO -— = == Se OR bRHKEKHKHKN 184.5 184.5 184.4 184.3 184.3 184.2 HRNNNW WHOWHRAR RANA NHNHYVNV 000000 fet tt ett = SS SR bbhRRKHL 184.2 184.1 184.0 184.0 183.9 183.8 Ser epaey Vener 18 =— = = ott 000000 ta SNS NDDDAAD DAH UHRA BRADOHOWD BDHHHWHH nH AbRRAR BRERRRERER BHOOHHO BOOKHDHNH WD BWAWWWO ° mo 183.7 SMITHSONIAN TABLES. D2Z2 TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sooo r (Derivation of table explained on pp. liii-lvi.) CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10/ longitude.| 20/ longitude.| 30/ longitude.| 40’ longitude.) 50/ longitude.) 1° longitude. even degree tances from parallels. Latitude of parallel Meridional dis- vy, x y y mm. Win. Wm. WIL.) LI WIM. . «| 270. mM. 459-4 459.2 TO3+7) |) Ep 27.5.0 183.7 ak | 27/55 183.6] .I | 275.4 TOSSS eeu eeyiyee 183.4] I | 275.1 183.3] -I | 275.0 a eee 000000 bbb bAL Ca Ga Go G2 Ca Co 183.3] -I | 274.9 183.2] .I | 274.8 183.1 | .I | 274.6 183.0] .I | 274.5 182.9| . 274.4 182.8] .I | 274.2 nomnonnooe YU I 000000 bbRKHHLA LOQ7 it vole ||) 27ARL 182.6| .I | 274.0 TO2.5 (eck |273:0 182.4 182.3 182.2 bb RHALH 000000 182.1 182.0 181.9 181.8 181.7 181.6 SUUNRDDAD DADDDD DWH AHHH CODOKDKD OOKO HH 0 0 0 0 :O 0 RN wNH NN NNN™N™N™N NP Vay bbbYHKHH 181.5 181.4 181.3 181.1 181.0 180.9 000000 eee &ONOHN SoS 400000 NN HNN WL NNNN™N™N 180.8 180.7 180.6 180.4 180.3 180.2 NN tb SMN™N on amon wWwWdwWwWW WHwWHhHbL 000000 Go G0 Go -— = SO et bm wt a 990 We O 180.1 179.9 179.8| . 179-7 179-5 179-4 dbHRHHKA 000000 179-3 179.1 179.0 178.8 178.7 178.5 000000 DN AARAA Hhhunah Hah HAARAA BRARARKR RRRRAD Bb Orda QOD wWwobRLL ° ® wWhWaWW BWWWwwWWoH 178.4 SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE apppo0- (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10! longitude.| 20/ longitude.| 30/ longitude.| 40/ longitude.| 50’ longitude.| 1° longitude. Latitude of tances from even degree parallel. Meridional dis- Wn. . nm. RM. . . WM. 89.2 | .o | 178.4 356.8 89.1 | .o | 178.2 350.5 89.0 | .o | 178.1 356.2 89.0 | . 177-9 355-9 83.9 | .0 | 177.8 355-0 88.8 | .o | 177.6 35533 88.7 355-0] 385 354-6 354-3 88.5 354.0 88.4 353-6 88.3 353-3 88.3 353-0 88.2 352.6 88.1 35213 88.0 352.0 87.9 351.6 87.8 351.3 351.0 350.6 350.2 349-9 349-5 349-2 . _ o 6eg 6) fe 6 = 177-5 177-3 177.2 177.0 176.8 176.7 000000 RRKKKK| mn WwW 9 ° 176.5 176.3 176.2 176.0 175.8 175-6 175°5 175-3 175-1 174-9 174.8 174.6 000000 bwHRKRKH Rw NN NHN 87.7 87.6 87.6 87.5 NNNNHNN NW OPO ONONON RHRKKHKHKH 000000 87.2 348.8 348.4 348.0 347-7 347:3 346.9 346.6 346.2 345.8 345-4 345-0 344.6 9. 9. 8. 8. 7. 6. 6. ¥ & 4. 4. 3. 3. 2: i I. O. Mannan MWnnnnin Munn wnunin RN NNN NN 000000 NNNNNN 000000 NKRNNNN 174.4] . W742i) 173.8 : 17337). 17355 \\ae 7 ai phe Ty ZO: E727 te 172:3)|\ 172.1'|\< 344.2 . 3438 . 343-4 . 343-0 342.6 342.2 174.0 173.1 172.5 171.9 171.7 171.5 171.3 171.1 000000 RKNN NN RRYHKKHbK 341.8 341.3 340-9 340-4 340.0 339-6 170.9 170.7 170.4 170.2 170.0 169.8 fA SHS > ww NN HNN NN NKNKHNN 000000 a Cait era @ NNN NNN Dm Rronnnn nDonddooOUY YVHUNSSY YVYYVGSNY VY YS YUARDAAD ADDADAAD ADnDADSD } iy BR RRRARR RARRRAR FRRRERR RRRRAR RARKRAR RARARA FREHDHOHH HOHOOHOW 169.6 339-2 f tw ° a Ww SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE aoeys0- (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10 longitude.| 20/ longitude.| 30/ longitude.| 40’ longitude.| 50/ longitude.| 1° longitude. even degree tances from parallels. parallel. Meridional dis- Latitude of bRHARNKHKLH mt tet et bbRKHKH mt tt ed at bdYKKBKHH bbhRKHHKK Cite (Cleon Ds Ot tee, SO = =e 2.7 2.6 2.5 2:4 2.2 2.1 mmomn cc Fee Ceca man eo NNN NN WN PPOVER UN HAI NNW CW CO Ww CW COLO SS Se Rt bbHKRKHN Oo a Gd G2 Wa Wd 02 Wd Wd a SSO Ot RRHKRHAKNNHN — oe NN NNNN om opese. Vera ere Seite! emia evel walle sel is to lng Miley Naito ensue, steels elitist sieticlh. iat iets EA CRM UTEn iat clin conn nts an an Mmmm Mmmm Unnn nh Mmmm nin Wnmnin Mma nian — oe Ciel tes Wet). en NNN NNN =e NY NN SE COO NOa Cr bok ORODAHA _— = ott C2 WW Od a SS OS Oe Ot RRHAHKKBA YNYNNYHVNN Gd Ga G2 Go Ga Gd Cm] NI SI. 00 CO NHNYNYNN RRHRKA A -— = = oe et in UWmmunim un m tv ON iS) i 315.0 SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE aya: [Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 1o/ longitude.| 20/ longitude.| 30/ longitude.| 4o/ longitude.} 50’ longitude.| 1° longitude. Meridional dis- tances from even degree Latitude of parallel mm. mm. nM. . . . . . nM. WUH.| jin. FOO a|) Ie || 5766 3938] 1-5] 472.5 Gfexey || Ctl egy a2 393-0] 1.5] 471.6 78.5 | .t | 156.9 392.3| 1-5} 470.8 78.3 | .1 | 156.6 391.6] 1.5} 469.9 78:2 ee || T5O.3 390.8] 1.5] 469.0 78.0 | .1 | 156.0 390.1} 1.5] 468.1 boYHNHKHAKLH 389-4} 1-5) 467-3 388.6] 1.5} 466.4 387-9} 1-5] 465.5 387.2] 1.6] 464.6 386.4 | 1.6] 463.7 385.7 | 1.6] 462.8 WOM lage 155-8 ETA |) OSS 7720)| ye 055-2 77-4 | -I | 154-9 77-3.| -1 | 154.6 well bbbRKHA NNNNNN G2 G2 Ga Ga Gd GD MRNNWOH LHRH 384.9 | 1.6] 461.9 384.2 | 1.6] 461.0 383-4] 1-6] 460.1 382.6| 1.6] 459.2 381-9| 1.6} 458.3 351-1 457-3 77:0 76.8 76.7 76.5 76.4 76.2 NNN NNN NN NOW UD CS KOCOOm ONONOK OA KO) OW SH DANO NNNNNN Gy dy Ga Ca Co 76.1 380.4 456.4 379-6] 1-6} 455-5 378.8] I. 4. 378.0 377-2 376.5 375-7 374-9 374-1 373+3 3725 371-7 NNNNNN NNN NNN NNNNN LN 3 3 “3 “3 5 a) 6) “3 “3 “3 3 3 CGS tee CA ONO ot NNNNNN NNNNN bt NNHK NNN 370-9 370.1 369.2 308.4 367.6 3606.8 366.0 365.1 364-3 363-5 362.6 361.8 NNNNN ND NR wN HNN Asn SOs SDD NNN N nN nN m= Ow BR ARAARDRHR AARARA PARWDHHH BODHOODW BWDHOWWW WowOoWwos N N S O90 an NNNNNN 3601.0 300.1 359°2 358-4 357-5 350.6 | NNNNNN BD WHWWHAHW BHHWOHHD BWHWWWW NS TP S550 (Le SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE zov 00" (Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10! longitude.| 20/ longitude.| 30/ longitude.) 40/ longitude.| 50/ longitude.| 1° longitude. even degree Meridional dis- parallels, Latitude of parallel tances from Mmm. nM. 77. +| mn. WM. TA2.3)) 23 284.6 142.0 283.9 141.6 283.2 141.3 282.6 140.9 281.8 140.6 281.1 140.2 139-9 139-5 139.2 138.8 280.4 bRR KRRARRAS NNNNNN i) Nob bs NN SQugas Sao osN BR BPARRRRR BRARRAR RRRRAR RARARRR BPARARA RARAAA BRAK NN NNN N NNNN NN ea ian | SG SS NH HN NN et NNHN NN WAu AN ¢ IN ADD IOI WwW WwW WwW NNNHNHNN I OD HO oe ee QNONON ST a tN _ >] et Soo GSS Ss NNN N N nN bk DOONH :S 5 3 “3 8) “3 “3 3 “3 oS) “3 3 a “3 i) 23 3 3 “i “3 3 “3 “3 “3 “3 “3 “3 °3 2) 3 “3 2) 3 °S o “3 3 3 3 3 “3 : 3 “3 5 3 2S NNNNNN mn ao NNNNNN hiunrmuiuiu1 NNN NN NY i DN DARDADAD DADDAAD BADAAAD ADADAD ARADAA AAADAD AAADAAAD ARAAAAGD SOREN Oo rN N Hes tN SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE ayq533- [Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10 longitude.| 20! longitude.} 30’ longitude.| 40’ longitude.| 50’ longitude.} 1° longitude. Meridional dis- tances from even degree Latitude of parallel NNAWWAA On QAOH ~- Pt NNNN NN ~ nN _ oO “3 “3 3 “3 “3 os 3 “3 3 “3 3 “3 3 “3 “3 3 Sy °3 “3 “3 “3 3 eS aS 3 co 3 “3 3 3 “3 ES 3 “3 oe) 3 °3 “3 3 2S 3 “3 3 3 ° 3 3 eS D ADADAD DAADDAD AKDADAD ADAADAAD ADADAD ARADAA ARADAA Anaad‘ iv SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE apeoov- [Derivation of table explained on pp. liii-lvi.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10 longitude.| 20/ longitude.| 30/ longitude.| 40’ longitude.| 50/ longitude.| 1° longitude. Latitude of parallel. Meridional dis- tances from even degree parallels. mm. nm. . mtn. min, 156.0 155°3 154-0 154.0 53:3 152.6 1.0 | 260.0 1.0} 258.9 1.0} 257.8 1.0] 256.6 I.0| 255.5 1.0] 254.4 bHRKHNWN YHVONHND bbb HOO 152.0 151.3 150.6 149.9 149.2 148.5 TeOllp 25352 1:0) |) 2152.1 1.0] 251.0 1.0} 249.8 1.0| 248.7 1.0] 247.6 RHRKHAKHbKN NPYHNNHNN beRHKHKHBKHN 246.4 245.2 244.1 243.0 241.8 240.6 147.8 147.2 146. 145. 145.1 144.4 et Qoob RARRAR RARRRR RRRRGA GHGGGR GOOG Gaaaaa wl iesinet (Ons euse NwKRNNN YN 143-7 143.0 142.3 141.6 140.9 140.2 239-5 238.4 237.2 236.0 234.8 233-6 — 4 2 ez 2 > oe ES 2 2 139. 138. 138.1 137-4 136.7 136.0 bhHKHHKHL — ot NHKNN ND DEALS S we 135:3 134.6 133-9 133-1 132.4 131.7 bRHAHKHKBHN YPNYKRNKNDN = RN HN be QNOAKA eet VON NO o'8 131.0 130.3 129.6 128.8 128.1 127.4 RHARHKBBKBLN ~~ = Se Oe Oe sss CNSSINO. 126.7 —~— ee ty ty iv to NN RADAR AAA Annan Ana AAA AAA AADDAAD ARDAADD 0 ODDDGHH OCOOKOH OOKHKOHD VSHWHS ove i ~ Ow SMITHSONIAN TABLES. TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sous: (Derivation of table explained on pp. liii.-lviii.] CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10 longitude.| 20/ longitude.| 30/ longitude.| 40’ longitude.) 50/ Jongitude.| 1° longitude. Meridional dis- tances from even degree Latitude of parallel Mn. Win. Wm. Ww. WHIM. WM. 163.1 | .9 | 203.9 162.2} .8 | 202.7 161.2 201.4 160.2 200.2 159.2 199.0 158.2 197.5 196.6 195:3 194.1 192.9 191.6 190.4 eee eeeee RkRKLHb Se oe ee ee HAHNNNDN Be atetehei a} 157.2 150.2 155-3 154-3 153:3 152.3 = = SS “I “MINI OS “I on NI Ni to bRHARNHKHNHNWN Ni oN ty 189.2 188.0 186.7 185.4 184.2 183.0 181.8 180.5 179.2 178.0 176.8 175-5 174.2 173.0 171.8 170.4 169.2 168.0 151-4 150.4 149-4 148.4 147.4 140.4 eee tens DPHKOKWOHD BDOWHWH WHWWW NN ON ON NNNNNN & NNN YN OdOnAS OAdfus bbe ROKK 000004 PRs sun 145-4 144.4 143.4 142.4 141.4 140.4 ee Oo an 000000 O70 Soe Nob NN bUWRY brhbbHRKL bHRKHKRKHA bRRRNN Ba teag ae: ha 7 7 7 7 7 Z 7 i ih 7 7 7 eer 130-4 138.4 137:4 130.4 135:4 134-4 O'S’ 6 0" 0'O AANADAD HOSS NS NN ONT SHAR KDN bRHRRKKLK 166.7 165.4 164.2 162.9 161.6 160.4 133-4 132.4 131.3 130.3 129.3 128.3 000000 RRHRAKANN | 159.1 157-8 150.6 155-3 154.0 152.7 eee eee ee brwHRAHNLKN pou as 000000 Ot NWwWwWHDNN NNN DN NW _ NS ~ . ~) 151.4 150.2 148.9 147.6 146.4 145-1 eee eeeee ~ 2 9 NS 000000 NNN NNN BR BPARRRR RRARRR RPRRRRR RRARRR RRRRAR RAREAG DDHHHH UHHH D Dowsss VHssss VBIGsss BUI HHdnnD Hndnnnn Hnnnnn Honnnww hb BANA AnNAaAdD~S } i - 1438 SMITHSONIAN TABLES. 130 TABLE 23. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE 200000" (Derivation of table explained on pp. liii-lvi.] | CO-ORDINATES OF DEVELOPED PARALLEL FOR— 10/ longitude.| 20/ longitude.| 30/ longitude.| 4o/ longitude.| 50/ longitude.| 1° longitude. Latitude of parallel. Meridional dis- tances from even degree ‘ . mm. nM. . -| mm. mm.) mm. -| mim. mm. 28.8 115.0 143.8 | 1.0 114.0 142.5 | 1.0 113.0 141.2 | 1.0 111.9 139.9 | 1.0 110.9 138.6 | 1.0 109.9 137.4 | 1.0 108.8 107.8 106.8 105.7 104.7 103.6 to oo Un 000000 NKNNNNN ti Nh ty WARANN Sy O00 un On tN 136.0 134.8 133-4 132:2 130.8 129.6 OnhYO®D 0010 070110 bt tot bt et wo H HN 128.2 127.0 125.6 124.4 123.0 121.8 102.6 101.6 100.5 oF5 98.4 97-4 000000 ot nN 96.4 95:3 94.2 93-2 92.2 OL.I go.0 89.0 87.9 86.9 85.8 84.8 120.4 119.2 117.8 116.5 115.2 113.8 NGO GaGa mic ap ania MDOW Awe 000000 = e Oe NN NNN 112.6 Tlts2 109.9 108.6 107.3 106.0 tn ae ee NN Ny buUN ORM 000000 a ole eae eanre — NNNN ND tN 104.6 103.4 102.0 100.7 99-4 98.0 96.8 95-4 94-1 2.8 91-4 go.I 83.7. 2.7 81.6 80.6 79-5 2 ty 399 NO to 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 °3 3 3 3 os) 3 3 3 3 3 3 3 3 3 3 3 3 SUGGS Lorem dn KHnaonrndodnwm OKDODDOHOH ODO UOUS 000000 Se “I ~ & 000000 et tet et NNN NNN NN™NNNI™N Dwar Os BN NWW 87.4 86.2 84.8 83.4 000000 PEGE Eed ea. bas bos NNN N NN RIBS = mmoodod G2 Od Ga Gd Ga Go BR RRRRARR RRRRRR RBEDHHH HQ Ah ADADAHR AARADAAAN ADAAAD DA DADADADR BAayyys Dm MReDODODoD O©00000 ° oo Nv i) » SMITHSONIAN TABLES. TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE soho [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF : DEVELOPED 30 PARALLEL. / / 7 7 10 15 20 25 / 5 Latitude of parallel. Meridional dis- tances from even degree parallels. longitude. | longitude. | longitude. | longitude.| longitude. | longitude. Longitude interval ‘ SMITHSONIAN TABLES. 132 TABLE 24, CO-ORDINATES FOR PROJECTION OF MAPS. SCALE Te [Derivation of table explained on pp. liii-lvi.] 2 ABSCISSAS OF DEVELOPED PARALLEL. Oo. | Ema ORDINATES OF 3s 3 gue ; . , i : DEVELOPED Ze |ESse| 5 10 15 20 25 30 PARALLEL, Hy | 37° | longitude. | longitude. | longitude. | longitude. | longitude. | longitude. CT oa 6 oO Ae ee 114.8 | 229.7 | 344.5 | 459-4 | 574-2 | 689.0 Ps 8 114.8 229.6 344.4 459-2 574-0 688.7. | 4°= 114.7 229.5 344.2 459.0 yety/ 688.4 |__ 114.7 229.4 344.1 458.8 573-4 688.1 ee eae 229.3 343-9 a5i6 573-2 ou 8 wiitee I14. 229.2 343 450-4 573-0 i Sale aa deca 114.5 | 229.1 343-6} 458.2 | 572.7 | 687.2 | 15| OF 114.5 | 229.0 | 343-4 | 457-9 | 572-4 | 686.9 | 279 | 02 114.4 | 228.9 | 343-3 | 457-7 57.2:2) |) (686.6) ||) = o:3 Peta | e227) | 343-1 | 2457-5. 571-04| 000.2 | do} oF 114.3 228.6 343-0 457-3 571.6 685.9 114.3 228.5 | 342.8 457-0 571-3) ||| sOe5.0 oe Sete riers 114.2 | 228.4 | 342.6 | 456.8 571.0 | 685.3 10° 114.2 228.3 342.4 456.6 570.8 684.9 |—— 114.1 228.2 342.3 456.4 570-4 684.5 a 114.0 228.0 342.1 456.1 570.1 684.1 is a 114.0 227.9 341.9 | 455.8 569.8 683.8 | | 5 | o1 113-9 | 227.8 | 341-7 | 455-6 | 569-5 | 6834 | 03] oO. pre eatciers 113.8 22704 41. 455-4 569.2 683.0 2Slgces ee 227.5 Se 455-1 68.8 | 682.6 | 3°| 5 LT 3+7 227.4 341.1 454-8 568.6 3 113.6 227.3 340.9 454.6 568.2 681.3) |= 113.6 227.1 340.7 454-3 567.8 681.4 12° eEs5 227.0 340.5 454-0 567.6 681.1 | peatetetecrere 113.4 226.9 340. 453-8 567.2 680.6 5 | 00 I a 226.7 Piet oe 566.8 | 680.2 | 10] oO. 113.3 226.6 339-9 | 453-2 566.5 679.8 | 15] 02 1D3:2 226.4 339.7 452-9 506.1 679:3) | 20] 0.3 Tit 3t2 226.3 339-4 452.6 565.8 678.9 | 2 0.4 113.1 226.2 339-2 452-3 565-4 | 678.5 | 30] 06 eects 113.0 226.0 339-0 452.0 565.0 678.1 | 112.9 225.9 338.8 451-7 564.6 677-6 a 112.8 225.7 338-6 | 451-4 564.2 677.1 14 112.8 225.6 338.3 451.1 563-9 6767) | 1527 225.4 | 330-1 450.8 563-5 | 676.2 an 112.6 | 225.2 | 337-9 | 450.5 | 5632 | 675.7 se ee te on ete 112.5 | 225.1 | 337.6 | 450.2 | 5627 | 675.2 | 15] 0? 112.5 | 224.9 | 337-4 | 4498 | §62.3 | 674.8 | 29 Be 112.4 224.7 337-1 449-5 561.5 674.2 ze og 2:3 224.6 330.8 | 449.1 561.4 673-7 | 9 : 112.2 224.4 330.6 448.8 561.0 673.2 TI2.1 224.2 336.4 448.5 560.6 672:7) ae peels 112.0 224.1 336.1 448.1 560.2 672.2 | III.9 223.9 | 335-8 447.8 559-7 671.6 111.8 Z2BUF 335-6 | 447-4 559-2 671.1 5 | 0.0 111.8 223.5 335-3 447.0 559.8 670.6 | 10 | oO! 111.7 223.3 335.0 | 446.7 558-4 | 670.00 | 15 | 0.2 111.6 223.2 334-7 446.3 557-9 | 669.5 a oe pamsrreiere TOI 223.0 | 334-5 | 446.0 557-4 | 668.9 | 30| 08 SMITHSONIAN TABLES. 133 TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE zoho: [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF P DEVELOPED 30 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. / Meridional dis- tances from even degree Latitude of parallel, parallels. WML Longitude interval Be 62 III.4 III.3 Wines III.1 111.0 to to 110.9 110.8 110.7 110.6 110.5 110.4 DOKKR AH O NNN HNN RNN NW WN OF Sem me 110.3 110.2 110.1 110.0 109.9 109.8 109.7 109.6 109.5 109.4 109.2 109.1 109.0 NNKRNHN CA OSC arte RLS ONONON RE ONNWO BD ADWNO NNN HNN WWW WwW WWW Ww won SRR N NS aR AOWN WWW WW to 09.09 rere) YN DN bv oO fit N . Ny “NM . N O22 Ro dv 99 os. af SaS bRYYR’N GUC ONIONS An Av - tw ta moO te Ny _ Ny > ° SMITHSONIAN TABLES. 134 TABLE 24, CO-ORDINATES FOR PROJECTION OF MAPS. SCALE Bodoo- {Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED Ly 10’ ihe 20° 25 30° PARALLEL. longitude. | longitude.| longitude.| longitude. | longitude. longitude. Latitude of parallel. Meridional dis- tances from even degree parallels. wim. t oe ° ee ey t phALAPAL NNN NN WD mB PNY) Annu RN Hh WN Longitude interval an~ RODROmM AKHOA Pe HH aes NN ~Mm9 99 WoMmndanr NWNHNNN HN HOsuAn nun Mmanmuitn Vt BR NQQnen Nn = OO ON NR NN NNN were enews SMITHSONIAN TABLES. TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE ,y}5)- (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF ; , DEVELOPED 5 10° 15 30 PARALLEL. longitude. | longitude. | longitude .| longitude. | longitude. | longitude. Latitude of parallel. Meridional dis- tances from even degree parallels. vo Sa Ze ee o£ — NINN™N™N™N Bn NWWS Nn nN HN SMITHSONIAN TABLES. TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE poboo: (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF - q F , DEVELOPED 10 IS 20 25 30 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. ¢ tances from even degree parallels. parallel. Meridional dis- Latitude of Longitude interval NNN NHN bo G2 G2 Gd Gd 399.8 398.6 397-4 N NNN NN WWwokh S CODON & NO DR H 396.2 394-9 393-0 392-4 391.2 390.0 DAaN Gy Gd Ga Gd WW ON Non NNN NHN N & iu 388.7 SMITHSONIAN TABLES. TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sutoo: [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED Si 10° 15 20° ina 30° PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. even degree tances from parallels. parallel). Meridional dis- Latitude of mm. 155-5 155-0 154-5 154-0 153-5 152.9 2 Longitude interval COORRG NNN HNN ty G2 Ga Gd Go 152.4 151.9 151.4 150.9 150.4 149-9 OAL ON - NONNLND N NHK HN WN NN HH N bd 149.4 148.8 148. 147. 147. 1468 SOR POR HUAI % NNHHNN NKNHNN mMONUW O 146.2 145-7 145.2 144.7 144.1 143.6 NN ~) 0S a 143-1 142.5 142.0 141.5 140.9 140.4 139-9 139. 138. 138.3 137-7 13722 136.6 136.1 035-5 135.0 134-4 133:9 133°3 132.5 132.2 131.7 1310 130.5 130.0 SMITHSONIAN TABLES. TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE Bodo [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED 5 10 15 PARALLEL. longitude. | longitude. | longitude. | longitude. | longitude. | longitude. 4 Latitude of parallel. Meridional dis- tances from even degree parallels. min. win. w1mn. witin. ‘ min. 389-9 388.3 386.6 interval. 195.0 260.0 194.1 258.8 193-3 257-7 192.4 256.6 191.6 255-5 190.8 254-4 189.9 | 253.2 189.1 252.1 188.2 251.0 187.4 249.8 186.5 248.7 185.6 | 247.5 65.0 64.7 64.4 64.2 63-9 ty Go Longitude GW OR G2 Ga Wo NNN bh OONQN & Oh DO IS HOSS = et RNQOAO tO NW by 184.8 246.4 183.9 245.2 183.1 244.1 182.2 242.9 181.4 241.8 180.5 | 240.6 1796 | 239.5 178.7 238.3 1779 \. 237-2 177.0 236.0 176.1 234.8 175-3 174-4 173-5 172.6 171-7 170.8 170.0 169.1 168.2 167.3 166.4 165.5 164.6 Wo Wo Wo Qo Go ENE ONC Oo KNHOS bt = NNN NN NNHNHNNN NwWEUND OO RWhNH ww ty NOS Ww 163.7 162.8 161.9 161.0 160.1 159-2 158.3 157-4 156.5 155-6 154-7 153-8 152.9 RSs ys WBANIOHD BANOHDAA NNN NN ND ee NKRN KN HN = NNN HN moO NWU™N in OV ~ ~ mono RORORO FPORORO Minin AAO Ad AID IVY No NH HNN N NHN NY t n wm - oo SMITHSONIAN TABLES. TABLE 24. CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sotoo (Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. ORDINATES OF DEVELOPED sf 10 by 20° PARALLEL. longitude. | longitude. | longitude. | longitude even degree tances from parallels. Meridional dis- Latitude of parallel Longitude interval 2 2 2 2 2 I 7. 5: 4. = 9. Ti 6. 4 3 I ° 2 2 2 2 2 2 : O° 5 ° 4 8 6 ik 6 .O wRKHNHN NH —_— Oo ia RN NHN bo OA KOHN Wd NNO _ _— S09 bw RHKHHNNL sae NN NH YN D Dns LH NS al SMITHSONIAN TABLES. 140 TABLE 24 CO-ORDINATES FOR PROJECTION OF MAPS. SCALE sohoo: [Derivation of table explained on pp. liii-lvi.] ABSCISSAS OF DEVELOPED PARALLEL. a a8 nae ee eee ee ORDINATES OF se | 8s3s , DEVELOPED 28 | bess 5 10’ is 20° 25 30° PARALLEL. = : : , : : a =~ ° ™ | longitude. | longitude. | longitude. | longitude. | longitude. longitude. mm. nm. mint. mm. win. mM. 35-9 71.9 | 107.8 | 1438 | 179.7 | 215.6 35-6 71.2 106.9 142.5 178.1 213-7 35:3 70.6 105.9 141.2 176.5 211.8 35.0 70.0 104.9 139.9 174.9 209.9 a 34-6 69.3 104.0 138.6 7362 207.9 5] 0.0 34-3 68.7 103.0 137.3 171.6 206.0° | 551 ox 34.0 68.0 102.0 136.0 170.0 204-1 | 55] 0.4 33:7; 67-4 IOI. 134.7 168.4 202:10 | 5 are 33-4 66.7 100.1 133-4 166.8 200.2 | 35 0.9 33.0 66.1 99.1 132.2 165.2 198.2 ‘ 2.7 65.4 98.1 130.8 163.6 196.3 64.8 97-1 129.5 161.9 194.3 192.4 190.4 Longitude interval 32.1 64.1 ; Bi-7 63-5 95-2 127.0 158.7 62.5 2 125.6 157-0 NHNHHN Sy Ou Sts nn Cnn © mn pp Go Ce = > ~ Oo oo ON - ww Wn ~ 53-0 79.5 106.0 132.5 26.2 52-3 78.5 104.7 130.8 107.08 |——— 25.8 51-7 77.5 103.4 129.2 155-0 78° 25.5 51.0 76.5 102.0 127.6 153-1 20.2 50.4 75.5 100.7 125.9 TS. Tey eee 24.8 49.7 74.6 99-4 124.2 149.1 5| 00 24.5 49.0 73-6 98.1 122.6 LA7Ate rose Ok 15 |0:2 24.2 48.4 72.6 96.8 121.0 145-1 | 20] 0.3 23-9 47-7 71.6 95-4 | 119.3 | 143-2 | 25] O4 Zot 47.1 70.6 94.1 117.6 141.2 | 30] 0.6 23.2 46.4 69.6 2.8 116.0 139.2 22.9 45-7 63.6 QI.4 114.3 137-2 22.5 45-1 67.6 go. 112.6 15:20) lee 222 44.4 66.6 88.8 III.0 133-2 21.9 43-7 65.6 87.5 109.4 Sq 2 |e | en 21.5 43-1 64.6 86.1 107.6 129.2 5 | 0.0 21.2 42.4 63.6 84.8 106.0 127-2 LON) Ost 20.9 41.7 62.6 83.5 104.4 25-2) | ES} O.1 20.5 41.1 61.6 82.1 102.6 123.2 | 20} ©.2 SMITHSONIAN TABLES. 141 TABLE 25. AREAS OF et ere OF EARTH’S SURFACE OF 10° EXTENT IN LATITUDE AND LONGITUDE. (Derivation of table explained on pp. I-lii.] Middle Latitude of Quadrilateral. Area in Square Miles. 474953 472895 467631 458891 446728 431213 412442 390533 365627 337890 307514 274714 239730 202823 164279 124400 83504 41924 SMITHSONIAN TABLES. 142 TABLE 26. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 1° - LATITUDE AND LONCITUDE. i: (Derivation of table explained on pp. 1-lii.] | Middle latitude} Area in Middle latitude} Area in Middle latitude | Area in of quadrilateral./ square miles. || of quadrilateral. square miles. || of quadrilateral.| square miles. 0° 00" 4752-33 26° 00° 4252.50 2950.58 o 47 52-16 26 30 4204.51 30 20783 I 4751.63 27 00 4240.20 00 2884. 47 50-75 27 30 4227.56 30 2851.68 4749.52 28 4208.61 oo 2818.27 4747-93 28 4189.33 2784.62 4740.00 29 4169.74 2750.76 4743-71 29 4149.83 2716.67 4741.07 4129.60 5 2682.37 47 38-08 4109.06 2647.85 4734-74 4088.21 2613-13 47 31.04 4067.05 2578.19 4727.00 4945-57 2543-05 4722.61 4023-79 2507.70 4717.86 4001.69 2472.16 4712.76 3979.30 2430.42 4707-32 3956-59 2400.48 4701.52 3933-59 2364.34 4695.38 3910.28 2338.02 4688.59 3886.67 2291.51 WOO MO NNAN UMih WWNN 4682.05 3862.76 2254.82 4674.86 3838.56 2217.94 4667.32 3814.06 2180.89 4659-43 3789.26 2143-66 4651.20 3764.18 2106.26 ramps 3738.80 2068.68 4033-71 3713-14 2030.94 4624.44 3087.18 1993-04 4614.52 3660.95 1954-97 4604.87 3634.42 1916.75 4594-57 3607.62 ee 4553-92 3580.54 1839.34 4572-94 3553-17 1801.16 4501.61 3525-54 1762.33 4549-94 3497-62 1723.30 4537-93 3469.44 1034.24 4525-59 3440.98 1645.00 4512.90 3412.26 1605.62 4499-87 3383.27 1506.10 4480.51 3354.01 1526.46 4472.81 3324-49 1486.70 4458.78 3294.71 1446.81 4444.41 3264.68 1406.81 4429.71 3234-39 1366.69 4414.67 3 3203.84 1326.46 4399-30 3173-04 1286.12 4333-60 3141.99 1245.68 4307.57 3110.69 1205.13 NRHN H WWwN hd 4351.21 3079-15 1164.49 4334-52 3947-37 an 232715 4317.51 3015.34 1082.91 4300.17 2983.08 1041.99 SMITHSONIAN TABLES. 144 TABLE 26, AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 1° EXTENT IN LATITUDE AND LONCITUDE., {Derivation of table explained on pp. I-lii.] Middle latitude Middle latitude Area in Middle latitude} Area in of quadrilateral./ square miles. || of quadrilateral.| square miles. | | of quadrilateral.| square miles. 78° 00° 82° 00’ 670.27 336.02 78 628.64 86 294.08 79 586.97 252.11 545-24 210.12 503-47 ee 461. 126.10 419.81 84.07 377-93 42.04 SMITHSONIAN TABLES. 145 TABLE 27. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 30’ EXTENT IN LATITUDE AND LONCITUDE. [Derivation of table explained on pp. I-lii.] Middle latitude} Area in Middle latitude} Area in Middle latitude! Area in of quadrilateral.| square miles. | {of quadrilateral.| square miles. |/ of quadrilateral.| square miles. ° 00" 1188.10 15 1188.08 30 1188.05 45 1188.00 ooo°o 00 1187.92 15 1187.82 30 1187.70 45 1187.56 ~~ 00 n137.39 c bose0 1187.20 : 1049.7 1186.99 : 1047.34 1186.76 : 1044.90 NHNN 1186.51 1143.25 1042.44 1186.24 1141.84 1039.97 1185.95 1140.41 1037-47 1185.62 1138.96 1034.95 1185.28 1137-50 1032.41 1184.92 1136.00 1029.85 1184.53 1134.49 1027.27 1184.13 1132.96 1024.68 1183.70 1131.41 1022.06 1183.24 1129.83 1019.43 1182.77 1128.24 1016.77 1182.28 1126.62 IOI4.10 1181.76 1124.98 IOII.40 1181.22 1123.32 1008.69 1180.66 1121.64 1005.96 1180.08 1119.93 1003.20 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 1179.48 2 1118.21 1000.43 1178.85 1116.47 997-64 1178.20 1114.71 994-83 1177-53 20 I112.92 992.00 1176.84 21 IIII.11 989.16 1176.13 21 1109.28 986.29 1175-39 2 1107.44 983-41 1174.63 I 1105.57 980.50 1173.86 1173.06 1172.23 1171.39 1103.68 977-58 I101.77 974-04 1099.54 971.68 1097.88 968.70 WUOO”wO Como NNNN wRNN HN NHN N 1095.91 965-70 1093.92 962.68 109t.9o 959-65 1089.87 950.60 1170.52 1169.63 1168.73 1167.80 N Oo NN Ww NR nN 1166.84 1165.86 1164.86 1163.85 1087.81 953-52 1085.74 950.43 1083.64 947-32 1081.52 944.21 tN > tN t > 1162.81 1079.39 941.05 1161.75 1077.23 937-88 1160.67 k 1075.05 934-71 1159.56 4 1072.85 931-51 NS nN SMITHSONIAN TABLES. 146 a AREAS OF QUADRILA Middle latitude Area in TABLE 27. TERALS OF EARTH’S SURFACE OF 30’ EXTENT IN LATITUDE AND LONCITUDE. {Derivation of table explained on pp. 1-lii.] Middle latitude Area in Middle latitude Area in of quadrilateral.| square miles. || of quadrilateral.| square miles. || of quadrilateral.] square miles. SMITHSONIAN TABLES. 928.29 925-06 921.80 918.53 915-25 OIT.94 908.61 905-27 901.91 898.54 895.14 891-73 888.30 884.55 881.39 877-91 74-41 870.90 867.37 863.82 860.25 856.67 853-07 849.46 845.82 842.18 838.51 $34.53 831.13 827.42 823.68 819.94 816.18 812.40 808.60 804.79 800.97 797-13 193-27 789-39 785.50 781.60 777-68 773-74 769.79 765.83 761.85 757-35 753-84 749-82 745-78 741.72 52° 52 737-65 733°57 729-47 725-36 721.23 717.08 TAOS 708.76 704-57 700.38 696.16 691.94 687.70 683.44 679.17 674.89 670.60 666.29 661.97 657-64 653.29 648.93 644-55 640.17 635-77 631.36 626.93 622.49 618.05 613-59 609.11 604.62 600.13 595-62 591.09 586.56 582.01 577-45 572.85 568.30 563.71 559-11 554-49 549.86 545-23 540.58 535-92 531-25 526.57 521.58 517-17 512.46 507-74 503-01 495.26 493-5! 458.75 453-97 479-19 474-40 469.60 464.78 459-96 455-13 450.29 445-45 440.59 435-72 430.84 425-96 421.06 416.16 411.25 406.34 401.41 396.47 391-53 386.58 381.62 376.65 371.68 366.70 361.71 350.71 35 IT -7 I 346.69 341.68 336.65 331.62 326.58 321.5 316.4 311.42 306.36 301.28 296.21 147 TABLE 27. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 30’ EXTENT IN LATITUDE AND LONCITUDE. [Derivation of table explained on pp. 1-lii.] Middle latitude Area in Middle latitude} Area in Middle latitude} Area in of quadrilateral.| square miles. || of quadrilateral.) square miles. || of quadrilateral.) square miles. if : 82° 00’ 167.57 84.01 82 162.37 78.76 82 30 157-16 Wa se 82 45 151.95 27 83 00 146.74 63.03 83 15 141.53 57-7 83 30 136.31 52.5 83 45 131.09 47.2 84 00 125.87 42.0 84 15 120.64 36.7 84 30 115.42 31.53 84 45 110.18 26.27 15 45 RNNN 104.95 i: 99-72 GY) 94.48 10.51 89.25 5-26 SMITHSONIAN TABLES. 148 TABLE 28. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 15’ EXTENT IN LATITUDE AND LONCITUDE. [Derivation of table explained on pp. 1-lii.] ; Middle latitude} Area in Middle latitude} Area in Middle latitude} Area in of quadrilateral. square miles. | | of quadrilateral./ square miles. || of quadrilateral.| square miles. [e} 289.47 289. 33 289.1 289.03 288.88 288.7 3 288.5, 288.43 o0o000 -OO00 2096.97 : 288.28 296.96 : 288.12 296.94 : 287.96 296.93 294.2 287.81 oe 206.91 : 287.65 296.89 : 287.49 296.87 22 : 287.33 296.85 8 287.17 NOR ee 296.82 : 287.00 296.80 : 286.83 296.77 2 286.67 286.50 NNN HN 286.33 286.16 285.99 285.82 28 5.64 285.46 285.28 285.10 284.92 284.74 284.56 284.38 284.19 284.00 283.81 283.62 283.43 283.24 283.05 282.86 282.66 282.46 282.26 282.06 12 i 281.86 295-57 12 " 281.66 295-51 2 22 . 281.45 295-44 2 290. 281.25 295-37 2 ; 290.03 281.04 295-31 2 . 280.83 295-24 12 : : 280.62 295-17 13 289. 280.41 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 SMITHSONIAN TABLES. TABLE 28. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 15’ EXTENT IN LATITUDE AND LONCITUDE. [Denvation of table explained on pp. 1-lii.] Middle latitude Middle latitude Area in Middle latitude Area in Area in of quadrilateral.| square miles. || of quadrilateral.| square miles. | | of quadrilateral.| square miles. 280.20 2¢ 30” 267. 251.15 279-99 00 . 250.80 279:77 20" 22) 30 200. 250.45 279-55 00 i 250.11 279.34 : 30 266.2 249.76 279.12 oo 205. 249-41 278.90 2 30 : 249.06 278.68 00 248.71 278.46 30 265. 248.36 278.23 00 : 248.00 278.00 30 264.52 247-65 Ts oo 4. 247.29 277-55 263. 246.93 277.32 263.62 246.57 277.09 3. 2 246.21 276.86 : 245-85 245-49 245-13 244.76 244.40 OV. ON Oo wn tO wb wh NNNIN 244.03 243-66 243-29 242.92 NNN WN 242.55 242.18 241.80 241.43 22 22 22 23 241.05 240.67 LS a) G2 Ws Oo Wo wun ONG NN wh Go Ga Goa Go Coe ee Hor CONIN™N Nv tN WW Go Wyo J re) oo oo b & SMITHSONIAN TABLES. TABLE 28. AREAS OF QUADRILATERALS OF FARTH’S SURFACE OF 15’ EXTENT IN LATITUDE AND LONCITUDE. [Derivation of table explained on pp. I-iii.] Middle latitude! Area in Middle latitude Area in Middle latitude} Area in of quadrilateral. square miles. || of quadrilateral.) square miles. || of quadrilateral.| square miles. 3 ut y : , 7 2 183.90 2" . 103:39 30 | 208.2 182.88 00 ; : 182.37 181.85 es 180.82 180.31 179-79 179.27 178.75 178.23 177-71 177-19 176.67 176.14 RN HN QU gvUT OVON RN NNN 175.62 175-10 174.57 174.04 173-51 172.99 172.46 171.93 171-30 170.86 170.33 169.79 169.26 168.72 168.19 167.65 NNN N wWNN YN “I \o NNN N NNN YN N Nn boy Go OWO RMOW A Drum 22 22 22 22 1.6 1.2 0.7 0.3 mn vy ™ ‘Oo ‘oO r= 167.11 166.57 166.03 165.49 164.95 164.41 163.87 163.32 162.78 162.2 161.6 161.14 160.59 160.04 159-49 158.94 158.39 157-54 157-29 156.73 SMITHSONIAN TABLES. TABLE 28. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 15’ EXTENT IN LATITUDE AND LONCITUDE. [Derivation of table explained on pp. I-lii.] Middle latitude} Area in Middle latitude} Area in Middle latitude Area in of quadrilateral.| square miles. || of quadrilateral.] square miles. || of quadrilateral. square miles. 156.18 65° 07’ 3 155-62 65 15 155-07 65 22 154-51 65 30 153-96 65 153-40 65 152.84 65 152.28 66 / 30” 94.78 00 94.16 3° 93-54 00 92.92 -~— = RNwHN BUGS) HNO MN ENW N On 30 92.30 00 91.68 30 Q1.05 00 90.43 151.72 aie 30 89.80 151.16 20. 45 00 89.18 150.60 22 20. 2 30 83.55 150.03 ; 00 87.93 a Nw WN NNO Oo MON 149-47 . 30 87.30 148.91 : 00 86.67 148.34 : 30 » 86.05 147-77 : 00 85.42 147.21 H 30 84.79 146.64 : 00 84.16 146.07 : 30 83.53 145.50 : 00 82.91 144.93 . 30 82.28 144.30 5 oo 81.65 143-79 : 22 30 81.01 143.22 00 80.38 142.6 . 30 79-75 142.0 : oo 79.12 141.50 2 ; 30 78.49 140.93 . 00 77.86 140.35 . 07 30 77.22 139.78 : 00 76.59 ae : 3° 75:95 138.62 00 75-32 138.04 oO : 30 74-69 137-47 00 7495 136.89 . . 30 7A 136.31 : oo 72.78 135-73 : 30 72.14 T60s 0. 00 71.51 134.56 69 4 22 30 70.87 133-98 . oo 70.24 133-40 2. 30 69.60 132.81 00 68.96 E3223 22 K 30 (8.32 131.64 7 00 67.68 131.06 ’ 7 67.04. 130.47 ). 66.41 129.88 é 22 65-77 129.29 : 65-13 128.70 ; 64.49 128.12 ! 63.85 127-53 . 63.20 126.94 : 62.56 GMITHSONIAN TABLES. 153 TABLE 28. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 15’ EXTENT IN LATITUDE AND LONGITUDE. [Derivation of table explained on pp. ]-lii.] Middle latitude} Area in Middle latitude} Area in Middle latitude} Area in of quadrilateral.| square miles. || of quadrilateral. square miles. || of quadrilateral.| square miles. 78° 07’ 30° 61.92 an 07” 30” 41.24 00 61.28 2 15 00 40.59 2 30 ; 82 22 30 39-94 00 : 30 00 39-29 30 ; 30 38.64 oo 8. 00 37-99 3° : 30 37°34 oo . 00 36.69 30 36.03 00 35.38 232 34-73 00 34.08 30 33-42 00 Bae 30 32.12 00 31.47 30 30.81 00 30.16 30 29.51 oo 28.86 30 28.20 oo 2.54 30 26.59 00 30 00 30 00 30 oO 30 00 me NN 8 RES NRK H HN SMITHSONIAN TABLES. 154 TABLE 29. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 10’ EXTENT IN LATITUDE AND LONGITUDE. (Derivation of table explained on pp. I-lii.] Middle latitude} Area in Middle latitude} Area in | Middle latitude} Area in of quadrilateral.| square miles. || of quadrilateral.| square miles. || of quadrilateral.| square miles. ° ¢ 132.01 3° 130.51 126.11 132.01 130.46 126.00 132.01 130.40 125.88 132.00 130.34 125-77 ooo0o°0 132.00 130.28 125.65 131.99 130.22 125.54 131.99 130.15 125-42 131.98 130.09 125.30 “Re OO” 131.97 130.02 125.18 £31.96 129.96 125.06 131.95 129.89 124.94 131.94 129.82 124.51 Oe 131.93 129.76 124.69 131.91 129.68 124.56 131.90 129.61 124.44 131.88 129.54 124.31 NNN N 131.86 129.47 20 124.18 131.84 129.39 124.05 131.82 129.32 2 123.92 131.80 129.24 20 123-79 131.78 2 129.16 20 123-66 131.76 12 129.08 2 123.52 131.74 12 129.00 2 123.39 131.71 12 128.92 21 123.25 131.68 2 128.84 123.12 131.66 12 128.76 122.98 131.63 13 128.67 122.84 131.60 13 128.59 131.57 128.50 131.54 128.41 131.50 128.33 131.47 128.24 | RNNN Nop = N Bun WwW ON 131.44 128.14 131.40 128.05 131.36 127.96 131.33 127.87 —_ NN = Cw Oo 131.29 127.77 131.25 ere 131.21 127.5 131.16 127.48 131.12 127.38 131.07 127.28 131.03 127.18 130.93 127.08 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 7 7 130.93 126.98 130.88 126.87 130.84 126.77 130.79 126.66 130.73 126.55 130.68 126.44 130.63 126.33 130.57 126.22 Como NNNN SMITHSONIAN TABLES. TaB_Le 29. UADRILATERALS OF EARTH’S SURFACE OF 10’ EXTENT IN BEER AEE S LATITUDE AND LONCITUDE. [Derivation of table explained on pp. I-lii.] —— Middle latitude Area in Middle latitude Area in Middle latitude Area in of quadrilateral.| square miles. || of quadrilateral.| square miles. || of quadrilateral.) square miles. 26° os’ 118.87 34° 45 108.94 43° 25° 96.50 26 15 118.71 34 55 108.73 43 35 s 90.24 26 2 118.54 35 95 108.51 43 45 95-98 26 35 118.37 35 15 108.29 43 55 95-71 26 45 118.21 35 2 108.07 44 05 95-45 26 55 118.04 35 35 107.85 44 15 95-19 27 05 117.87 35 45 107.63 44 25 94-92 27 117-69 35 55 107.41 44 35 94-65 272 117.52 36 05 107.19 44 45 94.38 27 3G 117-35 36 15 106.96 44 55 94.11 27/548 T0707 36 25 106.74 45 05 93-34 27 55 116.99 36 35 106.51 45 15 93-58 28 o 116.82 6 4 106.2 2 3.30 28 116.64 36 = 106.06 me a anes 28 2 116.46 37 05 105.83 45 45 92.76 28 35 116.28 7k 105-60 45 55 92.48 28 45 116.10 B72 105-37 46 05 92.21 28 55 115.92 2735 105.14 46 15 91.94 29 05 115.73 37 45 104.91 46 2 91.66 115.55 37 55 104.68 46 35 91.38 29 2 115-37 38 05 104.44 46 45 gI.10 29 35 115.18 38 15 104.21 46 55 90.82 29 45 114.99 38 2 103.97 47 05 90.55 114.81 38 35 103-74 47) 5 90.27 114.62 38 45 103.50 47 25 89.99 30 15 114.43 38 55 103.26 47 35 89.70 30 25 114.24 39 05 103.02 47 45 89.42 114.04 102.78 89.14 30 45 113.85 39 2 102.54 48 05 88.85 30 55 113.66 39 35 102.30 48 15 88.57 31 05 113.47 39 45 102.06 48 25 88.28 Bis K0G-27 390 55 101.82 48 35 88.00 31 125 113.07 40 05 101.57 48 45 87.71 BE 35 112.88 40 15 101.3 48 55 87.42 31 45 112.68 40 2 IOI.0 49 05 87.13 112.48 40 35 100.83 49 15 86.84 112.28 100.59 : 2.05 112.08 40 55 100.34 49 35 86.26 32 2 111.87 41 05 100.09 49 45 85-97 111.67 41 15 99.54 49 55 85-68 2 45 111.47 4I 25 99-59 2 55 111.26 41 35 99-33 50 15 85.09 33 05 111.06 4I 45 99-08 50 2 84.80 33 15 110.85 41 55 98.53 50°35 84.50 33925 110.64 2 05 98.57 50 45 84.21 33°35 110.43 2 15 98.32 50 55 83.91 33 «45 110.22 2a 98.06 EOS 83-61 3 97.80 83.31 97-55 . 34 15 109.59 2 55 97-29 5I 35 82.71 34 2 109.37 43 95 97-03 5I 45 82.41 96.77 82.11 SMITHSONIAN TABLES. TABLE 29. AREAS OF Qusen ee OF EARTH’S SURFACE OF 10’ EXTENT IN Middle latitude 52° 05 15 25 WnPwWh Muni wn Oo Mmmm Area in of quadrilateral.| square miles. 81.81 81.51 81.20 80.90 80.60 80.29 79-98 79.68 79-37 79.06 78.75 78.44 78.13 77.82 77-51 77:19 76.88 76.57 76.25 75:94 75-62 75:39 74-99 74:67 74-35 74-03 73:71 13:39 73-07 72-75 72-43 72.10 71.78 71.46 TIS 70.80 70.48 70.15 69.82 69.49 69.17 68.84 68.51 68.18 67.84 67.51 67.18 66.85 66.51 66.18 65.84 65.51 SMITHSONIAN TABLES. ATITUDE AND LONCITUDE. [Derivation of table explained on pp. I-lii.] Middle latitude Area in Middle latitude} Area in of quadrilateral.| square miles. || of quadrilateral. square miles. 65.17 69° 25° 64.84 64.50 69 45 64.16 55 63.82 63-48 63.14 62.80 62.46 62.12 61.78 61.44 61.10 60.75 60.41 60.06 59-72 59:37 38.68 58.33 57-99 57-64 57-29 56.94 56.59 50.24 55.89 55-54 55:19 54-83 54-48 54.1 53:7 53-42 53-06 52.71 52135 52.00 51.64 51.28 59:95 59-57 50.21 49.85 49-49 49-13 48.77 48.41 48.05 47-69 47-33 TABLE 29. AREAS OF QUADRILATERALS OF EARTH’S SURFACE OF 10’ EXTENT IN LATITUDE AND LONCITUDE. (Derivation of table explained on pp. 1-lii.] Middle latitude Area in Middle latitude Area in Middle latitude Area in of quadrilateral.| square miles.|| of quadrilateral.| square miles. || of quadrilateral.| square miles. 27.62 i 18.43 18.04 17.65 Lyo7 16.88 16.50 16.11 15-73 15-34 14-95 14.57 14.18 NNN N 13-79 13-40 13.02 12.63 5 4. 4. 4. 3 Bs Bs its 2 9 2 2 2 12.24 11.86 11.47 11.08 SMITHSONIAN TABLES. E59 TaBLE SO. DETERMINATION OF HEIGHTS BY THE BAROMETER. Formula of Babinet. Bo—B a C (in feet) = 52494 E a oe] — English Measures. 2 (4 +4) C (in metres) = 16000 [: + el — Metric Measures. In which Z = Difference of height of two stations in feet or metres. B., B = Barometric readings at the lower and upper stations respectively, corrected for all sources of instrumental error. t,, <== Air temperatures at the lower and upper stations respectively. el PE ae Values of C. ENGLISH MEASURES. METRIC MEASURES. eS t (¢ +2). Metres. 4.69834 C 4.18639 I 5360 z -Ig000 154 70339 -19357 15016 -70837 19712 15744 71330 -20063 15872 71818 4.20412 16000 -20758 16128 4.72300 21101 ee ; 21442 16334 ie 21780 16512 “737*5 .2211 16640 -74177 22448 16768 ae 16896 .2310 17024 4-74633 23431 17152 75085 “75532 .23754 17280 -75975 +2407 5 Tage 24393 1753 76413 -24709 17664 25022 17792 4-76847 :77276 4.25334 er g “25043 1504 ies 25950 18176 -78123 26255 18304 SMITHSONIAN TABLES. 160 TABLE 31. MEAN REFRACTION. Refraction. Refraction. Refraction. Refraction. Refraction. Apparent altitude. Apparent altitude. Apparent altitude. Apparent altitude. Apparent altitude. a & x ON OO W™ its sy wd G2 4 = |+ oO IF an nm Gs | WW Go Nv ty | Nit aN tN ° Mm~Iwun Loe > JO [or ge OWN eG luo Go [oS JoR]H lis pplp = NO Of|& 2 | ORS 1 tn | OV = Go \o tnd 0 0 bo |4 G2 Go OO) Ole Bla 2 [G2 Go jC i ON = _— oo mn =e ~~ -— oe Oa Go |Oo ty Oo wn NVO NS 1G \O | DI Go fs Go in Co WIRES Os HOODOO aU|O | : to nm | Go ~_ (os) N 4 flr t m |Gotn = = ty Go sOx0 Cro Cat O DD Ic OY)¢ -_ ty oo 4 W Oso = ON™N | Nob a Ne - NON om in OV ON tN NN A OR COnnbp vy _ by | to ty Go \o Ow _ — _ NNINTdR& v/v nN nn QQ Is Go | NN QW Gs =p IN OW bo fede tn nt POW co NO 0 Ww _ aN |S st No Nb N Ny PN OO ae ee See Ft S98) 110 esi & WW [Ko [Ko Wo PALAA AL NwWOokhb ARNO N & Gs tv Go Nh pa nN ~ Nn nN -_ _ oN mn iS to oe ° Nod Owlu DN BROW AOL Nob | af =m O10 -_ _— _ _ oe Ny ly | or] ¢ Ov. ND 0 0 A Gm NO | ALO 00 FARAH H — aS eS tp N ~ ~ ~ a _ 8 [Go ~ 01 CO CO10 10 10 Oo | | |, ty Ow nN ~ = to C0 mem) \ ww = N mn O- aL = = ° Gs SOD = N NNW A -_ nO § wn Cn oe UU in AL oo NI WWwwok]s Ra a be me] tm ENT ST SST Nw OI COO ale bd OO Wa)o lm | SiC Mmminu ro Wn tn co N _ \o N Ww aw N > Qo _— | : aN \o ty |X iy oe uM OINnN 0 ct SMITHSONIAN TABLES. Clo or Qngaw nO a TABLE 32. An Of O O° FOR CONVERSION OF ARC INTO TIME. HAHAHA LAL NOL OAN OL O WN NN aN Los] oO’ HAnd OL OAN OF WwWN ND ee a Oo 16 0! 300) 20 o 16 4 2/16 8 16 12 16 16 16 20 16 24 16 28 16 32 16 36 16 40 fA BA A LA un fp lp An COfL!'0 An OL O Oo oo mn wm Ad OF O An 3° b+ oe An Of O BDIRWWWWNNN NYY HNHNKHHNNHNN O° 16 44 2| 16 48 16 52 16 56 1750 17 4 7a 72 17 16 17 20 301 302 393 304 305 306 3°97 308 309) 310 311 312 313 314 315 316 317 318 319 320 20 4 20 § 20 12 20 16 20 20 20 24 20 28 20 32 20 30 20 40 20 44 20 48 20 52 20 56 21 oO 21 21 21 21 IAbwv COP ° O0000000 Nod oe Ee Ons DAUBRW vb a O C2 ODN OPO Oo Won NIN] A An Of ~ a oO _ OAN OF WN NNNNNDND Ld nN nN a | oO! op On COR MmMbeROWW DN NIN] ON ° WWOUOWOIOWOONO ~ Ww NNN] & WN NN] Hw a 17 24 2| 17 28 17 32 17 30 17 40 17 44 17 48 3} 17 52 17 56 18 oO a ANNANNANDADANUnMnnnMNMnMwn |i lan nnwn Dvn CHO AN CH!IO WwW NNN = = tN 18 4 18 8 18 12 18 16 18 20 18 24 18 28 3 20 J > Go| oO Be OO) OD) G2 G3 G2 GW Bus G2 Ga Go bw wh be NN KN O ON ADR bb NHKONNNANHNN N(KHHNKHNNNNN/!Y OQ QQ °o Bus G2 Go Go G2 G2 Go Go OB @ WH JO3 Ga Ga Go OOM! OF e (o]Ne) WON NIN] ee CH & Af OAN unk S ON Pr rm ef tN WWHNI |e An OL _ ae O° NNN NNN] Re Re ee eR ee te RH eS Dvd CFO DAN Of!'O NN hd Gao bv NNNKHNHNNN WON KK ee tN aN ° DAN COLO QAN COR oN Nn Unb p On nn NNN bd NY NN ND NNYNN/DN NN HK HIDN MumnpbfSip Ummnp DAdn CLO QN OL b NO Ny Oppo np —-1O w ft oO 0 pe aL 'DAN COL O Det NNONN ) CONI OV Ad CLO ANH OL!1O0 NNN YN _— Plo WW Wd Gd WWW 1 [J I OO NY DN Nd INWWWWNNNN t Oo Nd WO Sc oO ty ° op NNN Ww Go Gd BW N= tN QQ a CoM OV nab BAW DN] Ans Cf O AWN tv QW OW Oo YNNNHNNNNHNNIN|NNNONDND G2 Ga Ga G2 WG G2 G2 Ga Go [Ga [Ga Ga Ga G2 Go MmbhHWW DN NN) Unb fHWW Yb Ar Cb ODN COL NNN HN | | OIDANK OHO QAN Of | | OININENN™NNNN™NDNSIN NN SIN OO N S oO SMITHSONIAN TABLES. 162 TABLE 33. FOR CONVERSION OF TIME INTO ARC. Hours of Time into Arc. Time. | Arc. | Time.| Arc. | Time. | Arc. | Time. | Arc. | Time. | = Oe ty Ww by Nn Rob & NWN ee Re bdo Ww bo tb N Oo ON AW Os Mmonmon -_ in O SO OMNI AW Awd EH -_ Oo v2 OnNdnMNnd 1 3 4 5 6 i 8 9 0 I 3 +t Www nh tr Lrtats W ~On A © ~~ = = e ome Onodnmnod Gm» _ momon _ WODOO © COMmOnNN NN OOO Quiiitin Mmomon ~ WO OND Oe mMomndm ws Od Oo Nn BABB WW db f wat ARH ° Ny oO ° ° ° Hundredths of a Second of Time into Arc. Hundredths of a Sec- ond of Time. . . “ SIN SN + nina Mmmm ENAOH DuwWNo — ee N™N ON bv SMITHSONIAN TABLES. TABLE 34. CONVERSION OF MEAN O10 ON Qui Wb ~ ng SNANAAAAAAO ar nb BO WN eR OWN HMnOWN Mnf & Or Rn OF 12 16 34 12 22 40 12 28 45 12 34 50 12 40 55 1247 I 12153) (6 I2 59 II 1315.16 13 reer TIME INTO SIDEREAL TIME. m 3 hmes 18 15 44 18 21 49 18 27 54 18 33 59 18 40 °5 18 46 10 TS G25 18 58 20 19 426 19 10 31 19 16 36 YNNONNNNHNN WN w NN Sw wm Wm MPO NS NOHO KH HNNN DN lio AN Oui kW bd AIF CON HO + Unt pb I 6 I 6 7 7 3 3 3 8 S 9 WWWWW WW MmMOW AOL Umnb BW NN CW COUW™ vim POL 13107127 13 23 32 13 29 37 13 35 42 13 41 48 13 47 53 13 53 58 14 0 3 14609 19 22 41 19 28 47 19 34 52 19 40 $7 1947 2 19 53 7 19 §9 13 20 5 18 2011523 op wa al PHBH BWW WG) OG) [G2 [Go Go G2 Ga GC) Ga Ga Ga Gd Mma #2 DD NN Se N CON REN HO QOWIOlnN Cn KeNR OD Nor ON AOS ONIN OO] ONINNNNN NTS IN Mme BOW NH He Ulin BOW db Nee ROmMmnmnme nb BOW Nee tn 0 W _ no HF oo f. NIN NACL ODN QOWN wn WODODOOOWOO0O UmApWW bh WN HN ee PW CW COn™N os 14 30 30 14 36 35 14 42 40 14 48 45 14 54 SI I5 056 Lie 27 eae 15 19 12 15 25 17 15 3! 15 37 15 43 15 49 15 554 16: W™ ty SfWW dnd = CU © 20 17 28 20 23 34 20 29 39 20 35 44 20 41 49 20 47 55 20 54 O Ord 610 12 16 Tove 6 | a al UW a 17 Ondo mn \o mWmbRWW bd Wminnf WW bd bv NN NNHONHNN NIH] OY YNHONONODNDD SHS ee RR et ee Mmmm HPHO!|Y!|N NY ee NCOP RNW OO DN/O|n = COL ONWO Mamma B DP PWO|N) YN = A OnN OR ANW OLD NON De ecere yen OWlAWNnnnnian & Bip MPH HAA BAL &ICOn DOWN WN _— NIN Rk OAR | | | | nraimnmmmnmnun Ini bp RW NN ee Unf PWW DN paleo ste Cn CwW™N | MWIOW AOL COv OO oO _ 17 14 SI 17 20 56 V7eeriae 1 Ae ef 17 39 12 17 45 17 17 51 23 17 57 28 18 3 33 18 9 38 18 15 44 NAGA OW QO/PN =NOWN & NON KF OKLA OM OM Unb WO NY] by] WW NN | NIN SYN HNN N NININ NN NH NNN Sie NNN NNN PIP PD BOW WWW WD ID IW NN NNN NIN) N YON HS SMITHSONIAN TABLES. Ww oO wm Example: Let the given mean time be 14> 57™ 32°.56. The table gives first for 14°54" 518) 27/27* then for 2 41 0.44 2 27-44 The sum 14" 57™ 32°.56 +-2™ 27°.44 = 15> 0™0* is the required sidereal time. TaBLe 35. CONVERSION OF SIDEREAL TIME INTO MEAN TIME. hm i s 18 18 44 OT ~ wr 12 18 35 | 18 24 50 I2 24 42 | 18 30 56 12 3048 | 18 37 2 12 36 $4 | 1843 9 I2 43 0| 18 4915 12/49) 77) || tors 5).21 T2555 3) Lon ue 27 13 FI9| 19 7 34 _13_ 725° |_ 19.43 49 13 13 31 |_19 19 46 13 19 38 | 19 25 52 13 25 44 | 19 31 59 13 31 50 | 1935 5 13 37 56] 19 4411 1344 3| 195017 13 50 9| 19 56 23 13 5615 | 20 230 LAbg2) 200 |" 2005330 14 828 | 2014 42 Mb BWW Nee On not OWN Munk WYNN WNNN He — BSAA EON [we 00 ON Qui bb & |W ON MAP BW NN] ele WN RP ON OQOWIN | R-fOW ACWN & nin &QW bee CONININISINISIN STIS IN DAAADADAAG NY HDQOWN HUnOWNi an _ ia wm oo a 14 20 40 14 26 46 14 32 53 14 38 59 1445 5 W4e Sh ur 14 57 18 Dkr 924: 15_9 30 15 15 30 15 21 43 15 27 49 15 33 55 15 40 I 15 46 8 T5 52 14 15 58 20 16 426 10 418] 1610 33 IO 10 24 Ne & ON DO mae I OO] AWOMNbh © OF ONQADF Umm fwWwW bd mb RWW ND He H=nOnN QOQWOLN Ne ON DAO nakbww dvd I CWmOmDnmnnme MnP WwwW bd bd NOWN PLA HPHAHLA HAIL HP HAAW ADRWWW NN DN] Se] i An No bn cS) Cpr Un in ANON we KH ON |W RNS ee NINN NI] NR vv 4 ON [e) tN te ne WYNN NI DOWN aM ON NN HWYNN MnP Wb OK N WO ° Minin & & & Go G& | Qlo0Mm nd Mh ANY I I I I I I I I I I I I 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 37 41 45 45 52 56 59 3 nin & BONN OW AWf Mb OV 7 DIe365 17 17 41 17 23 47 17 29 54 17 30 0 17 42 6 17 48 12 17 54 19 18 025 18 631 18 12 37 18 18 44 NOMA (Alanna nip BOG) bw = = CnlAOWN Kf CON OV G2 o Example: Given 15" 0™o%. The table gives first for 14% 57™18* or a then for 2 42 0.44 Iv Jo #0 2 27.44 The difference 15° 0™ o* — 2™27°.44 = 14 57™ 32".56 is the required mean time. WARP PWN NFS OORN RNnNOWN AN num BW N MIOn QOWN MN RP BO Wo WW GW [Kn [Gn GH) ae MP PWWIN| = CON DOF ON DOWN “MN MWPWW NN Nn OOWN =f sale NNNKHNHNNNNIKRIN NNNNNNNN DO AnMnMmn vin |n AHAHAAAH _ - tv > wn oo SMITHSONIAN TABLES. 165 TABLE 36. LENGTH OF ONE DECREE OF THE MERIDIAN AT DIFFERENT LATITUDES. (Derivation of table explained on pp. xlvi-xlviii.] Geographic Geographic Latitude.| Metres. aeue Miles. Latitude.| Metres. sae Miles. es: 11’ of the Eq. * |1’ of the Eq. 110568.5 | 68.703 59-594 45° | 111132.1 | 69.054 59-898 o° I 110568.8 68.704 59-594 46 IIIIS1.9 69.067 59.908 2 110569.8 68.705 59-595 47 IIII71.6 69.079 59-919 3 IIOS71.5 68.706 59-590 48 IITIQI.3 69.091 59-929 4 110573-9 | 68.707 592597 49 III210.9 | 69.103 59-940 5 110577.0 68.709 59.598 50 III230.5 | 69.115 59-951 6 110580.7 68.711 59.600 SI I11249.9 69.127 59.901 7 I105985.1 68.714 59-603 52 111269.2 69.139 59-972 38 110590.2 68.717 59-606 53 111288.3 69.151 59.982 9 110595.9 68.721 59.609 54 111307.3 69.163 59-992 10 110602.3 | 68.725 59-612 55 I11326.0 | 69.175 60.002 II 110609.3 68.729 59-616 56 111344.5 69.186 60.012 12 I10617.0 68.734 59.620 57 111 362.7 69.198 60.022 13 110625.3 68.739 59.625 58 111380.7 69.209 60.032 14 110634.2 68.745 59-629 59 111398.4 | 69.220 60.041 15 110643.7 68.751 59-634 60 III415.7 69.230 60.051 16 110653.8 68.757 59-640 61 111432.7 69.241 60.060 17 110664.5 68.763 59-646 62 111449.4 69.251 60.069 18 11067 5.7 68.770 59.652 63 111465.7 69.261 60.077 19 110687.5 | 68.778 59.658 64 111481.5 | 69.271 60.086 20 110699.9 | 68.786 59-665 65 T11497.0 | 69.281 60.094 21 110712.8 68.794 59-672 66 II1512.0 69.290 60.102 22 110726.2 68.802 59-679 67 I11526.5 69.299 60.110 2 1107 40.1 68.810 59.686 63 III 540.5 69.308 60.118 2 110754.4 68.819 59-694 69 II1554.1 69.316 60.125 29 110769.2 68.829 59.702 70 I11567.1 69.324 60.132 26 110784.5 68.838 59-710 71 I11579.7 69.332 60.139 Z 110800.2 68.848 59.719 2 IIIS591.6 69.340 60.145 28 110816.3 | 68.858 59-727 73 I11603.0 | 69.347 60.151 2 110832.5 68.868 59-730 74 II 1613.9 69.354 60.157 30 110849.7 68.879 59-745 75 I11624.1 69.360 60.167 31 110866.9 68.889 59-755 76 111633.8 69.366 60.16 32 110884.4 68.900 59.704 By) 111642.8 69.372 60.173 33 110902.3 68.911 59-774 78 I11651.2 69.377 60.177 34 110920.4 | 68.923 59-734. 79 I11659.0 | 69.382 60.182 35 110938.8 68.934 59-794 80 111666.2 69.386 60.186 36 110957.4 68.946 59.804 81 111672.6 69.390 60.189 7, 110976.3 | 68.957 59.814 82 111678.5 | 69.394 60.192 38 110995.3 68.969 59.824 83 111683.6 69.397 60.195 39 IIIO14.5 68.981 59.834 84 111688.1 69.400 60.197 40 I11033.9 68.993 59-845 85 II1691.9 | 69.402 60.199 41 I11053.4 69.005 59.855 86 I11695.0 69.404 60.201 2 11107 3.0 69.017 59.866 87 111697.4 69.405 60.202 43 I11092.6 69.029 59.876 88 I11699.2 69.407 60.203 44 II1112.4 69.042 59-887 89 I11700.2 69.407 60.204 45 III132.1 69.054 59-898 90 I11700.6 | 69.407 60.204 SMITHSONIAN TABLES. 166 TABLE 37. LENGTH OF ONE DECREE OF THE PARALLEL AT DIFFERENT LATITUDES. [Derivation of table explained on p. xlix.] Latitude.| Metres. ° I1I321.9 111 305-2 111254.6 III170.4 I11052.6 ITOQOT.2 110716.2 110497-7 110245.8 109960. 5 109641.9 109290.I 108905.2 108487.3 108036.6 WOON AGM #FWNH OS 107 553-1 107037.0 106488. 5 105907-7 105294-7 104649.8 10397 3-2 103265.0 T0257 54 101754.6 100953-0 100120.6 99257.8 98364.8 97441-9 96489.3 95507-3 94496.2 93456.3 92387-9 QI291.3 g0166.8 8901 4.8 87835-6 86629.6 85397-0 84138.4 82854.0 81544-2 80209.4 788 50.0 Statute Miles. 69.171 69.162 69.130 69.078 69.005 68.911 68.796 68.660 68.503 68.326 68.128 67.909 67.670 67.411 67.131 66.830 66.510 66.169 65.808 65-427 65.026 64.606 64.166 63-706 63.227 62.729 62.212 61.676 61.121 60.548 59-956 59-345 58-717 58.071 57-407 56.726 56.027 Earl 54-578 53-329 53-063 2.281 51.483 50.669 49.840 48.995 Geographic Miles. Latitude. 1’ of the Eq. 60.000 59-991 59-964 59-91 8 59-355 59-773 59-673 59-550 59-420 59-266 59-095 55-905 58.697 58.472 58.229 57-969 57-690 57-395 57.082 56.751 56.404 56.039 55-657 55-259 54-843 54-411 53-963 53-498 53-016 52-519 52.006 51-476 50.931 50.371 49-795 49.204 48.598 47-977 47-341 46.691 46.027 45-349 44-650 43-950 43-231 42.498 Metres. 788 50.0 77466.5 76059.2 74628.5 73174-9 71698.9 70200.8 68681.1 67140.3 65578.3 63997-1 62395-7 6077 5.1 59135-7 57478-1 55802.8 54110.2 §2400.9 5067 5-4 48934-3 47178.0 45407-1 436022.2 41823.8 4001 2.4 38188.6 36353:0 34500.2 32648.6 30780.9 28903.6 Statute Miles. 48.995 48.135 47.261 46.372 45-469 44-552 43-621 42.676 41.719 40.749 39-766 38-771 37-764 36-745 35-715 34-674 33.622 32-560 31.488 30.406 29.315 28.215 27-106 25-988 24.862 23-729 22.589 21.441 20.287 19.126 17.960 16.788 15.611 14.428 13.242 12.051 10.857 9.659 Geographic Miles. 1’ of the Eq. 42.498 41.753 40.994 40.223 39-440 38.644 37-837 37.018 30.187 35-346 34-493 33-630 32-757 31.873 39-979 30.076 29.164 28.243 27.313 26.374 25.428 24-473 2z-Rit 22.542 21.566 20.583 19.593 18.598 17-597 16.590 15-578 14.562 13.541 12.515 11.486 10.453 9.417 8.378 7-337 6.293 5-247 4.200 3.151 2.101 1.051 0.000 J SMITHSONIAN TABLES. 167 TABLE 38. INTERCONVERSION OF NAUTICAL AND STATUTE MILES. 1 nautical mile * = 6080.27 feet. Nautical Miles. Statute Miles. Statute Miles. Nautical Miles. 0.8684 1.7368 2.6052 3-47 36 4.3420 5.2104 6.0788 6.9472 7.3155 WOON AD AW WOON AM Awd SMITHSONIAN TABLEs. * As defined by the United States Coast and Geodetic Survey. TABLE 39. CONTINENTAL MEASURES OF LENCTH WITH THEIR METRIC AND ENCLISH EQUIVALENTS. The asterisk (*) indicates that the measure is obsolete or seldom used. Measure. Metric Equivalent.| English Equivalent. El, Netherlands . . BLY a eee I metre. 3-2808 feet. Fathom, Swedish—=6feett ...... 1.7814 5.8445 Foot, Austrian, tte or eee 0.31608 1.0370 Old Brench®s.4 4, soe os ee 0.32484 1.0057 Russian . . 0.30480 I Rheinlandisch or * Rhenish (Prussia, Denmark, Norway)* .... . 0.31385 1.0297 SO WECISD EE mee, eo es ach dol hs 0.2969 0.9741 Spanish *——sivarage 4... Geb wos 2 0.2786 0.9140 *Klafter, Wiener cuicuna A ee 1.89648 6.2221 *Line, old French = =i foot ..... 0.22558 cm. 0.0888 inch. Mile, Austrian post*= 24000 feet. . . . 7.58594 km. 4.714 statute miles. “ “ German sea. 2 eee: 4 852 1.1508 Swedish = 36000 (ct ee 10.69 ee 6.642 Norwesian'— 36000 feet > ae 5. 11.2986 7.02 Netherlands \(mij]) ie core oe eee I 0.6214 Prussian aE? of eS) se ate Oe 7.500 4.660 Danish: 7: Saas Rs 7.5324 4.6804 Palm, Netherlands: <-> 3.'%.)) @s. ses O.1 : 0.3281 feet. *Rode, Danish. . Com sft As 3.7662 12:350N an *Ruthe, Prussian, Norwegian . Siuptee be sotut 3.7662 12.356 Sagene, Russian : Ase ane ene 2.1336 7 *Toise, old French=6 feet... . . . 1.9490 6.3943 *Vara, Spanish. . . eet ics tot Ie bal 0.8359 2.7424 Mexican . . ‘ 0.83 Werst, or versta, Russian = 500 sagene | ; 1.0068 SMITHSONIAN TABLES. 168 TaBLe 40. ACCELERATION (g) OF GRAVITY ON SURFACE OF EARTH AND DERIVED FUNCTIONS. &=9.77989 + 0.05221 sin? = 9.80599 — 0.02610 cos 2 metres.* ¢ = geographical latitude. Metres. 9.7798 8.70864-10 -7803 862 7814 857 -7834 -7859 -7893 7929 -7969 So14 8060 S105 S150 SOI .8227 8261 SMITHSONIAN TABLES. * From The Solar Parallax and its Related Constants, by Wm. Harkness, Professor of Mathematics, U. S.N.; Washington: Government Printing Office, 1891. + This is length of seconds pendulum. 169 TABLE 41. LINEAR EXPANSIONS OF PRINCIPAL METALS, IN ene PER METRE (OR MILLIONTHS PER UNIT LENGTH) Expansion per | Expansion per degree C. Name of metal. Aluminum Brass Copper . Glass Gold Tron; caSt,..5- Iron, wrought Lead , Platinum , Platinum- iridium p Silver . rae Steel, hard Steel, soft . Tin Zinc. ADAH AUK AAMUY MAH DONNA HOO — SMITHSONIAN TABLES. : . 1 Of International Prototype Metres. TABLE 42. FRACTIONAL CHANCE IN A NUMBER CORRESPONDING TO A CHANCE IN ITS LOCARITHM. Computed from the formula, AN _ Alog NV Na KB i #4 = modulus of common logarithms = 0.43429448. For For AN A log V A log V =I unit in = 4 units in (in round numbers) 4th place 4th place Woo pth Sthe qaban 6th “ 6th “* wth « 7th Toosd00 SMITHSONIAN TABLES. 170 APPENDIX. CONSTANTS. Numerical Constants. Base of natural (Napierian) logarithms, Log ¢, modulus of common logarithms, Circumference of circle in degrees, c « « in minutes, in seconds, Circumference of circle, diameter unity, “ “a “ Number. Logarithm. 2m = 6.2831853 0.7981799 " = 1.0471976 — 0.0200286 T — 0.3183099 ~—-_ 95028501 — 10 T mr = 9.8696044 0.9942997 The arc of a circle equal to its radius is in degrees, p? = 180/m in minutes, p’ = 60 p® in seconds, p” = 60 p’ For a circle of unit radius, the arc of 1° —=1T/po arc of 1’ = I/p arc (or sine) of 1”= 1/p” Geodetical Constants. Equatorial semi-axis in feet, in miles, Polar semi-axis in feet, in miles, a? — 3 a (Eccentricity)? = Biavenae = Perimeter of meridian ellipse, Circumference of equator, Area of earth’s surface, Mean density of the earth (HARKNESS) Surface density “ ‘“ “ Acceleration of gravity (HARKNESS) : g, at poles SMITHSONIAN TABLES. Number. =e = 2.7182818 = = 0.4342945 = 360 — 21600 = 1296000 = 3.14159265 1/x? = 0.1013212 1-7724539 — = 0.5641896 <= a| I = 1.4142136 = 1.7320508 3437-7468 206264.8” = 0.0174533 = 0.0002909 = 0.0000048 5 = a = 20926062. =a= 39633 = 6 = 20855121. =b6= 39498 e2 = 0,00676866 = f = 1/294.9784 57-29578° Logarithm. 0-4342945 9.6377843 — 10 2.5563025 4-3344538 6.1126050 0.4971499 g.0057003 — 10 0.2485749 9.7514251 — 10 0.1505150 0.238 5607 1.7581226 3-5362739 5-3144251 8.2418774 — 10 6.4637261 — 10 4-6855749 — 10 Dimensions of the earth (Clarke’s spheroid, 1866) and derived quantities. 7.320687 § 3-5980536 7.3192127 3-5965788 7.8305030 — Io 7.5302098 — 10 = 24859.76 miles. = 24901.96 = 196940400 square miles. = 5.576 0.016. = 2.56 £0.16. = 981.17. 171 g (cm. per second) = 980.60 (1 — 0.002662 cos 29) for latitude ¢ and sea level. g at equator = 977.99; g, at Washington = 980.07 ; g, at Paris = 980.94 ; = 983.21; g, at Greenwich Length of the seconds pendulum (HARKNESS) : 1 = 39.012540 + 0.208268 sin? p inches = 0.990910 ++ 0.005290 sin? @ metres. APPENDIX. CONSTANTS. -— Continued. ' Astronomical Constants (Harkngss). Sidereal year = 365.256 357 8 mean solar days. Sidereal day = 23% 56 4.s100 mean solar time. Mean solar day = 244 3 56.5546 sidereal time. Mean distance of the earth from the sun = 92 800 000 miles. Physical Constants. Velocity of light (HARKNEsS) = 186 337 miles per second = 299 878 km. per second. Velocity of sound through dry air = 1090 »/ 1 + 0.00367 ¢° C. feet per second. Weight of distilled water, free from air, barometer 30 inches : Weight in grains. Weight in grammes. Volume. 62° F. AG. 62° F. 4° C. 1 cubic inch (determination of 1890) 252.286 252.568 16.3479 16.3662 1 cubic centimetre (1890) 15-3953. 15-4125 0.9976 0.9987 1 cubic foot (1890) at 62° /. 62.2786 lbs. A standard atmosphere is the pressure of a vertical column of pure mercury whose height is 760 mm. and temperature 0° C., under standare gravity at latitude 45° and at sea level. 1 standard atmosphere = 1033 grammes per sq. cm. = 14.7 pounds per sq. inch. Pressure of mercurial column 1 inch high = 34.5 grammes per sq. cm. = 0.491 pounds per sq. inch. Weight of dry air (containing 0.0004 of its weight of carbonic acid) : 1 cubic centimetre at temperature 32° /. and pressure 760 mm. and under the standard value of gravity weighs 0.001 29305 gramme. Density of mercury at 0° C. (compared with water of maximum density under atmos- pheric pressure) = 13.5956. Freezing point of mercury = — 38.°5 C. (REGNAULT, 1862.) Coefficient of expansion of air (at const. pressure of 760%) for 1° C. (DO.): 0.003 670. Coefficient of expansion of mercury for Centigrade temperatures (BROCH) : A = A, (1 — 0.000 181 792 ¢ — 0.000 000 000 175 £2 — .000 000 000 035 116 #°), Coefficient of linear expansion of brass for 1° C., B = 0.000 0174 to 0.000 O10. Coefficient of cubical expansion of glass for 1° C., y = 0.000 021 to 0.000 028. Ordinary glass (RECKNAGEL) : at 10° C., yy = 0.000 0255 ; at 100°, y = 0.000 0276. Specific heat of dry air compared with an equal weight of water : at constant pressure, Ay = 0.2374 (from 0° to 100° C., REGNAULT). at constant volume, Ay = 0.1689. Ratio of the two specific heats of air (RONTGEN): A% /Av = 1.4053. gramme. cm. sec. [The quantity of heat that passes in unit time through unit area of a plate of unit thickness, when its opposite faces differ in temperature by one degree. ] Thermal conductivity of air (GRAETZ) : 4 = 0.000 0484 (1 + 0.001 85 2°, C.) Latent heat of liquefaction of ice (BUNSEN) = 80.025 mass degrees, C. Latent heat of vaporization of water = 606.5 — 0.695 7° C. Absolute zero of temperature (THOMSON, Heat, Excyc. Brit.) : — 273.°0 C. = — 459.°4 F. Mechanical equivalent of heat : * 1 pound-degree, /. (the British thermal unit) = about 778 foot-pounds. I pound-degree, C. = 1400 foot-pounds. 1 calorie or kilogramme-degree, C. = 3087 foot-pounds = 426.8 kilogram- metres = 4187 joules (for g = 981 cm.). SMITHSONIAN TABLES. * Based on Prof. Rowland’s determinations. (Proc. Am. Acad. Arts and Sci., 1880.) 172 APPENDIX. SYNOPTIC CONVERSION OF ENCLISH AND METRIC UNITS. English to Metric. Units of length. inch. foot. yard. mile. Units of area. square inch. square foot. square yard. acre. square mile. “ Units of volume. cubic inch. cubic foot. cubic yard. Units of capacity. Metric equivalents. 2.54000 0.304801 0.914402 1.60935 6.45163 929.034 0.836131 0.404687 2.59000 259.000 16.3872 0.028317 0.764559 gallon (U. S.) = 231 cubic inches. quart (U. S.). Imperial gallon (British). 277.463 cubic inches (1890). bushel (U. S.) = 2150.42 cubic inches. bushel (British). Units of mass. grain. pound avoirdupois. ounce avoirdupois. ounce troy. ton (2240 Ibs.). ton ee lbs.). 64.7990 0.453593 28.3496 BY O35 1.01605 0.907186 centimetres. metre. “ kilometres. square centimetres. “ “ square metre. hectares. square kilometres. hectares. cubic centimetres. cubic metres or steres. cubic metres or steres. 3-78544 litres. ee litres. 4.54683 litres. 35-2393 litres. 36.3477 litres. milligrammes. kilogrammes. grammes. grammes. tonnes. tonnes. Logarithms. 0.404 835 9.484 016 — 10 9.961 137 — 10 0.206 650 0.809 669 2.968 032 9-922 274 — 10 9.607 120 — Io 0.413 300 2.413 300 1.214 504 8.452 047 — Io 9.883 411 — 10 0.578 116 9.976 056 — Io 0.657 709 1.547 027 1.560 477 1.811 568 9.656 666 — Io 1.452 546 1.492 810 0.006 914 9.957 696 — 10 Units of velocity. foot per sec. (0.6818 miles per hr.) = 0.30480 metres per sec. 1.0973 km. per hr. mile per hr. (1.4667 feet per sec.) = 0.44704 metres per sec. 1.6093 km. per hr. Units of force. I poundal. Weight of 1 grain (for ¢ = 981 cm.). Weight of 1 pound av. (for g = 981 cm.). 4.140 682 1.803 237 5.645 335 13825.5 dynes. 63.57 dynes. 4.45 X 10° dynes. Units of stress —in gravitation measure. I pound per square inch = 70.307 grammes per sq. centimetre. 1 pound per square foot = 4.5824 kilogrammes per sq. metre. 1.846 997 0.688 634 Units of work—in absolute measure. 1 foot-poundal. 421 403 ergs. 5-624 698 —in gravitation measure. 1 foot-pound (for g = 981 cm.) = 1356.3 X 104 ergs = 0.138255 kilogram-metres. Units of activity (rate of doing work). 1 foot-pound per minute (for g = 981 cm.) = 0.022605 watts. 1 horse-power (33 000 foot-pounds per min.) = 746 wa s = 1.01387 force de cheval. Units of heat. I pound-degree, /. mal] calories or gramme-degrees, C. I pound-degree, C. 8 pound-degrees, / SMITHSONIAN TABLES. 173 | | APPENDIX. SYNOPTIC CONVERSION OF ENCLISH AND METRIC UNITS. Units of length. I metre (10° microns). “ce “ 1 kilometre. Units of area. I square centimetre. I square metre. oe “ 1 hectare. 1 square kilometre. Units of volume. I cubic centimetre. 1 cubic metre or stére. “ce “c “ Units of capacity. 1 litre (61.023 cubic inches). “ “ 1 hectolitre. “ Units of mass. I gramme. 1 kilogramme. “ “ I tonne. “ Units of velocity. I metre per second. “ “c “ 1 km. per hr. (0.2778 m. per sec.). Units of force. Metric to English. English equivalents. 39-3700 3-28083 1.09361 0.62137 0.15500 10.7639 Te19599 2.47104 0.38610 0.0610234 35-3145 1.30794 0.26417 1.05068 0.21993 2.83774 2.75121 15-4324 2.20462 35-2739 32.1507 0.98421 1.10231 3.2808 2.2309 0.62137 inches. feet. yards. miles. square inches. square feet. square yards. acres. square miles. cubic inches. cubic feet. cubic yards. gallons (U. S.). quarts (U.S.). Imp. gallons (British). bushels (U. S.). bushels (British). grains. pounds avoirdupois. ounces avoirdupois. ounces troy. tons (2240 lbs.). tons (2000 lbs.). feet per second. miles per hour. miles per hour. Logarithms. 1.595 165 0.515 984 0.038 863 9-793 350 — 10 9-190 331 — Io 1.031 968 0.077 726 0.392 880 9.586 701 — 10 8.785 496 — Io 1.547 953 0.116 589 9.421 884 — 10 0.023 944 9.342 291 — 10 0.452 973 0.439 523 1.188 433 0-343 334 1.547 454 1.507 190 9-993 086 — Io 0.042 304 0.515 934 0.349 653 9:793 350 — 10 1 dyne (weight of (981)! grammes, for ¢ = 981 cm.) = 7.2330 X 1075 poundals. Units of stress —in gravitation measure. 0 014223 pounds per sq. inch. 0.204817 pounds per sq. foot. I gramme per Square centimetre. 1 kilogramme per square metre. I standard atmosphere. Units of work —in absolute measure. I erg. 14.7 pounds per sq. inch. 2.3730 X 10-® foot poundals. I megalerg = 10° ergs; 1 joule = 107 ergs. —in gravitation measure. 1 kilogramme-metre (for ¢ = 981 cm.) = Units of activity (rate of doing work). I watt = 1 joule per sec. (= 44.2385 foot-pounds per minute, for g = 981 cm.) = 0.10194 kilogramme-metre per sec., for ¢ = 981 cm. I force de cheval = 75 kilogramme- metres per sec Units of heat. I calorie or kilogramme-degree = 3.968 pound-degrees, /. = 2.2046 pound-degrees, C. 1 small calorie or therm, or gramme-degree = 0.001 calorie or kilogramme-degree. SMITHSONIAN TABLES. 174 (See def. p. 172.) g8I X 10° ergs = 7.2330 foot-pounds. = 735} watts = 0.98632 horse-power. APPENDIX. DIMENSIONS OF PHYSICAL QUANTITIES. L = length; M = mass; T = time. Quantity. Dimensions Quantity. Area. [L?] Momentum. Dimensions. [LM T~4] Volume. [L*] Moment of Inertia. [M L?] Mass. [M] Force. [LM T~] Density. [M L?] Stress (per unit area). [iat Mi Te] Velocity. [L T7] Work or Energy. [L? M T~*] Acceleration. [LT] Rate of Working (Power). [L? M T~*] Angle. [o] Heat. [L? M T~] Angular Velocity. [TJ Thermal Conductivity. [L¢ MT 4 In Electrostatics. Quantity of Electricity. Surface Density: quantity per unit area. Difference of Potential: quantity of work required to move a quantity of electricity; (work done) ~ (quan- tity moved). Electric Force, or Electro-motive Intensity: (quantity) — (distance?). Capacity of an accumulator: e+ £. Specific Inductive Capacity. In Magnetics. Quantity of Magnetism, or Strength of Pole. Strength or Intensity of Field: (quantity) — (distance?). Magnetic Force. Magnetic Moment: (quantity) X (length). Intensity of Magnetization: magnetic moment per unit volume. Magnetic Potential: work done in moving a quantity of magnetism ; (work done) + (quantity moved). Magnetic Inductive Capacity. In Electro-magnetics. Intensity of Current. Quantity of Electricity conveyed by current: (intensity) X (time). Potential, or difference of potential: (work done) + (quantity of electricity upon which work is done). Electric Force: the mechanical force act- ing on electro-magnetic unit of quantity ; (mechanical force) + (quantity). Resistance of aconductor: Zz. Capacity: quantity of electricity stored up per unit potential-difference produced by it. Specific Conductivity: the intensity of current passing across unit area under the action of unit electric force. Specific Resistance: the reciprocal of specific conductivity. SMITHSONIAN TABLES. 175 Dimensions in Symbol. electrostatic system. é [L? M} T—] o [L mM? T7y E [L? M? T7] [L? MT] [L] [o] Dimensions in electro-magnetic system. [L? M? T7] [L Mt T-2] [L> mM? T7] [L? M? T7] [LM T7] [L} M T-4] Ke [o] Dimensions in Name of electro-magnetic practical unit. system. [L}M! T—] ~—- Ampére. [L} M?] Coulomb. [Li M? T=] Volt. [L? M? T2] Pit] Ea [LT] [L? Te] INDEX. PAGE Acceleration, dimensions of............+. 175 of gravity, formula for......-.secee.-s17I table of values of........... spaceltee) Air, cubical expansion, specific heat, thermal conductivity, and weight of.............. 172 Airy, Sir George, treatise cited...........xcviii Albrecht, Dr. Th., treatise cited.......... ]xxx Algebraic formulas..... Piaeisre cepts «+. Xili-xv PAIOMMENT CULV E% ia sieves le|= < «101 cisinl~ 21- ae teheteerore lvi Aluminum, linear expansion of...........- 170 Ampére, dimensions of.............+++++: 175 Angles, equivalents in arcs .......... sfepete VILL sum of, in spheroidal triangle...... selon VAl Angular velocity, dimensions of .........--175 Amnuluss circular jarea, OL sm)... 6 o<1 450 SRK Antilogarithms, explanation of use of ..... XC1x A-plaCeutapley OL ericiarsveleieiiclsclers elelsi<1-1= 26, 27 PRAIONICIR ee oa otaasnisiniciche'w siernfaie.€ Yorstevaters 171-175 Arcs, equivalents in angles.............-.-XVil of meridians and parallels.......... xlvi-l table of lengths of meridional....... 78-80 table of lengths of parallel....... .- 81-83 table of time equivalents............-- 162 STOR an aera Nelle taleiove etcleieloisle/eiel1s!oiereie!s sieleiel= xli VATE ANGE GILG le maiaielereicielel cle! Veis/ Ixxii PASTLOHODIY, «om. «ioicie's 01enie slaineisin ve ele Ixvii-]xxxii references to works on .......-..-+- 1xxxii Atmosphere, mass of earth’s........-.+++: Ixvi standard pressure of ............---.- 172 weight of unit of volume of.......---- 172 Average error, definition of .........--- 1xxxiv Azimuth, astronomical and geodetic........ lvii computation of differences of...... Iviii-}xi determination of..........++. inet atatere {xxix PAGE Babinet, barometric formula of............160 Barometer, heights by: ......-...- perise tO Binomial series..... crarSlcishe ohetsiehete salelevetet «XLV: Brass, linear expansion of........... eel ZO Briinnow, F., treatise cited.............. lxxxii Bushel, Winchester.......... Sioth, Statecstotne. = XXXV Equivalent ine Wires. 0 elelelelelo vere ereiereeete oe Gablemlengith er casleretersiesietere eieietets ore sishale SKULL Calorieyavalerofscrterrate citarsets fotcteleter cette art bi7 2: Capacity, measures of, British..........xxxviil MICErICe., tevoxnerstcrevskernctonneisretelerers reste XL) Centar rivers eis ches creveis crs cee Sioteleraveinereve xli Chauvenet, Wm., treatise cited.......... 1xxxil Circumference,of circles... cece ccieces XXvVili table of values of ..... Beet ieraterct te 23 Otgearthinece sr mferereicVcicretat tetaieiore ate XL Kel 7 ofsellipse aera cities ae leetsseieiesicte cere eters XXxix CG: SasyStemi Ob UMIts icteric sss steielere oie stele xlii Clarke, General A. R., spheroid of ........ xliii trEatiSencited'y sir -/scic/eeheierefeners siete are Ixvi Coefficient, of cubical expansion of air and IME KCULYteleieloisistet=te Bsteiveteiereteteteiett erecta 172 of linear expansion of metals.......... 170 Ofsrefia ctlOulsreteatectstelale cites sfelicisisierste Ixiii Gompressiony Ole calityerrscvcicreiseiete co cveriol-te xliii Computation, of differences of latitude, lon- PitUde yan GAZIMUEN 6 cree yereleie! marviele(el eto mionye lviii of mean and probable errors .......... XCV Conductivity, thermal, of air.............. 172 Cone; surface Of:... -. Js. 0s elsta oustersnsiotosere XXxXi VOLUMELOL saree lareiercin Stelecelelatelen(cletaieleiets XXXii Gonstants,;astronomiCall ceri. leiete ire iierater ts 172 PEOCELCAl oie ieinini-)... ........... Ixvii fOr Projection Of Maps... <2 .....s-- liii-lvi table of, scale 1/250000......... 84-91 table of, scale 1/125000........ g2-I01 178 Co-ordinates (continued). table of, scale 1/126720....... 102-109 table of, scale 1/63360........ 110-121 table of, scale 1/200000 .......122-131 table of, scale 1/80000 ........ 132-141 of generating ellipse of earth’s spheroid. .xliv Copper, linear expansion of...........-. ael7O Cords(of wood); volume \Of ce ca onic or XXxix Correction, for astronomical refraction, table of mean values of.. eletteLOl to observed angle for eccentric position Of instruments... cbisceteeiieeiretactetarye lxili to reduce measured base to sea level... 1xiv Cosines, tablecotinaturalicnacccewcissic +6 Ra20; 2 use of tableiexplained!)< <)-'sc:cic,0. «ee c Cotangents, table of natural ...... apoio 30, 31 use of stablejexplained sci. j-\civestarere'- c Coulomb, dimensions of.......... Nato te 175 Cubature, of volumes......... sloistetertelever XXL Cubes, ‘table votstiacrerescteretaresste esoteric eters 4-22 Cube ‘roots, tablevobs ccc esses Tare ehere —22 Cylinder, surface of........ seleciee eee XXX] VOIUMCIOL. 2 cisiasioers teleieettien canes XXxil Day, sidereal and solar............. oLxxil; 17-2 Degrees, number of, in unit radius ........xviii of terrestrial meridian..... ahiowee XLVI; LOO ofAerrestrial parallele cc 1-7...10) . -xlix, 167 Density, mean, Of earth’... icteiiesiciersiete'e eee LX mean, of superficial strata of earth .....1xv OLMMEN CUT cixciovelecsiatoteroicteyeichotetolelelctosel atere 172 Departures (and latitudes), table of...... 32-47 mode of use of table explained ...... c Depths, average, Of OCEANS). csicicleiarei cisieie cuete Ixv Determination, of azimuth......5......06 Ixxix of heights, | by barometers 1.s1ctreiereretes 160 by trigonometric leveling........ -1xi Of latitude? sc svtemectacras sterestere ielerero XXVIL Of TMC 4.0%. aie care tlaeeioeivacr sete ae ef CXLY, Difference, between astronomical and geo- detic:azimuth/...< <2... aia atoisna/siaiacd-s wtateleiere lvii of heights, by barometer... ....'.22... 0% 160 by trigonometric leveling.......... Ixi Differences, of latitude, longitude, and azi- muth, on earth’s spheroid ..... afofetsrsetetets lviii table for computation of........ 70-77 Differential formulas =). o.,- ciscitere opsieteron sete XXi Dimensions, Of Carth 12%. cicjciecieeece's ae che xliii, 171 ot physical quantities |. << cjec e's siete 'reie.c 175 Dip; of sea: horizon... ©...405 ene eer Ixiil Distance, of sea horizon .......... of akere hella of sun from: @arth....0:0. . <,c7<.0e a0 saber veka 172 Doolittle, Prof. C. L., treatise cited.......1xxxii eee ee aE EEE ann USSEEEEnSSSEnInSEISIESSSESERSR SERRE INDEX. © Earth (continued). density Ofy.acicmceiem ieee sere dimensions .O£ 5. x45 a =x» «i-'= dine ellipticity (Of...) , «<'clet «KEI EXAM Pler Oke. cieeisisislele'erei= viele ojeve + XXII Magnetic quantities, dimensions of ........175 Maps, co-ordinates for projection of (see Co-ordinates for projection of maps) ..++.+..liii projection of....... eicleleteieteloreitelcieltietere cli Mass, of earth of earth’s atmosphere <2... .0 «since cee IXVI of Prototype Kilogrammes Nos. 4 and 20 Peeierete craiateielar cin stetenroters oeieeiraeer ex Mayer’s formula for transit instrument ....lxxv Mean, arithmetic and geometric ...........Xiii Mean distance of earth from sun..........172 Mean error, definition Of... «0. ccs eceisicl eI XXXIV ConIputation Gb < «cas .cdens asmanente aes XCV Mean times... ccc ee Siajareratele! sisheleiares «es )Xxii table for conversion to sidereal time 164 Measuresies .c.ciocie a aiieaels Bieverevelerelele eX, of capacity, British..... eteleretsy= aieie eo XXX VIIE MEtriGnn seemis er eit niotncrinclalcie store xli Of length Britishisien acces vic aise es XXXVI] Continentallw...tcasvclziec cic ici cio Oes ICG Crersectaleratatarcrele ais aie wiaiiciemie stow IA 180 Measures (continued). Of surface Britishacesee sees cesses xxXULL DWetrie te ctstnisrpetatee or Aen eas conceal tables for interconversion of..2, 3, 173, 174 Mechanical equivalent of heat............. 172 Mechanical units, dimensions of..........-175 BECOSUFAUOD: wisc excise aciseee Sep e XXVili-xxxiii Mercury, density and cubical expansion of. .172 Meridian, arcs of terrestrial .............. xl vi tablejof lengths ofr. cias -\ 43. CO Ee Ca yer arse ae i bight cae a) elena nem ae 44. “« & 6h and oe zs «“ Sg” bay (cht GMs eee Man tals as, « Seana ete i ee 46. ie. Mee and éat & fractional valuesofx . . . 47. Probability of errors of observation . . .-. «© + © *'+ «© « + « 48 “ “cs “ce “cc “ < . . . . . . . . . . . . 49. Values of 0.6745 50. ar. 52. 53: 54- 55: 56. 57: 58. 59: 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70: 71. 72. 73: 74. “ Cross section and weight of copper, iron, and ee wire of Paireren “ “ “ TABLE OF CONTENTS. n(n—1) - h ee I o84sa\/ ; ie n/n—t1 i the logarithm of the gamma function re) for values of 2 between 1 and 2 the first seven zonal harmonics on gi oe to 6908, log M/4x7V aa! for facilitating the calculation of the mutual inductance between two coaxial circles - 2(1—sin’dsin*d) “Ue for different values of 6 with the loga- rithms of these integrals . . . diameters, British units Cross section and weight of copper, iron, atid brass wire op ceterent diameters, metric units Cross section and weight in various Gaile of eae wires of ‘differ- ent diameters Cross section and Rte in various Gute of platinum wires oe nifeeae diameters . Cross section and Teen in various one of ead wires of eed diameters... . aac Cross section and Weiohit in various units of ieee wires co different GUIAMELELS tal ol 3 ou 'syh', » : Weight, in grammes per square metre, ai nee fetal “ce “ec various British units, of sheet metal . Size, weight, and electrical constants of copper wire aecardine to Brome and Sharp’s gauge and British measure . Same data as 65, but in metric measure ce ce “ “c “ ec GS ‘* 67, but in metric measure “ 65, but Birmingham wire gauge “ 69, but in metric measure Strength of materials : (a) Metals and alloys . (6) Stones and bricks . (c) Timber Composition and phyeieal pranene sai peel Effect of the reduction of section ak rolling on the Benet of bar iron Effect of meee on die cee BE ce iron but British standard wire gauge vii 36 37 37 on 38 40 42 43 44 46 48 50 52 54 56 57 58 60 62 64 66 68 7O 79° 7° qin 72 72 go. gI. 92. 93- 94. 95: 96. 97- 99. Ioo. Iol. rO2. 103. 104. 105. 106. 107. 108. 109. 110. Pit. L12. ri; 114. IIs. 116. TABLE OF CONTENTS. . Strength of copper-tin alloys (bronzes) . . . . . 2. + «6 s 93 : “* copper-zinc alloys (brasses) . . . . 73 Pe “ copper-zinc-tin alloys . . othe 73 = Modal of netdity” «2. \.- 21 %s-es ae eae eee 74 . Young’s modulus of elasticity ....... rhs . Effect of temperature on rigidity 76 . Values of Poisson’s ratio : 76 . Elastic moduli of crystals, formule 77 es eer eae numerical results . 78 ; Pompiessiey of nitrogen at different pressures and femperarares 79 “cc hydrogen its ee cc “ ce 79 cc “cc methane “ “ “ce ce “ 79 6 ce ethylene “ “ cc 6c cc - 79 6 * carbon dioxide“ a as “value offv 80 “cc “cc cc 6c cc “ “ values of the ratio Av/p,7 80 4 “ air, oxygen, and carbon monoxide at different mee sures and ordinary temperature . ° 80 ce “sulphur dioxide at different pressures and tenipeia: tures . 81 4 “ ammonia at different p presets and feniperatures 81 as and bulk moduli of liquids . . . . 82 ce “cc “ee “ “ solids 83 Density of various solids 84 “ “ “ alloys 85 rs ft metals~. 86 . «woods . 87 ee GOS. 88 oe ee eases swede iy 89 . “« “aqueous splntins aE nies on se eta go ot < — water betweent'o and 32°C. -i9.y5, g2 Volume of water at different temperatures in terms of its pole at temperature of maximum density eeeret oc : 93 Density and volume of water in terms of the “delisity ad volunié at 4 C. . 94 ss oe «9 © mercury at different teihipetatures ; 95 Specific gravity of aqueous ethyl! alcohol . 96 Density of aqueous methyl alcohol . ° 97 Variation of density of alcohol with temperature . 98 Velocity of sound in air, principal determinations of . 99 “ “cc “cc “ solids 5 Ioo n Se 6 liquids; and eases) ox IOI Force of gravity at sea level and different feels . 102 Results of some of the more recent determinations of gravity . i 3 LOR Value of gravity at stations occupied by U. S. C. & G. Survey in 1894 . 104 Length of seconds pendulum for sea level and different latitudes . 104 Determinations of the length of the seconds pendulum . . 105 127. 118. 119. 120. 121. 122. 123. 124. 125. 126. 197. 128. 129. 130. rt. 132. £3. 134. 135. 136. 137. 138. 139. 140. I4I. 142. 143. 144. 145. 146. 147. 148. 149. 150. rst: 152. 153: 154. E55: 156. 157- TABLE OF CONTENTS. ix Miscellaneous data as to the earth and planets. . . . .. . . 106 Aerodynamics : Data for wind pressure and values of “in /, = Fa Py 108 Data for the soaring of planes . . - . . + + «© 109 Terrestrial magnetism, total intensity . a DLO 7 = secular variation of total itehaity a. tet Ede LO - S Gipr.' os a patie ees ena i ad secular variation of dip. . . +... + Sau . horizontal intensity . . . . .- ; - 112 4 - secular variation of horizontal intensity , 112 * formulz for value and secular variation of dec- lination . . . Sadr sens (tee s © secular variation of dédlination (eastern stations) 114 Ge ‘f rs 2 is : (central stations) 115 i x be i < (western stations) 116 _ 5 position of agonic line in 1800, e 1875, AMC DOQO! oo si slle) 1c . 3 ° = ny $ = date of maximum east sauelinanGn at various StaulOns. =. aie elses ERO Tables for computing pressure of mercury aad of wae “British and metric measures ... . Ark os sn) Soule sab oi Gelatin aE Reduction of barometric feat to standard pete =at20 Correction of barometer to standard ee British and metric mea- SUES errs site eal va . 121 Reduction of barometer to latitude 45°, British neat Steen Meebo Es - s r We MeL Scale camo memes, Gwe sees Correction of barometer for capillarity, metric and British measures . 124 Absorption of gases by i ee te eT eee thr Rea repeat Oca e m6 a RSG Wapor pressures: - -.- : eich eesti an yes E2O Capillarity and surface tension, water and Acotiel in air = 126 4 - «miscellaneous liquids in air . . . . 128 cs Pe “© aqueous solutions of salts . 128 : = s «liquids in contact with oe water, or mercury . . nis eee os : = liquids at spitting cine. upd see beg 5 a - “« thickness of soap films . - . 129 Golofs:6f thin-plates;, Newton's Rings.) . sks ey ©) 16, ie EGO Contraction produced by solution of salts . .... . ‘13% = SGMution OF SOlUtIONS! <4). *. “)> +. «nat eee ee Coefficients of friction . . . rar ener Mer ee tO SS Specific viscosity of water at aitetent ene ates oho ey a aie fF 230 Coefficients of viscosity for solutions of alcohol in water . . . . . 137 Specitic-viscosity: of mineral oilS) 0. 5 ew en en) | ot 137 - “ various “ fs ia Sas enn i a ES é “ various liquids een . 138 a ae a - “ temperature variation «£39 s “ solutions, variation with density and teh netatire . 140 a bs oa atomic concentrations. . .. -+ . »« 144 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. TUE. Ta: 173: 174. 175- 176. m7: 178. 1709. 180. 181. 182. 183. 184. 185. 186. 187. TABLE OF CONTENTS. Specific ween of gases and vapors. . . o Pa ta eotl ce) tocde e) me anne a aes - 169 SEO sox A ingsyie 188. 189. 190. Igl. 192. 193. 194. 195: 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. aii. 212. 253. 214. 25: 216. 217. + 218. 219. 220. 221. 222. 223. 224. TABLE OF CONTENTS. xi Index of refraction of rock salt, various authorities . . . - . . . 182 vast a AS SVLVINIE MER ARs tse. ss cee Se 8 182 a 6 ¢ Hum Spal yaw amt relied Gal et Coie Opi bat Rts 183 aes - “ yarious monorefringents. . . + + «+ « » 184 a - (iceland:spar a. Mii wah a by eh aes ae) a TOS ee . <. CQuUaTEZ: Gl ine a be SM tile Sh oes ip eead 186 rn aS : “ various uniaxial aaaals TA cba Dt idlhs Wie’ 08 DO aa = « «biaxial crystals’ 2°.) ==) 187 ane ys : “ solutions of salts and acids : (2) Solutions in water 188 (4) Solutions in alcohol . ge 188 (c) e “ potassium permanganate . 188 Index of refraction of various liquids 189 oe Pe. a “* gases and vapors 1g0 Rotation of plane of polarized light by solutions IgI . sega ener & «« “sodium chlorate ae on aunt . Ig Lowering of freezing-points by salts in solution . . . . + = - 192 Vapor-pressures of solutions of salts in water 194 Raising of boiling-points by salts in solution . . . - + + 196 Thermal conductivity of metals andalloys . . . . - + = + 197 cs se iC VATOUSISUDStANICES#.. (1 os 10 latices Wes) ame 198 a " ‘‘ water and solutions of salts. . ..- . 198 s as SCROLP AIG ICMIGS) ss tel fa to ts 198 RD ASE SI or Nel Wictia/s ah int gle: Wedghat crews age 198 Freezing mixtures... eee : 3 199 Critical temperatures, Penrod rolaracs and densities i paces 200 Heat of combustion . 201 « —“ combination 202 Latent heat of vaporization 204 o Se oe LOSLOTS 1 50" fe 206 Melting-points of chemical lenient 207 Boiling-points of a ue’. 207 Melting-points of various inorganic compounds 208 Boiling-points of e a as 210 Melting-points of mixtures. er ae ee es 211 Densities, melting-points, and Soilinetpoints of some organic com- pounds : (a) Paraffin series . ee: (6) Olefine series e252 (c) Acetylene series 202 (2) Monatomic alcohols . es (e) Alcoholic ethers roi (7) Ethyl ethers : é . 213 Coefficients of linear expansion §. chemical Semen 20h A of alte - * miscellaneous substances 205 fs “ cubical expansion of crystalline and other solids . 2ko “cc “ec “ “ce A liqg“tas . vs "te 2a xii TABLE OF CONTENTS. 225. Coefficients of cubical expansion of pases... 5, 2 « » 6 «sHER 226. Dynamical equivalent of the thermal unit . . .....4.. 227. as ff Reese “ historical table’. 5 .. 228. Specific heat of water, descriptive introduction. . ....... 228, specific heat of water. 2 <=. 0. 6 229. Ratio of specific heats of air, various eee 230. Specific heats of gases and vapors . . 231. Vapor pressure of ethyl alcohol. . . . 232. “c “ee oe methy] oe H r n ” : 233. Vapor pressures and temperatures of various ee (q) (Carbon disulphide 2 7-6... ee (6) Chlorobenzene (c) Bromobenzene (2) Aniline 2 0.55 “a Cy ne ee oe ee (6). Methyl'salicylate. <1 5.4 i a ee eee (7) Bromonaphthaline (g) Mercury . 2 Woe 234. Thermometers, comparisons of cc in pales aa air -gaeunosree 235: is comparison of various kinds with hydrogen thermometer 236. = ‘s . “« “ air thermometer . 237. a change of zero due to heating (Jena glass) . : 238. < : oes aa en «(various kinds of glass) . 239. s o too dae ei “effect of composition of glass 240. - slow changerof zero with time y 9. 2) oe eae 241. s correction for mercury in stem . 242. Emissivity of polished and blackened surfaces in air at ordinary p pres- SUES 7.m) : 243. Emissivity of parched a Blackened auraceee in air aoe Aiterene pres- sures 244. Constants of eee fe various aibuenees to vacuum . , 245. Effect of absolute temperature of surface on the eR constants of bright and blackened platinum wire ae 246. Radiation of bright platinum wire to copper envelope across air se dif. ferent pressures. . SWiatiae tye 247. Effect of pressure on Se at Patient reqierauies 248. Properties and constants of saturated steam, metric measure . 249. oh S es a es <6 British measure . 250. Ratio of the electrostatic to the electromagnetic unit of electricity, dif- ferent determinations Of... 0.8) s1 0 sickest nai ea 251. Dielectric strength : (2) Medium air and terminals flat plates . . . . . « « + « (2) ce yee oe balls of different diameter . (c) & Ee ae # balls comparison of the results of dif. ferent observers G9 .8 - 252. Dielectric strength of gases, effect of pressureon. . .... - 253° eS Hs ** various Substances). (ec eee ete wees) feah ee 254. 255. 256. 257: 258. 259. 260. 261. 262. 263. 264. 265. 266. 267. 268. 269. 270. a7t. 272. 273. 274. 275. 276. 277. 278. 279. 280. 281. 282. 283. 284. 285. TABLE OF CONTENTS, Data as to electric battery cells : (a) Double fluid batteries . «. + ¢ p¢ 2 es te (4) Single fluid batteries eae trea: Sel sta S fae erandard cells ee a ae ee Re 8 Be (d2) Secondary cells Thermoelectric power of various eae ae ‘alloys a se Fe <> BUD YS ade Bsa 5 Thermoelectric neutral point of various metals relative to ead Specific heat of electricity for metals Thermoelectric power of metals and solutions . Peltier effect, Jahn’s experiments é * 7) Le Roux’s:, “ : Conductivity of three-metal and pet lioneaes aileye ‘S * alloys : : ; see Specific resistance of metallic wires, various seneian units . ‘. & “* metals, various authorities ; g s «¢ «and alloys at low temperatures . xiii . 246 247 » 247 - 247 * £4 » 249 - 249 - 249 Bey fo) - 250 = 250 ET + 252 a 254 - 255 Effect of elastic and permanent eae on resistance of peel aS Wife ce fee! s Resistance of wires of ceierent diameter to ae currents . Conductivity of dilute solutions proportional to amount of dissolved salt Electrochemical equivalent numbers and densities of approximately nor- rao . 260 201 mal solutions .. . ‘ Hike Specific molecular aunt of ean Limiting values of specific molecular conductivities Temperature coefficients of dilute solutions . s250 256 Various determinations of the ohm, the pecnochomical pein a silver and the electromotive force of the Clark cell. . Specific inductive capacity of gases. “ “c “cc “cs solids “ec “ce “ “cc liquids Contact difference of potential, solids with quid ana ‘gamit liquids in air ier eane Contact difference of a afigt solids with salidei Ta ae age Potential difference between metals in various solutions . . Resistance of glass and porcelain at different temperatures. Relation between thermal and electrical conductivities : (a) Arbitrary units (4) Values inc. g. s. units (c) Berget’s experiments (@) Kohlrausch’s results 259. . 261 » 202 +, 263 . 264 with 265 . 266 . 268 . 269 . 270 275 ee 27% Electrochemical Gaon and atomic wreigtics a me enehical ne 27a - 274 ments . a Gaeho a Permeability of iron ae various inductions Permeability of transformer iron : (a) Specimen of Westinghouse No. 8 transformer . (2) 66 ‘““ “ “& 6 “ec zal - 274 - 275 xiv TABLE OF CONTENTS. (c) Specimen of Westinghouse No. 4 transformer 2h, ee (2) = “ Thomson-Houston 1500-watt transformer. . . . 275 286. Composition and magnetic properties of iron and steel 287. Permeability of some specimens in Table 286 . . . . . . - 288. Magnetic properties of soft iron at 0° and 100° C, 289. ‘ cs “ steel ato° and roo" C.. . . 290. ¢ < ‘ieobaAlE ati rOO wiGle = ane 2Q1. . - nickel-at too > C.\ seein Vales oan 292. eS ne Ee macmiettte: an.) i. ve. hen see 293. > . “ TLowmoor wrought iron in Peake fields 294. s “ Vicker’s tool steel in intense fields . ‘ - 295. : - Hadfield’s manganese steel in intense fields . 296. Saturation values for different steels . . . . - + ss. 297. Magnetic properties of very weak fields : aes 298. Dissipation of energy in the cyclic magnetization of raenede eubeence 299. s Oi Ree aces ae ce “* cable transformers . 300. Se Ts MAT ote dr * “* various substances . 301. SDS OSS aay cians aig ss “* transformer cores 302. o Cy ME inst aes oh ha . “* various specimens of soft iron Magneto-optic rotation, Verdet’s constant . . . . . + . 303. a s ID/SOLGS <0) )e0 oh eine os kee oe ee ee 304. oh sf “ liquids eee 305. Ee sf “ solutions of acids ya mek in eae ae 306. se s eS « ‘saltsiin;alcohol spawn sone. 307. “ i . “in hydrochloric acid . 308. r “ gases ian. 309. Miscellaneous values of Verdet’s and Kunde’ S eoreraare 310. _ “ “ susceptibility for liquids and gases 311. Kerr’s constants for iron, nickel, cobalt, and magnetite . 312. Effect of magnetic field on the electric resistance of bismuth Gatcet resistance of one ohm for zero field and various temperatures) 313. Effect of magnetic field on the electric resistance of bismuth (initial resistance one ohm for zero field and temperature zero Centigrade) 314. Specific heat of various solids and liquids . . . - « + = + ais.” Specific heat of metals” 20). )e) "5 a eee ren creas INTRODUCTION. UNITS OF MEASUREMENT AND CONVERSION FORMUL&. Units. — The quantitative measure of anything is a number which expresses the ratio of the magnitude of the thing to the magnitude of some other thing of the same kind. In order that the number expressing the measure may be intelligi- ble, the magnitude of the thing used for comparison must be known. This leads to the conventional choice of certain magnitudes as units of measurement, and any other magnitude is then simply expressed by a number which tells how many magnitudes equal to the unit of the same kind of magnitude it contains. For example, the distance between two places may be stated as a certain number of miles or of yards or of feet. In the first case, the mile is assumed as a known distance ; in the second, the yard, and in the third, the foot. What is sought for in the statement is to convey an idea of the distance by describing it in terms of distances which are either familiar or easily referred to for comparison. Similarly quantities of matter are referred to as so many tons or pounds or grains and so forth, and intervals of time as a number of hours or minutes or seconds. Gen- erally in ordinary affairs such statements appeal to experience ; but, whether this be so or not, the statement must involve some magnitude as a fundamental quan- tity, and this must be of such a character that, if it is not known, it can be readily referred to. We become familiar with the length of a mile by walking over dis- tances expressed in miles, with the length of a yard or a foot by examining a yard or a foot measure and comparing it with something easily referred to, — say our own height, the length of our foot or step, — and similarly for quantities of other kinds. This leads us to be able to form a mental picture of such magnitudes when the numbers expressing them are stated, and hence to follow intelligently descriptions of the results of scientific work. The possession of copies of the units enables us by proper comparisons to find the magnitude-numbers express- ing physical quantities for ourselves. ‘The numbers descriptive of any quan- tity must depend on the intrinsic magnitude of the unit in terms of which it is described. ‘Thus a mile is 1760 yards, or 5280 feet, and hence when a mile is taken as the unit the magnitude-number for the distance is 1, when a yard is taken as the unit the magnitude-number is 1760, and when a foot is taken it is 5280. Thus, to obtain the magnitude-number for a quantity in terms of a new unit when it is already known in terms of another we have to multiply the old magnitude- number by the ratio of the intrinsic values of the old and new units; that is, by the number of the new units required to make one of the old. xvi INTRODUCTION. Fundamental Units of Length and Mass. — It is desirable that as few dif- ferent kinds of unit quantities as possible should be introduced into our measure- ments, and since it has been found possible and convenient to express a large number of physical quantities in terms of length or mass or time units and com- binations of these they have been very generally adopted as fundamental units. Two systems of such units are used in this country for scientific measurements, namely, the British and the French, or metric, systems. ‘Tables of conversion factors are given in the book for facilitating comparisons between quantities ex- pressed in terms of one system with similar quantities expressed in the other. In the British system the standard unit of length is the yard, and it is defined as fol- lows: “The straight line or distance between the transverse lines in the two gold plugs in the bronze bar deposited in the Office of the Exchequer shall be the gen- uine Standard of Length at 62° F., and if lost it shall be replaced by means of its copies.” [The authorized copies here referred to are preserved at the Royal Mint, the Royal Society of London, the Royal Observatory at Greenwich, and the New Palace at Westminster. | The British standard unit of mass is the pound avoirdupois, and is the mass of a piece of platinum marked “ P. S. 1844, 1 Ib.,” which is preserved in the Exchequer Office. Authorized copies of this standard are kept at the same places as those of the standard of length. In the metric system the standard of length is defined as the distance between the ends of a certain platinum bar (the métre des Archives) when the whole bar is at the temperature o° Centigrade. The bar was made by Borda, and is preserved in the national archives of France. A line-standard metre has been constructed by the International Bureau of Weights and Measures, and is known as the Inter- national Prototype Metre. This standard is of the same length as the Borda stand- ard. A number of standard-metre bars which have been carefully compared with the International Prototype have lately been made by the International Bureau of Weights and Measures and furnished to the various governments who have con- tributed to the support of that bureau. These copies are called National Proto- types. Borda, Delambre, Laplace, and others, acting as a committee of the French Academy, recommended that the standard unit of length should be the ten mil- lionth part of the length, from the equator to the pole, of the meridian passing through Paris. In 1795 the French Republic passed a decree making this the legal standard of length, and an arc of the meridian extending from Dunkirk to Barcelona was measured by Delambre and Mechain for the purpose of realizing the standard. From the results of that measurement the metre bar was made by Borda. The metre is not now defined as stated above, but as the length of Borda’s rod, and hence subsequent measurements of the length of the meridian have not affected the length of the metre. The French, or metric, standard of mass, the kilogramme, is the mass of a piece of platinum also made by Borda in accordance with the same decree of the Republic. It was connected with the standard of length by being made as nearly as possible of the same mass as that of a cubic decimetre of distilled water at the temperature of 4° C., or nearly the temperature of maximum density. As in the case of the metre, the International Bureau of Weights and Measures INTRODUCTION. XVii has made copies of the kilogramme. One of these is taken as standard, and is called the International Prototype Kilogramme. The others were distributed in the same manner as the metre standards, and are called National Prototypes. Comparisons of the French and British standards are given in tabular form in Table 2; and similarly Table 3, differing slightly from the British, gives the legal ratios in the United States. In the metric system the decimal subdivi- sion is used, and thus we have the decimetre, the centimetre, and the millimetre as subdivisions, and the dekametre, hektometre, and kilometre as multiples. The centimetre is most commonly used in scientific work. Time. — The unit of time in both the systems here referred to is the mean solar second, or the 86,40o0th part of the mean solar day. The unit of time is thus founded on the average time required for the earth to make one revolution on its axis relatively to the sun as a fixed point of reference. Derived Units. — Units of quantities depending on powers greater than unity of the fundamental length, mass, and time units, or on combinations of different powers of these units, are called “derived units.” Thus, the unit of area and of volume are respectively the area of a square whose side is the unit of length and the volume of a cube whose edge is the unit of length. Suppose that the area of a surface is expressed in terms of the foot as fundamental unit, and we wish to find the area-number when the yard is taken as fundamental unit. The yard is 3 times as long as the foot, and therefore the area of a square whose side is a yard is 3 X 3 times as great as that whose side is a foot. Thus, the surface will only make one ninth as many units of area when the yard is the unit of length as it will make when the foot is that unit. To transform, then, from the foot as old unit to the yard as new unit, we have to multiply the old area-number by 1/9, or by the ratio of the magnitude of the old to that of the new unit of area. This is the same rule as that given above, but it is usually more convenient to express the transformations in terms of the fundamental units directly. In the above case, since on the method of measurement here adopted an area-number is the product of a length-number by a length-number the ratio of two units is the square of the ratio of the intrinsic values of the two units of length. Hence, if 7 be the ratio of the magnitude of the old to that of the new unit of length, the ratio of the cor- responding units of area is 7%, Similarly the ratio of two units of volume will be 7, and so on for other quantities. Dimensional Formule. — It is convenient to adopt symbols for the ratios of length units, mass units, and time units, and adhere to their use throughout ; and in what follows, the small letters, 7, ™, 4, will be used for these ratios. These letters will always represent simple numbers, but the magnitude of the number will depend on the relative magnitudes of the units the ratios of which they repre- sent. When the values of the numbers represented by 7, m, ¢ are known, and the powers of Z, m, and ¢ involved in any particular unit are also known, the factor for transformation is at once obtained. ‘Thus, in the above example, the value of 7 was 1/3 and the power of / involved in the expression for area is /”; hence, the factor for transforming from square feet to square yards is 1/g. These factors XVill INTRODUCTION. have been called by Prof. James Thomson “change ratios,” which seems an appropriate term. The term “conversion factor” is perhaps more generally known, and has been used throughout this book. Conversion Factor. — In order to determine the symbolic expression for the conversion factor for any physical quantity, it is sufficient to determine the degree to which the quantities length, mass, and time are involved in the quantity. Thus, a velocity is expressed by the ratio of the number representing a length to that representing an interval of time, or L/T, an acceleration by a velocity-number divided by an interval of time-number, or L/T*, and so on, and the correspond- ing ratios of units must therefore enter to precisely the same degree. ‘The fac- tors would thus be for the above cases, //¢and 7/7. Equations of the form above given for velocity and acceleration which show the dimensions of the quantity in terms of the fundamental units are called “ dimensional equations.” Thus Bb=MLa is the dimensional equation for energy, and ML*T~ is the dimensional formula for energy. In general, if we have an equation for a physical quantity O= CER where C is a constant and LMT represents length, mass, and time in terms of one set of units, and we wish to transform to another set of units in terms of which % \ ; the length, mass, and time are L,M,T,, we have to find the value of ae which in accordance with the convention adopted above will be 7/4, or the ratios of the magnitudes of the old to those of the new units. Thus L,=L4 M,=Mm, T,=T7~, and if Q, be the new quantity-number QO, — CL/°M/T SOL ie — OF xt or the conversion factor is /*m’t*, a quantity of precisely the same form as the dimension formula L*M°T*. We now proceed to form the dimensional and conversion factor formula for the more commonly occurring derived units. 1. Area. — The unit of area is the square the side of which is measured by the unit of length. The area of a surface is therefore expressed as SCs where C is a constant depending on the shape of the boundary of the surface and La linear dimension. For example, if the surface be square and L be the length of a side C is unity. If the boundary be a circle and L be a diameter C=7/4, and so on. The dimensional formula is thus L?, and the conversion factor 7*. 2. Volume. — The unit of volume is the volume of a cube the edge of which is measured by the unit of length. The volume of a body is therefore expressed as INTRODUCTION. Xix v= CG where as before C is a constant depending on the shape of the boundary. The dimensional formula is L’ and the conversion factor 2°. 3. Density. — The density of a substance is the quantity of matter in the unit of volume. The dimension formula is therefore M/V or ML~%, and conversion factor mf. Lxample.—'The density of a body is 150 in pounds per cubic foot: required the density in grains per cubic inch. Here m is the number of grains in a pound= 7000, and 7 is the number of inches in a foot = 12 ; .*. #/~* = 7000/12®= 4.051. Hence the density is 150 X 4.051 = 607.6 in grains per cubic inch. Nore. — The specific gravity of a body is the ratio of its density to the density of a standard substance. The dimension formula and conversion factor are therefore both unity. 4. Velocity. — The velocity of a body at any instant is given by the equation Vv Se or velocity is the ratio of a length-number to a time-number. The di- mension formula is LT~, and the conversion factor /¢—}. L£xample. — A train has a velocity of 60 miles an hour: what is its velocity in feet per second ? ete? —- ece.and.s— 7600... de = —=-*= 1.467. Hence the velo- city =60 X 1.467 = 88.0 in feet per second. 5. Angle. — An angle is measured by the ratio of the length of an arc to the length of the radius of the arc. The dimension formula and the conversion factor are therefore both unity. 6. Angular Velocity. — Angular velocity is the ratio of the magnitude of the angle described in an interval of time to the length of the interval. The dimen- sion formula is therefore T~, and the conversion factor is ¢—. 7. Linear Acceleration. — Acceleration is the rate of change of velocity or a = The dimension formula is therefore VT or LT-?, and the conversion factor is /f~*, Examples— A body acquires velocity at a uniform rate, and at the end of one minute is moving at the rate of 20 kilometres per hour: what is the acceleration in centimetres per second per second ? Since the velocity gained was 20 kilometres per hour in one minute, the accel- eration was 1200 kilometres per hour per hour. Here /= 100000 and ¢= 3600; .°. 4/-?= 100 000/36007—=.00771, and there- fore acceleration = .00771 X 1200= 9.26 centimetres per second. 8. Angular Acceleration. — Angular acceleration is rate of change of angu- XX INTRODUCTION. angular velocity _ - ang al eee or ia 7 and the lar velocity. The dimensional formula is thus conversion factor ¢~*. 9. Solid Angle. — A solid angle is measured by the ratio of the surface of the portion of a sphere enclosed by the conical surface forming the angle to the square of radius of the spherical surface, the centre of the sphere being at the area vertex of the cone. The dimensional formula is therefore or 1, and hence the conversion factor is also 1. ro. Curvature. — Curvature is measured by the rate of change of direction of the curve with reference to distance measured along the curve as independent © angle length variable. The dimension formula is therefore or L~}, and the conversion > factor is 77. 11. Tortuosity. — Tortuosity is measured by the rate of rotation of the tan- gent plane round the tangent to the curve of reference when length along the angle length curve is independent variable. The dimension formula is therefore L-—, and the conversion factor is 7. 12. Specific Curvature of a Surface. — This was defined by Gauss to be; at any point of the surface, the ratio of the solid angle enclosed by a surface formed by moving a normal to the surface round the periphery of a small area containing the point, to the magnitude of the area. The dimensional formula is solid angle therefore >--—*=~ or L~?, and the conversion factor is thus 7°. surface 13. Momentum. — This is quantity of motion in the Newtonian sense, and is, at any instant, measured by the product of the mass-number and the velocity- number for the body. Thus the dimension formula is MV or MLT~, and the conversion factor m/f”. Example. — A mass of 10 pounds is moving with a velocity of 30 feet per sec- ond: what is its momentum when the centimetre, the gramme, and the second are fundamental units ? ‘ Here m= 453.59, 7—= 30.48, and ¢=1; .*. mit*= 453.59 X 30-48 = 13825. The momentum is thus 13825 &K 10 K 30 = 4147 500. 14. Moment of Momentum. — The moment of momentum of a body with reference to a point is the product of its momentum-number and the number expressing the distance of its line of motion from the point. The dimensional formula is thus ML?T-, and hence the conversion factor is m/*t”’. 15. Moment of Inertia. —The moment of inertia of a body round any axis is expressed by the formula 7, where m is the mass of any particle of the body INTRODUCTION. Xxi and r its distance from the axis. The dimension formula for the sum is clearly the same as for each element, and hence is ML*. The conversion factor is there- fore m7. 16. Angular Momentum. — The angular momentum of a body round any axis is the product of the numbers expressing the moment of inertia and the angular velocity of the body. The dimensional formula and the conversion fac- tor are therefore the same as for moment of momentum given above. ; 17. Force. — A force is measured by the rate of change of momentum it is capable of producing. ‘The dimension formula for force and “time rate of change of momentum” are therefore the same, and are expressed by the ratio ~ of momentum-number to time-number or MLT~*, The conversion factor is thus mit. Nore. — When mass is expressed in pounds, length in feet, and time in seconds, the unit force is called the poundal. When grammes, centimetres, and seconds are the corresponding units the unit of force is called the dyne. Example. Find the number of dynes in 25 poundals. Here m = 453.59, 7 = 30.48, and ¢=1; .*. mit-*= 453.59 X 30.48 = 13825 nearly. The number of dynes is thus 13825 & 25 = 345625 approximately. 18. Moment of a Couple, Torque, or Twisting Motive. — These are dif- ferent names for a quantity which can be expressed as the product of two numbers representing a force and a length. The dimension formula is therefore FL or ML?T~, and the conversion factor is m/*¢-*, 19. Intensity of a Stress. — The intensity of a stress is the ratio of the num- ber expressing the total stress to the number expressing the area over which the stress is distributed. The dimensional formula is thus FL~* or ML~!T-%, and the conversion factor is m/—l4-?, 20. Intensity of Attraction, or ‘“‘ Force at a Point.’’ — This is the force of attraction per unit mass on a body placed at the point, and the dimensional for- mula is therefore FM~™ or LT~*, the same as acceleration. The conversion fac- tors for acceleration therefore apply. 21. Absolute Force of a Centre of Attraction, or “‘ Strength of a Cen- tre.”’ — This is the intensity of force at unit distance from the centre, and is there- fore the force per unit mass at any point multiplied by the square of the distance from the centre. The dimensional formula thus becomes FL?M— or L°T-2. The conversion factor is therefore /°¢~*. 22. Modulus of Elasticity. — A modulus of elasticity is the ratio of stress intensity to percentage strain. The dimension of percentage strain is a length divided by a length, and is therefore unity. Hence, the dimensional formula of a modulus of elasticity is the same as that of stress intensity, or ML~T-%, and the conversion factor is thus also m/—'¢-?, Xxli INTRODUCTION. 23. Work and Energy. — When the point of application of a force, acting on a body, moves in the direction of the force, work is done by the force, and the amount is measured by the product of the force and displacement numbers. The dimensional formula is therefore FL or ML?T~. The work done by the force either produces a change in the velocity of the body or a change of shape or configuration of the body, or both. In the first case it produces a change of kinetic energy, in the second a change of potential energy. The dimension formule of energy and work, representing quantities of the same kind, are identical, and the conversion factor for both is m/?t~*, 24. Resilience. — This is the work done per unit volume of a body in distort- ing it to the elastic limit or in producing rupture. The dimension formula is there- fore ML?T-*L? or ML“?!T-%, and the conversion factor m/—2~. 25. Power, or Activity. — Power — or, as it is now very commonly called, ac- tivity —is defined as the time rate of doing work, or if W represent work and P power PP a . The dimensional formula is therefore WT or ML?T~, and the con- ta version factor m/*t—*, or for problems in gravitation units more conveniently /7-}, where / stands for the force factor. Lxamples. (a) Find the number of gramme centimetres in one foot pound. Here the units of force are the attraction of the earth on the pound* and the gramme of matter, and the conversion factor is /7, where / is 453-59 and Z is 30.48. Hence the number is 453.59 X 30.48 = 13825. (4) Find the number of foot poundals in 1 000000 centimetre dynes. Here m == 1/453.59, 2==1/30.48, and ¢==1 3... wilt — v/Ass.56 6 eomon and 10°7/°F °==10 453.50 < g0:46-——==.873. (c) If gravity produces an acceleration of 32.2 feet per second per second, how many watts are required to make one horse-power ? One horse-power is 550 foot pounds per second, or 550 X 32.2 =17710 foot poundals per second. One watt is 10’ ergs per second, that is, 107 dyne centi- metres per second. The conversion factor is m/*t-*, where mm = 453.59, 7= 30.48, and ¢= 1, and the result has to be divided by 10’, the number of dyne centime- tres per second in the watt. Hence, 17710 mt */ 10! == 17710 X 453,50 30.454 10.— 7Ao.: (2) How many gramme centimetres per second correspond to 33000 foot pounds per minute ? The conversion factor suitable for this case is ///, where / is 453-59, Z is 30.48, and ¢ is 60. Hence, 33000 /t-*= 33000 X 453.59 X 30.48/60 = 7 604000 nearly. * It is important to remember that in problems like that here given the term “pound” or “gramme ” refers to force and not to mass. INTRODUCTION. XXili HEAT UNITS. 1. If heat be measured in dynamical units its dimensions are the same as those of energy, namely ML*I~*. The most common measurements, however, are made in thermal units, that is, in terms of the amount of heat required to raise the temperature of unit mass of water one degree of temperature at some stated temperature. ‘This method of measurement involves the unit of mass and some unit of temperature, and hence if we denote temperature-numbers by © and their conversion factors by @ the dimensional formula and conversion factor for quan- tity of heat will be M© and m@ respectively. The relative amount of heat com- pared with water as standard substance required to raise unit mass of different substances one degree in temperature is called their specific heat, and is a simple number. Unit volume is sometimes used instead of unit mass in the measurement of heat, the units being then called thermometric units. The dimensional formula is in that case changed by the substitution of volume for mass, and becomes L*9, and hence the conversion factor is to be calculated from the formula 2°¢. For other physical quantities involving heat we have : — 2. Coefficient of Expansion. — The coefficient of expansion of a substance is equal to the ratio of the change of length per unit length (linear), or change of volume per unit volume (voluminal) to the change of temperature. These ratios are simple numbers, and the change of temperature is inversely as the mag- nitude of the unit of temperature. Hence the dimensional and conversion-factor formule are ©? and 6, 3. Conductivity, or Specific Conductance. — This is the quantity of heat transmitted per unit of time per unit of surface per unit of temperature gradient. The equation for conductivity is therefore, with H as quantity of heat, e— Ht pak L and the dimensional formula 1 — M which gives mt for conversion factor. GEl > Lir In thermometric units the formula becomes L?T-', which properly represents diffusivity. In dynamical units H becomes ML?T~%, and the formula changes to MLT~“*O. The conversion factors obtained from these are 7¢ and m/t*67 respectively. Similarly for emission and absorption we have — 4. Emissivity and Immissivity. — These are the quantities of heat given off by or taken in by the body per unit of time per unit of surface per unit dif- ference of temperature between the surface and the surrounding medium. We thus get the equation EL‘@OT =H = M@, The dimensional formula for E is therefore ML~*T-}, and the conversion factor XXiV INTRODUCTION. mi~*t,_ In thermometric units by substituting 2* for m the factor becomes /¢-}, and in dynamical units mt*6--. 5. Thermal Capacity. — This is the product of the number for mass and the specific heat, and hence the dimensional formula and conversion factor are simply M and m. 6. Latent Heat. — Latent heat is the ratio of the number representing the quantity of heat required to change the state of a body to the number represent- ing the quantity of matter in the body. The dimensional formula is therefore M@/M or ©, and hence the conversion factor is simply the ratio of the tempera- ture units or 6. In dynamical units the factor is ?¢-*.* 7. Joule’s Equivalent. — Joule’s dynamical equivalent is connected with quantity of heat by the equation ML?T-?= JH or JM®. This gives for the dimensional formula of J the expression L*T~*®. The conver- sion factor is thus represented by 7¢-*6. When heat is measured in dynamical units J is a simple number. 8. Entropy. — The entropy of a body is directly proportional to the quantity of heat it contains and inversely proportional to its temperature. The dimen- sional formula is thus M@/® or M, and the conversion factor is #. When heat is measured in dynamical units the factor is m/*t67. Examples. (a) Find the relation between the British thermal unit, the calorie, and the therm. Neglecting the variation of the specific heat of water with temperature, or de- fining all the units for the same temperature of the standard substance, we have the following definitions. The British thermal unit is the quantity of heat required to raise the temperature of one pound of water 1° F. The calorie is the quan- tity of heat required to raise the temperature of one kilogramme of water 1° C, The therm is the quantity of heat required to raise the temperature of one gramme of water 1° C. Hence : — (1) To find the number of calories in one British thermal unit, we have m= .45399 and 6=§; .. mO=.45399 X 5/9 = -25199. (2) To find the number of therms in one calorie, #1000 and 6=1; .. m0 = 1000. It follows at once that the number of therms in one British thermal unit is 1000 XK .25199 — 251.99. (2) What is the relation between the foot grain second Fahrenheit-degree and the centimetre gramme second Centigrade-degree units of conductivity ? The number of the latter units in one of the former is given by the for- * It will be noticed that when @ is given the dimension formula L?T— the formule in thermal and dynamical units are always identical. The thermometric units practically suppress mass. INTRODUCTION. XXV mula mZ—¢—16°, where m= .064799, /= 30.48, and ¢=1, and is therefore = 3 .064 799/30.48 = 2.126 X Io™. (c) Find the relation between the units stated in (4) for emissivity. In this case the conversion formula is m/~*¢, where m/ and ¢ have the same value as before. Hence the number of the latter units in the former is 0.064 799/30.48"= 6.975 X 107°. (d) Find the number of centimetre gramme second units in the inch grain hour unit of emissivity. Here the formula is m/—*¢, where m=0.064799, /= 2.54, and ¢= 3600. Therefore the required number is 0.064799/2.54 X 3600 = 2.790 X 10%, (e) If Joule’s equivalent be 776 foot pounds per pound of water per degree Fahrenheit, what will be its value in gravitation units when the metre, the kilo- gramme, and the degree Centigrade are units? 24—2 The conversion factor in this case is zor 26, where 7=.3048 and 6=1.8; “2776 X .3048 X 1.8 = 425.7. (f) If Joule’s equivalent be 24832 foot poundals when the degree Fahrenheit is unit of temperature, what will be its value when kilogramme metre second and degree-Centigrade units are used? The conversion factor is 2¢-*6, where 7—= .3048, ¢=1, and 0=1.8; .*. 24832 aie 0 24632 < .30157 % 1.0.— 4152.5. In gravitation units this would give 4152.5/9.81 = 423.3. BEECTRIC- AND? MAGNETIC UNEES: There are two systems of these units, the electrostatic and the electromagnetic systems, which differ from each other because of the different fundamental suppo- sitions on which they are based. In the electrostatic system the repulsive force between two quantities of static electricity is made the basis. This connects force, quantity of electricity, and length by the equation f=a owhere J is force, a a quantity depending on the units employed and on the nature of the medium, g and g, quantities of electricity, and Z the distance between g and g,, The magnitude of the force f for any particular values of g,g, and 7 depends on a property of the medium across which the force takes place called its inductive capacity. The in- ductive capacity of air has generally been assumed as unity, and the inductive capacity of other media expressed as a number representing the ratio of the induc- tive capacity of the medium to that of air. These numbers are known as the spe- cific inductive capacities of the media. According to the ordinary assumption, then, of air as the standard medium, we obtain unit quantity of electricity when in the above equation g=g,, and f, a, and 7 are each unity. A formal definition is given below. In the electromagnetic system the repulsion between two magnetic poles or XXVi INTRODUCTION. quantities of magnetism is taken as the basis. In this system the quantities force, quantity of magnetism, and length are connected by an equation of the form S= a where m and m, are in this case quantities of magnetism, and the other symbols have the same meaning as before. In this case it has been usual to assume the magnetic inductive capacity of air to be unity, and to express the magnetic induc- tive capacity of other media as a simple number representing the ratio of the in- ductive capacity of the medium to that of air. These numbers, by analogy with specific inductive capacity for electricity, might be called specific inductive capac- ities for magnetism. ‘They are usually called permeabilities. (Vide Thomson, “Papers on Electrostatics and Magnetism,” p. 484.) In this case, also, like that for electricity, the unit quantity of magnetism is obtained by making m= m,, and J, @, and / each unity. In both these cases the intrinsic inductive capacity of the standard medium is suppressed, and hence also that of all other media. Whether this be done or not, direct experiment has to be resorted to for the determination of the absolute val- ues of the units and the relations of the units in the one system to those in the other. The character of this relation can be directly inferred from the dimen- sional formulz of the different quantities, but these can give no information as to the relative absolute values of the units in the two systems. Prof. Ricker has suggested (Phil. Mag. vol. 27) the advisability of at least indicating the exist- ence of the suppressed properties by putting symbols for them in the dimensional formule. This has the advantage of showing how the magnitudes of the different units would be affected by a change in the standard medium, or by making the standard medium different for the two systems. In accordance with this idea, the symbols K and P have been introduced into the formula given below to represent inductive capacity in the electrostatic and the electromagnetic systems respectively. In the conversion formule & and / are the ordinary specific inductive capacities and permeabilities of the media when air is taken as the standard, or generally those with reference tothe first medium taken as standard. ‘The ordinary for- mulz may be obtained by putting K and P equal to unity. ELECTROSTATIC UNITS. 1. Quantity of Electricity. — The unit quantity of electricity is defined as that quantity which if concentrated at a point and placed at unit distance from an equal and similarly concentrated quantity repels it, or is repelled by it, with unit force. The medium or dielectric is usually taken as air, and the other units in ac- cordance with the centimetre gramme second system. In this case we have the force of repulsion proportional directly to the square of the quantity of electricity and inversely to the square of the distance between the quantities and to the inductive capacity. The dimensional formula is there- fore the same as that for [force X length? X inductive capacity]* or M*L!T~K}, and the conversion factor is m*Z!¢-4A3, INTRODUCTION. XXVil 2. Electric Surface Density and Electric Displacement. — The density of an electric distribution at any point on a surface is measured by the quantity per unit of area, and the electric displacement at any point in a dielectric is mea- sured by the quantity displaced per unit of area. These quantities have therefore the same dimensional formula, namely, the ratio of the formule for quantity of electricity and for area or M'L~T~*K?, and the conversion factor mT 1k, 3. Electric Force at a Point, or Intensity of Electric Field. — This is measured by the ratio of the magnitude of the force on a quantity of electricity at a point to the magnitude of the quantity of electricity. The dimensional formula is therefore the ratio of the formula for force and electric quantity, or MLT* M!L!T“K} which gives the conversion factor mZ-'¢*2>*. = MLATAK4, 4. Electric Potential and Electromotive Force. — Change of potential is proportional to the work done per unit of electricity in producing the change. The dimensional formula is therefore the ratio of the formule for work and elec- tric quantity, or ML?T~? M!L?TK? which gives the conversion factor m'7¢1£7. = ML'TAK-, 5. Capacity of a Conductor. — The capacity of an insulated conductor is proportional to the ratio of the numbers representing the quantity of electricity in a charge and the potential of the charge. The dimensional formula is thus the ratio of the two formula for electric quantity and potential, or M'L'T"K? __ MUTIKS 7 which gives 2% for conversion factor. When K is taken as unity, as in the ordinary units, the capacity of an insulated conductor is simply a length. 6. Specific Inductive Capacity. — This is the ratio of the inductive capec- ity of the substance to that of a standard substance, and hence the dimensional formula is K/K or 1.* 7. Electric Current. — Current is quantity flowing past a point per unit of time. The dimensional formula is thus the ratio of the formulz for electric quan- tity and for time, or M?L!T-!K} - and the conversion factor m!/!t-*Z!, = ML'TK}, * According to the ordinary definition referred to air as standard medium, the specific inductive capacity of a substance is K, or is identical in dimensions with what is here taken as inductive ca- pacity. Hence in that case the conversion factor must be taken as 1 on the electrostatic and as {2 on the electromagnetic system. XXVili INTRODUCTION. 8. Conductivity, or Specific * Conductance. — This, like the corresponding term for heat, is quantity per unit area per unit potential gradient per unit of time. The dimensional formula is therefore M?L)T-1K} “iz TK FS Lae The conversion factor is ¢—2£. electric quantity ; area X potential gradient x time 9. Specific * Resistance. — This is the reciprocal of conductivity as above defined, and hence the dimensional formula and conversion factor are respec- tively TK and #21. 10. Conductance. — The conductance of any part of an electric circuit, not containing a source of electromotive force, is the ratio of the numbers represent- ing the current flowing through it and the difference of potential between its ends. The dimensional formula is thus the ratio of the formula for current and poten- tial, or M?L'T*K? from which we get the conversion factor 772471. D —Viek= 11. Resistance. — This is the reciprocal of conductance, and therefore the dimensional formula and the conversion factor are respectively L'TK and 772. EXAMPLES OF CONVERSION IN ELECTROSTATIC UNITS. (a) Find the factor for converting quantity of electricity expressed in foot grain second units to the same expressed in c. g. s. units. By (1) the formula is Z!¢2', in which in this case 7 = 0.0648, 7= 30.48, = 1, and =1; .*. the factor is 0.0648! X 30.48! = 4.2836. (6) Find the factor required to convert electric potential from millimetre milli- gramme second units toc. g. s. units. By (4) the formula is m'/'s-14+, and in this case = 0.001, = 0.1, ¢= 1, and k= 15's. the factor —'0, como.) —— 0.01. (c) Find the factor required to convert from foot grain second and specific in- ductive capacity 6 units to c. g. s. units. By (5) the formula is Zk, and in this case 7= 30.48 and k= 6; .*. the factor == 30.45 X 6 == 152.88. * The term “specific,” as used here and in 9, refers conductance and resistance to that between the ends of a bar of unit section and unit length, and hence is different from the same term in specific heat, specific inductivity, capacity, etc., which refer to a standard substance. E INTRODUCTION. Xxix ELECTROMAGNETIC UNITS. As stated above, these units bear the same relation to unit quantity of magne- tism that the electric units do to quantity of electricity. Thus, when inductive capacity is suppressed, the dimensional formula for magnetic quantity on this sys- tem is the same as that for electric quantity on the electrostatic system. All quan- tities in this system which only differ from corresponding quantities defined above by the substitution of magnetic for electric quantity may have their dimensional formule derived from those of the corresponding quantity by substituting P for K. 1. Magnetic Pole, or Quantity of Magnetism.— Two unit quantities of magnetism concentrated at points unit distance apart repel each other with unit force. The dimensional formula is thus the same as for [force X length? X in- ductive capacity] or M'L'TP!, and the conversion factor is m'J'¢77?. 2. Density of Surface Distribution of Magnetism. — This is measured by quantity of magnetism per unit area, and the dimension formula is therefore the ratio of the expressions for magnetic quantity and for area, or M*L~T™P*, which gives the conversion factor m'2~'s-1p3. 3. Magnetic Force at a Point, or Intensity of Magnetic Field. — The number for this is the ratio of the numbers representing the magnitudes of the force on a magnetic pole placed at the point and the magnitude of the magnetic pole. The dimensional formula is therefore the ratio of the expressions for force and magnetic quantity, or MLI+ and the conversion factor m'/¢-1p-, = ML7T“P4, 4. Magnetic Potential. — The magnetic potential at a point is measured by the work which is required to bring unit quantity of positive magnetism from zero potential to the point. The dimensional formula is thus the ratio of the formula for work and magnetic quantity, or Mir M?L!T—'P3 which gives the conversion factor m/!¢p-3. = MLITP3, 5. Magnetic Moment. — This is the product of the numbers for pole strength and length of a magnet. The dimensional formula is therefore the pro- duct of the formula for magnetic quantity and length, or M’L'T~'P!, and the con- version factor mJi¢-1p!. 6. Intensity of Magnetization. — The intensity of magnetization of any por- tion of a magnetized body is the ratio of the numbers representing the magni- XXX INTRODUCTION. tude of the magnetic moment of that portion and its volume. The dimensional formula is therefore the ratio of the formule for magnetic moment and volume, or MiLiT—P! L’ The conversion factor is therefore m/s". = M?L?T“'P}. 7. Magnetic Permeability,* or Specific Magnetic Inductive Capacity. — This is the analogue in magnetism to specific inductive capacity in electricity. It is the ratio of the magnetic induction in the substance to the magnetic induc- tion in the field which produces the magnetization, and therefore its dimensional formula and conversion factor are unity. 8. Magnetic Susceptibility. — This is the ratio of the numbers which repre- sent the values of the intensity of magnetization produced and the intensity of the magnetic field producing it. The dimensional formula is therefore the ratio of the formule for intensity of magnetization and magnetic field or M?L“T!P? MLAs % * The conversion factor is therefore #, and both the dimensional formula and con- version factor are unity in the ordinary system. g. Current Strength. — A current of strength ¢ flowing round a circle of radius 7 produces a magnetic field at the centre of intensity 27c/r. The dimen-: sional formula is therefore the product of the formule for magnetic field intensity and length, or M'L}T~!P-, which gives the conversion factor mJ't1p7+. 1o. Current Density, or Strength of Current at a Point. — This is the ratio of the numbers for current strength and area. The dimensional formula and the conversion factor are therefore M*L7?T“P> and mt tpt. rr. Quantity of Electricity. — This is the product of the numbers for cur- ‘rent and time. The dimensional formula is therefore M'L'T—P> « T= M!L}P™, and the conversion factor m/f. 12. Electric Potential, or Electromotive Force. — As in the electrostatic system, this is the ratio of the numbers for work and quantity of electricity. The dimensional formula is therefore ML*T-* MLIPS and the conversion factor m‘/!¢-*p', — M!L'T—P!, * Permeability, as ordinarily taken with the standard medium as unity, has the same dimension formula and conversion factor as that which is here taken as magnetic inductive capacity. Hence for ordinary transformations the conversion factor should be taken as 1 in the electromagnetic and /~f2 in the electrostatic systems. | . INTRODUCTION. XXxi 13. Electrostatic Capacity. — This is the ratio of the numbers for quantity of electricity and difference of potential. The dimensional formula is therefore M!?Lip+ MLIT=P! and the conversion factor 74777}, == Pe dekey 14. Resistance of a Conductor. — The resistance of a conductor or elec- trode is the ratio of the numbers for difference of potential between its ends and the constant current it is capable of producing. ‘The dimensional formula is therefore the ratio of those for potential and current or M!L!T—?P} MLITP4 The conversion factor thus becomes /¢~', and in the ordinary system resistance has the same conversion factor as velocity. sie, 15. Conductance. — This is the reciprocal of resistance, and hence the dimen- sional formula and conversion factor are respectively L~-'TP™ and 77-4, 16. Conductivity, or Specific Conductance. — This is quantity of electric- ity transmitted per unit of area per unit of potential gradient per unit of time. The dimensional formula is therefore derived from those of the quantities men- tioned as follows : — M?1}P—3 Mees ee L epee The conversion factor is therefore 7“. 17. Specific Resistance. — This is the reciprocal of conductivity as defined in 15, and hence the dimensional formula and conversion factor are respectively obs e and, es 18. Coefficient of Self-Induction, or Inductance, or Electro-kinetic In- ertia. — These are for any circuit the electromotive force produced in it by unit rate of variation of the current through it. The dimensional formula is therefore the product of the formula for electromotive force and time divided by that for current or M}L!T-?P} MTs * 7 = LP. The conversion factor is therefore /, and in the ordinary system is the same as that for length. 19. Coefficient of Mutual Induction. — The mutual induction of two cir- cuits is the electromotive force produced in one per unit rate of variation of the current in the other. The dimensional formula and the conversion factor are therefore the same as those for self-induction. XXXil INTRODUCTION. 20. Electro-kinetic Momentum.— The number for this is the product of the numbers for current and for electro-kinetic inertia. The dimensional formula is therefore the product of the formula for these quantities, or M'L’T“P+ x LP — M!L!T“P}, and the conversion factor is mJ't~1p', 21. Electromotive Force at a Point.— The number for this quantity is ! the ratio of the numbers for electric potential or electromotive force as given in | 12, and for length. The dimensional formula is therefore M’L'T~*P?, and the conversion factor m’*/*t—*p?. 22. Vector Potential. — This is time integral of electromotive force at a point, or the electro-kinetic momentum at a point. The dimensional formula may therefore be derived from 21 by multiplying by T, or from 20 by dividing by L. It is therefore M'L'T“P!, and the conversion factor m'Z'-1p'. 23. Thermoelectric Height. — This is measured by the ratio of the num- bers for electromotive force and for temperature. The dimensional formula is therefore the ratio of the formule for these two quantities, or M?L'T-?P!0~, and the conversion factor m'‘Z't"p°67. 24. Specific Heat of Electricity. — This quantity is measured in the same way as 23, and hence has the same formule. 2s. Coefficient of Peltier Effect.— This is measured by the ratio of the numbers for quantity of heat and for quantity of electricity. The dimensional formula is therefore MO MUP — M?L P30, and the conversion factor m'Z~''0. EXAMPLES OF CONVERSION IN ELECTROMAGNETIC UNITS. (a2) Find the factor required to convert intensity of magnetic field from foot grain minute units to c. g. s. units. By (3) the formula is m/z, and in this case m = 0.0648, 7 = Bono. — 60, and f= 1; .*. the factors = 0.0648! & 30.487' X 60°* = 0.00076 847. Similarly to convert from foot grain second units to c. g. s. units the factor is 0.0648! & 30.48? = 0.046 108. (2) How many c. g.s. units of magnetic moment make one foot grain second unit of the same quantity? By (5) the formula is /#—1}, and the values for this problem are 7 = 0.0648, 7 = 30.48, ¢—= 1, andp=r1; .*. the number = 0.0648! X 30.48! = 1305.6. (c) If the intensity of magnetization of a steel bar be 700 in c. g. s. units, what will it be in millimetre milligramme second units ? INTRODUCTION. XXXill By (6) the formula is m'/!¢-1g', and in this case # = 1000, /= 10, ¢= 1, and p=1;... the intensity = 700 X 1000! X 10! = 70000. (2) Find the factor required to convert current strength from c. g. s. units to earth quadrant 10-" gramme and second units. By (9) the formula is 'Z!¢-19-, and the values of these quantities are here m = to {= 10-7, #= 1, and p =r ; .°. the factor = 10% K 10 $= 10, (e) Find the factor required to convert resistance expressed in c. g. s. units into the same expressed in earth-quadrant 1o-" grammes and second units. By (14) the formula is /¢-'f, and for this case 7= 10°, ¢=1, and p=1; = the factot — 10. (f) Find the factor required to convert electromotive force from earth-quadrant 101 gramme and second units to c. g. s. units. By (12) the formula is mZ!¢—%p', and for this case m = 107%, 7= 10°, ¢=1, and. f— "7 *.5 the factor =='10". PRACTICAL UNITS. In practical electrical measurements the units adopted are either multiples or submultiples of the units founded on the centimetre, the gramme, and the second as fundamental units, and air is taken as the standard medium, for which K and P are assumed unity. The following, quoted from the report to the Honorable the Secretary of State, under date of November 6th, 1893, by the delegates repre- senting the United States, gives the ordinary units with their names and values as defined by the International Congress at Chicago in 1893 : — “ Resolved, That the several governments represented by the delegates of this International Congress of Electricians be, and they are hereby, recommended to formally adopt as legal units of electrical measure the following: As a unit of re- sistance, the zzternational ohm, which is based upon the ohm equal to ro® units of resistance of the C. G. S. system of electro-magnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grammes in mass, of a constant cross- sectional area and of the length of 106.3 centimetres. “As a unit of current, the zmternational ampere, which is one tenth of the unit of current of the C. G. S. system of electro-magnetic units, and which is represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, and in accordance with accom- panying specifications,* deposits silver at the rate of 0.001118 of a gramme per second. * “Tn the following specification the term ‘silver voltameter’ means the arrangement of appara- tus by means of which an electric current is passed through a solution of nitrate of silver in water. The silver voltameter measures the total electrical quantity which has passed during the time of the experiment, and by noting this time the time average of the current, or, if the current has been kept constant, the current itself can be deduced. “Tn employing the silver voltameter to measure currents of about one ampere, the following arrangements should be adopted : — XXXiV INTRODUCTION. “As a unit of electromotive force, the zternational volt, which is the electro- motive force that, steadily applied to a conductor whose resistance is one interna- tional ohm, will produce a current of one international ampére, and which is rep- resented sufficiently well for practical use by }$$% of the electromotive force between the poles or electrodes of the voltaic cell known as Clark’s cell, at a tem- perature of 15° C., and prepared in the manner described in the accompanying specification.* “As a unit of quantity, the ¢ternational coulomb, which is the quantity of elec- tricity transferred by a current of one international ampére in one second. “As a unit of capacity, the zfernational farad, which is the capacity of a con- denser charged to a potential of one international volt by one international cou- lomb of electricity.f “As a unit of work, the jow/e, which is equal to ro’ units of work in the c. g. s. system, and which is represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm. “As a unit of power, the waz/, which is equal to 10” units of power in the c. g.s, system, and which is represented sufficiently well for practical use by the work done at the rate of one joule per second. “As the unit of induction, the Zexry, which is the induction in a circuit when the electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second. ‘The Chamber also voted that it was not wise to adopt or recommend a stand- ard of light at the present time.” By an Act of Congress approved July 12th, 1894, the units recommended by the Chicago Congress were adopted in this country with only some unimportant verbal changes in the definitions. By an Order in Council of date August 23d, 1894, the British Board of Trade adopted the ohm, the ampere, and the volt, substantially as recommended by the Chicago Congress. The other units were not legalized in Great Britain. They are, however, in general use in that country and all over the world. “The kathode on which the silver is to be deposited should take the form of a platinum bowl not less than Io centimetres in diameter and from 4 to 5 centimetres in depth. “The anode should be a plate of pure silver some 30 square centimetres in area and 2 or 3 millimetres in thickness. “This is supported horizontally in the liquid near the top of the solution by a platinum wire passed through holes in the plate at opposite corners. To prevent the disintegrated silver which is formed on the anode from falling on to the kathode, the anode should be wrapped round with pure filter paper, secured at the back with sealing wax. “The liquid should consist of a neutral solution of pure silver nitrate, containing about 15 parts by weight of the nitrate to 85 parts of water. “The resistance of the voltameter changes somewhat as the current passes. To prevent these changes having too great an effect on the current, some resistance besides that of the voltameter should be inserted in the circuit. The total metallic resistance of the circuit should not be less than 10 ohms.” * “ A committee, consisting of Messrs. Helmholtz, Ayrton, and Carhart, was appointed to pre- pare specifications for the Clark’s cell. Their report has not yet been received.” + The one millionth part of the farad is more commonly used in practical measurements, and is called the microfarad. Pinole xi, TABEES TABLE 1. FUNDAMENTAL AND DERIVED UNITS. (2) FUNDAMENTAL UNITS. Name of Unit. Symbol. | Conversion Factor. Length. | Mass. | Time. Temperature. Electric Inductive Capacity. Magnetic Inductive Capacity. (4) DeRIvED UNITS. LI. Geometric and Dynamic Units. Name of Unit. Conversion Factor. Area. Volume. Angle. Solid Angle. Curvature. Tortuosity. Specific curvature of a surface. Angular velocity. Angular acceleration. Linear velocity. Linear acceleration. Density. Moment of inertia. Intensity of attraction, or “force at a point.” Absolute force of a centre of attraction, or “strength ) of a centre.” Momentum. Moment of momentum, or angular momentum. Force. Moment of a couple, or torque. Intensity of stress. Modulus of elasticity. Work and energy. Resilience. Power or activity. SMITHSONIAN TABLES. TABLE 1, FUNDAMENTAL AND DERIVED UNITS. IT. Heat Units. Name of Unit. Quantity of heat (thermal units). “ (thermometric units). és «(dynamical units). Coefficient of thermal expansion. Conductivity (thermal units). ff (thermometric units), or diffusivity. :. (dynamical units). Emissivity and imissivity (thermal units). : (thermometric units), “e “ce Thermal capacity. Latent heat (thermal units). = «(dynamical units). Joule’s equivalent. (dynamical units). Entropy (heat measured i in thermal units). (ae dynamical units). LTT. Magnetic and Electric Units. Name of Unit. Magnetic pole, or quantity of eat netism. | Density of surface distribution of } magnetism. Intensity of magnetic field. Magnetic potential. Magnetic moment. Intensity of magnetisation. Magnetic permeability. Magnetic susceptibility and mag-)} netic inductive capacity. j Quantity of electricity. Electric surface density and electric ) displacement. y Intensity of electric field. Electric potential and e. m. f. Capacity of a condenser. Inductive capacity. Specific inductive capacity. Electric current. SMITHSONIAN TABLES. Conversion factor for electrostatic system. m’ Li R- ms FB m* 1s ¢-? Bi m’ 13 ¢-? Rt m* 13) R-4 m* I-* kt I Tr? ?? lm m* [3 t-1 hi m* [4 ¢ Rh m’ I? ¢-* k-+ m: lt ¢-1 kt Lk k I m* [2 ¢-? he Conversion Factor. m 6 m [-* ¢-? Lt m Lt-* §- mi t+ Li Tt Oe m 6 pte Lut" 6 m Wel to Conversion factor for electromag- netic system. m* 13 ¢- ph m* I ¢ p m [>t p-4 m 1+ tp m 1? ¢7 ps m [tt ph I Bb m> 1* pi ms [3 p-4 m 13 t-* ph m* [3 ¢-* pi i g7 p+ rote I m [4 ¢71 p- TABLE 1. FUNDAMENTAL AND DERIVED UNITS. ITI. Magnetic and Electric Units. a Conversion factor Conversion factor Name of Unit. for electrostatic for electromag- system. netic system. Conductivity. 4 Pipe Specific resistance. tk aD | Conductance. Lie Lp | Resistance. LAG 27 Coefficient of self induction and Pl 4a pd 7 coefficient of mutual induction. 2 Electrokinetic momentum. ms 1? k m* 13 ¢1 ph Electromotive force at a point. mt [+t k4 m 1} tp} Vector potential. m* [3 k m* [* t-} p} Thermoelectric height and specific 1 7h eo 7 eh aes . heat of electricity. 8 DER CEN EE CT Coefficient of Peltier effect. ml tk 0 m I p 6 SMITHSONIAN TABLES. TABLE 2. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEICHTS AND MEASURES.* (1) METRIC TO IMPERIAL. LINEAR MEASURE. MEASURE OF CAPACITY. I ae = 0.03937 in. I are (ml.) (.oor — 0.06103 cub. in. .OOl m. itre I centimetre (.olm.) = 0.39371 “ clerccm, I decimetre (.1m.) = 3.93708 “ I centilitre (.o1 litre) : ee ‘ll {8 ¢ rials oe I METRE (m.) . .= 3.28089917 ft. I decilitre (.1 litre). . 0.17608 pint. 1.09363306 yds. I LITRE (1,000 mt ate “ centimetres or I 10.93633 cub. decimetre) 1 dekalitre (1o litres) . 2.20097 gallons. 1 hectolitre (100 “ ) . 2.75121 bushels. 1 kilolitre (1,000 “ ) . 3-43901 quarters. 1 dekametre } 1.76077 pints. (10 m.) 1 hectometre t (100 m.) 1 kilometre (1,000 m.) ' : I myriametre (10,000 m.) t ; 2022 ‘ 109.36331 s 0.62138 mile. 6.21382 miles. EH MICroOliire ws.) tons 0.001 ml. HMIcCrOny . «) -O1 X G1001°E Lrgfoo'h| + €106S9'F | or X OSo9S-b | ShzZo1S | cor X LghLS-1] ghzoSEE| gor X OOObe"z | O19gOS'S | gor X O9Szz" Oo t =a NEN cy “BoT ‘ON “B0'T ‘ON ‘B07 ‘S0'T ‘307 ‘ON *JU9d) -0 18 *yuad 90 1 ‘arqawiUuas “your *JO0J “sql ozz = 00} BUD Aindiaw Jo sa1jauijuad Ammpiaw jo sayouy azenbs iad sauueig aienbs 1ad spunog aivnbs 19d spunog ‘yout aivnbs sad suo y, ‘sL'1/ W = suotsuow qd Comsveyy WoHNIyALIH) ‘voIY 11U Jed eo10Z IO SseNS JO Wo[ssodxg 10J SIOJO’ WoTsIOAUON — ‘OZ ATAVL SMITHSONIAN TABLES. 19 TABLES 22, 23. CONVERSION FACTORS. Oo 000000°S $9SS6z'0 ZQQorI'y ziLibyZ of606b4 ‘Bo, O bE Loob'z zfgiSz'2 oSgzZ1'1 ‘B0T *aaqjaurt}u99 Jvaury tad soumurery i ggzfOS"1 o1 X £Q616°E g-Ol X £118S°2 Oo iT zOl X 64S Q2'1 9608 F9" I o1 X c0000'Z Ol X QIggh'l L16S9L'z gol X CELEgS ‘ON ‘30, ‘ON your avauty Jed suteig "aL / W = suolsuautcy iE cOI X 00000"! LoS L6'1 yO X SSzgl"1 01 X oS QL'z 101 X 16960° ‘ON *SO1JOUII}UIT) OUIUIRIL) "gL / eI = suoisuoung (COIMSVOT WOT}E}JALIP) 000000°'S | gO X 00000°I 0 p9SS62S T gibvolb 901 X LoS L6"1 0 T zggorr'r | ;_o1 X SSzgE"1| g6oShge't zilibhz| ,o1 Xo1Sg4'z| gz1ghid of606b'z | 701 X 16960'f |orES61-Z *B0'T ‘ON ‘B0'T *SaajOT DUIUIRADO[IY *SUILI) JOO] gorgh Le coors 1°z 0 61g0z6'z g-O1 X 9L668°S z-Ol X VSgzr'r 1 g-O1 X ELELE*g ‘B07 ‘ON ‘your vault sed spunog gibrol-1| 01 X o1£g0'S 701 X O1fgo'S gOI X 00000'L OI X COCOF'I 101 X COgOS'1| ghzoSE-E ofo10£'f Q1£6S9'S | p01 K OOLEz°Z gi£6S9'0 zo6rS 1° | --01 XK PS gz I ooffz°Z 0 T gOI X 00000°z gOl X C0Ohz*z ‘ON ‘spunog 00,4 (‘sq[ 000z = 0} 280Q) rE Lzg'z ree z-Ol X 14614'9 gobtz: t g-Ol X gehviLi 1g16Lo'1 Ol X 00002"! 0 T ON *JOo} avsut, Jed spunog “OJSUOT, OOVJING 10 WIT JO UojSsoAdxT LOZ s10jOvF Wojsteau0N — “es ATAVL 0£060S'g| gor X zobzz'E e-O1 X OSQIO'E 0Lo60$ £ | gor X zo6ze" g0l X Sgehi‘L| PSobog's| g—O1 X SSLLE-9 ;-01 X 00000°S | z$ L6Fg'F | ,01 X Oz both T: z9Z0$6'1 | ;~o1 X LS gz6'g oo00zI'! O rT: p01 X OFQI19°E ‘ON ‘BOT ‘ON (‘sql obez = U0} BNO) ‘suoy, }004 suo], 004 (OMSBOTT WOpe}ALID) *AdIoug 10 HIOM Jo WOysseldEg_ Loy s10j9vJ WoysteaudopH — ‘oe ZIGVG SMITHSONIAN TABLES. 20 TABLES 24, 25. FACTORS. CONVERSION T gIf6So°S | g-O1 X 66zEz°Z | 699166°S sO1 X SSzof'1 oO i ISEzE 1-0 301 X ZE610'1 | 6tgZgg'r | ;o1 X gok 464 Oo g-Ol X LE610'1 | GtgZog'g | g-Ol X gofZE-Z | coooco'Z gol X SQS6z-h | LeEzorz | 5-01 X FoLoI'E | gb6gbhzg'z | | Petals Ne 2 ety *B0T ‘ON fer | oN ‘ON *B0'T “sodjeuIUaD suUTWeID (FoSgi-zE=3) ‘spunog 1004 ‘aL / cI = suoisuewiqe e—OI X 000196 6z9S "1 y—-OI X 00000'I T z-Ol X Lohiz 6991662 Eclr-Z o000000°4 O g6ghzg'S ‘SOT zOI X 00019°6 101 X 6zoStr1 101 X 00000°1 T gl X Lobiz'b ‘ON *soud(y aijoumjuad 10 s8iq IZ699£°€ | o_o1 X F6Lz£-z ESo40$"1 oI X OSgiz‘€ zo LE:z zoe l£'z T ‘ON ‘sjepunog j00 4 ComMsveyl oynjosqy) ‘ASIouq 10 HIOM Bupssoidxy 10J s10j9¥,z wWoTs1eAMON — ‘Gz TTAVL ic g10h66'1 1-01 X 61£9g°6 | GzZogg’z | Or X ghLSEL | Gzlogg'6 | ,o1 X QhLSE-Z Lefto'1 iG erdzdgz | zor K OSOSb-Z | Erlzle" gOl X 9S6Sh°Z g-OI X g16SE"1 : g—OI X 9SoPE'1 Oo Tt oooooo'Z | ,O1 X 00000"! gs le : ot—-Ol X Diese ot-Ol X gSobE+1 | Coo000'L | , O01 X 00000'1 oO ic ul g—-O1 X SSLzL'S : g=O1 X L16b9°S | g6gbzg'z | z-01 X LCobizb | g6grzg'S | .o1 X LohIZ a kK ‘ON ‘BOT *B0'T ‘ON E z a *[RAVYO ap 9010.7 (1g6=3) ‘1samod assozy Say aotencer ae auinnety *‘puodas sad sjepunog 30044 = ¢ Hua, cS 7) "eL / ce IIN = suotsuowiq (oMSvell oynjOsqyY) ‘ARTATOY 10 IupAIOM Jo opvy ‘omog JO UOssordxgq 10F SLOJOV WOTsIoATON — "Zz ATAVL 2I TABLES 26, 27. CONVERSION FACTORS. Oo ic PE Loobz z-O1 X b11SS'z 1££g00'F gO X LE610°1 6L1bbL-o PS obSS (‘2as aad ‘:9as rad ‘suo 1g6 = 3) "wd vault sad sawurein ‘cL / W = suotsuewiqg (‘OIMSvETT ONTOS Ty) 0 iL 000000°z z-O1 X 00000°1 Cro €-1 o1 X S6zhI'z oSgzZ1'1 TOI X 9I99h'I ‘ON ‘aajat oienbs sod saudpesoyy *sL'I / W = suoisuswiqd (‘OINSvOT ONTOSGT) or X 19616°E T zoI X £LS66°E gOl X OOF L1'z ‘oT ‘ON (‘oas tad ‘das 19d ‘suo 196 = 3) ‘yout avour aed surein z01 X 000196 t-Ol X Lgzo$:z ie gol X zIEPPS ‘ON ‘your avout] Jed saudq ‘MOJSUOT, OOVJING IO WTTJ JO WOTsseldxy Oy S10jO¥J WoTsIeaTON — ‘youl ivauty red sjepunog 42 TIEVL 000000'z Oo £r1o1£€-€ oSg9zZ1'I 7zOl X 00000"! G iE eOl X S6zh1'z OI X O199h'1 Le6.99q9'% Lg6g99'h oO LEgibgé ‘B07 ‘ON ‘So, z-O1 X gbggg'h ,-O1 X ObQ90'F Ec e-OI X thhh6'9. “ON 6rELz9'0 126129 ortlzgz z-0O1 X 126129 zQlQS 1°z zOl X OoorF'! 0 T ‘30'T ‘ON ‘aqjauues aienbs sad saudqy ‘yout oivnbs sad sjepunog *JOoj o1enbs sad sjepunog ‘voIW JO 1JUM I0d e010 10 SSONG JO WOTsseldxq Oy s10}Ov, WOFSIEATO 0—'92 TT&Vi SMITHSONIAN TABLES. 22 TABLES 28, 29. CONVERSION FACTORS. ‘}IUN Sv UAV], Oo 06086¢'S | e_o1 X g6£S9°Z] 060869'9 | 9 _o1 XK 96£S eZ caotbl-g| g—O1 X EFS" | G0rg6h'S | oor & PS Qhr€ o16Forb O i 000000'1 | ;O1 X 00000" | zEogtg'h | ;_o1 X Oz ZSo°Z] 610£09'1 | or & PQQ00'F o16tor's | « "I }O00000°1} OI X C000"! Oo T zloghgt | -o1 KX ozZSo'Z] 610£09'0 | togoo'h O 168108 “+ *€ | 19696£'0 gbhhorz | 1g696£°1 | ;-01 X ghh6bz | €1SShz'£ | » or X C00gL"1 Oo iT ‘20T ‘ON *B0T ‘ON ; : ‘B07 Pac etlitielitie) (‘wut 1 = p) (‘wd 1 = p) (‘Tur auo = p) (‘your r = p) dIQQD & JO voueR}sISAy # WII V JO dduL}stsayy x WJIWO[LY BJO VdUL}SISOY x PARA BJO VdUR\sISAXT x ITT, & JO dduR}sIsayy “\L”/JT = suotsuswiq “OOWBISISOY [BOTIIOTA Ojyyoedg yo worsserdxq oy s10,0",7 WOISI9AMON — ‘6% AIAVL Oo T PE6zob'c| or X 16gzS-z]oFgZSS:z | zor X PLzI9E]og€S6L1| jor X 1gzbz-9]zSzzqq°6 | ~or X QOF6S*P 990ZL6S'E | 901 X gzbS6'E Oo iT coors | ,01 X LSgzhilobbc6£1 _O x re 118682" 101 x SggIg'! boichhr O1 X 66294'z] g60S bg'E| gor X COO0O'L Oo T brS lez] ,or xX oogeZ:1]Srbbor11| 01 X 6Z1Zz° ozgboz'z | z-O1 X P1091} PS $Zo9°0 L6oSo'bloStzglb | ,01 X FoLgZS Oo iT: zLggqg°Z | ,01 X 060S€: | ghZZEE ‘Ot ot-O1 X broL1-2|Eggobd'g! ._o1 X SoboS'S [hgSS6gz1| g01 X £6zgg"L] gz1FE1°g] , OF X ZLESE- oO “B0T ‘ON ; ‘30, ‘ON E *‘SoT *uitjU99 oIqnd aad sawueIg "yout o1qno aad sureigy ‘yout o1qno zed spunog "JO0} OIqno 19d spunog oni SAI UCeRrE ‘g1/ W = suolsusung "SORISUO JO Woysseldxy 10} sIojovZ woysIeAUON — ‘SZ ATAVL TABLES. SMITHSONIAN 23 TABLES 30, 31. CONVERSION FACTORS. oO LzlS¢L-1 PLEere-€ PEEEPEl-o “B0T ie t-O1 X 9£ 9098'S gOl X cQroz'z zQror'z (‘D 224139p punog) 0 iS1gllz 999989'1 oz L6g$-E ‘B0'T zlzbSz: 9961 Oo ic 909965" gOI X z£Qq6'E gogg6S‘o z£Q06'E *S0'T ‘ON (‘q 9213ap punog) ‘JlUC) [euLOyy, ysuug 99998 9'h POE 1ob-F oO o00000'f ‘B0'T 7-01 X LOSES -b 7-01 X 9061S'z T gOl X 00000°! ‘ON (‘<2 9a13ap aurmtesrn) *OUO[eD [[euWIg 10 ‘ULIaY J, 9999S9"1 1-01 X LOSES“ FOL 1oh'1 TOI X 96618 ‘z 000000°f g—-O1 X 00000'1 0 T ‘B0T ‘ON (‘2 xeadap swuMesso] ry) *aLO[eD, ‘@W = suorsuoung T z-O1 X 00000'9 OI X £6SES gO X HOLEg'E ‘ON ‘ajnurut sad soumumessopry o1 X 49999"! T 996SS°Z z-O1 X 6962-9 ‘ON *“puosas aod SOUIUUIBIL) ‘JOH JO SopWuend Jo wopsserdxq oy s10jowy woysieaw0g — "Te ATAVL t-O1 X Llzzt'1 iE g-O1 X EF125°9 ‘ON ‘aynutu Jad spunog ‘L/W = suotsuaunq zgboz'c ogzort'z cfroor'l a L£b6gg90°z mn 0 F < ‘07 z ° o x *‘puosas aad sureisy = = a "MONSoded ,ATONIETH JO woysserdxq 10y s1010v,7 MOIsisAT0N — "0S TTIVL 24 TABLES 32, 33. CONVERSION FACTORS. TABLE 32.—Conversion Factors for Expression of Temperatures. Dimension = 0. Centigrade. Fahrenheit. Réaumur. No. 1 af : y 8.00000 X 1071 5.55550 X 10-4 1.744727 4.44444 X 1071 1.25000 0.096910 : : 1 In many of the derived units for the measurement of physical quantities, the unit of time may be taken as constant, because it is seldom that any other unit than the second is used. This is the case, in particular, for the electric and magnetic units. Tables 33-37 below, giving the factors for the conversion of units depending on different dimensional equations in M and L from one set of fundamental units to another, will be found sufficient for almost all cases. TABLE 33.— Electric Displacement, etc. Dimensions = M?L 3 T", Foot Grain Metre Gramme Centimetre Gramme or } Second Second Units. Second Units. Millimetre Milligramme J§ Units. Log. No. Log. FoRE273 0.179760 Le5I2795< 100" 3-179760 E O 1.00000 X 1073 3.000000 x 1.00000 X 10% 3.000000 SMITHSONIAN TABLES. 25 TaBLes 34, 35. CONVERSION FACTORS. 0 LE 000000'z z01 X 00000" I o00000'f gO I X 00000" I zOLLh1°z gol X gfSor'1 ‘ON ‘swuy) puosag SUITES OUTIL ‘uly TQW = suoisueung 0 u 000000'z zOl X 00000'I 000000" I OI X 00000°1 zLLEqg'0 $Lo19'v eoOn]) *syluy) puossg SUMMIT O4}OUNTT [LAT “yLg_Tg WN = suorsuauig Q00000°¢ z-Ol &K 00000'I Oo iE 000000’ I OI X 00000'I z6LLh1'0 gf Sor'1 ‘BOT ‘ON ‘suuy) puosag aUWIWILID d1JBWIUID oooo00'£ | ¢ Ol XK COOOO'! 00000071 | Ol X 00000°1 0 T c6LLZbrr | ~01 X QgeSor'1 ‘BOT ‘ON *‘s}tuy) puosag DURAN a1}9]T "ojo ‘WOWeZHouseI Jo AysueyUT— "Ge DIGVL o00000°z | z_OI X 00000°1 0 T o00000'r | ;_OI X 00000"! zll£og'z | z-01 X SLo19'F 000000'T T-OI X 00000" I 000000'I OI X 00000'I 0 T zZltgg'i | 7-01 X S4o19°h *BO'T ‘ON ‘sug puosag DUIWIRAD) 91} 9WIUID ‘B0T ‘ON ‘slup) puosag DUIWIVAT) B1JATT eO1 X HSS 11° t-O1 X HSS 112 pSSi1rZ T ‘ON *sylu~) puorag ulvID) }00q t-OI X PgggI OI X P8ggI Pggol ic *s}ta) puosas UIvIt) JOO] 0} “MISoUTeM JO Aysuod eovjMs — ‘be TIAVL SMITHSONIAN TABLES. 26 TABLES 36, 37. CONVERSION FACTORS. Oo T Oo0000"F =| ;0I X 00000°1 000000°S$ | OI X 00000°1 begsirZ | ,or X FoSo€-x ‘0, “SHUG, puods3sg SUUBLSY [LY PAFOUUTTTIAT oo0000o"r | zOI X 00000'I 0 T 000000'I OI X 00000°1 begS1r€ gOIl X FOSOf'r 000000'S 000000" I e—OI X 00000°1 {-OI X 00000'1 ae zOl X boSot-1 0 begs irz g-O1 X Lo6Sg'Z ¥ | x01 X Lo6Sg°Z gLibggt | g o1 XK Lo6Sg°Z 0 Ec gLibges gLibgoh ‘ON ‘s}luy) puovag sWIWeIF) aajaWII}UID *30'T ‘ON *s}luf) puosag DUIWEID) atOP “doy ‘ON ‘s}lUQ) puosag uleviy joo 4 ‘wL e1yN = suoisuewg O T o00000'€ | .oI & 00000"! 000000'9 | ,OI X 00000"! gogitg'h | 01 X 6S€gz'h ‘20T ‘ON ‘s}Iuf) puosas SUIURASIL YL erg aMUTT LAY ‘019 “JUSMOYL OouseM — "Ze ATAVL o00000°€ | »_O1 X C0000"! Oo i o00000'f gOI X 00000°1 gogrfg'1 O1 X OS£9z'h 20, "ON, ‘s}u(Q) puosag SUIUILIL) a1j}aWIT]UID 000000°9 oo00000'f 0 gogitgrz g-OI X 00000'1 g—OI X 00000°1 T z-Ol X OS£9z'h ZOIQOQE'S | gor XK OFFEE'z zO1g9£°0 OFPEE-z ZOIQOLI OI X 6bFEE'z 0 T *B0'T ‘ON *s}luf) puosag oUURIL) a1}0Y “30, "ONT *sytu~) puorvag Urery) 1004 ‘wl g Ty = suorsuoung ‘O19 ‘TeNUeOd 00IT — ‘98 ATAVL SMITHSONIAN TABLES, 27 TABLE 38. RynnN rp “3 4 oO 6 7 8 9 0 I 3 4 22.339 24.691 WWWWW WHNUuw Ww 27.290 30.162 33-336 30.543 40.719 45-003 49-7 37 54-969 60.751 67.141 OONAM FOKHHO OON AY SSSA RP BLSDD HYPERBOLIC FUNCTIONS.* Hyperbolic sines. 0.0100 1102 2115 3150 -4216 0.5324 6485 Le -QOI 5 1.0409 1.1907 “3524 527 -7182 OZ 50) 2.1529 -4015 .6740 ‘97 34 3-3025 3-6647 4.0035 4.5030 4.9876 5.5221 6.1118 6.7628 7-4514 8.2749 g.1512 10.119 11.188 12.369 13-674 15-116 16.709 18.470 20.415 22.564 24-939 27.504 30.465 33-671 37-214 41.129 45-455 59:237 55.522 61.362 67.316 * Tables 38-41 are quoted from ‘‘ Des Ingenieurs Taschenbuch,” herausgegeben vom Akademischen Verein (Hiitte). SMITHSONIAN TABLES. 28 0.0500 1506 2526 SY fe -4053 0.5782 .6967 8223 9501 1.0995 1.2539 -4208 6019 7991 2.0143 2.2496 5075 7904 3.1013 4432 3.8196 4.2342 4.6912 5.1951 5-7 510 6.3645 7:0417 7-7894 8.6150 9.5208 11.534 12.647 12.876 14.234 15-734 17.392 19.22 21.249 23.486 25.958 28.690 31-799 35-046 38-733 42.805 47.311 2.288 57-788 63.866 70.554 Values of “i 0.0701 -1708 2733 +3785 “4875 0.6014 7213 8484 9840 1.1294 1.2862 -4555 -6400 -8406 2.0597 2.2993 5620 8503 3.1671 51 56 38993 4.3221 4.7880 5.3020 5.5689 6.4946 7.18 54 7-9450 8.7902 9-7 203 11.748 12.883 13.137 14.522 16.053 17-744 19.613 21.679 23-9601 26.483 29.270 32-350 35-754 39-515 43-073 48.267 53-344 59-955 65-157 72.010 0.0901 -IQII 2941 -4000 5098 0.6248 -7401 8748 .O122 1.1598 1.3190 -4014 -6788 8829 2.1059 2.3499 -6175 -OI1I2 3-2341 “5894 3.9806 4-4117 4.8868 5.4109 5.9892 6.6274 73319 8.1098 8.9689 9-9177 11.966 12.124 13.403 14.816 16.378 18.103 20.010 22.117 24-445 27.018 29.862 33-004 36.476 40.314 44-555 49.242 54.422 60.147 66.473 73-465 HYPERBOLIC FUNCTIONS. Values of eto. Hyperbolic cosines. 49-747 54-978 60.759 67.149 PPP PEER RP HHHHWW HWHWY f > p OON AN POKHHO OONUAUGH SWdH SMITHSONIAN TABLES. 1.0008 .0098 0289 0584 .0984 -1494 2119 2865 -3740 “4753 1.5913 7233 8725 2.0404 .2288 2.4395 .6746 9364 3:2277 5512 39103 4.308 5 4-7499 5.2388 5-7901 6.3793 7-0423 7-775 8.5871 9.4844 10.476 11.574 12.786 14.127 15.610 17.248 19.059 21.061 23-273 25-719 28.422 31-409 34-711 38.360 42.393 46.851 51-777 57-221 63-239 69.859 29 1.0013 0113 0314 0619 -1030 -ISSI -2188 -2947 +3835 .4562 .6038 7374 8884 0583 2488 2.4619 -6995 9642 3-2585 “5855 3-9483 4-3507 4.7966 5.2905 5.5373 6.4426 7.1123 78533 8.67235 9-5791 10.581 11.689 12.915 14.269 15.766 NNN He NO ST Onn df STO eSSiiGra Nb Of i) me OO Unb 1.0018 .0128 0340 0055 .1077 1.1609 2258 «3030 "3932 -4973 6164 7517 9045 2.0704 2091 2.4845 -7 247 3.2897 3 .6201 3-9867 4.3932 4.5437 5.3427 5.5951 6.5066 7.1831 7-9136 8.7594 9.0749 10.687 11.806 13.044 14.412 15.924 17.596 19.444 21.486 23-743 26.238 28.996 32-044 35-412 39-135 43-250 47-797 ee 59-377 64.516 71.300 1.0025 0145 0307 0692 1125 1669 +2330 3114 4029 5085 .6292 -7662 9208 0947 -2896 2.5073 7502 3.0206 3212 6551 4.0255 4.4362 4.8914 5.3954 5-9535 6.5712 7-2546 7.0100 8.8469 9.7716 10.794 11.925 13-175 14.550 16.084 NNN eS DY AON Mons On mown NW KO N ° TABLE 39. 1.0032 -O162 0395 .07 31 1174 1.1730 .2402 +3199 -4128 “5199 1.6421 7808 9373 ZIG2 3103 2.5305 -7760 3-0492 -3530 -6904 4.0647 4-4797 4-9395 5.4487 6.0125 6.6365 7.3268 8.0905 8.9352 9.5693 10.902 12.044 13.307 14.702 16.245 17.951 19.536 21.919 TaBLe 40. HYPERBOLIC FUNCTIONS. Common logarithms + 10 of the hyperbolic sines. 8.— 0.1 0007 0.2 BO5b tl ee 0.3 4836 9.6136 9.7169 8039 0.7 8800 0.8 9485 IO.O114 10.0701 Tan 1257 1.2 1788 8 2300 2797 10.3282 3758 7 4225 | 4 1.8 4087 5143 10.5595 21 6044 6491 6935 7377 Nv Wh 10.7818 $257 8696 oe OS pypepypd 11.0008 0444 0880 1316 1751 11.2186 2621 3056 3491 3925 11.4360 4795 §22 5664 6098 11.6532 6967 7401 7836 8270 AM POKHO OBNAHW F£HKHHO OONAH Ob Y SPSL P SPEER P YOY DN YWYYW DY com] © SMITHSONIAN TABLES. TABLE 41. HYPERBOLIC FUNCTIONS. Common logarithms of the hyperbolic cosines. 6 ih 8 9 0.0 | 0.0000 | 0000 | ooo! ooo8 | oolt OO14 oo18 OI 0022 | 0026 | 0031 0055 | 0062 | 0070 0078 We 0086 | 0095 | O104 O145 | o156 | 0168 | o180 0.3 0193 | 0205 | o219 0270 | o291 | 0306 | 0322 0.4 0339 | 0355 | 0372 0444 | 0463 | 0482 | oso2 0.5 | 0.0522 | 0542 | 0562 0648 | 0670 | 0693 0716 0.6 0739 | 0762 | 0786 0884 | ogo | 0935 og61 0.7 0987 1013 1040 1149 Malea7, 1200 1234 0.8 1263 | 1292 | 1321 1440 | 1470 | ISorI 1532 0.9 1563 | 1594 | 10625 1753) L705) |) Tore 1551 1.0 | 0.1884 | 1917 1950 2086 | 2120 | 2154 2189 Tel 2223 | 2258 | 2293 2435 | 2470 | 2506 | 2542 ie 2578 | 2615 | 2651 2798 | 2835 | 2872 290 1.3 2947 | 2984 | 3022 3173 | 3211 | 3249 | 3288 1.4 | 3326 | 3365 | 3403 3559 | 3598 | 3637 | 3676 15 | 0.3715 | 3754 | 3794 3952 | 3992 | 4032 | 4072 1.6 4112 | 4152 | 4192 4353 | 4394 | 4434 | 4475 1.7 | 4515 | 4556 | 4597 4760 | 48or | 4842 | 4883 1.8 4924 | 4965 | 5006 5172 | 5213 | 5254 5290 1.9 5337 | 5379 | 5421 5587 | 5629 | 5671 | 5713 2.0 | 0.5754 | 5796 | 5838 6006 | 6048 | 6090 | 6132 2.1 6175 | 6217 | 6259 6428 | 6470 | 6512 | 6555 2.2 6597 | 6640 | 6682 6852 | 6894 | 6937 | 6979 2.3 7022 | 7064 | 7107 7278 | 7320 | 7363 | 7406 2.4 7448 | 7491 | 7534 7795 | 7748 | 7791 | 7833 2.5 | 0.7876 | 7919 | 7962 8134 | 8176 | 8219 | 8262 2.6 8305 | 8348 | 8391 8563 | 8606 | 8649 | 8692 27 735 | 8778 | 8821 8994 | 9037 | 9080 | 9123 2.8 9166 | g209 | 9252 9425 | 9463 | 9511 | 9554 | 29 9597 | 9641 | 9684 9850 | 9900 | 9943 | 9986 3.0 | 1.002 0073 | o116 0289 | 0332 | 0375 | 0418 |) eset 0462 | o505 | 0548 0721 | 0764 | o808 | o8sr a2 0894 | 0938 | o9S1 1154 1197 1241 1254 3.8 132 1371 1414 1597 1631 1674 L7L7, 3.4 1761 1804 | 1847 2021 2004 | 2107 2151 3.5 | 1.2194 | 2237 | 2281 2454 | 2497 | 2541 2584 3.6 2628 | 2671 | 2714 2888 | 2931 | 2974 3018 | 37 3061 | 3105 3148 3322 | 3305 | 3408 | 3452 | 35 3495 | 3538 | 3582 3755 | 3799 | 3842 | 3856 ie 3:0 3929 | 3972 | 4016 4189 233 | 4278 | 4320 4.0 | 1.4363 | 4406 | 4450 4623 | 4667 | 4710 | 4754 4.1 4797 | 4840 | 4854 5057 | SOL | 5144 | 5188 4.2 5231 | 5274 | 5318 $492 | 5535 | 5578 | 5622 43 5005 | 5709 | 5752 5926 | 5969 | Gor2 | 6056 4.4 6099 | 6143 | 6186 6360 | 6403 | 6447 6490 4.5 | 1.6533 | 6577 | 6620 6794 | 6837 | 6881 | 6924 | 4.6 6968 | 7oIr | 7055 7228 | 7272 | 7315 | 7358 | 4:7 7402 | 7445 | 7459 7662 | 7706 | 7749 | 7793 4.8 7836 | 7880 | 7923 8097 | 8140 | 8184 | 8227 4.9 8270 | 8314 | 8357 8531 | 8574 | 8618 | 8661 SMITHSONIAN TABLES. 31 Sa ee TABLE 42. EXPONENTIAL FUNCTIONS. Values of e* and of e-* and their logarithms. Values of e% and e—* for values of x intermediate to those here given may be found by adding or subtracting the values of the hyperbolic cosine and sine given in Tables 38-39. 8 log ex ° ° COON DD UPWH EH a 0.90484 81873 74082 67032 60653 0.04343 08686 13029 17372 207L5 ° . - . COON HD NUAWNEH DOONHD Usawn Ee 0.54881 1.73942 49659 69599 44933 65256 40057 60913 36788 56570 0.26058 30401 34744 39087 43429 2.43205 47545 51891 56234 60577 a COOND UshwnkF _ ND a eS a COON OD UbwWdEe a) COONOD UBWwnEe SS 0.33287 1.52228 30119 47885 27253 43542 24660 39199 22313 34856 0.20190 1.30513 18268 26170 16530 21827 14957 17484 13534 T3141 2.64920 69263 7 3006 77948 82291 2.86634 90977 95320 99663 3.04006 0.47772 52115 56458 60801 65144 0.69487 73530 78173 82516 863559 ! tb to N to es J CO ONO Usbwne NO 0.12246 1.08798 11080 04455 10026 _ OO1I2 09073 2.95769 i 05208 91426 0.91202 95545 993885 1.04231 05574 3:08349 12692 17035 21378 25721 3.30064 34407 38750 2697-3 43093 2981.0 47430 0.074274 2.87083 067205 82740 060810 78398 055023 74055 049787 69712 1.12917 17260 21602 25945 30288 nN COONOD UbwndEe aL. 3 4 5 2.6 7 8 9 .O WO w o COON OD Mmawn ke WO w OO w 0.045049 2.65369 040762 61026 036883 56683 033373 2340 ©30197. 47997 1.34631 38974 43317 47660 52003 3294-5 3:51779 3641.0 56121 4023.9 60464 4447-1 64807 4914.8 69150 1.56346 60689 65032 49.402 69375 54-598 73718 0.027324 2.43654 024724 39311 022371 34968 020242 30625 018316 26282 5431-7 3-7 3493 6002.9 778306 6634.2 82179 7332.0 86522 8103.1 90865 o COOND UAWdke w COOND UshHOndEH Pop Oo Pp 60.340 1.78061 66.686 82404 73-7 86747 81.451 QI0go 99.017 95433 0.016573 2.21939 014996 17596 013569 13253 012277 OSg10 OI1109 04507 8955- 3-95208 9897. 9955" 10938. 4.03894 12088. 05237 13300. 12580 0.010052 2.00225 00909 5 3-95882 008230 91539 007447 87196 0067 38 82853 99-48 1.99775 109.95 2.04118 121.51 08461 134.29 12804 148.41 17147 14765. 4.16923 16318. 21266 18034. 25609 19930. 29952 22026. 34295 uw » COCNO UAWdn EH © COOND NUBAwWdE = Oo wn » ' COON DO UsAwnke SMITHSONIAN TABLES. 32 -TaBLe 43. EXPONENTIAL FUNCTIONS. Value of e2” and e-** and their logarithms. The equation to the probability curve is ¥ = e-*", where x may have any value, positive or negative, between zero and infinity. ext log ex? log e-2? ° 1.0101 0.00434 0.99005 1.99566 1.0408 01737 96079 95263 1.0904 03909 96091 1.1735 06949 9305! 1.2840 10857 89143 °o 1.4333 0.15635 ; 1.84365 1.6323 21280 78720 1.8965 2779 72205 2.2479 3517 64822 2.7183 43429 56571 3°3535 0.52550 . 1.47450 4.2207 62538 37402 5-4195 73399 5 26604 7-0993 85122 14878 9.4877 97716 02284 _ =) 1.2936 X Io I.1II79 0.77306 X 107} 2.88821 1.7993“ 255t1 55576“ 74489 2 encadey nse 40711 39164“ 59289 36996 56780 Z7ORGe ee 43220 5.4598 73718 sisi (eya | 26282 tn N 8.2209, 1.91524 0.12155 2.08476 1.2647 X 1 2.10199 79070 X 107-2 3.89801 1.9834 29742 soq1S 70258 3.1735 50154 SnCEL, 49846 5.1802 71434 19304 “ 28506 nN 8.6264 2.93583 O11s92 3.06417 3.16601 68233 X 10-8 4.83400 40487 39307 5951 65242 22263 «=f 3475 90865 12341 “ 09135 1.4913 X 10 4-17357 0.67055 X 10-4 5-82643 2.8001 ‘“ 44718 35713 eo 55283 5.2960“ 72947 18644 “ 27053 1.0482 X 10° 5.02044 95402 X 1075 6.97956 2.0898 32011 47851 “ 67989 al 3 4 5 .6 7 8 9 .O ale 3 4 5 1.6 7 8 9 0 ak 2 3 4 5 6 7 8 9 .O WO w 4.2507 5-62846 0.23526“ 6.37154 8.8205 94549 £2337 05451 6.27121 53554 X 10% 7-72879 60562 24796 39438 94871 11254 “ 05129 Qo COON D UbwWnd EH Pop 7.30049 0.50062 X 1077 8.69951 a 6609 5 21829 =“ 33905 I aS X 108 8.03011 93303 X 10~ 8 9.96989 2.5583“ 40796 39088 59204 6.2297“ 79447 T6052“ 20553 1.5476 X 109 9.18967 0.64614 X 1079 10.81033 59357 25404“ __ 40643 10.0061 5 99595 X 10-0 1.99385 42741 a7a70) aS 57259 85736 13888 “ 14264 un » ' COON OD UbWdeH SMITHSONIAN TABLES. 33 4. oe EXPONENTIAL FUNCTIONS. Tw ae Values of @**and@ * and their logarithms. | 1 2.1933 0.34109 0.45594 6589 2 4.5105 .08219 .20788 3178 3 1.0551 X 10 1.02328 .94780 X 107} 2.976 4 2.3141 < 30438 43214 Fs 635 5 5.0754“ -70547 -19793 294 6 TU s2e aon 2.04656 0.89833 X 107? 3-953 7 2:AATG |< -38766 4095s“ 61232 8 Segivey -72875 18674“ 2702 9 1.1745 X 108 3.0698 5 85144 X 10-8 4.93015 O 2 s -4109. 30820 “ 58900 11 5.6498 “ 3-7 5204 0.17700 “ 4.2479 12 1.2392 X 108 4.09313 80699 X 10-4 5-9c68 13 2716S. as 43422 30794“ -5057 14 SOLO Ma -77 532 10770 _-224 15 1.3074 X 10° 5.11041 .76487 X 107° 6.883 16 2807/6 5.45751 0.34873“ 6.54249 17 6.2893 “ -79800 15900 _+20140 18 1.3794 X 108 6.13969 “72405 XX 1On° 7.8603 19 3.0254 “ -48079 -339253 “5192 20 6.6356“ 82189 “L5070; = 17812 TABLE 45. EXPONENTIAL FUNCTIONS. Vir Vir Values of @ ** and @ + and their logarithms. a -20405 16992 -10909 0377 14.277 1.15465 0.070041 2.84535 22.238 34709 044968 652 34.636 53953 .028871 -40047 53-948 73198 018536 -20802 54.027 92442 -OLIQOL 07558 at 130.87 2.11686 0.0076408 3.98314 12 203.85 30930 .0049057 -69070 13 317-50 50174 0031496 .49826 14 494.52 £09418 .0020222 30582 15 770.24 88063 0012983 11337 16 1199-7 3-07907 0.00083355 4.92093 17 1868.5 27151 .00053517 -72849 18 2910.4 -46395 .000343600 53005 1g 4533-1 .65639 00022060 34361 7000.5 84853 00014163 GO L7 SMITHSONIAN TABLES. 34 EXPONENTIAL FUNCTIONS. PRSEEIRE? Value of e* and e~* and their logarithms. log e-# 0.00679 : 1.99321 01357 : -98043 .02714 9394 97286 04343 : 95057 04525 5948 95175 0.05429 88250 1.94571 paar 86638 93796 .0723 ‘ 92762 08636 8187 ‘Ol 314 10857 7798 SO143 0.14476 : 1.85524 21715 : Toes -32572 472. 07.42 43429 -3678 -56571 -54287 -2505 -45713 0.65144 122 1.34856 -70002 : 23998 50859 : 13141 97716 ; _.02284 1.03574 7 2.91426 TABLE 47. LEAST SQUARES.* 2 Teac Values of P= S e- (2)? (hav) 0 This table gives the value of P, the probability of an observational error having a value positive or negative equal : ome he to or less than x when /is the measure of precision, P= vif re (iz)? dh) 0 8 ,02256 | .03384| .04511 | .05637] .06762| .07886| .ogoo8} .10128 |. .13476| .14587] .15694| -16799] 17901 | .18999 | .20094 21184 .22430| .25502]| .26570| .27633] -.28690| .29742| .30788 | .31528 34913 | -35928 | -36936| .37939] -38033| -33921 | -40901 | .41874 .44747 | .45689 | 88623 | .47548] -48466] .49375| -50275] -51167 53790 | -54646| -55494| -56332| -57162| -57982| .58792] .595904 61941 | .62705| .63459| .64203] -64938 | . .66378 | .67084 .69143,| -69810] .70468 | .71116] -71754| -723° .73001 | .73610 |. 75381 | -75952| -76514| .77067] -77610| .7814¢ .78669 | .79184 80188 | .80677| .81156| .81627 | .82089] .82542 | .82987 | .83423 | 83851 84681 | 85084] 85478] .85865| .86244] .86614 | .86977| .87333| .87680 88353 | -88679]| .88997 | -89303 | .89612 89910 | : .90484 | .g0761 .91296| .91553| -91805] .92051 | .92290] .92524| .92751 | -92073] -93190|- .93606 | .93807 | -94001 | .94191 | .94376] -94556 | .947 .94902 | -g5067 95385 | -95538| - 95830 | -95970] -96105 | .96237 |) -96365 | .96490 .96728 | .96841 | .9695 97059 | .97162] .97263 | -97: 97455 | -97546].- .97721 | .97804 | .97884| .97962| .98038] .98110| . 318 95249 | .98315 98441 | .g8500] . 8 | .98613 | .98667 | .98719| .98 98817 | .g8864 .98952| .98994| -99035| -99074| -991II | -99147 | . 99216 | .99248 99309 | -99338 | - -99392 | -99415] .99443 | - -99489 | -99511 * Tables 47-52 are for the most part quoted from Howe’s “ Formule and Methods used in the application of Least Squares.” SMITHSONIAN TABLES. 35 7 eyo aN TABLE 48. LEAST SQUARES. This table gives the values of the probability P, as defined in last table, corresponding to different values of x/ +r where ¢ is the “‘ probable error.”” The probable error 7 is equal to 0.47694 / A. 88078 89595 90954 92166 93243 94195 95033 al 96346 99431 99943 bponnN nnvwp 0 ODN AG £O b + ¢ TABLE 49. LEAST SQUARES. Values of the factor ee OTN eel ne This factor occurs in the equation e, = 0.6745 Sta the probable error of a single observation, and other ernlae equations 0.3894 | 0.3372 | 0.3016 | o. 27 54 0.2549 0.2248 | 0.2 202 : “1S7t 1742 | .1686| .1636 1547 3 | -1472)|" 1438 | -14o6\) 1349 ||| .1323%|)ssl200 1252 a2 PLLOZ | ele ee LE4O |) LIZA elo .1080 : : 1029] . -1005 | .0994 | .0984 0.0964 | 0.095 .0C i 0.0926 | o. 0.0909 | 0.090I | 0.0893 .0878 | .0871 .08 .08 850} . .0837 | .0830 | .0824 0812; |... .o8 : .0789 } .078. 0778 | .0773 | .0768 0759 | .075¢ : q cog4go}] . (O7 Sai O7 274.0723 20705 |1: : : 0699] . .0692 | .0683 | .0635 SMITHSONIAN TABLES. 36 LEAST SQUARES. aol LL Values of the factor 0. e745) n(n—1)" This factor occurs in the equation e,, = 0. sy mee for the probable error of the arithmetic mean. 0.0901 0386 .0245 0.0180 0142 .OI17 LEAST SQUARES. Secon Values of the factor 0. essay/— 3 n(m—1l) : : = This factor occurs in the equation e, = 0.8453 Vas WG =) for the probable error of a single observation. 0.3451 | 0. : : 0.1304 | 0.1130 .0677 | .062 SO5OR nee 0513 | .0483 Heley Xe) || .03 0332 | .0319 | .0307 0.0260 | 0.0252 | 0.02 0.0238 | 0.0232 | 0.0225 .O199 | .O10¢ ; 018 .0182 | .0178 SOLOTIIe : 0152 | .O150}] .0147 TABLE 52. LEAST See ge Values of 0.8453 —, —_ LY vt— This table gives the average error of the arithmetic mean when the probable error is one. 0.4227 | 0.1993 | 0.1220 | 0.0845 | 0.0630 | 0.0493 0212 | .o188 | .o167 | .o151 | .0136 | .0124 0090 | .0084 | .0078 | .0073] .0069| .0005] .0061 0.0050 | 0.0047 | 0.0045 | 0.0043 }| 0.0041 | 0.0040 | 0.0038 .0033 | .003I | .0030] .002 .0028 | .0027 | .0027 10023% || 5.00231) ".0022) [7 .002I | .0020 }|° .0020 SMITHSONIAN TABLES. TABLE 53. 7 GAMMA FUNCTION.* o Value of we e720" dx +10. 0 oo Values of the logarithms + ro of the ‘‘ Second Eulerian Integral ”” (Gamma function) f e-*z"—\dx or log T(2)-++-10 0 for values of » between 1 and 2. When z has values not lying between 1 and 2 the value of the function can be readily calculated from the equation I'(z+-1) = T(z) = x(z—1) . . « (u—7)I(x—7). 9:99: 92512 75287 | 728 68011 51279 44212 27964 | 2 21104 05334 95077 9-9883379 | 8122 76922 62089 55830 41469 28 35392 21409 15599 02123 22 90442 9.9783407 77914 65313 8 | 60005 47534 2 42709 30962 2 26017 14689 09922 9-9699007 | 97: 94417 53910 | 52432 79493 69390 65145 55440 : 51366 42054 39147 9.9629225 25484 16946 5 13369 | 12188 05212 01796 | 00669 594015 | 92 90760 | 89685 383350 | 82 80253 | 79232 9-9573211 70271 | 69301 60806 | 59888 51855 | 50988 43410 | 42593 35467 | 34700 9.9530203 | 29470 28021 | 27303 23100 | 22417 21065 | 20396 16485 | 15850 14595 } 13975 10353 | 09706 08606 | 08034 046098 | 04155 03094 | 02508 9.9499515 | 99023 98052 | 97573 94800 | 94355 93477 | 93044 90549 | 90149 | 897 89363 | 88977 86756 | 86402 85707 | 85366 83417 | 83108 82503 | 82208 9.9480528 | 80263 79748 | 79497 78084 | 77864 77437 | 77230 76081 | 75905 75565 | 75402 74515 | 74352 74130 | 74010 73382 | 73292 73125 | 73049 eae * Quoted from Carr's “Synopsis of Mathematics,” and is there quoted from Legendre’s “ Exercises de Calcul Intégral,’’ tome ii. SMITHSONIAN TABLES. 38 | | CAMMA FUNCTION. ors 99472677 72397 72539 73097 74008 72437 72452 72886 737 34 74992 9.947 5449 ) 6 76658 77237 2|)7 2 78502 | 78727 79426 81196 82015 3258 328 3758 | 84062 84998 87321 SNNNIN OWN N G2 wR QUIN mtn MD OO CN WN t 9.9488374 | 88733 5 | 89. 37 | 90969 Been | 95004 Bees 99422 500822 2255 04220 05733 09395 9.951 1020 eae 14943 16680 20862 22710 | 23 2 2 27149 29107 33801 35867 40815 9.9542989 ) 48187 50408 7 55916 55303 : 63998 66491 72430 75028 / S121 9.9583912 39409 | 90337 93141 : 99805 602712 6 2 5 | 09614 12622 7 19760 22869 | 2 2 2 2 2 30241 9-9633451 41055 . 44304 2 52200 55606 5 63671 onde PACS foee. 79070 2 5 5 87588 | 88815 9.9691287 70 | 00029 | OT291 703823 5¢ 12788 14082 16678 2 2 7 2322 2 25864 | 27189 29845 305 39254 | 40610 43331 571 | 52955 | 54342 9.97 57126 22 f 5 66966 | 68384 71230 | 72 5 552 783 5 81285 | 82734 85640 38 2 95910 | 97359 800356 8 8 Re 10837 | 12346 15374 5 22¢ 26066 | 27606 9.98 30693 93 | 35348 82 028 | 41595 40311 471 | 51055 232 25 | 57421 2226 | 638: 5 a i ‘a 73542 78436 8 33 3 St | 8 89957 94938 3 03299 30 | 06663 9.99117 32 3530 | 20237 23659 28315 22 35728 | 37464 | 39202 | 40943 46188 3213 | 54977 58513 63840 2 | 70982 | 72774 | 7 76368 81779 2 4 | 90854 | 92 | 94504 SMITHSONIAN TABLES. TABLE 54. ZONAL HARMONICS.* The values of the first seven zonal harmonics are here given for every degree between 6 = 0° and 8 = go°. ° * Calculated by Prof. Perry (Phil. Mag. Dec. 1891). See also A. Gray, ‘‘ Absolute Measurements in Electricity and Magnetism,” vol. ii., part 2. - 7 SMITHSONIAN TABLES. 40 TABLE 54. ZONAL HARMONICS. SMITHSONIAN TABLES. 4 TABLE 55. MUTUAL INDUCTANCE.* M Values of log aNaal M 47Vaal radii a, a’, at distance apart 6. The table is calculated for intervals of 6/ in the value of cos— for facilitating the calculation of the mutual inductance M of two coaxial circles of { (a—a! )? + 8 } 4 (a—al 2 + 8? Table of values of log from 60° to 90°. 0’ 6’ 12’ 18’ 24’ 30° 36’ 42’ 48’ 54’ 60° |1.4994783}| 5022651 | 5050505! 5078345) 510617 315133989! 5161791 | 5189582] 5217361 | 5245128 61 | 5272883) 5300628 5328361 | 5356084] 5383796] 5411498) 5439190) 5466872) 549454 5| 5522209 5549864) 5577 510] 5605147 5632776) 5660398] 5688011) 571 5618) 5743217| 5770809) 5798394 5825973) 5853546| 5881113, 590867 5) 5936231) 5963782) 5991 322|601887 1|6046408 |607 3942 6101472 6128998|61 56522 6184042 621 1 560]6239076) 6266589 6294101 |6321612/6349121 1.6376629 6404137 |6431645 64591 53|6486660}6514169/ 6541678) 6569189) 6596701/6624215 6651732 6679250 6706772)/67342966761824]6789356|6816891 |6844431|687 1976/6899526 6927081 }6954642|6982209|7009782 7092 544|7120146|7147756\7175375 7 203003|7230640|7258286|7285942|7 31 3609}7 341287 7 30897 5|7 39667 5)7424387 |7452111 7479848|7 507 597 |7 535361 |7 5031 38|7 §90929]7618735|7646556|7674392|7702245|77 30114 1.77 58000|7785903 781 3823]7841762|78697 2017897 696| 792 5692|7953709|79817 4 5|8009803 8037882)8065983|8094107 |8122253)8150423]8178617 |82068 36/823 5080/8263 349/8291645 8319967 |8348316|8376693/8405099 8433534]8461998 8490493 8 519015/8 54757 5/8576164 860478 5 8633440 |8662129 86908 52/87 19611]8748406 8777 237|8806106/883 501 3/8863958 8892943/8921969 895103689801 44|900929 5}9038489 9067725 | 909701 2/9126341|91 55717 T.9185141 921461 392441 35/927 3707 9303330193 33005 93627 33/939251 5|9422352/9452246 9482196 9512205 |954227 2/957 2400, 9602590]9632841 |96631 57 9693537 |9723983|97 54497 9785079 9815731 |9846454/9877249|9908 1 18]9939062 99700820001 181 |032359|0063618 0.0094959|012638 5|01 57896 0189494|0221 181 ]02529 59|0284830/0316794/03488 55/038 1014 041 327 3|0445633|0478098 05 10608] 0543347105761 36,0609037 |0642054|067 5187|0708441 0.0741816|077 5316|0808944|0842702|0876592]0910619|0944784|0979091 | 1013 542|10481 42 1082893] 1117799|11§2863|1188089] 1223481]1 259043) 1294778) 1330091 | 1 366786) 1403067 1439539) 1476207 | 151307 5|15501 49) 1587434] 1624935 | 1662658) 1700609) 17 38794) 1777219 1815890) 185481 5| 1894001 |1933455| 1973184] 201 3197|2053502|2094108| 213 5026) 2176259 2217823] 22597 28|2301983|2344600] 2387 591]24 30970) 2474748|2518940| 2563 561/2608626 0.26541 §2|27001 56|274665 5|2793670] 2841 221| 2889329] 293801 8| 2987 312) 3037 238] 3087823 3139097 | 3191092) 3243843) 3297 387 |3351762] 340701 2/ 3463184) 3520327|3578495)/ 3037749 36981 53/37 59777 | 3822700) 3887006] 3952792] 40201 62| 4089234) 41601 38| 4233022] 4308053 4385420) 4465341 |4548064| 4633880] 47 23127]4816206) 491 3595| 501 5870) 5123738] 5238079 5 360007 | 5490969| 5632886) 5788406] 5961 320]61 5737016385907 |6663883 7027765] 7 586941 * Quoted from Gray’s ‘‘ Absolute Measurements in Electricity and Magnetism,”’ vol. ii., p. 852. SMITHSONIAN TABLES. 42 } TABLE 56. ELLIPTIC INTEGRALS. Values of f 7(1— sin? 6 sin® tt dp. 0 This table gives the values of the integrals between o and m /2 of the function ( t—sin?@sin?¢)** ad for different val- ues of the modulus corresponding to each degree of @ between o aud go. = dé pe crt | a db i (osintosinegll “(1—sin*6sin*p) "dp 3 (sin? sin? $) “(1—sin*@sin*p )?dp 0 i—sin* 6 sin- ~/* 0 0 I—s1n-@ sin- 0 0 Number. Log. ‘ Number. Log. Number. Log. ° ° 1.5708 | 0.196121 0.196121 5709 196148 | 196093 5713 | 196259 195953 5719 | 196425 195517 5727 | 190646 195595 1.8541 | 0.268133 |1.3506 |0.130527 5091 271632 3418 127688 8848 275265 3329 124798 gor 279005 3238 121822 g180 252849 3147 118827 1» CI AH Oo Q #UnNH ° a oO ~o ° +5738 | 0.196949 | I. 195291 $75 | 197305 5 | 194930 5767 | 197749 194457 5785 | 197245 2 | 194014 §505 | 195794 19343 .5828 | 0.198934 | 1. 0.192818 5854 200139 1g2121 5882 200905 191367 5913 201752 190528 5940 | 202652 7 189659 9356 | 0.286816 | 1.3055 | 0.115777 9539 | 290902 | 20963 112705 9729 | 295105 | 2570 109575 9927 | 299442 | 2776 | 106395 .0133 303908 } 2681 103153 Oo COON Oo = Q Bond ° a 0347 os7I oOS04 1047 1300 2587 | 0.099922 2492 096632 2307 OSS 27, 2301 059940 2206 086573 Go Ga GG) Go Oo Oo Oo ONO =) -SQ8I | 0.203604 | 1. 188703 6020 204662 187662 6061 205773 186589 6105 200961 185429 6151 208199 184209 a 1565 |0. .211I | 0.083180 1842 2 2015 079724 2132 2 1920 076276 2435 1826 072838 2754 §7058 | 1732 | 069372 .3088 | 0.363386 | 1.1638 | 0.065878 3439 309939 1545 062394 3809 | 376741 | 1453 | 058919 4198 | 383779 | 1362 | 055455 4010 391112 1272 052001 Oo I 3 4 5 6 7 8 9 0 tw oO WON QAM fhWNH .6200 | 0.209515 | 1.523 182928 6252 210907 181586 6307 212374 180155 6365 213916 178089 6426 | 215532 177161 ° N Q fy H 1.6490 6557 6627 J °o ° “175541 173985 172130 6701 170350 6777 168497 6858. | 0.2265 ; .166578 6941 164591 7028 162534 7119 160438 7214 5 158272 5046 | 0.398738 } 1.1184 | 0.048597 5507 406659 1096 | 0451606 5998 | 414940 1OII 041827 6521 423590 | 0927 038501 7081 432065 | 0544 035189 th NN hb oO oOo COON Oo Q 0.442182 | 1.0764 | 0.031974 452201 0086 | 028815 462787 oor! 025756 474056 | 0538 | 022758 485963 | 0408 | o19864 | WOON AD fhHondeH QQ OON DGD BWNH © >} °7312 |0. 3 156034 (At5 z 1537 54 7522 E 151400 7933 2 148973 7748 146531 -7868 7992 8122 8256 8396 0.498779 | 1.0401 | 0.017075 512591 0338 014430 527617 0278 O11909 544118 223 009578 562519 o172 007406 » © ° oO WOON QAM Pwd A 143982 1414158 138776 130086 1335347 1.8541 | 0.268133 0.130527 0.583391 | 1.0127 | 0.005481 607755 | 0086 | 003719 637300 | 0053 002296 677026 0026 oo1128 735192 0008 000347 NR bwHKNb © °o ° ao 1.0000 SMITHSONIAN TABLES. 43 TAREE ES: BRITISH UNITS. Cross sections and weights of wires. This table gives the cross section and weights in British units of copper, iron, and brass wires of the diameters given in the first column. For one tenth the diameter divide section and weights by roo. For ten times the diameter multiply by 100, and so on. Area of Copper — Density 8.90. Iron — Density 7.80. Brass — Density 8.56. cross section Mils. in Pounds Feet per] Pounds Feet per} Pounds Feet ver Sq. Mils. | per Foot. , d. | per Foot. ; Pound. | per Foot. " Pound. Diam. in 78.54 | .000303 | 4.48150 bite .42420 | 3765. }.0002915 | 4. 3431- 95-03 0367 | .56429 : : 3112. 03527 2836. 113-10 0436| .63986 : 25| . 2615. 04197 295 | 2353: 132375 0512| -70939 3 65208 | 2228. 04926 2030. 0594] -77376 ; : 1921. 05713 1750. .000682 | 4.83368 . | .0005976| 4. 1674. | .0006558 | 4. 1525. 0776] .85974 . 06799| .83244| 1471. 07461} .87282 | 1340. 0876} .94240| 1142. 07675] .88 1303. 08423| .92 1187. 0982} _.99205 ; 08605] - 1162. 09443] - 1059. 1094 | 3.03902 : 09588 | .98 1043. }|-0010522 001212 | 3.08357 I |.001062 | 3.02626] 941.4 | .001166 1336| .12594| 749. 117i | .068 853-5 1285 1467| .16634 8 1286 | . 7778 I41I 1603| -20496 : TAOS) ||. 717 1542 1746| .24192 : 1530 | -18 653-7 1079 nN .001894 | 3.27738} 528.0 | .co1660 | 3.22 602.4 | .001822 2046| .31146| 488. 7 -254 557-0 } 1970 2209| -34423 2. 3 .28 516.5 2125 2376] .37583 : 2082 | .3 480.3 2285 2549} -40630 . +346 447-7 | 2451 OW ON OG NN Nb Q 3 002727 | 3-43575 418.4 }| .002623 2912| .46424 : .406 391.8 2801 3103] -49181 22 4345 2985 3300] -51854] 303- -40 3174 3503| -54446 3309 .003570 | 3.55271 3777 | -57719 3990 | .60098 4218 | .62514 4433 | -64671 .003712 | 3.56964 4927| -59412 4149] -O1791 4376] .64108 4609} .66364 NR wH Nb me NO BU 004249 | 3.62 .3 | 004664 | 3.66871 4405 | .6¢ : 4900 | .69015 5346] .72801 4085 | .6707 ; 5141 -71108 : . 5603| -74845 4g1r | . 5389 | -73152 | 5867 | -70842 : 5142 | . : 5043 | -75149 .004849 3:68 563 5094] -70703 MI C.D O PI AN AK EK 1590.43 | .006137 | 3.78793 .Q |.005378 | 3. .9 | .005902 | 3.77101 : 1661.90 6412| .80703 : 5620 | .7¢ : 6167 | .790I10 | 1734-94 6694} .82569 7 5867 | .768 : 6438 | .80878 , 1809.56 6982| .84399 ; 6119 || -7 : 6715 82706 ‘ 1885.74 7276| .86289 i 6377 | -80< ; 699) 84497 | 1963.50 | .007576 | 3.87945 .0 |.006640 | 3.82 6 | .007287 | 3.86252 2042.82 7882] .89664| 126. 6908 | . : 7581 | .87972 2123.72 8194| .91352 f 7181 | .8562 : 7881 | .89659 2206.18 8512] .93005 ; 7400 | .87275 F 8187 | .91313 2290.22 8337 | -94630 . 7744 | : . 8499 | -92937 2375-83 | 009167 | 3.9622 I | .008034 | 3-90493 .5 | .008817 | 3.94531 SMITHSONIAN TABLES. BRITISH UNITS. Cross sections and weights of wires. TABLE 57. Area of Copper — Density 8.90. Iron — Density 7.80. cs oS cross ES ae Pounds Feet per} Pounds Feet per a Sq. Mils. RenitGot Log. Beane: per Foot. Log. Hone 2375-83 | 009167 | 3.96223 | 109.1 | .008034 | 3-90493 | 124.5 2463.01 09504 97789 | 105.2 08329 | .92055 | 120.1 2551.76} 09846] _.99325 | 101.6 08629 | .93595| 115.9 2642.08 | 10195 | 2.00837] 98.1 08934 | -95106] 111.9 2733-97 | 10549] .02320] 94.8 09245 | -90591 | 108.2 2827.43 ].o1o91 | 2.03782] 91.66 | .00956 | 3.98050 | 104.59 2922.47 | 1128 | .05216] 88.68 0988 -99456 | 101.19 3019.07 | 1165 | .06628] 85.54 1021 | 2.00898} 97.95 3117.25 | 1203 | .o8019} 83.14 1054 .02288 | 94.87 3216.99] 1241 | .09386] 80.56} 1058 .03656| 91.83 65 | 3318.31 ].01280 | 2.10732] 78.11 | .o1122 | 2.05003] 89.12 66 | 3421.19] 1320 | .12061|] 75.76 1157 .06329| 86.44 67 | 3525.65] 1360 | .13367| 73-51 1192 07635] 83.88 68 | 3631.65] r40or | .14655| 71.36 1228 .08922}| 81.42 69 | 3739.28] 1443 | -15924] 69.30 1264 -I01g0| 79.09 70 | 3848.45 ].01485 | 2.17174| 67.34 | 01302 | 2.11451] 76.82 71 | 3959-19] 1528 | .18404] 65.46 1339 -12672| 74.69 2| 4071.50] 1571 | .19618| 63.65 1377 .13887 | 72.63 73, | 4185.39] 1615 | .20817] 61.92 1415 -15085| 70.66 74 | 4300.84] 1660 | .22000| 60.26] 1454 -16267 | 68.76 75 | 4417.86] .01705 | 2.23165] 58.66 | .o1494 | 2.17432] 66.95 76 | 4536.46} 1751 | .24317| 57-13] 1534 | -18583] 65.19 77 | 4056-63} 1797 | -25453| 55:65] 1575 | -19718| 63.50 78 | 4778.30] 1844 | .26574] 54.23 1616 -20839 | 61.89 79 | 4901.07 | 1892 | .27081] 52.87 1658 | .21946| 60.33 80 | 5026.55 |.01939 | 2.28769| 51.56 | .01700 | 2.23038] 58.83 81 | 5153-00] 1988 | .29848] 50.29 1743 -24117| 57.39 82 | 5281.02] 2038 30914] 49.07 1786 .25183| 56.00 83 | 5410.61 | 2088 31966 | 47.90 1830 .20230| 54.66 84 | 5541-77 | 2138 | -33006| 46.77 1874 27276] 53.36 85 | 5674.50 | .02189 | 2.34034] 45-67 | .o1919 | 2.28304] 52.11 86 | 5808.80] 2241 35050] 44.62 1964 29320] 50.91 87 5944-08 2294 | .30054] 43.60 2010 -30324| 49.75 88 | 6082.12} 2347 | -37047| 42.61 | 2057 | .31317| 48.62 89 | 6221.14 | 2400 | .38028] 41.66 2104 32298 | 47-54 90 | 6361.73 | .02455 | 2.38999] 40.74 | .02151 2.33209 | 46.49 QI | 6503.88 | 2509 | .39958| 39.85] 2199 | -34228| 45-47 2 | 6647.61 | 2565 -40908 38-99 2248 -35178| 44-49 93 6792.91 2621 -41847 | 38.15 2207 30116] 43-54 94 | 6939.78 | 2678 | .42775| 37-35] 2347 | -37046| 42.61 95 | 7088.22 | .02735 2.43094} 36.56 | 02307 | 2.37965] 41.72 96 7238.23 2793 .44604| 35.51 2448 .38874| 40.86 97 | 7389-81 | 2551 | -45404| 35:07 } 2499 | -39775| 49.02 98 | 7542.96] 2910 | .46395| 34-36 2551 .40065| 39.20 99 | 7697-69] 2970 | .47277| 33-67 | 2603 | -41547| 38.42 100} 7853.98 | .03030 | 2.48150| 33.00 | .02656 | 2.42420] 37.65 Brass — Density 8.56. Pounds Feet per per Foot. Log Pend: 008817 | 3.94531 | 113-4 09140 | .96096| 109.4 09470 | .97633 | 105.6 09805 | _-99144 | 102.0 10146 | 2.00629| 98.6 01049 | 2.02088] 95.30 1085 .03524| 92.21 1120 .04936| 89.2 1157 .06326] 86.45 1194 | .07094| 83-77 01231 | 2.09041] 81.21 1270 10367 | 78.76 1308 11673] 76.43 1348 .12960| 74.20 1388 .14228| 72.06 01429 | 2.15489| 70.00 1469 .10710| 68.06 ISI .17925| 66.19 1553 19123] 64.38 1596 | .20304]) 62.66 .01639 | 2.21460] 61.01 1634 -22621| 59.40 1728 -237 56 57:87 1773 -24577 | 50.39 IS19 | -25974| 54-99 01865 | 2.27076} 53.61 Igi2 20155] 52.2 1960 | .29221] 51.03 2008 .30274| 49.80 2057 31314] 48.63 02106 | 2.32342] 47-49 2156 | .33358| 46-39 2206 34362] 45-33 2257 35355} 44:39 2309 30330] 43-31 02360 | 2.37207| 42.37 2414 38266] 41.43 2467 -39216| 40.54 2521 40154| 39.67 2575 | -41034| 38.83 .02630 | 2.42003] 38.02 2036 42912] 37-37 2742 .43812| 36.46 2799 44793} 35-72 2857 | -45555| 35-01 02915 | 2.46458] 34-31 SMITHSONIAN TaB LES. TABLE 58. METRIC UNITS. Cross sections and weights of wires. This table gives the cross section and the weight in metric units of copper, iron, and brass wires of the diameters given in the first column. For one tenth the diameter divide sections and weights by 100. For ten times the diameter multiply by 100, and so on. Copper — Density 8.go. Iron — Density 7.80. Brass — Density 8.56. Log. i Log. Diam. in thou- sandths of acm. Area of cross section. Grammes 78.54 | 0.06990| 2.84448 |14.306 | 0.06126] 2.78718 | 16. 2.82756 | 14.874 95-03} .08458| .92725 |11.823 | .07412| .86996 | 13. : 91034 | 12.293 113.10] .10065| 1.00285 | 9.935 | -.08822] .94556 | II. ; _-98594 10.330 132.73] -11813] .07236 | 8.465 | -10353] 1.01506 | 9.6 . 1.05544 | 8.501 153-94] -13701] .13674 | 7.299 | -12008] .07945 | 38. : 11983 | 7-589 176.71 0.1573 | 1.19665 | 6.358 }0.1378 | 1.13936 | 7. I.17974 | 6.611 201.06] .1789 | .25272] 5.588 | .1563 | .19542]| 6. : 23580 | 5.810 226.98] .2020 | .30538 | 4.951 1770 | .24808 ‘ : .28846 | 5.147 254.47] .2265 | .35503 | 4.415 | -1985 | -29773 | 5- : -33811 4-591 283.53] -2523 | -40199 | 3.963 | -2212 | .34469 | 4. : 38507 | 4.120 314.160.2796 | 1.44654 | 3.577 [0.2450 | 1.38925 | 4. : .42963 | 3-719 346.36] .3083 | .48892] .244 | .2702 | .43162 | 3. : -47200| .373 380.13] .3383 | -52932 | 2.956 | .2965 | -47203] . -51241 073 415.48] .36098 | .56794| .704 | -3241 | .51064] . : -55103 2.812 452-39] .4026 | .60490|] .484 | -3529 | -54761 | 2. asey7A0%8) ||, = 490.87 ]0.4369 | 1.64036 | 2.289 | 0.3829 | 1.58306 | 2. 62344 530-931 -4725 | -67443] .116 | .4141 | -61713]| . 65751 572-50] .5096 | .70721 | 1.962 | .4466 | .64992]| . -69030 615.75] -5480 | .73880] .825 | .4803 | .68150| . 72188 660.52] .5879 | .76928| -7or | .5152 | .71198 | I. 75236 706.86] 0.6291 | 1.79872 | 1.590 ]0.5514 | 1-74143 | I. 1.78181 754-77] -6717 | .82721 489 | -5887 | -76991 : ; 81029 804.25] 7158 | -85478 | .307 | -6273 | -79749 | - 83787 855-30] -7612 | .88151 314 | .6671 | .82421 . 86459 907.92] .8081 | .90744| .238 | .7082 | 85014] . 89052 962.11]0.856 | 1.93261 | 1.168 | 0.7504 |1.87531 | I. 1.91570 1017.88} .906 | .95709] .104 | -7939 | -89979| - -94017 1075.21] .957 98088 | .045 | -8357 | .92359| . .96397 1134.11 ]1.012 |0.00504 | 0.985 | .8566 | .94775 | .- 98513 1194.59] .063 02061 | .g4r J .9318 | .96931 : .00969 1256.64]1.118 | 0.04861 | 0.8941} 0.980 | T.99131 .03169 1320.25] .175 07005 | .S8S5II] 1.030 | 0.01275 : 05313 1385.44] .233 0909s | .8110} .odsr 03308 07 400 1452.20] .292 11142 | .7738] -133 05412 09450 1520.53] -353 13139 | -7389] .180 .07 409 : 11447 1590.43]1.415 |0.15091 | 0.7065] 1.241 | 0.09361 13399 1661.90] .479 17000 | .6761] .296 .11270 : 15308 1734.94] .544 .18868 | .6476] .353 13138 : 17176 > | 1809.56] .611 ; .6209]° .411 14907 -1Q005 1885.74] .678 .2248 5958] -471 16758 20796 1963.50} 1.748 2042.82] .818 2123.72] .890 2206.18] .964 0.572241.532 | 0.18513 22551 5500] -593 .20232 .24371 5291] .057 -21919 5 25957 -5093] -72I 23574 : 27612 .4900] .786 25197 : +29235 ODO NUNt NOn noOf OL NWO 8 bY G®NNKN 10 WG pees toms 0.4729] 1.853 | 0.26791 : 0.30829 SMITHSONIAN TABLES. 46 TABLE 58. METRIC UNITS. Cross sections and weights of wires. 5 E Copper — Density 8.go. Iron — Density 7.80. Brass — Density 8.56. ro} n é2 | 8 eee fel oa 8 6 | 3 é | 3 3 gs 9 ATAVL saouno AOI], Ul U9ATS o1e JOATIS puL P[OX) » 96¢°L1 gor'gl Lit'v1 L£zS'z1 gt Zor gr6'g QS 1°Z 69£°S 625° o6L'1 yoo ‘bs sad saoung | ted spunog | 12) SgIl'l Lgoo'! gh6g ofl: 1149° €6SS° bLrr: gfe: LEzz° 6111" ‘joo, “bs ‘uNUye Vz7z'z ZO000'Z ogLZ1 L£SSS°1 Ceee-r cIII'l 0699" £999" Crrr ccze ‘yoo ‘bs o69f1" 10SzI° ZI1II’ €zZ60° bEEgor $t6g0° gSSSo° Lg1to- gZlzo: 6gf10" ‘yoo "bS d saoung | tad spunog | 10d spunog “UUNTUTUIN,y 10f9F- 1491" 1voLe: 11bz2e: ogllz- oS 1fz" ozSgr° o6ef 1" 09260" ofgfo- 00g “bs iad spunog sraddop | | glSor ozSgf° Egret: Sotgz" Letrz: 69zoz" 1£zgi° €Liz1° g11g0" gS obo "00,7 ‘bs aad spunog ‘uOly AAMT ONO DO “STUN ut ssoUyoryL SMITHSONIAN TABLES. 57 TaBLe 65. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight. Square of Feet Diameter in Diameter Section in Gauge Number. OO nshwnke Ooo ON SMITHSONIAN Inches. 0.4600 .4096 3048 *3249 0.2893 2576 .2204 -2043 1819 .1620 -1443 1285 -1144 -1019 09074 .08081 .07 196 .06408 05707 0.05082 .04526 .04030 03589 03196 0.02846 02535 .02257 02010 .01790 0.01 594 01419 .01264 .O1126 01003 0.008928 007950 .007080 .006304 005614 0.005000 -004453 003905 .003531 (Circular Inches). 0.2116 1678 “1331 1055 0.08 369 .06637 05203 04174 .03310 0.02625 02082 -O1051 01309 01038 0.008234. 006530 005178 004107 .003257 0.00258 pone .001624 .001 288 001021 0.0008 101 .0006424 .0005095 .0004040 0003204 0.0002541 000201 5 0001 595 -O001 267 .OOOI005 0.00007970 00006321 00005013 0000397 5 000031 52 0.00002 500 00001983 .00001 372 00001247 00000989 Sq. Inches. 0.1662 .1318 1045 0829 0.06573 05213 04134 03278 .02600 0.02062 01635 01297 .01028 0081 5 0.006467 005129 .004067 003225 002558 0.002028 .001609 .001276 .OOIOI2 .000802 0.0006363 0005046 0004001 .0003173 0002517 0.0001996 .0001 583 0001255 0000995 0000789 0.00006260 .00004964 00003937 .000031 22 .00002476 0.00001963 00001 557 00001235 .00000979 00000777 0.6412 5085 “4033 -3195 0.2536 .2011 1595 1265 -1003 0.07955 .06309 05003 0396 03146 0.02495 01979 .01 569 .O1244 00987 0.007827 .006207 004922 003904 .003096 0.002455 001947 001544 O01 224 00097 I 0.0007700 .0006107 0004843 .0003841 0003046 0.000241 5 .OOOTOTS .0001 519 0001 205 .0000955 0.00007 576 .00006008 POPS .0000377 00002996 TABLES. 58 1.80701 -70631 60560 -50489 1.40419 30348 20277 -10206 .001 36 2.90065 79994 69924 -59553 -49752 2.39711 29041 -19570 _:09499 3:99429 389358 -79287 -69217 -59146 -49075 3-39004 -25934 18863 .08792 4-987 22 4.88651 -78550 08 510 -58439 48303 4-38297 .28227 18156 08085 5-98015 587944 -77873 -67802 °5$7732 -470601 per Pound. 1.560 1.967 2.480 3.127 3-943 4-972 6.270 7-905 9.969 12.57 15.85 19.99 25-20 31.78 40.08 50-54 63.72 80.35 101.32 127.8 101.1 203.2 256.2 323-1 408.2 513.6 647-7 816.7 1029.9 1208. 1638. 2005. 2004. 3283. 4140. 5221. 6583. 8301. 10468. 13200. 16644. 20988. 26465. 3337 2- Taste 65. CONSTANTS OF COPPER WIRE. according to the American Brown and Sharp Gauge. British Measure. Temperature 0° C. Density 8.90. Electrical Constants. Resistance and Conductivity. Ohms Ohms Pounds per p per per Foot. r Pound. Ohm. 0.00004629 5-665 51 , 0.00007 219 13852. .0000 5837 76622 - .OOO11 479 8712. .00007 361 86693 ; .00018253 5479. 00009282 96764 : 00029023 3445. 0.0001 170 4.06834 : 0.000461 5 2166.8 0001476 16905 : .0007 338 1362.8 .ooo1861 26976 : .001 1668 857.0 0002347 37046 : 0018552 539.0 .0002959 47117 ; 0029499 339.0 0.00037 31 4.57188 ; 0.004690 213.22 .0004705 .67259 : 007458 134.08 0005933 77329 ‘ 011859 84.32 .0007 482 87400 : .0188 57 53-03 10009434 97471 060. 1029954 33-35 0.001190 3.07541 : 0.04768 20.973 .OOI 500 -17612 : .07 581 13-191 001892 27683 28. 12054 8.296 002385 37753 ; -19g166 5.218 003008 47824 : 30476 3.281 5 0.4846 2.0636 .004783 67966 : -7705 1.2979 006031 -78036 ; 1.2252 0.8162 .007604 .88107 ; 1.9451 -5133 .009589 98178 . 3.0976 3228 0.003793 3-5789 0.01209 2.08248 os 4.925 0.20305 01525 18319 3 7.832 nel .01923 .28390 2. 12.453 08030 .02424 -38461 : 19.801 05051 03057 48531 ; 31.484 .03176 NNW WN nk OW WN 0.03855 2.58602 : 50.06 0.019976 04861 .68673 ; 79.60 .012563 .061 30 -78743 . 126.57 .007 90I 07729 83814 : 201.26 .004969 .097 46 .9888 5 . 320.01 003125 0.1229 T.08955 ; 508.8 0.0019654 1550 19926 : : 0012359 1954 -29097 : 286. .0007773 -2404 39168 ; : .0004889 -3107 49238 .218 52. .000307 4 0.3918 T.59309 ; ; 0.0001934 4941 69380 z : .0001 216 -6230 -79450 : * 0000765 7856 89521 é ; .0000481 9906 99592 4 : .0000303 SMITHSONIAN TABLES, TABLE 66. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight. , Square of one, Gauge | Diameter in Diameter Section in ~ Number. | Centimetres. (Circular Sq. Cms. hice Cms.). . Grammes Metres per Gramme. 1.1684 1.3652 1.0722 : 0.001048 0405 .0826 0.8503 ; 001 322 0.9266 0.8586 -674 ; .001666 8251 6309 534 ; 002101 0.7348 0.5400 0.4241 : 0.002649 6544 4282 -3303 : P 003341 5927 -3396 -2607 : , .004213 .5189 -2093 pats 38.2 2 005312 .4021 .2130 -1677 ; : 006099 OO uspwordske 0.4115 0.16936 0.13302 ; : 0.00845 .3665 13431 -10549 : ; -O1005 3264 10651 .08 306 3 3 01343 2906 .08447 .06034 E : 01094 .2588 .06699 .05201 ; : .02130 OO ON 2305 0.05312 0.04172 : : 0.02693 .2053 .04213 .03309 ; .46906 03390 1828 03341 02024 a: : 04282 1628 .02049 02081 5. 7 .05400 .1450 .O2101 01650 : , 00809 .12908 0.016663 0.013087 : 0.0859 T1495 013214 010378 : 1083 10237 010479 .008 231 ; .1365 Ogi 16 .008 330 006527 : 1721 08118 006591 005176 : .2171 0.0722 0.00522 0.004105 ; 0.2737 . .06438 1004145 .003255 : : 3450 05733 .003287 002552 22 : 4352 05100 .002607 .002047 82 : 5488 04545 .002067 001624 ; : .6920 NHN ini Go b 0.04049 0.0016394 0.001 2876 : 0.873 .03606 .OOI 3001 .OO102II E 1.100 03211 0010310 .00080g8 02859 .0008176 .0006422 02546 0000484 0005093 wornnnNnd OO ON O 0.02268 0.00051 42 0.0004039 02019 0004078 0003203 .01798 0003234 0002540 .O1601 0002505 .000201 4 01426 0002034 .0001 597 0.01270 0.0001613 0.0001 267 .O1131 .0001279 .OOOI005 .O1007 ,OOOIO1 4 .0000797 .00897 .0000804 .00006 32 .00799 .0000638 .0000 501 SMITHSONIAN TABLES. 60 TABLE 66. CONSTANTS OF COPPER WIRE. according to the American Brown and Sharp Gauge. Metric Measure. Temperature 0° C. Density 8.90. Electrical Constants. Resistance and Conductivity. Gauge Ohms Metres Ohms Grammes Wonber: per : p per per Metre. : Gramme. Ohm. 0.0001 519 ; ; 0.0000001 592 6283000. .OOOIQI 5 .28 : .0000002 531 3951000, 0002415 38 : 0000004024 245 5000. 0003045 .48 : .0000006398 1 563000. 0.0003840 4. 2604. 0.000001017 982900. .0004842 : a‘ .000001618 618200. 0006106 : 7 .000002572 388800. 0007699 8 ; -000004.090 244500. 0009709 : : 000006504 153800. 0.001224 a 0.00001034 96700. 001 544 188 .00001644 60820. -001947 a2 3. .0000261 5 38250. 002455 : .000041 57 24050. .003095 : .00006610 15130. 0.003903 3.59140 O.00010511 9514. .004922 69210 00016712 5984. .006206 79281 .00026574 3763. 007826 89352 .00042254 2367. .009868 99423 .00067 187 1488. 0.01244 2.09493 0.0010683 936.1 01 569 19564 -0016987 588.7 .01979 29035 0027010 370.2 02495 39705 0042948 232.8 03140 -49776 .0068 290 146.4 0.03967 2.59847 0.010859 92.09 .05002 .69917 017266 57-92 06308 -79988 : .027454 36.42 07954 _-90059 043053 22.91 -10030 1.00130 069411 11.88 0.12647 T.10200 0.11037 9.060 15948 .20271 17549 5.698 -20110 -30342 -27904 3-584 .25358 40412 -44309 2.254 -31976 -50483 70550 1.417 0.4032 1.60554 1.1218 0.8914 5054 -70624 ‘ 1.7837 .5606 6411 80695 2.8362 3526 8085 .g0766 4.5097 2217 1.0194 0.00837 7.1708 1394 1.2855 0.10907 11.376 0.08790 1.6210 .20978 18.130 05516 2.0440 -31049 28.828 -03469 2.5775 41119 45.838 .02182 3.2501 51190 72.835 .01 372 SMITHSONIAN TABLES. 61 TABLE 67. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Gauge Number. 7-0 GMITHSONIAN TABLES. Diameter in Inches. 0.500 -404 0.432 -400 -372 -348 324 0.300 .276 .252 =232 212 192 176 .160 -144 .128 0.116 104 092 .080 072 Square of Diameter (Circular Inches). 0.2500 62153 0.1866 -1600 1384 e205 1050 0.09000 .07618 .06350 05382 04494 0.03686 .03098 02560 02074 01638 0.013456 .010816 .008464 .006400 005184 0.004096 .0031 36 002304 -001600 .001 296 0.0010240 .0007840 0005760 .0004840 .0004000 0.000 3240 .0002690 0002190 .00018 50 .0001 538 0.0001 3456 .0001 1664 .00010000 .00008464 00007056 0.00005776 .00004624 .00003600 .00002704 .00002 304 0.00001936 .00001600 .00001296 00001024 .00000784 0.00000576 .00000400 .000002 56 .000001 44 .00000100 Size and Weight. Section in Sq. Inches. 0.1963 1691 0.1466 1257 -1057 0951 0825 0.07069 05983 -049838 0422 03530 0.02895 02433 .02010 .01629 .01 287 0.010568 os .00664 005027 .00407 I 0.003217 002463 -OO1810 .001 257 001018 0.0008042 00061 57 0004 524 .000 3801 00031 4I 0.0002 545 .0002112 .0001728 .0001 453 0001 208 0.00010 568 .0O0009I 61 .000078 54 .00006648 00005542 0.000045 36 00003632 .00002827 .000021 24 .00001810 0.00001 521 .00001 257 .00001018 .00000804 .00000616 0.000004 52 00000314 .0000020I 00000113 .00000079 62 Pounds per Foot. 0.75760 65243 0.56554 .48456 -41936 -36699 31812 0.27274 23084 19244 -16310 .13620 O.ILI71 .09387 .07758 .06284 04965 0.04078 .03278 02565 01939 01571 0.012412 009503 .000982 004849 .003927 0.003103 .002376 .001746 .001 467 .OO1212 0.00098 18 00081 51 .0006638 0005605 .0004660 0.0004078 0003535 0003030 2 5Up 000213 0.00017 50 .OOO1 404 .OOOIOQI 0000819 .0000682 0.0000 5867 .00004849 .00003927 00003103 00002381 0.000017 46 .O0001 212 .00000776 .000004 36 .00000303 Log. 1.87944 81453 1.75247 .68 562 62258 56406 50259 1.43574 30332 28430 .21246 13417 1.04810 2.97252 88974 -79822 69592 2.61041 “5155/7 40907 -28768 -19616 2.09386 3-97787 84398 68562 “59410 3.49180 +37 581 24192 16634 08356 4-99209 -QIIIQ 02202 74858 -668 34 4.61041 54535 48150 40907 33006 4-24313 147 92 _.03780 §-9135! 84398 5-76840 .68 562 59410 -49180 37681 5.24192 .08356 6.88974 go2° 48150 Feet per Pound. 1.320 reas 1.768 2.062 2.385 2.725 3-143 3-667 4-332 5.196 6.131 7-342 8.95 10.65 12.89 15-91 20.14 24.52 30.51 38-99 51.56 63-06 80.6 105.2 143.2 206.2 254.6 2213 420.9 $72.9 681.8 824.9 1o18. 1227. 1506. 1784. 2146. 2452. 2829. 3300. 3899. 4677. 5713: 7120, 9167. 12200. 14660. 17050. 20620. 25460. 32230. 41990. 7290. 2490. 128900. 229200. 330000. CONSTANTS OF COPPER WIRE. TABLE 67. according to the British Standard Wire Gauge. British Measure. Temperature 0° C. Density 8.90. Electrical Constants. Resistance and Conductivity. Gauge Number. Ohms per Foot. Log. Feet per Ohm. Ohms per Pound. Pounds per Ohm. 0.00003918 5.59310 | 25520. 0.000051719 19335; 00004550 65799 | 21980. 000069736 | 14339. 0.0000 5249 5-7 2006 19050. 0.00009281 10775. .000061 22 -78691 16330. .00012627 7920. .00007078 84994 14130. .0001 6880 5924. .00008089 .90787 12360. .00022040 4537: 00009331 .96994 10720. 00029333 3409. 0.0001088 4-03679 9188. 0.0003991 2505.8 0001 286 10921 Poa Na 0005570 1795.2 0001 543 18823 6483. 000801 5 1247.7 0001820 26005 5495: OO1I15S 896.2 .0002180 -33836 4588. .0016002 624.2 0.0002657 4-42443 3763. 0.0023786 420.4 0003162 -50000 3162. 0033688 296.9 .00038 26 -58279 2613. 0049323 202.7 .00047 24 .67 430 2117. 0075176 133.0 0005979 -77001 1673. 0084978 117-7 0.0007280 4.86211 1373-6 0.017853 56.013 .0009056 95696 1104.2 .027631 36.191 .OO11 573 3.06345 864.1 045121 22.163 001 5305 18485 653-4 078927 12.669 0015896 .27636 529.2 -120282 8.314 0.002391 3.37867 418.1 0.19267 5.1902 003124 49465 320.2 -32863 3.0423 004252 62855 235-2 60893 1.6423 .0061 22 .78691 163.3 1.26268 0.7919 .007 558 87842 132.3 1.92451 -5196 0.00957 3-98073 104.54 3.0827 0.32439 .01249 2.0967 I 80.04 5.2599 -IQOIL .O1701 .23061 58.80 9.7429 10264 02024 -30618 49-41 13.7988 .07240 02506 -38897 39-91 20.2028 04951 0.03023 2.48048 33.08 30.792 0.032478 03642 56134 27.46 50.254 017778 04472 -65051 22.36 67.373 014843 .05296 72395 18.88 94.488 010583 .06371 80419 15.70 136.724 007314 0.07449 2.87211 13.42 182.68 0.005474 .08398 92418 II.QI 237-59 004209 09796 _-99103 10.21 323-25 -003094 -11573 1.06345 8.64 451.21 002216 -13883 -14247 7.20 649.25 -0O1 540 0.169 59 1.22940 5-397 968.9 0.0010321 21184 -32601 4.720 1508.3 0006630 .27210 43473 3.675 2494.2 0004009 -36226 -55902 2.760 4421.0 0002262 42515 62855 2.352 6089.3 .0001642 0.5060 1.70412 1.976 8624. 0.00011 596 .6122 78691 633 12627. -00007919 7558 87842 323 19245. 0000 5196 9506 .98073 045 30827. 00003244 1.2494 0.0967 I 0.800 52468. 00001906 1.7006 0.23061 0.5880 97429. 0.000010264 2. 3° 59 -38897 3991 202028. 000004950 3.8204 58279 .2613 493232. .000002027 6.8025 83267 -1470 | 1555851. .000000642 9.7956 99103 -I02I | 3232451. 000000196 SMITHSONIAN TABLES. 63 TABLE 68. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight. | : . Square of er Gauge Diameter in Diameter Section in Grammes Number. | Centimetres. (Circular Sq. Cms. per Metre. Cms.). 1.2700 1.6129 1.267 : 305209 0.000887 1786 -3890 -O9I : 2.987 19 -001032 1.0973 1.2040 0.9456 : 2.92512 0.001188 .0160 0323 .S107 : 85827 .001 386 0.9449 0.8928 7012 ; -79524 .001002 8839 7815 6136 : 73741 .001831 8230 6773 5319 : -63524 002004 0.7620 0.58065 0.4560 ; 2.60839 0.002464 -7010 -49157 3558 : 53607 002910 -6401 -40970 3218 7 -45695 003492 -5893 34725 2727 . 38512 .0041 20 5385 28996 2277 : 30682 004934 0.4877 0.23783 0.18679 ; 2.22075 0.00601 5 -4470 -19984 15696 7 14517 007159 4064 -16516 12973 : .06239 008662 3658 -13378 -10507 ; 1.97087 -010694 3251 -10570 .08 302 8 868 57 013533 0.2946 0.08681 0.06818 : 1.78307 0.01648 2642 .06978 .05480 : 68522 .02051 =2337 05461 04289 : 58172 .02620 .2032 04129 03243 3 -46033 03465 1829 03344 .02627 , 36881 04278 0.16256 0.026426 0.020755 : 1.26751 0.05401 1422 020233 O01 5890 : 15053 07071 12192 .014865 .O11675 : .01663 09625 -10160 010323 .008107 ‘ 0.85827 13858 09144 .008 361 006567 , 76675 -I7109 0.08128 0.006606 0.005188 ; 0.66445 0.2165 .O7112 005058 003972 : -54847 2828 .06096 .003716 002922 -598 -41457 3850 105595 003123 .002452 2. -33899 4581 05080 002581 002027 5 25621 5544 0.04572 0.0020903 0.0016417 : 0.16509 0.6838 04166 .0017352 001 3628 212 _ 08384 8245 03759 .OOI 41 32 .OO1 1099 : 1.99467 1.0123 03454 0011922 .0009 363 : .92083 -2000 03150 .0009920 0007791 : 84099 +4422 0.02946 0.000868 1 0.00068 18 F 1.78307 1.648 .02743 .0007 525 0005910 52 72100 1.901 -02540 .00064 52 .000 5067 . -65415 2-207 02337 .0005461 .0004289 38 50172 2.620 02134 0004552 0003575 : 50271 3.143 0.01930 0.00037 26 0.0002927 : 1.41578 3.839 .01727 .0002983 .0002343 : 31917 4-784 01524 0002323 0001824 ; 21045 6.160 .O1 321 0001746 .OOOT 370 : 08616 8.201 01219 .0001 486 .0001 167 : .01663 9.625 0.01118 0.0001 249 0.000098 2 : 2.94105 11.45 -O1016 .0001032 .00008 13 0722 85827 13.86 0091 4 .00008 36 .0000656 : 70075 T7eUE 00813 .0000661 .0000 519 0462 66445 21.65 .OO7 11 0000 506 .0000397 . 54847 28.28 0.00610 0.000037 16 0.0000292 .02 2.41457 38.5 00508 .00002 581 0000203 : 25621 55-4 .00406 .00001652 .00001 29 . 00239 $6.6 00305 00000929 .000007 3 .0065 3.51251 154.0 .00254 -00000645 .0000051 7 65415 221.8 Metres Log. per Gramme. — SMITHSONIAN TABLES. 64 TABLE 68. CONSTANTS OF COPPER WIRE. according to the British Standard Wire Gauge. Metric Measure. Temperature 0° C. Density 8.90. Electrical Constants. Resistance and Conductivity. Gauge Ohms per Metre. ; Metres perOhm.} Ohms per Gramme. Grammes per Ohm. Number. 0.0001 286 4- 7779. 0.0000001140 | 8770000. 7-0 .0001493 2 6699. .0000001 537 | 6504000. 0.00017 22 4.2 5814. 0.0000002046 | 4887000. 0002009 -3028 4979. 0000002784 | 3592000. .0002 322 : 3 4300. -00000037 21 2687000. 0002653 : 3769. 0000004857 | 2059000. 0003001 48592 3260. 0000006319 | 1583000. 0.000357I 4 2801. 0.0000008798 | 1137000. .0004218 62 2371. .O00001 2275 814700. .000 5061 : 1976. .000001767 I 565900. .000597 I : 1075. .0000024600 406500. 0007151 854 1398. 0000035279 283500. 0.00087 18 4.94041 1147.1 0.000005244 190700. 0010375 3-01 599 963.9 000009350 107000. 0012554 09877 790.6 .00001087 4 91960. .0O1 5499 -19029 645.2 000016573 60340. OO1QO15 -29259 509.8 .000026547 37670. 0.002388 3.37810 418.7 0.00003936 25410. .002978 -47295 335-8 .00006092 16420. 003796 57934 263.4 -0000994 5 10060. .00 5022 -70083 199.1 .00017398 5748. 006199 -79235 161.3 .00026518 377M 0.007846 3-89465 127.45 0.0004238 2359.6 .010248 2.01004 97-58 .0007 246 1380.1 .013949 14453 71.69 10013425 744-9 .020086 30289 49-79 .0027837 359-2 024798 39441 40.32 .0042428 235-7 0.03138 2.49671 31.86 0.005398 .04099 .61270 24.39 O11 594 05579 -74659 17.92 .021479 .06040 82217 ;) 15,06 030421 08034 90495 12.45 044539 09919 2.99647 10.082 0.06782 -11949 1.07733 8.369 .098 51 -14672 -16649 6.516 14853 -17391 -24034 5-750 20869 .20901 -32017 4-784 -30142 .2388 1.37810 4.187 0.3936 +2755 -44017 3.629 5238 3214 50701 ii -7126 -3797 57944 2.634 -9947 4555 -65846 2.196 1.4313 5564 1.74539 1.7973 2.136 .6950 .84200 4388 3.333 8927 -95070 -1202 7.019 1.1885 0.07 501 0.8414 9-747 -10260 -3949 -14453 -7169 13-424 .07 449 1.660 0.22011 0.6024 19.01 0.05260 2.009 30289 -4979 27.84 03592 2.480 39441 +4033 42.43 -02357 3.138 -49671 -3186 7.96 .O1471 4.099 .61270 2440 115.94 00863 5-579 0.74659 0.1792 210.4 0.0047 53 8.034 -90495 1245 445-4 002245 12.554 1.09877 -0797 1087.4 -000920 22.318 -34865 .0448 3436.7 .00029I 32.138 50701 0311 7126.3 .000T 40 go38 F OOD ON DuAwWnNEe O SMITHSONIAN TABLES, 65 TABLE 69. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight. ; Square of ’ , Meet Gauge Diameter Diameter Sections in rs ae | Number. | in Inches. (Circular Sq. Inches. B- Pound Inches). : 0000 0.454 0.2061 0.16188 0.6246 1.79561 1.601 000 -425 -1806 .14186 5474 -7 3828 1.827 00 «380 .1440 11341 4376 .64107 2.285 -340 “1156 09079 +3503 -54446 2.855 1 0.300 0.09000 0.07069 0.2727 1.43574 3.666 2 .284 08065 06335 -2444 38514 4.091 3 259 .06708 05269 +2033 30810 4-919 4 .238 .0 5064 -04449 L707 23405 5.526 5 .220 .04840 .03801 .1467 16634 6.818 6 0.203 0.04121 0.03237 0.12488 1.09649 8.008 7 .180 .03240 02545 09818 2.99204, 10.185 8 165 02723 02138 08250 -91647 12.121 9 148 .02190 .01720 .06638 82202 15.065 10 134 01796 -O1410 05441 73571 18.379 ay 0.120 0.014400 0.011310 0.04364 2.63986 22.91 12 109 .O11881 009331 .03600 55035 27.77 13 .095 009025 007088 0273 4.3695 36.56 14 083 .006889 .005411 .0205 31965 47.90 15 072 005184 004072 O1571 -19616 63-65 16 0.065 0.00422 0.0033183 0.012803 2.10733 78.10 17 058 003304 0026421 .OL0194 00835 98.10 18 049 002401 .00188 57 007276 3-86189 137-44 19 042 .0017 64 0013854 005346 .72800 187.06 20 035 .OO1 22 .0009621 003712 56963 269.40 21 0.032 0.001024 0.0008042 0.003103 3.49180 322.3 22 .028 .000784 0006158 002376 37581 420.9 23 .02 .000625 0004909 001594 .27738 528.0 24 .022 .000484 0003801 .001 467 16634 651.8 25 .020 .000400 .0003 142 001212 08356 824.9 26 0.018 0.000324 0.000254 5 0.0009818 4.99204 1018. 27 .016 .000256 .00020II .0007758 58974 1289. 28 O14 000196 0001 539 0005940 7875 1684. 29 O13 .000169 .0001 327 .O005121 70939 1953. 30 O12 000144 .OOOII3I 0004 304 .63986 2292. 31 0.010 0.000100 0.000078 54 0.00030 304 4.48150 3300. 32 .009 .00008 I .00006362 .00024 546 38998 407 4. 33 008 .000064 00005027 .00019395 .28768 5150. 34 .007 .000049 .00003848 .0001 4849 17169 67 34. 35 .005 000025 00001963 .00007 576 537944 13200. 36 0.004 0.000016 0.00001 257 0.00004849 5-68 562 20620. GMITHSONIAN TABLES. 66 CONSTANTS OF COPPER WIRE. according to the Birmingham Wire Gauge. 0.000047 52 00005423 .00006784 .00008474 0.0001088 .OOOI 214 .0001 460 0001729 .0002024 0.0002377 .000302 .0003595 .0004472 -0005455 0.0006802 0008245 00108 54 0014219 0018896 0.002318 .002980 .004080 005553 .007990 0.009566 012494 015709 .020239 024489 0.02887 03826 .04998 05796 06802 0.09796 .12095 15306 .19Q91 39182 0.61222 Electrical Constants. British Measure. Temperature 0° C. Density 8.90. 2.46048 58279 .69877 76314 83266 2.99103 1.08254 18485 .30083 -59309 1.78691 SMITHSONIAN TABLES. Resistance and Conductivity. Ohms per Pound. 0.00007 61 .0000g9I .0001 550 0002419 0.0003991 0004969 .0007183 .OO1007 4 0013799 0.001903 .003079 004301 .0067 37 010025 0.01559 .02290 .03969 .OOSII .12028 o.18II .2923 .5607 1.0388 2.1541 3.083 .259 -275 13-799 20.203 20.41 49.32 84.14 113.18 155.88 323.2 492-7 789.2 1346.3 5171.9 12627. 67 0.034006 020275 011885 008835 006415 0.0030936 .0020290 0012671 .0007 420 .0001933 0.00007920 TABLE 69. Gauge Number. DO upwone Oowo ON NO wprrnn COON DD UbWN WNHN wwwu 0 nO N a oa TABLE 70. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight. Gauge Number. wNN ND neo N wrrpnNd Ooo ON OD Diameter in Centimetres. 1.1532 0795 0.9652 8636 0.7620 7214 6579 6045 5585 0.5156 -4572 4191 -3759 +3404 3048 -2769 2413 -2108 -1829 -16510 14732 -12446 -10658 08890 0.08128 .O7112 06350 05558 05080 0.04572 .04004 03556 .03302 .03048 0.02540 .02286 .02032 -01778 .01270 0.01016 Square of Diameter (Circular Cms.). 1.3298 1653 0.9316 7458 0.5806 5216 4328 +3055 3123 0.2659 -2090 .1756 1413 155 0.09290 .07665 05823 04445 203345 0.027258 021703 .O1 5490 O11381 007903 0.006606 005058 .004032 .003123 002581 0.0020903 -OO16516 0012645 0010903 .0009290 0.00064 52 .0005226 0004129 .0003161 0001613 0.0001032 Section in Sq. Cms. 1.0444 QI 52 7317 5058 0.4560 4087 ees) .2870 .2452 0.20881 -16417 13795 «11099 .09098 0.07297 .06160 04573 03491 .02627 0.021409 .017046 .O12166 008938 .006207 0.005189 003976 .003167 002452 .002027 0.0016418 0012972 .0009932 0008 563 .0007 297 0.0005067 0004104 0003243 .0002483 .0001 267 0.000081 1 SMITHSONIAN TABLES. 68 Grammes per Metre. 929-5 814.6 651.2 521.3 405-9 363-7 302.5 255-4 218.3 185.84 146.11 122.78 98.78 80.98 64.94 54:83 40.70 31.07 23-43 19.054 15.171 10.828 7-955 5-524 4.618 3-536 2.820 2.183 1.804 1.4611 1545 8339 -7621 6494 0.4510 3053 2886 2210 -LI27 0.0722 Pp Gramme. 0.001076 .001228 .001 536 001918 0.002464 .002749 003306 003915 004581 0.005381 .000344 008145 -O10124 -012349 0.01540 01824 02457 03219 .042608 0.05248 00592 -09235 we c7 a -18103 0.2165 2828 3547 4581 +5544 0.6844 TABLE 70. CONSTANTS OF COPPER WIRE. according to the Birmingham Wire Gauge. Metric Measure. Temperature 0° C. Density 8.0. Electrical Constants. Resistance and Conductivity. Gauge Ohms Metres Ohms Number. per ig. per per Metre. Ohm. Gramme. 0.0001 559 4. F 0.0000001 677 5962000. .0001779 : ; 0000002184 4578000. 0002226 : : 0000003418 2926000. .0002780 : ; .000000 5333 187 5000. 0.000357 I 252 ; 0.0000008798 1137000. 0003985 600: ; -O000010955 912800. .000479I : : .000001 5837 631400. .000 567 4 : i .0000022210 450200. .0006640 : ; .00000 30420 328700. O mapwn Fe 0.0007799 4. 0.000004196 238300. 0009257 : .000006789 147 300. Oot 1804 : .0000096I 5 104000. .001 4672 1664 .00001 4853 67 330. 0017898 ; 3 .000022103 45240. Ooo ON 0.002232 a 0.00003437 29100. 002643 : 6 .00004822 20740. 003501 a5 US7 .000087 49 11430. 004065 : .OOOI 5016 6660. .00018 5 : 00026396 3789. 0.007607 2 0.0003992 2504.9 009553 : .0006297 1588.0 013385 2.12 0012362 08.9 018219 .26052 : .0022902 430.6 026235 . 0047489 210.6 N 0.03138 DZ, 0.006796 147.14 04099 6127 011594 86.25 05142 : 018243 54-82 .00640 .822 030421 32.87 08034 E 044539 22.45 NNN HL nO nN oa 09919 9 0.06789 14.731 12583 .098 10874 9.196 .16397 2 .18550 5.391 19016 “2 24951 4.008 -22138 -34865 -34307 2.910 WYN Oo ON oO WwW On 0.3214 mes 0.7126 1.4032 3968 59857 1.0862 0.9206 5022 -7008 1.7398 5748 6559 81682 : 2.9801 3349 1.2555 0.10907 11.4020 -0877 2.0086 0.30289 27.8370 0.0359 SMITHSONIAN TABLES. 69 TABLE 71. STRENCTH OF MATERIALS.* (az) METALS. Tensile strength in Name of metal. pounds per sq. in. Aluminium wire. ; A Brass wire, hard drawn . 50000-I 50000 Bronze, phosphor, hard drawn I [0000-1 40000 a silicon & te 5000-1 I 5000 Copper wire, hard drawn 60000-70000 Goldt+ wire . ; 38000-41000 Iron,} cast . . . I 3000-29000 “« wire, hard drawn . 80000-1 20000 E “annealed. 50000-60000 Lead, cast or drawn : 26000-33000 Palladiumt . : 39000 Platinum + wire : 50000 Silvert wire . . 42000 30000-40000 Ke Shard Zinc, cast «drawn Basalt . Brick, soft hard Granite Limestone Marble Sandstone Slate Ash . 4 Beech , Birch f Chestnut . Elm . : Hackberry Hickory . Maple ° Mulberry . Oak, burr. reds “water “white Poplar . Walnut Tin, cast or drawn . “ vitrified . Steel, mild, hard drawn . “ (4) STONES AND BRICKS. Name of substance. Name of wood. Tensile strength in pounds per sq. in. I 1000-21000 I 1000-18000 12000-18000 I0000~I 3000 12000-18000 10000-16000 I 5000-25000 8000-1 2000 8000-1 4000 I 5000-20000 I 3000-18000 12000-16000 . 20000-25000 IO0000-I 5000 8000-14000 100000—200000 I 50000-33000 4000-5000 7000-1 3000 22000-30000 Resistance to crush- ing in pounds per sq. in. 18000-27000 300-1 500 1500-5000 9000-26000 17000-26000 4000-9000 9000-22000 4500-8000 I 1000-30000 Resistance to crushing in pounds per sq. in. 6000-9000 9000-10000 5000-7000 4000-6000 6000-10000 7000-1 2000 6000-8000 7000-10000 5000-7000 4000-6000 6000-9000 5000-8000 4000-8000 Se a a * The strength of most materials is so varia have been obtained. limits between which the strength of fairly good s tion of strength to composition in the case of a in other than the ordinary inch pound units. ¢ On the authority of Wertheim. + The crushing strength of cast iron is from 5.5 to 6.5 times the tensile strength. Nores. — According to Boys, quartz fibres have a tensile strength of between 116000 and 167000 pounds per square inch. ecimens may lie. ble that very little is gained by simple tabulation of the results which A few approximate results are given for materials of common occurrence, mainly to indicate the Some tables are also given indicating the rela- It has not been thought worth while to state these results Leather belting of single thickness bears from 400 to 1600 pounds per inch of its breadth, SMITHSONIAN TABLES. 70 PHYSICAL PROPERTIES OF STEEL.* TABLE 72. | Percentages of Ps Si. Modulus oung’s in inch pounds ~ roo. Resilience to yield point in inch pounds. Resilience to rupture Elongation per cent. Strength at yield PERO -uIRWU N NWW Gon ¢ NA WYN O mw CO OWOM OO eH Nee trace Ww 036 .016 .076 .O18 045 4 oa CO a Om WO = NN uns wD oo 054 | - 549 007 8 .040 |. 484 049 | - 543 073 | - 505 .007 | . 510 O18) ||| 557 052 |. 652 .000 | . 516 SOLGh |e 590 5050) |< 631 .003 | .003 | « 555 .OOI | .002 | . 608 038 | .000 | . 614 = oe AR MODY WON: 0 ON On _ STEEL CONTAINING CHROMIUM. 612) Cr. LOZ Ors 1.044 Cr. 2.200 Cr. 4.000 Cr. STEEL CONTAINING TUNGSTEN. — | — | .o9 | 1.99 | «19 | 7.81 per cent tungsten . 1464 — | .05 | 2.06 12.66] 673 “ “ 760 Same after heating to dull red and quenching in oil. 940 _ | — | .21 | 1220/35 | 6.45 per cent tungsten . 1900 STEEL CONTAINING MANGANESE. j one test 98 ) another test . * The samples here given are arranged in the order of ultimate strength. The table illustrates the great com- plexity of the problem of determining the effect of any given substance on the physical properties. It will be noticed that the specimens containing moderately large amounts of copper are low in ductility, —that high carbon or high sum of carbon and manganese generally gives high strength. The first specimen seems to indicate a weakening effect of silicon when a moderate amount of carbon is present. It has to be remembered that no table of this kind proves much unless nearly the same amount of work has been spent on the different specimens in the process of manufacture. Most of the lines give averages of a number of tests of similar steels. The table has been largely compiled from the ere of the Board on Testing Iron and Steel, Washington, 1881, and from results quoted in owe’s ‘‘ Metallurgy of Steel. + The strengths and elasticity data here given refer to bar or plate of moderate thickness, and are in pounds per square inch. Mild steel wire generally ranges in strength between rooooo and 200000 pounds per square inch, with an elongation of from 8 to 4 per cent. Thoroughly annealed wire does not differ greatly in strength from the data even in the table unless it has been subjected to special treatment for the purpose of producing high density and ne-grained structure. Drawing or stretching and subsequent rest tend to increase the Young’s Modulus. SMITHSONIAN TABLES. 71 TABLE 73. ELASTICITY AND STRENCTH OF IRON.* Area of cross sec- tion of the bar in percentage of the area of the cross section of the pile. Relative values of. | ultimate strength. 194 170 144 140 130 114 100 92 _— MmMOnNunbO Wd TABLE 74. APPROXIMATE VARIATION OF THE STRENCTH OF BAR IRON, WITH VARIATION Relative values of the stress at the | yield point. The variation of the yield point is not regular, and seems to have been much affected by the temperature of rolling. OF SECTION.? Diameter in inches. Strength per sq. in. in pounds. bar. Total strength of Total strength of bar. Diameter Strength per sq. in inches. i in. in pounds. 224000 203000 182000 163000 145000 129000 113000 99000 85000 73000 62000 59000 58500 58000 57600 57100 50700 50300 59909 55509 55100 54700 mooHb 52000 42000 34000 27000 20000 14900 10300 6600 3700 1600 400 54300 54000 53700 §3309 53000 52700 52400 52100 51900 51600 51300 * This table was computed from the results published in the Report of the U.S. Board on Testing Iron and Steel, Washington, 1881, and shows approximately by the relative effect of different amounts of reduction of section from the | pile to the rolled bar. A reduction of the pile to 10 per cent of its original volume is taken as giving a strength of | 100, and the others are expressed in the same units. + The strength of bar iron may be taken as ranging from 15 per cent above to 15 per cent below the numbers here given, which represent the average of a large number of tests taken from various sources. Notes. — The stress at the yield point averages about 60 per cent of the ultimate strength, and generally lies be- | tween so and 70 percent. The variation depends largely on the temperature of rolling if the iron be otherwise fairly pure. According to the experiments of the U. S. Board for Testing Iron and Steel, above referred to, a bar of iron which a been subject to tensile stress up to its limit of strength gains from ro to 20 per cent in strength if allowed to rest ree from stress for eight days or more before breaking. The effect of stretching and subsequent rest in raising the | Ciastic limit and tensile strength was discovered by Wohler, and has been investigated by Bauschinger, who shows Hat the modulus of elasticity is also raised after rest. The strengthening effect of stretching with rest, or continuous ery slowly increased loading, has been rediscovered by a number of experimenters. enn TABLES. 72 TABLES 75-77. EFFECT OF RELATIVE COMPOSITION ON THE STRENCTH OF ALLOYS OF COPPER, TIN, AND ZINC.* TABLE 75.—Copper-Tin Alloys. (Bronzes.) TABLE 76.—Copper-Zinc Alloys. (Brasses. strength. a bog to =a “uo Rg Oo per square inch. Percentage of Percentage of Percentage elongation. Percentage compression. Percentage of Percentage of Tensile Crushing ¢ strength Percentage elongation. Pounds per square inch. 27000 | 14000 | 41000 12000 | 28000 17000| 46000 | Io. 10000 | 29000 54000] 4. 2 eoooa le adore 8000 | 39000 74000] I. goco | 46000 28000 | 124000 see | sees 13000 | 63000 18000 | 150000] ©. 17000 | 74000 6500 | 143000 20000 | 9go00o 24000 | 116000 2800] 75000] ©. 14000 | 126000 14000] 42000 TABLE 77. — Copper-Zinc-Tin Alloys.$ Percentage of Tensile Percentage of Tensile Strength strength in pounds : in pounds per sq. in. Copper. Zinc. ‘in, per sq. in. a B Copper. Zinc. 50 45 40 43 40 35 30 15000 50000 15000 = 45000 20 44000 ) 37900 65000 10 30000 62000 5 24000 | ! _ ~— MAnMmMOMNd OUNn 15000 Is 45000 37 60000 IO 43000 35 52500 41000 30 40000 45000 20 10000 45000 30 50000 47500 25 42000 43500 20 30000 46500 15 18000 42000 10 12000 * These tables were compiled from the results published by the U. S. Board on Testing of Metals. The numbers refer to unwrought castings, and are subject to large variations for individual specimens. + The crushing strengths here given correspond to 10 per cent compression for those cases where the total com- pression exceeds that amount. ¢ For crushing strength, ro per cent compression was taken as standard. § This table covers the range of triple combinations of these three metals which contain alloys of useful strength and moderate ductility. The weaker cases here given, and those lying outside the range here taken, are generally weak and brittle. The absolute strength may of course be varied by the method of fusing and casting, and certainly can be greatly increased by working. The object of the table is to show relative values, and to give an idea of the strength of sound castings of these alloys. SMITHSONIAN TABLES. 73 TABLE 78. ELASTIC MODULI. Rigidity Modulus.* Modulus of Rigidity. Substance. Pounds per Grammes per Authority. square inch square centi- — 108, metre — 10°, Metals : — Aluminium 3 - Brass and Bronze wire Copper, drawn oe “ 241-335 Thomson}-Katzenelsohn. 320-410 Various. 393-473 Thomson.t 352 Katzenelsohn. 432 “ 490 Gray. Katzenelsohn. Thomson.f Wertheim. Various. Thomson.t Pisati. ‘Thomson.t Pisati. Baumeister. Wertheim. Pisati. Kiewiet. Thomson.t Kiewiet. Wertheim. Kowalski. CE Pat ON = N00 CO German silver “ “ Gold, pure . “ “ oft om OAs NO 290 Oo = OV ft Iron, soft “drawn Platinum “ Silver . oe “ Steel, cast . o “ Tin Zinc “ Glass “ _— WWD A OWWWO NR NWO ONT Ld NW OOM KR ON Wunnrk OFM Qn Stone :— Clay rock Granite Marble Slate Tuff Wood Gray & Milne. RUHNU Kn Ob HH DODHODOA | dy = eb _ Gray. * The modulus of rigidity as used in this table may be shortly defined by the following equation : — Modulus of rigidity — Intensity of tangential stress. Distortion in radians. To interpret the equation imagine a cube of the material, to four consecutive faces of which a tangential stress of uniform intensity is applied, the direction of the stress being opposite on adjacent faces. The modulus of rigidity is the number obtained by dividing the numerical value of the tangential stress per unit of area by the number repre- senting the change of the angles on the nonstressed faces of the cube measured in radians. + Lord Kelvin. SMITHSONIAN TABLES. 74 TABLE 79. ELASTIC MODULI. Young’s Modulus. * Young’s Modulus, Substance. Authority. Pounds per Grammes per square inch square centi- — 10%, metre — 10°, Metals : — Brass and bronze, cast . : 600-700 Various. Brass, drawn : , 1000-1 200 oe Copper, drawn. ; 1150-1250 . “annealed . : : 1052 Wertheim. German silver, drawn . 1209-1400 Various. Gold, drawn ; : 813-980 < “annealed. 558 Wertheim. Iron, cast . : 550-1200 Various. “wrought. : 1700-2100 Iron wire . 5 ia a “ Lead, cast or drawn : 156-200 « Palladium, soft . 979 Wertheim. ss hard . 1176 as Platinum, drawn 1600-1700 Various. s SOttn es 1552 Wertheim. Silver, drawn : : 700-750 Various. steel: : : 1600-2100 : «hard drawn. 1900-2100 Various. Tin ; 417 Wertheim. Zinc : 870-960 Various. Bone . : : 160 - Carbon 2-3. 151-255 Beetz. Glass . : : : 600-800 Various. ites 500-700 & Stone : — Clay rock E 329 Granite : 416 Gray Marble. : 400 & Slate. ; : 686 Milne. Doky: : 189 Whalebone : : 60 - Wood ; , .0-2. Various. * The Young’s Modulus of elasticity is used in connection with elongated bars or wires of elastic material. It is the ratio of the number representing the longitudinal stress per unit of area of transverse section to the number rep- resenting the elongation per unit of length produced by the stress, or: — Young’s Modulus = Intensity of longitudinal stress. Elongation per unit length. In the case of an isotropic substance the Young’s Modulus is related to the elasticity of form (or rigidity modulus) and the elasticity of volume (or bulk modulus) in the manner indicated in the following equation : — E —_9%k_ 3k+n where Z is Young’s Modulus, » the rigidity modulus and & the bulk modulus. The bulk modulus is the ratio of the number expressing the intensity of a uniform normal stress applied all over the bounding surface of a body (solid, liquid or gas) to the number expressing the change of volume, per unit volume, produced by the stress. + The modulus for cast iron varies greatly, not only for different specimens, but in the same specimen for different intensities of stress. It is diminished for tension stress by permanent elongation. ¢ See also Table 72. GMITHSONIAN TABLES. 75 TABLES E ae ELASTIC MODULI. TABLE 80.—Variation of the Rigidity of Metals with Temperature.* The modulus of rigidity at temperature ¢ is given by the equation 7, = %p (1 + af + Be + yf), Metal. Do Authority. .000001 36 00000048 | — .0000000032 00000023 | — .0000000047 .00000025 — .0000001 2 — 00000019 | + .o0000000TT 00000050 | -+ .0000000008 .00000038 | — .000000001 1 .00000059 | ++ .0000000009 Brass ; : . | 320X 108 00045 oy : - | 265 Xao° 002158 Copper . ; » 307/108 002716 : 5 ‘ 390 X 10° 000572 Iron : : . | 694 X 108 000483 ie : 2a) | OL Lele .000206 Platinum . 663 X 108 .OOOITI Silver . . | yee acer .000387 Steel ‘ ; =) (2029 ><10% .000187 TABLE 81.— Ratio p of Transverse Contraction to Longitudinal Extension under Tensile Stress (Poisson’s Ratio). Range of the value of p. Authority. Name of substance. —- — 46 Everett. 0.340-0.500 Baumeister. — 3 Kirchhoff. — , Mallock. —_— ; Wertheim. — : Littmann. Copper : — Tron “ce Lead : Steel, hard “ “ .224-0.441 0.250-0.420 0.214-0.268 0.293-0.29 0.275-0.32 0.260-0.303 Mallock. Thomson. Everett. Mallock. Baumeister. Littmann. Mallock. Kirchhoff. Okatow. Schneebeli. Okatow. —_- — : Schneebeli. —_-_ — . Mallock. : 3 : : : —_- — : Goetz & Kurz. Zinc : : : : ; : 0.180-0.230 Mallock. Ebonite . ; ; : : _- — ae Ivory . ‘ : : . 5 —- — Paratfin . . 5 > 3 , —_- — Cork ‘ ‘ : = é “ —- — ; a Caoutchouc (for small extensions) 0.370-0.640 § Rontgen. sf Ss — ; | Amagat. “ “ 0.500 Jelly ; : . é : : — — 0.500 ; Maurer. Katzenelsohn gives the following values, together with the percentage variation 5 between 0° and 100° C, Substance. _ Aluminium Brass : German silver Gold Tron Platinum Silver VUNG NHQM NaANUNARON _ * According to the experiments of Kohlrausch and Loomis (Pogg. Ann. vol. 141), and of Pisati(N. Cim. (3) vols. 4,5). SMITHSONIAN TABLES. 6 TABLE 82. ELASTICITY OF CRYSTALS.* The formulz were deduced from experiments made on rectangular prismatic bars cut from the crystal. These bars were subjected to cross bending and twisting and the corresponding Elastic Moduli deduced. The symbols a B y, a By, y, and ay By yo represent the direction cosines oh the length, the greater and the less transverse dimensions of the prism with reference to the principal axis of the crystal. E is the modulus for extension or compression, and T is the modulus for terminal rigidity. The moduli are in grammes per square centimetre. Barite. 10 = = 16.130 + 18.518! + 10.42y!-++ 2(38.79B°y?-+ 15.21y°a? + 8.88a7B?) 1010 7 = 69.52at + 117.668 +116.4674 + 2(20.16B?y? + 85.2977a? + 127.3528?) Beryl (Emerald). rol” 2 : h Thi ia ae 4 4 BQ ete 24 { where $4; $2 are the angles which E 4-325 sin’ + 4.619 cos + 13.328 sin’ cos’6 the length, breadth, and thickness 0 of the specimen make with the principal axis of the crystal. L + = 15.00 — 3.675 costd2 — 17.536 cos?¢ cos" Fluor spar. 10 io eld oe 10 > = 58.04 — 50.08 (By? + 77a” + ap?) Pyrites. 1010 7 = 5.08 — 2.24 (at + Bt-+ 4) I old “= 18.60— 17.95 (By? + 7a? + a2") Rock salt. 1010 Fr 33-48 — 9.66 (at + B+ ¥*) 1010 “ar = 154-58 — 77.28 (BY? + Ya? a8’) Sylvine. tol 75:1 — 48.2 (at + B+ vy) rol “Tr = 306.0 — 192.8 (By? + 77a? + 026") Topaz. 10 a = 4.341a* + 3.460B* + 3.77174 + 2 (3.879877? + 28. 56770? + 2.390°8?) a = 14-88at + 16.5484 + 16.4574 + 30.8987? + 40.89/70? + 43.51078? Quartz. 19 “ = 12.734 (1 —vy")?+ 16.693 (1 —y7*)7 a 9.70571 — 8.460By (32 — B2) T — 19-665 + 9.06072" ++ 22.9847"y1? — 16.920 [(yB + By1) (3401 — BB1) — B272)] * These formule are taken from Voigt’s papers (Wied. Ann. vols. 31, 34, and 35). SMITHSONIAN TABLES. 77 TABLE 83. ELASTICITY OF CRYSTALS. Some particular values of the Elastic Moduli are here given. Under E are given moduli for extension or compression in the directions indicated by the subscripts and explained in the notes, and under T the moduli for torsional rigidities round the axes similarly indicated. (a) REGULAR SYSTEM.* Substance. E, E, E, Ab Authority. Fluor spar . . .| 1473 X10 | 1008X10% | 910 X 108 345 X 108 | Voigt.t Pyrites)) . - . «|| 3530 >< 10" | 25308 109 "I" 232To xX Too sl aTo7e moe 8 | Rock salt. . . .| 416X108 | 346X108 | 311X108 | 129X108 “ os ole ne eal B4OSPanOS 339 X 108 — _ Koch.t Sylvine <7 e-.) se. e-7|| wOle aTOo 209 X 10% _ _ - SO iGey eal cheval | 72E Xen 196 X 108 — 655 X 108 | Voigt. Sodium chloride .]| 405 X 108 319 X 108 — _— Koch. Potash alum. . . 181 X 108 199 X 108 — _ Beckenkamp.§ Chrome alum . . 161 X 108 177 GTO? _— — se “cc Tron:alum: sees 186 X 108 (4) RHoMBIC SysTEmM.||| | Substance. FE, E, | Es Ey E; E, Authority. | Barite .| 620 xX 108 5° X 10] 959 X 10°} 376X108] 702 X 108| 740 X 10°] Voigt. | Topaz . | 2304 X 108 | 2890 X 10°| 2652 X 108 | 2670 X 10% | 2893 X 10°| 3180 X 106 se Substance. | T10=Toe1 Ti3=Ts31 Tog = T3¢ Authority. | Barite Res eee: 283X510" 293 X 108 121X108 | Voigt. [{OpaZ. si Naat, ven tates 1330 X 108 1353 X 108 1104 X 108 ss In the MONOCLINIC SysTEM, Coromilas (Zeit. fiir Kryst. vol. 1) gives § Emax = 887 X 10° at 21.9° to the principal axis. Enin = 313 X 108 at 75.4° ce fs Mics } Enax = 2213 X 108 in the principal axis. Enin = 1554 X 10% at 45° to the principal axis. Gypsum In the HEXAGONAL SysTEM, Voigt gives measurements on a beryl crystal (emerald). The subscripts indicate inclination in degrees of the axis of stress to the principal axis of | the crystal. Eo = 2165 X 108, Eyg==1796 X 108, Ego = 2312 X 108, To = 667 X 10°, P99 883 10%. The smallest cross dimension of the prism experimented on (see Table 82), was in the principal axis for this last case. In the RHOMBOHEDRIC SysTEM, Voigt has measured quartz. The subscripts have the same meaning as in the hexagonal system. Eo = 1030 X 108, E_4;=1305 X108, E,45—=850 X 10%, E9785 X 10%, | To= 508 X 10°, To9= 348 X 108. Baumgarten {| gives for calespar Eo= 501 X 10%, E_4s—=441 X108, E.4;=772 108, Eg9=790 X 10% * In this system the subscript @ indicates that compression or extension takes place along the crystalline axis, and distortion round the axis. The subscripts 4 and c correspond to directions equally inclined to two and normal to the third and equally inclined to all three axes respectively. t Voigt, ‘‘ Wied. Ann.” vol. 31, 34-35. ¢ Koch, ‘‘ Wied. Ann.” vol. 18. § Beckenkamp, “ Zeit. fiir Kryst.’’ vol. 10. || The subscripts 1, 2, 3 indicate that the three principal axes are the axes of stress; 4,5, 6 that the axes of stress are in the three principal planes at angles of 45° to the corresponding axes, | Baumgarten, “‘ Pogg. Ann.”? vol. 152. SMITHSONIAN TABLES. 78 TABLES 54-87. COMPRESSIBILITY OF CASES.* These tables give the relative values of the product pu for different pressures and temperatures, and hence show the departure from Boyle’s law. The pressures are in metres of mercury, or in atmospheres, the volume being arbitrary. The temperatures are in centigrade degrees. TABLE 84. — Nitrogen. TABLE 85.— Hydrogen. Relative values of fv at — Relative values of sv at — = Pressure in metres of mercury. Pressure in metres of mercury. 17%.7 | 30°%1 | 50°.4 | 75°.5 | 100°.1 ° 17°57) | AO°ed 3430 | 3610 3500 | 3680 3620 | 3780 3710 | 3880 2830 | 3045 2855 | 3110 2985 | 3200 3080 3185 30 2875 | 3080 | 3330 60 2875 | 3100 | 3360 2930 | 3170 | 3445 140 3049313275 | 3559 3150 | 3390 | 3675 3285 | 3530 | 3820 260 3440 | 3055 | 3975 3600 | 3840 | 4130 3675 | 3915 | 4210 TABLE 86. — Methane. Relative values of sv at — Pressure in ee ne ere metres of mercury, 29°.5 | 40°.6 | 60°.1 | 792.8 | 200% 2745 | 2880 | 3100} —- - 2590 | 2735 | 2095 373 3460 2480 | 2640 | 2035 | 3180 | 3435 2480 | 2655 | 2940 3460 2560 | 2730 | 3015 3525 2690 | 2840 | 3125 3625 | TABLE 87. — Ethylene. : Relative values of Jv at — Pressure in metres of a 5 mercury. y ; 40°.0 50°.0 60°.0 7o°.0 79°-9 | 89°.9 | 10% 30 2410 | 2580 2865 | 2970 | 3090 | 3225 1535 | 1875 2310 | 2500 | 2680 | 2860 1325 | I510 1930 | 2160 | 2375 | 2565 1540 | 1660 1950 | 2115 | 2305 | 2470 1785 | 1880 2125 | 2250 | 2390 | 2540 2035 | 2130 2450 | 2450 | 2565 | 2700 22015) ||| 2375 2680 | 2680 | 2790 | 2910 2540 | 2625 2910 | 2910 | 3015 | 3125 2790 5 3150 | 3150 | 3240 | 3345 2960 | 3040 3380 | 3350 | 3470 | 3560 3200 | 32 3545 | 3545 | 3625 | 3710 |f ft _______t_i__i}_f_}} * Tables 84-89 are from the experiments of Amagat; ‘‘ Ann. de chim. et de phys.,”’ 1881, or “ Wied. Bieb.,”’ 1881, p. 418. SMITHSONIAN TABLES. 79 TABLES 88-90. COMPRESSIBILITY OF GASES. TABLE 88. — Carbon Dioxide. Relative values of pv at— Pressure in |__ metres of | mercury. liquid 625 825 1020 1210 1405 1590 1770 1950 2135 TABLE 89.— Carbon Dioxide.* Value of the ratio Jv /A,7, at — Pressure in atmospheres. TABLE 90.— Air, Oxygen, and Carbon Monoxide at Temperature between 18° and 22°.7 The pressure /; is in metres of mercury; the product Av is simply relative. Carbon monoxide. é pv * Similar experiments made on air showed the ratio Av /A,7, to be practically constant. + Amagat, ‘‘Compte Rendu,” 1879. SMITHSONIAN TABLES. 80 TABLES 91, 92. RELATION BETWEEN PRESSURE, TEMPERATURE AND VOLUME OF SULPHUR DIOXIDE AND AMMONIA.* TABLE 91.—Sulphur Dioxide. Oniginal volume rooo0o under one atmosphere of pressure and the temperature of the experi- ments as indicated at the top of the different columns. Corresponding Volume for Ex- Pressure in Atmospheres for periments at Temperature — Experiments at Temperature — Volume. 58°.0 99°.6 183°.2 Pressure in Atmos. —_ » O 9.60 10.35 11.85 13.05 14.70 16.70 20.15 23.00 26.40 30.15 35-20 TABLE 92.— Ammonia. Original volume 100000 under one atmosphere of pressure and the temperature of the experiments as indicated at the top of the different columns. Corresponding Volume for Ex- Pressure in Atmospheres for Experiments periments at Femperature — at Temperature — Pressure in 183°.0 18.60 22.70 25-40 29.20 34-25 41.45 49.70 59-65 * From the experiments of Roth, “‘ Wied. Ann.” vol. 11, 1880. SMITHSONIAN TABLES. 8I TaBLe 9S. COMPRESSIBILITY AND BULK MODULI OF Acetone . Benzene . “ “ Carbon bisulphide Glycerine Mercury . Methyl alcohol. “ “oe “ “ec Nitric acid Oils: Almond . Olive . Paraffine Petroleum . Rock . Rape seed . Turpentine. Sulphur dioxide Toluene . Xylene Compression per unit vol- ume peratmo, o ba _ > N NaN to t Oo NW Danan _ 1 2» OWN © Don ~ \o Oo range of pres- Pressure or sure in at- mospheres. 8.5-37-12 I 50-200 I 50-400 150-200 I 50-400 I 50-200 150-400 I 50-200 I 50-300 150-400 Authority. Amagat . “ Pagliani & Palazzo “ Colladon & Sturm Quincke . Amagat . Grassi. a“ “ Amagat . “ Colladon & Stan Tait Amagat Barus “ Quincke . . Colladon & Sturm Amagat Grassi. “ Amagat : Colladon & Sturm Quincke . De Metz . Martini . Quincke . “ “oe Colladon & Sturm De Heen. LIQUIDS. Calculated values of bulk modulus in — Pounds per sq. in. Grammes per sq. cm. 94 X 10° | 1.34 X 10° 115 od 119 1.69 93 1.32 133 1.59 2.35 1.69 1.84 2.35 2.35 2.26 0.87 0.26 0.28 0.49 0.50 0.77 1.55 2.00 1.45 Tr 1.31 1.34 1.47 0.87 I.II 0.46 O54 0.60 nNhaD G HOD O RAD Ww OWWMNWNNU 00° to SMITHSONIAN TABLES. 82 aes: TABLE SS. COMPRESSIBILITY AND BULK MODULI OF LIQUIDS. Calculated values of bulk modulus in — Liquid. Authority. Grammes Pounds per sq. cm. per sq. in. Compression per unit vol- ume per atmo. X 108, Pressure or range of pres- sure in atmos- pheres. Water, sea ~ pure chines See othe ss Q Colladon & Sturm NAD Gr ea ale ts Pagliani & Vincentini “ 10° “ _— =O “ aoe “ “ | tN an ee ee | MMnUnaA nnn aint OF we “ “ “ Qe WO LO OAK AN OO DOWWW Qw + “ =— = eee eal WwW WW WH WW GW PU ROIs wm QNNNN TABLE 94, COMPRESSIBILITY AND BULK MODULI OF SOLIDS. Calculated values of bulk modulus in — Authority. Grammes Pounds per sq. cm. per sq. in. ume per atmo, X 108, Compression per unit vol- Crystals : Barite Voigt. . 535X108 | 7.61 X 108 Beryl . se eee ee 1384 “ 19.68 “ IMGYS Pate .w tee ees ee oes 360 E22 A YEIUCSe etc ce eee ied fel cs Ore og 906 12.89 = \O Oo Quartz son cee) ton ee ; ae: 387 5.50 RROGKESAIEs Se fons ce fe ; ne 246 3-50 VIWINGs ects. oy esene) aeeke aes 138 1.97 ROPAZ ys 4. Mse cet se he ee 1694 24.11 Mourmaline =< 39s =): os gI40 130.10 BBrASS) ervey. cy cet ne ne ; Amagat . 10go 15.48 Copper soi) heats ee ae ee ee Buchanan 1202 17.10 Welta*metal’ so5 secs ey war ey et oe c Amagat . 1012 14.41 Lead PY) ciel ch ieee ftp Wee ee : “ : 374 Kee2 tCEll ais ogy were, | Pe) ecalceien Pe : : 1518 21.61 KE 1LASS iio kon cote 3 aa ee eee e : 405 5:76 * Tait finds for fresh water the value .0072 (1 — 0.034 9) and for sea water .00666 (1 — 0.034) where Z is the pres- sure in tons per square inch. The range of variation of # was from 1 to 3 tons. + Réntgen and Schneider by piezometric experiments obtained 5.0 X 10—8 for rock salt and 5.6 X 10-6 for sylvine (Wied. Ann., vol. 31). SMITHSONIAN TABLES. 83 TaBLe 95. DENSITY OR MASS IN CRAMMES PER CUBIC CENTIMETRE AND POUNDS PER CUBIC Grammes per cubic centimetre. Substance. Agate . Alabaster: Carbonate Sulphate . Alum, potash Amber Anthracite . Apatite Aragonite Arsenic Asbestos Asphaltum . Barite . Basalt Beeswax : ; Bole . . : .| 2.2—2. Bone . : Boracite Borax A 4 : ‘ Borax glass : : : Boron 2.68-2.69 Brick . 2.0-2.2 Butter . 0.86-0.87 Calamine 4-1-4.5 Calcspar 2.6-2.8 Carbon. See Graphite, etc. Caoutchouc . | 0.92-0.99 Celestine . 5 . 3.9 Cement: Pulverized loose Pressed Set . Cetin . Challe: Charcoal : Oak Pine : ; Chrome yellow . Cinnabar Clay Clayslate Coal, soft Cobaltite | Cocoa butter | Coke . | Copal . Corundum . | Diamond Anthracitic Carbonado Diorite Dolomite Earth, dry . Ebonite Emery Epsom salts : Crystalline Anhydrous Feldspar Flint Fluor spar . Gabronite Gamboge Galena Garnet N in qo % Www Y%Ow [oo eny Oo co FOOT OF VARIOUS SOLIDS.* Pounds per cubic foot. 150-168 168-173 | I4I-145 106 66-69 87-112 122-162 175-180 75-94 175-193 | 175-181 100-120 72 250 106-112 || 196-198 181-187 Grammes per cubic centimetre. Substance. | Gas carbon . Glass: Common. Flint Glauber’s salt Glue Gneiss Granite Graphite Gravel Gray copper ore Green stone / Gum arabic Gunpowder : Loose Tamped . Gypsum, burnt Hornblende Ice 3 : | Iodine Ivory . Kaolin lence Basaltic Trachytic Lead acetate Leather : Dry | Greased . | Lime: Mortar Slaked | Lime Limestone . Litharge: Artificial . Natural Magnesia Magnesite Magnetite Malachite Manganese: Red ore Black ore | Marble || Marl Masonry Meerschaum | Melaphyre . Mica Mortar Mud | Nitroglycerine | Ochre . eats ae ° . Phosphorus, white We ette biges | Porcelain _ Porphyry | Potash Pyrites Pyrolusite Pounds per cubic foot. 119 1$0-175 180-280 87-93 80 150-168 156-187 120-140 Q4-112 27 5-335 180-185 80-85 175-185 125-105 150 54 64 103-III 81-87 144-200 154-178 580-585 489-492 200 187 306-324 231-256 216 243-256 157-177 100-156 116-144 143-156 162-151 141 306-324 231-287 * For metals, see Table 97. 84 SMITHSONIAN TABLES. 4 DENSITY OF VARIOUS SOLIDS. TASnSIOR Grammes Pounds Grammes Bas Substance. per cubic per cubic Substance. per cubic per cubic | centimetre. foot. centimetre. | — foot. SAS A J J ff Pumice stone. - | 0.37-0.9 23-56 | Soapstone, Steatite .| 2.6-2.8 Quartz : ; : 2.65 Soda: Resin . ; : , 1.07 Roasted . Rock crystal : : 2.6 2 Crystalline Rock salt . : . | 2.28-2.41 2-150 | Spathic iron ore Salammoniac . .| 1.5-1.6 | Starch Saltpetre . : . | 1.95-2.08 Stibnite Sand: | Strontianite Dry . : 7 ome : 5 | Syenite Damp . : stilt : | Sugar . Sandstone... : iF | Talc Selenium . 3 , .2—4.8 | Tallow Serpentine . | Tellurium Shale . | Tile Silicon Tinstone Siliceous earth Topaz Slag, furnace | Tourmaline Slate | Trachyte Snow, loose | Trap yf & ee ie oY BS eVaeQwia Ne iS) aS | to iS} o Ny oS) nN t Nb Mee Ov? in | bo NO ° a's al Wm TABLE 96. DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND POUNDS PER CUBIC FOOT OF VARIOUS ALLOYS (BRASSES AND BRONZES). Grammes Pounds per cubic per cubic centimetre. foot. Brasses : Yellow, 70Cu ae 30Zn, cast. : ; ; 2 d : 527 Ss rolled . : : c : : : 534 rk és drawn : : ; , : 5 542 Red, goCu + toZn : ; : : ; : : 536 White, so>Cu-++ soZn_ ; : ; : : : : SII : goCu-+ 10Sn . * 0 f ; “ : ; : 7 548 85Cu-+ 15Sn . 7 : : : : : : : 3. 555 SoCu + een : : : ; : : ; : ; ; 545 75Cu + 2 : : : . z : 551 German Silver: Chivese, 26.3Cu £ 36. 6Zn x 36.8 ING : : i 518 s Berlin (1) 52Cu + 26Zn + 22Ni ; : : : 527 rf “ (2) 59Cu + 30Zn + 11Ni. , : : 5 520 5 (3)i63Cu jozn “oe 6Ni . : : : 518 Nickelin ‘ : : : é 7 547 Lead and Tin: 87.5Pb + 12.5Sn . ; : : ; ‘ ‘ : 661 “ 84Pb + 16Sn . ; 3 : : ; ; : 644 77-8Pb + 22.2Sn . 2 : : : : : 627 63.7Pb + 36.3Sn . : : : : . : 588 46.7Pb + 53.3Sn . j ; : : : : : 545 30. sPb + 69. 5Sn : : ; : . 514 Bismuth, Lead, and Tin: 53Bi + 4oPb i 7C dan. : : : : 659 Wood’s Metal: 50Bi + 26Pb + 12. ad + 12. zsEn . : : ; 605 Cadmium and Tin: 32Cd+ 68Sn . : : a : 480 Gold and Copper: 95Au-+ 2Cu . : Z 2 ; : : 3.8 1176 fe g6Au+ 4Cu . : : ; : : ; ; 1145 94Au+ 6Cu . : A ; : : ‘ : 1120 g2Au+ 8Cu . : : ; ; ; : . 1093 goAu-+ 10Cu . ‘ : : : : : . 1071 ss8Au + 12Cu . : . : : : ; : 1049 86Au+ 14Cu . : : ; ; ; . 5 1027 Aluminium and Copper: 10Al + goCu ; : ; ; ; i 480 cs = 5Al + 95Cu ° . . : : : 22 oc “ “ 34 Al = 97Cu , 5 4 a i Aluminium and Zinc: 91Al + 9Zn Platinum and Iridium: goPt + tolr « — 8sPt + slr = s 66. 67Pt + 33-33Ir ¢ . 5Pt + 95Ir : SMITHSONIAN TABLES. 85 TASLE 97. DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND POUNDS PER CUBIC FOOT OF THE METALS.* When the value is taken from a particular authority that authority is given, but in most cases the extremes or average from a number of authorities are given. Metal. Aluminium. “ Antimony . “ee Jarium . Bismuth. “ft “ | Cadmium “ Caesium. Calcium . Cerium . Chromium . Cobalt | ‘“ Columbium Copper . ““ 5 “ce : , Didymium . Gallium . Germanium | Glucinium . Gold . “cc Indium . Iridium . Iron ce banthanurs Lead . “ Lithium . Magnesium Manganese. “ Mercury . Molybdenum . Nickel Osmium. Palladium . Platinum Potassium . “ “ee Rhodium Ruthenium. | Silver “é “ Physical state. Cast . Wrought . Solid Amorphous . Solid Liquid . Cast aa-am. Wrought . Solid Liquid . Caste: Wrought . Liquid . Cast Wrought . Liquid . Casta a: Wrought . Gray cast. White cast Wrought . Liquid . Cast Wrought . Solid Liquid . Solid Solid Liquid . Cast. ie Wrought . Liquid . Grammes per cubic centi- metre. wPann OREO ° S cr 8.366 7:989 1.88-1.90 1.580 6.62-6.72 6.52-6.73 8.50-8.70 g.100 7.10-7.40 8.80-8.95 8.85-8.95 8.217 6.540 5-930 5-460 1.86-2.06 19.26-19.34 19-33-19-34 7:27-7-42 21.78-22.42 7-03-7-13 7-59-7-73 7.80-7.9O 6.880 6.05-6.16 11.340 11.360 11.005 10.645 0.590 1.69-1.75 6.56-8.03 Av. abt. 7.4 13-596 8.40-5.60 8.30-8.90 21.40-22.40 II.00—1 2.00 21.20-21.70 0.86-0.88 0.8510 0.5298 II.00-12.10 II.00-I1.40 10.40-10.50 10.55-10.57 g. 500 Pounds per cubic foot. 160-161 165-175 418-419 388 234-250 605-618 604 624 5337035 541 22 22 1202-1207 1207 454-463 1359-1399 439-445 473-482 649-655 658-659 593 271 271 318 318 ww NNN G2 G2 unk Authority. Vincentini and Omodei. Vincentini and Omodei. Roberts & Wrightson. Lecog de Boisbaudran. Winkler. Roberts & Wrightson. Hildebrand & Norton. Reich. Vincentini and Omodei. Vincentini and Omodei. Roberts & Wrightson. * This table has been to a large extent compiled from Clark’s ‘‘ Constants of Nature,’’ and Landolt & Bérnstein’s “ Phys. Chem. Tab.’’ + When the temperature is not given, ordinary atmospheric temperature is to be understood. SMITHSONIAN TABLES. 86 TABLE 97. DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND POUNDS PER CUBIC FOOT OF THE METALS. Physical state. Solid Liquid . At boiling pt. Strontium . Thallium Tin Cast “ Wrought ; Crystallized . Solid Liquid . Titanium ft . Thorium { . Tungsten Uranium 1/ Zinc “ Cast “ Zirconium . Wrought Liquid . Grammes per cubic centi- metre, 0.97-0:99 0.9519 0.9287 0.7414 2.50-2.58 11.8-11.9 7.290 7.300 6.97-7.18 7:1835 6.988 5-300 9.4-10.1 19.120 18.33-18.65 7.04—7.16 Pounds per cubic foot. 93 1143-1163 439-447 Authority. | Vincentini and § Omodei. Ramsay. Matthieson. Matthieson, Roscoe. Vincentini and Omodei. Roberts & Wrightson. Froost. TABLE 98. MASS IN GRAMMES PER CUBIC CENTIMETRE AND IN POUNDS PER CUBIC FOOT OF DIFFERENT KINDS OF WOOD. The wood is supposed to be seasoned and of average dryness. Alder . Apple . ASHE PP 430 hase es Basswood. See Linden. | Beech . wes | Blue gum Birch. Box Bullet tree Butternut Cedar . Cherry White Larch . Pitch. Red Scotch Spruce Yellow Grammes per cubic centimetre. 0.70-0.90 0.84 0.51-0.77 0.95-1.16 1.05 0.38 0.49-0. 57 0.70-0.90 0.22-0.26 I.1I-1.33 0.54-0.60 0.3 5-0. 50 0.50-0.56 0.83-0.55 0.48-0.70 0.43-0.53 0.48-0.70 0.37—-0.60 Greenheart . | Hazel . | Hickory . Iron-bark Laburnum | Lancewood . | Lignum vitae Linden or Lime-tree . | Locust ae eens _ Mahogany, Honduras } Walnut . Spanish . Maple. ees Oak | Pear-tree . | Plum-tree Poplar Satinwood |) Sycamore Teak, Indian “African . Water gum . | Willow Grammes per cubic centimetre. 0.93-1.04 0.60-0.80 0.60-0.93 1.03 oO. 0.68—1.00 I.17-1.33 0.32-0.59 a 0.85 0.62-0.7 5 0.60-0.90 0.61-0.73 0.66-0.78 0.35-0.5 0.95 0.40-0.60 0.66-0.88 0.98 0.64-0.70 1.00 0.40-0.60 * When the temperature is not given, ordinary atmospheric temperature is to be understood. t The density of titanium is inferential, and actual determination a year or two ago gave a lower value. + The lower value for thorium represents impure material. SMITHSONIAN TABLES. 87 TABLE 99, Density or mass in grammes per cubic centimetres and in pounds per cubic foot of various liquids. Liquid. Acetone ; Alcohol, ethyl & methyl i proof spirit Anilin 6 : Benzene Bromine Carbolic acid (crude) . Carbon disulphide Chloroform . Ether Glycerine Mercury ; Naphtha (wood) . Naphtha (petroleum ether) : Oils: Amber Anise-seed . Camphor Castor Cocoanut . Cotton seed Creosot ards. Lavender Lemon Linseed (boiled) Mineral (lubricating) . Olive . Palm . Pine Poppy Rapeseed (crude) a gn Resin Train or Whale. Turpentine Valerian Petroleum : ‘ (light) . Pyroligneous acid Sea water Soda lye Water . SMITHSONIAN TABLES. DENSITY OF LIQUIDS. 88 Grammes per cubic centimetre. 0.792 0.791 0.810 0.916 1.035 so) 0.848-0.810 0.665 0.800 0.996 0.910 0.969 0.925 0.926 1.040-1.100 0.920 0.877 0.844 0.942 0.900-0.92 5 0.918 0.905 0.8 50-0.560 0.924 0.915 0.913 0.955 0.918-0.925 0.873 0.965 0.5878 0.795-0.805 0.800 1.025 1.210 1.000 Pounds per cubic foot. 49-4 49-4 50-5 57-2 64.5 alin ile! oO CO0OOMMMAaDADCAOONC ND ~ in TaBLe 100 DENSITY OF CASES. The following table gives the specific gravity of gases at o° C. and 76 centimetres pressure relative to air at o° and 76 centimetres pressure, together with their mass in grammes per cubic centimetre and in pounds per cubic foot. GS Grammes per Pounds per Pets cubic centimetre. cubic foot. Par : : . i ; : S : 0.001293 Ammonia : : ; : : : 0.000770 Carbon dioxide , : : : : 0.001974 Carbon monoxide . : . : 0.001234 Chlorine . ee. : ; : 0.003133 0.000421 Coal gas . 0.000558 Cyanogen . ; : 0.002330 0.14546 Hydrofluoric acid . , 0.002937 0.18335 Hydrochloric acid 0.001616 0.10088 Hydrogen : 2 0.000090 0.00562 Hydrogen sulphide . 0.001476 0.09214 Marsh gas : : 0.0007 27 0.04538 Nitrogen ; ; 0.001257 Nitric oxide, NO. 0.001 343 Nitrous oxide, N20. 0.001970 Oxygen . : 5 0.001430 Sulphur dioxide . : : : : 0.002785 Steam at 100°C... ; ‘ : : . 0.000581 SMITHSONIAN TABLES. 89 TABLE 101. DENSITY OF AQUEOUS SOLUTIONS.* The following table gives the density of solutions of various salts in water. The numbers give the weight in grammes per cubic centimetre. For brevity the substance is indicated by formula only. Weight of the dissolved substance in 100 parts by weight of the solution. Substance. ; Authority. [eo OReeeave eran nL: 1.098 KOT een creche 1.082 [IN Orcas rege 1.144 | NaQl s =-2., 1.055) | 0-004) |e : : : : NHs. . . .|0.978]0.949]0. i f ; - . | Carius. ING Civs ae alate 1.030} I. : ; . | Gerlach. KCl eer ecuere|ile 1.005 5 NaGli 3 ao Ai O2 ih r-072 EiCn ye.) oy el .020) e057 |}CaCle . . .|1.041}1.086 Ca ar erat) : 1.040 | I. .083 | I. 128] 1. : ; . | Schiff. AIGIE” Ean. 035] 1.072 I. : : 22 : - - | Gerlach. MgCle . . O41 | 1.085 : : : cs MgCl +6H20 7 1.032 | I. ; : : : : Tis - | schitt, ZnCle .043 | 1.089 | I. 184] 1. : ; : In .5| Kremers. Cd€le> 3s 32/1043) | 087 |. L SON. LO 3/T-2 : : ‘ : : « Sr@lony ; I.092 | 1.1. 195] I. n32 . | Gerlach. SrCle + 6H20 027 | 1.053 5 : : “ Baca. ‘ 1.094 | I. -205| I. : xe BaClo+ 2H,0 .035| 1.075] I. : : : . | Schiff. a CuClo ae re te. |e I.091| I. . : ; Franz. NClo. . . «| 1.048] 1.098] I. Ls ; : i RS Oly 5 cena) Le I.092| — ~ Mendelejeff. HesCley il >stas | 1 1.086 Hager. Bt lariat aaeimnel [ie 1.097 Precht. SnClo+ 2H_20 | 1.032 1.067 SnClq4-+ 5H20 | 1.02 apes [ev Bras oats 1.070 ISD rie ec ates 5| 1.073 INCI 8) i Ooh ee ee o2 oO i) Nn Ne) Gerlach. Kremers. ‘ n OOM © Cus fin nnn inv m \O Ww bhRAH MoiBroe se. seer (Ts 1.085 ZnBrg «+ . «| 1.043] 1.091 CdBra vic. aneslile 1.088 | CaBre, 2: . .042 | 1.087 | BaBrg 3 30% |r. 1.090 a+ COI nn NN HOH N Duin ° Mui 3 |SrBre . . . (1. 1.089 Oe oe ieee au [ike 1.076 DUD, a eat ben deals 1.077 |Nal 274) 2%. 11.038) 1-080 PS Coe .043 | 1.089 bhebRbKA WnNh OO eee SSGHS GOOGOS GOSS 2| 1.086 1.086 2} 1.088 3| 1.089 3,| 1.089 Anu Mw bao COOoOn = mn mimi bRwRRAK tee ON ‘© mn NaClO3g. . .|1.035]1.068} 1. : 183] 1. : ae | NaBr( Veer var eel he 3 1.081 o . — 9:5 |KNOs . . .|1.031| 1.064] 1. 15 Gerlach. | NaNOg. . .|1.031] 1.065] 1. ; é 7 -313| 1. 20.2 | Schiff. AgNOg sis). 21] 25 1.090 | 1. ; : 3 ; 5 1.918 15. | Kohlrausch. * Compiled from two papers on the subject by Gerlach in the “‘ Zeit. fiir Anal. Chim.,” vols. 8 and 27 SMITHSONIAN TABLES. go , TABLE 101. DENSITY OF AQUEOUS SOLUTIONS. Weight of the dissolved substance in 100 parts by weight of the solution. Substance. 5 Authority. INETINOpeet es «| 2: : : : : : : 2 , -5} Gerlach. ZaNOs. seen = | l<0d5)| Te ; ; : ; : : -5| Franz. ZnNOs+6H20 . : : , 3 2 F . | Oudemans. Ca(NOs)2 . . .|T. ‘ : : : : , ; : -5§| Gerlach. Gn(NOs)aens we || 0. : : : : .328] 1. .5| Franz. DrN@s)an ee ©. ||I- : ‘ : .S| Kremers. PH(NOs)e 2 = «(T: : : ; ‘ - -5|} Gerlach. Cd NOs)e Miao" 18 : ‘ . ; . . ‘ . Franz. Co(NOs)e2 eee (rad. Z é ; : -40 ‘ ue Ni(NOs)2 ; : Fee(NOs)¢ Se: ae . . : . . Mg(NOs)2+6H20 | 1.018 | 1. ‘ : ‘ {232 Schiff. Mn(NOs)2+6H20O | 1.025} 1. : , ; : a Oudemans. K5GOsi. so) « L.OAd iT. ’ ; : ; Gerlach. KeCOg3 + 2H20 .« | 1.037 . NagCOstoH20 . | 1.019} 1. : : ; - : a6 (NH4)2SO4 « e| 1.027) T. ; ° . . : . Schiff. Feo(SOz)s . . «| 1045/1. ; : . : ~ . | Hager. FeSO,+7H20 .|1.025]1. : : : 238 Schiff. WSO Go 6) olprOepe |i : : Gerlach. MgSO +720 .|1.025 NaeSo4-+ 10H20 | I.o1g/ 1. ; : - ; CuSO4-+ 5H20 .} 1.031} 1. ! ; : . | Schiff. MnSO4-+ 4H2O . | 1.031 | 1. : : : : : . | Gerlach. ZnSOqg+ 7H20 «| 1.027] 1. é ‘ : -269 | I. Schiff. Feo(SO)3+K2SO4 . | 1.026 ; rede Franz. +24H2O0. . Cro(SO)3s+KeSO4 . +24H20 . MgSO4 ob KeSO4 6H20. . 1.016| 1.033 20 . . | 1.032] 1.066 .138 (NH4)2SO4 + FeSO, + 6H20 | 1.028} 1.058 Ke @r@gkee 8.) fe11/1.039)|' 1-082 KeCreO7 . . «| 1.035! 1.071 - Fe(Cy)gK4 . . «| 1-028] 1.059 -126 Fe(Cy)gKg . - «| 1-025] 1.053 Pb(C2H302)2 a. HeOrye 2) 2 il-031 | 1-064 1.137 “2 . | Gerlach. 2NaOH + AseO05 + 24H2,O0 . .| 1.020} 1.042 1.089 . | Schiff. coe; \o “SI Kremers. Schiff. FIO 5 10 15 20 30 | SOs = = =) | 2-040)'T.054 |'-032)T-07.9))1-277 SOg . . . « +} 1.013] 1.028] 1.045| 1.063] — NOs. . . - -| 1-033] 1.069| 2.104] 1.141 | 1.217 C4HeO¢g . . - «| 1-021 | 1.047 | 1.070| 1.096] 1.150 CeHsO7. . . «| 1.018] 1.038} 1.058 | 1.079] 1.123 Cane sugar. . .|I.019| 1.039] 1.060] 1.082] 1.129 HCl . . . . ~| 1.025] 1.050} 1.075] 1.101 | 1.151 10.35 | 1.073] 1.114] 1.158 | 1.257 1.037 | 1.077 | 1.118 | 1.165 | 1.271 . | 1.032 | 1.069 | 1.106] 1.145 | 1-223 1.040 | 1.082] 1.127] 1.174| 1.273 7.5 | Stolba. 1.035 | 1.077 | 1.119] 1.167 | 1.271 .67 7.5 | Hager. 1.027 | 1.057 | 1.086| 1.119] 1.188 ; . | Schiff. 1.028 | 1.056| 1.088 | 1.119} 1.184 ; : 528/15. | Kolb. CoHgO2. . «. «| 1.007] 1.014] 1.021] 1.028 | 1.041 1. S| 1. ; 115. | Oudemans. — ——___———__—— } Brineau. Schiff. | Kolb. Gerlach. “ — weuns inmnnrfbun “ Kolb. Topsoe. = bd bt =~ Kolb. Nn SMITHSONIAN TABLES. gI TABLE 102. DENSITY OF WATER AT DIFFERENT TEMPERATURES BETWEEN 0° AND 32° C.* The following table gives the relative density of water containing air in solution, —the maximum density of water free from air being takenas unity. The correction required to reduce to densities of water free from air are given at the foot of the table. For all ordinary purposes the correction may be neglected. ‘The temperatures are for the hydrogen thermometer. Temp. C. .O a 5 3 4 2 6 ad 8 9 0.99987 42 0.99987 42 9287 | 9332 | 9376 | 9419 90 | 9499 9572 9671 | 9701 | 9729 | 9755 | 9780 | 9803 | 9825 | 9846 | 9864 | 9881 9897 | 9911 | 9923 | 9934 | 9944 | 9952 | 9958 | 9963 | 9966 | 9968 9908 9964 6 2 0.9999886 9656 | 9625 | 9592 9522 9407 9322 9278 | 9232 | 9185 | 9137 | 9087 | 9035 | 8982 | 8928 | 8873 | 8815 8758 | 8697 | 8636 | 8573 | 8509 | 8443 | 8376 | 8308 | 8238 | 8167 8095 | 8021 | 7946 | 7869 | 7791 | 7712 | 7631 | 7549 | 7466 | 7381 10 0.9997295 | 7208 | 7119 | 7029 | 6937 | 6844 | 6750 | 6654 | 6558 | 6459 6360 | 6259 | 6157 | 6053 | 5949 | 5842 | 5735 | 5626 | 5516 | 5405 12 5292 | 5178 | 5063 | 4947 | 4829 | 4710 | 4590 | 4468 | 4345 | 4221 13 4096 | 3969 | 3841 | 3712 | 3581 | 3450 | 3317 | 3182 | 3047 | 2910 2772 2351 | 2208 | 2064 | 1919 | 1772 | 1624 | 1475 15 0.9991325 | 1174 | 1021 | 0867 | o712 | 0556 | 0399 | 0240 | oc080 | 9919 16 89757 | 7594 | 9429 | 9264 | 9097 | 8929 | 8760 | 8589 | 8418 | 8245 17 8071 | 7896 | 7720 | 7543 | 7365 7185 7004 | 682 6640 | 6456 18 6270 | 6084 | 5897 | §708 | 5518 | 5325 | 5136 | 4943 | 4749 | 4553 19 4357 | 4160 | 3961 | 3762 | 3561 | 3359 | 3157 | 2953 | 2748 | 2542 20 0.9982335 | 4126 | 1917 | 1707 | 1496 | 1283 | 1070 | 0855 | 0640 | 0423 21 0205 | 9987 | 9767 | 9546 | 9325 | 9102 | 8878 | 8653 | 8427 | 8200 22 77972 | 7744 | 7514 | 7283 | 7051 | 6818 | 6584 | 6340 | 6114 | 5877 2 5639 | 5400 | 5160 | 4920 | 4678 | 4435 | 4191 | 3947 | 3701 | 3455 22 3207 | 2959 | 2709 | 2459 | 2208 | 1956 | 1702 | 1448 | 1193 | 0937 25 0.9970681 | 0423 | 0164 | 9904 | 9644 | 9382 | 9120 | 8357 8592 | 8327 26 68061 | 7794 | 7527 | 7258 | 6988 | 6718 | 6447 | 6175 | S901 | 5628 27 5353 | 5077 | 4801 | 4523 | 4245 | 3966 | 3686 | 3405 | 3124 | 2841 28 2558 | 2274 | 1989 | 1703 | 1416 | 1129 | O840 | O551 | 0261 | 9971 29 59679 | 9387 | 9094 | 8800 | 8505 | 8209 | 8913 | 7616 | 7318 | 7019 30 0.9956720 | 6419 | 6118 | 5816 | 5514 | 5210 | 4906 | 4601 | 4296 | 3989 31 3682 | 3374 | 3066 | 2756 | 2446 | 2135 | 1823 | 1511 | 1198 | 0884 If we put D% for the density of water containing air and D, for the density of water free from air, we get the following corrections on the above table to reduce to pure water : — ft oO a 2 3 4 5 6 7 8 9 10 107(D.-D’;) = 25 27 29 31 32 33° 33 34 34 33 32 t= ll 12 33-14 #25 16 17 2418. 197520 — s2 10°(D.-D’) = 31 20027, 25 Ate 22a IG ep ene) 8 4 negligible. * This table is given by Marek in ‘‘ Wied. Ann.,”’ vol. 44, P- 172, 1891. SMITHSONIAN TABLES. 92 TABLE 103. VOLUME IN CUBIC CENTIMETRES AT VARIOUS TEMPERATURES OF A CUBIC CENTIMETRE OF WATER AT THE TEMPERATURE OF MAXI- MUM DENSITY.* The water in this case is supposed to be free from air. The temperatures are by the hydrogen thermometer. oO 069 > 189 OONQAD pwownnd 1.000269 363 471 59! 29 “< 1.000868 1025 194 374 566 1.001768 gst 2205 438 632 1.002935 3199 472 754 4045 NWO DAW O Nb QO - Orn N 1.004345 653 971 5297 631 wn to \o 1.005973 * The table is quoted from Landolt and Bérnstein’s ‘‘ Physikalische Chemie Tabellen,” and depends on experi- ments by Thiesen, Scheel, and Marek. SMITHSONIAN TABLES. 93 TABLE 104. DENSITY AND VOLUME OF WATER.* The mass of one cubic centimetre at 4° C. is taken as unity. Temp. C. —10° cone —8 ame. —6 —5 Density. 0.999871 9928 9969 9991 I.000000 0.999990 9970 9933 9856 9824 0.9997 47 9655 9549 9430 9299 0.999160 goo02 8841 8654 8460 0.998259 0.997120 Volume. 1.001858 1575 1317 1089 0883 1.000702 0545 0410 0297 0203 1.000129 0072 0031 0009 0000 1.000010 0030 0067 O1l4 0176 1.000253 0345 0451 0570 0701 1.000841 0999 1160 1348 1542 1.001744 1957 2177 2405 2041 1.002888 Density. 0.99712 687 660 633 605 0.99577 547 517 0.99235 197 158 118 078 0.99037 8996 954 g1o 805 SMITHSONIAN TABLES. * Rossetti, ‘‘ Berl. Ber.’’ 1867. 94 Volume. 1.00289 314 341 308 396 1.00425 455 456 518 1.00971 O14 057 Iol 148 1.00195 439 691 964 256 1.00566 887 221 567 oS: 1.00312 TABLE 105. DENSITY OF MERCURY. Density or mass in grammes per cubic centimetre, and the volume in cubic centimetres of one gramme of mercury. The density at 0° is taken as 13.5956,* and the volume at temperature ¢ is Ve = Vo (1 + .000181792 4+ 175 X 10712 #2 +- 35116 X 10— 178). F Mass in Volume of Mass in Volume of grammes per I gramme in Temp. C. grammes per 1 gramme in cub. cm. cub. cms. cub. cm. cub. cms. 13.6203 0.07 34195 30° 13.5218 0.0739544 6178 4329 31 5194 9678 6153 4403 5169 9812 6129 4590 5145 9945 6104 4730 5120 40079 13.6079 0.07 34864 13-5096 0.0740213 6055 4997 5071 0346 6030 5131 5047 0480 6005 5265 5022 0614 5981 5398 4998 0748 13.5956 0.0735532 13-4974 0.07 40882 5931 5066 4731 2221 5907 5800 448 3561 5882 5933 4246 4901 5857 6067 4005 6243 1: 58 33 0.07 36201 13.3764 0.0747586 5808 334 3524 8931 5783 6408 3284 50276 5759 6602 3045 1624 5734 6736 2807 2974 13.5709 0.07 36869 .2569 0.07 54325 5685 7003 2331 5079 5660 7137 2094 7035 5635 7270 1858 8394 5611 7404 1621 9755 13.5586 0.07 37538 13.1385 0.0761120 5562 7672 I150 2486 5537 7505 O9I5 3854 5513 7939 0680 230 5488 8073 0445 6607 13.5463 0.07 38207 13-0210 0.0767988 5439 $340 12.9976 9372 5414 8474 9742 70760 5390 8608 9508 1252 5365 8742 9274 3549 0.073887 5 12.9041 0.0774950 goog 8807 6355 9143 8573 7795 9277 $340 9180 Q4II 8107 80600 ~ Go N oN NOG 0.0739544 12.7873 0.0782025 7640 3455 7406 4891 * Marek, “‘ Trav. et Mém. du Bur. Int. des Poids et Més.’’ 2, 1883. +t Broch, l. c. SMITHSONIAN TABLES. 95 TABLE 106. SPECIFIC GRAVITY OF AQUEOUS ETHYL ALCOHOL. (a) The numbers here tabulated are the specific gravities at 60° F., in terms of water at the same tempera- ture, of water containing the percentages by weight of alcohol of "specific gravity .7938, with reference to the same temperatures. * Specific gravity at 15°.56 C. in terms of water at the same temperature. P g y Percentage of alcohol by weight. 9981 9965 9947 | - 9914 | 9898 | .9884 | .9869 9828 | .9815 | .9802 | . 9778 | -9766 | .9753 | -974I 9703 | .9691 | .9678 | . 9052 0638 9623 | .9609 9560 | .9544 | .9528 | . 9490 | -9470 | .9452 | -9434 -9376 | .9356 | -9335 | - 9292 | -9270 | -9249 | .9220 9160 | .9135 | -9113 | .9090 | .9069 | .9047 | .g025 | .goor 8932 | .8908 | .8886 | . 8840 | .8816 | .8793 | .8769 .8696 | .8672 | .8649 | .8625 | .8603 | .8581 | .8557 | .8533 8459 | .8434 | 8408 | 8382 | .8357 | .8331 | .8305 | .8279 20199 | 8.6172 |.O045 9|'. 8089 | .S061 | .8031 (b) The following are the values adopted by the “ Kaiserlichen Normal-Aichungs Kommission.’? They are based on Mendelejeff? s formula,t and are for alcohol of specific gravity .79425, “at 15° C., in terms of water at 15° C.; temperatures measured by the hydrogen thermometer. 0 1 2 3 4 5 | 6 | a, | 8 | 9 Percentage of alcohol by weight. Specific gravity at 15° C. in terms of water at the same temperature. 99812 -99630 99454 99284 -99120 .98963 -98812 .98667 | .98528 -98262 | .98135 “98010 97888 | .97768 | .97648 -97 528 | .97408 | .97287 97040 96913 | .96783 | .96650 | .96513 96373 .96228 | .g6080 | .95927 95008 | .95443 | -95273 | -95099 | 94920 | .94735 | -94552 | 94363 | .94169 -93773 | -9357° | -93305 | -93157 | 92947 | 92734 | -92519 | -92303 | .g2088 -91644 | .Q1421 | .QIIQ7 | .90972 | .90746 | .g0519 | .90292 | .g0063,| .89834 89373 | 89141 | .88909 | .88676 | .88443 | .88208 | .87974 | .87738 | .87502 87028 | .86789 | .86550 | .86310 | .86070 | .85828 | .85586 | .85342 | .85098 84606 | .84358 | .84108 | .83857 | .83604 | .83349 | .83091 | 82832 | .82569 82036 | .81763 | .81488 | .81207 | .80923 | .80634 | .80339 | 80040] .79735 (c) The following values have the same authority as the last; the percentage of alcohol being given by volume instead of by weight, and the temperature 15°.56 C. on the mercury in Thuringian glass thermometer; the specific gravity of the absolute alcohol being .79391- Ol Cas ai a) lees alate e|7{s| » sce Specific gravity at 15°.56 C. in terms of water at same temperature. of alcohol E volume. | -99847 | .99699 | 99555 | -99415 | -99279 | .99147 | .90019 | .98895 93543 | 98432 | -98324 | .98218 | .98114 | .g8or1 | .97909 | .g7808 97608 | .97 507 | .97406 | .97304 | -97201 | .97097 | .g6991 | .96883 | .96772 90541 | .96421 | .96298 | .96172 | .96043 | .95910 | -95773 | -95632 | .95487 I.00000 | ‘95185 | .95029 | .94868 | .94704 | .94536 | .94364 | .94188 | .94008 | .93824 .98657 93250 | .93052 | .92850 | .92646 | .92439 -92229 | .92015 | .91799 ‘91134 | .90907 | .90678 | .90447 | .90214 | .89978 | 89740 | .89499 88762 | 88511 | .88257 | 88000 | .87740 | .87477 | .87211 | .86943 86116 | 85833 | .85547 | .85256 | 84961 | .84660 84355 84044 80359 0-93445 91358 .Sgoro 86395 | 83400 | .83065 | .82721 | £82365 | .81997 | .81616 | 81217 * Fownes, “ Phil. Trans. Roy. Soc.’’ 1847. t “ Pogg. Ann.’? vol. 138, 1869. SMITHSONIAN TABLES. 96 T . DENSITY OF AQUEOUS METHYL ALcoHoL.* § 'A7F 197 Densities of aqueous methyl alcohol at 0° and 15.56 C., water at 4° C. being taken as 100000. _ The numbers in the columns @ and 4 are the coefficients in the equation ps = py — at — 42 where pt is the density at temperature 4. This equation may be taken to hold between 0° and 20° C. Percent- Density Density Percent- Density Density at age of at ake of at at CH,O. 0° GC. XEOs5G\ Gy CH,O. = sor; Ts°.56.C, 99987 | 99907 92873 | 91855 99806 99729 y : 92691 91661 99631 | 99554 68 92507 | 91465 994602 99352 : 92320 91267 99299 99214 : 92130 91066 99142 99048 — 2.2 91938 90863 98990 | 98593 . . 91742 | 90657 98543 | 98726 2 91544 | 90450 98701 | 98569 O. 91343 | 90239 98563 98414 2. : 91139 go026 98429 98262 . 90917 89798 soe? am : : ae 89580 171 97902 : c 90492 935 98048 97814 - : 90276 89133 97926 97668 : : goos6 97806 | 97523 89835 97689 | 97379 . 89611 97573 | 97235 89384 97459 | 97093 . 80154 97340 g6950 : ; 88922 OON AD fuNnHO 97233 96808 88687 97120 96666 : 88470 97007 96524 ; : 88237 96894 96381 2 88003 96780 96238 i : 87767 96665 | 96093 . 87530 96549 | 95949 . 87290 96430 95802 k : 87049 96310 95655 ; 3 86806 96187 95500 : : 86561 Equation ps = pp — at 86314 Bee So $6066 96057 | 95367 85816 95921 95211 85564 95783 | 95053 85310 95043 | 94804 9§500 | 94732 85055 84795 95354 | 94567 84539 95204 | 94399 84278 505: ||" "94226 84015 94895 | 94055 94734 | 93877 94571 | 93697 94400 93510 94239 93335 94076 3155 93911 92975 82404 82129 93744 | 92793 81853 93575 92610 81576 93403 92424 81295 93229 | 92237 93052 | 92047 81015 | 79589 83751 83455 83218 82948 82677 Term 4@ negligible. * Quoted from the results of Dittmar & Fawsitt, ‘Trans. Roy. Soc. Edin.” vol. 33. SMITHSONIAN TABLES. 97 TABLE 108. VARIATION OF THE DENSITY OF ALCOHOL WITH TEMPERATURE. (a) The density of alcohol at #° in terms of water at 4° is given * by the following equation: d,= 0.80025 — 0.0008340f — 000000292, From this formula the following table has been calculated. Density or Mass in grammes per cubic centimetre. 80541 79704 -78860 -78012 79451 -78606 77750 (b) Variations with temperature of the density of water containing different percentages of alcohol. Water at 4° C. is taken as unity.T Percent- age oO alcohol by weight. Density at temp. C. 0.99988 | 0.9997 5 ‘99135 95493 97995 97500 0.97115 -96540 95734 94939 93977 0.92940 OOLIS -93409 97816 97203 0.96672 95998 -O5174 94255 93254 0.92182 0.99831 “98945 ‘95195 97527 .96877 0.96185 95403 94514 93511 92493 0.91400 30° 0.99579 .98080 .97892 97142 96413 0.95628 94751 93813 92787 .QI710 0.90577 Percent- age of alcohol by a Oo weight. Si 0.92940 91848 -907 42 89595 -88420 0.87245 86035 -84789 83482 82119 0.80625 * Mendelejeff, ‘‘ Pogg. Ann.” vol. 138. + Quoted from Landolt and Bornstein, ‘‘ Phys. Chem, Tab.’ p. 223. SMITHSONIAN TABLES. 98 Density at temp. C. 0.91400 -90275 89129 -97961 86781 0.85580 84366 83115 81801 80433 0.78945 0.84719 8 2232 80918 79553 0.78096 TABLE 109. VELOCITY OF SOUND IN AIR. Rowland has discussed (Proc. Am. Acad. vol. 15, p. 144) the principal determination of the velocity of sound in atmospheric air. The following table, together with the footnotes and references, are quoted from his paper. Some later determinations will be found in Table 111, on the velocity of sound in gases. (See References below.) to o° C. and ordi- Velocity reduced to o° and dry air. mately reduced to o° C. and dry air Estimated weight of observation. Place of determi- Number of obser- vations made Temperature ob- Velocity observed Velocity reduced Velocity approxi- ran) Oe X nN 5 France . Diisseldorf India. , 1822 | France . Oo 1822 | Austria. . 88 yin ~ 1823 | Holland ae Ss Rien 349-37 14 core. 339-27 1824-5] Port Bowen 51 : - 1839 == = 1844 |Alps. .. 34 1868*| France . .| 149 OD ON AMUk OY one ae N WH DH NN _ General mean deduced by Rowland, 331.75. Correcting for the normal carbonic acid in the atmosphere, this becomes 331.78 metres per second in pure dry air at 0° C. REFERENCES. 1 French Academy: “ Mém. de l’Acad. des Sci.” 1738, p. 128. 2 Benzenburg: Gibberts’s “ Annalen,” vol. 42, p. I. 3 Goldingham : “ Phil. Trans.” 1823, p. 96. 4 Bureau of Longitude: “ Ann. de Chim.” 1822, vol. 20, p. 210; also, “ GEuvres d’Arago,” “Mem. Sci.” ii. 1. 5 Stampfer und Von Myrbach: “ Pogg. Ann.” vol. 5, p. 496. 6 Moll and Van Beek: “ Phil. Trans.” 1824, p. 424. 7 Parry and Foster: “ Journal of the Third Voyage,” 1824-5, App. p. 86; “ Phil. Trans.” 1828, p. 97. 8 Savant: “ Ann. de Chim.” sér. 2, vol. 71, p. 20. Recalculated. 9 Bravais and Martins: “ Ann. de Chim.” sér. 3, vol. 13, p. 5: 10 Regnault: “ Rel. des Exp.” iii. p. 533. a I believe that I calculated these reduced numbers on the supposition that the air was rather more than half saturated with moisture. & Reduced to 0° C. by empirical formula. ¢ Wind calm. @ Moll and Van Beek found 332.049 at 0° C. for dry air. They used the coefficient .00375 to reduce. I take the numbers as recalculated by Schréder van der Kolk. e An error of 0.21° C. was made in the original. See Schréder van der Kolk, “ Phil. Mag.” 1865. J Corrected for wind by Galbraith. g Recalculated from Savart’s results. * This is given as 1864 in Rowland’s table. The original paper is in ‘‘ Mém. de l'Institut,” vol. 37, 1868. SMITHSONIAN TABLES. 99 TABLE 110. VELOCITY OF SOUND IN SOLIDS. The numbers given in this table refer to the velocity of sound along a bar of the substance, and hence depend on the Young’s Modulus of elasticity of the material. The elastic constants of most of the materials given in this table vary through a somewhat wide range, and hence the numbers can only be taken as rough approximations to the velocity which may be obtained in any particular case. is to be understood. Metals: Various: Woods: Substance. Aluminium Brass Cadmium Cobalt Copper . ; Gold (soft) Gold (hard)... Tron and soft steel Tron ; “ “ B : * cast steel “ “ “ “ “ “ Magnesium f : Nickel Palladium Platinum “ “ee Silver Tin Zinc Brick Clay rock Granite Marble Slate Tuff A . from Glass i fe Ivory . . : : Vulcanized rubber (black) sf (red): “ “ “cs Ash, along the fibre “« “across the rings “ along the rings Beech, along the fibre . “« across the rings “along the rings Elm, along the fibre “* across the rings “ along the rings Fir, along the fibre Maple c , Oak < ; Pine Poplar cf Sycamore “ Temp. ° 100 200 100 200 20 100 200 20 100 200 20 I0o 200 20 100 c Velocity in | Velocity in metres per | feet per second. second. 5104 16740 3500 11480 2307 7570 4724 15500 3560 11670 3290 10800 2950 9690 1743 5717 1720 5640 1735 5691 2100 6890 5000 16410 5130 16820 5300 17390 4720 15480 4990 16360 4920 16150 4799 15710 4602 15100 4973 16320 3150 10340 2690 8515 2570 8437 2460 8079 2610 8553 2640 8658 2480 8127 2500 8200 3700 12140 3652 11980 3480 11420 3950 12960 3810 12500 4510 14500 2550 9350 5000 16410 6000 19690 3013 9886 54 177 31 102 69 226 34 III 4670 15310 1390 4570 1260 4140 3340 10960 1540 6030 1415 4640 4120 13516 1420 4005 Tors 3324 4640 15220 4110 13470 3850 12620 3320 10900 4280 14050 4460 14640 SMITHSONIAN TABLES. 100 When temperatures are not marked, between 10° and 20° Authority. Masson. Various. Masson. “ Wertheim. “ Various. “ Wertheim. Melde. Masson. Various. Wertheim. Various. “ Chladni. Gray & Milne. Various. “ee Ciccone & Campanile. Exner. “ “ “ Wertheim. TABLE 111. VELOCITY OF SOUND IN LIQUIDS AND CASES. Cc. Velocity in | Velocity in metres per | feet per Authority. second. second, Substance. Se Liquids: Alcohol , : . : 8.4 1264 4148 Martini. : 7 ; : 1160 3806 Wertheim. Ether : : : 1159 3803 ‘e Oil of turpentine : ; 1212 3977 s Water (Lake Geneva) . 1435 4708 Colladon & Sturm. “(from Seine river) 1437 4714 Wertheim. “ “ “ “ I 528 Sol 3 “ 1724 5657 2. 1399 4591 Martini. 1437 4714 . 1457 4780 i 333 1092 Dulong. 331.6 1087 Wertheim. 333 1092 Masson. 330-7 1085 Le Roux. 332.1 1089 Schneebeli. 332-5 IOQI Kayser. 331-9 1089 Wullner. BB1-7 1088 Blaikley. 331.2 1086 Violle & Vautier. 326.1 1070 Greely. 317-1 1040 e 309.7 1016 a 305.6 1002 ¢ 332.4 I0QI Stone. 415 1361 Masson. 337-1 1106 Wullner. 337-4 1107 Dulong. 2601.6 858 ce 189 606 Masson. 206.4 677 Martini. 205.3 674 Strecker. 314 1030 Dulong. 1269.5 4105 <¢ 1286.4 4221 Zoch. 490.4 1609 422 1385 Masson. 325 1066 261.8 859 Dulong. 317.2 1041 a 230.6 3 Masson. 179.2 588 $6 401 1315 pe 410 1345 a “ “ “ “ Water “ NNO “ Gases: Air “ —I rae —4 3: 3: ie Oo oO Oo Oo Oo Oo O oO Oo O. 5. 7 re Oo Oo Oo oO ° Oo Oo Oo Oo oO Oo Oo oO Oo oO Oo Oo oO OV CONT \O Ammonia Carbon monoxide “ dioxide . Carbon eeuphide Chlorine Tacs Hydrogen Illuminating gas . Methane r Nitric oxide Nitrous oxide Oxygen Vapors : Ricobol Ether Water Oo ano SMITHSONIAN TABLES. IOI TABLE 112. : FORCE OF CRAVITY FOR SEA LEVEL AND DIFFERENT LATITUDES. This table has been calculated from the formula Sh = S45 [1 —.002662 cos 2$],* where ¢ is the latitude. : g g e @, | in cms. per Log. in inches per Log. in feet per Log. “| sec. per sec. sec. per sec. sec. per sec. 977-989 2.990334 | 385-034 2.585498 32.0862 1.506318 8.029 0352 050 5517 0875 6336 147 0404 096 5570 -O916 +339 0490 173 5055 0977 600 0605 275 S771 -1062 978.922 2.990748 35. 2.585914 1168 1.506732 9.295 0913 548 6079 -1290 6398 0949 58 6114 -1316 6933 0985 612 6150 1343 6909 1021 . 6187 -1370 7005 2. 991059 : 2.586224 1398 | 1.507043 1096 : 6262 1425 7080 1135 : 6300 1454 7119 1173 : 6339 .1490 7167 1212 2 6377 sUSLE 7196 2.991251 84 2.586417 1540 1.507236 1291 88 6457 .1570 7275 1331 : 6496 -1607 7325 1372 . 6537 -1630 7356 1411 6577 -1659 7395 2.991452 ; 2.586617 1688 1.507436 1492 6657 -1719 7476 1532 : 6698 1748 7516 1573 . 6738 1778 7557 1613 : 6778 -1808 7597 2.991653 2 2.586818 1838 | 1.507637 1693 . 6358 .1867 7677 1732 : 6898 1896 7716 1772 6937 1924 7756 1810 6975 “1954 7794 2.991849 | 386.380 2.587014 -1983 1.507833 1887 414 7053 -2011 7871 1925 447 7090 -2039 7909 1962 .480 7127 2067 7946 1998 “513 7164 +2094 7983 2.992034 | 386.545 2.587 200 .2121 1.508018 2070 -576 7235 2147 8054 2234 723 7400 2276 822 2377 849 7542 -2375 8361 952 7657 -2460 8476 387.028 | 2.587742 .2523 | 1.508561 074 7794 2562 8613 090 7812 2575 8631 * The constant .002662 is based on data given by Harkness (Solar Parallax and Related Constants, Washington, 1891). The force of gravity for any latitude ¢ and elevation above sea level % is very nearly expressed by the equation &h = S15 (1 — .002662 cos 2) [»—% (1-34) ], 4 where & is the earth’s radius, 6 the density of the surface strata, and A the mean density of the earthe When S=0 we get the formula for elevation in air. For ordinary elevations on land = IF is nearly 3, which gives for the correction at latitude 45° for elevated portions of the earth’s surface b= 980.6 x= = 1225.75 4 in dynes, = 386.062 ar sf = 482.562 4 in inch pound units. = 32.1719 X = 40.2149 Si in poundals. This gives per 100 feet elevation a correction of .00588 dynes -00232 inch pound units? diminution. .200193 poundals SMITHSONIAN TABLES. 102 rT ; GRAVITY. ene In this table the results of a number of the more recent gravity determinations are brought together. They serve to show the degree of accuracy which may be assumed for the numbers in Table 112. In general, gravity is a little lower than the calculated value for stations far inland and slightly higher on the coast line. Gravity in dynes. Elevation Refer- in metres. ence. Observed: Reduced to sea level. a | | | Latitude. Place. NEES Sineapores c) covese. sen hs iy Toml7” I4 978.07 978.07 I Georgetown, Ascension . . . .| —7 56 5 978.2 978.24 2 Green Mountain, Ascension. . .| —7 57 686 978.08 978.21 2 Loanda, Angola. . . . . s - —8 49 46 978.14 978.15 2 GarolmeislandS. . . -<°. « .|/==I0' 00 2 978.36 978.36 3 Bridgetown, Barbadoes . . . . 13 04 18 978.16 978.16 2 Jamestown, St. Helena . . . .|—I5 55 10 978.66 978.66 2 Longwood, zi oe ee poe) S77 533 978.52 978.58 2 Pakaoao, Sandwich Islands. . . 20 43 3001 978.27 978.54 3 Lahaina, re SS romney: 20 52 3 978.85 978.85 3 Haiki, ee se an = 20 56 117 978.90 978.92 3 Honolulu, ss Sais 21 18 3 978.96 978.96 3 St. Georges, Bermuda -.. . 22 2 979-75 979-7 2 Sidney, Australia .... . -|—33 52 43 979-07 araee I Cape Town eee ) staat) 5 BT eAT 114 979-95 979-97 4 tae ee . ee Bee es 37 47 114 980.02 980.04 5 Washington, D.C.* .... . 38 53 10 980.10 980.10 4 Denver, Colo.. . . 2. - +; 39 54 1645 979-68 979-98 5 Mole 18a Gc. Ge le Vousoihas Beit 39 «(58 122 980.12 980.14 6 BenSDURG Hye asgse ie) | fies) 0) 40 2 651 980.08 980.20 6 AlleghenywPa.\s.) euysrte 1+) | 40 28 348 980.09 980.15 6 HMobokensiNeer. @) cers) 1 « 40 44 II 980.26 980.26 4 Salt Rake GitywUitabi. (3 >= <1) 40 46 1288 979-82 980.05 5 Chonrerieyo) NG Te os ao BBs 41 49 165 980.34 980.37 5 Pampaluna, Spain... . . ; 2 49 450 980.34 980.42 7, Montreal,Canada .....- - 45 31 100 980.73 980.75 5 Geneva, Switzerland .... .- 40 12 405 980.58 980.64. 8 ee < cehcwisc + 46 12 405 980.60 980.66 9 Berne, e SA ise oie 46 57 572 980.61 980.69 9 Zurich, ss Smee 47 2 466 980.67 980.74 fe) (Pans Hranceys |<) <) Peis) id i, 48 50 67 980.96 980.97 8 Kew, England .... -- > 51 28 7 981.20 981.20 8 Berlin,,;Germany. «5 «,% > 2530 49 981.26 981.27 8 Port Simpson, B.C. . .. « - 54 34 6 981.45 981.45 4 Burroughs Bay, Alaska . . . - Go 5O Oo 981.49 981.49 4 Wrangell, ‘“ Pony 50, 2 7 981.59 981.59 4 Sitka, « ees 57 03 8 981.68 981.68 4 St. Paul’s Island, “ oP eeeatey |: «157 OF 12 981.66 981.66 4 Juneau, “ Mt oe 58. 18 5 981.73 981.73 4 Pyramid Harbor, “ Pek) 59 10 5 981.81 981.81 4 Yakutat Bay, sf Ai ee 59 32 4 981.82 981.82 4 1 Smith: “United States Coast and Geodetic Survey Report for 1884,” App. 14. 2 Preston: “ United States Coast and Geodetic Survey Report for 1860,” App. 12. 3 Preston: Ibid. 1888, App. 14. 4 Mendenhall: Ibid. 1891, App. 15. 5 Defforges: “ Comptes Rendus,” vol. 118, p. 231. 6 Pierce: “U.S. C. and G. S. Rep. 1883,’”’ App. 19. 7 Cebrian and Los Arcos: “ Comptes Rendus des Séances de la Commission Perma- nente de I’Association Géodesique International,” 1893. 8 Pierce: “U.S. C. and G. S. Report 1876, App. 15, and 1881, App. 17.” 9 Messerschmidt: Same reference as 7. ee eee * In all the values given under references 1-4 gravity at Washington has been taken at 980,100, and the others derived from that by comparative experiments with invariable pendulums. SMITHSONIAN TABLES. 103 TABLE 114. SUMMARY OF RESULTS OF THE VALUE OF CRAVITY (9) AT STATIONS IN THE UNITED STATES, OCCUPIED BY THE U. S. COAST AND GEODETIC SURVEY DURING THE YEAR 1894.* Station. Latitude. Longitude. Elevation. g observed. ~ beget Metres. Dynes. 03 50 22 980.382 07 4 14 980.384 4 39 2 64 980.164 Philadelphia, Pa. II 40 16 980.182 Washington, C. & G. S, ; ; 00 32 14 980.098 Washington, Smithsonian. : : OI 32 10 980.100 Appalachian Elevation. ithaca, Nien Vien ee 2 : ; ; 29 00 247 980.286 Charlottesville, Va. . ; : : 30 16 166 979-924 Deer Park, Md. s 0 , ; 19 50 770 979-921 Central Plains. Cleveland, Ohio . : : 36 38 980.22 Cincinnati, Ohio : : : : 25 20 2 979-990 Terre Haute, Ind. . , : ; 980.058 Chicago, Ill. . c ; : : } 980.264 St. Louis, Mo. . ; : : . 979.987 Kansas City, Mo. . : : : 979-976 Ellsworth, Kan. . . . : . 979-912 Wallace, Kan. . ; : : 979-741 Colorado Springs, Galant. é : ! 979-476 Denver, Col. . . . . 979-595 Rocky Mountains. Pike’s Peak, Col. . : . 3 2 978.940 Gunnison, Col. . : : ° : 979.328 Grand Junction, Col. : : : 979-619 Green River, Utah . 7 : 7 979.622 Grand Canyon, Wyo. : ; : 3 979.885 Norris Geyser Basin, Wyo. . ; 979-930 Lower Geyser Basin, Wyo... : Bn2 979.918 Pleasant Valley, Jct., Utah : ; 979.498 Salt Lake City, Utah ; ; : 979-789 Atlantic Coast. Boston, Mass. Cambridge, Mass. Princeton, N. J. ~Od ~ OG = nimi WN ly TABLE 115. LENCTH OF SECONDS PENDULUM AT SEA LEVEL FOR DIFFERENT LATITUDES.? Latitude. Length in centimetres. Length in inches Latitude. Length in centimetres. on ° 4 99.0910 | 1.996034 | 39.0121 | 1.591200 || 50 | 99.4014 | I. 997393 39-1344 | 1.592558 10950 6052 | .0137 1217 -4459 7587 | +1520 2753 1079 6104 0184 1270 || 6 .4876 7770 1683 2935 1265 6190 0261 1356 5255 7935 1832 3100 1529 6306 0365 1471 5501 8077 1960 3242 99-1855 | 1.996448 | 39.0493 | 1.591614 99-5845 1g9bI92 39-2065 | 1.593358 2234 6614 .0042 1779 -6040 8277 .2141 3442 eeu 6796 0806 1962 6160 8329 2188 3494 -3096 6991 0982 2157 -6200 8347 2204 3512 +3555 7192 | .1163 2357 . R. Putnam, Phil. Soc. of Washington, Bull. vol. xiii. ; Taken as standard. The other values were obtained from this by means of invariable pendulums. + Calculated from force of gravity table by the formula 7=g/7?. “For each 100 feet of elevation subtract 0.000596 centimetres, or 0.000235 inches, or .c000196 feet. SMITHSONIAN TABLES. 104 TABLE 116. LENGTH OF THE SECONDS PENDULUM." Correspond- Range of latitude included by Length of pendulum in metres | ing length | Refer- the stations. for latitude ¢. of pendulum] ence. for lat. 45°. Date of determi- nation, Number of obser- vation stations. 1799 From + 67° os’ to ’ | 0.990631 + .005637 sin? $ | 0.993450 1816 «+74 53“ 2 0.990743 + .005466 sin? ¢ | 0.993976 1821 + 38° 40’ 0.990880 + .005340 sin? @ | 0.993550 $ ? wore Drum 1825 + 79° 50° 2 0.990977 + .005142 sin‘ 0.993548 1827 + 79° 50° cis 0.991026 + .005072 sin? 0.993562 1829 0° 0 0.990555 + -005679 sin? | 0.993395 1830 =n el 0.991017 + .005087 sin? | 0.993560 1833 _ ‘ 0.990941 + .005142 sin? @ | 0.993512 1869 0.990970 + .005185 sin? | 0.993554T 1876 2a O.99IOII + .005105 sin? ¢ | 0.993563 1884 2 0.990918 -+ .005262 sin? ¢ | 0.993549 me OO ON On fW NH = Combining the above results . . . . «. «| 0.990910 + .005290 sin? | 0.993555 ~ NS In 1884, from the series of observations used by Dr. Fischer, Dr. G. W. Hill # found = 0.9927148 metre + 0.0050890 p~* (sin? ¢ — 4) -++ 0.0000979 p~* cos? ¢ cos (2w’ +29° 04’) — 0.0001355 p-° (sin? ¢ —# sin )¢ + 0.0005421 p—* (sin? ¢ — 4) cos ¢ cos (w’ + 217° 51’) + 0.0002640 p—* sin ¢ cos? ¢ cos (2w’ + 4° 49’) + 0.0001 248 p—* cos? ¢ cos (3w’ + 110° 24’) -+ 0.0001 489 p~° (sint ¢ — $ sin? @ + 3) + 0.0007386 p—° (sin? ¢ — 7 sin ¢) cos ¢ cos (w’ + 3°02’) + 0.0002175 p~° (sin? ¢ — +) cos? ¢ cos (2w” + 262° 17’) + 0.0003126 p—® sin ¢ cos® @ cos (3w” + 148° 20’) + 0.0000584 p~° cos? ¢ cos (4w’ + 248° 19’) where ¢ is the geocentric latitude, w’ the geographical longitude, and p a factor, varying with the latitude, such that the radius of the earth at latitude ¢ is zp where a is the equa- torial radius of the earth. 1 Laplace: “Traité de Mécanique Céleste,” T. 2, livre 3, chap. 5, sect. 42. 2 Mathieu: “Sur les expériences du pendule;” in ‘ Connaissance des Temps 1816,” Additions, pp. 314-341, p. 332. 3 Biot et Arago: “ Recueil d’Observations géodésiques, etc.” Paris, 1821, p. 575. 4 Sabine: “ An Account of Experiments to determine the Figure of the Earth, etc., by Sir Edward Sabine.” London, 1825, p. 352. 5 Saigey: “ Comparaison des Observations du pendule a diverses latitudes ; faites par MM. Biot, Kater, Sabine, de Freycinet, et Duperry;” in “ Bulletin des Sciences Mathe- matiques, etc.,” T. 1, pp. 31-43, and 171-184. Paris, 1827. 6 Pontécoulant : “ Théorie analytique du Systeme du monde,” Paris, 1829, T. 2, p. 466. 7 Airy: “ Figure of the Earth;” in “ Encyc. Met.” 2d Div. vol. 3, p. 230. 8 Poisson: “Traité de Mécanique,” T. 1, p. 377; “ Connaissance des Temps,” 1834, pp: 32-33; and Puissant: “ Traité de géodésie,” T. 2, p. 464. 9 Unferdinger: ‘“ Das Pendel als geoditisches Instrument ;’ 1869, p. 316. 10 Fischer: “ Die Gestalt der Erde und die Pendelmessungen ; ” in “ Ast. Nach.’ 1876, col. 87. 11 Helmert: “Die mathematischen und physikalischen Theorieen der héheren Geo- dasie, von Dr. F. R. Helmert,” II.,Theil. Leipzig, 1884, p. 241. 12 Harkness. 13 Hill, Astronomical paper prepared for the use of the “ American Ephemeris and Nautical Almanac,” vol. 3, p. 339- ? in Grunert’s “ Archiv,” * The data here given with regard to the different determinations which have been made of the length of the seconds pendulum are quoted from Harkness (Solar Parallax and its Related Constants, Washington, 1891). + Calculated from a logarithmic expression given by Unferdinger. SMITHSONIAN TABLES. 105 TABLE 117. MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS.* — I — ——z=z————————————_—_—_——_—————— Length of the seconds pendulum at sea level : : , . ; 7 39-012540 + 0.208268 sin? ¢ inches. 3-251045 + 0.017356 sin? ¢ feet. 9909910 + 0.005290 sin” metres. I Il J 0. Acceleration produced by gravity per sec- ond per second mean solar time . a — 27 32-086528 +- 0.171293 sin? @ feet. 977-9856 + 5.2210 sin? @ centimetres. II Il Equatorial semidiameter . , _ - =a = 20925293 + 409.4 feet. = 3963.124 ++ 0.078 miles. = 6377972 + 124.8 metres. Polar semidiameter . . A ; - ==6= 20855590 -+ 325.1 feet. = 3949.922 -++ 0.062 miles. = 6356727 -++ 99.09 metres. 393775819 -- 4927 inches. 32514652 -+ 410.6 feet. 6214.896 -++ 0.078 miles. 10001816 + 125.1 metres. One earth quadrant . : . : tl Al _a@—b I - “@ ~~ 300.205 -- 2.9064. sear = 0.006651018. a Flattening Eccentricity = Difference between geographical and geocentric latitude = ¢ — @’ = 088.2242” sin 2 ¢— 1.1482” sin 4 ¢ + 0.0026” sin 6 ¢. Mean density of the Earth = 5.576 + o.o16. Surface density of the Earth = 2.56 + 0.16. Moments of inertia of the Earth; the principal moments being taken as A, B, and C, and C the greater: C—A = 0.00326521 = ———; = 0.0032 152 oa 306.259" C — A =0.001064767 Ea?; A = B = 0.325029 Ea?; C= 0.326094 La? ; where £ is the mass of the Earth and a its equatorial semidiameter. Length of sidereal year = 365.2563578 mean solar days ; —= 365 days 6 hours 9 minutes 9.314 seconds. O25) Say 314 Length of tropical year 1850 — = 365.242199870 — 0.0000062124 Foo mean solar days ; | 365 days 5 hours 48 minutes ( 46.069 — 0.53675 ES) seconds. Length of sidereal month t— 1800 27.321661162 — 0.00000026240 Taco days; | d t— 1800 27 days 7 hours 43 minutes (11.524 — 0.022671 ee) seconds. Length of synodical month = 29.530588435 — 0.00000030696 = days ; I — = 29 days 12 hours 44 minutes (2841 — 0.026522 fo) seconds. Length of sidereal day = 86164.09965 mean solar seconds. N. B.— The factor containing ¢ in the above equations (the epoch at which the values of the quantities are required) may in all ordinary cases be neglected. * Harkness, ‘ Solar Parallax and Allied Constants.” 106 SMITHSONIAN TABLES. TABLE 117. MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS. MASSES OF THE PLANETS. Reciprocals of the masses of the planets relative to the Sun and of the mass of the Moon relative to the Earth : Mercury = 8374672 + 1765762. Venus = 408968 ++ 1874. Earth * == 327214 -+ 624. Mars = 3093500 ++ 3295. Jupiter = 1047.55 -+ 0.20. Saturn = 3501.6 + 0.78. Uranus = 22600 -++ 36. Neptune = 18780 -}- 300. Moon =81.068 + 0.238. Mean distance from Earth to Sun = 92796950 +- 59715 miles ; = 149340870 ++ 96101 kilometres. Eccentricity of Earth’s orbit = ¢, t— 180\2 = 0.01677 1049 — 0.0000004245 (¢ — 1850) — 0.000000001 367 (=>) : Solar parallax = 8.80905” -+|- 0.00567”. Lunar parallax = 3422.54216” -+| 0.12533”. Mean distance from Earth to Moon = 60.26931 5 ++ 0.002502 terrestrial radii; = 238854.75 -+ 9.916 miles; = 384396.01 -++ 15.9558 kilometres. Lunar inequality of the Earth = Z = 6.52294” + 0.01854”. Parallactic inequality of the Moon = Q = 124.95126” + 0.08197”. Mean motion of Moon’s node in 365.25 days = w= —19° 21’ 19.6191” + 0.14136” ——o Eccentricity and inclination of the Moon’s orbit = ¢2 = 0.054899720. Delaunay’s y = sin + 7= 0.044886793. L = 5° 08’ 43.3546”. Constant of nutation = 9.22054” +1 0.00859” + 0.00000904” (¢ — 1850). Constant of aberration = 20.45451” + 0.01258”. Time taken by light to traverse the mean radius of the Earth’s orbit = 498.00595 -+. 0.30834 seconds. Velocity of light = 186337.00 + 49.722 miles per second. = 299577.64 ++ 80.019 kilometres per second. * Earth + Moon. SMITHSONIAN TABLES. 107 TABLE 118. AERODYNAMICS. The pressure on a plane surface normal to the wind is for ordinary wind velocities expressed by P= kwav where £ is a constant depending on the units employed, w the mass of unit volume of the air, A the area of the surface and v the velocity of the wind.* Engineers generally use the table of values of P given by Smeaton in 1759. This table was calculated from the formula = .00492 v2 and gives the pressure in pounds per square foot when wv is expressed in miles per hour. The corresponding formula when v is expressed in feet per second is P= OO225 Ue. Later determinations do not agree well together, but give on the average somewhat lower values for the coefficient. The value of w depends, of course, on the temperature and the baro- metric pressure. Langley’s t experiments give 4w = .00166 at ordinary barometric pressure and 10° C. temperature. For planes inclined at an angle a less than go° to the direction of the wind the pressure may be expressed as (Pie, Pop Table 118, founded on the experiments of Langley, gives the value of Aa for different values of a. The word asfect, in the headings, is used by him to define the position of the plane relative to the direction of motion. The numerical value of the aspect is the ratio of the linear dimension transverse to the direction of motion to the linear dimension, a vertical plane through which is parallel to the direction of motion. TABLE 118.— Values of F, in Equation Pa—=FaPm. Plane 30 in. X 4.8 in. Plane 12 in. X 12 in. Plane 6 in. X 24 in. Aspect 6 (nearly). Aspect 1. Aspect }. Fa * The pressure on a spherical surface is approximately 0.36 that on a plane circular surface of the same diameter as the sphere; on a cylindrical surface with axis normal to the wind, about o.5 that on a rectangular surface of length equal to the length, and breadth equal to the diameter of the cylinder. + The data here given on Professor Langley’s authority were communicated by him to the author. SMITHSONIAN TABLES. 108 Sr NE A Nee ee ee ee tm ta i TABLE 119, AERODYNAMICS. On the basis of the results given in Table 118 Langley states the following condition for the soaring of an aeroplane 76.2 centimetres long and 12.2 centimetres broad, weighing soo grammes, —that is, a plane one square foot in area, weighing 1.1 pounds. It is supposed to soar in a horizontal direction, with aspect 6. TABLE 119. — Data for the Soaring of Planes 76.2 X 12.2 cms. weighing 500 Grammes, Aspect 6. Weight of planes of like form, capable of soaring at speed v with the ex- Inclination penditure of one horse to the hori- power. zontal a, Work expended per minute (activity). Soaring speed v. Metres per Feet per | Kilogramme Foot sec. sec, metres. pounds. Kilogrammes. | Pounds. 66 24 174 95-0 209 50 297 Ge 122 41 474 34- 37 623 26.5 35 1268 13.0 37 2434 6.8 ap Reeaweight In general, if p= ere Soaring speed v= \/ ae *— =f Activity per unit of weight =v tana The following data for curved surfaces are due to Wellner (Zeits. fiir Luftschifffahrt, x., Oct. 1893). Let the surface be so curved that its intersection with a vertical plane parallel to the line of motion is a parabola whose height is about 7; the subtending chord, and let the surface be bounded by an elliptic outline symmetrical with the line of motion. Also, let the angle of incli- nation of the chord of the surface be a, and the angle between the direction of resultant air pressure and the normal to the direction of motion be 8. Then B N ODOM de a oO ONAN DN PF NUAND YHhEHR YYWWYWW DW ANtOob FP UND HYHHH HHHWW S NUM Mw wm &ACMOWO o aoe mn wm > _ Fort Vancouver 4-51 wn vo SMITHSONIAN TABLES. ep . TERRESTRIAL MACNETISM. ABLE 120 Secular Variation of Declination in the Form of a Function of the Time for a Number of Stations. More extended tables will be found in App. 7 of the United States Coast and Geodetic Survey Report for 1888, from which this table has been compiled. ‘The variable » is reckoned from the epoch 1850 and thus = ¢ — 1850. Seton Tactode: West The magnetic declination ()) expressed as ongitude. a function of time. (a) Eastern Series of Stations. ° / ° °o St. Johns, N. F.. : ; -| 47 34-4 8.89 sin (1.05 m + 63.4)* Quebec, Canada . : ” -| 46 48.4 3.03 sin (1.4 -+ 4.6) 0.61 sin (4.0m -+ 0.3) 7.78 sin (1.2m + 49.8) 4.17 sin (1.5 7 — 18.5) 0.36 sin (4.9 m -+ 19.0) 3-55 sin (1.30 ” + 8.6) 4-53 sin (t.00 m + 46.1)* 3.02 2.6 ° Charlottetown, P.E.I. -| 4614.0 Montreal, Canada. ; 5145 30:5 Bangor, Me. “ ; , -| 44 82.2 Halifax, N.S. . : _ -| 44 39.6 Albany, N.Y. . a : iin 42-3012 Cambridge, Mass. . - SEAze225Q Con .02 sin (1.44 m — 8.3) .69 sin (1.30 m + 7.0) .18 sin (3.20 m + 44.0) 3.11 sin (1-40 me — 22.1) 2.77 sin (1.30 m — 18.1) 0.14 sin (6.30 7 + 64.0) 2.98 sin (1.50 + 0.2) 3-17 sin (1.50 m — 26.1) 0.19 sin (4.00 m + 14.6) 2.57 sin (1.45 # — 21.6) 0.14 sin (12.00 m + 27) 2.25 sin (1.47 m — 30.6) 2.75 sin (1.40 m — 12.1)* nae oOo f™N FHF EEHET H+ t+ t+444t4+ New Haven, Conn. . : at ea ash New York, N. Y. : -| 40 42.7 on Harrisburg, Pa. . : : “1 40) 05.0 Philadelphia, Pa. : : -| 39 50.9 G2 \O Ow ws Washington, D.C. . . -| 38 53:3 NS “a ww Cape Henry, Va. SE SOn55.0 Charleston, S. C. : . -| 32 46.6 ue os Nob Oo Paris, France . : : -| 48 50.2 .479 + 16.002 sin (0.765 m + 118.77) 85 —0.35 sin (0.69 2)] sin [(4.04 .0054 2 + .000035 7") 7]f + 0.0145 m + 0.00056 m? * + 9.91 sin (0.80 m — 10.4)* nO oun [oS St. George’s Town, Bermuda Rio de Janeiro, Brazil _ York Factory, B.N. A. . -| 56 59.9 Fort Albany, B. N. A. : aS 222-0 Sault Ste Marie, Mich. . -| 46 29.9 Toronto, Canada : : -| 43 39-4 16.03 sin (1.10 7 — 97.9) 5 sin (1.20 7 — 99.0)* o sin (1.45 7 — 58.5) > _ WHS 9 Se 82 sin (1.40 7 — 44.7) .09 sin (9.30 m + 136) .08 sin (19.00 m + 247) Chicago, Ill. ‘ : : 450.0) .48 sin (1.45 72 — 62.5) Cleveland, Ohio : ; .| 41 30.4 Denver, Colo. zx Athens, Ohio Cincinnati, Ohio St. Louis, Mo. New Orleans, La. Key West, Fla. . 3 : : Kingston, Port Royal, Jamaica . .OII m + 0.0005 m2? .63 sin (1.40 m — 24.7) 6 2 ° ° ° 2 .43 sin (1.42 mt — 37.9) 3.00 sin (1.40 — 51.1)* .98 sin (1.40 m — 09.8) 8 “3 +tt+t++tt+4+4+++4++ 6 2 2.39 sin (1.30 # — 14.8) 2 2 2 eee al Sl WhO d Hin Od CW NOMMW ANI me = ORO KF ONN 6 sin (1.30 7 — 23.9) 9g sin (1.10 m — 10.6) (4) Stations on the Pacific Coast, etc. eee City of Mexico, Mex. . : 99 11.6 Cerros Island, Lower Cal., Mex. | 2804.0] I15 12.0 : San Francisco, Cal. . : : lplee2773 Vancouver, Wash. . 5 : : 122 39.7 Sitka, Alaska. : : : 9 | 135\ 19-7 Port Etches, Alaska . : 7 , 146 37.6 Petropavlovsk, Siberia : .28 sin (1.00 m — 87.9)* 61 sin (1.05 #2 — a .65 sin (1.05 # — 135-5 os .12 sin (1.35 7 — 134-1) .30 sin (1.30 7% — 104.2) .89 sin (1.35 7 — 80.9) .97 sin (1.30 + 12.2) CIWOORW * Approximate expression. EB + East longitude. + Compiled from a series of observations extending back to 1541. The primary wave follows the sum of the con- stant and first periodic term closely. The period seems to be about 470 years. In the expression for the secondary wave 2 —?— 1700. SMITHSONIAN TABLES. 113 PABEE Eee TERRESTRIAL MACNETISM. Secular Variation of the Declination. — Eastern Stations.* Station. 1800 1810 |1820 1830 | 1840 | 1850 | 1860 | 1870 ° St. Johns, N. F. . Quebec, Canada . Charlottetown, Pa ake ; Montreal, Canada Eastport, Me. . = ht w Goo deo DARD OO HO EO 13.8 16.9 = N OV Wun _ 20.7 : 23-4 9-4 16.4 MN ao $y ao wR OD mm th -_ cas ° -_ -_ 13.6 13.9 8.9 79 10.8 Bangor, Me. . Halifax, N.S.. Burlington, Vt. Hanover, N. H. . Portland, Me. . — AKADHA CANIN CORNRDCO WHARHH HANNAH _ woos BRROD BEY min CONI\O Ko a mun OonnA NO Rutland, Vt. Portsmouth, N. H. . Chesterfield, N. H. . Newburyport, Mass. Williamstown, Mass. ~ SCO © ONO _~ NO a hOUA AD Albany, N. Y. Salem, Mass. . Oxford, N.Y... .. Cambridge, Mass. Boston, Mass. . Ak ODOULK Provincetown, Mass. Providence, R. I.. Hartford, Conn. . New Haven, Conn. . Nantucket, Mass. MEUODY YYBWONM UYANA wCoOVas SEG ONO) SI 00) STi OUNNWO OO OT SONON OONnNNA OWMmnIO DNKHAN Ou NOMNb Cold Spring Harbor, NoYo 2a : New York, N. Y. Bethlehem, Pa. Huntingdon, Pa. . New Brunswick, N.J Onan nNBU OP > OW AN Ce Le min O OV MPU mindn™ NON NIN WO OG ty OOO R DA AOR ° a ~ \o DAL RW Jamesburg, N. J.. Harrisburg, Pa. . Hatboro, Pa. =. . Philadelphia, Pa. Chambersburg, Pa. . SUDO SY WOAH NANDA ND wun NODOUA WN WONWNO ONNOW &w Ongnw + NBM S ON ON OD oO -SNNOO on 0 mb nO Of CO CWwWrne f Baltimore, Md. . Washington, D.C. . Cape Henlopen, Del. Williamsburg, Va. Cape Henry, Va.. 9° kO -_ N =~ mO> N - QWHWARUA UNINS YW UI090 Conk HANAN NW BP AWOC OANINY OOKARKR WO DKW fRrWOO ow Te NN none. | NAN AO PRAY WADA YW EUW COnABRUnO PORN D BRADNER UW PHYAD PNB py oO OW DN New Berne, N. C. Milledgeville, Ga. Charleston, S. C. Savannah, Ga. Paris, France . nO n | wn ° | | Sonn wl || OWnn _ WMAOWhs ape RO mw DWN | St. George’s Town, Bes “seks os a \o ao & Rio de Janeiro, Bra- PI Meee 6s es * ° ax Un Co * This table gives the secular variation of the declination since the year r80o0 for a series of stations in the Eastern States and adjacent countries. Compiled from a paper by Mr. Schott, forming App. 7, Report of the United States Coast and Geodetic Survey for 1888. The minus sign indicates eastern declination. SMITHSONIAN TABLES. 114 TABLE 128. TERRESTRIAL MACNETISM. Secular Variation of the Declination. — Central Stations.* | Station. 1810 | 1820 | 1830 | 1840 | 1850 | 1860 | 1870 | 1880 | 1890 York Factory, Brit. N. A. —8.5| —8.6] —8.2} —7.2 Fort Albany, Brit. N. A. 8.9} 8.8) 9.1] 9.6 Duluth, Minn. 8 Superior City, Wis. Se ela eho re Sault Ste. ie Mich... P f : i : 8] —o.3 0.2 0.8 Pierrepont Manor, BR VIcue a tonto. 7, : 5-4 Toronto, Canada . - 7 3 t PAPA) dg) Grand Haven, Mich. —5.0 : .2 .Q| —4.4| —3-7 Milwaukee, Wis. . - - .4| —6.9] —6.2 Buffalo, N.Y. . . .2 n2) Ong ; 13 ; 2:8|, 3.7, Detroit, Mich. . .| —3.2| —3-1] —2.9 .5| —2.1 .6) —1.0] —o.4 Ypsilanti, Mich. .| -— | —4.1} —3.6 .O| —2.2 -4| —o.6| 0.2 Erie, Pa... . . «| —0.5| —0.5]}/ —0.4 7 0.4 7 T:Gl0 2-3 Chicaco sly a. - | —6.2 .3) —6.2 .o| —5.6) —5.1 Michigan City, Ind.| - - - 6) —5.4 .o| —4.6]) —4.0 Cleveland, Ohio .| —1.9| —1.7} —1.5} —1.1| —o.6) —o.1] 0.4) 0.9 Omaha, Neb. . .| —- = |—12.5|—12.6|—12.6 —12.4|—12.0|—11.5|—10.9|—I0.2 Beaver, Penn. . . | —1.1| —1.3} —1.3| —1-1) —o0.8} —0.3} 0.2} 0.9] 1.5 Pittsburg, Pa. . .| — - - 0:2] 0:7) steal eL-O|e 255 Denver, Colo. . .| - - = — |—15-1|—14.9)—14. si—r4. I Marietta, Ohio. . .Q| —2.8 ‘ 3) —1.9 .3) —o0.6} o.1 Athens, Ohio . . 3 I) —3.9 : I] —2.6 .0| —1.4] —o.7 Cincinnati, Ohio . ‘ 0} —5.0 : 5] —4-1 6] —3.0] —2.4 St. Louis, Mo. . .| - - : .6| —8.2 .7| —7.1| —6.4 Nashville, Tenn. . —6.7 : .9| —O.7 3} —5-8] —S.1 Florence, Ala. . . .5| —5-6 .4| —6.1 .7| —5.3) —4.8 Mobile, Ala.. . . .3| —6.7 aes Oo : : .7| —6.4) —5.8 Pensacola, Fla.. . .2| —7.5| —7-6 7 : .6| —6.0] —5.3 New Orleans, La. . .6| —8.0) —8.1 , : .7| —7.2| —6.6 San Antonio, Texas} —- —9.8|—I0.1 ; : ; .7| —9.3 Key West, Fla. . —6.9) —6.5 ; ; : .2| —3.6 Havana, Cuba. . : .9| —6.6} —6.3 ; ; 8 -2| —3.6 Kingston, Port Royal, Jamaica . : a: 5} —5.1 : ; : .3|.—2. Barbadoes, Car. Isl. 2 : .5| —2.0 : ; i : 0.5 Panama, New Gra- nada... - : : 6} —7.3 * This table gives the secular variation of the declination since the year 1800 for a series of stations in the Central States and adjacent countries. The minus sign indicates eastern declination. Reference same as Table 127. SMITHSONIAN TABLES. IIs TABLE 129, TERRESTRIAL MACNETISM. Secular Variation of the Declination. — Western Stations.* Station. 1800 | 1810 1820; 1830 1840/ 1850 | 1860| 1870} 1880; 1890 Oo 8.1 7.0 8.1 9.0 9.6 10.5 11.9 3} 13-3 14.8 Acapulco, Mex. Vera Cruz, Mex. . City of Mexico, Mex. San Blas, Mex. : Cape San Lucas, Mex. . AL NWU Cw DANO ne DAOWO Magdalena Bay, L. Cal. Ceros Island, Mex. . E] Paso, Mex. . : San Diego, Cal. . Santa Barbara, Cal. . nk ~ nin 1 9 1 HOO 90, 1 HO BO HO 0 eee _ Noe _— = QS OW 15.9 16.5 17.7 16.6 21.0 Monterey, Cal. San Francisco, Cal. . Cape Mendocino . Salt Lake City, Utah Vancouver, Wash. Ont OF DATaP BPNNHEO WO 000000 RON CO WU &O ~ £97 (OE Ne a me Ny 9 _ tN _ _ Walla Walla, Wash. Cape Disappointment, Wash. Seattle, Duwanish Bay, Wash. Port Townsend, Wash. Nee-ah Bay, Wash. t ° Oo ty 4 ON 14.4 15.4 16.9 19.6 19.8 I Nn Nv Ne N t oe et OW NO oh 99 | Ww 3 o Nb wb RwHH 2 Nad Oo NI CU N tN te tN RAD nN ~ Nootka, Vancouver Island Captain’s and Iliuliuk Har- bors, Unilaska Island Sitka, Alaska . . St. Paul, Kadiak Island Port Mulgrave, Yakutat Bay, Alaska . NN oe Oe Wn CO WwW HOD A NN eS WOO NN Oo ~O > Ny SOO WwW = nN oO bt oo to ND oS on Port Etches, Alaska. Port Clarence, Alaska . Chamisso Island, Kotze- bue Sound - Petropavlovsk, Kamchatka, Siberia ae Ow i N Ny a bs 9 : SG Rn ty Nv \o nN * This table gives the secular variation of the declination since the year 1800 for a series of stations in the Western States and adjacent countries. The declinations are all east of north. Reference same as Table 127. 116 SMITHSONIAN TABLES. TaBLe 130. TERRESTRIAL MACNETISM. Agonic Lines.* The line of no declination is moving westward in the United States, and east declination is decreasing west of, while west declination is increasing east of the agonic line. Longitudes of the agonic line for the years — 1800 1850 1875 1890 * Reference same as Table 127. SMITHSONIAN TABLES. 117 TABLE 131. TERRESTRIAL MACNETISM. Date of Maximum East Declination.* This table gives the date of maximum east declination for a number of stations, beginning at the northeast of the United States and ex- tending down the Atlantic coast to New York and west to the Pacific. Station. Halifax,t N.S. Eastport, Me. Bangor, Me. Portland, Me. Boston, Mass. ; New Haven, Conn. New York, N. Y. Jamesburg, N. J. Philadelphia, Pa. Pittsburg, Pa. Cincinnati, Ohio Florence, Ala. St. Louis, Mo. Nashville, Tenn. Chicago, Ill. Denver, Colo. Salt Lake, Utah Vancouver, Wash. Cape Mendocino, Cal. San Francisco, Cal. * Reference same as Table 127. + The opposite phase of maximum west declination is now located at Halifax. SMITHSONIAN TABLES. 118 TABLE 132. ‘ PRESSURE OF COLUMNS OF MERCURY AND WATER. British and metric measures. Correct at 0° C. for mercury and at 4° C. for water. Metrric MEASURE. BRITISH MEASURE. Pressure Pressure in grammes per in pounds per Pressure | Pressure E : he in grammes per in pounds per Inches of Hg. sq. cm. sq. inch. Sq. cm. sq- inch. 0.193376 34-533 0.491174 27.1912 0.3867 52 69.066 0.982348 40.7868 0.580128 103.598 1.473522 54-3824. 0.773504 138.131 1.964696 67.9780 0.966880 172.664 2.455870 81.5736 1.160256 207.197 2.047044 1.353632 241.730 3.438218 1.547008 276.262 3-929392 1.740384 310.795 4.420566 1.933760 345-328 4.911740 Pressure Pressure Pressure Pressure in grammes per in pounds per in grammes per ip pounds per s Inches of q. cm. sq. inch. 20- sq: inch. 0.01 42234 ; 0.03622 0.0284468 : 0.072255 0.0426702 : 0.108382 0.05689 36 0.144510 0.071 1170 3 0.180637 0.08 53404 0.216764 0.0995658 0.252892 0.1137872 0.289019 0.1280106 0.325147 0.1422 340 0.361274 SMITHSONIAN TABLES. 119 TABLE 133. REDUCTION OF BAROMETRIC HEICHT TO STANDARD TEMPERATURE.* Corrections for brass scale and f Corrections for glass scale and metric measure. metric measure. Corrections for brass scale and English measure. Height of barometer in inches. a in inches for temp. F. Height of a barometer in in mm. for mm. temp. C. SO 16.0 17.0 17-5 18.0 18.5 19.0 19.5 NhyKN WL NS » WWNN NHNN NN SN DOU tN N 8 @ tN Nob ty ORDER KHOND HONONOND HNONdON~ SOOOSS QW S36 3 +N Go Ga Ga Ga G2 G2 RS ie ROnO AL NO COD 0.00135 00145 001 54 .001 58 .00163 .00167 .0O172 00176 0.00181 00185 00190 00194 .0O0199 00203 .00208 .00212 0.00217 -0022I .00226 00231 0023 .00240 00245 .00249 0.00254 00258 .00263 00265 .00267 .00268 00270 .00272 0.00274 .00276 .00277 .00279 .00281 .00283 .0028 5 .00237 400 0.0651 410 .0608 420 .0634 43 .0700 440 .0716 450 0732 460 :07 49 0765 0781 0797 0.0813 0830 .0846 .0862 .0878 0894 .OOII .0927 0943 0959 0.097 § .0992 1008 1024 1040 1056 1073 1089 IOS DL2T 0.1137 1154 1170 .1186 .1202 .1218 1295 ele gr 1267 1283 1299 Height of barometer in mm. 50 a in mm. for temp. C. 0.0086 0172 0258 0345 0431 0517 0003 0.0689 0775 0861 -c898 -0934 .0971 -1007 0.1034 -I05I -1068 -1085 1103 -1120 -1137 O.1154 O41] . 045] .046] .048 0.039 0.043 | 0.044 038 | .07 041] .043] .044 .036| . .039| .041 | .042 2034 |" 037] .039] .040 £032 )|/ : : .038 0.031 .029| . : : .034 027)\\-: ; ; .032 .025 || : : .02 Inch. | Inch. 0.074 | 0.077 0.073 | 0.076 .076 :075 :074 073 0.073 .072 .O71 .069 Inch. 0.080 0.079 078 :077 077 076 0.075 SMITHSONIAN TABLES. * “Smithsonian Meteorological Tables,” p. 58. 122 TABLE 136. REDUCTION OF BAROMETER TO STANDARD CRAVITY.* Reduction to Latitude 45°. — Metric Scale. N. B. — From latitude 0° to 44° the correction is to be subtracted. From latitude 90° to 46° the correction is to be added. Height of the barometer in millimetres. Latitude. * “Smithsonian Meteorological Tables,” p. 59. SMITHSONIAN TABLES. 123 TABLE 137. CORRECTION OF THE BAROMETER FOR CAPILLARITY.* 1. METRIC MEASURE. HeiGutT oF Meniscus 1N MILLIMETRES. Diameter ene 04 | 06 | 08 | 10 | 12 | 14 | 16 | 18 in mm. Correction to be added in millimetres. 0.83 1.54 1.98 2.37 - -47 0.86 1.19 1.45 1.80 2 : 56 0.78 : 1.21 .40 “53 : 0.82 -29 38 . -56 .21 .28 : -40 anc -20 : .29 10 14 : .21 .07 10 : =L5 -O4 .O7 : 12 2. BRITISH MEASURE. HEIGHT OF MENISCUS IN INCHES. Diameter of tube i : | .03 | 04 | 05 | .06 | in inches. Correction to be added in hundredths of an inch. 6.56 9-23 11.56 3.28 4-54 5.94 1.92 2.76 3-68 1.26 ey 2.30 0.82 ia as 1.49 61 0.81 1.02 232 aot 0.68 -20 “39 “47 03 .20 31 See On eee Se Stn On Con! © ODWnN ESHN * The first table is from Kohlrausch (Experimental Physics), and is based on the experiments of Mendelejeff and Gutkowski (Jour. de Phys. Chem. Geo. Petersburg, 1877, or Wied. Beib. 1867). The second table has been calcu- lated from the same data by conversion into inches and graphic interpolation. A number of tables, mostly based on theoretical formule and the capillary constants of mercury in glass tubes in air and vacuum, were given in the fourth edition of Guyot’s Tables, and may be there referred to. They are not repeated here, as the above is probably more accurate, and historical matter is excluded for convenience in the use of the book. SMITHSONIAN TABLES. 124 TABLE 138. ABSORPTION OF CASES BY LIQUIDS." ApsorpTION COEFFICIENTS, a, FOR GASES IN WATER. Temperature | Centigrade. Ae A Carbon Carbon Nitric Nitrous t dioxide. monoxide. H N oxide. oxide. CO, 0.02110 0.02399 ; z 02022 02134 10 : .028 01944 .o1g18 15 : : 01875 .O1742 20 : : .01809 -01599 25 . F 01745 01451 30 : 01690 01370 40 ; : 01644 O1195 50 : 01608 .01074 100 ; .01600 OIOIL Temperature Hydrogen Sulphur ae : orine. | Ethylene. | Marine | sulphide. | dioxide. ai ‘ H.S SO, 0.02471 0.2563 | 0.05473 4.371 79:79 02179 2153 .04889 3.965 67.48 01953 -1837 .04 367 3.586 56.65 01795 1615 .03903 3.233 47.28 .O1704 : 1488 03499 2.905 39.37 = 02542 2.604 32.79 ABSORPTION COEFFICIENTS, a, FOR GASES IN ALCOHOL, C,H;OH. Temperature Centigrade. | Carbon Nitrous {Hydrogen} Sulphur oxide. sulphide. | dioxide. a N.O HS SOs dione: ene Methane. Eiscresen: ye CO. 0.5226 | 0.0692 0.1263 : 17.89 | 328.6 -5086 068 5 ey |i) e Sie 14-79) ||) 25%e7 495 .0679 sT220ui\ ; 11.99 | 190.3 .482 .0673 T2td |) y ‘ 9.54 | 144.5 -4710 .0667 204) |. K 7.41 II4. .4598 0662 sTL90) ||) - ; 5.62 pas 4-329 3.591 3°514 3:199 2.946 2.756 PP NQWH * This table contains the volumes of different gases, supposed measured at 0° C. and 76 centimetres’ pressure, which unit volume of the liquid named will absorb at atmospheric pressure and the temperature stated in the first column. The numbers tabulated are commonly called the absorption coefficients for the gases in water, or in alcohol, at the temperature ¢ and under one atmosphere of pressure. The table has been compiled from data published by Bohr & Bock, Bunsen, Carius, Dittmar, Hamberg, Henrick, Pagliano & Emo, Raoult, Schonfeld, Setschenow, and Winkler. The numbers are in many cases averages from several of these authorities. Nore. — The effect of increase of pressure is generally to increase the absorption coefficient. The following is approximately the magnitude of the effect in the case of ammonia in alcohol at a temperature of 23°C Eo 45ers. 50 cms. 55 cms. 60 cms. 65 cms. oz = 69 74 79 84 88 According to Setschenow the effect of varying the pressure from 45 to 85 centimetres in the case of carbonic acid in water is very small. SMITHSONIAN TABLES. 125 TABLE 139. VAPOR PRESSURES. The vapor pressures here tabulated have been taken, with one exception, from Regnault’s results. The vapor pressure of Pictet’s fluid is given on his own authority. Chloro- | Ethyl Ethyl Ethyl | Methyl | Turpen Acetone. | Benzol. form. | alcohol. ether. | bromide.| alcohol. CsHeO | CoHe " loride. | CHCis | CzHe0 | CyHi0 | CeHsBr 6.89 8.93 11.47 14.61 Veer ert oe Leese ee iia 18.44 23.09 28.68 35-36 43-28 52-59 63.48 76.12 90.70 107.42 126.48 148.11 172.50 199.59 230.49 264.54 302.28 34395 389.83 440.18 495-33 555.62 621.46 693-33 771.92 GMITHSONIAN TABLES. 126 Tem- pera- ture, Centi- NHs grade. —30°| 86.61 —25 —20 —10 ae 110.43 139.21 173-65 214.46 264.42 318.33 383-03 457-40 543-34 633.78 747-79 870.10 1007.02 1159.53 1328.73 1515.83 1721.98 1948.21 2196.51 2467.55 2763-00 3084.31 3433-09 3810.92 4219-57 4660.82 Ammonia. Carbon dioxide. CO, 1300.70 1514.24 1758.25 2034.02 2344.13 2690.66 307 5-38 3499-86 3964-69 4471.66 5020.73 5611.90 6244.73 6918.44 7631.46 Ethyl chloride. C3H,Cl SMITHSONIAN TABLES. VAPOR PRESSURES. Methyl chloride. CH;Cl 57-90 71.78 88.32 107.92 130.96 157-37 189.10 AAP 260.38 313.41 306.69 426.74 494.05 569.11 127 Methylic ether. C,H,O 57-65 71.61 88.20 107.77 130.66 157-25 187.90 222.90 262.90 307.98 358.60 415.10 477.80 Nitrous oxide. N,O 1569.49 1758.66 1908.43 2200.80 2457-92 2742.10 3055-86 3401.91 3783-17 4202.79 4664.14 5170.8 6335: Pictet’s fluid. 64CS2 + 46CO, Weight per cent. 58.52 67.64 74-48 89.68 101.84 121.60 139.08 167.20 193-80 226.48 258.40 297.92 338.20 383-80 434-72 478.80 Sulphur dioxide. TABLE 139. Hydrogen sulphide. H.S SO, 28.75 37-38 TaBLes 140-142. CAPILLARITY.—SURFACE TENSION OF LIQUIDS.* TABLE 140.— Water and Alcohol in Contact with Air. Surface tension | in dynes per | centimetre. Temp. er Ta | , Ethyl Water.| a)cohol. Temp. C. Surface tension in dynes per centimetre. Water. Ethyl alcohol. Surface tension Temp. | P&T cen- C. | Water. in dynes | timetre. OR NKYREN NP RK Cin YO OD OOF NY NWO & COUR DARN RY wHHN NN WL NSININI SIN NIT NTS 70.0 69.3 68.6 67.5 67.1 66.4 65.7 65.0 TABLE 141. — Miscellaneous Liquids Temp. Cc fe) Surface tension in dynes per cen- timetre. Aceton Acetic acid . Amyl alcohol Benzene . Butyric acid 3 Carbon disulphide Chloroform . Ether . Glycerine Hexane Mercury 2 Methyl] alcohol @Olivevoull. hese Petroleum Propyl alcohol. “c “ Toluol “ Turpentine . Ax dWNHNWN RAO DHS OHS OM to Nee Go Url CON A N= HEN NG Sore Go G00 in Contact with Air. Authority. Average of various. “ Quincke. Average of various. “ce Hall. Schiff. Average of various. “oe Magie. Schiff. “ Average of various. TABLE 142.—Solutions of Salts in Water.t ae Tension toa on Density. aan z dynes per cm. 1.2820 81.8 a 1.0497 | 15-16] 77.5 CaCl aL Twa 95-0 122773) ) 19 90.2 HCl I.1190| 20 73.6 1.0887] 20 74.5 . 1.0242| 20 75-3 Kel 1.1699] 15-16} 82.8 I.1O1I | 15-16] 80.1 s 1.0463 | 15-16] 78.2 MgClg | 1.2338} 15-16] 90.1 = 1.1694] 15-16] 85.2 « 1.0362 | 15-16] 78.0 NaCl 1.1932] 20 85.8 Ss 1.1074] 20 | 80.5 s 1.0360] 20 77.6 NH4Cl | 1.0758] 16 | 84.3 1.0535| 16 81.7 1.0281] 16 78.8 1.3114] 15-16] 85.6 1.1204| 15-16] 79.4 1.0567 | 15-16) 77.8 1.3575| 15-16| 90.9 1.1576| 15-16] 81.8 1.0400| 15-16] 77.5 | 1.1329| 14-15] 79.3 1.0605] 14-15| 77.8 1.0283] 14-15] 77.2 1.1263] 14 78.9 1.0406] 14 77-6 1.3022| 12 83.5 TePo Us| ene 80.0 1.1775] 15-16] 78.6 1.0276] 15-16] 77.0 1.8278| 15 63.0? 1-4453| 45 79-7 1.2636] 15 79.7 1.0744] 15-16] 78.0 1.0360 | 15-16] 77.4 MgSOg | 1.2744|15-16| 83.2 as 1.0680 | 15-16} 77.8 MneSO4] 1.1119} 15-16} 79.1 s 1.0329] 15-16] 77.3 1.3981 | 15-16] 833 1.2830 | 15-16] 80.7 1.1039 | 15-16] 77.8 * This determination of the capillary constants of liquids has been the subject of many careful experiments, but the results of the different experimenters, and even of the same observer when the method of measurement is changed, The values here quoted can only be taken as approximations to the actual values for the do not agree well together. liquids in a state of purity in contact with pure air. In the case of water the values given by Lord Rayleigh from the wave length of ripples (Phil. Mag. 1890) and by Hall from direct measurement of the tension of a flat film (Phil. Mag. 1893) have been preferred, and the temperature correction has been taken as 0.141 dyne per degree centigrade. The values for alcohol were derived from the experiments of Hall above referred to and the experiments on the effect of temperature made by Timberg (Wied. Ann. vol. 30). The authority for a few of the other values given is quoted, but they are for the most part average values derived om a large number of results published by different experimenters. + From Volkmann (Wied. Ann. vol. 17, p. 353). SMITHSONIAN TABLES. 128 TABLES 143-145. TENSION OF LIQUIDS. TABLE 143. — Surface Tension of Liquids.* Surface tension in dynes per cen- timetre of liquid in contact with — Specific gravily. Mercury. Water . . : : 1.0 oO | 0.0 (392) Mercury oO . : ; , : 13.543 7 392.0 Bisulphide of carbon : : ; 1.2087 30.5 41.7 (387) Chloroform . , : : : : 1.4878 31. 26.8 (415) Ethyl alcohol : 0.7906 - 304 Olive oil : : : 2 : : : 0.9136 : 18.6 B07 Turpentine . : ; . , 0.8867 Tiss 241 Petroleum. ; : : ; 5 ; 9.7977 (28.9) 271 Hydrochloric acid ; ‘ : : 1.10 - (392) Hyposulphite of soda solution 1.1248 - 429 “Sy bb NW co a TABLE 144. — Surface Tension of Liquids at Solidifying Point.t Tempera- Tempera- ture of ture of Substance. solidifi- cation. Cent.° Surface tension in Ss oy: tension in ubstance. solidifi- dynes per b aor dynes per | centimetre. Cent. | centimetre. Surface Platinum. . | 2000 1691 Antimony. ; 432 249 Gold. : 1200 1003 Borax . : % 1000 216 TAKER 36 : 360 877 Carbonate of soda 1000 210 Tin c : 230 599 Chloride of sodium = 116 Mercury - | —40 588 Water . : : : oO ead 330 457 Selenium. : : 217 Silver . 1000 427 Sulphur : : III sismuth 2605 1390 Phosphorus . 43 Potassium 53 371 Wiakcl 63 Sodium go 258 TABLE 145. — Tension of Soap Films. Elaborate measurements of the thickness of soap films have been made by Reinold and Rucker.|| They find that a film of oleate of soda solution containing 1 of soap to 70 of water, and having 3 per cent of IKNOgs added to increase electrical conductivity, breaks at a thickness varying between 7.2 and 14.5 micro-millimetres, the average being 12.1 micro- millimetres. The film becomes black and apparently of nearly uniform thickness round the point where fracture begins. Outside the black patch there is the usual display of colors, and the thickness at these parts may be estimated from the colors of thin plates and the refractive index of the solution (wzde Newton’s rings, Table 146). When the percentage of K NO; is diminished, the thickness of the black patch increases. For example, KNOg id I 0.5 0.0 Thickness = 12.4 13.5 14.5 22.1 micro-mm. A similar variation was found in the other soaps. It was also found that diminishing the proportion of soap in the solution, there being no KNOs dissolved, increased the thickness of the film. I part soap to 30 of water gave thickness 21.6 micro-mm. I part soap to 40 of water gave thickness 22.1 micro-mm. I part soap to 60 of water gave thickness 27.7 micro-mm. I part soap to 80 of water gave thickness 29.3 micro-mm. * This table of tensions at the surface separating the liquid named in the first column and air, water or mercury as stated at the head of the last three columns, is from Quincke’s experiments (Pogg. Ann. vol. 130, and Phil. Mag. 1871). The numbers given are the equivalent in degrees per centimetre of those obtained by Worthington from Quincke’s results (Phil. Mag. vol. 20, 1885) with the exception of those in brackets, which were not corrected by Worthington; they are probably somewhat too high, for the reason stated by Worthington. The temperature was about 20° C. t Quincke, ‘‘ Pogg. Ann.” vol. 135, p. 661. + It will be observed that the value here given on the authority of Quincke is much higher than his subsequent measurements, as quoted above, give. | ‘‘ Proc. Roy. Soc.” 1877, and “ Phil. Trans. Roy. Soc."? 1881, 1883, and 1893. Norte. — Quincke points out that substances may be divided into groups in each of which the ratio of the surface tension to the density 1s nearly constant. Thus, if this ratio for mercury be taken as unit, the ratio for the bromides and iodides is about a half: that of the nitrates, chlorides, sugars, and fats, as well as the metals, lead, bismuth, and antimony, about 1; that of water, the carbonates, sulphates, and probably phosphates, and the metals platinum, gold, silver, cadmium, tin, and copper, 2}; that of zinc, iron, and palladium, 3; and that of sodium, 6, SMITHSONIAN TABLES. 129 TABLE 146. NEWTON’S RINGS. Newton's Table of Colors. The following table gives the thickness in millionths of an inch, according to Newton, of a plate of air, water, and g g ‘ ‘ : : 5 glass corresponding to the different colors in successive rings commonly called colors of the first, second, third, etc., orders. Thickness in Thickness in millionths of an Col millionths of an = sich for . olor inch for — calor sare ga Color for re- | for trans- mS ere : flected light. | mitted eae light. Color for re- flected light. Very black — O. : : Yellow. Black”. 5.) Wibiter: Beginning Red. .. of black . = Bluish red Blue. .| Yellowish FEC need ieee : : . | Bluish White . .| Black. . : : : green — Yellow. .| Violet .| 7. : : Green . .| Red . Orange . — 3 : ; Yellowish Red: ire PBIUe Fm.) 10: : : green. “= Red. . .| Bluish Violet. =| White |. \)11: t : green Indigo. . _ : Blue . .| Yellow .|14. : : . | Greenish Green pty eapedy acus.t| lc: : : blue. .| Red . Yellow. .| Violet . : ‘ : Rediy ccc) | (Gerlach. ) 7.895 IOT.4 102.59 1.16 15-790 102.5 105.17 2.55 7.990 104.6 104.59 0.076 23-685 104.0 107.76 3-43 15.980 109.3 109.18 0.106 31.580 105-5 110.34 4:39 39-950 124.4 122.96 1.170 39-475 107.2 112.93 5.07 79.900 149.8 145.92 2.060 SMITHSONIAN TABLES. 132 we TABLE 147. CONTRACTION PRODUCED BY SOLUTION. Per cent of contraction. Grammes of the salt in 100 of water. Observed volume. Calculated volume. Ca(NOs)o. M. W.= 163.68. Density = 2.36 (Clarke). (Gerlach.) 1.637 3-274 4.910 6.547 8.184 16.3608 32-7 36 49.104 65.472 81.840 100.45 100.90 IO1.35 101.85 102.30 104.70 109.90 115-55 121.50 127.65 100.69 101.39 102.08 102.77 103.47 100.94 113.87 120.81 127.74 134.68 Ba(NOs)o. M. W. = 260.58. Density = 3.23 (Clarke). (Gerlach.) 100.81 101.61 102.42 Sr(NOs)e: M. W. =210.98. Density =2.93 (Clarke). (Gerlach.) 100.48 100.95 IOI.40 101.95 102.45 104.95 110.20 116.15 Pb(NOs)2. M. W. = 165.09. Density = 4.41 (Clarke). (Gerlach.) 16.509 33-018 82.545 jp 102.4 105.1 114.0 103-74 107-49 118.72 K,CO3. M. W. = 137.93. Density 2.29 (Clarke and Schroeder). (Gerlach. ) 103.01 106.02 109.08 112.05 130.12 142.16 6.897 13-793 20.689 27.586 68.965 96.551 100.96 102.22 103.78 105.44 118.20 128.10 Se 4.52 8.695 Grammes of the salt in 100 of water. Calculated volume. Observed Per cent f volume. oO contraction. NaeCOs. M. W. = ros.83. Density 2.476 (Clarke and Schroeder). (Gerlach. ) 100.00 100.44 101.06 102.14 104.27 106.41 5.292 10.582 15.875 K,SO,4. M. W. =173-90. Density 2.647 (Clarke). (Gerlach.) 101.94 103-29 (N H4)oSO4. M. W. = 131.84. Density 1.762 (Clarke). (Schiff. ) 102.92 105.96 109.20 112.60 135-20 154.50 103-74 107.48 112.26 114.97 137-42 156.13 FeSQ,. M. W.= 151.72. Density 2.99 (Clarke). MgSO,. M. W.=197.6. Density 2.65 (Clarke). * 5-988 11.976 17.964 23.952 102 26 104.52 106.78 109.04 100.13 100.40 101.26 102.10 Na,SO,. M. W. = 141.80. Density = 2.656 (Clarke). (Gerlach. ) 100.96 102.26 102.67 105-34 * Authority not given. SMITHSONIAN TABLES. 133 TABLE 147. CONTRACTION PRODUCED BY SOLUTION. | Grammes of Observed Calculated Per rare Grammes of Observed Calculated Per cent the salt in , ° the salt in of 100 of water. volume. volume. contraction. || 100 of water. volume. volume. contraction. ZnSQ,. KC.H30,. M. W.= 160.72. Density 3.49 (Clarke). M. W. = 97.90. Density = 1.472 (Gerlach). * (Gerlach.) 8.036 100.06 102.30 ; 9-79 105.2 106.65 1.36 16.072 100.44 104.61 . 19.58 110.5 113.30 2.47 24.108 101.08 106.91 ; 48.95 127.3 133-26 4-47 32.144 101.90 109.21 : 97-90 156.4 166.51 6.07 40.180 102.86 111.51 . Al,Ko(SO4)4- K.CyH 405. M. W.= 128.99. Density = 2.228 (Clarke). M. W.= 225.72. Density 1.98 (Gerlach). (Gerlach. ) (Gerlach. ) 6.450 100.58 102.90 2.25 22.572 108.8 111.39 t 45-144 118.3 122.79 67.716 128.2 134.18 NaC.H,0s.. 90.288 138.7 145-58 M. W.= 81.85. Density = 1.476 (Gerlach). 112.860 149.2 156.97 135-432 159.7 168.36 (Gerlach. ) 158.004 170.6 179.76 8.185 104.1 105.55 16.360 108.3 111.09 Pb(C2H30e)s. NaCyH 40g. . = 162.06. Density 3.251 (Schroeder). M. W. = 193.62. Density 1.83 (Gerlach). (Gerlach. ) (Gerlach.) ———— | —_——— 16.206 104.7 32.412 109.5 81.030 124.6 TABLE 148. CONTRACTION DUE TO DILUTION OF A SOLUTION.t The first column gives the name of the salt dissolved, the second the amount of the salt required to produce saturation and the third the contraction produced by mixing with an equal volume of water. Parts of an- Parts of an- Water with equal volume | hydrate salt | Contraction || Water with equal volume | hydrate salt | Contraction of saturated solution of | dissolved by | when mixed. of saturated solution of | dissolved by | when mixed. following salts. 100 parts of Per cent. following salts. roo parts of Per cent. H,O at 10° C. H.Oat 10° C. KCl KeSO,4 KNO3. KoC( dg NaCl . NaeSO4 NaN¢ dg NaeCOg ° . . . NH,Cl ; : ; Pb(NOs)2 (NH,4)2SO, . * Authority not given. t R. Broom, “ Proc. Roy. Soc. Edin.” vol. 13, p. 172. SMITHSONIAN TABLES. 134 TaBLe 149. FRICTION. The following table of coefficients of friction / and its reciprocal 1/f, together with the angle of friction or angle of repose ¢, is quoted from Rankine’s ‘‘ Applied Mechanics.” It was compiled by Rankine from the results of General Morin and other authorities, and is sufficient for all ordinary purposes, Material. Wood on wood, dry a“ “ “ soapy . Metals on oak, dry “ce “ “ wet “ “ce soapy “elm, dry Hemp on oak, dry “oe “ wet Leather on oak “metals, dry . “ “ wet. “ “ greasy “ “ oily Metals on metals, dry . “ce “ “ee wet a Smooth surfaces, occasionally greased . § continually greased . Y e best results Steel on agate, dry * “ce “ “cs oiled * r Tron on stone Wood on stone ; 7 ; : 5 Masonry and brick work, dry ; : : .60-. : s 33-0-35.0 i “damp mortar 36.5 ondry clay . : : : : : : ; 27.0 “ moist clay . : ; 2 : : =38 : 18.25 Earth on earth , : ; ; : ; ; : : : i 14.0-45-0 uae dry sand, clay, and mixed earth . .38-. z : 21.0-37:0 damp clay . E : ; F : E 45-0 wet clay. : . 7 3 : 17.0 shingle and gravel . : : SI-1. é : 39.0-48.0 * Quoted from a paper by Jenkin and Ewing, “ Phil. Trans. R. S.”? vol. 167. In this paper it is shown that in cases where “static friction” exceeds “ kinetic friction’ there is a gradual increase of the coefficient of friction as the speed is reduced towards zero. SMITHSONIAN TABLES. 135 TaBLE 150. VISCOSITY. The coefficient of viscosity is the tangential force per unit area of one face of a plate of the fluid which is required to keep up unit distortion between the faces. Viscosity is thus measured in terms of the temporary rigidity which it gives to the fluid. Solids may be included in this definition when only that part of the rigidity which is due to varying distortion is considered. One of the most satisfactory methods of measuring the viscosity of fluids is by the observation of the rate of flow of the fluid through a capillary tube, the length of which is great in compari- son with its diameter. Poiseuille * gave the following formula for calculating the viscosity coef- rhrts 5 ; - ficient in this case: p= gee where /# is the pressure height, ~ the radius of the tube, 8 the density of the fluid, v the quantity flowing per unit time, and Z the length of the capillary part of the tube. The liquid is supposed to flow from an upper to a lower reservoir joined by the tube, hence % and / are different. The product 4s is the pressure under which the flow takes place. Hagenbach ¢ pointed out that this formula is in error if the velocity of flow is sensible, and sug- gested a correction which was used in the calculation of his results. The amount to be sub- v= tracted from /, according to Hagenbach, is ——, where g is the acceleration due to gravity. a ay rey Gartenmeister } points out an error in this to which his attention had been called by Finkener, 2 and states that the quantity to be subtracted from 4 should be simply “; and this formula is or o used in the reduction of his observations. Gartenmeister’s formula is the most accurate, but all of them nearly agree if the tube be long enough to make the rate of flow very small. None of the formule take into account irregularities in the distortion of the fluid near the ends of the tube, but this is probably negligible in all cases here quoted from, although it probably renders the results obtained by the “ viscosimeter”’? commonly used for testing oils useless for our purpose. The term “ specific viscosity ” is sometimes used in the headings of the tables; it means the ratio of the viscosity of the fluid under consideration to the viscosity of water at a specified temperature. TABLE 150.—Specific Viscosity of Water at different Temperatures relative to Water at 0° C. Authorities. Absolute value in yiGass Poiseuille. Graham. Rellstab. | Sprung. : Slotte. units. 100.0 : 0.0178§ 85.3 } : 0.0151 73-5 3- 0.0131 63-0 : 63. 0.0113 Goes : : : 0.0100 48.7 : - 0.0089 45.0 : : : 0.0080 40.0 s : 0.007 2 37.2 : : : : 0.0066 34.5 : 5 0.0061 31.2 ; : 0.0056 * ‘Comptes rendus,” vol. 15, 1842. ‘ Mém. Serv. Etr.’’ 1846. t “ Poge. Ann.” vol. 109, 1860. t “ Zeits. fiir Phys. Chim.”* vol. 6, 1890. § The value 0.0178 is taken from a paper by Crookes (Phil. Trans. R. S. L. 1886), where the coefficient is given as p.—=0.0177931P, where P—!'= 1 + .0336793 T + .00022099367"%, where 7 is the temperature of the water in degrees Centigrade. The numbers in the table were calculated not from the formula but from the numbers in the column headed ‘‘ mean value.’’ SMITHSONIAN TABLES. 130 TaBLes 151-153. VISCOSITY. TABLE 151.— Solution of Alcohol in Water.” Coefficients of viscosity, in C. G. S. units, for solution of alcohol in water. Percentage by weight of alcohol in the mixture. 16.60 34.58 43-99 53-36 75:75 87-45 99-72 0.0453 | 0.0732 | 0.0707 | 0.0632 | 0.0407 | 0.0294 | 0.01 80 0351 0558 0552 0502 0344 0250 0163 0231 0435 0438 -0405 0292 0223 0145 .0230 0347 0353 0332 0250 0195 .0134 0193 .0283 0280 .0276 0215 .O172 .O122 0.0163 | 0.0234 | 0.0241 | 0.0232 0.0187 | 0.0152 | 0.0110 O14 0196 .0204 0198 0163 0135 .0100 0122 .0167 .O174 .OI7I 0144 0120 .0092 0108 0143 0150 0149 .O127 .O107 .0084 .0095 0125 .O131 .0130 0113 .0097 .0077 0.0085 | 0.0109 | O.OII5 | 0.0115 | 0.0102 0.0088 | 0.0070 .0076 .0096 0102 .O102 00g .0086 .0065 .0069 .0086 .009I .0092 .0083 .0073 .0060 The following tables (152-153) contain the results of a number of experiments in the viscosity of mineral oils derived Roe petroleum residues and used for lubricating purposes. f TABLE 152. — Mineral Oils.+ TABLE 153. — Mineral Oils. I. Sp. viscosity. Water at 207 Gia. ° Flashing point a ° Burning point oO Viscosity at 19° C., water atrg°C. ° Flashing Q point. ° Burning rs) CO “I Cylinder oil . Machine oil . Wagon oil “ cc = es me Nt Wwiunikhm -_™ Naphtha residue Oleo-naphtha Oleonid ce best quality bn N me NbN Nb WN Olive oil Whale oil “ “ * This table was calculated from the table of fluidities given by Noack (Wied. Ann. vol. 27, p. 217), and shows a ea for a solution containing about 4o per cent of alcohol. A similar result was obtained for solutions of acetic acid. t Table 152 is from a paper by Engler in Dingler’s “‘ Poly. Jour.” vol. 268, p. 76, and Table 153 is from a paper by Lamansky in the same journal, vol. 248, p. 29. _The very mixed composition of these oils renders the viscosity a very uncertain quantity, neither the density nor the flashing point being a good guide to viscosity. t The different groups in this table are from different residues. SMITHSONIAN TABLES. 137 TABLE 154. VISCOSITY. This table gives some miscellaneous data as to the viscosity of liquids, mostly referring to oils and paraffins. The viscosities are in C. G. S. units. Coefficient Temp. G. % of Sparel Authority. viscosity. Cent. © zi Ammonia . . ; , , 0.0160 11.9 Poiseuille. oe 0.0149 14.5 sf Anisol . : O.O1II 20.0 Gartenmeister. Glycerine. : . , 42.20 ; Schottner. - ; . : 25.18 . as , ; : : 13.87 ; : , ; 8.30 : a : ; ; : 4.94 : Glycerine and water 7 ; 7.437 3 s 1.021 0.222 0.092 “ “ 0.0219 ; Arrhenius. 0.0184 |—20 Koch. 0.0170 0.0 se 0.0157 20.0 0.0122 | 100.0 0.0102 | 200.0 0.0093 | 300.0 Meta-cresol . , : ‘ 0.1878 20.0 Gartenmeister. Olive oil . 2 : 3.2653 t 0.0 Reynolds. Paraffins : Decane ‘ 0.0077 Dodecane . , ; 0.0126 Heptane . : : 0.0045 Hexadecane ; : 0.0359 Hexane. : : 0.0033 Nonane : : : 0.0062 Non Bartolli & Stracciati. “e “ NNN dS PQ REG WN dn OWL Octane . : 0.0053 Pentane. : : 0.0026 Pentadecane ° . 0.0281 Tetradecane : ; 0.0213 Tridecane . : 0.0155 Undecane . : : ©0095 ROS PAD NWO 008 NNNONNN Petroleum (Caucasian) 0.0190 Petroff. “ “ Rape oil : 3 ; i O. E. Meyer. * Calculated from the formula « = .017 — .000066f +- 0000002142 — .00000000025¢3 (vide Koch, Wied. Ann. vol. 14. ps'k); + Given as = 3.2653 e—-9l237, where 7 is temperature in Centigrade degrees. SMITHSONIAN TABLES. 138 TABLE 155. VISCOSITY. This table gives the viscosity of a number of liquids together with their temperature variation. The headings are temperatures in Centigrade degrees, and the numbers under them the coefficients of viscosity in C. G. S. units.* Liquid. Acetone’. . . Acetates: Allyl Amyl Ethyl Methyl. Propyl . Acids: t Acetic Butyric Formic Propionic Salicylic . Valeric Alcohols: Allyl. Amyl Butyl Ethyl Isobutyl Isopropyl . Methyl . Propyl . Aldehyde . Aniline . Benzene Cae Benzoates: Ethyl. . Methyl . Bromides: Allyl Ethyl . Ethylene . Carbon disulphide Carbon dioxide (ard) Chlorides: Allyl ee : Chloroform . . : iBthene : Ethyl sulphide 2 Iodides: Allyl . Ethyl . Metaxylol . Nitro benzene “butane ethane. “propane . «toluene Propyl aldehyde Toluene Temperatures Centigrade. Authority. Pribram & Handl. Gartenmeister. “ Rellstab. Pribram & Handl. Rellstab. Pribram & Handl. “ “ Gartenmeister. “ Rellstab. Wijkander. Rellstab. Pribram & Handl. Wijkander. Warburg & Babo. Pribram & Handl. * Calculated from the specific viscosities given in Landolt & Boernstein’s ‘‘ Phys. Chem. Tab.” p. 289 e# seg., on the assumption that the coefficient for water at 0° C. is .o178. + For inorganic acids, see Solutions. SMITHSONIAN TABLES. 139 TABLE 156. VISCOSITY OF SOLUTIONS. This table is intended to show the effect of change of concentration and change of temperature on the viscosity of a specific viscosity X 100 is given for two or more densities and for several tem- solutions of salts in water. peratures in the case of each solution. » stands for specific conductivity, and ¢ for temperature Centigrade. Percentage by weig ht of sait in solution. Density. Ba(NOs)2 CaCle Cd(NOs)e “ CdSO4 Co(NOs)e “ CoSO4 Cu(N Os)o “ CuSO, i Authority. Sprung. “ee Wagner. Sprung. SMITHSONIAN TABLES. 140 TABLE 156 VISCOSITY OF SOLUTIONS. Percentage by weight 5 , of salt in Density. Authority. solution. 8.37 1.067 ? 4.8] 2 : Wagner. 1.116 ae 1.178 1.065 1.130 1.200 2 Ow Boo AUN B: Rs 6.32 12.19 17.60 5 9. G2 G2 G2 Od N™N af QbHH Slotte. Sprung. NEB NOar J “SIN ONO “SIDR WNH FH AAW Own SE Seay Ano Oo Slotte. “ Sprung. “ “ Mg(NOs)e2 5 : || Sr. : : Wagner. “ “ ‘ “ MgSO4 E : 5 Sprung. “ MgCrOg “ MnCle SMITHSONIAN TABLES. TABLE 156. VISCOSITY OF SOLUTIONS. Percentage | by weight of salt in solution. Density. Mn(NQOs)o 3 1.148 as : 1.323 ‘ : 1.500 MnSO4 ey 1.147 cc } 1.257 1.306 Pe OAD WO oA oO On! NO On bo Ww “I OWE WRU ao. NOG oO OV a nb CONT in COnNINI EA Coe OOnmN nib Oo Soyo OfW _ mon eee ee NONnD tn GOI WD QO DY _ tN COL) \O RTOS NOOO Nv wee Oo “+ nO © oe NOM BWM nw © 2 Od Wa &) ON AND SINTO 4 Oa NH4Br NNN HU &A ROD fps “ WOW NH4NOz3 Cn ADA AON = me NTI ONO (NH4)2SO4 ° ea oO “ SMITHSONIAN TABLES. TaBLE 156. VISCOSITY OF SOLUTIONS. Percentage by weight of salt in solution. Density. Authority. (NH4)oCrO4 10.52 Slotte. 19.75 - 28.04 (NH4)eCreO7 ‘ 6.85 ne 13-00 19.93 II.45 22.69 30.40 Ni(NOs)2 16.49 7%: 30.01 : 40:95 NiSO, 10.62 18.19 i 25-35 Pb(NOs)z 17.93 32.22 Sr(NOs)a 10.29 “ ZnCle “cc Zn(NOs)e ZnSO4 “ SMITHSONIAN TABLES. TABLE 157. SPECIFIC VISCOSITY.* Normal solution. + normal. } normal. $ normal. Dissolved salt. Authority. Density Specific viscosity Density. Specific viscosity Density. Specifie viscosity. Specific viscosity Acids : ClpOs ‘ .0143 | I. 1.0074 | 0.999 | Reyher. HCl. . : 2 : 0045 | I. 1.0025 | 1.009 i HClO [ 0126 | 1. 1.0064 | 1.006 HNOg . .|1. ‘ : .0086 | I. 1.0044 | 1.003 HeSQ4 - | 2. : : 0074 | I. 1.0035 | 1.008 = ° oO wo “ ° to | Aluminium sulphate | r. t 2 .0138 | I. .0068 | 1.038 Barium chloride. . : : .0226 | I. O14 | 1.013 "nitrate sya : 0259 | I. .0130 | 1.005 Calcium chloride. | 1.04. : : .O105 | I. .0050 | I.017 ‘s nitrate. .| 1, ; : SOLS Ty |e .0076 | 1.008 Cadmium chloride . | 1. eRe ‘ .O197 | I. .0098 | 1.020 nitrate .| I. -10 : 0249 | I. .O11g | 1.018 se sulphate. | 1. =345'] I. 0244 | I. .0120 | 1.033 Cobalt chloride . .| I. : .028 .O144 | I. .0058 | 1.023 i onitrate mes =-a|pl.O720" (ire .036¢ 0184 | I. 0094 | 1.018 sulphate 204) 01: : .038 0193 | I. -OITO | 1.040 Copper chloride. .| 1.0624 | I. d .O158 | I. .0077 | 1.027 “ nitrate. .. | 1.0715 : 4 .O185 | I. .0092 | 1.018 ‘= sulphate | 31.0; . : 0205 | I. .0103 | 1.038 Lead nitrate: =) #1) 241.06 ; : .0351 | I. .O175 | 1.007 Lithium chloride. | 1.02 s : 0062 | I. 0030 | 1.012 hs sulphate .| TI. 2 7 : OL L5H} idic -0057 | 1.032 Magnesium chloride | 1. : ‘ .OOOI | I. .0043 | 1.021 5 nitrate . | 1.0512 | 1.17 : -0130 | I. .0006 | 1.020 of sulphate | 1.058 ; .02¢ .O1 52 | 1.078 | 1.0076 | 1.032 Manganese chloride | 1.0513] I. : 0125 | 1.048 | 1.0063 | 1.023 < nitrate . 183 | 1.03: 0174 | I. 0093 | 1.023 sulphate | 1.0728 | I. .036 0179 | I. .0087 | 1.037 Nickel chloride . 1.0591 | I. .0308 .O144 | I. 0067 | 1.021 <° “Wnltrates % 9 ta s1-07/5 Sip LO- 0192 | I. .0096 | 1.019 “sulphate. .)| 1.0773)|\1.: .03 .O198 | I. .OO17 | 1.032 Potassium chloride . | 1.0466 | 0.98 .0235 .O1I7 .0059 | 0.993 - chromate | 1.0935 | I.113 } 1.0. 0241 .OI2I | 1.012 + nitrate .| 1.0605 | 0.975 | 1.030: O10! .007 5 | 0.992 sulphate | 1.0664 | I. : ; .O170 | I. .0084 | 1.008 | Sodium chloride. . | 1.0401 | I. E OLO7 || Mle .0056 | 1.013 “bromide. . | 1.0786 | 1.064 | 1.03¢ 0190 | I. .O100 | 1.008 «chlorate. | 1.0710 | 1.0¢ £035 0180 | I. .0092 | 1.012 Nitrate = |) T0554) "1.06 02 OTT || 1s .007I | 1.007 Silver nitrate. . . | 1.1386] 1.055 | I. 0348 | I. .0173 | I.000 | Strontium chloride . | 1.0676 | 1. 03. Lop i Addy at 0084 | 1.014 nitrate .| 1.0822 | I. 02 .0208 | I. -O104 | I.OII | Zinc chloride . . .| 1.0509} I. S08 : .O152 | I. .0077 | 1.02 © nitrate —S> s< 2 \MO750ultr ; .OIQI | 1.07 .0096 | 1.019 “ sulphate. . .| 1.0792 | I. : 1.0198 | I. 0094 * In the case of solutions of salts it has been found (wzde Arrhennius, Zeits. fiir Phys. Chem. vol. 1, p. 285) that the specific viscosity can, in many cases, be nearly expressed by the equation #—=p,”, where p, is the specific viscosity for a normal solution referred to the solvent at the same temperature, and 2 the number of gramme molecules in the solution under consideration, The same rule may of course be applied to solutions stated in percentages instead of gramme molecules. The table here given has been compiled from the results of Reyher (Zeits. fiir Phys. Chem. vol. 2, p- 749) and of Wagner (Zeits. fiir Phys. Chem. vol. 5, p. 31) and illustrates this rule. The numbers are all for 25° C. SMITHSONIAN TABLES. 144 TABLE 158. VISCOSITY OF CASES AND VAPORS. The values of « given in the table are r0® times the coefficients of viscosity in C. G. S. units. Substance. KB Authority. Substance. r c Authority. Acetone. .. . >| Puluj. Carbon dioxide .| 12.8 Schumann. a“ “ce 100.0 “ AT ume vais + .O| I Thomlinson. Sal 8 | Obermeyer. || Carbon monoxide | 0.0 Obermeyer. = Puluj. Chlorine .. .| 00 Graham. Alcohol: Methyl . 35 | Stendel. Bi Ethyl is Normal Chloroform propyl 2 Ether Isopropyl 8 Normal Ethyl iodide butyl Methyl “ . Tsobutyl Tertiary Mercury butyl s Ammonia “ “ . . . Benzene. .. . Schumann. Nivelee "G8 Gio c : Puluj. “ec oe “ “ Ge cae L. Meyer & Carbon disulphide i: Schumann. * The values here given were calculated from Koch’s table (Wied. Ann. vol. 19, p. 869) by the formula # = 489[1 + 746 (¢— 270)]. SMITHSONIAN TABLES. 145 TABLE 159. COEFFICIENT OF VISCOSITY OF CASES. The following are a few of the formule that have been given for the calculation of the coefficient of viscosity of gases for different temperatures. Value of pu. Authority. Ho (I + .002751 ¢ — .00000034 ) Holman. .000172 (I + 0027372) O. E. Meyer. .0001683 (I + .00274 7) Obermeyer. Carbon dioxide . . Ho (1 + .003725 t— .00000264 ¢2-+- .00000000417 ¢) | Holman. cs 0001414 (I + .00348 2) Obermeyer. Carbon monoxide . 0001630 (1 + .00269 ¢) Ethylene? s--sa5— 0000966 (1 + .00350/) Ethylene chloride. 0000935 (I + .00381 Z) Hydrogen . ... .0000822 (1 + .00249 2) Nitrogen . . . . | .0001635 (1 + .00269 4) Nitrous oxide (N20) 0001408 (1 + .00345 ¢) Oxygen. . . . . | .0001873 (I + .00283 7) SMITHSONIAN TABLES. TABLE 160. DIFFUSION OF LIQUIDS AND SOLUTIONS OF SALTS INTO WATER. The coefficient of diffusion as tabulated below is the constant which multiplied by the rate of change of concentration in any direction gives the rate of flow in that direction in C. G. S. units. Suppose two liquids diffusing into each other, and let p be the quantity of one of them per unit volume at a point 4, and p/ the quantity per unit volume at an adjacent point B, and x the distance from 4 to B. Then if x is small the rate of flow from A towards & is equal to & (p — p’)/x, where & is the coefficient of diffusion. Similarly for solutions of salts diffusing into the sol- vent medium, p and p/ being taken as the quantities of the salt per unit volume. The results indicate that & depends on the absolute density of the solution. Under ¢ will be found the concentration in percentage of ‘‘normal solu- tion” of the salt; under # the number of grammes of water per gramme of salt or of acid or other liquid. Substance. } ke X107 | Temp. C. Authority. Ammonia . : : : 123 : Scheffer.* ri : : : : 7 123 ; ee Ammonium chloride. . . 135 ‘ Schumeister.t ss a : : 152 7 Scheffer Barium chloride . : , : 76 : « Calcium chloride. 83 ; re o oe © 4 74 “ce “ “ f u x 79 ; “ “ . 79 : Schumeister. Cobalt chloride . s Ee Copper “ : 50 Copper sulphate : 2 24 Hydrochloric acid : 267 i Scheffer. “ “ 215 “ 195 170 161 309 245 234 213 Lead nitrate : : 70 “ “ ‘ 82 Lithium chloride : 8I Schumeister. “bromide 93 : < “ “ I0O “ iodide . : : 93 i ss Magnesium sulphate : 32 se Se o : 32 Scheffer. “cc 37 “ “ 31 a oi 39 Potassium chloride. 98 “ “ h 106 “ I 27 “ : 147 bromide : : 131 i : : : 144 iodide : : 130 “cs . 145 S : 168 nitrate : 93 sulphate . 87 Sodium chloride “ “ “ “ 97 : 106 bromide ; 5 99 iodide . : 93 _ : : 100 nitrate . : ; 2 69 carbonate. : 45 sulphate . : 76 Nitric acid . 3 s : : ; 22 < See . . . . 234 es : 206 ec 7 200 Sulphuric acid : : 124 “ “ce I 15 = h 132 a : 150 “ : 144 * “Chem. Ber.” vol. 15, p. 788. + ‘Wien, Akad. Ber.’’ vol. 78, 2. Abth. p. 957- SMITHSONIAN TABLES. 147 TABLE 161. DIFFUSION OF GASES AND VAPORS. Coefficients of diffusion of vapors in C. G. S. units. The coefficients are for the temperatures given in the table and a pressure of 76 centimetres of mercury.* Kee for vapor | ke for vapor | Ae for vapor Temp. C. diffusing into | diffusing ato diffusing Tito Vapor. 2 hydrogen. air. carbon dioxide. Acids: Formic ; ; 0.0 0.5131 0.1315 : : : : 65.4 0.7873 0.2035 ss : : ; : 84.9 0.8830 0.2244 Acetic : ; : 0.0 0.4040 0.1061 a : : s 65.5 0.6211 0.1578 SS : : : 95.5 0.7481 0.1965 Isovaleric . ; : 0.0 0.2118 0.0555 Ue . 0.3934 0.1031 Alcohols: Methyl . : : ; 0.5001 0.1325 o ; : : , : 0.001 5 0.1620 ss ; : : ; Y 0.6738 0.1809 Ethyl . : ; : 0.3806 0.0994 s : : . . 0.5030 0.1372 sf : : 2 : 0.5430 0.1475 Propyl . 7 : . : 0.3153 0.0803 es ; 0.4832 0.1237 : : : : 0.5434 0.137 Butyl . : : : ; Bee eerer s¢ ; : : , 0.5045 0.1265 Amyl . ; ; ; 0.2351 0.0589 = A : : ; 0.4362 0.1094 Hexyl © =. 2 : q 0.1998 0.0499 = ; : ; : 0.3712 0.0927 “ce Benzene . , : : : ; : 0.2940 0.07 51 - . A : : : i 0.3409 0.0877 , : : : : . 0.3993 O.IOII Carbon disulphide . : ; : 0.3690 0.0883 . . . . 0.4255 O.1OIS “ “ } r ee 5 i 0.4626 0.1120 Esters: Methyl acetate . : , 3 3357 0.08 52 a ef : ; ; 0.3928 0.1013 Ethyl a : ; ; : 0.2373 0.0630 a ‘ : : : 3729 0.0970 Methyl butyrate. ; : 7 0.2422 0.0640 ¢ ¢ ; . ; 0.4308 0.1139 Ethyl . : : : : 0.2238 0.0573 f* “s : : 7 ; 0.4112 0.1064 ** ‘valerate, : : : 0.2050 0.0505 i ae : ; : E 0.3784 0.0932 0.2960 0.0775 0.3410 0.0893 0.6870 0.1980 1.0000 0.2827 1.1794 0.3451 * Taken from Winkelmann’s papers (Wied. Ann. vols. 22, 23, and 26). The coefficients for 0° were calculated by Winkelmann on the assumption that the rate of diffusion is proportional to the absolute temperature. According to the investigations of Loschmidt and of Obermeyer the coefficient of diffusion of a gas, or vapor, at o° C. and a pressure of 76 centimetres of mercury may be calculated from the observed coefficient at another temperature and pressure by the formula hy =hy (22)" oe where 7 is temperature absolute and # the pressure of the gas. The 7 exponent 7 is found to be about 1.75 for the permanent gases and about 2 for condensible gases. The following are examples: Air—CO,, x—=1.968; CO,—N,O, x=2.05; CO.—H, #=1.742; CO—O, x=1.785; H—O, = 1.755; O—N, x=1.792. Winkelmann’s results, as given in the above table, seem to give about 2 for vapors diffusing into air, hydrogen or carbon dioxide. SMITHSONIAN TABLES. 148 TABLE 162. COEFFICIENTS OF DIFFUSION FOR VARIOUS CASES AND VAPORS." Gas or vapor diffusing. Gas or vapor diffused into. . Ce” ortcent. Authority. Air “a Carbon dioxide . “ o Carbon disulphide Carbon monoxide “es it Ether 7 Hydrogen Nitrogen Oxygen “ Sulphur dioxide Water : : “ Carbon dioxide Oxygen Air oe Carbon monoxide “ oe Ethylene Hydrogen Methane Nitrous oxide Oxygen Air ‘ ; Carbon dioxide Ethylene Hydrogen Oxygen “ee Air , Hydrogen Air 3 : Carbon dioxide “monoxide Ethane. Ethylene Methane Nitrous oxide Oxygen Oxygen Carbon dioxide Hydrogen Nitrogen Hydrogen Air “cc Hydrogen (oMomo mo momomemeomomemeomeomeomemeomemememe) mmmMOdDOAODDIDGIDDIUOIDIOIODO ~ 0.1343 0.1775 0.1423 0.1 360 0.1405 0.1314 0.1006 0.5437 0.1465 0.0983 0.1802 0.0995 0.1314 O.1164 0.6422 0.1802 0.1872 0.0827 0.3054 0.6340 0.5354 0.6488 0:4593 0.4863 0.6254 0.5347 0.6788 0.1787 0.1357 0.7217 0.1710 0.4828 0.2390 0.247 5 0.8710 Obermayer. “ Loschmidt. Waitz. Loschmidt. Obermayer. a“ Loschmidt. “ Stefan. Obermayer. “ Loschmidt. “se Obermayer. Stefan. “ Obermayer. “ Loschmidt. Obermayer. Loschmidt. Guglielmo. “ “ * Compiled for the most part from a similar table in Landolt & Boernstein’s “ Phys. Chem. Tab.” SMITHSONIAN TABLES. 149 TABLE 163. OSMOSE. The following table given by H. de Vries* illustrates an apparent relation between the isotonic coefficient +t of solu- tions and the corresponding lowering of the freezing-pomt and the vapor pressure. The freezing-points are taken on the authority of Raoult, and the vapor pressures on the authority of Tammann.} Molecular owering of the vapor pressure X 1000. Molecular I lowering of the freezing point X roo. Tsotonic Substance. coefficient X 100. Glycerine. : : ; CsHsOs 178 7 Cane sugar . , : - | Cy2He20y4 188 185 Tartaricacid . : : C4606 202 195 Magnesium sulphate . : MgSO4 196 192 Potassium nitrate 5 : KNOgs 300 308 Sodium nitrate. : ; NaNO3 300 337 Potassium chloride. : KCl 287 336 Sodium chloride . c : NaCl 305 351 Ammonium chloride . ‘ NH.Cl 300 348 Potassium acetate : -| KC.H302 300 345 Potassium oxalate. : KoCeO4 393 450 Potassium sulphate. , KeSOq4 392 390 Magnesium chloride . : MgCle 433 488 Calcium chloride : : CaCle 433 466 TABLE 164. OSMOTIC PRESSURE. The following numbers give the result of Pfeffer’s § measurement of the magnitude of the osmotic pressure for a one per cent sugar solution. The result was found to agree with that of an equal molecular solution of hydrogen. The value for the hydrogen solution is given in the third column of the table. Temperature | Osmotic pressure Cc. in atmospheres. 0.649 (1 ++ .00367 2) 6.8 0.664 | E3:7; 0.691 | 14.2 0.671 | E525 0.634. 22.0 0.721 | 32.0 0.716 30.0 0.746 * “ Zeits. fiir Phys. Chem.” vol. 2, p. 427. + The isotonic coefficient is the relative value of the molecular attraction of the different salts for water or the relative value of the osmotic pressures for normal solutions. In the above table the coefficient for KNO, was taken . as 3 arbitrarily and the others compared with it. The concentrations of different salts which give equal osmotic pres- sures are called by Tammann and others isosmotic concentrations; they are sometimes called isotonic concentrations. The reciprocals of the numbers of molecules in the isotonic concentrations are called by De Vries the isotonic coeffi- cients. $+ See also Tammann, ‘‘ Wied. Ann.” vol. 34, p. 315. | § Winkelmann’s ‘‘ Handbuch der Physik,” vol. 1, p. 632. | SMITHSONIAN TABLES. | 150 | TABLE 165. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT. The last four columns were calculated from the data given in the second column and the density of mercury. . nn s w” : $ 3 : : % a ; —. - o *@. 53 8 S x c oo “a op e i go 5 ae 5 a 2 A as 3 ea = 8 a <5 oe i ar 9 * ao = o hs oom m for) Y Q vo vB vo v VE oh ov * oe E-s n. eo uO aS B-s is uy Es ae ea vs ae aE Be == wo 36 Be E &°O Ee £0 Do av sc i “4s Doe ao Se ng us vo fo S:= a) 26 Ro Lo on vo vs = Oo a a a Py o A A a 6.254 | 0.0890 | 0.181 | 0.0061 ; ; 74.653 162] 0.07 O ° & E e Oo I 6.716] .0955] .194] .0065] 33.5 d 78.675 : .076 2 1025] .209| .0070 d A 82.947 : 080 3 -IIOO| .224] .0075 : . 87.488 533] .085 4 1180] .240] .0o80 : : 92.165 Q 089 5 .1263 | 0.257 | 0.0086 F 97.059 . 0.094 6 .1354| .276] .0092 .16| 102.184 : .099 7 1452] .295| .0099 : .09 | 107.528 -II4| .104 8 1551] .316| .o107] 46. 33.20] 113.115 : 109 9 .1657| .338| -O114 37.50} 118.962 444] .115 10 .1773| 0.361 | 0.012 .98|125.05 |tI. : 0.121 II 1893] .386] .o13 8 .66} 131.42 |1.8 8 12 12 | Io. : .2023| -412| .o14 : .54|138.04 | 1. 134 13 jII. : 2158] .439| -O15 : .64}144.98 | 2. : 140 TAe Los ; .2303| .469| .o10 .95| 152.20 | 2. : 147 15 2 2456] 0.500 | 0.017 .48}159.72 | 2.27 0.155 16 | 13 ; 2018] .533| .018 23.24|167-55 | 2.39 16 17 |14. : .2789| .508| .o19 .25]/175-72 | 2.50 .170 18 ]15. ; .2970| .605] .020 51/184.23 | 2.62 178 19 | 10. 3162] .644| .022 2.02] 193.08 | 2.75 .187 20 | 17. : 0.3363 | 0.685 | 0.023 .79| 202.29 | 2.88 0.196 21 |18. : +3577 728} .02 3.01 +205 22 3802] .774] .026 3.16 215 23 .4040| .822] .028 3.30 22 24 -4289) .873 3-46 235 25 0.927 62 0.246 i 984 78 257 2 1.044 95 .267 28 -106 1 281 29 “172 32 -494 3: a 3: 4. 4: 30 0.6101 | 1.242 2 316.90 | 4.51 0.306 31 133-41 45. 6461] .315 2 330-90 | 4.71 320 B2135- .074| .6838] .392 2 4-91 334 33) [S75 ; 1234) -473 2 5-12 “349 34 |39- 798!) -7655} -558 ° 5-35 304 35 /4I. : 0.810 | 1.647 288. 5-58 0.380 36 144-2 093 855 | -740 300.8 5.52 -396 37 [4 : 903 | .838 B13) 6.06 414 38 149. : 954 | .94I 326.81 6.32 -430 39 152. ; 1.007 | 2.049 6.58 448 SMITHSONIAN TABLES. TABLE 165. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT. . | - . e o * 2 0 52 = = S : - 3 7 uw O 5 ae Z -5 | -S] & Oo ac ahs 2) ae rae ° one YE = 25 | 2a ° ° 25 ar wi 25 La a) ge | BS | Be) ge) Se4 oc) el eee ees | ee) eee P| #3 | gs | 38) 80) 8a) 6 | Beco eee ioe) fo | ee - iv Oo Ay Ay ay a H a Oo py Ay Ay 80] 354.64) 482.15| 6.85 | 13.96) 0.446}176.0|| 120} 1491.28 | 2027.48 28.85| 58.71} 1.962 81] 369.29| 502.07] 7.14]14.54| .486]177.8]| 121]1539.25|2092.70|29.78| 60.61|2.02 $2] 354.44 522.67) 7-44]15-14| .506]179.6|| 122]1588.47 | 2159.62) 30.73) 62.54] .091 83] 400.10] 543.96] 7.74/15.75] -526]181.4|| 123]1638.96] 2228.26) 31.70) 64.53] .157 84] 416.30] 565.99) 8.05|16.39| .548]183.2|| 124] 1690.76| 2298.69|32.70| 66.56] .22 85] 433.04] 588.74] 8.37|17.05/0.5701185.0|| 125] 1743.88 | 2370.91 | 33-72| 68.66] 2.295 86] 450.34| 612.26] 8.71|17.73]) -593]180.8)| 126]1798.35| 2444.96 34.78| 70.80] .366 87| 468.22] 636.57| 9.05|18.43] .616]188.6]| 127]1854.20| 2520.89] 35-86| 73.00] .430 88] 486.69} 661.08| 9.41/19.16| .640]180.4]| 128] 1911.47 | 2598.76] 30.97| 75-25] -515 89] 505-76] 687.61] 9.78|19.91| .665]192.2]} 129]1970.15| 2678.54|38-11| 77-57| -592 90] 525.45| 714.38] 10.16] 20.69) 0.691 }194.0|| 130} 2030.28 | 2760.29] 39.26] 79.93] 2-671 QI} 545-78| 740.31 |10.56| 21.49] .719}195.8|| 131] 2091.94] 2844.12|40.47| $2.36] .753 92 566.76 770-54 | 10.95 | 22.31 746]197.6|| 132]2155.03| 2929.89] 41.68! 84.84] .836) 93] 588.41] 799.98| 11.38) 23-17| -774]199.4|| 133]2219.69| 3017-80|42.93| 87.39] .921}2 94] 610.74| 830.34|11.81|24.04| .804]201.2|| 134]2285.92| 3107.85|44.21| 89.99] 3.008} 2 95] 633.78] 861.66) 12.26] 24.95] 0.834 |203.0|| 135] 2353.73] 3200.04|/45.52] 92.67] 3.097 96] 657.54] 893.97|12-71|25-89| -865]204.8|| 136]2423.16| 3294.43] 46.87| 95.39] .188 97| 632.03| 927.26|13.19|26.85] .897]206.6|| 137]2494.23| 3391-06] 48.24) 95.19] .282 98] 707-25) 961.59] 13-68} 27.85] .931]208.4|| 138]2567.00) 3489.99 49.65] 101.06 -378 99] 733-31| 996.98|14.18| 28.87] .965]210.2|| 139]2641.44 | 3591.29| 51.00) 103.99| -476 100] 760.00} 1033.26) 14.70| 29.92! 1.000}212.0|| 140] 2717.63 | 3694.78 | 52.55 | 106.99] 3.576 101} 787-59| 1070.78 | 15-23 |31-01| .036]213.8|| 141]2795.57 | 3800.75| 54-07|110.06] .678 102] 816.01 | 1109.41 | 15-79} 32.13] -074]215.6]| 142]2875.30] 3909.14] 55.60|113.20] .783 103] 845.28] 1149.21 | 16.35 | 33-28] .112]217.4]| 143]2956.86| 4020.03] 57.16|116.41| -890}2 104] 875.41 |1190.17|16.94| 34.46] .152]219.2]| 144] 3040.26] 4133.42 | 58-79] 119.69] 4.000} 2 105] 906.41 |1232.32/17.53| 35-69] 1.193]221.0|| 145] 3125.55 | 4249.37 |60.44|123.05] 4.113 106] 938.31 |1275-69| 18.15] 36.94] .235]222.8|| 146]3212.74] 4367.91 |62.13|/126.48)] .227 107] 971.14] 1320.32| 18.78 | 38.23] .278]224.6|| 147]|3301.87 | 4489.09] 63.86/129.99] .344 108 |1004.91 | 1366.24 | 19.44 | 39.56| .322]226.4]| 148]3392.98 | 4612.96 | 65.62|133.58] .464 109 ]1039.65 | 1413-47 |20.11 | 40.93] .368]228.2|| 149] 3486.09] 4739.55 |67-41/137-25| -587]300.2 110 }107 5.37 | 1462.03] 20.80 | 42.34] 1.415]230.0|| 150] 3581.2 | 4868.9 |69.26|141.0 | 4.7121302.0 ILL |L112.09/ 1511.97 |21.51 | 43-78| .463]231.8|] 151]3678.4 | Soo1.r |71.14/144.8 | .840]303.8 112 1149.83 1563.26|22.24|45.25] .5131233-6|| 152|3777-7 |5136.1 |73-.06/148.7 | .971]305.6 113 1188.61 | 1015.99|22.99| 46.80] .564]235.4|| 15313879-2 |5275.0 |75.02/152-7 | 5-104]307.4 114 |1228.47 | 1670.18 | 23.76] 48.37| .616]237.2|| 154]3982.8 | 5414.8 |77.03]150.8 | .240}309.2 115 }1 269.41 | 1725.84] 24.55 | 49.98) 1.670]239.0|| 155] 4088.6 | 5558.6 |79.07|161.0 | 5.380]311.0 116]1311.47 | 1783.02 |25.37 | 51.63] .726]240.8|| 156]4196.6 | 5705.5 |81.22|165.2 | .5221312.8 117 [1354-66] 1841.74 |26.20| §3.34| .7821242.6|| 15714306.9 | 5855.5 |83.29|169.6 | .6671314.6 118 |1 399.02 | 1902.05|27.06| 55.08] .841]244.4|| 15814419.5 |6008.5 |85.47|174.0 | .8151316.4 119]1 444.55 | 1963-95 | 27.94| 56.87| .go1}246.2|| 159]4534-4 |6164.7 |87.69/178.5 | -966}318.2 SMITHSONIAN TABLES. 152 TaBLe 165. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT. Pressure: inches Pressure: mm. of mercury. Grammes per sq. centimetre. Pounds per sq. Pressure: inches | of mercury. atmospheres. mm. of mercury. centimetre. of mercury. atmospheres. Pressure: Grammes per sq. Pounds per sq. Pressure: Pressure: 4651.6 4771.3 4593-4 5017-9 5145.0 195} 10519.6| 14302.7 | 203.43 414.1|13.842 383.0 196] 10746.0] 1 4609.8} 207.81 423.1/14. 1303) 84.8 197] 1097 5-0] 14921.2}212.25/432.1/14.441 386.6 198] 11209.8] 15240.4]216.77|441.3}14.749 388.4 199] 11447.5] 15563-5] 221.37 450.7 15.062] 390.2 SOW Wb mo Gs Gs G3 Os WD DAXOXONG N Qf WY = O&O 5274-5 5400.7 5541-4 5678.8 5518.9 6.940]329.0|| 200} 11689.0} rs891.9 15.380} 392.0 7.114]330-8]| 201]11934.4|16225.5 Seas 15.703} 393-8 7.291] 332.6|| 202]12153.7]| 16564.7 Be 61 479-7|16.031] 395.6 7.4721 334-4|| 203]12437.0| 16908.8] 240.54 459.6 16.364] 397-4 7.656] 336.2|| 204]12694.3] 17257.3| 245-49| 499.8|16.703} 399.2 | NwN WN be RN ee O Ce wus = Anon 5961.7 .2|11§.29| 234.1] 7.844]338-0|| 205]12955.7/17614.0| 250.53 §10.1|17.047| 401.0 | 6107.2 .1]118.11}240.4] 8.036]339.8|| 206]13221.1|17974.9| 255-07| §20.5|17. 396) 402.8 6255.5 4.7 |120.98 8.231] 341.6]| 207]13490.8] 18341.5] 260.88] 531.2|17.7 51} 404.6 6400.6 -2|123.90] 2 8.430]343-4|| 208]13764.5|18713.7| 266.18) 541.9|18.11 1,406.4 6560.6] 8919.5 120. 87 .3| 8.632]345-2|| 2009]14042.5! 19091.6| 271.55) 552.9|18.477| 408.2 8.8391347-0]| 210) 1 4324.8) 19475.4| 277-01 564.1|18.848 410.0) 9.049] 348.8]| 211] 14611.3| 19864.9| 282.58 57 5.3|19.226) 411.8 | 9.263] 350.6]| 212]14902.2|20260.5] 288. 21| 586.7 7|19.608} 41 3.6 9-481} 352-4|| 213]15197.5| 20661.9| 293-92| §98.3|19.997| 415.4 9.7031354-2]| 214]15497.2|2 3) 299.72 610.2 20.3911 417.2 6717.4] 9132.8|129.91 6877.2} 9350.0|133-00 7040.0] 9571.3}136.15 7205-7| 9796.6]1 39-35 7374-5|10026.1 |142.62 Con~rI~sI OV COI Of Cun Gob ww WN \o 7546.4|10259-7 |145.93|297-1| 9-929}356.0)| 215] 1 5801.3) 7721.4|10497-7 |149-32 | 304.0|10.150]357 .8|| 216} 16109.9 7899.5 |107 39-9|152-77 | 311-0|10.394} 359-6); 217] 16423.2 S080. 8|10986.4 156.32| 318.1 |10.033 361. 4 218 16740.9 8265.4|11237.3|159-54| 325-4 |10.876]363.2|| 219]17063.3 20.791| 419.0 | ZL] 4208) Gos G2 G2 G2 GO Wh ss O OW AM Quin mnnnt on S 8453-2|11490.0|163.47 | 332-3 |11-123]365.0|| 220} 17390.4|23643.2 8644.4|11752.5|167-17 | 340.3]11.374] 366.8 17722.1| 24094.3] 8838.8 |12016.9]170.94| 348. ‘O}LT. 630] 368.6 18058.6|24551.8 188] 9036.7 |12285.9|174.76) 355.8) 11. 885 370-4 18399.9|25015-8|355- 9238.0|12559.6|178.65 | 363.7 |12.15 5] 372. 18746.1 |25486.4 | 362.50} .666} 435. 2 9442.7 |12837.9| 182.61 | 371.8|12.425 374-0 19097.0 | 25963.5 369.2917 51-9|25- 128\ 437.0 9650.9|13121.0|186.63 380.0) 12.699] 375-5 19452.9 | 26447.4|3 370.17|765. 525, 596) 438.8 9862.7 |13408.9|190.72| 388.3|12.977]377-6 1981 3.8 | 26938.0| 383.1 5|780. -9|26.07 1} 440.6 0078.0 3701.7 |194.88 30638 13.261|379-4 20179.6| 27435-4| 390-22/794-5|26.552] 442.4 194|10297.0 |13999-4 199.13} 405-4 13-549] 381.2 20550. 5| 27939-6 | 397-40) S09. sia ee 2| } | SMITHSONIAN TABLES. TABLE 166. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO BROCH.* op. OO OO 0 wy no Oo QY x oo COu2r Om OMnN NM HODO bv Ga WUD . Dn BOI tN nN m=O OV Un fo ef w ™N NI om ° “NI NOUR ach C2 COENEN WNWU nN DW O . . wo nN ~ an oOo NOOO KN OM Od Cun nin — e to ENOO SIAM BOWHD =NMWO DW LW Ne ROL Wah OF I I 4.04 | I I OMS \O te BAW W D bhuHRAN Ny Nb 180.48 195.67 | 197.42 213.79 | 215.68 * This table is based on Regnault’s experiments, the numbers being taken from Broch’s reduction of the obser- vations (Tray. et Mém. du Bur. Int. des Poids et Més. tom. 1), The numbers differ very slightly from those of Regnault (see Table 16s). ‘Ihe direct measurements of Marvin given in Table 169 show that the numbers in this table are high for temperature below zero centigrade. SMITHSONIAN TABLES. 154 TABLE 166. BROCH. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO 1.2 1.4 245-72 | 247.85 267.65 | 269.93 291.19 | 293.64 316.45 | 319.07 343-52 | 346.33 | 3 MW NONUN Nf HEN OWN =» = CVO A GOs Nb ty 372-49 | 375-50 | 378.53 | 381.58 403-49 | 406.70 ; 413.19 410.47 23.06 20. 33: 430.60 | 440.04 | 443. 440.97 450.47 457- 405.32 471.96 | 475.63 ; 483.03 450.76 : 509.69 | 513-60 5 521.48 525-47 “5I : 549-90 | §54-07 | 558.26 | 562.47 506.71 ; : 3: : 592.74 | 507-17 | 601.64 | 606.13 610.64 : 29. 4 638.35 | 643.06 | 647.81 | 652.59 657-40 z I. 656.57 | 691.89 ; 702.02 707.13 44 | 72 16 | 738.46 | 743.80 17 | 754-57 760.00 : : ; - = TABLE 167. WEICHT IN GRAINS OF THE AQUEOUS VAPOR CONTAINED IN A CUBIC FOOT OF SATURATED AIR.* —10| 0356 —o] 0.564 +0] 0.564 10 | 0.873 20 | 1.321 30 | 1.956 40 2.849 50 | 4.076 60 | 5-745 70 | 7.980 80 | 10.934 9° | 14-790 100 | 19.766 110 | 26.112 totn \t Ax 5 bo NNO N _— Cu A OCC to Go tN ty NO TABLE 168, WEICHT IN GRAMMES OF THE AQUEOUS VAPOR CONTAINED IN A CUBIC METRE OF SATURATED AIR. 9 ° 13 ° 32 I II 2 Ne oO. 4. 5 O. 9- 3. > Sean pe ae Oa * See ‘‘ Smithsonian Meteorological Tables,’’ pp. 132-133. 155 SMITHSONIAN TABLES. TaBLe 169. PRESSURE OF AQUEOUS VAPOR AT LOW TEMPERATURE.* Pressures are given in inches and millimetres of mercury, temperatures in degrees Fahrenheit and degrees Centigrade. —50° | 0.0021 .0939 .0c69 0126 0222 0.0383 0383 .0631 -1026 16041 (a) Pressures in inches of mercury ; temperatures in degrees Fahrenheit. .0037 -0005 -OLIQ -O210 0.0263 .0403 0665 -1077 1718 0.0019 | 0.0018 0035 -OOOI .O112 0199 0.0244 0423 0699 -1130 1798 0.0017 0033 .0057 .0106 .o188 0.0225 0444 -0735 -1185 0.0016 .0031 0054 .O100 .0178 0.0307 .0467 0772 1242 0.0291 0491 -OSIO 1302 (b) Pressures in millimetres of mercury ; temperatures in degrees Fahrenheit. 1°.0 0.049 2004 165 .301 we 0.922 1.023 1.6835 2.735 4-304 2°.0 0.046 089 155 284 505 0.873 1.075 1.776 2.869 4.508 (c) Pressures in inches of mercury ; temperatures in degrees Centigrade. | Temp. C. | coed ——bC) —20 —30 | 0°.0 | 0.1798 .0772 .0307 0112 .0040 0.1655 .0700 .0278 OL! .0036 L 0.1524 | 0.1395 | 0.1290 0588 0645 0252 OOO! .0032 O22 .0052 .0029 0537 .0208 .007 3 .0025 0.1185 | 0.1091 | 0.0998 0491 0188 0065 .0022 0449 .OI71 .0059 .0020 O4f1I 0153 0053 .OO17 (d) Pressures in millimetres of mercury; temperatures in degrees Centigrade. 4.208 | 3.875 1.794 0.706 0.256 0.090 1.637 0.641 0.231 0.081 * Marvin's results (Ann. Rept. U. S. Chief Signal Officer, 1891, App. 10). SMITHSONIAN TABLES. 156 SOU TABLE 170. PRESSURE OF AQUEOUS VAPOR IN THE ATMOSPHERE. This table gives the vapor pressure corresponding to various values of the difference ¢—7Z, between the readings of dry and wet bulb thermometers and the temperature 4, of the wet bulb thermometer. The differences ¢— 4, are given by two-degree steps in the top line, and 4 by degrees in the first column. Temperatures in Centigrade degrees and Regnault’s vapor pressures in millimetres of mercury are used throughout the table. The table was calculated for barometric pressure B equal to 76 centimetres, and a correction is given for each centimetre at the top of the columns.* t—t | Sy Corrections for £ per centi- metre.f Difference per 4° of t—t, —10 eae —s Example. NNNN DQ 03 & OV t—4,= 7.2 4,= 10.0 B=74.5 Tabular number=6.12 —6 X .10o1 = 5.51 Correction for B=1.5 X.048..—= .07 Hence we get Z..-= 5.58 Nn Cn O SIUnW Oo f EYOOOH N ON GDH oT" ° in \o Qurtn G2 \O OSO# DN ty \O 828 te ° fon} Ov nn = PDH moO & 0 Qwuum © - O 1c Mur Om 3: 3: 4. 4.50 4.98 5: 5. 6. 7- 7° 8. HRN WO No AL ON mOWN~IO me NI™NI RO ~ Oo \o -_ 9 VSIA PEYDND > NOW NOW DAO = NI DO ANW+F NE mH NO tintin Gtr dU Ww Noe o Ne) O19 1 I ANY NY NH WL OW Le O° | Nb Oo” ON me Cdn) RO DAdWO _ ~ fo) nn N a ~ © > Cnus OD OOM Mav ~ On BN W™ VN = Us RbHHHN oO On OV NYHNNHN tO WDALG nn Seon in CWO KOM bY HHN OO Ww © Om _ ie) oO b NNhH WN Ga wv — AS \o to AQ AO ug PO Cus AbhdKK_KA A oOmMnnmndo WNN WN lv PSO Sr Oo =O Ono to PO PARR O SIU bd SI NGQOQu& N o& Wor YN OO mm Mm a Oo & ~ Sm G SONU Krad KO NN tv Sh WWWWW © wn > nO wm oO 22 > wo Oo > * The table was calculated from the formula = /, — 0.00066 B (¢—+#,) (1-+-0.00115¢,) (Ferrel, Annual Report U.S. Chief Signal Officer, 1886, App. 24). 5 oy) + When B is less than 76 the correction is to be added, and when J is greater than 76 it is to be subtracted, SMITHSONIAN TABLES. 157 TABLE 171. DEW- The first column of this table gives the temperatures of the wet-bulb thermometer, and the top line the difference ted for a barometric pressure of 76 centimetres. When the barometer differs the table. NNN N BROWN O S7/8B = pnrrpenN onan! Ne) 1 5 7/5B - sw @ 7 OO ND 57/8B - 3 Ww an WwW Oo ON Dew-points corresponding to the difference of temperature given in the above line and the wet-bulb thermometer reading given in first column. —7.1 ryt N CN Did. On DoO a NHOO Piste Corn 000 MO N eee om al 2° ae 10.2 11.2 12.3 1333 .Ol 14.4 15.4 NNHNHH tm LONER OD, RID SOV Gy. Ovin x: OCA nn Un NNHNNN 5D, SN OMS CONNINI oa AO WwW WwW w bd Qpaos ° ° Ww un oo o# WwW WWW 0 in + Oot 'O) Go G6 Go } SMITHSONJAN TABLES. t—t.=1 | The dew-points were compu and the resulting number added to or su 2 rT — 17-9 16.0 al Nb NHN WL Dis COIs OU Te CaN AGC OfWWWNONDKN ° Oo +22 mae et NO hb ib oR OF NWSE AMOK N “I al n ~_ DPONH, ee OY SIRODF DHONMKOOOKNDONK OR HOHO HAO wo O15 RNHN NN AI DEY WWW Nd Wn = ON” por) BRR QW wRHKROKROOUOUO ao GK WOd WU OM Oui 3 | 4 | 5 49 — 24.0 20.3 -) © Sania - ew = oe RO’ mum OV Oe a CON Qw NOW CoH aw Noy ty NEO bRNNN N CO Ou Ge, ¢ CO CONI QurM OfW bv bs n Wwwnh bv BOS & Ooo oo GQ ° 6 | 7 +31 “43 — 24.5 20.1 16.8 |— 23.4 13.9 18.9 11.5 15.4 |— 21.0 14 .19 .26 —9.3 |—12.3 |—16.5 7.6 10.2 13.5 6.1 8.3 TLL 4.6 6.4 8.9 3.1 4-7 6.9 .09 -II 14 — 1.6 — 3.2 — 5.0 0.2 7 he + 1.1 0.3 1.5 2. +11 0.3 3.9 2.6 + 1.2 .06 .08 -10 5 4.1 2.8 : 5 4. 7 a8 a8 9.1 8.2 Wad, 10.3 9.05 8.6 .05 .06 07 LU:5 10.8 9.9 12:7 12.0 1.3 13.9 1353 12.6 Toad 14:5 13.8 16.3 15-7 15.1 .027 .033 .04 17.4 16.9 16.3 18.6 18.1 17.5 19.7 19.2 18.7 20.8 20.4 19.9 212210 21.5 2a .025 .03 .035 2351 22.7 22.2 24.2 23.8 23-4 25:3 24.9 24-5 20.4 26.0 25-7 27.4 27.1 20.8 .O17 .019 .022 28.5 _28.2 27.9 29.6 29.3 29.0 30.7 30-4 30.1 31-7 31.5 Bis 32.8 32.5 82:3 013 .o16 O19 338 33-6 33-4 34-9 34-6 34-4 36.0 35-7 35:5 37:0 38.0 30.8 30.0 30.4 | 37-9 | 37-6 | 37-5 btracted from the tabular number according as the barometer is below or eo sm me to oc a a OF Or Oa coe ODKN RUKH OL DN FH HRIONWOW bd SS WARY = co eR FA ONO Cn WWNh ty RNHNN ROOST Anko a. Ow ON Cy OE SCS OC ORY oo ° NS 33-1 34-2 35-3 t . POINTS. ASCE EES between the dry and the wet bulb, when the dew-point has the values given at corresponding points in the body of from 76 centimetres the corresponding numbers in the lines marked 87'/68 are to be multiplied by the difference, or above 76. See examples. t t—t,=9 10 | 11 12 Dew-points corresponding to the difference of temperature given in the sane line and the wet-bulb thermometer reading given in first column, | | | | EXAMPLES. (1) Given B= 72, 4; =10, ?—4,= Then tabular number for in = 3 ‘and {—4,=5i8 5.2 Also 76—72=4 and 67/$8=.06. . Correction = 0.06 X 4= ° , + 024 Hence the dew-pointis . : ° am Bold (2) Given B=71.5, 4}=7,—24,;= Then, as above, ebidared a 4 « $4 spin Ea Cpe e 15 X4. as P ‘ . - 67 Dew-point=_. ; : : . + 4.07 67/58 = 45 67 0 I 2 — 20.0 3 15.8 — 22.2 4 12.4 16.8 87/62 = 23 .29 37 44 54 66 72 5 — 19.8 — 131 — 17.7 6 7d 10.1 13.4 — 18.1 7 3 7.6 10.1 13.5 — 18.3 8 Bg inte 7.4 10.1 T3305 — 18.3 ‘ 9 1.6 3-2 cn 7.2 9.9 131 — 17.2 87/5sB= 14 AG) .20 22 .25 .29 .36 10 0.0 —1.3 — 3.0 — 4.7 — 6.8 — 9.4 — 12.5 II + 1.8 + 0.3 1.0 2 4:3 6.3 8.8 12 355 22 + 0.8 0.6 2:1 Bu 5-7 er Sel 3-9 Be + 1.3 o.1 1.6 200 14 6.7 5.6 4.5 33 + 1.9 + 0.5 0.9 87/62 = 09 ace 12 14 .16 18 .20 15 8.2 eee 6.2 Gol 3-9 7 + 1.3 16 9-6 8.7 7.8 6.8 5.3 4-7 3-5 17 110} 10.2 9.4 8.5 7.5 6.5 5:5 18 12.4 EI7, 10.9 10.1 9.2 8.3 7.4 19 13.8 Ru 12.4 11.6 10.8 10.0 g.1 67/58 = .06 07 .08 .09 .10 aur 13 20 15.1 14.5 13.8 13-1 12.4 11.6 10.8 21 16.4 15.3 15.2 14.5 13-9 13.2 ie 22 17.6 17.1 16.5 15.9 15-3 14.7 14.0 2 18.9 18.4 17-9 1723 16.8 16.2 15-7 D 20.1 19.6 19.2 18.7 18.1 17.6 17.0 87/sB= 045 05 .06 .06 .07 .08 09 25 21.4 20.9 20.4 20.0 19.5 19.0 18.5 2 22.6 22.1 217 21.3 20.5 20.3 19.9 2 23-7 23.4 22.9 22.5 22.1 21.7 21.2 2 24.9 24.5 24.2 23.5 23-4 23.0 22.6 2 26.1 25.7 25-4 25.0 24.6 24.2 23-9 87/58 = .031 035 O41 047 053 .06 07 30 27a 26.9 26.6 26.2 25-9 25-5 25.2 31 28.4 28.1 27.8 27.4 27.1 26.5 26.4 32 20.5 29.2 28.9 28.6 28.3 28.0 27-7 33 30.7 30.4 30.1 29.8 29.5 29.2 28.9 3 31.8 31.5 Br2 30.9 30.7 30-4 30.1 87/58 = .024 .027 .029 .032 037 037 04 35 32.9 32.6 32-4 32.1 31.8 31.6 31-4 36 34:0 33:7 33-5 33:3 33:0 32.8 32-5 32 351 34-9 34-6 34-4 3 ak 334 3 30-2 ge 337, 33°95 35; . : 39 ae 37-1 30.8 30.6 30.4 36.2 36.0 SMITHSONIAN TABLES. 159 TABLE 172. VALUES OF 0.378e.* This table gives the humidity term 0.378e, which occurs in the equation = 6) 4 =a tere for the calcu- lation of the density of the dry air in a sample containing aqueous vapor at pressure e ; 69 is the density at normal barometric pressure, B the observed barometric pressure, and / the pressure corrected for humidity. For values of ee see Table 174. Temperatures are in degrees Centigrade, and pressures in millimetres of mercury. Vapor Vapor Vapor Dew- Dew- ; Dew- pressure. 0.378 e. e . ssure. . ressure. : point. aS a e Pp e point. sie II.QI 33-37 12.61 35:32 13-35 37-37 14.13 39-52 14-94 41.78 15-79 44.16 10.69 40.65 17.63 49.20 18.62 52.00 19.66 wR He & oS em WO NN bv bo 54.87 20.74 57.87 21.86 61.02 23.06 64.31 24.31 67.76 25.61 71.36 26.97 75.13 28.40 79-07 29.89 83.19 31-45 87.49 33-07 91.98 34-77 96.66 36.54 101.55 38.39 106.65 40.31 II1.97 42.32 117.52 44.42 123.29 40.60 129.31 48.88 135-58 B25 142.10 53-71 * This table is quoted from ‘‘ Smithsonian Meteorological Tables,”’ p. 225. SMITHSONIAN TABLES. 160 TABLE 173. RELATIVE HUMIDITY.* This table gives the humidity of the air, for temperature ¢ and dew-point d in Centigrade degrees, expressed in percentages of the saturation value for the temperature ¢. 5 Dew-point (d). 3 Dew-point (d). Depression of Swept Depression of P (@) IES eT MEETS (CREO STC g e ay a + 20 20 © bhHO MORRO’ et elt ete oO ane HFOD oovoe 9 mMmamm ond an neon OC MOR KRODO WORKHOD WTA HO WOLRKHO’ -_ = uw 3. a 3 3 a 4. 4 4. 4 4. 5! 5- 5: 5 5 6. 6. 6. 6 6 ae 7 7 7 7 8. O PORKRO BORKHO BAKRKHO MWAH DH * Abridged from Table 45 of ‘ Smithsonian Meteorological Tables.” SMITHSONIAN TABLES. 161 TaBLes 174,175. DENSITY OF AIR FOR DIFFERENT PRESSURES AND HUMIDITIES. TABLE 174.— Values of at 0” from kh —1 to h — 9, for the Computation of Different Values of the Ratio of Actual to Normal Barometric Pressure. This gives the density of air at pressure 4 in terms of the density at normal atmosphere pressure. When the air contains moisture, as is usually the case with the atmosphere, we have the following equation for the dry air pressure: 4 = B—o.378e, where e is the vapor pressure, and & the observed barometric pressure corrected for temperature. When the necessary observations are made the value of e may be taken from Table 170, and then 0.378e from Table 172, or the dew-point may be found and the value of 0.378e taken from Table 172. h ExAMPLES OF USE OF THE TABLE. 760 To find the value of A when 4 = 754.3 760 h = 700 gives .g2105 0.0013158 50 “065789 “ce 0026316 “ a 3 0039474 Peas. 5028895 754-3 992497 4 0.0052632 Ta .006575 2 Gorole To find the value of % when 2 = 5.73 7 a hsenen =, gives goen7e9 .0092 7 -0007895 8 or Ze 203 -0000395 9 0184210 5-73 -0074979 TABLE 175. —Values of the logarithms of a for values of & between 80 and 340. Values from 8 to 80 may be got by subtracting 1 from the characteristic, and from 0.8 to 8 by subtracting 2 from the characteristic, and so on. Values of log es 760 4 5 to Co 1.03300 1.04347 | 1.04861 | 1.05368 | 1.05871 | 1.06367 | 1.06858 08297 09231 | .og691| .10146| .10596| .11041] .11452 saa} oOo SIN aie T2770 NL. 1.13622 | 1.14038 | 1.14449 | 1.14857 | 1.15261 | 1.15661 -16840] . -17609| .17988| .18364| .18737] .19107]| .19473 205 55a -21261| .21611| .21956| .22299] .22640] .22978 23976] . -24629| .24952| .25273] .25591| .25907| .26220 .27147| . 2| .27755| -28055| -28354] .28650| .28945] .29237 COO WwW me OI™N 1.30103 i 1.30671 | T.30952 | 1.31231 | 1.31509 | 1.31784 | 1.32058 .32870] . -33403 | -33607| -33929] 34190] .34450| .34707 -35471| - -35974| -36222| .36470| .36716| .36961| .37204 37926] . 38400 | .38636| .38870] .39128 39334 39505 -40249| . .40699| .40922| .41144| .41365| .41585] .41804 42454 | -42882 | 1.43094 | 1.43305 | 1.43516 | 1.43725 | 1.43933 347 | -44552| - -44960| .45162| .45364| .45565| .45764] .45993 40161 | .46358) .46554| -40943| .47137| .47329| .47521| .47712| .47902 -48091 | . -48467 | . -48540 | .49025| .49210| .49393| -49576| 49758 -49940| .50120} .50300| . -§0658| .50835] .51012| .51188] .51364| .51539 Wr -51713| 1.51886 | 1.52059 | I. T.52402 | 1.52573 | 1.52743 | 1-52912 | 1.53081 | 1.53249 -53416| .53583| -53749| -53 -54079| -54243| -54407| .54570| .54732] -54804 -55055| -55216) .55376| . -55694| .55852| .56010] .56167| .56323] .56479 -§6034| .56789| .56944| . -57250| -57403| -57555| -57707| -57858| .58008 “55158 | .55303) .58457] . -58753| 58901} .59045| .59194| -59340| 59486 -§9631 | 1.59775 | 1.59919 | T. 1.60206 | 1.60349 | 1.60491 | 1.60632 | 1.60774 | 1.60914 61055| .61195! .61334| . -61611| .61750| .61887]| .62025] .62161| .62298 -62434| .62569| .62704| . -62973| .63107| .63240|] .63373| .63506| .63638 -63770| .63901| .64032| . 64293| .64423| .64553| .64682] .64810| .64939 -65067 | .65194| .65321 -65574| -65701| .65826| .65952| .66077| .66201 SMITHSONIAN TABLES. 162 a . 760 77° 780 790 67549 -68739 1.77240 ‘75194 79128 $0043 8093 T.S1816 82676 83519 84346 85158 1.85955 807 37 87506 58261 89004 1.89734 90452 -QI158 .91853 | 292597, 1.93210 93873 94526 95170 95804 1.96428 .97044 .97652 | 98251 .98842 1.99425 0.00000 .00568 .o1128 .O1681 DENSITY OF AIR. TaBLe 175. Values of logarithms of 500 for values of % between 350 and 800. 1.72233 ook -74347 +7 5306 .70362 1.77336 -78289 79221 80133 .81027 1.81902 82761 83602 84428 85238 1.86034 S681 5 87282 88336 .89077 1.89806 -90523 91228 .Q1g22 92604 1.93277 5794 -94591 5-92 95800 | 1.96490 | .97106 97712 98310 98900 | 1.99483 0.00057 | .00624 .O1184 .017 30 SMITHSONIAN TABLES. ¥.66573 | 1.66696 | 1.66819 -67790 08973 -70125 -71247 1.72341 -73405 74450 -7 5407 70401 1.77432 -78383 79313 .80223 SIIIS T.81989 82846 83686 84510 85319 1.86113 86892 87658 .OS411 QI 51 1.89878 90594 91298 Q1990 92672 1.93343 .94004 94656 95297 95929 1.96552 -97 167 97772 -95370 98959 1.99540 0.00114 .00680 .01239 .O1791 -67909 -69090 -70239 71358 1.72449 73514 74553 -75507 70559 1.77528 -79477 79405 80313 81203 1.82075 82930 83769 84591 85399 T.S6191 80969 87734 85456 89224 1.89950 90605 .91 307 -92059 .92740 1.93410 .94070 -947 20 953601 95992 1.96614 97 228 97532 95429 -g9o18 1.99598 0.00171 :007 37 01295 .01846 Values of log a 760 4 5 1.66941 .68148 .69322 -70465 -71578 1.72664 73723 .68029 69206 76657 1.77624 78570 -79496 80403 81291 1.82162 83015 83852 84673 85479 1.77720 -78664 -79588 .80493 81379 1.82248 83099 83935 54754 85558 1.86348 87123 87885 88634 89370 1.86270 .87047 87810 .88 560 89297 1.90022 99735 -91437 92128 .92807 1.90094 .go8o06 .Q1 507 .92196 92875 1.93543 -94201 94849 95488 .QO117 1.93476 94135 94785 95424 -9005 5 1.96676 .97 288 | ieo2 || eoeaa .98488 | 95547 -99076| -99134 1.99713 0.0028 5 .008 49 .01 406 -O1955 1.967 38 -97349 1.99656 0.00228 00793 .01350 .OI1QOI 163 1.67064 .68267 69437 79577 71088 1.72771 -73828 .74860 -75867 .708 52 1.77815 -787 57 -79679 80582 81467 1.82334 83184 84017 84535 85638 1.86426 .87200 87961 88708 89443 1.90166 -90877 -91576 92264 .92942 1.93601 94266 94913 ‘95551 .g6180 1.96799 97410 -QSo12 - 98606 “O9I9S 1.99771 0.00342 00905 .O1 461 .02010 1.67185 £68385 69553 -70090 -71798 1.72878 -73932 -74901 -75967 -70949 1.77910 78850 -79770 .80672 81554 1.82419 83268 .84100 84916 85717 1.86504 87277 88036 88752 89516 T.90238 -90947 -Q1645 "92333 +93009 1.93675 94331 94978 Q5014 -90242 1.96861 97471 .9807 2 .98665 99251 1.99828 | 0.00398 | .0og6! .O1516 .02064 1.67428 68621 -69783 -70914 72016 1.67 307 68503 69665 -70802 71907 1.72985 74030 -7 5063 -76066 -77046 T.73091 74140 -75164 76165 77143 1.78005 -78943 78061 .80761 81642 1.78100 79036 19952 .808 50 81729 1.82505 83352 84182 84997 85797 1.86582 87353 SST 888 56 89559 1.90309 .QIO17 QI715 .92401 93076 T.82590 83435 84204 85076 85876 1.86660 87430 88186 88930 89661 1.90380 -g108$ 91784 92469 93145 1.93807 94461 95106 95741 96366 1.93741 94396 -95042 ‘95077 -90304 1.96922 ‘975314 95132 98724 “99399 T.99886 0.00455 .O1017 01571 .02119 1.96983 -97 592 .QS19I -98783 -99307 7 1.99942 0.00511 .01072 .01626 02173 TABLE 176. VOLUME OF PERFECT CASES. Values of 1 + .00367¢. The quantity 1 + .003677 gives for a perfect gas the volume at #° when the pressure is kept constant, or the pressure at ¢° when the volume is kept constant, in terms of the volume or the pressure at 0°. (a) This part of the table gives the values of 1-+.00367# for values of ¢ between 0° and 10° C. by tenths of a degree. (b) This part gives the values of 1 ++ .00367 ¢ for values of # between —g0° and + 1990° C. by 10° steps. These two parts serve to give any intermediate value to one tenth of a degree by a sim- ple computation as follows:—In the (4) table find the number corresponding to the nearest lower temperature, and to this number add the decimal part of the number in the (a) table which corresponds to the difference between the nearest temperature in the (4) table and the actual temperature. For example, let the temperature be 682°.2: We have for 680 in table (4) the number . . : + 3.49560 And for 2.2 in table (z) the decimal . ; , ° + 00807 Hence the number for 682.2 is . fs : . : + 3.50367 (c) This part gives the logarithms of 1-+-.00367¢/ for values of ¢ between — 49° and + 399° C. by degrees. (d) This part gives the logarithms of 1 + .00367 7 for values of ¢ between 400° and 1990° C. by 10° steps. (a) Values of 1+ .00367¢ for Values of ¢ between O° and 10° C. by Tenths of a Degree. 0.2 0.3 1.00073 .OOIIO 1.00147 .00440 .00477 .00514 .00807 .00844 00881 .O1174 .O1211 .01248 O1541 .01578 -O1615 1.01908 T.01945 1.01982 .02275 .02312 02349 .02642 02679 .02716 03009 03046 03083 -03376 03413 03450 Oo I 2 3 4 5 6 7 8 9 0.6 0.7 0.8 1.00220 1.00257 .00294 .00587 00624 .00661 .009 54 .0099I 01028 .O1321 .01358 01395 01088 01725 .01762 1.02055 1.02092 1.02129 .02422 02459 02496 .02789 .02826 .02863 03156 03193 03290 103523 -03560 -03597 WON ADM pawnx SMITHSONIAN TABLES. 164 TABLE 176. VOLUME OF PERFECT GASES. (b) Values of 1-++.00367¢ for Values of ¢ between — 90° and -++- 1990° O. by 10° Steps. 00 10 30 40 1.00000 0.96330 ; 0.88990 0.85320 1.00000 1.93070 : I.11010 1.14680 1.36700 1.40370 : 1.44710 1.51380 1.73400 1.77070 807 ¢ 1.84410 1.58080 2.10100 2.13770 ; 2.21110 2.24780 2.46800 2.50470 ; 2.57810 2.61480 2.83500 2.87170 . 2.94510 2.98180 ‘3.20200 3.23870 s 3-31210 3-34880 3.56900 3-60570 .642 307910 3-71580 3-93600 3.97270 : 4.04610 4.08280 4-30300 | 4.33970 . 4-41310 | 4.44980 4.67000 4.70670 : 4.78010 4.81680 5-03700 5-07370 : 5-14710 5.18380 5.40400 5.44070 4774 5.51410 5.55080 5-77100 5.80770 ; 5.58110 5.91780 6.13800 6.17470 7 6.24810 6.28480 6.50500 6.54170 5 6.61510 6.65180 6.87200 6.90870 6. 6.98210 7.01880 7:23900 | 7.27570 312 7-34910 | 7.38580 7.60600 7.04270 i 7.71610 7.75280 7-97 300 8.00970 Koy 8.08310 8.11980 8.34000 8.37670 : 8.45010 8.48680 0.74310 1.25690 1.62390 1.66060 1.99090 2.02760 2.55790 2.72490 3.05520 3.09190 3.42220 3-45890 5323 3-78920 3.82590 3-59930 4.15620 4.19290 4.26630 4.52320 | 4.55990 4.03330 4.85350 4.89020 4.92690 5.00030 5.22050 5.25720 5.29390 5-367 30 5.58750 | 5.62420 | 5.66090 5-7 3430 5:95450 5-99120 6.02790 6.10130 6.32150 6.35820 6.39490 6.46830 6.68850 | 6.72520 | 6.76190 6.83530 7.05550 7.09220 7.12890 . 7+20230 7.42250 7.45920 7-49590 7-56930 7.78950 7.82620 7.86290 7-93630 , 8.15650 8.19320 8.22990 8.30330 8.52350 8.56020 8.59690 : 8.67030 GMITHSONIAN TABLES. TABLE 176. VOLUME OF (c) Logarithms of 1+ .00367 ¢ for Values Mean diff. per degree. 4 1.931051 1.929179 1.927299 1.925410 1.923513 1884 -949341 -947 546 945744 943934 -942117 1805 .966592 -965169 -903438 -901701 -959957 1733 .983762 982104 -980440 978769 977092 1607 0.000000 998403 .Qg680r 995192 993577 1605 0.000000 0.001591 0.003176 0.004755 0.006329 1582 .01 5053 .017188 .O18717 020241 .021760 1526 030762 032244 033721 -035193 036661 1474 045362 .046796 .048224 049645 051068 1426 059488 .00087 5 062259 063037 .065012 1381 0.073168 0.074513 0.075853 0.077190 0.078522 1335 086431 087735 0890306 .090332 .091624 1299 .099301 -100507 .101829 103088 -104344 1259 -I11500 -11 3030 114257 115481 116701 ~ 1226 123950 125146 126339 127529 128716 11g 135768 0.136933 0.138094 0.139252 0.140408 1158 147274 .248408 -149539 -1 50667 151793 1129 158483 159588 -160091 161790 162887 IIOI 169410 170488 171563 172635 .173705 1074 180068 -I181120 182169 183216 .184260 1048 19047 2 0.191498 0.192523 0.193545 194564 1023 .200632 -201635 202635 -203634 -204630 1000 210559 -211540 212518 213494 214408 976 2202605 .222180 223136 .224087 956 -229959 -230097 231033 232507 -233499 935 -239049 0.239967 .240884 0.241798 .242710 »248145 -249044. -249942 250837 251731 257054 257935 259814 259692 -260507 205784 206048 .207 510 208370 269228 274343 .275189 -276034 276877 277719 0.282735 0.283566 284395 0.285222 0.286048 -290969 -291784 292597 -293409 294219 «299049 299849 300048 301445 -302240 300982 -307768 -308 552 309334 31015 -314773 -315544 -316314 -317083 -317850 322426 0.323184 0.323941 324696 0.325450 -329947 -330692 -331435 -332178 -332919 -337339 .338072 -338503 -339533 «340262 -344608 -345329 -345048 -346706 -347482 -352406 353174 -353880 354585 359488 0.360184 360879 361573 -306399 307084 307768 368451 +373201 -373875 “374549 +37 5221 379898 -380562 301225 381887 386494 387148 387801 388453 SMITHSONIAN TABLES. 166 PERFECT CASES. of ¢ between — 49° and + 399° ©. by Degrees. 1.921608 940292 958205 -97 5409 991957 0.007897 .023273 .038123 052482 .006382 0.079847 -092914 -105595 -I17917 -129899 0.141559 152915 163981 174772 -185301 0.195581 -205624 -21 5439 225038 -234429 252623 -201 441 -369132 -37 5892 -382548 389104 SMITHSONIAN TABLES. 1.919695 -938460 9564.47 973719 990330 0.009459 .024781 039581 1053593 .067745 0.081174 094198 106843 -I19130 -131079 0.142708 154034 -164072 175836 -186340 0.196596 -20061 5 -216409 .225986 -235357 -244529 253512 262313 .270940 279398 -287694 -295835 -303827 -311673 319381 0.326954 -334397 “341715 -348912 355991 0.362957 369813 -376562 .383208 3897 54 1.917773 -930619 954081 .97 2022 988697 0.011016 .026284 041034 055208 -009109 0.082495 095516 -108088 120340 .132256 0.1438 54 155151 -166161 176898 .187377 0.197608 207605 .217370 .220932 236283 .245436 «254400 .203184 -271793 280234 288515 .290860 .304618 .312450 320144 1.915843 934771 952909 +970319 987058 0.012567 027782 .042481 .050699 .070466 0.08 3811 096715 109329 121547 -133430 0.144997 156264 .167246 177958 188411 0.198619 -208 592 218341 227876 .237 207 -246341 255287 204052 -272644 .281070 0.289326 -2907445 -305407 -313226 -320906 0.328453 -335871 -343164 -350337 357394 -364337 371171 -377900 +384525 391052 1.913904 ‘932915 Q51129 -908609 985413 0.014113 029274 043924 055096 071819 0.085123 .09803I 110506 122750 134601 0.146137 -157375 168330 -I79014 -189443 0.199626 “209577 219904 228819 .238129 247244 -250172 .204919 -273494 -281903 .290153 .298248 306196 -31 4000 .321667 329201 .336606 -343587 351048 -358093 0.365025 -371549 -378567 355153 “391699 TABLE 176, Mean diff. per degree. | 1926 1545 1771 1699 1636 1554 1500 1450 1402 1359 1315 1281 1243 1210 1175 1144 IIIS 1087 1060 1035 IOIr TABLE 176. VOLUME OF PERFECT CASES. (a) Logarithms of 1+ .00367¢ for Values of ¢ between 400° and 1990° C. by 10° Steps. 00 10 20 30 40 0.392345 0.3987 56 0.405073 0.411300 0.417439 0.452553 0.458139 0.463654 0.469100 0.474479 505421 510371 515264 -520103 -524889 552547 -556990 -561388 -565742 -570052 -595055 -599086 -603079 .607037 610958 633771 637460 -O41117 -644744 -648341 0.669317 0.672717 0.676090 0.679437 0.6827 59 702172 705325 708455 711563 714648 ‘732715 735955 738575 741745 744356 -701251 -704004 -706740 -769459 772160 -788027 -790616 -793190 795748 -798292 0.813247 0.81 5691 0.818120 0.820536 0.822939 837083 839396 841697 843986 846263 859679 861875 864060 866234 868398 881156 883247 885327 887 398 889459 .go1622 .903616 -905602 -907578 909545 50 60 70 80 90 0.423492 0.429462 0.435351 0.441161 0.446894 0.479791 0.485040 0.49022 0.495350 0.500415 529623 -534 53993 543522 548058 574321 ‘ 5927 34 -586880 -590987 -614545 : 622515 .626299 -630051 651908 : -658955 662437 665890 0.68605 5 ] 0.692574 0.695797 0.698996 -717712 2 : 23776 -726776 729756 747218 Y .752886 -755692 Tee 7 774845 : -780166 -782802 5422 .800820 ; 805834 808319 .810790 0.825329 0.827705 0.830069 0.832420 0.834758 848828 850781 853023 855253 857471 870550 872692 874824 876945 879056 891510 893551 895583 897605 899618 -QTI 504 -913454 915395 917327 -o1g25! SMITHSONIAN TABLES. 168 TABLE 177. DETERMINATION OF HEICHTS BY THE BAROMETER. Formula of Babinet: Z = C BS i C (in feet) = 52494 [x + fob e— Se] English measures. goo C (in metres) = 16000 [: + | metric measures. 1000 In which Z = difference of height of two stations in feet or metres. Bo, B = barometric readings at the lower and upper stations respectively, corrected for all sources of instrumental error. ?, ¢ = air temperatures at the lower and upper stations respectively. Values of C. ENGLISH MEASURES. METRIC MEASURES. 4 (+2). Log € b(t +2). G Metres. 4.69834 15360 4.18639 70339 15488 «19000 15616 19357 4-70837 15744 “19712 -71330 15872 20063 4.71818 16000 4.20412 .72300 16128 16256 4:72777 16384 73248 16512 4.73715 16640 74177 16768 16896 4.74633 17024 .75085 17152 4-75532 17280 75975 17408 17536 17664 17792 NN NN Car N 4.76413 -70847 QQ °o 4.77276 -777 02 17920 18048 18176 18304 G2 Ga We Ar, N 4.78123 SMITHSONIAN TABLES. 169 TABLE 178. BAROMETRIC Barometric pressures corresponding to different This table is useful when a boiling-point apparatus is used (a) British Measure. | Temp. F. Zs 2 2. oO 5 97 45 94 44 9 4 5 6 body G2 N bit Non Mo stb bob oy Sb 36 an +f in OV Or tbo COO NN Cu NN “SI Noh ON ONS SIC Trt CoOL Coa une ONIONS Cr Ca CSG On OF On “IDR Qe R ees Wo NO Nob ty to boob bot N™ oN ORO OD Ce eesiess no wo ss SIO RO Mm oO bb Hu Of On bh wv dt Oo OW ty Ga wn na amo SMITHSONIAN TABLES. TABLE 178. PRESSURES. temperatures of the boiling-point of water. in place of the barometer for the determination of heights. (b) Metric Measure.* * Pressures in millimetres of mercury. SMITHSONIAN TABLES. 171 TABLE 179. STANDARD WAVE-LENCTHS. This table is an abridgment of the table published by Rowland (Phil. Mag. [5] vol. 36, pp. 49-75). The first column gives the number of the line reckoned from the beginning of Rowland’s table, and thus indicates the number of lines of the table that have been omitted. The second column gives the chemical symbol of the element repre- sented by the line of the spectrum. The third column indicates approximately the relative intensity of the lines recorded and also their appearance; X stands for reversed, d for double, ? for doubtful or difficult. The fourth column gives the relative “weights ” to be attached to the values of the wave-lengths as standards. The last column gives the values of the wave-lengths in Angstrém’s units, 2. e., in ten millionths of a millimetre in ordinary air at about 20° C. and 760 millimetres pressure. When two or more elements are on the same line of the table it indicates that they have apparently coincident lines in the spectrum for that wave-length. When two or more lines are bracketed it means that the first one has a line coinciding with one side of the corresponding line in the solar spectrum and so on in order. Lines marked A(e) and A (wz) denote lines due to absorption by the oxygen or water vapor in the earth’s atmosphere. The letters placed in front of some of the numbers in the first column are the symbols of well-known lines in the spectrum. The footnotes are from Rowland’s paper. = Inten- Inten | Waves e aoe Weight.| length (arc Bose Element. pak Weight. ance. spectrum). ance. IIS 2937-020 117 2954-058 121 2967.016 124 2973-358 126 298 3.089 NNN N WN wRwHN He WNNN HS 129 2994-547 131 2997-430 rai 3001.070 136 3006.978 141 3008.25 5 Tot 3020-759 103 3047-720 169 3059-200 (Sun spectrum.) NO bd -& 136 144 154 158 164 171 3005.160 3012.557 3024-475 3035-550 3050.212 3001.930 3078.148 3094-739 3121.275 3140.869 3167.290 3188.164 3200.032 3218.390 3224.368 3247-080 NUubvk ON NNN KN 177 187 197 201 203 moO WW Ww ewnN NHK NW 207 209 211 215 9222 a2e WW ANM NMOOD UMnNn OSH * Seems to be the only single carbon line not belonging to a band in the arc spectrum. It was determined to belong to carbon by the spark spectrum. + This line appears as a sharp reversal, with no shading, in the spectra of all substances tried that contained any trace of a continuous spectrum in the region. + There is a faint line visible on the violet side. SMITHSONIAN TABLES. 172 TABLE 179. STANDARD WAVE-LENCTHS. Inten- | I ft. ; nten- | Wave- Wave- sity and . ‘ No. of . sity a : Element. appear- Weight. length (sun Tine. Element. cei Weight.| length (sun ance, spectrum). ea: spectrum), Io 3267.839 409t r 10 4005.305 6 3302. 501 410 4010.575 TO | 3318.163 417 4045-975 8 3356-222 420 4055-701 12 3389.887 22 4003.7 56 tN mow ol 18 | 3406.955 424 10 | 3455-384 428 3478.001 431 3500.7 21 434 3518.487 430 407 3-920 4085.7 16 4114.600 4157.948 4185.063 Co, Fe, Ni Fe Co Fe 202.188 aD : 4226.892 4254-502 4271.924 4295249 3540-266 439 & 445 3564.680 448 3581.344 451 3583-453 456 3597-192 3609.015 || G 462 3612.217 3618.924 || £465 3623-332 467 f QR WM MWnprp Pp NFO "~S ~_ > +O 4307-904 4.308.034 4308.071 4325-940 4352-993 min Ww own Ff ONOMN Ww nt un 3631.619 || @ 471 3647-995 473 3667.397 477 48ot 3683.202 484 _ WwW NOV HOLS NH LON Une CO 4383.721 4404.927 4425-609 4447-599 4494-735 4508.4 56 4554-213 4572-157 4602.183 4629.51 5 4643-645 4679.028 4686.395 4703-180 4783.601 482 3.697 4861.496 4919.183 4973-274 3707-186 490 3720.086 493 3132542 496 3789-633 500 3781.330 508 3804.153 512 3820.567 515 3826.024 518§ 3843.406 524 3860.048 528 3883.472 || 531 3897-599 537 3924-669 3933-809 || 545 3944-159 549 3950.101 558 3960.429 561 3968.620 564 3981.914 567 4994-316 5020.210 5050.008 5068.946 5099-959 nkunw * This line is doubly reversed and spread out in broad shading for 6.000 to 7.000 on either side. In each case the second reversal is slightly excentric with respect to the other, being displaced towards the red. + Seven or eight lines, the brightest, and most of the others are due to iron. ¢ There is a faint side line towards the red. § This line is shaded towards the violet, probably due to a close side line. SMITHSONIAN TABLES. 173 TABLE 179. STANDARD WAVE-LENCTHS. — hae ie Wave: iemily ci | wane oo Element. "UY @ Weight.| length (sun 2 a -| length (sun Line. anceas spectrum). spectrum). _ 5109.825 ‘ 5930-410 5127.530 5948.761 | 5141.916 5987.286 | 5162.448 6013.717 6024.280 570 575 550 589 _~ 5167.501 5167-572 BeOS es 5107: 102.941 5169.066 6122.428 5169.161 6162.3383 5169.218 8 6191.770 6230.946 6252.776 6265.347 6301.719 6335-550 6393-818 6411.864 6439-298 6471.881 6495-209 6546.486 6563-054 6593-161 6643-482 6678.232 5172.871 5183.792 5215-352 5233-124 5253-649 5269.722 5270.448 5279-495 5279-533 5283-803 = oe oO #0 WinwWWN Ww Wind ANuN™N ~ iS) 5307-546 5324-373 5307-670 5383-576 5405.987 5347-130 5.463.493 5477-128 5501.685 5528.636 NADAOH Ww 67 50.412 6768.044 6810.519 6441.591 6870.186 688 4.083 6909-675 6919.245 6947-781 6956.700 5569.848 5588.980 5001.501 5624.2 53 5624.76 695 699t Fnho coc co 00 ~~ 5662.745 7935-159 5088.434 7122.491 5732-973 7 200.753 5753-342 i 7243-904 5752.346 984 7 290.714 706 710 Na 717 Fe 720 Fe 725 |Cu?Co? ii 7 7 5 7 6 ° 5 5 5 4 4 3 3 4 4 6 4 8 8 6 6 —~ RUIN Dur ~F NRE QU NSfAN +N wo OOnvo “NI 5806.954 990 7 7389.696 5857-672 9971I 7594-059 587 5.982 998 7621.277 5890.182 1004 A(o) 7660.778 5896.1 54 IO1O ? 7714.086 732 Fe 737t| Ca D3 740§ He D2743 Na P1745 Na ~ yb oo * Component about .o88 apart on the photographic plate. It is an exceedingly difficult double. + Lines used by Pierce in the determination of absolute wave-lengths. + There is a nickel line near to the red. § This value of the wave-length is the result of three series of measurements with a grating of 20,000 lines to the inch and is accurate to perhaps .o2. || Beginning at the head of A, outside edge. SMITHSONIAN TABLES. 174 ees “a TaB_Le 180. WAVE-LENCTHS OF FRAUNHOFER LINES. For convenience of reference the values of the wave-lengths corresponding to the Fraunhofer lines usually designated by the letters in the column headed “ index letters,’’ are here tabulated separately. The values are in ten mil- lionths of a millimetre on the supposition that the D line value is 5896.156. ‘The table is for the most part taken from Rowland’s table of standard wave-lengths, but when no corresponding wave-length is there given, the number given by Kayser and Runge has been taken. ‘These latter are to two places of decimals. Wave-length in Wave-length in centimetres X 10%, Index letter. Line due to — ; . centimetres X 104, Index letter. Line due to— 7621.277* 5 4340.66 § 7594-059" i 4308.071 7184.781 4308.034 6870.186t 4307-904 C or Ha 6563.054 4226.892 a 6278.289 4101.87 D, 5896.1 54 3968.620 De 5890.182 3933-809 Ds 5875-982 3820. 567 5270.533 3727-763 Ej 5270.495 3581-344 5270.448 3441-135 5269.722 3361.30 5183-792 3286.87 5172.871 3181.40 5169.218 3179-45 5169.161 3144.58 (?) 5169.066 3100.779 5167.686 3100.415 5167.572 3100.064 5167.501 3047.720 4861.496 3020.7 59 4353-721 4325-940 * The two lines here given for A are stated by Rowland to be: the first, a line “ beginning at the head of A, out- side edge; ”” the second, a “single line beginning at the tail of A.” + The principal line in the head of B. + Chief line in the a group. § Ames, “ Phil. Mag.” (5) vol. 30. | Cornu gives 3179.8, which, allowing for the different value of the standard D line, corresponds to about 3180.3. {J Cornu gives 3144.7, which would correspond to about 3145.2. 175 SMITHSONIAN TABLES. TABLE 181. DETERMINATIONS OF THE VELOCITY OF LICHT, BY DIFFERENT OBSERVERS.* Interval worked across in No. of experi- ments made. Date of determi- nation. Method. Toothed wheel 8.633 Revolving mirror | 0.02 Toothed wheel 10.310 “ “ 22.91 Revolving mirror 0.6054 Toothed wheel } Pere 5-1019 1880 to 7.4424 1882 1879 1880 Revolving mirror 7-4424 1882 0.6246 Mean from all weighted measurements Mean from those having weights >1 . 1 Fizeau, “ Comptes Rendus,” 1849. 2 Foucault, “ Recueil des travaux scientifiques,” Paris, 1878. kilometres. Velocity in kilometres per second. 315324 298574 + 204 298500 + 995 300400 -}-. 300 299910 + 51 301384 + 263 299709 299776 299860 299853 + 60 299835 + 154 299893 -+ 23 3 Cornu, “ Jour. de l’Ecole Polytechnique,”’ Paris, 1874. 4 Cornu, “ Annales de l’Observatoire de Paris,” Memoires, tome 13, p. A. 298, 1876. 5 Michelson, “ Proc. A. A. A. S.” 1878. 6 Young and G. Forbes, “ Phil. Trans.” 1882. 7 Newcomb, “Astronomical Papers of the American Ephemeris,” vol. 2, pp. 194, 201, and 202. Velocity in miles per second. 195935 185527 + 127 185481 + 618 186662 +- 186 186357 + 31.7 187273 + 164 186232 186274 186326 186322 +} 37 186310 +- 95.6 186347 + 14.3 Wt. of obser- vation Refer- | as esti- ence. 9 9 8 Michelson, “ Astronomical Papers of the American Ephemeris,” vol. 2, p. 244. , P P P- 244 9 Harkness. TABLE 182. PHOTOMETRIC STANDARDS.} * Quoted from Harkness, ‘‘ Solar Parallax,”’ Pp: 33. t This table, founded on Violle’s experiments, is quoted from Paterson’s translation of Palaz’ ‘‘ Industrial Pho- tometry,”* p. 173. + The Violle unit is sometimes called the absolute standard of white light. normally by one square centimetre of the surface of melted platinum at the temperature of s SMITHSONIAN TABLES. 176 It is the Gnaneye a light emitted olidification. : : Hefner- Violle units t 1.000 2.08 16.1 16.4 18.5 18.9 Carcels 0.481 1.00 7-75 7.89 8.91 9.08 Star candles 0.062 0.130 1.00 1.02 Tents 1.17 German candles 0.061 0.127 0.984 1.00 1.13 1.15 English candles 0.054 0.112 0.870 0.886 1.00 1.02 Hefner-Alteneck lamps 0.053 0.114 0.853 0.869 0.98 1.00 TaBLe 183. SOLAR ENERCY AND ITS ABSORPTION BY THE EARTH ATMOSPHERE. This table gives some of the results of Langley’s researches on the atmospheric absorption of solar energy.* The first column gives the wave-length A, in microns, of the spectrum line, while the second and third columns give the corresponding absorption, according to an arbitrary scale, for high and low solar attitudes. The fourth column, E, gives the relative values of the energy for the different wave-lengths which would be observed were there no terrestrial atmosphere. TABLE 184. THE SOLAR CONSTANT. The “ solar constant ”’ is the amount of heat per unit of area of normally exposed surface which, at the earth’s mean distance, would be received from the sun’s radiation if there were no terrestrial atmosphere. The following table is taken from Langley’s researches on the energy of solar radiation.| The first column gives the wave-length in microns. The second and third columns give relatively on an arbitrary scale an upper and a lower limit to the possible value of spectrum energy. Spectrum Spectrum Spectrum Spectrum energy energy energy energy (upper (lower : (upper (lower limit). limit). limit). limit). 105.0 78.2 65.1 45.0 39.2 29.1 19.4 7.0 The areas of the energy curves are respectively ; ° . 149,060 and 95,933 The solar constants deduced from these areas are .- ° + 3-505and 2.630 Langley concludes that ‘‘in view of the large limit of error we can adopt ¢hree calories as the most probable value of the solar constant,” or that ‘‘at the earth’s mean distance, in the absence of its absorbing atmosphere, the solar rays would raise one gramme of water three degrees per minute, for each normally exposed square centimetre of its surface.” * “Am. Jour. of Sci.” vols. xxv., xxvii., and xxxii. + “Professional Papers of U. S. Signal Service,’”? No. 15, 1884. SMITHSONIAN TABLES. 177 TABLE 185. INDEX OF REFRACTION FOR CLASS. The table gives the indices of refraction for the Fraunhofer lines indicated in the first column. The kind of glass, the density, and, where known, the corresponding temperature of the glass are indicated at the top of the different columns. When the temperature is not given, average atmospheric temperature may be assumed. (a) FRAUNHOFER’s DETERMINATIONS. (Ber. Miinch. Akad. Bd. 5s.) Flint glass. Crown glass. 1.62775 1.60204 1.55477 1.52583 62965 .60380 55593 52685 -63504 -60549 -55908 -52959 64202 61453 50315 53301 : -64826 -62004 50674 53005 . .66029 63077 57354 54166 -67106 -64037 -57947 “54657 | (b) BarLte’s DETERMINATIONS. (Quoted from the Ann. du Bur. des Long. 193, p. 620.) Flint glass. 2.98 ae : 3-44 Boe, b 1.5659 | 1.5766 | 1. 1.6045 | 1.6131 -5075 | .5783] . .6062 | .6149 5715) | 5o22 6109 | .6198 5770 | .5887 6183 | .6275 -5813 | .§924 | .6141 | .6225 | .6321 -§902 | .6018 | .6246 | .6335 | .6435 -§979 | -6098 | .6338 | .6428 | .6534 Crown glass. (Baille, zz.) Density 2.49 2.50 2.55 2.80 Temp. C. 23°05 17°.8 18°.4 Zio 1.5126 1.5244 1.5226 1.5157 “5134 5254 5237 “5166 -5100 +5280 5265 5192 5198 -5320 5307 -5234 +5222 5343 +5332 +5256 -5278 5397 5392 +5313 5323 5443 5442 -5360 (c) Hopxinson’s DeTeRMINaTIONS. (Proc. Roy. Soc. vol. 26.) Titani- Hard Soft irate . silicic Flint glass. crown. crown. Renn Density = 2.486 2.550 2.553 2.866 3-206 3-659 3-889 4-422 511755] 1.508956 - 1.534067 - - 1.639143 | 1.696531 -513625| -510916| 1.539155] -536450| 1.568558 | 1.615701 | .642874] .701060 -514568] .511904| .540255| .537673] .570011| .617484| .644866 703478 -SI7II4| «514591 | .543249| -541011| .574015| .622414] .650388] .710201 -520331| -518010| 547088} .545306| .579223| .628895| .657653| .719114 -520967 | .518686| .547852| .546166| .580271| .630204| .659122| .720924 -523139| -520996| .550471| .549121| .583886| .634748| .664226| .727237 -526207| .556386| .555863] .592190| .645267| .676111| .742063 526595 | -550830| .556372| .592824| .646068| .677019| .743204 -559999 | .500010| .597332| .651840 083577 ‘751464 529359 | -531416| .562392] .562760| .600727| .656219 5°9 | 757785 N. B. —D is the more refrangible of the pair of sodium lines; (G) is the hydrogen line near G. SMITHSONIAN TABLES. 178 INDEX OF REFRACTION FOR CLASS. — (d) Mascart’s eee (Ann. Chim. Phys. ] (@) Lanciey’s Determinations. (Silliman’s Jour- 1 . nal, 27, 1884.) Flint glass. Crown glass. Flint glass. Density = 3-615 3-239 2.578 Wave length Index of Lenn 30°.0 26°.0 28.0 in mm. X 10%. | refraction. A 1.60927 | 1.57829 1.52814 1.551 B 61268 -5oI14 53011 oa 5535 C -61443 -58261 53113 5544 D -61929 58671 -53380 5572 5576 E ‘62569 | .59197 53735 5004 bg .62706 59304 -53801 .5616 -5636 F -63148 -59673 -54037 -5668 G -64269 -60589 -54607 ; 567 4 +507 H -65268 .61390 55093 -5687 L 65317 .62012 55349 5697 “5714 M 66211 62138 “55531 5757 N 66921 -62707 55853 5798 5862 O ‘67733 | -63341 -56198 5899 1 - 63754 -56419 .6070 Q ~ 64174 50646 -6266 (f) Errecr oF TEMPERATURE. (Vogel, Wied. Ann. vol. 25.) ne-- nt —a(t—?2/) + 6B E—?2)3, where zz is the absolute index of refraction for the temperature 7, and a and § are constants. For tem- eratures ranging from 12° to 260° Vogel obtains the ollowing values of a and B for the Fraunhofer lines given at the tops of the columns. ae 10° = 6 | 12 2 White glass j B 1! 3 3 327 a .10® =| 190 B.10oM—| ror Flint glass } (g) EFFEcT oF TEMPERATURE. (Miiller, Publ. d. Astrophys. Obs. zu Potsdam, 1885.) Flint glass. Crown glass. Density = 2.522. Density = 3.218. 5 Temp. C.=— 5° to 23°. Density = 3-855. Temp. C. = — 3° to 21°. Temp. C. =— 1° to 24°. 1.643776 + .00000474 ¢ 1.574359 + .00000324 ¢ 1.512588 — .00000043 ¢ -645745 + .00000486 ¢ 651193 + .00000495 ¢ -659632 + .00000710 ¢ .664936 + .00000653 ¢ .676720 + .00000783 ¢ .684144 + .co000861 ¢ +57 5528 + .00000333 ¢ 579856 + .00000323 ¢ «586000 + .00000443 ¢ -§89828 + .00000439 ¢ ee + .00000560 ¢ 6033 + .00000636 ¢ 513558 — .00000033 ¢ -516149 + .00000017 ¢ 520004 -++ .00000054 ¢ 522349 + .00000048 ¢ ; 60 + .00000082 ¢ N. B. — The above examples on the effect of temperature give an idea of the order of magnitude of that effect, but are only applicable to the particular specimens experimented on. fn ——__—_—_—— ee SMITHSONIAN TABLES. 179 TABLE 186. INDEX OF REFRACTION. Indices of Refraction for the various Alums.* Index of refraction for the Fraunhofer lines. Aluminium Alums. RAI(SO,).+12H,O.t _Na 1.667 17-28 | 1.43492 | 1.43563 | 1.43653 | 1.43884 | 1.44185 | 1.44231 | 1.44412 NH3(CHs) | 1.568] 7-17] -45013| 45062] .45177| -45410| .45691| .45749] -45941 K 1-735| 14-15] -45226] -45303] -45398} -45645| -45934| -45996| -46181 Rb | 1.852] 7-21] .45232] .45328| -45417| -45660| .45955| -45999| .46192 Cs 1.961 | 15-25] .45437| -45517| -45618| .45856| .46141| .46203| .46386 NHgq | 1.631] 15-20] .45509] .45599| -45693] -45939| -46234] .46288) .46481 Te 2.329 | 10-23] .49226| .49317] -49443] -49748] .50128| .50209] .50463 Indium Alums. RIn(SO,4).+12H,0.t | 45942 | 1.46024 | 1.46126 | 1.46381 | 1.46694 | 1.46751 | 1.46955 | 1.49402 .46091 | .46170| .46283] .46522] .46842| .46897] .47105|] .47562 -46193| -46259| -46352] -46636| .46953| -47015] -47234| -47750 Gallium Alums. 2Ga(SO4).4-12H,0.t 1.46146 | 1.46243 | 1.46495 1.47034 5 -47093 .47126 -47412 51387 Chrome Alums. RCr(SO4)o+12H.0.t -47627 | 1.47732 | 1.47836 | 1.48100 | 1.48434 | 1.48491 | 1.48723] 1.49280 -47642| .47738| -47865| .48137| -48459| -48513| -48753| -49309 -47660| .47756| .47868| .48151] .48486| .48522| .48775| .49323 47911} .48014) .48125| .48418| .48744| .48794| .49040] .49594 51692] .51798] .51923| -52280] .52704| .52787| .53082| .533808 Iron Alums. RFe(SO,).4+-12H,O.t -47639 | 1.47706 1.47837 1.48169 | 1.48580 1.48939 -47700| -47770| .47894| .48234] .48654 -49003 -47825]| .47921| .48042] .48378| .48797 -49136 -47927 | .48029| .48150] .48482| .48921] . -49286 -51674] .51790| .51943| -52365] .52859 +53284 * According to the experiments of Soret (Arch. d. Sc. Phys. Nat. Genéve, 1884, 1888, and Comptes Rendus, 1885). + & stands for the different bases given in the first column. SMITHSONIAN TABLES. 180 TABLE 187. INDEX OF REFRACTION. Index of Refraction of Metals and Metallic Oxides. (a) Experiments of Kundt* by transmission of light through metallic prisms of small angle. Index of refraction for Name of substance. White. Silver . . . . . . . - 0.27 - Gold : : eae : : : 0.38 0.58 1.00 Copper . ‘ . . ° ° : 0.45 0.65 0.95 Platinum . : : ; : - : 1.76 1.64 1.44 Tron : : : . : ; : 1.81 173 1.52 Nickel . é : : ; 5 : 2.17 2.01 res Bismuth . : : ‘ ; ; : 2.61 2.26 2.13 Gold and gold oxide ; . : ! 1.04 ~ 1.25 as s . . . : : 0.89 0.99 Ta33 oe 6 oral : : : : - 2.03 - Bismuth oxide . - . . : : - 1.91 - Tron oxide : of yale : : . 1.78 2.11 2.36 Nickel oxide. : 5 : 5 : 2.18 2.23 2.39 Copper oxide . : : : : . 2.63 2.84 3.18 Platinum and platinum oxide . é : 3-31 3.29 2.90 4-99 4.82 4.40 (b) Experiments of Du Bois and Rubens by transmission of light through prisms of small angle. ncn cn eee EEEEEEEEEEEREEEEEE EE The experiments were similar to those of Kundt, and were made with the same spectrometer. Somewhat greater accuracy is claimed for these results on account of some improvements intro- duced, mainly by Prof. Kundt, into the method of experiment. There still remains, however, a somewhat large chance of error. i Index of refraction for light of the following color and wave-length. Name of metal. Red (Lig). “Red.” Yellow (D). Blue (F). Violet (G). Nickel : : : Iron : . 3.12 .06 272 2.43 2.05 Cobalt ; (c) Experiments of Drude. The following table gives the results of some of Drude’s experiments.§ The index of refrac- tion is derived in this case from the constants of elliptic polarization by reflection, and are for sodium light. Index of Metal. refraction. Metal. Index of refraction. Aluminium . : ; 1.44 Mercury 4 ; ; 172 Antimony. : . 3-04 Nickel . . : . 1.79 Bismuth : : : 1.90 Platinum ; : 2.06 Cadmium : : : 1 fc Silver. 5 : : 0.181 Copper . : ; : 0.641 Steel : : ‘ : 2.41 Gold E ; ; : 0.366 Tin, solid ‘ ; ; 1.48 Iron : : : ; 2.36 “fluid ‘ : : 2.10 Lead . : : : 2.01 Zinc . ‘ . ; 2.12 Magnesium * “Wied. Ann.” vol. 34, and “ Phil. Mag.” (5) vol. 26. + Nearly pure oxide. + Wave-lengths A are in millionths of a centimetre. § “Wied. Ann.” vol. 39. SMITHSONIAN TABLES. 181 TABLES 188, 189. ae INDEX OF REFRACTION. TABLE 188. —Index of Refraction of Rock Salt. Determined by Langley. Determined by Rubens and Temp. 24° C. re Determined by other authorities. Wave- length in cms. Wave- length Index of in cms. | refraction. | Line of spec- Line of | spec- Index of |} Line of Taeciot refrac- spec- Authority. refraction. * tion. m. trum. | X 108. trum X 108. tru M 1.57486 .4 | 1.5607 1.54046 L 38.20 | .57207 : 5531 -55319 | ¢ Haagen at 20° C. He 39-33 | -56920 : 5441 -50056 Hy 39-65 | .56833 5 -5404 G 43-03 | -.56133 : 5370 1.54095 | ) Bedson and F 48.61 | .55323 : 5358 -55394 | ¢ Carleton Williams bg 51.67 | .54991 I] -5347 bi 51.83 | -54975 ‘6 | .5337 57-89 | -54418 -5329 55-95 | -54414 . +5321 65.62 54051 5313 68.67 | 53919 +5305 76.01 | .5367 -5299 5328 +5293 +5305 5280 5287 5280 5268 5275 .5270 5204 5257 5247 "5239 .5230 5217 5208 “5197 5184 5163 5138 Stefan at 17° and 22> ©. The'up- per values are at 17° and the lower at 22° for each line. Zz QO 3s te OO we Pe soa TABLE 189. — Index of Refraction of Sylvine (Potassium Chloride). Determined by Rubens and Snow. Determined by other authorities. Wave- Tadex‘of Line of length in . spec- cms. X 108, refraction. trum. Index of Wave-length Index of refraction. in cms. X 10%. | refraction. Authority. 1.5048 : 1.4766 4981 ; 4761 “4900 . “4755 4868 : -4749 1.48377 -48597 48713 -49031 40455 Stefan at 20 C. -498 30 50542 51001 -4754 “4707 4825 for 4877 Grailich. -4903 5005 -4904 Tschermak. -4930 Groth. 1.4829 ; 1.4742 4819 : 4732 .4809 : 4722 -4807 ; 4717 1.4795 : 1.4712 -4789 : -4708 .4781 534- .4701 -4776 -4693 A B Cc D E F G H B ce D E F G D D 1.4771 s 1.4681 SMITHSONIAN TABLES. 182 TaBLe 19C. INDEX OF REFRACTION. Index of Refraction of Fluor-Spar. Determined by Determined by Determined by the Rubens and Snow. Sarasin. authorities quoted. Wave-length Index Line Wave- Index i Index 7 in cms. of of length in of of Authority. X 108, refraction. || spectrum. | cms. X 10%,| refraction. spectrum. | refraction. 43-4(Hy) : : P Fizeau. 48.5(F) . . 431575 58.9(D) 43¢ ;. 431997 65-6(C) : ; 432571 80.7 . -433937 85.0 : 3. 437051 Miilheims. 89.6 . ; 441215 95.0 : ‘ 442137 100.9 ; t 445350 107.6 42 4. .446970 115.2 -42 4. 447754 124.0 : . -449871 134.5 . . -459576 146.6 : : .464760 161.3 . : .47 5166 179.2 ; 22. 477622 201.9 . : 481515 “f ? DesCloi- j 230.3 , ; 484031 Yellow} .435 ee 268.9 : : 487655 322.5 : : .490406 Na 1.4324* ? 403-5 . 20.2 493256 43421 J 462.0 ; : .496291 538-0 : ; «502054 646.0 ; s 509404 807.0 * Gray at 23° C. t Black at 19° C. GMITHSONIAN TABLES. 183 TABLE 191. INDEX OF REFRACTION. Various Monorefringent or Optically Isotropic Solids. Substance. Agate (light color) Ammonium chloride . Arsenite Barium nitrate Bell metal Blende Boric acid Borax (vitrified) Camphor Diamond (colorless) . Diamond (brown) . Ebonite ‘ 7 Fuchsin Garnet (different varieties) Gum arabic ‘ ‘ “ Hanyne Helvine Obsidian . Opal . Pitch .« A . Potassium bromide 6 chlorstannate 6 iodide Phosphorus Resins: Aloes . Canada balsam Colophony Copal . Mastic . Peru balsam Selenium, vitreous f bromide Silver 2 chloride . iodide : blue . 5 Sodalite clear like water Sodium chlorate 5 Spinel 3 Strontium nitrate Line of Spectrum. Meleloloks ™~p i oO MOOF0OHZ o of oO 5 _—“ ee a 4 oc“ OOD 58 UO HMOwPOMS sua yo UY Ud nan ees 4 oO RQ. - SMITHSONIAN TABLES. 184 Index of Refraction. Authority. De Senarmont. Grailich. DesCloiseaux. Fock. Beer. Ramsay. Bedson and Carleton Williams. Kohlrausch. Mulheims. DesCloiseaux. Schrauf, Ayrton & Perry. Wernicke. Various. Jamin. Wollaston. Tschichatscheff. Levy & Lecroix. Various. “ Wollaston. Tops6e and Christiansen. Gladstone & Dale. Jamin. Wollaston. Jamin. “ Wollaston. Baden Powell. Sirks. Wernicke. Feusner. | Dussaud. DesCloiseaux. Fock. TABLE 192. INDEX OF REFRACTION. Index of Refraction of Iceland Spar. The determinations of Carvallo, Mascart, and Sarasin cover a considerable range of wave-length, and are here given, any other determinations have been made, but they differ very little from those quoted, Index of refraction for — Index of refraction for — Wave- . Wave- length in ‘ poet length in | ems. X 108, | Ordinary Extraordi- P “lems. X 10%] Ordinary Extraordi- ray. nary ray. ray. nary ray. Authority: Carvallo. Authority: Sarasin. o*53 1.70740 27.46 -74151 20 7T -76050 23.12 80248 6361 22.64 81300 -6403 2 21.93 83090 6424 21.43 84580 76.04 .65006 48275 Authority : Mascart. 68.67 65293 1.65013 Authority: Sarasin. 65162 a 76.04 1.65000 1.48261 65296 .48409 71.84 65156 48336 65446 .48474 68.67 65285 48391 65846 48654 64.37 .65501 .48481 66354 .4888 5 58.92 65839 .48644 66446 - 53:77 -66234 48815 -66793 49084 53-30 .66274 48843 G .67620 49470 50.84 -66525 48953 68330 48.61 .66783 49079 .68706 47-99 .668 58 -4Q112 68966 46.76 .67023 49185 69441 44-14 67417 -49367 -69955 41.01 68036 49636 70276 39-68 68319 49774 70613 36.09 -69325 50228 71155 34-65 | 69842 | .50452 71.580 34-01 -70079 “50559 71939 SMITHSONIAN TABLES. 185 TaBLe 193. | Line or wave- length in cms. 6 ray. 1.54227 54419 “54655 54675 -54825 55014 55104 *55318 -56348 -50617 56744 57094 58750 -59624 -61402 61816 -62502 -63040 -63569 -64041 64566 -65070 -65990 .67500 Ordinary INDEX OF REFRACTION. Index of Refraction of Quartz. Index for — Line of Extraordinary spectrum. ray. Index for — Ordinary ray. Extraordinary ray. Quincke (right-handed quartz). Authority: Sarasin.* 1.55124 55335 55573 55595 55749 55943 56038 -50270 257319 “57.999 57741 58097 59812 60713 -62561 62992 -63705 .64268 64813 65308 65852 -66410 67410 68910 Authority: R 1.5538 *5499 5442 5419 5376 +5364 *5953 5342 5325 5310 5287 “5257 5216 -5160 43-4( Hy) 45.5(F) 59.0(G) 65.6(C) 83-9 90-4 97-9 106.7 117.4 130.5 146.8 167.9 195-7 ubens. ROWOZZSCMOATS HU OWD > SMITHSONIAN TABLES. * For wave-lengths, see Tables 190 and 192. 186 1.53958 -54057 -54335 -54049 548603 55241 Authority: Mascart. 1.53902 54018 -54099 54188 54423 -54718 54770 -54966 55429 55816 50019 -50150 -56400 50668 56842 1.53914 -54097 “54185 54419 “54715 -54966 55422 55811 Quincke (left-handed quartz). Authority: Van der Willigen (left-handed quartz). 1.54806 -54998 -55035 55329 55633 +55855 50305 -56769 INDEX OF REFRACTION. TaBLes 194, 195. TABLE 194. — Uniaxial Crystals. eer Index of refraction. Substance. spec- os Authority. trum. | Ordinary | Extraordi- ray. nary ray. Alunite (alum stone) . : : : : 1.573 1.592 Levy & Lacroix. Ammonium arseniate . < . . : red) |) 16577 4.524 De Senarmont. Anatase. : : . . : . 2.5354 | 2.4959 Schrauf. Apatite : : : : : . : 1.6390 | 1.6345 ig Benzil . . ; : A : . 7 1.6558 1.6784 DesCloiseaux. 1.589 to] 1.582 to| ] . poy : ; ae ne f Various. Brucite 2 ; : : : ; . 1.560 1.581 Kohlrausch. Calomel_. : : : : ; ; 1.96 2.60 De Senarmont. Cinnabar . : : ; : : ; 2.554 3-199 DesCloiseaux. : 1.767 1.7 Corundum (ruby, sapphire, etc.) : : } 1.769 fd Dioptase . : : : : ; 1.667 1.723 Emerald (pure) : : 2 : : 1.584 1.578 Iceat—s8°C. . ; : , 2 : D 1.309 1-33 Meyer. I.71¢ é ‘ Idocrase . ; : . : ; ; E 719 cS to) DesCloiseaux. Ivory . , : : . : ; : 1.539 1.541 Kohlrausch. Magnesite . ; ; : ; : : 1.717 1.515 Mallard. Potassium arseniate : : : : . 1.564 1.515 DesCloiseaux. Ke 7 : : : : 1.493 1.501 De Sernamont. Silver (red ie) : : : : : ; 3.084 2.581 Fizeau. Sodium arseniate : : : ; ; 1.459 1.467 Baker. eet atent. : : ; : ; 1.557 1.336 Schrauf. “© phosphate . . ; : : 1.446 2.452 Dufet. Strychnine sulphate . : : : : 1.614 1.519 Martin. Tin stone. 7 : ; ; 1.997 2.093 Grubenman. Tourmaline (colorless) : : ; : 1.637 1.619 Heusser. : (different colors) ae = rege c Zircon (hyacinth) 3 : : : : 1.92 1.97 De Senarmont. “ < : : 1.924 1.968 Sanger, Jeroféjew. TABLE 195. — Biaxial Crystals. P Index of refraction. Line of Substance. Spee | pee | i a Authority. trum. Interme- Minimum. Maximum. Arzruni. Miilheims. Glazebrook. Rudberg. DesCloiseaux. Various. Dufet. é Kohlrausch. 1.5228 ; Miilheims. 1.5936 .50 Pulfrich. 1.675 3 DesCloiseaux. 1.5237 f “ 1.7380 8 Dufet. 1.5056 -506. Schrauf. 1.4946 .498 Topsoe & Christiansen. Sugar (cane) : 1.5067 or Calderon. Sulphur (rhombic) 2.038 ; Schrauf. Topaz (Brazilian) : D : 1.63 6: Miilheims. .631 t ree Topaz (different kinds) eon ae Various. 1.616 Zinc sulphate 1.4801 I 4836 Tops6e & Christiansen. Anglesite Anhydrite Antipyrin Aragonite Axinite Barite . Borax . ‘ Copper sulphate : Gypsum Mica (muscovite) . Olivine . Orthoclase Potassium bichromate . _ nitrate ed sulphate DUUN oO a. wholelelelelelelelejole, oD SMITHSONIAN TABLES. 187 TaBLe 196. INDEX OF REFRACTION. Indices of Refraction relative to Air for Solutions of Salts and Acids. Indices of refraction for spectrum lines. Authority. Substance. Density. | Temp. C. Cc Ammonium chloride | 1.067 | 279.05 |1.37703] 1.37936) 1.38473 1.39336) Willigen. eo ; 025 | 29.75 | .34850| -35050 “35515 36243 * Calcium chloride 398 | 25.65 | -44000] .44279| .44938 .46001 f e <205) || 2220 39411] .39652] .40206 -41078 . iC « 143 | 25.8 37152] -37369] .37876 -38666 1.42816 &s 41901 ¢ .41637 | Fraunhofer. — |Bender. 1.166 | 20.75 |1.40817 -359 | 18.75 | .39893 -416 | 11.0 40052 normal solution} .34087 double normal | .34982 triple normal | .35831 Hydrochloric acid . | Nitric acid ; Potash (caustic) . Potassium chloride . “ “ 1.41109 .40181| .40857 .40281| .40808 -34278| 34719 -35179} -35045 36029] .30512 “ “ “ 1.42872 | Willigen. — |Schutt. “ Soda (caustic) Sodium chloride . “ : 41071 18.07 | .37562 18.07 | .35751 18.07 | .34000 1.41334] 1.2 -37789| -38322 -35959| -36442 -34191| .34628 “ “ “ Sodium nitrate 22.8 |1.38283]1.38535| 1.39134 1.40121 Willigen. Sulphuric acid 18.3 -43444] .43069| .44168 44883 s cs sc 18.3 .42227| .42466| .42967 iC cS 18.3 36793] -37009| .37468 -33063] .33862| .3428 Zinc chloride . 1.40222 “ce “ce -37515| .38026 1.39977 26.4 37292 Ethyl alcohol. . .| 0.789 1.37094| Willigen. “ ‘“ 36662 a Fuchsin (nearly sat- ILateG)) ys oars Cyanin (saturated) . ~ 3759 |Kundt. 3821 ‘ Nore. — Cyanin in chloroform also acts anomalously ; for example, Sieben gives for a 4.5 per cent. solution w44= 1.4593, Mn = 1.4695, ur(green) = 1.4514, me (blue) = 1.4554. For a 9.9 per cent. solution he gives w41= 1.4902, wr (green) = 1.4497, wa (blue) = 1.4597. (c) Sotutions oF PorasstuM PERMANGANATE IN WATER.* Wave- : Wave- : Spec- | Index Index Index Index Spec- | Index Index Index Index soneee | rum ie for for for jengeh frum for dor for for SCiro8: | . |r %sol. | 2% sol. | 3% sol. | 4 % sol. X 106. | line. |x % sol. | 2 % sol. | 3 % sol. | 4 % sol. 68.7 | B_ | 1.3328 | 1.3342 - - | 1.3368 | 1.3385 = = 65.6 | C | .3335 | -3348 | 1.3365 — | -3374 | -3383 | 1.3386 | 1.3404 61.7| - | .3343 | .3365 | .338% Fy 13377) = | .3408 59-4 | - | -3354 | -3373 | -3393 — | -3381 | -3395 | -3398 |. -3413 58.9 | D +3353 | -3372 = = +3397 | -3402 | -3414 | -3423 56.3 | - | .3362 | .3387 | .3412 - | .3407 | .3421 | .3426 | .3439 553 | - | -3366| .3395 | -3417 | eSaral e = +3452 52-7 | E | .3363 57 = — | 343 | 3442 | -3457 | 3468 2.2 - 13302 1133377. 1| 3306 - - = a = * According to Christiansen. 188 SMITHSONIAN TABLES. TaBLe 197. INDEX OF REFRACTION, Indices of Rofraction of Liquids relative to Air. Index of refraction for spectrum lines. Substance. Cr — — > Authority. H Acetone 9s. . « 1.3626 1.3694 Korten. Almond oil . . . 4755 -4847 Olds. mnauee 5... 5993 .6041 Weegmann. Aniseed oil . . . : 5410 5647 Willigen. A Fee 5508 5743 A Baden Powell. Benzenet. .. .« 1.4983 1.5148 Gladstone. ert de “4934 “5095 Bitter almond oil 5391 562 Landolt. Bromnaphtalin . . 6495 6819 Walter. Carbon disulphide + 1.6336 1.6688 Ketteler. i. es 6182 6523 : e “ .6250 6592 Gladstone. * se 6189 6352 Dufet. Cassia Olle es 7 .6007 -6389 Baden Powell. “ “ “ . 5930 ‘6314 Chinolin.. .....- 1.6094 1.6361 Gladstone. Chloroform .. . -4400 4555 Gladstone & Dale. ee . . . a an = eek 24437 || -452 Lorenz." Cinnamon oil . . 35 |) 00077 65 Willigen. theme. beter 1.3554 1.3606 Gladstone & Dale. ee nt ae Ge < a573 3641 Kundt. Ethylalcohol . . eB0770 |e -3739 Korten. fs As , 262671): 3698 | . ay =3590) ||. eg0S7mi lure a -3021 -3683 Gladstone & Dale. Glycerine. . . .| 20 | 1.4706 1.4784 Landolt. Methyl alcohol . .| 1 .3308 : : Baden Powell. Olive oil . ... % .47 38 : Olds. ROCK Ossian 4345 : i Turpentine oil . .| 10.6] 1.4715 Fraunhofer. es OT el 20:7) 4092 -4793 Willigen. Moliene) oie |) 220 4911 5070 Bruhl. WiaterSn cae ene) riLG -3318 “33770 | Dufet. ee SS Feo ye .3318 -3378 Walter. * Weegmann gives p= 1.59668 — .0005187. Knops gives wp— 1.61500— .00056 #. + Weegmann gives p= 1.51474— 0006657. Knops gives wp = 1-51399 — 000644 #. + Wiillner gives u g—= 1.63407 — .00078 ¢ ; Mp 1.66908 — .o0082 4; My, = 1.69215 — .0008 5 #. § Dufet gives 4p = 1.33397 — 10-7 (125 #4 20.6 f — .000435 #&—.o0115 4) between 0° and 50°; and nearly the same variation with temperature was found by Ruhlmann, namely, p= 1.33373 — 10—7 (20.14 # +- .000494 #4), SMITHSONIAN TABLES. 189 TABLE 198. INDEX OF REFRACTION. Indices of Refraction of Gases and Vapors. A formula was given by Biot and Arago expressing the dependence of the index of refraction of a gas on pressure and Mo— 1 == = wh 1 aloo. mz is the index of refraction for temperature 7, 7% for temperature zero, a the coefficient of expansion of the gas temperature. More recent experiments confirm their conclusions. The formula is #,—1 with temperature, and 4 the pressure of the gas in millimetres of mercury. Taking the mean value, for air and white light, of 7» —1 as 0.0002936 and a as 0.00367 the formula becomes pee -0002936 PB ___-0002895 P : 1+ .00367#% 1.0136 X 108 1+ .00367 10°” where P is the pressure in dynes per square centimetre, and ¢ the temperature in degrees Centigrade. (a) The following table gives some of the values obtained for the different Fraunhofer lines for air. Index of refraction according to— 2 Index of refraction according to Kayser & Runge. Spectrum line. Ketteler. Lorenz. Kayser & Runge. 1.0002929 1.0002893 1.0002905 2935 2899 2911 2935 2902 2014 2947 2911 2922 2958 2922 2933 1.0002993 3003 3015 1.0003023 3031 T.0002968 1.0002931 1.0002943 3043 2987 2949 2962 3003 2963 2978 - 2980 = re 2987 QW HOaQAWP _ ~ 1.0003053 3064 3075 nw GHn WOV ozz - ‘ (b) The following data have been compiled from a table published by Briihl (Zeits. fiir Phys. Chem. vol. 7, pp. 25-27). The numbers are from the results of experiments by Biot and Arago, Dulong, Jamin, Ketteler, Lorenz, Mascart, Chappius, Rayleigh, and Riviére and Prytz. When the number given rests on the authority of one observer the name of that observer is given. The values are for 0° Centigrade and 760 mm. pressure. Kind of | Indices of refraction light. and authority. Kind of | Indices of refraction light. and authority. Substance. Substance. white white Acetone 1.001079-I.00I 100 Ammonia I.000381I-1.00038 5 ie vr 1.00037 3-I.000379 Hydrogen 1.0001 38-1 .000143 S 1.0001 39—1.0001 43 1.000644 Dulong. Argon. senzene 3romine . a Carbon dioxide “ “ Carbon disul- phide Carbon mon- oxide Chlorine . “ Chloroform . Cyanogen “ Ethyl alcohol Ethyl ether . Helium Hydrochloric acid . 000281 Rayleigh. .001700-1.001823 001152 Mascart. .000449-1.0004 50 .000448-1.0004 54 001500 Dulong. .001 478-1.001485 .000340 Dulong. .009335 Mascart. .000772 Dulong. 000773 Mascart. .001430-1.001 464 .000834 Dulong. .000784-1.00082 5 .00087 I-1.00088 5 .OOI §21-1.001 544 .000043 Rayleigh. .000449 Mascart. -000447 me SMITHSONIAN TABLES. Hydrogen sul- D phide Methane . “ Methyl alcohol. Methyl ether Nitric oxide . “ “ Nitrogen . “ Nitrous oxide “ “ Oxygen ce . . . Pentane ie) so Sulphur dioxide “ “ Water. “ D white D D D D D D D D D D 1.000623 Mascart. 1.000443 Dulong. 1.000444 Mascart. 1.000549-1.000623 1.000891 Mascart. 1.000303 Dulong. 1.000297 Mascart. 1.00029 5-I.000300 1.000296-1.000298 1.000503-I.000507 1.000516 Mascart. 1.000272-1.000280 1.00027 I-1.000272 1.001711 Mascart. 1.000665 Dulong. 1.000686 Ketteler. 1.000261 Jamin. 1.000249-I.000259 190 ROTATION OF PLANE OF POLARIZED LicHt. -*@* 19% A few examples are here given rok the effect of wave-length on the rotation of the plane of polarization. The rotations are for a thickness of one decimetre of the solution. ‘The examples are quoted from Landolt & Burn- stein’s ‘‘ Phys. Chem. Tab.’’ ‘The following symbols are used : — f/= number grammes of the active substance in 100 grammes of the solution. —_ ae “ solvent “ “ee as “ ae oF active ae “ cubic centimetre “ Right-handed rotation is marked +-, left-handed —. Wave-length | Tartaric acid,* CuH,Qy,, Camphor,* Cy) Hy,O, Santonin,t Cy,;H 40s, Line of | according to dissolved in water. disselved in alcohol. dissolved in chloroform. spectrum. | Angstrém in 7=50to 95, 9g = 50 to gs, 9 =75 to 96.5, cms. X 108, temp; =a4 Ge temp. = 22.9” C. temp. = 20° C, B 68.67 —140°.1 -+ 0.20859 ce 65.62 + 2°.748 + 0.094469 | 38°.549 —0.0852¢ — 149.3 +0.1555¢ D 58.92 + 1.950 + 0.130309 51.945 — 0.0904 7 — 202.7 + 0.3086¢ E 52.69 + 0.153 + 0.175149 74-331 — 0.13437 — 285.6 + 0.5820¢ by 51.83 - - ~ - — 302.38 + 0.6557 7 be 51.72 — 0.832 + 0.19147 9 79.348 — 0.1451 7 ~ ooh F 48.61 — 3.598 + 0.23977 7 99.001 — 0.1912 9 — 365.55 + 0.8284 7 e 43-83 — 9.657 + 0.314379 | 149.696—0.23469 | -— 534-98 -+ 1.52409 Santonin,t CisH120s, Santonic acid,t : aa ee ea On dissolved in | dissolved in | djssolyed in vith 2314 alcohol. chloroform | chloroform, | @8s0lved in ¢ = 4.046. |C= 3.1-30.5.| ¢—=27,192. _Water. temp. = temp.= | temp. = 20° C. P= 70 se 20" .C. Santonin,t Cy;Hy.Os, » dissolved in alcohol. C= 16782. temp. = 20° C, B 68.67 — 110.49 442° 484° — 49° 47°.56 C 65.62 — 118.8 504 549 — 57 52.70 D 58-92 — 161.0 693 754 —74 60.41 E 52.69 — 222.6 gg 1088 — 105 84.56 by 51.83 — 237.1 1053 1148 — 112 ~ bo 51.72 - = - - 87.88 F 48.61 — 261.7 1323 1444 — 137 101.18 e 43-83 — 380.0 2011 2201 — 197 ~ G 43-07 - - - - 131.96 g 42.26 - 2381 2610 — 230 - * Arndtsen, “‘ Ann. Chim. Phys.” (3) 54, 1858. ¢ Narini, “‘R. Acc. dei Lincei,’’ (3) 13, 1882. + Stefan, ‘‘ Sitzb. d. Wien. Akad.” 52, 1865. TABLE 200. ROTATION OF PLANE OF POLARIZED LICHT. Quartz (Soret & Sarasin, Arch. de Gen. 1882, or C. R. gs, 1882).* Spec- Wave- Rotation Wave- Rotation Wave- Rotation nae length. Cc per mm. length. per mm. length. 71.769 12°.668 ; 36.090 67.889 14.304 65.073 15.746 59.085 53:233 Te 45.912 2 21.084 45-532 s wr 42.534 so7i4 | 13 27-543 30-412 ¥ ae 43 37-352 ip aes 35-544 33-931 47-481 32.341 51.193 30.645 : §2-155 29.918 28.270 55.625 25.038 55.894 ww NW mom a B E D E F G G H iL M N P Q R e 201.824 220.731 235-972 OD Ga Goa mini NN he ~ = * The paper is quoted from a paper by Ketteler in “‘ Wied. Ann." vol. 21, p. 444- The wave-lengths are for the Fraunhofer lines, Angstrém’s values for the ultra violet sun, and Cornu’s values for the cadmium lines. SMITHSONIAN TABLES. 191 TABLE 201. LOWERING OF FREEZINC-POINT BY SOLUTION OF SALTS. Under P is the number of grammes of the substance dissolved in 100 cubic centimetres of water. Under C is the amount of lowering of the freezing-point. The data have been obtained by interpolation from the results pub- lished by the authorities quoted. Substance and Substance and Substance and observer. observer. observer. AgNOs3 ZnSO4 MgCle F. M. Raoult.* : F. M. Raoult.* S. Arrhenius.t CuSO4 F. M. Raoult.* BaCle Harry C. Jones.§ ° _ _ \o Ca(NOs)e F. M. Raoult.* 9° to wo p SrCle S. Arrhenius. t OO ON ANALW bd _ CdSO4 Cd(NOs)z oO. F. M. Raoult.* Harry C. Jones.§ NaeSO4 F. M. Raoult.* AnnbfWyNyano OnNOMONOMNOMNOM CuCle Lt 2H20 KeSO4 S. Arrhenius.t S. Arrhenius. NaCl S. Arrhenius.t WWN Kee OtnhOn Ot MOM DWNONEYWD 4 WNNHRO KCl Harry C. Jones. 1 CHONOHNONOHNONONON “VFWHH NAN POW Nd MH OnNdONnNdNoMm HII AAMAS ROW DD AHO Harry C. Jones.§ = O mon LiCl MgSO4 S. Arrhenius.t F. M. Raoult.* CaClz S. Arrhenius.t nbW Nw ° wm NH,Cl Harry C. Jones. *In “ Zeits. fiir Physik. Chem.’ vol. 2, p. 489, 1888. + Ibid. vol. 2, p. 491, 1888. ¢ Ibid. vol. 11, p. rr0, 1893. § Ibid. vol. 11, p. 529, 1893. 192 SMITHSONIAN TABLES. TABLE 201. LOWERING OF FREEZINGC-POINT BY SOLUTION OF SALTS. Substance and co Substance and P rer Substance and observer. observer. observer, ZnCl oO. 5 Alcohol, CoH¢O} 0.1 | 0.044] HeSOz Harry C. Jones.* | 1. Harry C. Jones.}| 0.2 |0.057] S. Arrhenius.t 0.129 0.170 0.212 0.402 CdBre Harry C. Jones.* OnNONON WhNKRee O Acetic acid, Cdl, . CoH4Oo S. Arrhenius. ; Harry C. Jones. PAQIMNE LOW NHAHO OnN ON OM OMN OM OM OM H2SO4 Harry C. Jones. P(OH)s S. Arrhenius.t NaOH Harry C, Jones. HgPO,4 S. Arrhenius.t HIO3 KOH : S. Arrhenius.t Harry C. Jones.}{ Cane sugar. F. M. Raoult.§ NH,OH Harry C. Jones. HCl Harry C. Jones. NaC Oz Harry C. Jones. Glycerine. || HNOsz : S. Arrhenius.t KoCOg : Harry C. Jones. Harry C. Jones. RmOAL VN NdHe eo O OO 9 COU Coma Ww niWe =eN HS NW * In “ Zeits. fiir Physik. Chem.” vol. 11, p. 529, 1883. + Ibid. vol. 2, p. 491, 1888. $ Ibid. vol. 12, Poa) 1893. of F. M. Raoult, C. R. 114, p. 268. ; 5 : Fao ; 50% solution solidifies at —31° C., according to Fabian, ‘‘ Ding. Poly. Journ.” vol. 155, p- 345+ This gives an average of .3 per gramme. SMITHSONIAN TABLES. 193 TABLE 202. VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER.* The first column gives the chemical formula of the salt. The headings of the other columns give the number of gramme-molecules of the salt in a litre of water. The numbers in these columns give the lowering of the vapor pressure produced by the salt at the temperature of boiling water under 76 centimetres barometric pressure. ° a Substance. Als(SO4)s AlCl; . Ba(SOs)e Ba(OH)2 Ba(NOs)2 Noe — he DHAAM WN AL Ch DOD WW QOun © Ba(ClOs)e - BaCle . BaBre . Ca(SOs)2 Ca(NOs)2 CaCle . . . . ° Cabrz. 3 ; : ‘ : : 283. | CdSO4 . . . | Cdl. . . . . . . CdBrs:) 2 sae ; | CdCl. . Cd(NOs)e . Cd(C1O3)2 . CoSO4 2 CoCle . — Bp ON EN, oo Co(N Os)e2 FeSO, HsBO3 HsPO4 Hs3AsO4 ~ Ny wh CO on OMAR Oo WN NAR OO ow ° HeSO,4 K HePO4 KNOs. KCI1O3 KBrO3 NN hw 0 MH & Frees PRBW OO BO Wb OG b KHSO, KNOg KC104 Koi KHCOg No NHN bh DROW OO BAHU coda SA OND ut Oo on Kae ioCaOs KoWO4 KsCOs KOH . mi Oo eS NWwWWNN KeCrO4 LiNOs LiCl LiBr | LigSOg s=NUnOMN tn 0 OWN RNyNH HN PARAS © LiHSO,4 Lil LigSiF lg LiOH . LigCrO4 WwwWhdh VIE ON ALP OAO * Compiled from a table by Tammann, ‘“‘ Mém. Ac. St. P: a? ; : “Zei eee ee y on, ém. Ac. St. Petersb.’’ 35, No. 9, 1887. See also Referate, “‘ Zeit. f. | SMITHSONIAN TABLES. 194 TABLE 202. VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER. 2.0 3.0 | 40 | 6.0 | 60 | 80 | 10.0. Substance. MgSO4 : ‘ } MgCh. ; : wl) 16. 39.0 100.5 183-3 277.0 | 377.0 Mg(NOs)2 . . . 17.6 42.0 | Mgbre : : -| 17.9 | 44.0 MgH.(SO4)2 A : 18.3 | 46.0 MnSO,_ ss. : : 6.0 | 10.5 MnCle. : : - |) X5.0' |) 34.0 NaHePO, . : 10.5 20.0 NaHSO, . : < | 10:9) |p 22.0 NaNOs : : ; 10.6 22. NaClOs , 3 ; 10.5 23.0 (NaPOs)6_ - : : 11.6 NaOH A ; 11.8 NaNOz : ; : 11.6 NaHPO, . : : 12.1 nh ty Qe nuit @* NaHCOg 12.9 | 24.1 NaSO4 12.6 | 25.0 NaCl . E223) ee25-2 NaBrOg 12.1 25.0 Nabr . 12.6 | 25-9 INAML % : : ale Deda 25:0 NagP2O7 . ‘ : 3:2 22.0 NagCOg_ . ; ntti |e 2753 NagCoO4 . ; ‘ 14. 30.0 Na2WOq . : orl) Las 33-6 NagPO,_ : -| 16.5 | 30-0 (NaPOs)3_ - 2 ai etzers ||| 30:5 NH4NO3 . : : 12.8 22.0 (NH4)eSiFle + > | eELeSe|, 25-0 NH,4Cl . : set 2.O> eat? NH,4HSOsg. ; ; 11.5 22.0 (NH4)2SO4. : : II. 24.0 | NH4Br : : -| I1.9] 23.9 NHglI . 2 : -|| -£2.9 || "25-1 NiSO, : : : 5.0 | 10.2 NiCle . : , ee LOnta eg y7-O) Ni(NOs)o_ - 2 oh) LOD |) (3793 Pb(NOs)2 - : Sule E2ese 2355 Sr(SOs)2_ : . 52 i 20:3 Sr(NOs)2 15. 5 31.0 SrCle . 16.8 | 38.8 SrBro . 17.8 | 42.0 ZnSO4 4-9 ZnCl, . 9.2 Zn(NOs3)2 16.6 SMITHSONIAN TABLES. TaBLe 203. RISE OF BOILING-POINT PRODUCED BY SALTS DISSOLVED IN WATER.* This table gives the number of grammes of the salt which, when dissolved in 100 grammes of water, will raise the boiling-point by the amount stated in the headings of the different columns. The pressure is supposed to be 76 centimetres. Salt. BaCle + 2H20 . : d ‘ .3| 63.5 | (71.6 gives 4°.5 rise of temp.) | CaCle ; 5 : : '5| 21.0) 2 32.0| 41.5| 55-5] 69.0 | Ca(NOs)2 + 2H,0 : 2 : ; * 98.7 | 152-5] 2400] 331.5 KOH ; : ; : 13.6 : -5| 26.4] 34:5] 47-0] 57-5 | KCoH302 .« ; : i : : ; 0| 44.0] 63.5] 98.0] 134.0 KClie- . : : : ; : 7 .2| 48.4] (57.4 gives a rise of 8°.5) KeCOg ° : : ; : : : -5| 60.5] 78.5| 103.5] 127.5] 152.5 KCI]O3 2 : : ; : . Ki , : aenise : : 0] 99.5| 134. | 185.0 |(220 gives 18°.5) | KNO3 , ; . e230. : : 2.0| 120.5] 188.5] 338.5 KeC4H4Og +4H20 . : ; : 2. .0| 126.5 | 182.0] 284.0 KNaC4H4Og Ws . . : 6) 119.0]}171.0] 272.5] 390.0] 510.0 KNaCaHi0s + 4120 ; : : : 0 | 266.0 | 554.0 | 5510.0 Lic] . : : : : 20] STOs5}] o2O:01|) 3 5:0)|| naa2n5 50.0 LiCl + 2H20 : 7 : f ¥ : 0} 44.0] 62.0] 92.0] 123.0] 160.5 MgCle+6H20 . : ‘ ; : : 55:0] 77.0] 110.0] 170.0] 241.0] 334.5 MgSO4 + 7H20 < eGilhor7s 38. : 262.0 NaOH : : : “4 : ; : 17.0 .4] 30.0] 41.0] 51.0 60.1 INaGly- ; : 2 .6| 12. o2h 20 25.5 Ny 7 gives 8°.8 rise) NaNOs . : ; , : 0} 38. 48.0 : 156.0| 222.0 NaC2H302 + 3H20 . 9. 194.0| 484.0 | 6250.0 NagSeO3 Cy ; ; : : : 9. .O | 104.0] 147.0] 214.5 Na,HPO,. . .4| 68. 35. NagC4H4Og + 2H20. 44. 12 ‘Olle 20-8 .0 | (237.3 gives 8°.4 rise) NagS2O3 + 5H20.. | 2 23.8 | 50. 2 oi 39:8 .0 | 400.0 | 1765.0 NaeCO3+ 10H20 . ; -6| 369.4 | 1052.9 NaebsyO7 + 10H20 . . | 93-2 | 254.2 3.5 | (5555-5 gives 4°.5 rise) NHC) a WGN A ie : 29.7| 39-6] 56.2| 88.5 NH4NO3 . : : .0 | 20. ; ‘ 52.0] 74.0] 108.0! 172.0] 248.0 INEVSOLs 2 ; : : F : : 71.8] 99.1] (115.3 gives 108.2) | SrClo + 6H2O . . . ; : -O| 103.0] 150.0] 234.0] 524.0 Sr(NOs)o_ : ~ N24. : i : 97.6 es sHg0, ; : : E : 87.0 | 123.0| 177.0] 273.0] 374.0 CoH: 204 + 2He Ga? : f : .O| 112.0] 169.0 | 262.0] 536.0] 1316.0 CsHgO7 + H20 . | 29. 7 : .O| 145-0 | 208.0 | 320.0] 553-0] 952.0 € 120° | 140° |; 160° | 180° | 200° | 240° CaCl, . . oct . . | KOR. ; ‘ A ; 219.8 | 263.1] 312-5] 375-0] 444.4 623.0 NaOH : : ; : 526.3 | 800.0 | 1333-0 | 2353.0 | 6452.0 NH4NO 3 | 682.0 1370.0 2400.0 4099.0 Ree co CyH 606 2 - | 980.0 | 3774.0 {eee gives Ta * Compiled from a paper by Gerlach, “ Zeit. f. Anal. Chem.’’ vol. 26. SMITHSONIAN TABLES. 196 ei iim CONDUCTIVITY FOR HEAT. Metals and Alloys. TABLE 204. The coefficient & is the quantity of heat in therms which is transmitted per second through a plate one centimetre thick per square centimetre of its surface when the difference of temperature between the two faces of the plate is one degree Centigrade. The coefficient 4 is found to vary with the absolute temperature of the plate, and is ex- pressed approximately by the equation &,= & 9 (1+ af). ture Centigrade, and a Substance. Aluminium Antimony . Bismuth . . Brass (yellow) “ (red) Cadmium . Copper German silver Tron “ (wrought) * Lead Mercury | 4 4 4 4 4 1 4 | 3 4 1 Magnesium Steel (hard) . os (soft) Silver shine. : Wood’s alloy Zinc . ; 1 Lorenz. 2 Berget. a constant. 3 J. Forbes. 4 H. F. Weber. 005357 .OOIO4I 0007 35 .00244 5 nh &# BUND w _ —~ = N _ ~ _ _ - -_ | Authority. AUTHORITIES. Kohlrausch. 6 H.L. & D.t Substance. Clay slate, (Devonshire) . Granite . AAG ey from Slate: along cleav- ao from age . eaae cleav- av om Mepe in- cluding lime- stone, cal- | from cite, and] to compact do- lomite Micaceous flagstone : along cleavage across cleavage . Sand (white dry) . Sandstone and hard grit (dry) Serpentine (Cornwall red) . from to Snow. in . layers ; Plaster of Paris Pasteboard . Strawboard . compact Paraffin . Sawdust . Vulcanite Vulcanized § from rubber (soft) ]_ to Wood, Fir: parallel to axis . perpendicular to axis Wax (bees) 7 Hieltstrom. 8 G. Forbes. In the table & is the value of Ae for 0° C., ¢ the tempera- Authority. mo CB ANG KOO MHMON 9 R. Weber. 10 Stefan. * A repetition of Forbes’s experiments by Mitchell, under the direction of Tait, shows the conductivity to increase (Trans. R. S. E. vol. 33, 1887.) + Herschel, Lebour, and Dunn (British Association Committee). GMITHSONIAN TABLES, with rise of temperature. 197 TABLES 205-208. CONDUCTIVITY FOR HEAT. TABLE 205.— Various Substances. TABLE 206. — Water and Salt Solutions. Substance. Density. Substance. Carbon. Cement Cork Cotton w ole Cotton pressed . Chalk Ebonite Felt . Flannel an : Solutions in | water. se NN ee ee et Glass CuSO, . .| 1.160] 4.4 PKG eo. s.|er-o205|) ars NaCl. . «| 333% | 10-18 1.054 | 20.5 1.100 5 1.180 1.134 1.136 s ee Haircloth . Ice | Caen stone (build- } ing limestone) . § Rn Ree WS Calcareous sand- stone (freestone) tN RNUUinN OL N AUTHORITIES. AUTHORITIES. 1 Bottomley. 4 Graetz. 2 El. b. \Wieber. 5 Chree. 3 Wachsmuth. 6 Winkelmann. 1 G. Forbes. 3 Various. 2 H.,. Lb... D* 4 Neumann. TABLE 207. — Organic Liquids. TABLE 208. — Gases. Substance. Substance. Authority. | | Authority. Air Ammonia Carbon monoxide “« dioxide tN | ;Aceticacid).. t1 11] (O=15 | Alcohols: amyl «| 9-15 ethyl .| 9-15 methyl | 9-15 | Carbon disulphide | 9-15 Chloroform. . .| 9-15 thers". ~s. pais Glycerine . . .| 9-15 Oils : olive castor . .| - petroleum .| 13 turpentine.| 13 0 see OHO WN DON Ethylene. 2 72) 0 Hydrogen . . .| O Methane.) 1-7-0 Nitrogen . . .| 7-8 Nitrous oxide. .| 7-8 Oxygen ee) eri 7eo NR NHWW DN HS ee Re NU NOW MOU NIG O31 W Wo kD Oe bokRROA AUTHORITIES. AUTHORITY. | 1 H. F. Weber. 2 Graetz. 3 Wachsmuth. 1 Winkelmann. * Herschel, Lebour, and Dunn (British Association Committee). SMITHSONIAN TABLES. 198 TaBLe 209. FREEZING MIXTURES.* Column 1 gives the name of the principal refrigerating substance, 4 the proportion of that substance, 4 the propor- tion of a second substance named in the column, C the proportion of a third substance, D the temperature of the substances before mixture, & the temperature of the mixture, /” the lowering of temperature, G the tempera- ture when all snow is melted, when snow 1s used, and // the amount of heat absorbed in heat units (therms when A is grammes). Temperatures are in Centigrade degrees. Substance. NaCoH 302 (cryst.) H20-100 NH,Cl1. : : “ . NaNOs3. ; NazS Og (cryst.) KI CaCl (cryst.) NH4NO3s _. : - (N H4)2504 . . NH4NO3-25 NH,Cl. : : Ss * CGaClais. : ; ‘e “s KNOgs . : : NH,4Cl-25 NagSO4 . . Me ~ NaNOs. : : < ae KoSO4 . ‘ : Snow 100 NagCOsz (cryst-) . | 2 : KNOs3 . 7 : CaCle . NH,Cl1 . NHgNOs NaNOg . NaCl HHH NNH ON AIH NS COONKMN me te 399 ooo Os ow —“ vo \O “I ~ ow Oo H.SO.+ HO (66.1 % H2SO4) OOHON Conn OG NEE Oo nr CaCle _ 6H20 “ =) 41-23 5) 2.46 “ 4.92 “ 73 COz solid Con DF Hr OR “N IN A HR Re RR ROR RO et > \o Alcohol at 4° Chloroform Ether . Liquid SO2 H,O-1.20 Snow “ H20-1.3 Snow “ H.20-3.61 Snow “ be new no OSIKOE AG 1 Awm0onmoondoao ~~ OOO OO Oe * Compiled from the results of Cailletet and Colardeau, Hammerl, Hanamann, Moritz, Pfanndler, Rudorf, and Tollinger. ; + Lowest temperature obtained. SMITHSONIAN TABLES. 199 TABLE 210. CRITICAL TEMPERATURES, PRESSURES, OF CGASES.* 6 = Critical temperature. P= Pressure in atmospheres. ¢ = Volume referred to air at o° and 76 centimetres pressure. d= Density in grammes per cubic centimetre. VOLUMES, AND DENSITIES Substance. Air. Alcohol (Ge HO) <') (CHO) Ammonia Argon Benzene. Carbon dioxide “ “ Chloroform | Chlorine Ethylene Hydrogen “ Methane Nitric oxide (NO) . Nitrogen Oxygen . | Sulphur dioxide monoxide . disulphide . chloride sulphide —1 40.0 243-6 2ash 239-95 | 78.5 130.0 | II5.0 —I21.0 50.6 288.5 47-9 30292 ANH, —I41.1 35:9 2 Tey 78.1 260.0 54-9 141.0 83-9 148.0 ~ 19.7 35-77 | 0.01584 194.4 35-61 | 0.01344 9.2 59.0 = 13.0 0.00569 —220.0 51.25 oe 100.0 —81.8 —99:5 —93°5 —146.0 —146.0 as ee (N20) 354-0 —118.0 155-4 157-0 358.1 0.00187 4 370.0 : ~ Observer. Olszewski. Ramsay and Young. Jouk (lowest value | recorded). Ramsay and Young. Dewar. Olszewski. Young. Andrews. Wroblewski. Dewar. Sajotschewski. Dewar. Ladenburg. Battelli. Ramsay and Young. Van der Waals. Cailletet. Olszewski. Ansdell. Dewar. Olszewski. Dewar. Olszewski. Wroblewski. Dewar. Wroblewski. Sajotschewski. Clark. Nadejdine. Dewar. * Abridged for the most part from Landolt and Boernstein’s ‘‘ Phys. Chem. Tab.”* Norr. — Guldberg shows (Zeit. fiir Phys. Chem. vol. 5, p. 375) that for a large number of organic substances the ratio of the absolute boiling to the absolute critical temperature, although not constant, lies between 0.58 and o.7, the majority being between .65 and .7. CS,, N.O, and O gave about .59. SMITHSONIAN TABLES. 200 Methane, ethane, and ammonia gave approximately 0.58. H,S gave .566, and TABLE 211. HEAT OF COMBUSTION. Heat of combustion of some common organic compounds. Products of combustion, CO, or SO, and water, which is assumed to be in a state of vapor. Substance. Acetylene . Alcohols: Amyl Ethyl Methyl Benzene Coals: Bituminous Anthracite Lignite . Coke Carbon disulphide Dynamite, 75% - Gas: Coal gas . Illuminating Methane . Naphthalene Gunpowder Oils: Lard Olive Petroleum, Am. crude Se “refined . el Russian . Woods: Beech with 12.9% H2O Birch ety l.030 ss 13-3 12.17 SMITHSONIAN TABLES. Therms per gramme of substance. 11923 8958 7183 53°7 9977 7400-8 500 7800 6900 7000 3244 1290 5800-1 1000 5200-5500 13063 9618-9793 201 Authority. Thomsen. Favre and Silbermann. Stohmann, Kleber, and Langbein. Various. Average of various. Berthelot. Roux and Sarran. Mahler. Various. Favre and Silbermann. Various. “ “ Stohmann. Mahler. ae “ Gottlieb. TABLE 212. HEAT OF Heat of combination of elements and compounds expressed in units, such that when unit mass of the substance is units, which will be raised in temperature | Combined Substance. with oxygen forms — Combined eat Combined with chlorine Se with sulphur forms — ; forms — Heat units. Author- ity. Calcium . P ; . CaO 3284] CaCle Carbon — Diamond . ; CO, 7859 ~ = os : : CO 2141 «“ —Graphite . : CO, 7790 Chlorine . : : : Cl2,O — 254 Copper . : : ; CuO 321 ec : : : : CuO 585 “ce e 7 - s “ 593 Hydrogen* . . : H,O 34154 : ; : : “ 34800 < : 5 : ; se 34417 Iron . 7 ; . . FeO 1353 1464 ae 5 : ; : - = 1714 Iodine ; ; : . T,O; 177 - - Lead ; : E ; PbO 243 400 PbS Magnesium. , ; MgO 6077 6291 MgS Manganese ; : .| MnOH2O 1721 2042 | MnSH._O02 Mercury . , A -| Hg2O 105 206 = a ; : ; ; HgO 153 310 HgsS Nitrogen* ; ; 3 N,O — 654 - - S : ; 7 ; NO —I54I ss 2 ; : . NO2g — 143 Phosphorus (red). : 5272 S (yellow) . 5747 “ “ . “ 5904. = Potassium : : ; K,O0 1745 KCl Silver : ; : : AgeO 2 AgCl Sodium . ; . : Na,O 3293 NaCl Sulphur . ; ; : SOz 2241 - cc : : , : 2165 ~ Tinks: : ‘ : ; 573 SnCle - SnCly Zinc . i 1185 - ieee , : é : 1314| ZnCle BPN BDH OR CORN HR HH RR Oe ee OW OW BH HR ROW ND A Combined Combined Combined Substance. with SO, with NO, with COs to form — to form — pas to form — Author- ity Calcium . < ; =| eCas@, 7997 | Ca(NOsz)o | 5080} CaCOg Copper . ; rl aCus@y 2887 | Cu(NOs)2 | 1304 - Hydrogen ; . -| HeSO4 96450} HNOs | 41500 - Tron . ; . : »| “FeSO, 4208 | Fe(NOs)e | 2134 - Lead : 2 : 21) SEbS Os 1047 | Pb(NOs)e 512) PbCOs Magnesium ; ; -| MgSO, 12596 Mercury . : . ~ - - = - Potassium ; ; -| KeSO4 4416| KNOg 3061 | KeCOg Silver . . . . AgeoSO4 776 AgNO3 206 AgoCOg Sodium . : ; -| NagSO4 7119| NaNOg | 4834| NagCOg Zinc. : 5 3 -| ZnSO, 3538 - ~ Leen len ee | AUTHORITIES. 1 Thomsen. 3 Favre and Silbermann. 5 Hess. 7 Andrews. 2 Berthelot. 4 Joule. 6 Average of seven different. 8 Woods. * Combustion at constant pressure. SMITHSONIAN TABLES. 202 TABLE 212. COMBINATION. caused to combine with oxygen or the negative radical, the numbers indicate the amount of water, in the same from o° to 1° C. by the addition of that heat. In dilute solutions. Substance. Author- ity. Heat He: . root Forms — Heat ont its. Forms — : : units, units. Forms — Calcium . -| CaOH,O 3734 CaClH2,0 4690 | CaS + H2,O Carbon — Diamond ‘ - - az = ae “ 2457 “ce _ Gepiite ; Chlorine : Copper “ Hydrogen “ front 4a) wo? 6. eee eOe EO 12 o* FeCly + Ha0 1785 lw Nitrogen . “ SH : ; : - FeC 2280 ~ ~ Iodine : : . - - - - ~ Lead . : : - - PbCly 368 ~ ~ Magnesium : -| MgOoHe goso MgCl 7779 MgsS 4784 Manganese : - = MnCle 2327 ~ - Mercury - - - ~ ~ - : - - HgCle 299 - - “ Phosphorus (red) ; ~ = = (yellow) : - ~ = = S Potassium . : 2 Silver : : : - - - - - Sodium. : : Na2O 3375 NaCl 4190 NaeS Sulphur : Tin “ MPN A OOK CORN HR RRR RR QW BROWNS In dilute solutions. ‘ Substance. ss) pomms— | Het | vorm— | Het | rom— | iis | <* Calcium - - Ca(NOs)e 5175 - - I Copper. CuSO4 3150 Cu(NOs3)e 1310 - - I Hydrogen . H2SO4 10530 H2.NOg3 24550 - = a) Tron . FeSO, 4210 Fe(NOs)3 2134 ~ - I | Lead. - - Pb( NOs)a 47 5 - - 1 | Magnesium MgSOq4 | 13420 Mg(NOs)e 8595 - - I Mercury - ~ Hg(NOs)2 335 - - I Potassium . KeSO4 4324 KNOg3 2560 ~ - I Silver AgeSO4 753 AgNOg 216 - - I Sodium NaoSO4 7160 NaNOgs 4620} NagCOg | 5995] I Zinc . ZnSO4 3820 Zn(NOs)e 2035 - - | AUTHORITIES. 1 Thomsen. 3 Favre and Silbermann. 5 Hess. 7 Andrews. 2 Berthelot. 4 Joule. é Average of seven different. 8 Woods. ee * Thomsen. SMITHSONIAN TABLES. 203 TABLE 213. LATENT HEAT OF VAPORIZATION. The temperature of vaporization in the vapor at the temperature 7. degrees Centigrade is indicated by 7’; the latent heat in calories per kilogramme or in therms per gramme by //; the total heat from o° C. in the same units by #’. The pressure is that due to Substance. Acetic acid Alcohol: Amyl Ethyl Ammonia “ Benzene Bromine Carbon dioxide, solid liquid . disulphide “ “ Chloroform | Ether i “ | Iodine Sulphur dioxide “ “ Turpentine Water “ SMITHSONIAN TABLES. Formula. C3H402 CpHi.O C2H,O NN Ee ty OSKRHOMNI mMmOowW NunbuN Go wy wh Authority. Ogier. Schall. Favre and Silbermann. Wirtz. | Regnault. | “ “ “ Wirtz. Ramsay and Young. Regnault. “ “ Wirtz. Andrews. Favre. Cailletet and Mathias. “ “ “ Mathias. “ “ “ce Wirtz. Regnault, “ Wirtz. Andrews. Regnault. “ “ Favre and Silbermann. Cailletet and Mathias. “ oc “ “ “ “ Brix. Andrews. Regnault. TABLE 213. LATENT HEAT OF VAPORIZATION.* Authority. Substance, formula, and ?=total heat from fluid at 0° to vapor at 7°. temperature. 7 = latent heat at 2°. Regnault. Acetone, /= 140.5 + 0.36644 ¢— 0.000516 CsH¢O, /= 139.9 + 0.23356 ¢ + 0.00055358 ¢2 Winkelmann. — 3° to 147°. r = 139.9 — 0.27287 ¢ + 0.0001571 Regnault. Benzene, CeHe, Z2= 109.0 + 0.24429 ¢— 0.0001315 # Fo LOL ros Carbon dioxide, 3 r= 118.485 (31 — ¢) — 0.4707 (31 — 2°) Cailletet and Mathias. Oo — 25° to 3I° Regnault. Winkelmann. “ 7=090.0 + 0.14601 ¢ — 0.000412 = 89.5 + 0.16993 ¢— 0.0010161 £2 + 0.000003424 # Carbon disulphide, —6 to 143°. r = 89.5 — 0.06530 ¢ — 0.0010976 #7 + 0.000003424 7 Carbon tetrachloride, | 7= 52.0 + 0.14625 ¢— 0.000172 # Regnault. CEl = 51.9 + 0.17867 ¢ — 0.0009599 2 + 0.000003733 47 | Winkelmann. r = 51.9 — 0.01931 £— 0.0010505 2? + 0.0000037 33 4 ‘ Chloroform, 7= 67.0 + 0.13752 Regnault. CHCls, 7 = 67.0 + 0.14716 ¢ — 0.0000437 2? Winkelmann. — 5° to 159°. r= 67.0 — 0.08519 ¢ — 0.0001 4.44 2 se Cailletet and Mathias. r2= 131.75 (36.4 — 2) — 0.928 (36.4 — 2)? Nitrous oxide, 7 2“ — 20° to 36°. Mathias. Sulphur dioxide, SOs, r= 91.87 —0.3842 ¢ — 0.000340 7 0° to 60°. * Quoted from Landolt and Boernstein’s ‘‘ Phys. Chem. Tab.” p. 350. SMITHSONIAN TABLES. 205 TABLE 214. This table contains the latent heat of fusion of a number of solid substances. Landolt and Boernstein’s tables. heat. Substance. Alloys: 30.5Pb + 69.5Sn . 36.9Pb + 61.35n . 63.7Pb + 36.3Sn . 77-8Pb + 22.2Sn . Britannia metal, 9Sn + 1Pb Rose’s alloy, Bromine Bismuth Benzene Cadmium . : Calcium chloride Iron, Gray cast . White “ Slag . Iodine Ice “ “(from sea-water) ead. Mercury Naphthalene Palladium . Phosphorus Potassium nitrate Phenol Paraffin Silver 2 Sodium nitrate .- Sodium phosphate Spermaceti Sulphur Wax ADCe) Zinc SMITHSONIAN TABLES. LATENT HEAT OF FUSION. It has been compiled principally fron: C indicates the composition, 7’ the temperature Centigrade, and H the latent 24Pb + 27.3Sn + 48.7Bi eneee 25-8Pb + 14.7Sn W ood’s alloy } + 52.4Bi -- 7Cd H,O H2O + 3.535 | of solids ~ § b * Total heat from 0° C, 206 Authority. Spring. Ledebur. Mazzotto. “ Regnault. Person. Fischer. Person. “ce Gruner. “ “ Favre and Silbermann. Regnault. Bunsen. Petterson. Rudberg. Person. Pickering. Violle. Petterson. Person. Petterson. Batelli. Person. “ results obtained by different observers. one observation differed so much from all others as to make its accuracy extremely improbable. headed ‘‘ Mean” gives a probable average value. Substance. Aluminium . Antimony Arsenic . Barium Beryllium Bismuth . Boron, amorph. Bromine . Casmine. Cesium . Chlorine, liquid . jabovet Chromium . Cobalt Copper Gallium. . Germanium Gold Indium Iodine .. Iridium . Iron (pure) . “ teel . <<" \(cast)i: Lanthanum. Lead . Mallet. Frey. Debray. Despretz. TABLE 215. MELTING-POINT OF CHEMICAL ELEMENTS. The melting-points of the chemical elements are in many cases somewhat uncertain, owing to the very different se ere pig) gray pig) Range. Min. Max. : Cine anise 600. | 850. | 625. 425- | 450 | 435: bet. Sb anu Ag above that of cast iron below that of silver 266.8 | 269.2 | 268.1 melts in elect. arc —7.2 | —7.3 |—7-27 Sire Wg2te| ests: - - 26.5 —102. at of platinum 1800. | 1650. 1330. | I 100. - 30-15 goo. 1080. 176. rns Ba 2225. 1635- Ce 1500. 1050. 1035. | 1250. 107. 1950. 1500. 1050. 1100. 1300. = = 137 5- between Sb and Ag 335: | 326. IIS. 1500. 1800, 1100. | 1075. 2275. | 1200. 1400. | 1360. 29 ore: 6 Olszewski, 1884. 7 Deville, 1856. 8 Lecoq de Bois- baudran, 1876. Setterberg, 1882. ® Winkler, 1886. ee se ae ge ee Substance. Observer. Lithium . Magnesium. Manganese . Mercury Molybdenum Nickel Osmium . Nitrogen Palladium Phosphorus Platinum Potassium Rhodium Rubidium Ruthenium . Silenium . Silicon Silver . Sodium Strontium Sulphur . Tellurium Thallium Tin Tungsten Zinc 19 Winkler, 1867. 11 Ledebur, 1881. 12 Hildebrand and Norton, 1875. 18 Bunsen. This table gives the extreme values recorded except in a few cases where The column Range. Observer. Min. Max. Ce C9 iGo - ~ 180. 750. | 800. = - 1900. + |-—38.50|—39.44|—39.0 above white heat 1450. | 1600. | 1500. - | 2500. —203. | —214. 1950. 44-4 2200. 63. —z208. 1600. 44.25 1900. 60. 2000. 38-5 1800. 217. bet. cast iron and steel 916. | 1040. | 950. 95-6 |—97-6| 97.6 red heat Ties ||P nz0: 452. | 525. 288. | 290. onl |e22Oa5 i 23h. above that of manganese 400. | 433: | 415: 1350. 44.2 775: 55 T15.1 470. 280. 230. Carnelley, 1879. 16 Buchholz. 16 Pictet, 1879. 7 Hittorf, 1851. 8 Matthieson, 1855. 19 Wohler. TABLE 216. BOILING-POINT OF CHEMICAL ELEMENTS. The column headed “‘ Range” gives the extremes of the records found. Where the results are from one observer the authority is quoted with date of publication. Substance. Aluminium . Antimony Arsenic Bismuth . Bromine . Cadmium Chlorine. Iodine Lead . Magnesium . Mercury . 1 Deville, 1854. ® Regnault, 1863. ® Carnelley, 2 Conechy. Range. Min. Max. above white heat 1470. | 1700. | 1535. 449- | 450- mi 10go. | 1700. | 1413. 59-27 | 63.05 62.08 720. | 860. | 779. over 200° bet. 1450° and 1600° - - 100. 357: * Stas, 1865. SMITHSONIAN TABLES, —33-6 6 Ditte, 1871. Substance. Observer. Nitrogen. Oxygen Ozone. Phosphorus Potassium Selenium Sodium Sulphur . Thallium . Tin Zinc 207 1879. 7 Regnault, 1862. 8 Olszewski, 1884. Range. Min. | Max. —181. | —184. 287.3 667. | 664. 742. 290. 725. 683. 997- 448.4 . | 1800. bet. 1450° and 1600° Sor. | 1040. | 958. 9 Olszewski, 1887. TABLE 217. MELTING-POINTS OF VARIOUS INORGANIC COMPOUNDS.* Melting-points. a subs . shemical for : orhedian |S Date of | Substance Cele eee ee | values. | < | Aluminium chloride . AICI - - 190. I 1888 s nitrate Al(NOs)3 + 9H20 ~ ~ 72,0 '| 2 1859 Ammonia . : NHsg - - —75. | 3 1875 Ammonium nitrate . (NH4)NOg 145. 166. 156. | - - as sulphate (NH4)2SO4 = ~ 140. | 4 1837 ee phosphite NH 4He2POs - - 123, 5 1837 | Antimonietted hydrogen . SbHs _ - —9gI.5| 6 1886 Antimony trichloride : SbCls 2s 73-2 72.8 | — - ae pentachloride . SbCl; - - —6. | 7 1875 | Arsenic trichloride AsCl3 = ~ —18. 8 1889 | Arsenietted hydrogen AsHsg3 - - —113-5] 6 1854 | Barium chlorate Ba(C1O3)¢ - - 414. 9 1878 “ nitrate Ba(NOs)o - - 593. | 9 1878 i “perchlorate . Ba(ClO4)e - - 505. | 10 1884 | Bismuth trichloride . BiCls 22ic 230. 227.5,| 11 1876 | Boric acid : HsBO 3 184. 156. TOS al 1878 | “anhydride BoO3 - - ele 1878 | Borax (sodium borate) NaoByO7 = ~ 561. 9 1878 | Cadmium chloride CdCl ~ ~ 541. 9 1878 ‘s nitrate Cd(NOs)2 + 4H2O - - 59-5] 2 1859 Cc alcium chloride : CaCle 719. 723% 721. 9 1875 | . : : CaCly + 6H2O 28. 29. 28.5] - - : nitrate : Ca(NOs3)e ~ - 561. 9 1878 | ce re : -| Ca(NOs)o + 4H2O - = 44. 2 1859 Carbon tetrachloride : CCl - —24.7 | 12 1863 | “trichloride . : CoCle 182. 187. 184.5] - _ | “monoxide. s CO —I99. | —207. 203. | - = “dioxide COzg —56.5 57-5| —57. | 3 1845 «disulphide CSe - —i10. | 13 1883 | Chloric acid HC104 + HeO - - 50. | 14 1861 Chlorine dioxide ClO. = ~ —76. 3 1845 | Chrome alum KCr(SO4)2 + 12H2O — - 89. | 15 1884 1 Chrome nitrate Cro(NOs)¢ + 18H20 - ~ Bik 2 1859 Cobalt sulphate CoSO4 96. 98 O7- eas 1834 Cupric chloride CuCle - - 498. | 9 1878 Cuprous CueCly - - 434. | 9 1878 as nitrate Cu(NOs3)2 + 2H20 - - TIALS ee 1859 | Hydrobromic acid HBr - ~ —86.7} 3 1845 | Hydrochloric acid : HCl - - —I12.5| 6 1854 | Hydrofluoric acid. : He - - —92.3| 6 1886 Hydroiodic acid ; : HI - - —49-5| 3 1845 Hydrogen peroxide . THy.02 ~ - —30. | 16 1818 phosphide PHs - - —132.5] 6 1886 ce sulphide . Hy ~ - —85.6] 3 1845 Iron chloride FeCls 301. 307 308 a0 ea aa “* nitrate Fe(NOs)3 + 9H20 - - ree ee 1859 | “ sulphate FeSO, + 7H2O - _ 64. | 15 1854 | Lead chloride . : PbCle 498. 580. 520. | - = “* metaphosphate Pb(P Os) - - S00. 9 1878 Magnesium chloride MgCl - - 708. | 9 1878 s nitrate Meg(NOsz ae -+ 6H2O - - go. 2 1859 a sulphate MgSO, + 5H20 - - 54. | 15 1834 Manganese chloride . MnCls + 4H2O - - 87-5] 17 = Ee nitrate Mn(NOs)o a 6H20 ~ - ZITO ae, 1859 oe sulphate . MnSQ,4 + 5H2O - - 54. | 15 1884 | Mercuric chloride HgCly 287. 2093. 290.) |= = 1 Friede] and Crafts. 5 Amat. 2 Ordway. 6 Olszewski. 3 Faraday. 7 Kammerer. 4 Marchand. 8 Besson. 13 Wroblewski and Olszewski. 14 Roscoe. 15 Tilden. 16 Thénard. 9 Carnelley. ro Carnelley and O’Shea. 11 Muir. 12 Regnault. 17 Clark, “Const. of Nat.” * For more extensive tables on this subject, see Carnelley’s “‘ Melting and Boiling-point Tables,” or Landolt and Boernstein’s ‘‘ Phys. Chem. Tab.” SMITHSONIAN TABLES. Substance. Nickel carbonyl . « nitrate «© sulphate . Nitric acid . : “ anhydride. ‘ . “ “ (pyro) _ Sulphur trioxide : Tin, stannic chloride . “stannous “ Zinc chloride “ “ “ nitrate “ sulphate 1 Mond, Langer & Quincke. 2 Ordway. 6 Olszewski. Chemical formulz. re § AS pub-| Min. | Max. : 3 Pea aeae probable | = value. | < | NiCO, ~ ~ —25. 1 1890 Ni(NOs)2 + 6120 - - 50.7 2 1859 NiSO4 + 7H20 98. | 100. 99. 3 1884 HNOs - _ —47. 4 1875 N205 - - 30. 5| 1872 NO ~ - |—167 6 1885 N2O4 = - |—10.14] 7] 1890 oe - - |—82. 8 1889 20 - - |—99. 9 1873 H P04 Sel idee caeec ents HsPOg3 70.1 74. 72% - ~ PCs - - 111.8 | 10 1883 PCIO3 - - —1.5 | 1! 1871 PS2 296. | 208. 297. 12 1879 P2S5 2745, | 270. 275: 13 1879 P4S3 142. 167 155. - - PoSs3 - ~ 290. 14 1864 KCOs 834. |1150.?| 836. = - KCI1O3 334 | 372, | 354 | 7 = KC1O, - ~ 610. 15 1880 KCl 730. | 738 | 734 | - - KNOg3 B27 358 340. = = KH2PO4 - - 96. 3 1884 KHSO, - - 200. 16 1840 AgCl : = - AgNOs3 198 224. 214. = = AgNs - ~ 250. 20 1890 AgClO4 - ~ 486. 18 1884 AgsPO4 - - 849. 15 1878 AgPO3 - - 482. 15 1878 AgoSO4 = ~ 654. 15 1878 NaCl 772. | 960. W72s - - NaOH - ~ 60. 17 1884 NaNO3 298 330 315 = - NaClOg ~ ~ 302. 15 1878 NaClO, - = 482. 18 1884 NagCOs3 814. | 920. 884. = - NagCO3 + 10H20 ~ 34. 3 1884 Na2H PO, + 4H20 20. 36.4 eieeAme ic - NaPOg3 - - 617. 15 1878 NayP207 = = 888. Ls 1878 (H2NaPQOs)2 os 5H20 = aa 42. 19 1885 NazSO4 86 865 863. 15 1875 NagSO4-+ 10H20 - - 34- 3 1884 NagS203 + 5H20 45: 48.1 47- - ~ SOz 70. 79. 78, | = ~ H2S04 10.1 10.6 10.4 | 21 1884 12H_,SO4 + H2,0 - - —o.5 | 22 1853 H2.SO,4 t HzO 7°5 5 5 8. = = H25207 - - 35- 22 1853 SOs 148] 15. 14.9 | 5 | 1876-1886 SnCly - - —33: 23 1859 SnCly - - 250. 24 - ZnCl - - 262. | 25 1875 ZnCly + 3H20 - - re 26 1886 Zn(NO3)2 + 6H2O Be a 36.4 | 3| 1884 ZnSO, + 7H20 ~ - 50. 3 1854 3 Tilden. 7 Ramsay. 12 Ramme. 17 Cripps 4 Berthelot. 8 Birhaus. 13 V. & C. Meyer. 18 Carnelley & O g Wills. 14 Lemoine. 19 Amat. MELTING-POINTS OF VARIOUS INORGANIC COMPOUNDS. Melting-point. TaBLe 217. | 1o Wroblewski & Olszewski. 15 Carnelley. 11 Genther & Michaelis. 16 Mitscherlich. *Shea. | | } | 20 Curtius. 21 Mendelejeff. 22 Marignac. 23 Besson. 24 Clark, ‘‘ Const. of Nat.”’ 25 Braun. 26 Engel. Mecie Weber. SMITHSONIAN TABLES. * Under pressure 138 mm. mercury. 209 TABLE 218. | BOILINC-POINTS OF INORGANIC COMPOUNDS.* Boiling-point. Date of | publication. Substance. Chemical formula. ; Particular} or aver- age values. | Authority. Airf . : : ; - - —I92.2 a ‘= : . . . - NOTA. Aluminium chloride . : AICls 207.5 = nitrate . . Al(NOs)3 -f gH2,O 134. Ammonia . ‘ NHs3 —=30.5 Antimonietted hydrogen ; SbHs —15. Antimony pentachloride§ . SbCl; 2s : ~ cs trichloride . ‘ SbCls 216. 220. | Bismuth trichloride . , BiClg 427. 435: Cadmium chlorlde . : CdCle 301. : god. cs nitrate : -| Cd(NOs)o + 41 ae = 132 1859 Calcium nitrate . : .| Ca(NOs)2 + 4H2O - 192. 1859 Carbon dioxide . . : COs —78.2 . | —70.1 1863-1880 xe disulphide. : Gs, : : 40.6 8, 9 1880-1883 =) -monoxide sem. : CO ; - | —I9QI.5 | 2, 1 1854 Chromic oxychloride . : CrOeCle 5. 3. wae - - Chromium nitrate. - | Cre(NOs a ee IH O - 12535 1859 Copper nitrate. , . - 170. 1859 Cuprous chloride : : Ci 2Cle 4. 032. | 993. 1850 | Hydrobromic acid ||. : ; 25.5 - 1870 | Hydrochloric acid. : e 110. 1859 Hydrofluoric acid : : 210: 3 ~ 1869 Hydroiodic acid. ; 5 - r27e 1870 Iron nitrate : : -| Fe(NOs); 2 25. 1859 Magnesium nitrate. -| Mg(NOs a 2 BN d 1859 Manganese chloride . : MnCl. ‘ = 95: 5: - go. | 10. = 85. | ©5: - 80. | 20. i 75: | 25: - FO.) |) 30. a 65. | 35 - 60. | 40. ms 55: | 45: ~ 50. || 50: rs 45. | 55: - 40. | 60. = 35: | 65: ~ 30, | 70: = 25. |] 75: - 20. | 8o. = 15. | 85. - 10. | go. | = 5- | 95: - — | 100. 6 Von Hauer, ae 7 W. Spring, “‘ F 107 5: 1100. 1130. 1160. | 1190. 1220. 1255: | 1255. 1320. ° 1 350. 1335. 1420. 1460. 1495- 1535 | 1570. 1610. | 1650. | 1690. | 1730. | “ec 1775: . f. prakt. Ch.” (1), 94, 436. ort. d. Phys. ” 1875. 8 Svanberg, ** J. B. f. Ch.” 1847-48. 9 Daniell, Bolley’s ‘‘ Hab. f. ch. Techn.” 8, 45- 10 Erhard and Schutel, ‘‘ Fort. d. Phys.’’ vol. 35- 211 * From Landolt and Boernstein’s ‘‘ Phys. Chem. Tab.” TABLE 220. DENSITIES, MELTING-POINTS, AND BOILINC-POINTS OF SOME ORGANIC COMPOUNDS. N. B. — The data in this table refer only to normal compounds. Temp. | Den- | Melting- Cc sity. point. Boiling-point. Authority. Substance. Formula. (a) Paraffin Series: Cn Methane* . . . —164.| 0.415 |—185.8| —164. Olszewski. Ethanej. . . - - - = Propane: sa e.mer ‘ - —25 to —30/ Roscoe and Schorlemmer. Butane’ <>... -60 +1. Butlerow. Pentane .. 0 3) eC 2 : .626 +37. Schorlemmer. Hexané=s 5 ee || Cok : 663 +69. ss Heptane. . . «| 'C .701 98.4 Thorpe. Octane.) f.) 7-0. |eCak: 719 125.5 s Wonane <0. ye sae- 2 718 : 150. Krafft. Decane.. 4.) a ’ 730 : 173. se Undecane’. . . 20. W774 ; 195. Dodecane.. . . Lora | Tridecane . . % an ees Tetradecane . . Se lh sev Pentadecane . . : 776 Hexadecane . . : TS Heptadecane. . ; 775 Octadecane. . ; 777 Nonadecane . . ; 77, Bicosane” *- tea : 778 Heneicosane . . : 778 IDocesane; =). = 44. -778 Tricosane . . .| CogH4s E -779 Tetracosane . . ; 779 Heptacosane . . -780 Pentriacontane . 751 Dicetyl -.45 5 = ; 781 Penta-tria-contane : 782 (b) Olefines, or the Ethylene Series: C,H,,. Ethylene . . .| CoHy - — | —169. —103. Wroblewski or Olszewski. Propylene . . .| CsHe i = = am Butylene . . .| CgHg | —13.5 | 0.635 ~ I Sieben. Amylone . . .| CsHio 30. Wagner or Saytzeff. Hexylene . . .| CoHie oO -76 69. Wreden or Znatowicz. Heptylene . . .| C7Hig} 19.5 | .703 96.-99. Morgan or Schorlemmer. | Octylene . . .| CgHie 7: w22 122.-123. | Moslinger. | Nonylene . . .| CoHig - - - TES. Bernthsen, “ Org. Chem.” | Decylene . . .| CioHaeo - 175: Ee x § Undecylene . .| Cy, Hee - = 195- ss rs s Dodecylene . .| Cy2Hez | malezO5 : 96. Krafft. | Tridecylene . .| CygHo¢ - ~ 233: Bernthsen. Tetradecylene. .| Cy4Ho ll a7O4 ; 127. Krafft. Pentadecylene . | CysH 30 - 247. Bernthsen. THexadecylene. .} CygHs2| +4. 792 3 155-¢ Krafft, Mendelejeff, etc. Octadecylene . .| CygHa¢ 4 ‘ . Krafft. | Eicosylene . . .| CooH4o Cerotene eet a) CozHs54 7 Bernthsen. Melene ... .| Cgo0Ho6o : os * Liquid at — 11r.° C. and 180 atmospheres’ pressure (Cailletet). “ O “ 46 “ “ee “ os see + Boiling-point under 15 mm. pressure. SMITHSONIAN TABLES. 212 TABLE 220, DENSITIES, MELTINC-POINTS, AND BOILING-POINTS OF SOME ORGANIC COMPOUNDS. Substance. Chemical Temp. Specific| Melting- Boiling- formula. C°’. | gravity. | point. point, Authority, (c) Acetylene Series: C,H... PAGEHVIENe rae. ¢ 3, « CoH, - PUIVIGNG Hire os e's CsHy, = Ethylacetylene . . . CyHo +18. | Bruylants, Kutsche- roff, and others. Propylacetylene. . . CsHg 48.-s50. | Bruylants, Taworski. Butylacetylene . . .| CgHio 68.-70. | Taworski. Oenanthylidene. . . C,H» 106.-108. | Bruylants, Behal, and others. 0.771 ~ 133--134. | Behal. = = 210.-215.| Bruylants. S10 | —9. 105.* | Krafft. 806 | + 6.5 134." * 804 20. 160.* fe 802 30. 184.* re Caprylidene . . . «| Cpls Undecylidene. . . .| Cy,Ha9 Dodecylidene . . .| CyaHoe Tetradecylidene. . .| Cy4Ha¢ Hexadecylidene. . .| CiegHso Octadecylidene ... . CysH 34 Wb Fi I Co9ag!o0 in (ad) Monatomic alcohols: C,,H,,,4 ,OH. Methyl alcohol . . .| CHs0H 0.812 - 66. Ethyl alcohol. . . .| CoH;O0H 806 | —130.T 78. Propyl alcohol . . .| CsH;OH S17 - 97- From Zander, “ Lieb. Butyl alcohol. . . .| CgHo9OH 823 117. Ann.” vol. 224, p.85, Amyl alcohol. . . .| C5H1OH 829 138. and Krafft, “ Ber.” Hexyl alcohol . . .| CgH,30H 157- vol. 16, 1714, Heptyl alcohol . . .| C;Hi;0H 176. 19; 2220, Octyl alcohol. . . .| CgsHi;OH 195. ‘Sn 29) 2300) Nonylalcohol . . .) CoHigOH 213. and also Wroblew- Decyl alcohol . . .|CyoH210H 2a ski and Olszewski, Dodecyl alcohol. . «| Cy2H2;0H 143.* “ Monatshefte,” Tetradecyl alcohol . «| CyyHo90H 167.* vol. 4, p. 338. Hexadecyl alcohol . .| CigH330H 190.* Octadecyl alcohol . .| CigH3;0H 211.* 9999999990 ~) oes ewe Oo “I wn Bac (e) Alcoholic ethers: C,,H,,,1,0. Dimethyl ether . . .| C2HeO - - ~ 22. Erlenmeyer, Kreich- baumer. Diethyl ether. . . «| C4Hi00 : B Regnault. Dipropylether . . . CgHy4O ; ; : Zander and others. Di-iso-propyl ether. .| Ce6Hi40 " 5 : ae: : Di-n-butyl ether. . .| CgHisO F 78 : Lieben, Rossi, and others. Di-sec-butyl ether . «| CgH1sO0 2X ; 2 Kessel. Di-iso-butyl “ . | CgHysO0 15. -762 7 Reboul. Di-iso-amyl “ - «| CioH220 O. : 170.-175. | Wurtz. Di-sec-hexyl “ . «| Ci2H260 - 203.-208. | Erlenmeyer and Wanklyn. Di-norm-octyl “ . «| Ci¢H3s4O0 7s ; 280.-282. | Moslinger. (f) Ethyl ethers: C,,H,,,4,0. Ethyl-methyl ether. .| Cs3HsO : Wurtz, Williamson. «propyl “ . .| CsHi20 « | 0.739 64. | Chancel, Brihl. iso-propyl ether .| Cs5Hi20 ; 745 5 Markownikow. norm-butyl ether | CgHi40 ; -709 : Lieben, Rossi. iso-butyl ether .| CeH140 s7RE So. | Wurtz. iso-amyl ether .| C7H 60 : .704 : Williamson and others. norm-hexyl ether | CsHisO - : ; Lieben, Janeczek. norm-heptyl ether | C9H200 , .790 5. | Cross. norm-octyl ether Cyi9H220 - 794 y . | Moslinger. * Boiling-point under 15 mm. pressure. ; + Liquid at —11.° C. and 180 atmospheres’ pressure (Cailletet). SMITHSONIAN TABLES. 213 TABLE 221. COEFFICIENTS OF THERMAL EXPANSION. Coefficients of Linear Expansion of the Chemical Elements. In the heading of the columns T is the temperature or range of temperature, C the coefficient of linear expansion, A, the authority for C, J/ the mean coefficient of expansion between o° and 100° C., a and B the coefficients in the equation 4—=/, (1+ a¢-+ 8), where Zo is the length at o° C. and / the length at 7° C., 4. is the authority for a, B, and m. Substance. Calvert, John- son and Lowe. Aluminium . . 40 0.2313| Fizeau. . . “ a 600 -3150 | Les Chatelier. | Antimony: Parallel to cryst. Praia. 0.6 6 .1692 | Fizeau. Perp. to axis. 0882 «s Mean... . aT L52 sc orien : : Matthieson. ATSENICy.. 1 8-ene 0559 Bismuth : Parallel to axis 1621 Perp. to axis. .1208 Mean). som. .1346 fee : : Matthieson. Cadmium. -n- -3069 s | Carbon: Diamond. . . 0118 Gas carbon. . 0540 Graphite. . . .0786 Anthracite . . 2078 Cobalt . . 1236 WGoppere. 6 mee. .1678 cre ele ; c Matthieson. Gold. . . 1443 s [nciumigsrae sas -4170 Tron: Sottien fk wi 1210 Casta ne. wees 1061 Wrought. . ./|—18tor1oo}) .1140] Andrews. Steel i 40 1322 | Fizeau. “annealed 40 1095 Cirle ey Wonca ie : : Benoit. SeaAdiee eh eo kote 40 .2924 ancl ie : : Matthieson. Magnesium . . 40 -2094 | INickely sy vas. 40 1279 | Osmium™ys.- ee 40 0057 | Palladium) 7: 50: 40 1176 See Phosphorus . .] 0-40 2530 | Pisati and De Franchis, Platinum) e-aeue 40 .0899 | Fizeau. . : Z Matthieson. Potassium . . .| 0-50 8300 | Hagen. Rhodium .. . 40 .0850 | Fizeau. Ruthenium. . . 40 0960 cS Selenium .. . 40 3680 . 5 ald Spring. | Silicon, ve) ome 40 .0763 “ | Silver.) aces er 40 : < om worl ee : : Matthieson. Sulphur: Cryst. mean. . 40 6417 eee e0- Spring. Tellurium .. . 40 < ‘Thallium roo | 2 X 100, 2 < < Air. : : : oe ue z Air . : ne ee 3 = : : : é a 37 i ° ; . 257: I 3 As : : : : 7.6 Soe : Hydrogen : : : 76. o50013 eS a : : : : 10.0 3 : ; : : 254 0.36616| 3 ue ; : : : 26.0 .3660 | 1 | Carbon dioxide : 76. 0.3710 | 3 t : : : : 37.6 3062] I ss ae : 252. |0.3845 | 3 f ; , : ; 75.0 .3065]| I ae “ 0%-64° | 17.1 atm. |0.5136 | 6 “ $ PB ; - 2 .2607 2* “ce “c Om O u “ 5 eo Nee | Seals Ile eee eee er ae ee as F ; 5 : 17-24 | .3651| 3 s s o°-64° 24.81 “ |0.6204 | 6 ss . : : oi, B7=SE 3050s ce ce 64°-100° 24.81 “ 10.5435 | 6 “ 4 “ “ O_ny -O ; «“ s oS Ce Se Ib a © cane ene ea a : : : : 2000 -3887 | 3 s “ 0%100% 34.49 “ 10.6574 | 6 s¢ ; ; : -| 10000 |.4100] 3 | Carbon monoxide . 76. |0.3669 | 3 és : at ; 7 .3069 | 3*] Nitrous oxide . : 76. {0.3719 | 3 K : : : s 7 .3671 | 4 | Sulphur dioxide . 76. | 0.3903 | 3 és ; : ; -\) matm: ||-3670)|75* se ss : 98. |0.3980 | 3 Carbon dioxide . =i meat nace -3700 | § | Water vapor, 0°119°| 1atm. |0.4187 | 7 a ee 2 =|) ekones -3726| I x sc (Ore) || oT saa OinSOn aay ‘ a : .| 76-104 | .3686] 3 S <6 OF =T622 |e reas 7 g ae -| 174-234 | -3752] 3 ce « 0%=200°| I 7 “ “ f . 793 -4252 3 “ “ 0°-247° I yi ae “ — 0°-64°. | 16.4 atm. | .4754| © bs “ 64°-100°| 16.4 “ | .4607| 6 e “ 0°-64°. |. 25.87 “| 5728) 6 AUTHORITIES. ge “ 64°-100° | 25.87 “ | .5406] 6 L fe 10° =6 42 133-53) 110073) 1 Melander. 5 Jolly. ss 164°—100% | 33:53" 111:6384)| 0 2 Magnus. 6 Andrews. Carbon monoxide To a B07; nes 3, Regnault. 7 Hirn. Hydrogen 1 “ |.3669| 3 | 4 Rowland. s ; =: AL en ee SOS Ol INES Nitrogen. : oi| Le we et eQOO0 || es Nitrous oxide Je 1 eg67O)53 “ ae I “ -3707 5 Oxygen , é Pee RO eo yiilh I Sulphur dioxide, SO2.| 1 re tey il) * Corrected by Mendelejeff to 45° latitude and absolute expansion of mercury. Rowland gets almost the same correction on Regnault, using Wiillner’s value of the expansion of mercury. , + The series of results at different pressures are given because of their interest. The absolute values are a little too low. (See preceding footnote.) SMITHSONIAN TABLES. 218 TaBLe 226. DYNAMICAL EQUIVALENT OF THE THERMAL UNIT. Rowland in his paper quoted in Table 227 has given an elaborate discussion of Joule’s determinations and the cor- rections required to reduce them to temperatures as measured by the air thermometer. The following table con- tains the results obtained, together with the corresponding results obtained in Rowland’s own experiments. The variation for change of temperature in Rowland’s result is due to the variation with temperature of the specific heat of water. Joule’s value reduced to air thermometer and latitude of a), S Method of experiment. f joules Baltimore. Relative weight of Joule’s value Eng. units.| Met. units. Friction of water . 781.5 787.0 442.8 Shas waS? : Oe 778.0 426.8 mercury 772.8 779.2 427.5 775-4 | 781-4 | 428.7 776.0 782.2 429.1 773-9 780.2 428.0 Electric heating. . - - 428.0 Friction of water . 776.1 425.8 ee ee es 778.5 776-4 770-5 777-0 From the above values and weights Rowland concludes as the most probable value from Joule’s experiments, at the temperature 14.6° C. and the latitude of Baltimore, 426.75, and from his own experiments 427.52. The mean of these results is 427.13 in metric units, or 778.6 in British units. Correct- ing back for latitude, and to mercury thermometer, this gives about 774.5 for the latitude of Manchester, instead of 772, as has been commonly used. An elaborate determination recently made by Griffith and referred to in Table 227 gives a value about one tenth of one per cent higher than Rowland’s. Probably when a mer- cury thermometer is involved in the measurements we may take 776 as the nearest whole number in foot-pounds and British thermal units for the latitude of Manchester, and 777 for that of Baltimore. The corresponding values in the metric system will be 425.8 and 426.3, or in round numbers 426 for both latitudes. The following quantities should be added to the equivalent of Baltimore to give the equivalent at the latitude named : — Latitude ... .0° 10° 20° 30° 40° 50° 60° 70° 80° 90° Kilogramme-metres 0.89 0.82 0.63 0.34 0.08 —o.41 —0.77 —1.06 —1.26 Foot-pounds. . . 1.62 1.50 1.15 0.62 0.15 —0.7§ —I.4I —I.93 a 219 SMITHSONIAN TABLES. TABLE, ads MECHANICAL EQUIVALENT OF HEAT. The following historical table of the principal experimental determinations of the mechanical equivalent of the unit of heat has been, with the exception of the few determinations bearing dates later than 1879, taken from Rowland.* The different determinations are divided into four groups, accordin to the method used. Calculations based on the constants of gases and vapors as determined by others are not included in this table. Method. Observer. | Date. Result. Compression of air . ; Joule } 1845 443.8 Expansion “ “ , ; : ; : Joule 1 1845 437.8 Experiments on steam engine . : ; Hirn 2 1857 413.0 < ae aaa : : Hirn 2 1860-1 420-432 ; ( 443.6 Expansion and contraction of metals . Edlund 3 1865 430.1 ) 428.3 “ “ “ “ “ 4 437- : Haga 1881 ; oe Measurement of the specific volume of vapor . : ‘ : : : é Perot ® 1886 424.3 Boring of cannon. : : : Rumford & 1798 940 ft.-Ibs. Friction of water in tubes ; P : Joule? 1843 ‘ ae y . . . as Ee oe al remainder we obtain, with a somewhat large Se ee probable error, the value 1.4070. Favre and Silbermann. : ae | Masson. The values obtained indirectly from the | Weisbach. velocity of sound are undoubtedly much | Hirn. more accurate, judged either by the greater Cazin. ease of the experiment or by the better | Dupré. . Cant Aan Rawls agreement of the results. Assuming that | Tresca and Laboulaye. the value 332 metres per second is good for Kohlrausch. the velocity of sound, the ratio of the specific Rontgen. heats must be near to 1.4063. Probably Amagat. 1.4065 may be taken as fairly representing Miiller. present knowledge of the subject. * Variation assumed uniform below 7 with same slope as from 7 to 5. Nors. — For specific heats of metals, solids and liquids, see pp. 294 to 296. SMITHSONIAN TABLES. 223 TABLE 230. Substance. Acetone. “ Alcohol, ethyl a methyl Ammonia “ Benzene. “cc “ Bromine. “ Carbon dioxide “ “ Carbon monoxide . “ “ Carbon ee: Chlorine “ Chloroform “ Ether “ Hydrochloric acid . Hydrogen a (H2S) Methane ; 7 Nitrogen Nitric oxide (NO) . Nitrogen tetroxide (NO; 4) “ “ “ Nitrous oxide ‘ “ Sulphur dioxide (SOz) . Water SMITHSONIAN TABLES. SPECIFIC HEAT. Specific Heat of Gases and Vapors. Range of temp. C.° 26-110 279) 129-233 —30to-+10 0-100 0-200 20-100 mean 108-220 1OI-223 23-100 27-200 24-216 mean 34-115 35-180 116-218 83-228 19-388 -|—28 to +7 15-100 11-214 mean 23500 26-198 86-190 13-202 16-343 27-118 28-189 69-22 27-189 25-111 mean 22-214 13-100 28 to +9 12-198 21-100 mean 20-206 18-208 0-200 13-172 27-67 27-150 27-280 16-207 26-103 27-206 mean 16-202 128-217 100-125 mean | Sp. ht. pressure constant. 0.3468 0.3749 0.4125 0.23771 0.23741 0.23751 0.2389 0.23788 0.4534 0.4580 0.5202 0.5350 0.5125 0.5228 0.2990 0-3325 0.3754 C:0599 90555 0.1843 0.2025 0.2169 0.2012 0.2425 0.2426 0.1596 0.1210 0.1125 0.1441 0.1489 0.4797 0.4618 0.4280 0.4565 0.1852 0.1940 3.3996 3-4090 3.4100 3.4062 0.2451 0:5929 0.2438 0.2317 1.625 TUES 0.650 0.2262 0.2126 0.2241 0.2214 0.1544 0.4805 0.3787 0.4296 224 Authority. Wiedemann Regnault “ “ Wiedemann Regnault “ Wiedemann “ Regnault Wiedemann “ Regnault Strecker Regnault “ “ Wiedemann “ Regnault “cc Strecker Wiedemann “ Regnault Wiedemann Regnault Strecker Regnault “ Wiedemann Regnault “oe “ “ Berthelot and Ogier Regnault Wiedemann “ Regnault “ Macfarlane Gray Mean ratio of sp. hts. Authority. Calculated vol. const. sp. ht. Jaeger ae Neyreneuf Cazin ) Willner Strecker Roéntgen Willner { Cazin . Wiillner Beyne Strecker { Beyme { Miller Miiller Strecker Wiillner Cazin Miller Various TABLES 231, 232. VAPOR PRESSURE. TABLE 231.—Vapor Pressure of Ethyl Alcohol.* Vapor pressure in millimetres of mercury at 0° C. 14.15 | 15.16] 16.21 | 17.31 | 18.46] 19.68] 20.98 | 22.34 13.18 27.94 | 28.67 | 30.50 | 32.44 | 34.49 | 36.67 | 38.97 | 41.40 25-31 82.50 | 87.17 | 92.07 | 97.21 | 102.60 | 108.24 | 114.15 120.35 126.86 148.10 | 155.80 | 163.80 | 172.20 | 181.00 | 190.10 | 199.65 | 209.60 242.50 | 253.80 | 265.90 | 278.60 | 291.85 | 305.65 | 319.95 334-35 383-10 | 400.40 | 418.35 | 437-00 | 456.35 | 476.45 | 497.25 | 518.85 588.35 | 613.20 | 638.95 | 665.55 | 693.10 | 721.55 | 751.00 | 781.45 140.75 230.80 306.40 564.35 ae 49-47 | 52-44 | §5.50| 58.86} 62.33 | 65.97 | 69.80 | 73.83 From the formula log 4 = a + 4a’ + cB* Ramsay and Young obtain the following numbers.t 0° | 10° | 20° | 30° | 40° | 60° | 60° | zoo | go° | 90° Vapor pressure in millimetres of mercury at 0° C. o° : : 43: : 33-42] 219.82] 350.21 $40.91) 811.81) 1186.5 | 100 | 1692.3 : 3223. : 9409.9 |11558. |14764. | 1818s. 200 |22182. : : TABLE 232.— Vapor Pressure of Methyl Alcohol. | 2° | 8° | 4° | 6° | 6° Vapor pressure in millimetres of mercury at 0° C. Win OV _ Wn DOr bh On 5 9. 4 9. i Sinn Ninn ty nn oO 0 OWN Cnw vv * This table has been compiled from results published by Ramsay and Young (Jour. Chem. Soc. vol. 47, and Phil Trans. Roy. Soc., 1836). + In this formula 2= 5.0720301; log = 2.6406131; log ¢ = 0.6050854; log a= 0.003377538; log B= 1.99682424 (c is negative). + Taken from a paper by Dittmar and Fawsitt (Trans. Roy. Soc. Edin. vol. 33). SmitHsonian TABLES. _ 225 TABLE 233. Carbon Disulphide, Chlorobenzene, Bromobenzene, and Aniline. VAPOR PRESSURE.* 8.65 14.95 25.10 40.75 64.20 97-90 144.50 208.35 292.75 402.55 542.80 718.95 16.00 26.10 41.40 63.90 96.00 140.10 198.70 274-90 | 372-65 | 495.50 649.05 18.80 30.10 45-90 638.50 | 100.40 | 144.70 | 204.60 515.60 | | By 15 | 16.82 27.36 43.28 606.64 99-54 145.26 205.48 283 3-65 | 383. 75 509-70 666.25 19.78 31-44 47.80 71.22 104.22 149.94 211.58 283 -70 | 292. 8o 386.00 | 397-65 | 409.60 | 421.80 530-20 | 95:39 17.68 28.68 45-24 69.48 103-50 150.57 | 212.44 292.60 395-19 523.90 683.80 | 20.79 32.83 49.78 | 74-04 108.17 155-34 218.76 302-15 | 545-20 | | 71375 (a) CARBON DISULPHIDE. 146.45 224.95 334-70 454.15 682.90 (b) CHLOROBENZENE. 153-10 234-40 347-79 501.65 795:99 10.79 18.47 30.58 49.05 76.30 114.85 168.00 239-35 333-35 454.05 608.75 160.00 244.15 301.10 519.65 729.50 11.40 19.45 32-10 51-35 79-60 119.45 174.25 247.70 344-15 468.50 626.15 (c) BROMOBENZENE. 18.58 30.06 47.28 72.42 107.88 156.03 219.58 SOL-75 406.70 538-40 701.65 21.83 34-27 51.54 76.96 ns 25 | 160.90 | 226. 14 311-75 560.45 732: °5 19.52 31.50 49.40 75-46 112.08 161.64 220.90 B00-05 418.60 553.20 719-95 166.62 233-72 321.60 434-30 570.10 7 51:99 12.40 20.50 33-00 51.60 78.60 116.40 167.40 234.40 320.80 439-75 508.35 738-55 13-75 22.59 36.18 56.25 85-20 125.46 179.41 250.00 340.50 455-99 599-65 779.95 (d) ANILINE. 15.22 24.88 39.60 61.26 92.28 135-08 192.10 266.40 361.80 482.20 632.2 816.90 * These tables of vapor pressures are quoted from results published by Ramsay and Young (Jour. Chem. Soc. vol. 47). The tables are intended to give a series suitable for hot-jacket purposes. SMITHSONIAN TABLES. 226 TaBLe 233. VAPOR PRESSURE. Methyl Salicylate, Bromonaphthaline, and Mercury. (e) METHYL SALICYLATE. 9.60 9.52 9:95 14.47 | 15.15 | 15.85 22-55 | 23-53 | 24-55 34-21 35:63 | 37-10 50.96 | 52.97 | 55.05 74.38 77-15 | 980.00 106.10 | 109.80 | 113.60 148.03 | 152.88 | 157.85 202.49 | 208.72 | 215.10 271.90 | 279.75 287.80 359-05 | 368.85 | 375-90 467.25 | 479.35 | 491-70 600.25 | 615.05 630.15 761.90 | 779.85 | 798.10 (f) BROMONAPHTHALINE. 4.22 4-40 6.51 6.80 10.15 | 10.60 15.55 | 16.20 3:74 5-70 8.89 13.72 20.59 23-11 | 24.00 29.90 42.12 59.27 1 107.12 142.30 186.65 242.05 310.90 93:23) |) 734-40 46.50 | 48.05 64.06 | 66.10 87.10 | 89.75 116.81 | 120.20 154.57 | 158.85 ; 176.95 | 202.00 | 207.3 212.8 230.00 | 261.20 | 267.55 .65 295-95 | 334-55 | 342-75 . 377-30 | 424-45 | 434-45 4 476.35 533-35 | $45-35 57: : 595-60 | 663-55 | 677-95 22.15 | 737-45 | 395-60 498.55 622.10 2.97 3.18 3-40 5-44] 574] 6.05 (g) MERCURY. 123.92 130.08 | 133.26 | 136.50 | 139.81 157.35 164.86 163. 172.67 | 176.79 198.04 207.10 | 211.76 | 216.50 | 221.33 246.81 257-65 268.87 | 274.63 304-93 317-75 331.08 | 337-89 373-67 388.81 | 404.43 | 412.44 454-41 472.12 | 490.40 | 499-74 548.64 509.25 590.48 | 601.33 658.03 681.86 706.40 | 718.94 794-31 GMITHSONIAN TABLES. 227 TABLE 234. AIR AND MERCURY THERMOMETERS. Rowland has shown (Proc. Am. Acad. Sci. vol. 15) that, when o° and 100° are chosen for fixed points, the relation between the readings of the air and the mercury in glass thermometers can be very nearly expressed by an equation of the form t= T—at(100—?)(5—2D), where # is the reading of the air thermometer and 7 that of the mercury one, a and é being constants. The smaller a is, the more nearly will the thermometers agree at all points, and there will be absolute agreement for ‘=o or 100 or 6, enault found that a mercury thermometer of ordinary glass gave too high a reading between o° and 100°, and too Tow a reading between 100° and about 245°. As to some other thermometers experimented on by Regnault, little is recorded of their performance between 0° and 100°, but all of them gave too high readings above 100°, indicating that below 100% the mercury thermometer probably reads too low. Regnault states this to be the case for a thermometer of Choisy le Roi eryatal glass, and puts the maximum error at from one tenth to two tenths of a degree. Regnault’s comparisons of the air and mercury thermometers and a comparison by Recknagel of a mercury thermometer of common glass with the air thermometer are compared with the above formula by Rowland. The tables are interesting as showing approximately the error to be expected in the use of a mercury thermom- eter and the magnitude of the constants a and 4 for different glasses. ‘They are given in the following Table. Regnault’s results above 100° C. compared with the formula ¢= 7—at(100— #) (6—2), give for the constants a and 6 the following values: Cristal de Choisy le Roi Verre ordinaire . : Re @= 0.00000032, b=0°. @=0.00000034, 4—= 245°. Verre vert . , ° @=0.000000095, = —270°.* Verrede Suéde ... @=0.00000014, b=10°. Common glass (Recknagel) a@=0.00000033, 4=290°. (a) TEMPERATURES BETWEEN 0° AND 100° C, There are no observed results with which to compare the calculations for the Choisy le Roi thermometer through this range, and in the case of the verve ordinaire, the specimen for which the readings below 100° are given was not the same as that used above 100°, from which the constants @ and 4 were calculated. Row- land shows that a=o0.00000044 and = 260 give considerably better agreement. | ee oe EE eee Regnault’s thermometers. Recknagel’s thermometer. Air thermome- Choisy Verre ordinaire. ter. le Roi. |» itrerences Observed. Calculated. | Difference. Calculated. Observed. Calculated. | 00.00 ; 00.00 10.00 10.07 19.99 20.12 29.98 30.15 30-97 40.17 49.96 50.17 59-95 60.15 69.95 70.12 79.96 $0.09 89.97 90.05 100.00 100.00 in G2 99 oO NRO N oO mM NNN be onl oO Choisy le Roi. Verre ordinaire. Obs. Calc. | Diff. Obs. Calc. Diff. 100.00 | +.00 100.00] .00]} 100.00 120.09 | +-.03 119.90 | +.05 | 120.07 140.25 | +.04 | 13 139.80 | +.05 | 140.21 159.72 | +.02 | 160.40 —.03 179.68 | —.05 | 180.60 —.03 199.69 | +.01 | 200.80 86 | —.04 219.78 | +. 221.20 .56|—.o1 | 2: 239.96 241.60 .46 | —.02 260.21 262.15 52 | —-04 280.00 282.85 .76 | —.04 301.12 -20 | —.05 321.80 88 | +.42 342-64 S OrIufPWwWn a> t — N COON Oo NR ohn OMmn WWWNHNHNN 4 * Misprinted [+] 270 in Rowland’s paper. 228 SMITHSONIAN TABLES. om TaBLes 235, 236. COMPARISON OF THERMOMETERS.* Chappius gives the following equations for comparing glass thermometers: 1000 ( Ty — Tq) = -00543 (100 — Ty) Ty + 1.412 X 10-4 (100? — T,?) Ty — 1.323 X 10-8 (1008 — 7°,,5) 7. 1000 (T go, — T 7) = -0359 (100 — 7) Ty, — 0.234 X10~4 (100? — 7,7) Ty, — 0.510 X 1078 (1009 — Tq") Tq. N= nitrogen; H= hydrogen; CO, = carbon dioxide; m = mercury. TABLE 235.— Hydrogen Thermometer compared with others. This table gives the correction which added to the thermometer reading gives the temperature by the hydrogen thermometer. Chappius’s experiments. f Marek’s experiments.t Tempera- ture by | Hard hydrogen French . Carbon thermom- glass Nitrogen dioxide eter mercu thermome- therm : a ter. ermome- Hard French Jena ther- ter. French crystal normal |— mometer. Mercury in glass. Thuringian glass. 1830-40. +0.172 +0.073 0.000 —0.052 —0.055 —o.102 —0.107 —0.103 —0.090 —0.072 —0.050 —0.026 0.000 TABLE 236.— Air Thermometer compared with others. This table gives the correction which added to the thermometer reading gives the temperature by the air thermometer. Mercury in Jena | Temperature Mercury in Jena||Temperature) p. ydin alcohol glass thermome- by air glass thermome- by air slieenanieter ter (Wiebe and | thermome- | ter (Wiebe and thermome- (White 7) Bottcher ||). ter. Bottcher {{). ter. aes Mercury in Thuringian glass thermometer (Grommach §). Temperature by air thermome- ter. +0.03 —0.07 0.02 —0.09 0.00 K —0o.10 —0.03 —o.10 —O.II —o.08 —o.12 —o0.06 —o.08 —0.02 - +0.04 —o 04 +o.11 ~ +o.21 - +0.32 —0o.06 +0.46 - +0.63 —0.04 +0.82 +1.05 +1.30 +1.58 +1.91 2. “ 3: 3 6 8 5 8 OS On + oS {,. ; =O SUN “I Onn OO SIN ON Wwniake aN ~~ | * These two tables are taken with some slight alteration from Landolt and Boernstein’s ‘‘ Phys. Chem, Tab.” + P. Chappius, “Trav. et Mém. du Bur. internat. des Poids et Més.”’ vol. 6, 1888. + Marek, “‘Zeits. fiir Inst.-K.” vol. ro, p. 283. § Grommach, “ Metr. Beitr. heraus. v. d. Kaiser. Norm.-Aich. Comm.” 1872. j| Wiebe und Bottcher, “‘ Zeits. fiir Inst. K.” vol. 10, p. 233+ { White, ‘‘ Proc. Am. Acad. Sci.’’ vol. 21, ps 45: SMITHSONIAN TABLES. 229 TABLE 237. CHANCE OF THERMOMETER ZERO DUE TO HEATING.* When a thermometer is used for measurements extending over a range of more than a few degrees, its indications are generally in error due to the change of volume of the glass lagging behind the change of temperature. Some data are here given to illustrate the magnitude of the change of zero after heating. This change is not permanent, but the thermometer may take several days or even weeks to return to its normal reading. Time at maximum temp. in hours. No. of Maximum experi- temp. In ment. deg. cent. N OU O bd TABLE 238. Kind of glass. Composition of Jena glass Normal Jena glass. ~; ae Thuringian I. Il. glass. used. Depression of freezing-point. 1.0 1.0 3 1.5 1.5 ey 1.6 1.8 17, 1.9 1.8 2.0 2.0 2.2 ZnO 7% CaORe aac, NagO 14.5 % AleO3 2.5 % BoO3 2 % SiOg 67 % POWHW Db NN OL SN CHANCE OF THERMOMETER ZERO DUE TO HEATING. Description of thermometer. Humboldt, No. 2 J. G. Greiner, Fy “c “ Fo “ “ F3 2 : Ch. F. Geissler, No. 13 . G. A. Schultze, No. 3 Rapp’s Successor, F'4 Ratio of soda and potash : Depression of in the glass. zero due to one hour’s heating to K.O / Na,O 100° C. Year of manufacture. Na.O / KO Before 1835 0.04 0.06 1848 0.08 O.I 1856 0.22 38 1872 : 0.38 1875 0.40 1875 0.44 1878 ; 0.65 * Allihn, “‘ Zeits. fiir Anal. Chem.”’ vol. 29, p. 385. + W. Fresenius, “ Zeits. fiir Anal. Chem.’ vol. 27, p. 189. See also, for this and following table, Wiebe in the “ Zeitschrift fiir Instrumentenkunde,” vol. 6, p. 167, from which Fresenius quotes. The thermometer referred to in this table belonged to the Kaiserlichen Normal-Aichungs Commission. SMITHSONIAN TABLES. 230 ee TABLE 239. EFFECT OF COMPOSITION ON THERMOMETER ZERO.* Jena Glasses. Depression of Descriptive 3 . 7 zero due to See 2* CaO Alg( dy B,C dy ZnO one hour’s heating to 100° C, 0.08 0.05 1.05 1.03 1.06 0.17 0.05 0.05 0.05 IV VIII XXII ST ee XXu XTvim + XVpu XVIII ~ IMO DH 1 um ~~ Mino wonn il TABLE 240. CHANGE OF ZERO OF THERMOMETER WITH TIME. Closely allied to the changes illustrated in Tables 235-237 is the slow change of volume of the bulb of a thermometer with age. The following short table shows the change for the normal Jena thermometer.} Date of observation. Thermometer 1889 number. Rise of zero. * Fresenius, “ Zeits. fiir Anal. Chem.” vol. 27, p. 189. + Normal Jena glass. + Allihn, “ Zeits. fiir Anal. Chem.” vol. 29, p. 385+ SMITHSONIAN TABLES. 231 TABLE 241. CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER STEM.* T =t—0.0000795 ” (¢/—7#), in Fahrenheit degrees; T=¢—0.000143 # (¢/—?), in Centigrade degrees. Where T = corrected temperature, 7= observed temperature, ¢/—= mean temperature of glass stem and mercury column, n — the length of mercury in the stem in scale degrees. (a) CORRECTION FOR FAHRENHEIT THERMOMETER =value of 0.0000795 # (¢/— 2). u—t (b) CorRECTION FOR CENTIGRADE THERMOMETER = value of 0.000143 2 (¢/— 7). v—t 0.17 0.20 Y 0.40 0.23 : 0.46 : 0.26 } 0.51 ; 0.77 0.29 0.43 0.57 : 0.86 N. B. — When # —Z is negative the correction becomes additive. * “Smithsonian Meteorological Tables,” p. 12. SMITHSONIAN TABLES. 232 TABLE 241. CORRECTION FOR TEMPERATURE a MERCURY IN THERMOMETER STEM. non oO Anon fm CON OON DW OW a a: Gr 4 4. 4. Bi 5 5: SOQ On * This table is quoted from Rimbach’s results, “ Zeit. fiir Instrumentenkunde,”’ vol. ro, p. 153. The numbers represent the correction made by direct experiment for thermometers of Jena glass graduated from 0° to 360° C., the degrees being from x to 1.6 mm. long. The first column gives the length of the mercury in the part of the stem which is exposed in the air, and the headings under ¢—7Z give the difference between the observed temperature and that of the air. SMITHSONIAN TABLES. 233 TABLES 242, 243. EMISSIVITY. TABLE 242.— Emissivity at Ordinary Pressures. According to McFarlane * the rate of loss of heat by a sphere placed in the centre of a spherical enclosure which has a blackened surface, and is kept at a constant temperature of about 14° C., can be expressed by the equations € = .000238 + 3.06 X 10-8 — 2.6 X 10-82, when the surface of the sphere is blackened, or € = .000168 + 1.98 X 10-84 — 1.7 X 10-822, when the surface is that of polished copper. In these equa- tions e is the emissivity in c. g. s. units, that is, the quantity of heat, in therms, radiated per second per square centimetre of surface of the sphere, per degree difference of tempera- ture ¢,and ¢ is the difference of temperature between the sphere and the enclosure. The medium through which the heat passed was moist air. The following table gives the results. Differ- Value of e. | ence of tempera- ae Polished surface. | Blackened surface. 000178 000252 000186 .000266 000193 .000279 000201 .000289 000207 .000298 000212 .000306 000217 000313 .000220 .000319 .00022 .000323 .00022 .000326 .000226 .000328 000226 000328 TABLE 243.— Emissivity at Different Pres: sures. Experiments made by J. P. Nicol in Tait’s Labo- ratory show the effect of pressure of the en- closed air on the rate of loss of heat. In this case the air was dry and the enclosure kept at about 8° C. Polished surface. et Blackened surface. et PRESSURE 76 CMS. OF MERCURY. .00987 00862 .007 3 .00628 00562 00438 .00378 00278 .00210 PRESSURE 10.2 .00492 00433 .00383 .00340 .00302 .00268 61.2 50.2 41.6 34-4 27.3 20.5 .01746 01360 .01078 -00860 .00640 00455 OF MERCURY. O dybhRUN SQ 3G WP ni OM NUN .01298 .O11Ss .01048 00898 .00791 .00490 PRESSURE 1 CM. OF MERCURY. 00388 -00355 00256 .00219 00157 .OO1 24 * “ Proc, Roy. Soc.”’ 1872. +t ‘ Proc. Roy. Soc.’? Edinb, 1869. SMITHSONIAN TABLES. 234 to NNWWAhUNN OO BUSY REN NM OMUN NUiuH or 182 -O1074 01003 .007 26 .00639 00509 .00446 00391 TABLES 244, 245, EMISSIVITY. TABLE 244.— Constants of Emissivity. The constants of radiation into vacuum have been determined for a few substances. The object of several of the investigations has been the determination of the law of variation with temperature or the relative merits of Dulong and Petit’s and of Stefan’s law of cooling. Dulong and Petit’s law gives for the amount of heat radiated in a given time the equation ee Asa® (at — 1) where 4 is a constant depending on the units employed and on the nature of the surface, s the surface, @ a constant determined by Dulong and Petit to be 1.0077, @ the absolute temperature of the enclosure, and ¢ the difference of temperature between the hot surface and the enclosure. The following values of 4 are taken from the experiments of W. Hopkins, the results being reduced to centimetre second units, and the therm as unit of heat. G1aSS) ones seat | Foul —=5 OO0OL 927 Dry chalk. 5 . «< ', A==,.0000rrgs Dry new red-sandstone A = .00001162 Sandstone (building) . 4 = .00001232 Polished limestone. . dA = .00001263 Unpolished limestone (same block) . . . A =.0001777 Stefan’s law is expressed by the equation f= o5(7;4 — 75), where and s have the same meaning as above, o is a constant, called Stefan’s radiation con- stant, 7} is the absolute temperature of the radiating body and 7% the absolute temperature of the enclosure. Stefan’s constant would represent, if the law held to absolute zero, the amount of heat which would be radiated per unit surface from the body at 1° absolute temperature to space at absolute zero. The experiments of Schleiermacher, Bottomley, and others show that this law approximates to the actual radiation only through a limited range of temperature. Graetz* finds for glass. ; . : : - | 21.400; 7) —0, 7 —T.0040 x ton : . : : 7, = 1085, 7o>=0, o=0.185 X 10-2 Schleiermacher { find for polished platinum wire . } 7, =1150, Th=0, ¢=0.177 X 10-8 F id 7,=850, Zo—=0, ¢—0.600 X 10-8 or copper oxide. ; : 3 : : -) 7; = 1080, 7=0, e=0.701 X 10-2 TABLE 245. — Effect of Absolute Temperature of Surface. The following tabular results are given by Bottomley. The results of Schleiermacher were calculated from data given in the paper above quoted. The temperatures /, are in degrees centigrade, and ¢ is the emissivity or amount of heat in therms radiated per square centimetre of surface per degree difference of temperature between the hot body and the enclosure. The results are all for high vacuum. | Bottomley’s results for polished platinum, the enclosures being at 15° C. Schleiermacher’s results. Temperature of enclosure, 0° C. “ye, ¢e¢a, refer to polished platinum wire, /s¢3 to blackened platinum wire. | | ey es ON yy = oo Qn om wn 21.6 X 1078 ’ 16 | 60.9 X 10-6 32010) ) © Z 38 67.6 “ 53:8 232 94 | 83.7 137.0 y 228 | 147.0 315.0 . 403 | 293-0 : 585 | 540.0 Sto 000W0 Own tn Ga * “ Wied. Ann.” vol. 11, p. 297- t ‘‘ Wied. Ann.” vol. 26, p. 305. ¢ ‘Phil. Trans. Roy. Soc.” 1887, p. 429. 235 SMITHSONIAN TABLES. TABLES 246, 247. EMISSIVITY. TABLE 246.— Radiation of Platinum Wire to Copper Envelope. Bottomley gives for the radiation of a bright platinum wire to a copper envelope when the space between is at the highest vacuum attainable the following numbers : — ¢~= 408° C., ef = 378.8 X 10-4, temperature of enclosure 16° C. ¢#= 505° C., ef=726.1 X 10, ss s Toe. It was found at this degree of exhaustion that considerable relative change of the vacuum produced very small change of the radiating power. The curve of relation between degree of vacuum and radiation becomes asymp- totic for high exhaustions. The following table illustrates the variation of radiation with pressure of air in enclosure. Temp. of enclosure 16° C., = 408° C. Temp. of enclosure 17° C., ¢= 505° C. Pressure in mm. et Pressure in mm. 740. 8137.0 X 10-# 0.094 1688.0 X 1074 | 440. 7971.0 “ 053 £255.0) | 140. 7975.0) 0 034 1126.0 42. 7591.0 013 920.4 4. 6036.0 .0046 831.4 0.444 2633.0 000 52 707.4 .070 1045.0 .OOOI9 746.4 034 727.3 Lowest reached } 726.1 O12 539-2 but not measured oo 0051 436.4 -00007 378.8 “ TABLE 247.— Effect of Pressure on Radiation at Different Temperatures. The temperature of the enclosure was about 15° C. ‘The numbers give the total radiation in therms per square cen- timetre per second. Pressure in mm. Temp. of wire in C°. Nore. — An interesting example (because of its practical importance in electric light- ing) of the effect of difference of surface condition on the radiation of heat is given on the authority of Mr. Evans and himself in Bottomley’s paper. The energy required to keep up a certain degree of incandescence in a lamp when the filament is dull black and when it is “flashed ” with coating of hard bright carbon, was found to be as follows : — Dull black filament, 57.9 watts. Bright “ s 39:8 watts. SMITHSONIAN TABLES. 236 TABLE 248. PROPERTIES OF STEAM. Metric Measure. The temperature EesGerde and the absolute temperature in degrees Centigrade, together with other data for steam or water vapor stated in the headings of the columns, are here given. The quantities of heat are in therms or calo- ries according as the gramme or the kilogramme is taken as the unit of mass. =—H—h. H —(h+ Apo). e, Sl Heat of evapora- ternal-work heat Apo.* Total heat of Inner latent or in- | ternal-work heat Ratio of inner la- tent heat to vol- ume of steam.t Absolute temp. Pressure in mm. of mercury. Pressure in grammes per sq. centimetre = 2. Pressure in atmospheres. Total heat of evap- oration from 0° at Heat of liquid Outer latent or ex- steam —H —A sv. Litres per gramm or cubic metres per kilog. tion 31.07 | 575-4 | §75-4| 210.66 31-47 | $76.5 | 571.5 | 150.23 31.89 577-7 567.7 | 108.51 32.32 | 578-5 | 563.7) 79-35 32:75 | 5798) 5598) 78.72 33-20 | §80.9| 555.9) 43.96 33-66 | 582.0 | 552.0) 33.27 34.12 583-1 §48.2| 25.44 34-59 | 584-1 | 544.1) 19.64 35.06 | §85.2| 540.1] 15-31 35-54| 586.2 | 536.1] 12.049 30.02 | 587.2| 532.1| 9.561 36-51 | 588.3 | 528.1} 7.653 37-00] §89.3| 524.2] 6.171 37-48 | 590.4 520.2] 5.014 37-96} 591-4| 516.2| 4.102 35-42 | 592.5) 512.2) 3-379 38.88 | 593-5 | 508.2} 2.500 39-33 | 594-0 | 504.2} 2.334 39-79 | 595-7 | 500.3] 1-957 40.20] 596.8] 496.3] 1.6496 40.63 | §97-9| 492.3] 1.3978 41.05| §99.0| 488.4} 1.1903 41.46] 600.1 | 484.4] 1.0184 41.86 | 601.2 | 480.4; 0.8752 42.25 | 602.4/476.5| 0.7555 42.63 | 603.5| 472.5] 0.6543 43-01 | 604.7 | 468.6] 0.5698 43-38 | 605.8 | 464.6] 0.4977 43-73 | 607.0 | 460.7] 0.4363} 1 Ow ~ tn Gs WW GO AG so 44.09 | 608.2 | 456.7} 0.3839 44-43] 609.3] 452.8] 0.3388 44.70 610.5| 448.8] 0.3001 45-09 | 611.7| 444.8} 0.2665 45-40 | 612.9| 440.9 Ore 45-71 | 614.2] 436.9] 0.2122] 2059. 46.01 | 615.4 | 433-0] 0-IQOI | 2277. 46.30 | 616.6| 429.0} 0.1708 | 2512. 46.59 | 617.9 | 425.0 0.1538 | 2763. 46.86] 619.1} 421.1] 0.1389} 3031. a Ot WG = 6 47-73 620.4/417.1| 0.1257 | 3318. * Where A is the reciprocal of the mechanical equivalent of the thermal unit. + —H —(h+ Ap) — ___internal-work pressure __ Where v is taken in litres the pressure is given per square v mechanical equivalent of heat ss ; } decimetre, and where v is taken in cubic metres the pressure 1s given per square metre, —the mechanical equivalent being that of the therm and the kilogramme-degree or calorie respectively. SMITHSONIAN TABLES. 237 aeciaiac PROPERTIES OF STEAM. British Measure. The quantities given in the different columns of this table are sufficiently explained by the headings. The abbrevia- tion B. T. U. stands for British thermal units. With the exception of column 3, which was calculated for this table, the data are taken from a table given by Dwelshauvers-Dery (Trans. Am, Soc. Mech. Eng. vol. xi.). a Oo — » 5 5 : 4 2 3 22 Ez z 3& a. a. a 5 » ae <5 23 25 » 3 ao a 3 a) GI 568 ben $ sOg SOs £Oc¢ yiass oe 29 “75 o& as a3 = re Aer Sore oan gop oUs oto 2 i : ae Sate : 3 Sa se =r pee en Pes! #24 | Sap | BSED | SED] BSED] 2 9,; a rs) S350 3H ae’ En aay ° Q,8 as as ~ “aac aoe ZO 2 S/.; BRO: if a Bee PG Stee ies ea] sy Pa ca ere oad “ad ae ES pes Sa So] sesh | Seok | Sere | S85 vo v oO OD 2 Qs or =~ 0 « oc 2 ete aS » & Yo CTS Bee o.: BE Ow,- Ou: Oo Ow 26 aA) wes Qs Bo > aw da] Tam |/AcscmQ | wMese | esom] Has 144 | 0.068 | 102.0 | 334.23 | 0.0030 | 70.1 | 980.6 | 62.34 | 1043. II13.0 432 -204 | 141.6 | 117.98 0085 109.9 | 949.2 66.58 1olt. 1127.0 Z 3 4 576 272 | 153.1 | 89.80 | .or1r | 121.4 | 940.2 67.06 | 1007. 1128.6 5 720 -340 | 162.3 | 72.50 | .0137 | 130.7 | 932.8 67.89 | Ioot. 1131.4 6 864 | 0.408 | 170.1 | 61.10 | 0.0163 | 138.6 | 926.7 68.58 | 995.2 | 1133.8 7 1008 -476 | 176.9 | 53.00] .o189 | 145-4 | 921.3 69.18 990.5 | 1135.9 8 1152 -544 | 182.9 | 46.60 | .0214 | 151.5 | 916.5 69.71 986.2 | 1137.7 9 1296 612 | 188.3] 41.82 | .0239 | 156.9 | 912.2 70.18 982.4 | 1139.4 10 1440 680 | 193.2 | 37-80] .0264 | 161.9 | 908.3 | 70.61 979.0 | 1140.9 rT 1584 | 0.748 | 197.8 | 34.61 | 0.0289 | 166.5 | 904.8 70.99 975-8 | 1142.3 12 1728 816 | 202.0 | 31.90 | .0314 | 170.7 | 9go0I.5 71.34 972.8 | 1143.5 13 1872 884 | 205.9 | 29.58 | .0338 | 174.7 | 898.4 71.68 970.0 | 1144.7 14 2016 952 | 209.5 | 27-59 | .0362 | 178.4 | 895.4 | 72.00 | 967.4 | 1145.9 15 2160 | 1.020 | 213.0 | 25.87 | .0387 | 181.9 | 892.7 22 905.0 | 1146.9 16 2304 | 1.088 | 216.3] 24.33 | o.o4rr | 185.2 | 890.1 72I87 962.7 | 1147.9 17 2448 -156 | 219.4 | 22.98 | .0435 | 188.4 | 887.6 72.82 960.4 | 1148.9 18 2592 224 | 222.4 | 21.78 | .0459 | 191.4 | 885.3 73.07 958.3 | 1149.8 19 2736 -292 | 225.2 | 20.70 | .0483 | 194.3 | 883.1 73.30 956.3 | 1150.6 20 2880 300 | 227.9] 19.72 0507 | 197.0 | 880.9 73:53 954-4 | 1151.4 21 3024 | 1.429 | 230.5] 18.84 | 0.0531 | 199.7 | 878.8 7374) \ 52.0) 4| RiR22 22 3168 -497 | 233.0] 18.03 0554 | 202.2 876.8 73-94 950.8 | 1153.0 2 3312 565 | 235-4 | 17-30 | .0578 | 204.7 | 874.9 74.13 949.1 | 1153-7 24 3456 033 |-237-7. ||| 10:02 1} 06027 1/"207:0 |'"557 350 74.32 947-4 | 1154.4 25 3600 7OI | 240.0| 15.99] .0625 | 209.3 | 871.3 74.51 945-8 | 1155.1 26 3744 | 1.769 | 242.2 | 15.42 | 0.0649 | 211.5 | 869.6 74:69 944-3 | 1155.8 Zr 3888 837 | 244.3 14.88 | .0672 | 213.7 867.9 74.85 942.8 | 1156.4 28 4032 905 | 246.3 | 14.38 | .0695 | 215.7 866.3 75.01 941.3 | 1157.1 20 4176 973 | 248.3 13.91 061g | 217.8 864.7 75.17 939-9 | 1157.7 30 4320 | 2.041 | 250.2 | 13.48] .0742 | 219.7 | 863.2 75:33 938-5 | 1158.3 31 4464 | 2.109 | 252.1 13.07 | 0.0765 | 221.6 | 861.7 75.47 937-2 | 1158.8 2 4008 177 | 253-9 | 12.68 | .0788 | 223.5 | 860.3 75-01 935-9 | 1159.4 33 | 4752 | -245 | 255-7 | 12.32] .o81r | 225.3 | 858.9 | 75-76 | 934.6 | 1159.9 34 4896 B03 RZ2o7 25 i PIL ILOo :0335 227 a 857-5 75-89 933-4 | 1160.5 35 5040 381 | 259.2 | 11.66] .0858 | 228.8 | 856.1 76.02 932-1 | 1161.0 36 5184 | 2.449 | 260.8 | 11.36 | 0.0881 | 230.5 | 854.8 76.16 | 931.0 | 1161.5 37 5328 e517 I 20200) | | LIsO7})| 09034) 423202) eaScanc 76.28 929.8 | 1162.0 38 5472 585 | 264.0 | 10.79 | .0926 | 233.8 | 852.3 760.40 928.7 | 1162.5 39 5616 -653 | 265.6 | 10.53 | .0949 | 235.4 | 851.0 76.52 927.6 | 1162.9 40 5760 722) e207e1 10.2 0972 | 230.9 | 849.8 76.03 926.5 | 1163.4 41 5904 | 2.789 | 268.6 | 10.05 | 0.0995 | 238.5 | 848.7 76.75 925-4 | 1163.9 2 6048 857 | 270.1 9.83 | .1018 | 239.9 | 847.5 76.86 924-4 | 1164.3 43 6192 O25. (0270-5 9.61 -1040 | 241.4 | 846.4 76.97 923-3 | 1164.7 44 6336 993 | 272.9 9.41 | .1063 | 242.9 | 845.2 77.07 92253) || ro Re 45 6480 | 3.061 | 274.3 9.21 -1086 | 244.3 | 844.1 77.18 921.3 | 1165.6 46 6624 | 3.129 | 275.6 9.02 | 0.1108 | 245.6 | 843.1 77.29 | 920.4 | 1166.0 47 6768 .197 | 277.0 8.84 | .1131 | 247.0 | 842.0 77.39 919.4 | 1166.4 48 6912 265 | 278.3 8.67 | .1153 | 248.3 |] 841.0 77-49 | 918.5 | 1166.8 49 7056 333 | 279.6 8.50 | .1176 | 249.7 | 840.0 77-59 917.5 | 1167.2 SMITHSONIAN TABLES. TABLE 249. PROPERTIES OF STEAM. British Measure. foot. feet. per pound ound of steam | _ in Internal latent heat per pound steam in of steam in External latent heat per pound Pressure in pounds per square inch. Pressure in pounds per square Pressure in atmospheres. Temp. in degrees Fahr. Volume per pound in cubic Weight per cubic foot Heat of water heat of Total latent of steam in Total heat per ASLoe yb wHN ee mom - Oo ~¢ me ROaD & ADOW Anko d Qn MH.O O NWN NOOO momMmmMm boy wh ht ANI Go GD tO wy wk ly WwCOOO Cuomo YUN AH $HObKW4 aeons 28S EN DAAAH DADDY BWyyWW Wy og HE NWhU nN moma n RPNHNRNAN SHO 909" NCO os ROO FPNOMHA fNOON G2 ° rs) “NI ° on ce 00 bony bow PRROD 27 27 27 27 27 3. 4. 5: 6. 7 8. Q. oO. O. ee ONIWO NbvNN AN mmmmem Om ONIN moorhn &itin Onl =e WOM aN & YHHHDHD A A ining Anko Roun O™ Nw N DAAASG OP SO Wor WO GW 2 Ga Go DHNHHN bb RAH DRVN SMITHSONIAN TABLES. TABLE 249. PROPERTIES OF STEAM. British Measure. U. heat per pound of steam in pound of steam in B. T. U. Been. Total heat per Internal latent heat per pound External latent heat per pound Heat of water of steam in pounds per square foot. Pressure in atmospheres. Temp. in degrees Fahr. Volume per pound in cubic feet. Weight per cubic foot in er pound in Bt. vU. of steam in Bits Total latent Pressure in ~ aS _ ° ° yg aS Y O2 G2 mun OAoOd7 oo = O QO.” On ~ fe i) G2 G2 Gd Gd GRNNNN DOO os PNOWD t bbb bK ~ _ Oo mn 8 b WO Wo Wd _ Go G2 G2 Ga Ga Ga QOH tv 0 OS Leieiaae wR NH HN fff WWwwWwwW Chin oH 0A WO OT ARO us G aor wn 1950 ‘O17 885 853 .790 -760 -730 -700 643 2) |(sOUS 587 560 ° ee 481 .456 -431 RN Nh WO mOmnwm m\O “In Go Mw Nw 3-406 .382 358 “334 “310! |) 9-302 : 2. ; 1188.5 1188.7 1188.8 1189.0 1189.2 1189.4 1180.5 1189.7 1189.9 1190.0 1190.2 3.287 .205 424 220 199 3-177 156 135 IDS 094 G2 Ga Ga Gd Go NHNNNN WADA HOYHDHD NN a=W Oo On Axe NHN N 355-5 | 3-074 350.0 | 054 356.6 | .035 Boyar .O16 357-6 | .997 1190.4 1190.5 1190.7 1190.9 IIQI.0 02 WG) Ga G2 Wd Ga Ga Wd WnNHN bv OS HH Ono SMITHSONIAN TABLES. TaBle 249. PROPERTIES OF STEAM. British Measure. pound of steam in B. 2. per foot. B. T. U. ound in pound of steam External latent heat per pound of steam in BT. Ui; Total heat per square inch. Pressure in Pressure in atmospheres. Temp. in degrees Fahr. Volume per cubic feet. Weight per cubic foot in Heat of water aig pound in ees le Internal latent heat per Total latent | heat per pound of steam in pounds per pounds square Pressure in P “I “I es ~~ oe oat io) 4 * in _— ~ num Qnna © Fees NaN AAAS Mow © = n SMITHSONIAN TABLES. TaBLe 249. PROPERTIES OF STEAM. British Measure. hr. pound of steam In pound of steam in pound of steam External latent heat per pound in B. T. U. of steam in By Ty U: Pressure in pounds per square inch. Pressure in pounds per square foot. Pressure in atmospheres. degrees Fa Volume per pound in cubic feet. Weight per cubic foot in Heat of water per pound in Internal latent heat per heat per Total latent Total heat per NN N bRRHKA Ow khuU™ ON mm N VOD Co mo > Qo rx oO) :0) 0 SOS Se 2oT SMITHSONIAN TABLES. | 242 TABLE 250. RATIO OF THE ELECTROSTATIC TO THE ELECTROMACNETIC UNIT OF ELECTRICITY (v) IN RELATION TO THE VELOCITY OF LICHT. Date of determina- tion. 1856 1868 1869 1872 1879 1879 1880 1881 1881 1882 Ratio of electrical units. vw in cms. per sec.* 3-107 X 101 2.842 X 1010 2.808 X 1010 2.896 X 101° 2.960 X 101° 2.968 X 10! 2.955 X 1010 2.99 X I0!} 3-019 X 101 2.923 X 10% 2.963 X 101 3-009 X 101” 2.981 X 1019 3,000 X 101? 3-004 X 101° 2.995 X 1010 Determined by — Weber & Kohlrausch . Maxwell W. Thomson & King . McKichan Ayrton & Perry Hocken Shida Stoletow Klemenci¢é Exner J. J. Thomson Himstedt Rowland Rosa W. Thomson J. J. Thomson & Searle Reference. Publication. Pogg. Ann. Phil. Trans. B. A. Report . Phil. Trans. Jour. Soc. Tel. Eng. B. A. Report . Phil. Mag. Soc. de Phys. . Wien. Ber. Wien. Ber. Phil. Trans. Wied. Ann. 35 Phil. Mag. Phil. Mag. Phil. Trans. * The results in this column correspond to a value of the B. A. ohm = .98664 X 108 cms, per sec. If we neglect the first four determinations, and also that of Exner and Shida, because of their large deviation from the mean, the remaining determinations give a mean value of 2.9889 + .0137, a value which practically agrees with the best deter- minations of the velocity of light. + Given as between 2.98 X 1010 and 3.00 X 1019, SMITHSONIAN TABLES. (Cf. Table 181.) 243 TaBLE 251. DIELECTRIC STRENCTH. Difference of Electric Potential required to produce a Spark in Air. (a) Mepium, Arr. ELecrropg TERMINALS, FLAT PLarTgs. Difference of potential in volts required to produce a spark according to — Spark length in centimetres. | WoThomson.1| Dela Rue.? | MacFarlane.? Baille.4 Freyberg.5 1340 0.04 1840 1900 = = - 0.07 2940 3179 7 Pe yi 0.10 4010 4339 3597 440I 4344 5300 = 1 “‘ Reprint of Papers on Elect. and Mag.”’ p. 252. 2 ‘‘ Proc. R. Soc.” vol. 36, p. 151. 8 “ Phil. Mag.” vol. 10, 1880. 4 “ Ann. de Chim. et de Phys.” vol. 25, 1882. 5 “ Wied. Ann.” vol. 38, 1889. (b) Mepvium, Arr. ELecTropE TERMINALS, BALLS oF DIAMETER @ IN CENTIMETRES. Experiments of Freyberg. Spark length ; in ad =o (points). d=0.50 aro ad=2.0 d= 4.0 d=6.0 centimetres. O.I 3720 050 4660 4560 - 4530 0.2 4700 600 9500 8700 8400 7900 0.3 5300 11100 11700 11600 11200 10500 0.4 6000 13500 14000 14400 14200 12800 0.6 6900 16600 19300 19500 20100 19200 0.8 8100 18400 23200 24000 25800 26000 1.0 8600 19500 25800 29000 29900 31600 2.0 10100 24000 35400 - - - 5-0 13100 30700 = — - = From the above table it appears, as remarked by Freyberg, that for each length of spark there is a par- ticular size of ball which requires the greatest difference of potential to produce the spark. (¢G) CoMPARISON OF RESULTS OF DETERMINATIONS, THE TERMINALS BEING BALLS. Difference of potential required to produce a spark in air according to — Spark : length Baille. Bichat aod Paschen. | Freyberg.] Paschen. | Freyberg. | Quincke.2] Baille. | Freyberg. in cms. Balls 1 centimetre diameter. Balls 2 cms. diameter. Balls 6 cms. diam. I 4590 | 4200 | 4860 | 4660 | 4830 | 4560 | 4440 | 4440 | 4 33° 2 8040 8130 8430 9500 8340 8700 7920 7680 7860 2 III90 | 10860 | 11670 | 11670 11670 | I1550 | I1190 10830 10470 4 3650 | 14130 | 14830 | 13980 | 14820 | 14400 | 14010 13500 | 12750 fs 16410 | 16800 | 17760 | 16800 | 18030 | 17040 | 16920 16530 | 16410 6 19560 | 19350 | 20460 | 19260 | 20820 | 19470 | 19980 }| 19560 | 19200 7 21690 | 21030 | 22640 | 20970 | 23670 | 22530 | 22590 | 22620 | 22590 8 23280 | 23190 | 24780 | 23220 - 24630 | 25770 26400 | 26010 9 24030 | 24540 - 25110 - 27240 - 29220 | 28770 | 1.0 24930 | 2:800 - 25770 ~ 29040 - 33870 | 31620 1 “ Electricien,’? Aug. 1886. 2 “Wied. Ann.’ vol. 19, 1883. SmitHSONIAN TABLES. 244 TABLES 252, 253. DIELECTRIC STRENCTH. TABLE 252. — Effect of Pressure of the Gas on the Dielectric Strength.* Length of spark is indicated by Zin centimetres. The pressure is in centimetres of mercury at 0° C. Hydrogen. ir. Carbon dioxide. Pressure. aoe =0.6 =. i=0o.28 l=04 | 7=0.6 - 1536 1125 1446 | 1650 1437 2259 143! 1971 237 1839 3012 1755 2484 | 3105 2172 3084 2070 2913 | 3813 2463 4272 | 2355 | 3285] 4275 3330 5736 | 2991 422 39? 4020 7074 370 5235 01 4668 5 8346 3 6120 8004 533! 9570 4707 6921 | 9147 5997 10797 5163 | 7737 | 10293 6681 3 12009 5772 8543 | 11397 7347 13224 222 9393 | 12453 7971 14361 6489 | 10035 | 13557 8583 15441 6789 | 10650 | 14610 9222 16548 7197 | 11397 | 15702 9867 17688 7605 | 12114 | 16740 10476 18804 8001 | 12816 | 1772 11040 d 19896 8388 | 13506 | 18705 Paschen deduces from the above, and also shows by separate experiments, that if the product of the pressure of the gas and the length of spark be kept constant the difference of potential required to produce the spark also remains constant. In the following short table Z is length of spark, P pressure, and V difference of potential, the unit being the same as above. The table illustrates the potential difference required to produce a spark for different values of the product 2.P. V for Air. V for CO, Ps V for H V for Air. V for CO, 669 873 i 2481 4251 4443 1110 7 3507 6162 6198 1281 5835 10392 IOOII 1599 8004 13448 13527 2271 11013 19848 18705 3468 TABLE 253.— Dielectric Strength (or Difference of Potential per Centimetre of Spark Length) of Different Substances, in Kilo Volts.t Substance. Substance. Substance. Dielectric strength. Dielectric strength. Dielectric strength. Beeswaxed paper . . | Kerosene oil « Paraffined paper. . | Oil of turpentine Paraffin (solid) . . . | Olive oil : Paraffin oil . . Paraffin (melted) Air (thickness 5 mm.) Carbon dioxide . Coal gas : Hydrogen Oxygen PNURY Wn as oO Nn Nb * Paschen. ; + MacFarlane and Pierce, ‘‘ Phys. Rev.’ vol. 1, p. 165, 1893. 245 SMITHSONIAN TABLES. TABLE 254. COMPOSITION AND ELECTROMOTIVE FORCE OF BATTERY CELLS. The electromotive forces given in this table approximately represent what may be expected from a cell in good work- ing order, but with the exception of the standard cells all of them are subject to considerable variation. (a) Douste FLuip BATTERIES. Positive Negative pole. Solution. Solution. { 1 part HgSOy4 to Amalgamated zinc ) 12 parts H2O Fuming H2,NO3 “ “ “ HNOs, density 1.38 12 parts KgCrgO7 to 25 parts of H,SO,4 and 100 parts H20 . I part H2SO4 to 12 parts H2,O - l 12 parts H2O. to 100 parts H2O § I part H2SOx, to § Saturated solution 4 parts H,O . | of CuSO4+5H20 I part HgSOx4 to a 12 parts H2O. { I part H2SO4 to : j 12 parts KeCr20; 1 | , ZnSO4 + 6H20 I part NaCl to] 18 5% solution ~ of § ) 4parts H,0 .f § 1 part H2SO,4 mi ) 12 parts H2O Platinum) Fuming HNOs . Solution of ZnSO4 s HNOs, density 1.33 H2SO,4 solution, density 1.136 . Concentrated HNOgs 2SO,4 solution, density 1.136 . HNOs, density 1.33 density 1.06 H2SO,4 solution, density 1.14 H.SOj, solution, density 1.06 z i } H2SOx4 solution, 7} | 5 NaCl solution. . < “density 1.33 Paste of protosul- + I t H2SO4 t Marié Davy } Lotparts Ho Carbon Di Partz) =. Solution of MgSO4 Solution of KgCr207 * The Minotto or Sawdust, the Meidinger, the Callaud, and the Lockwood cells are modifications of the Daniell, and hence have about the same electromotive force. SMITHSONIAN TABLES. 246 TaBLe 254, COMPOSITION AND ELECTROMOTIVE FORCE OF BATTERY CELLS. Negative pole. E. M. F. Name of cell. : in volts, Solution. Positive pole. (b) Since Fiurip Barrerigs. Carbon surround- Meclanchar.: Renal, ware § Solution of sal-ammo- ||] ed by powdered a6 rales <= Uo oniac. . . . . .§]) carbon and perox- 3 ide of manganese Chaperon § eens of caustic | Copper and CuO Edison-Lelande . a « Mhlonde of silver | Zinc 23 % solution of sal- } Silver surrounded ammoniac : by silver chloride RaW fe 15% S Carbon . I pt. ‘ZnO, I pt. NH4Cl, 3 pts. plaster of paris, 2 pts. ZnCl, and water to make a paste l J { Solution of FL Dry cell (Gassner) Poggendorff . .| Amal. zinc 1 of potash \ I2 parts KgCregO7 + a ) 25 parts HeSO,4 io 100 parts H2,O I part HygSO, a 12 parts H2gO + at fee ali Volta couple . . See : : Copper . J. Regnault. Cadmium (c) STANDARD CELLs. ZnSO solution, den- t Electrolytic cop- { i 1.072 [I —.o0o0016 (4—15)] 1.434 [1 — ae (t—15)] | a 50 tem- ,/ Kelvin, Gravity, Haniel 3; Amal. zinc erin CuSQ,4 sol. sity 1-40 5 aa 1.10 Mercurous sulphate in paste with saturated solution of neutral ZnSO4 . Clark standard . Mercury. perature coeffic’t about -OOOIT 1.387 [1 ¢ —-0002 ( (e—12)] Lodge’s standard cell and Fleming’s standard cell are, like the Kelvin cell above, modifications of the Dan- iell zinc-zinc sulphate, copper-copper sulphate cell. Baille & Ferry . Zinc chloride, density | | Lead dered rials by powdered PbCl, . Oxide of mercury in a ! Gouy sf 10 % sol. of ane Mercury. (paste) . 2 (d) S—EcoNDARY CELLS. Faure-Sellon- l § H2SQx4 solution of l (Volckmar) . § Lead. . 1 density 1.1 oy PbOs - Regnier (1) . . |Copper .| CuSOg-+ HeSO, . (2) . . |Amal.zinc}] ZnSOgsolution. . Main .. . . |Amal.zinc] HgSO, density ab’t 1.1 * F. Streintz gives the following value of the temperature variation eo at different degrees of charge : — dE {dtX108| E.M. F. | 42 7ae x rt 285 255 228 2.0084 2.0105 140 2.0031 | 335 SMITHSONIAN TABLES. 247 T 2 . oe THERMOELECTRIC POWER. The thermoelectric power of a circuit of two metals at mean temperature ¢ is the electromotive force in the circuit for one degree difference of temperature between the junctions. It is expressed by d# / dt = A + Bt, when aE / dt =0,t =—A / B, and this the neutral point or temperature at which the thermoelectric power vanishes. The ratio of the specific heat of electricity to the absolute value of the temperature ¢ is expressed by —B for any one metal when the other metal is lead. The thermoelectric power of different couples may be inferred from the table, as it is the difference of the tabulated values with respect to lead, which is here taken as zero. The table has been compiled from the results of Becquerel, Matthieson, and Tait. In reducing the results the electromotive forces of the Grove’s and the Daniell cells have been taken as 1.95 and 1.07 volts respectively. Substance. BX 10-2 Aluminium ; . . | Antimony, comm’! pressed wire v axial : : equatorial ordinary . | Argentan.., (%: 3. We “ Arsenic ; . : Bismuth, comm’! pressed wire . “ pure “ “ crystal, axial “equatorial commercial ° Cadmium . ; j ‘ Gfused ss cum Cobalt : ; . Copper ; “commercial “ galvanoplastic Gold . : : : eS . . . . Iron . : . “pianoforte wire . “commercial 77 “ . Lead . : : | Magnesium | Mercury Nickel : , : “« (—18° to 175°) « (250°=300°) “(above 340°) . Palladium . ; : Phosphorus (red) Platinum : , < (hardened) (malleable) . ; wire 2 ; another specimen Platinum-iridium alloys : 3 85% Pt+15%Ir 90% Pt+10%Ir 95% Pt+ 5 flr Selenium . ; Silver ; A “« (pure hard) “wire Steel . Tellurium . “ Tin (commercial) “ce “ . Zinc “oe pure pressed B= Ed. Becquerel, ‘‘ Ann. de Chim. et de Phys.” [4] vol. 8. T= Tait, ‘Trans. R. S. E.”’ vol. 27, reduced by Mascart. Thermoelectric power _ at mean temp. of penal junctions (microvolts). ee ANOS 4 aad ity. 2001s 50° C. 2 0.68 0.56 a —6.0 - M —22.6 ce —20.4 a —17.0 B 12.95 xz - B 13.56 97-0 89.0 65.0 ao —3.48 —1.52 —o.10 —3.8 —I.2 “—3.0 —16.2 —I17.5 0.00 —2.03 tN Idi «oo | Ny ODI NI WEAWEHS s an Hs M = Matthieson, “‘ Pogg. Ann.” vol. 103, reduced by Fleming Jenkin. SMITHSONIAN TABLES. 248 relative to lead, and for a mean temperature of 50° C. TaASLE 256. THERMOELECTRIC POWER OF ALLOYS. The thermoelectric powers of a number of alloys are given in this table, the authority being Ed. Becquerel. They are the thermoelectric power of lead to copper was taken as —1.9. Substance. Antimony . Cadmium Antimony . Cadmium Zinc Antimony Cadmium Bismuth Antimony . Zinc Antimony . Zinc Bismuth Antimony . Cadmium Lead . Zinc Antimony . Cadmium Zinc sltin: Antimony . Zinc Tin Antimony . Cadmium Zinc Antimony . Tellurium NEUTRAL POINTS WITH LEAD.* Relative quantity. ao 6. 0 ANNAN AD en eee aoe Sooo enn Ieee ae a een i Cocs5 ae oleae a eo no © 0 - to _ mn 00 OV ON 406 ~ y ~ a] HOWONn KH Be NP He DOD _ Thermo- electric power in microvolts. Antimony . Bismuth Antimony Iron Antimony . Magnesium Antimony [ead . Bismuth Bismuth Antimony . Bismuth Antimony . Bismuth . Antimony . Bismuth . Antimony . Bismuth Antimony Bismuth Tin Bismuth Selenium . 3ismuth ZinCus Bismuth Arsenic Bismuth Bismuth sulphide : Substance. In reducing the results from copper as a reference metal, Thermo- electric power in microyolts. Relative quantity. i) —- Orn Oeh KO ~ _ _ _ es my en SO FN BN HO HR OHH HN ~ een ee a an een 0 0 Ore 0 eee Ser Oe See Sem TABLE 257. TABLE 258. SPECIFIC HEATS OF ELECTRICITY.t+ ae The numbers are the coefficients B in the equation “~ = A-+ Bt, and have to be multiplied by the absolute at Substance. Bismuth . Nickel Gold Argentan Cobalt Palladium Antimony Silver . Copper SS > Cadmium . Platinum Tin Rhodium Ruthenium Aluminium Magnesium Tron. also Table 255.) Metal. Alumin- 1UnT ce Antimony Argentan Bismuth . Cadmium Cobalt Copper Gold Iron Iridium | Lead temperature 7 to give the specific heat of electricity. Sp. ht. of el. (See Sp. ht. of el. Metal. 7 Magnesium Nickel : —.00094 To 175° C. .|—.00507 250°-310° 00219 Above 340° . | —.00351 Platinum (soft) | —.co10g Palladium - | —.00355 Rhodium - | —.00113 Rubidium . —.00206 Silver .00148 Tin 00055 Zinc 00235 * Tait’s “* Heat,’’ p. 180. : : - + Calculated from a table given by Tait by assuming the electromotive force of a Grove's cell = 1.95 volts. SMITHSONIAN TABLES. 249 Thermoelectric power of cir TABLE 259. THERMOELECTRIC POWER OF METALS AND SOLUTIONS." cuits, the two parts of which are either a metal and a solution of a salt of that metal or two solutions of salts. The concentration of the solution was such that in 1000 parts of the solution there was one half gramme equivalent of the crystallized salt. Thermoelec- tric power in Substances forming circuit. : microvolts. Cuand CuSO, . ; : 754 Zn and ZnSO, . . 5 Cu and CuAc (acetate) . 660 Pb and PbAc : : : Zn and ZnAc Cd and CdAc Zn and ZnCle Cd and CdClg Zn and ZnBreg Zn and ZnIz Cd and Cdl CuSO, and ZnSO4 CuAcand ZnAc. ZnAc and CdAc. CuAc and CdAc. PbAc and ZnAc. PbAc and CdAc. PbAc and CuAc. ZnCly and CdClg Znbrg and CdBr2g ZnIyg and Cdl, The circuit is indicated symbolically ; for example, Cu and CuSO, indicates that the circuit was partly copper and partly a solution of copper sulphate. Insoluble salts mixed with a solution of the corresponding zinc or cadmium salts for the purpose of acting as a conductor. The other part of the circuit was the metal of the insoluble salts. The results are com- plex and of doubtful value. Substances forming circuit. Ag and AgCl in ZnCl, Ag and AgCl in CdCl, Ag and AgBr in ZnBrg Ag and AgBr in CdBrg Ag and AglI in ZnI, Agand AglinCdlI2 . Hg and HgeCle in ZnCle Hg and HggClz in CdCle Hg and Hg2Bre2 in Zn bre Hg and Hg2Brg in CdBr2 Hg and Hggls in ZnIg. Hg and Hggly in Cdl, Thermoelectric power in microvolts. 143 310 327 461 414 unsuccessful 680 673 650 81 94 8g1 TABLES 260, 261. PELTIER EFFECT. TABLE 260.—Jahn’s Experiments.t TABLE 261.—Le Roux’s Experiments.+ Current flows from copper to metal mentioned. on ' Table gives therms per ampere per hour, and current flows Table gives therms per ampere per hour. from copper to substance named. Metals. Therms. Metals. Therms. Cadmium ; : —o.616 Tron. ; ; ; — 3-613 Nickel . : : : 4.362 Platinum. 2 2 0.320 Bismuth (pure). ; Silver , : —0.413 cs (Becquerel’s) || ZC a. ; ; : —0.585 ~ th Antimony (Becquerel’s) § (commercial) oo No oon PO MS £@ _ Cadmium German silver Cd to CdSO,4 Cu to CuSO4 : : Ag to AgNO3 _ .. : : tron Zn to ZnSO, ; . ; Zinc * Gockel, ‘‘ Wied. Ann.” vol. 24, p. 634. t ‘‘ Wied. Ann.” vol. 34, p. 767. ¢ ‘Ann. de Chim. et de Phys.”’ (4) vol. 10, p. 201. § Becquerel’s antimony is 806 parts Sb -+- 406 parts Zn + 121 parts Bi. || Becquerel’s bismuth is 10 parts Bi-+1 part Sb. SMITHSONIAN TaBLes. 250 TABLE 262. CONDUCTIVITY OF THREE-METAL AND MISCELLANEOUS ALLOYS. Conductivity Ce= Co (1 + at+ df). Metals and alloys. Composition by weight. : a X 108 bX 10° Gold-copper-silver . . .| 58.3 Au+ 26.5 Cu-+ 15.2 Ag ‘s as Rae cua ae Peete Cuaaande “ . . .|7-4Au-+ 78.3 Cu-+ 14.3 Ag { 12.84 Ni + 30.59 Cu + 1.6.57 Zn by volume ; to Authority. Nickel-copper-zinc . Brassigee fh de) -) | Waklous.) . Se eee eel 2:2—08.0 Seeehardedrawni 22s] 70-2 Cu + 29. 8Zn Santee: 12.1 eee LONE a CC ca ment ae 14.35 Gennansilvemunsm met \Valiousieone : Bao 60.16 Cu + 25. 37 Zn ah it < » «© + «1414.03 Ni-+.30 Fe with trace 3-33 ! of cobalt and manganese . Aluminium bronze. . . ~ 7.5-8.5 Phosphor bronze .. . 10-20 Silicium bronze . Manganese-copper . . .|30Mn-+70Cu . Nickel-manganese-copper | 3 Ni-+ 24 Mn+ 73Cu ( 18.46 Ni + 61.63 Cu + Nickelin 19.67 Zn + 0.24 Fe + ! o.19Co+o18Mn . 25s Ni+ 74.41 Cu+ | 0.42 Fe + 0.23 Zn + 0.13 Mn+ trace of cobalt j gI Patent nickel . Cu-+ 25.31 Ni+ Rheotan 53-28 16.89 BASES ly oe ti : 1Cu ~ to ° +71Mn+1.9Fe . . | 70.6 Cu + 23.2 Mn-+ 6.2 Fe s “« . | 69.7 Cu + 29.9 Ni-+ 36Fe . Manganin. . .. . .|84Cu+12Mn+4Ni | Copper-manganese-iron ay “ee ae ty nN ND iS ° NFRD hENn COMmMDmOnnnwm IAD 1 Matthieson. 3 W. Siemens. 5 Van der Ven. 7 Feusner. 2 Various. 4 Feusner and Lindeck. § Blood. 8 Lindeck. SMITHSONIAN TABLES. TABLE 263. CONDUCTING POWER OF ALLOYS. base eas This table shows the conducting power of alloys and the variation of the conducting power with temperature.* : Si eee 108 The values of Cy were obtained from the original results by assuming silver= 7.585 taken as Cf = C, (1 — t+ A#*), and the range of temperature was from 0° to roo” C. : The table is arranged in three groups to show (1) that certain metals when melted together produce a solution which has a conductivity equal to the mean of the conductivities of the components, (2) the behavior of those metals alloyed with others, and (3) the behavior of the other metals alloyed together. It is pointed out that, with a few exceptions, the percentage variation between o° and 100° can be calculated from the formula P= P, a and P, is the calculated mean variation of the metals mixed. mhos. The conductivity is where Z is the observed and / the calculated conducting power of the mixture at 100° C., Weight % | Volume % Variation per 100° C. a X 108 & X 109 | of first named. Observed. |Calculated. Group 1. _— _ UW ARON AxmrhuU HN CN HAO OON Lead-silver (PbgoAg) . Lead-silver (PbAg) Lead-silver (PbAg2) Tin-gold (SnygAu). . SS (Suga). 9 ‘in-COppery js eeu = ‘ | cay “ Tin-silver . ace “e Zinc-copper “ “ Nore. — Barus, in the “ Am. Jour. of Sci.’’ vol. 36, has pointed out that the temperature variation of platinum . . . n : alloys containing less than 10% of the other metal can be nearly expressed by an equation y= —~— m, where y is the temperature coefficient and x the specific resistance, #z and 7 being constants. If a be the temperature coefficient at o° C. and s the corresponding specific resistance, s (a +-#z) =. For platinum alloys Barus’s experiments gave #z =— .o00194 and # = .0378. For steel 72 = —.000303 and 2 = .o620. Matthieson’s experiments reduced by Barus gave for Gold alloys #z = — .000045, 7 = .00721. Silver ‘* #%=—.000112, 2 = .00538. Copper ‘* #2 = — .000386, 72 =.00055. * From the experiments of Matthieson and Vogt, ‘‘ Phil. Trans. R. S.’’ v. 154. + Hard-drawn. SMITHSONIAN TABLES. i) ur Wd TABLE 263. CONDUCTING POWER OF ALLOYS. Group 3. Weight % | Volume % Variation per 100° C. Co 74 a X 108 10 of first named. Observed. |Calculated. Gold-coppert . . .| 99.23 98.36 4 Sap RSA eeksG 81.66 An Und meRHK COM Wn Gold-silver a“ “ t 87.95 79.86 = ye Ge cell Rey ROS 79.86 het) = |) O40 52.08 oe ein ay ee OA.50 52.08 t 31.33 19.86 * 31.33 19.86 Gold-coppert . . .| 34.83 19.17 s see Peace cers Te52 0.71 Ww ALU COn ano tN Platinum-silvert . .| 33-33 19.65 “ et ieee 9.51 5:05 % cere ie eins 5.00 2.51 Bt 7 9. 9. 6. 6. 8. 8. 8. 5: 3: We Tr on hn Cun al Palladium-silver tf . .| 25.00 23.28 ae N _ ° Copper-silvert . . «| 98.08 98.35 os OPS 6 oll Cy) 95-17 76.74 | 77-64 42.75 | 46.67 7.14 8.25 1.3% 1.53 Ir®n-goldf .... 27.9 “ “ + 21.1 t ay oles 10.96 NdHKHHNN SOIC Oe NIUn OO WH NNO bv = Iron-copper t Phosphorus-copper : : Arsenic-copper tf “ “ t * Annealed. + Hard-drawn. SMITHSONIAN TABLES. 253 TABLE 264, SPECIFIC RESISTANCE OF METALLIC WIRES. This table is modified from the table compiled by Jenkin from Matthieson’s results by taking the resistance of silver, gold, and copper from the observed metre gramme value and assuming the densities found by Matthieson, namely, 10.468, 19.265, and 8.95. Substance. wire one cm. long, one sq: cm. in section. resistance for 1° C. in- crease of temp. at 20° C. Resistance at 0° C. of a Resistance at o° C. of a wire one metre long, one mm. in diam. Resistance at 0° C. of a wire one metre long, weighing one gramme. Resistance at 0° C. of a wire one foot long, youn in. in diam. Resistance at 0° C. of a wire one foot long, Percentage increase of weighing one grain. Silver annealed . ; : 0.01859 8.781 2184 a in Ww ° I ww NI NI “ hard drawn. : : 0.02019 : 9-538 .2379 Copper annealed : : 0.02017 . 9.529 2037 Gold annealed . : : 0.02659 -4025 | 12.56 O77 “ hard drawn : : 0.02706 .4094 | 12.78 -5870 Aluminium annealed . : 0.03699 .0747 | 17.48 -IO7I Zinc pressed. : : 0.07146 -4012 | 33.76 5753 Platinum annealed . ; O.I1 50 1.934 54-35 2.772 Iron x iba 0.1234 7551 | 58.31 1.083 Nickel Sie 0.1583 1.057 74.78 1.515 Tin pressed : > ; 0.1678 9608 | 79.29 1.377 “hard drawn . : 0.02062 : 9.741 2078 Lead “ : : . 0.2437 2.227 | DESI 3-193 Antimony pressed. ; 0.4510 2.379) | 213-1 3-410 | Bismuth < 5 ; 1.667 12.86 787.5 . | 18.43 Mercury «f : : 1.198 12.79 565-9 18.34. Platinum-silver, 2 parts Ag, 0.3098 2.919 | 146.4 4.186 1 part Pt, by weight German silver . . - 0.2660 1.825 | 125.7 2.617 0.1380 1.646 65.21 2.359 Gold-silver, 2 parts Au, 1 part Ag, by weight SMITHSONIAN TABLES. 254 TABLE 265. SPECIFIC RESISTANCE OF METALS. The specific resistance is here given as the resistance, in microhms, per centimetre of a bar one square centimetre in cross section. Substance. Physical state. Aluminium Antimony . “ Arsenic Bismuth “ “ Boron Cadmium . “ “ Gold Calcium Cobalt . Copper . Iron . ““ Tron ; Indium . Lead Lithium Magnesium Nickel . Palladium . Platinum Potassium . “ Silver Strontium . Tellurium . “ FE ine “ Liquid Electrolytic soft “ hard Commercial Pulverized and com- pressed Solid Liquid Commercial “ Electrolytic Tempered glass hard light yellow yellow blue light blue SMITHSONIAN TABLES. 110-268 8 X 1010 6.2-7.0 16.5 37:9 2.04-2.09 7 08 1.58-2.20 9.7-12.0 11.2 105. 114. 118.3 19.1 85.8 104.4 113.9 1 + .oo1617) + .00244?) + .00280/) 25.13 deere 10° 55:05 9.53-11-4 860 Oo 318 318 ° 16.8 oO ° oO Ordinary Red heat Yellow heat Tron magnetic heat Ord. temp. Red heat Yellow heat Nearly white heat zt QooOC0DGIIOOO NAHAS ~ 80 -_ So FO 5 5 -point Nw °ofghkoo Meltin “ gq Various. “c De la Rive. “ Matthieson and Vogt. Van Aubel. Various. Moissan. Various. Vassura. “cc Various. Matthieson. “ Varieus. “ Kohlrausch. Barus and Strouhal. Erhard. Various. Matthieson. Various. “ “ Matthieson. “ce Various. Matthieson. rai Vincentini and Omodei. Various. Vassura. “ “ De la Rive. TABLE 266. RESISTANCE OF METALS AND The electrical resistance of some pure metals and of some alloys have been determined by Dewar and Fleming and increases as the temperature is lowered. The resistance seems to approach zero for the pure metals, but not for temperature tried. The following table gives the results of Dewar and Fleming.* When the temperature is raised above 0° C. the coefficient decreases for the pure metals, as is shown by the experi- experiments to be approximately true, namely, that the resistance of any pure metal is proportional to its absolute is greater the lower the temperature, because the total resistance is smaller. This rule, however, does not even zero Centigrade, as is shown in the tables of resistance of alloys. (Cf. Table 262.) Temperature = Metal or alloy. Aluminium, pure hard-drawn wire . ; . 4745 3505 Copper, pure electrolytic and annealed . : 1920 1457 Gold, soft wire : : : a e- 2 2665 2081 Iron, pure soft wire : : ; ; ° 13970T 9521 from compound of nickel and carbon monoxide) Nickel, pure (prepared by Mond’s process 19300 13494 Platinum, annealed : : ; 10907 8752 8221 Silver, pure wire. : ; : 2139 1647 1559 Tin, pure wire : : : : : 13867 10473 9575 6681 German silver, commercial wire. : ° 35720 34707 34524 33664 Palladium-silver, 20Pd-+ 80 Ag . : ; 15410 14984 14961 14482 Phosphor-bronze, commercial wire : 2 9071 8588 8479 8054 44590 43823 43001 43022 Platinoid, Martino’s platinoid with 1 to 2% tungsten 7 Platinum-iridium, 80 Pt-+ 20Ir . : : 31848 29902 29374 27 504 Platinum-rhodium, 90 Pt-+ 10 Rh . : ‘ 18417 14586 13755 10778 Platinum-silver, 66.7 Ag + 33.3 Pt. : ; 27404 26915 26818 26311 Carbon, from Edison-Swan oe aree ; 4046X 103 | 4092 108 | 4189 X 103 lamp Carbon, f Edison-S i d t iarae rom 1sOn-OWan Incandescen t ; 3834 X 108 3908 X 103 3955 X 108 4054 X 108 Carbon, adamantine, from Woodhouse and Rawson incandescent lamp i. 6168 X 108 | 6300 X 108 | 6363 X 108 | 6495 X 108 * “ Phil. Mag.” vol. 34, 1892. t This is given by Dewar and Fleming as 13777 for 96°.4, which appears from the other measurements too high. SMITHSONIAN TABLES. 256 TABLE 266. ALLOYS AT LOW TEMPERATURES. by Cailletet and Bouty at very low temperatures. The results show that the coefficient of change with temperature the alloys. The resistance of carbon was found by Dewar and Fleming to increase continuously to the lowest ments or Miiller, Benoit, and others. Probably the simplest rule is that suggested by Clausius, and shown by these temperature. This gives the actual change of resistance per degree, a constant ; and hence the percentage of change approximately hold for alloys, some of which have a negative temperature coefficient at temperatures not far from Temperature = — 100° | — 182° — 197° | Mean value of temperature co- efficient between : : : ; — 100° and Metal or alloy. Specific resistance in c. g. s. units. | +4 yo0° C.* Aluminium, pure hard-drawn wire ; 1928 Copper, pure electrolytic and annealed . 757 Gold, soft wire ; . : z : 1207 Iron, pure soft wire E : : : 4010 Nickel, pure (prepared by Mond’s process from compound of nickel and carbon monoxide) Platinum, annealed Silver, pure wire Tin, pure wire . German silver, commercial wire Palladium-silver, 20 Pd-+ 80 Ag . A 14256 Phosphor-bronze, commercial wire . 5 7883 42385 Platinoid, Martino’s platinoid with 1 to 2% tungsten } Platinum-iridium, 80 Pt-+-20Ir . : 26712 Platinum-rhodium, 90 Pt-++ 10 Rh. : 9834 Platinum-silver, 66.7 Ag + 33-3 Pt. 26108 Carbon, from Edison-Swan incandescent 9 {103 22 3 op t 4218 X 108 | 4321 X10 uae from Edison-Swan ae ae _ | 4079x108 | 4180X 108 Carbon, adamantine, from Woodhouse and ( Rawson incandescent lamp tie 6533 X 108 * This is a in the equation R = Ry (1 +7), as calculated from the equation a =Ar0e— Foi00 . o SMITHSONIAN TABLES. 257 TABLE 267. EFFECT OF ELONCATION ON THE SPECIFIC RESISTANCE OF SOFT Substance. Copper Tron German silver METALLIC WIRES.* Increase of specific resistance for 1 % of elongation — Permanent elongation. From .50 % to .60 % “ -70 “ « 80 “ “ 50 “ 55 “ Elastic elongation. From 2.5 % to 7.7 % “ 4.6 oc 4.8 “ “ 0.7 oc o« 1.0 “ TABLE 268. EFFECT OF ALTERNATING THE CURRENT ON ELECTRIC RESISTANCE. This table gives the percentage increase of the ordinary resistance of conductors of different diameters when the current passing through them alternates with the periods stated in the last column.t Diameter in — Area in — Number of Percentage increase of complete oo ; ordinary resistance. periods per Millimetres. + in. second. Less than 7, oH 8 17.5 68 3.8 times 35 times Less than yy 25 8 17-5 Less than yyy 2.5 8 17-5 * T. Gray, ‘ Trans. Roy. Soc. Edin.’’ 1880. +t W. M. Mordey, “ Inst. El. Eng. London,” 1889. GMITHSONIAN TaABLeEs, 258 TABLES 269, 270. CONDUCTIVITY OF ELECTROLYTIC SOLUTIONS. This subject has occupied the attention of a considerable number of eminent workers in molecular physics, and a few results are here tabulated. It has seemed better to confine the examples to the work of one experimenter, and the tables are quoted from a paper by F. Kohl- rausch,* who has been one of the most reliable and successful workers in this field. The study of electrolytic conductivity, especially in the case of very dilute solutions, has fur- nished material for generalizations, which may to some extent help in the formation of a sound theory of the mechanism of such conduction. If the solutions are made such that per unit volume of the solvent medium there are contained amounts of the salt proportional to its electro- chemical equivalent, some simple relations become apparent. The solutions used by Kohlrausch were therefore made by taking numbers of grammes of the pure salts proportional to their elec- trochemical equivalent, and using a litre of water as the standard quantity of the solvent. Tak- ing the electrochemical equivalent number as the chemical equivalent or atomic weight divided by the valence, and using this number of grammes to the litre of water, we get what is called the normal or gramme molecule per litre solution. In the table, 7 is used to represent the number of gramme molecules to the litre of water in the solution for which the conductivities are tabulated. The conductivities were obtained by measuring the resistance of a cell filled with the solution by means of a Wheatstone bridge alternating current and telephone arrangement. The results are for 18° C., and relative to mercury at 0° C., the cell having been standardized by filling with mercury and measuring the resistance. They are supposed to be accurate to within one per cent of the true value. The tabular numbers were obtained from the measurements in the following manner : — Let A,,— conductivity of the solution at 18° C. relative to mercury at 0° C. AY, = conductivity of the solvent water at 18° C. relative to mercury at 0° C. Then A,, —A %, = 4,, = conductivity of the electrolyte in the solution measured. a == = conductivity of the electrolyte in the solution per molecule, or the “specific molecular conductivity.” TABLE 269.—Value of #,, for a few Electrolytes. This short table illustrates the apparent law that the conductivity in very dilute solutions is proportional to the amount of salt dissolved. KC,H;0. 0.000001 1.024 0.939 0.00002 : 1.886 0.00006 : 5.610 0.0001 : 9.34 TABLE 270. —Electro-Chemical Equivalents and Normal Solutions. The following table of the electro-chemical equivalent numbers and the densities of approximately normal solutions of the salts quoted in Table 271 may be convenient. They represent grammes per cubic centimetre of the solution at the temperature given. Salt dissolved. |Grammes ~ "| Density. | Salt dissolved. Crammes cal Density. | per litre. per litre. G | P' eaert ee ered te Ge as : Bs eth Oper ak 18.9 | 1.0658 INE CI ee er) 53-55, | I: 6 | 1.0152 =|) e709 18.6 | 1.0602 NaGl 3. 58.50 : 1.0391 . | 55-09 | 1.0445 ET wea er | AZedOy |) Me , 1.022 A || ele ey, ABaCle . .| 104.0 : 18.6 | 1.0888 . | 80.58 5 6 | ESKe: 15.0 | 1.0592 79:9 165.9 : 18.6 | 1.1183 . | 69.17 n@highiy/ || ie 18.6 | 1.0601 . | 53-04 85.08 | I. 18.7 | 1.0542 oe peego.27 169.9 - - 36.51 65.28 | 0. - 61.29 | oO. 18. 98.18 18. - 63.13 3 | 1.0367 . | 49.06 6 | 1.0467 * “ Wied. Ann.” vol. 26, pp. 161-226. 259 SMITHSONIAN TABLES. TABLE 271. SPECIFIC MOLECULAR CONDUCTIVITY pw: MERCURY=10°. Salt dissolved. 11SO, . BaCle KCI1O3 2 BagN2O0¢ $CuS( )4 . AgN Og 4ZnSO4 . 4MgSO,q . tNaoSO4 4ZnCle NaCl NaNO; . KC2H,02 1Na.COg LH2SO,4 . C2H,O HCl HNO; . LHsPO, . KOH NHs Salt dissolved. 1K,SO, « KCl KI. NH,Cl KNOs KC1O3 BagN20¢ 4CuSO4 . AgNOgs . AZnSO4 . IMgSO, . bNagSO4 ZnCl NaCl NaNOg . KCeH,O2 1Na,COs LH SO, . C2H,O HCl HNO; . LH3PO, . KOH NH; SMITHSONIAN TABLES. * Acids and alkaline salts show peculiar irregularities. 260 TABLE 272, LIMITING VALUES OF uz. This table shows limiting values of » = & .108 for infinite dilution for neutral salts, calculated from Table 271. mn $BaCle .. 4MgSO4 .| 1080 AHeSOg 4KClO3 . 4NagSO4 .| 1060 HCl 4BaNoOg . $ZnCl . .| 1040 HNO; . $CuSQ, . NaCl . .}] 1030 4H 3PO4 AgNO 3 . NaNO s . 980 KOH 4ZnSOq . KeCoH30¢ 940 4NaeCOz . If the quantities in Table 271 be represented by curves, it appears that the values of the specific molecular conductivities tend toward a limiting value as the solution is made more and more dilute. Although these values are of the same order of magnitude, they are not equal, but depend on the nature of both the ions forming the electrolyte. When the numbers in Table 272 are multiplied by Hittorf’s constant, or o.coor1, quan- tities ranging between 0.14 and 0.10 are obtained which represent the velocities in milli- metres per second of the ions when the electromotive force gradient is one volt per millimetre. Specific molecular ‘conductivities in general become less as the concentration is in- creased, which may be due to mutual interference. The decrease is not the same for different salts, but becomes much more rapid in salts of high valence. Salts having acid or alkaline reactions show marked differences. They have small specific molecular conductivity in very dilute solutions, but as the concentration is in- creased the conductivity rises, reaches a maximum and again falls off. Kohlrausch does not believe that this can be explained by impurities. HsPO4 in dilute solution seems to approach a monobasic acid, while H2SO4 shows two maxima, and like HsPO4 approaches in very weak solution to a monobasic acid. Kohlrausch concludes that the law of independent migration of the ions in media like water is sustained. TABLE 273. TEMPERATURE COEFFICIENT. The temperature coefficient in general diminishes with dilution, and for very dilute solutions appears to approach a common value. The following table gives the temperature coefficient for solutions containing o.o1 gramme mole- cule of the salt. Salt. Rene sl 0: KI NH,Cl. .| 0. KNO; . NaCl . .| ©. NaNO. Tih to! AgNOs. HNO; . 4BaCle os 8 4Ba(NOs3)o ° . . 4HoSO4 hom Clay. | Os KClOs . 4H2SO4 4MgCle_.. ; KCoH 302 . i for m= .oo1 § SMITHSONIAN TABLES. TABLE 274, VARIOUS DETERMINATIONS OF THE VALUE OF THE OHM, ETC.* Observer. Mascart . Rowland Kohlrausch Glazebrook O ON OA MN Jones. Strecker. Hutchinson Salvioni . Salvioni. Roti . Heinstedt Dorn. Wild . Lord Rayleigh Lord Rayleigh Wuilleumeier . Duncan & Wilkes H. F. Weber . H. F. Weber . 1882 to 1888 1890 1890 1891 1885 1888 1890 1884 1884 1885 1889 1883 Method. Rotating coil Lorenz method. Induced current Mean of several methods Damping of mag- nets. oth ne Induced currents . Lorenz method. Lorenz method. Mean . An absolute de- termination of re- sistance was not made. The value .98656 has been used. Mean . Induced current Rotating coil Mean effect of in- duced current Damping of mag- NCC te ier aay y= Damping of mag- Value of Bara. in ohms. (.95412) 995374 95349 -95338 95352 95355 95341 Absolute measure- ments compared with German silver wire coils issued by Siemens or Strecker. Value of 100!) Value of cms. of Hg in B. A.U. ohm in cms. of Hg. 106.31 106.27 106.33 106.32 106.32 106.29 106.31 106.34 106.31 106.31 106.32 106.30 106.33 106.30 106.31 105-37 | 106.16 105.89 105.98 | 106.24 TOGA) We. Mes tie ta Lorenz method. 106.03 1885 105.93 Lorenz The Board of Trade committee recommended for adoption the values .9866 and 106.3. The specific resistance of mercury in ohms is thus .9407 X 1074. Also 1 Siemens unit = .9407 ohm. = .9535 B.A. U. 1 ohm 1.01358 B. A. U. | The following values have been found for the mass of silver deposited from a solution of silver nitrate in one second by a current of one ampere : — Mascart, “ J. de Physique,” iii. 1884 ; Rayleigh, “ Phil. Trans.” ii. 1884. > Kohlrausch, “ Wied. Ann.” xxvii. 1886 . T. Gray, “ Phil. Mag.” xxii. 1886. ; : Portier et Pellat, ‘‘J.de Physique,” ix. 1890 . OOTTI 56 .OOITI79 : » .0O11183 about ¢ .oo1118 ,OOLT1Q2 The following values have been found for the electromotive force of a Clark cell at 15° C. They have been reduced from those given in the original papers on the supposition that 1 B. A. U. = .9866 ohm, and that the mass of silver deposited per second per ampere is .OOI118 gramme. Rayleigh, “Trans.” ii. 1884 Carhart : ; ; : ; ; : Kohle, “ Zeitschrift fiir Instrumentenkunde,” 1892 Glazebrook and Skinner, “ Proc. R. S.” li. 1892 1.4345 volt. 1.4340 “ 1.4341 1.4342 * Abstract from the Report of the British Association Committee on Practical Standards for Electrical Measure- ment, ‘‘ Proc. Brit. Assoc.’’ 1892. + .oo00002 T. G. SMITHSONIAN TABLES. 262 TABLE 275. SPECIFIC INDUCTIVE CAPACITY OF CASES. With the exception of the results given by Ayrton and Perry, for which no temperature record has been found, the values are for o° C. and 760 mm. pressure. Sp. ind. cap. Authority. Vacuum = 1. Air=1. 1.0015 1.0000 Ayrton and Perry. 1.00059 1.0000 Klemenéit. 1.00059 1.0000 Boltzmann. Carbon disulphide Zane 1.0029 1.0023 Klementié. Carbon dioxide, CO, . ; 1.0023 1.0008 Ayrton and Perry. 1.00098 1.00039 Klement. 1.00095 1.00036 Boltzmann. Carbon monoxide, CO. 3 ; 1.00069 1.00010 Klementit. “ ‘ ; : F 1.00069 1.00010 Boltzmann. Coal gas (illuminating) ; : : 1.0019 1.0004 Ayrton and Perry, Hydrogen . : ; 1.0013 0.9998 Ayrton and Perry. 1.00026 0.99967 Klementit. 1.00026 0.99967 Boltzmann. Nitrous oxide, N2O : ; 3 5 1.00116 1.00057 Klementix, N SMITHSONIAN TABLES. 273 TABLES 284, 285. PERMEABILITY OF IRON. TABLE 284. — Permeability of Iron Rings and Wire. This table gives, for a few specimens of iron, the magnetic induction B, and permeability 4, corresponding to the magneto-motive forces # recorded in the first column. The first specimen is takén from a paper by Rowland,* and refers to a welded and annealed ring of ‘“‘ Burden’s Best”? wrought iron. The ring was 6.77 cms. in mean diameter, and the bar had a cross sectional area of 0.916 sq. cms. Specimens 2-4 are taken from a paper by Sosanquet,t and also refers to soft iron rings. The mean diameters were 21.5, 22.1, and 22.725 cms., and the thickness of the bars 2.535, 1.295, and .7544 cms. respectively. These experiments were intended to illustrate the effect of thickness of bar on the induction. Specimen 5 is from Ewing’s book,} and refers to one of his own experiments on a soft iron wire .o77 cms. diameter and 30.5 cms. long. Specimen 1 bility he specimen is a thin drawn force re- wire is noticeable in specimen 5. 33° 1450 4840 9880 8884 12970 11388 14740 13273 | 664 16390 13890 | 278 = 14837 | 148 | Nore. — The comparatively high uired for maximum permea value of the magnetizing when t q TABLE 285.— Permeability of Transformer Iron.$ This table contains the results of some experiments on transformers of the Westinghouse and Thomson-Houston types. Referring to the headings of the different columns, JZ is the total magneto-motive force applied to the iron; 1/7 the magneto-motive force per centimetre length of the iron circuit: 4 the total induction through the mag- netizing coil; B/a@ the induction per square centimetre of the mean section of the iron core; 47/8 the magnetic reluctance of the iron circuit; B//J/a the permeability of the iron, 2 being taken as the mean cross section of the iron circuit as it exists in the transformer, which is thus slightly greater than the actual cross section of the iron. (a) WesTINGHOUSE No. 8 TRANSFORMERS (ABOUT 2500 WaTTS CAPACITY). First specimen. Second specimen. B a a B 0.917 X 1074 | 23 1.25 0 10p- 0.681“ C O02) 0.683 0.73 0.734 0.77 0.819 0.85 0.903 0.97 0.994 1.07 1.090 1.18 1.180 1.29 1.270 1.41 1618 e 1.360 1.53 1692 1.540 YOUN EO YH mmo 7 * “ Phil. Mag.*’ 4th series, vol. xlv. p. 151- + Ibid. sth series, vol. xix. p. 73. + ‘* Magnetic Induction in lron and Other Metals.” § T. Gray, from special experiments. SMITHSONIAN TABLES. 274 TABLE 285. PERMEABILITY OF TRANSFORMER IRON. (b) WestinGHousE No. 6 TRANSFORMERS (ABOUT 1800 Watts Capacity). First specimen. Second specimen. 147X108 442 “ 697 862 949 IO1O 1060 1090 1120 1150 a 4-3 4-9 555 6.1 Ans = (c) WestTinGHousE No. 4 TRANSFORMER (aBouT 1200 Watts Capacity). ) B M B a Ma | pe beh | 1] 20 | 0.69 | 147X108 | 1470 ; 1560 | 2.86X10-4| 373 S160) |) 2.0mm 3780 | 40 | 1.38] 406 “ | 4066 | o. ; 4770 | 2.81 3790 5910 | 3.02 3520 60 | 2.07 | 573 5730 | I. : 6890 | 3.24 3280 A 7760 | 3. 3080 80 Ss 6590 | I. : gIoo | 3. 2710 10200 | 4. 2430 100 | 3-45 | 714 7140 5.04 | 4 11000 | 4. 2190 | 11690 | 5. 1990 120 | 4.14 | 748 7490 : 12270) ane 1820 2 12780 | 6. 1690 140 | 4.83 | 777 777 Ol) |els wf 13180 | 6. 1570 13470 | 7. 1460 TABLE 286. COMPOSITION AND MACNETIC This table and Table 289 below are taken from a paper by Dr. Hopkinson * on the magnetic properties of iron and steel. which is stated in the paper to have been 240. “ Coercive force”? is the magnetizing force required to reduce the magnetization to zero. by 47. The maximum magnetization is not tabulated; but as stated in the The “ demag- previous magnetization in the opposite direction to the “‘ maximum induction” stated in the table. The “energy which, however, was only found to agree roughly with the results of experiment. Description of specimen. Wrought iron . ° Malleable cast iron Gray cast iron . Bessemer steel . ‘ Whitworth mild steel “ “ “ “ “ “ “ “ Oo ON AnfW Dw Hadfield’s manganese steel Manganese steel “ “cc “ “ “ “ Silicon steel ac “cc “ “ Chrome steel “ “ “e “ “ “ Tungsten steel . “ “ “ (French) “ Gray cast iron Mottled cast iron Wikite? ccs as Spiegeleisen Temper. Annealed “ Annealed Oil-hard- } ened Annealed Oil-hard- ened As forged Annealed Oil-hard- } ened As forged Annealed Oil-hard- } ened As forged Annealed Oil-hard- } ened As forged Annealed § Oil-hard- ) ened As forged Annealed § Oil-hard- ) ened As forged Annealed Chemical analysis. Total Carbon. Phos- ‘| phorus. Other substances, Manga- nese Sulphur. | Silicon Hardened cian ) in co water Hardened in tepid water § Oil-hard- ) ened Very hard * Phil. Trans. Roy. Soc. vol. xxxv. SMITHSONIAN TABLES. + Graphitic carbon. 276 TABLE 286. PROPERTIES OF IRON AND STEEL. The numbers in the columns headed ‘‘ magnetic properties’? give the results for the highest magnetizing force used, paper, it may be obtained by subtracting the magnetizing force (240) from the maximum induction and then dividing netizing force ” is the magnetizing force which had to be applied in order to leave no residual magnetization after dissipated *? was calculated from the formula: — Energy dissipated = coercive force X maximum induction ~ 7 Magnetic properties. Specific dlectu-\= = le calresis-| Maxi- | Residual] Coer- |Demag- tance. {mum in-| induc- cive |netizive duction.| tion. force. | force. Energy dis- Description of sipated per y specimen. Temper. Wrought iron . : . | Annealed | .01378) 18251| 7248 | 2.30 13350 Malleable cast iron . : ss .03254| 12408] 7479] 8.80 34742 Gray cast iron . : : - 10560) 10783} 3928 : I 3037 Bessemer steel . : - 01050] 18196| 7860 . 17137 Whitwor th mild steel . | Annealed | .oroSo| 19840 7080 : 10259 : AGA .01446| 18736] 9840 ; 40120 See .01390| 18796 | 11040 65786 Annealed | .01559| 16120 : 42366 j Oil-hard- ) ened 01695) 16120 : 99401 Hadfield’ anganese tee eta: : in 106554} 310 = Manganese steel : . | As forged 05368 4623 : ‘ 34567 : : aes .03928| 10578 ! ; : 113963 } ened |-05556) 4769]. 2 29] 41941 As forged |.06993| 747 - Annealed | .06316| 1985 4. 7 15474 ee 07066} 733 - . . . | As forged | .06163) 15148 : Zs 45740 : E : pune .06185] 14701 8 ! 30485 ea .06195| 14696 2 : 59619 As forged | .o2016| 15775 ; 3.8 61439 Annealed .01942| 14548 7 ; 2.22 42425 } pe .02708] 13960 8.15] 48. 169455 As forged 01791 14680 é 22.03 85944 eee 01849] 13233 ; Fi 64842 il-hard- ened As forged | .02249| 15718 ; 2 78568 nea ed .02250| 16498 “3 .93| 80315 ardened in cold |.02274] —- water Oo AN ANLWN HS al ° .0303 5] 12868 ; a7 167050 ( Hardened in tepid | .02249| 15610 : 7 149500 / water § Oil hard- | (French) . ey .03604| 14480 : : 216864 : . Very hard | .04427| 12133 2 : 197660 Gray cast iron . ; : - -I1400] 9148 3: : 39789 Mottled castiron . : .06286| 10546 2.2 41072 | White ms. ge Vee os .05661| 9342 2.22 f 36383 Spiegeleisen . . : 10520] 385 | SMITHSONIAN TABLES. 277 TABLE 287. PERMEABILITY OF SOME OF THE SPECIMENS IN TABLE 286. This table gives the induction and the permeability for different values of the magnetizing force of some of the speci- mens in Table 286. ‘The specimen numbers refer to the same table. The numbers in this table have been taken from the curves given by Dr. Hopkinson, and may therefore be slightly in error; they are the mean values for rising and falling magnetizations. Specimen 8 Specimen 9g (same as Specimen 3 (annealed steel). 8 tempered). (cast iron). Magnetiz- Specimen 1 (iron). | ing force. B Ke Tables 288-292 give the results of some experiments by Du Bois,* on the magnetic properties of iron, nickel, and cobalt under strong magnetizing forces. ‘The experiments were made on ovoids of the metals 18 centimetres long and 0.6 centimetres diameter. The specimens were as follows: (1) Soft Swedish iron carefully annealed an having a density 7.82. (2) Hard English cast steel yellow tempered at 230° C.; density 7.78. (3) Hard drawn best nickel containing 99 % Ni with some SiO, and traces of Fe and Cu; density 8.82. (4) Cast cobalt giving the following composition on analysis: Co = 93.1, Ni=5.8, Fe=0.8, Cu=o.2, Si=o.1,andC=o0.3. The speci- men was very brittle and broke in the lathe, and hence contained a surfaced joint held together by clamps during the experiment. Referring to the columns, 4, 3, and have the same meaning as in the other tables, S is the magnetic moment per gramme, and / the magnetic moment per cubic centimetre. AY and S are taken from the curves published by Du Bois; the others have been calculated using the densities given. TABLE 288. MACNETIC PROPERTIES OF SOFT IRON AT O° AND 100° C. Soft iron at 0° C. Soft iron at 100° C. 17720 19190 20660 21590 22040 22300 me NOUWNO™ coon Ny OVN TABLES 289. MACNETIC PROPERTIES OF STEEL AT O° AND 100° C. Steel at 0° C. Steel at 100° C. | I 1283 1408 1500 1552 1553 1595 1650 * © Phil. Mag.’’ 5 series, vol. xxix. + The results in this and the other tables for forces above 1200 were not obtained from the ovoids above referred to, but from a small piece of the metal provided with a polished mirror surface and placed, with its polished face nor- mal to the lines of force, between the poles of a powerful electromagnet. The induction was then inferred from the rotation of the plane of a polarized ray of red light reflected normally from the surface. (See Kerr’s ‘‘Constants,”? p. 292.) 278 TaBLesS 290-296. MACNETIC PROPERTIES OF METALS. TABLE 290. — Cobalt at 100° C. TABLE 291. —Nickel at 100° 0. H 35.0 3980 300 ; 43.0 4906 500 ) 2 F 40.0 5399 700 3 f 50.0 6043 1000 : Gn 6409 wie 53-0 6875 2500 } 50.0 7707 4000 : 58.4 8973 6000 4 59.0 10540 gooo g ! 1192 ! 23980 ’ 59.2 12501 At o° C. this specimen gave the fol- 59-4 15585 : lowing results : 59-6 15606 vs 7900 | 154 | 1232 | 23380 | 3.0 At o®° C. this specimen gave the fol- lowing results : 12300 | 67.5 | 595 | 19782 | 1.6 TABLE 292. — Magnetite. The following results are given by Du Bois * for a specimen of magnetite. Professor Ewing has investigated the effects of very intense fields on the induction in iron and other metals.t The results show that the intensity of magnetization does not increase much in iron after the field has reached an in- tensity of 1000 c. g. s. units, the increase of induction above this being almost the same as if the iron were not there, that is to say, @B/ dH is practically unity. For hard steels, and particularly manganese steels, much higher forces are required to produce saturation. Hadfield’s manganese steel seems to have nearly constant susceptibility up toa magnetizing force of 10,000. The following tables, taken from Ewing’s papers, illustrate the effects of strong fields on iron and steel. The results for nickel and cobalt do not differ greatly from those given above. TABLE 293. —Lowmoor TABLE 294. — Vicker’s TABLE 295.— Hadfield’s Wrought Iron. Tool Steel. Manganese Steel. ff LT B “Me 25480 | 4.10 1930| 55] 2620] 1.36 29650 | 2.97 2380| 84] 3430] 1.44 31620 | 2.60 3350] 84] 4400] 1.31 34550 | 2.36 §920| 111] 7310] 1.24 35820 | 2.31 6620] 187| 8970] 1.35 7890 | 191 | 10290 | 1.30 8390 | 263 11690 | 1.39 9810 | 396| 14790 | 1.51 PHNe_QAY = = Nin OO CO W112 U1 00 0 Go 3essemer steel containing about 0.4 per cent carbon . Siemens-Marten steel] containing about 0.5 per cent carbon Crucible steel for making chisels, containing about 0.6 per | Celts CanDONR es ss) cn \liee ot Com eee anon «ee Finer quality of 3 containing about 0.8 per cent carbon . Crucible steel containing I per cent carbon Whitworth’s fluid-compressed steel . * “© Phil. Mag.” 5 series, vol. xxix. + “Phil. Trans. Roy. Soc.’ 1885 and 1889. 279 TABLE 297. MACNETIC PROPERTIES OF IRON IN VERY WEAK FIELDS. The effect of very small magnetizing forces has been studied by C. Baur* and by Lord Rayleigh.t The following short table is taken from Baur’s paper, and is taken by him to indicate that the susceptibility is finite for zero values of # and for a finite range increases in simple proportion to #7. He gives the formula &—15 + 100 H, or J— 15 +100 H%. The experiments were made on an annealed ring of round bar 1.013 cms. radius, the ring having a radius of 9.432 ems. Lord Rayleigh’s results for an iron wire not annealed give #=6.4-+5.1 H, orlJ=6.4 7 -++s.1 H%. The forces were reduced as low as 0.00004 ¢. g. S., the relation of & to H remaining constant. First experiment. Second experiment. TABLES 298, 299. DISSIPATION OF ENERGY IN CYCLIC MACNETIZATION OF MACNETIC SUBSTANCES. When a piece of iron or other magnetic metal is made to pass through a closed cycle of magnetization dissipation of energy results. Let us suppose the iron to pass from zero magneti- zation to strong magnetization in one direction and then gradually back through zero to strong magnetization in the other direction and thence back to zero, and this operation to be repeated several times. The iron will be found to assume the same magnetization when the same magne- tizing force is reached from the same direction of change, but not when it is reached from the other direction. This has been long known, and is particularly well illustrated in the permanency of hard steel magnets. That this fact involves a dissipation of energy which can be calculated from the open loop formed by the curves giving the relation of magnetization to magnetizing force was pointed out by Warburg ¢ in 1851, reference being made to experiments of Thomson, § where such curves are illustrated for magnetism, and to E. Cohn, || where similar curves are given for thermo- electricity. The results of a number of experiments and calculations of the energy dissipated are given by Warburg. The subject was investigated about the same time by Ewing, who pub- lished results somewhat later. ] Extensive investigations have since been made by a number of investigators. TABLE 298.— Soft Iron Wire. (From Ewing's 1885 paper.) Horse- | TABLE 299. — Cable Transformers. | Total Dissipation power | | induction | of energy | wasted per | This table gives the results obtained by Alexander Siemens with one of en Peres eeles ner Siemens’ cable transformers. The transformer core consisted of goo : sec. | soft iron wires 1 mm. diameter and 6 metres long.** The dissipation of energy in watts is for 100 complete cycles per second. 0.74 1.41 2.18 3.01 Total ob- served dis- | Calculated sipation of | eddy current energy in the | loss in watts core in watts] per 112 lbs. per 112 lbs. Hysteresis loss of energy in ergs per cu. cm. per cycle. Mean maxi- mum induc- tion density in core. Hysteresis loss of energy in watts per 112 lbs. 3:89 4.88 6.10 7-43 8.84 10.30 11.59 13-53 15.30 17.10 432 96.2 158.0 231.2 309-5 390.1 Noe eS Oo ON OW GNOESENT ORD. stn db ONN N > * “ Wied. Ann.” vol. xi. ¢ ‘Phil. Mag.” vol. xxiii. + ‘ Wied. Ann.” vol. xiii. p. 141. § “ Phil. Trans. Roy. Soc.” vol. 175. \| ‘* Wied. Ann.’ vol. 6. 7 “ Proc. Roy. Soc.’’ 1882, and ‘‘ Trans. Roy. Soc.” 1885. ** “ Proc. Inst. of Elect. Eng.’’ Lond., 1892. SMITHSONIAN TABLES. 280 TaBLe 300. DISSIPATION OF ENERCY IN THE CYCLIC MACNETIZATION OF VARIOUS SUBSTANCES. C. P. Steinmetz concludes from his experiments * that the dissipation of energy due to hysteresis in magnetic metals can be expressed by the formula eal, where ¢ is the energy dissipated and @ a constant. He also concludes that the dissipation is the same for the same range of induction, no matter what the absolute value of the terminal inductions may be. His experiments show this to be nearly true when the induction does not exceed -| 15000 c. g. s. units per sq. cm. It is possible that, if metallic induction only be taken, this may be true up to saturation ; but it is not likely to be found to hold for total inductions much above the satura- tion value of the metal. The law of variation of dissipation with induction range in the cycle, stated in the above formula, is also subject to verification.t+ Values of Constant a. The following table gives the values of the constant @ as found by Steinmetz for a number of different specimens. The data are taken from his second paper. Number of specimen. Kind of material. Description of specimen. Value of Iron . : Norway iron . . soe , Wrought bar Commercial ferrotype plate Annealed ES Thin tin plate Medium thickness tin plate Soft galvanized wire Annealed cast steel . Soft annealed cast steel Very soft annealed cast steel 2 Same as § tempered in cold water . ; Tool steel glass hard tempered in water «© tempered in oil : annealed . : ( ( Same as 13, 14, and 15, after havi ing ‘been subjected / : to an alternating m. m. f. of from 4000 to 6000 : \ / ampere turns for demagnetization j Cast iron . Gray cast iron . . : : : o oN - « “containing iy % aluminium “ “ 2 “cs “ “ + “ ( re square rod 6 sq. cms. section and 6.5 cms. ‘long, Magnetite . eon the Tilly Foster mines, Brewsters, Putnam S | OW ON QAnfW WN = _ “ “ County, New York, stated to be a very pure sur Soft wire . : Annealed wire, calculated by Steinmetz from Ewing’s experiments bs : Hardened, also from Ewing’s experiments Cobalt § Rod containing about 2 % of iron, also calculated * |) from Ewing’s experiments by Steinmetz Consisted of thin needle-like chips obtained by Tron filings | (3d Nickel “ milling grooves about 8 mm. wide across i. pile of thin sheets clamped together. About 30 % by vol- ume of the specimen was iron. Ist experiment, continuous cyclic variation of m. m. | f. 180 cycles per second oe experiment, 114 cycles per second 79-91 cycles per second . * “ Trans. Am. Inst. Elect. Eng.’? January and September, 1892. + See T. Gray, ** Proc. Roy. Soc.” vol. lvi. SMITHSONIAN TABLES. 281 Taste 301. DISSIPATION OF ENERCY IN THE CYCLIC MACNETIZATION OF TRANS- FORMER CORES.* This table gives, for the most part, results obtained for transformer cores. The electromagnet core formed a closed iron circuit of about 320 sq. cms. section and was made up of sheets of Bessemer steel about 1-20 inch thick. The No. 20 transformer had a core of soft steel sheets about 7-1000 inch thick insulated from each other by sheets of thin paper. The cores of the other transformers were formed of soft steel sheets 15-1000 inch thick insulated from each other by their oxidized surfaces only. The following are the particulars of the data given in the different columns : — Column 1. Description of specimen. “2. The total energy, in joules per cycle, required to produce the magnetic induction given in column B 3. The energy, in joules per cycle, returned to the circuit on reversal of the magnetizing force. “¢ 4. The energy dissipated, in joules per cycle, or the difference of columns 2 and 3. “5,6, and 7. The quantities in columns 2, 3, and 4 reduced to ergs per cubic centimetre of the core. «© B. The maximum induction in c. g. s. units per sq. cm. Electromagnet. Westinghouse No 20 transformer Westinghouse No. 8 transformer, specimen I Westinghouse No. 8 transformer, specimen 2 Westinghouse No. 6 transformer, specimen I Westinghouse No. 6 transformer, specimen 2 Westinghouse No. 4 transformer .. . Thomson-Houston 1500 watt transformer * T. Gray, from special experiments; see Table 285 for other properties. SMITHSONIAN TABLES. 282 TaBLe 302. DISSIPATION OF ENERCY DUE TO MACNETIC HYSTERESIS IN IRON.* The first column gives the maximum magnetic induction B per square centimetre in c. g, s. units. The other col- umns give the dissipation of energy in ergs per cycle per cubic centimetre for the iron specified in the foot-note, The iron for which data are given in columns 1 to 7 is described as follows : — 1. Very soft iron wire (taken from a former paper). 2a. Sheet iron 1.95 millimetres thick 2b, Thin sheet iron 0.367 millimetres thick . Iron wire 0.975 millimetres diameter. . Iron wire of hedgehog transformer 0.602 millimetres diameter. . Thin sheet iron 0.47 millimetres thick. . Fine iron wire 0.2475 millimetres diameter. . Fine iron wire 0.34 millimetres diameter. almost alike. * Ewing and Klassen, “ Phil. Trans. Roy. Soc.’’ vol. clxxxiv. A, p. rors. 283 TABLE 303. MACNETO-OPTIC ROTATION. Faraday discovered that, when a piece of heavy glass is placed in magnetic field and a beam of plane polarized light passed through it in a direction parallel to the lines of magnetic force, the plane of polarization of the beam is rotated. This was subsequently found to be the case with a large number of substances, but the amount of the rotation wes found to depend on the kind of matter and its physical condition, and on the strength of the magnetic field and the wave-length of the polarized light. Verdet’s experiments agree fairly well with the formula — dr\ r? od (r—aZ)S, where c is a constant depending on the substance used, / the length of the path through the substance, 7 the intensity of the component of the magnetic field in the direction of the path of the beam, x the index of refraction, and A the wave-length of the light in air. If / be dif- ferent, at different parts of the path, /# is to be taken as the integral of the variation of mag- netic potential between the two ends of the medium. Calling this difference of potential 7, we may write @= Av, where A is constant for the same substance, kept under the same physical conditions, when the one kind of light is used. ‘The constant 4 has been called “ Verdet’s con- stant,” * and a number of values of it are given in Tables 303-310. For variation with tempera- ture the following formula is given by Bichat : — R = Ry (1 — 0.00104 ¢ — 0.000014 2”), which has been used to reduce some of the results given in the table to the temperature corre- sponding to a given measured density. For change of wave-length the following approximate formula, given by Verdet and Becquerel, may be used : — 2. 2— 2 ive y see 6, Ba a 1)A? ’ where p is index of refraction and A wave-length of light. A large number of measurements of what has been called molecular rotation have been made, particularly for organic substances. These numbers are not given in the table, but numbers proportional to molecular rotation may be derived from Verdet’s constant by multiplying in the ratio of the molecular weight to the density. The densities and chemical formule are given in the table. In the case of solutions, it has been usual to assume that the total rotation is simply the algebraic sum of the rotations which would be given by the solvent and dissolved substance, or substances, separately; and hence that determinations of the rotary power of the solvent medium and of the solution enable the rotary power of the dissolved substance to be calculated. Experiments by Quincke and others do not support this view, as very different results are obtained from different degrees of saturation and from different solvent media. No results thus calculated have-been given in the table, but the qualitative result, as to the sign of the rotation produced by a salt, may be inferred from the table. For example, if a solution of a salt in water gives Verdet’s constant less than 0.0130 at 20° C., Verdet’s constant for the salt is negative. The table has been for the most part compiled from the experiments of Verdet,t H. Becque- rel,t Quincke, § Koepsel,|| Arons,— Kundt,** Jahn,ft Schonrock,tt Gordon, §§ Rayleigh and Sidgewick,|||| Perkin, {‘] Bichat.*** As a basis for calculation, Verdet’s constant for carbon disulphide and the sodium line D has been taken as 0.0420 and for water as 0.0130 at 20° C. * The constancy of this quantity has been verified through a wide range of variation of magnetic field by H. E. J. G. Du Bois (Wied. Ann. vol. 35). + ‘Ann. de Chim. et de Phys.” fs] vol. 52. + “Ann, de Chim. et de Phys.” [5] vol. 12; **C. R.” vols. go and 100, § “ Wied. Ann.” vol. 24. ' || ‘‘ Wied. Ann.” vol. 26. 7 ‘* Wied. Ann.”’ vol. 24. ** “Wied. Ann.” vols. 23 and 27. tt ‘* Wied. Ann.” vol. 43. tt “ Zeits. fiir Phys. Chem.” vol. rz. §§ ‘Proc. Roy. Soc.” 1883. Ii] ‘* Phil. Trans, R. S.” 1885. 1 “ Jour. Chem. Soc.’ vols. 8 and r2. *=* © Tour. de Phys.” vols. 8 and 9. SMITHSONIAN TABLES. 284 MACNETO-OPTIC ROTATION. Substance. oe Amber. ; 2 : : ~ Blende . : ; : : ZnS Diamond . ; : : : Cc Fluor spar : : 5 -| CaFlg Glass : Crown . 3 ; : : - Faraday A . : ; : = sé Bie : : ‘ - Flint - ‘ z: “« as “dense _ “ “ é = Plate . ; : : 7 - Lead borate . : : . | PbB2O4 Quartz (perpendicular to axis) - Rock salt 4 : . : NaCl Selenium . 5 k nV a Se Sodium borate : : . | NagB4O7 Spinel (colored by chrome) . - Sylvine . : : : : KCl Ziqueline (suboxide of copper) Cu,0 SMITHSONIAN TABLES. Solids. Density rs Verdet’s or paid constant grammes | }; ont in per c. c. Bat. | minutes. = D 0.0095 = ‘ 0.2234 = “ 0.0127 = . 0.0087 = S 0.0203 5-458 f 0.0782 4.284 ce 0.0649 = o 0.0420 = ze 0.0325 - ¢ 0.0416 = ss 0.0576 - ss 0.0647 - ss 0.0406 = s 0.0600 = ie 0.0172 = 3 0.0355 = B 0.4625 - D 0.0170 = a 0.0209 = e 0.0283 - B 0.5908 285 TABLE 303. Authority. Quincke. Becquerel. Quincke. Becquerel. Quincke. Becquerel. TABLE 304. MACGNETO-OPTIC ROTATION. Substance. Acetone “ “ Acids: (see also solutions in water) Acetic . Butyric . Formic . ~ Hydrochloric “ Hydrobromic Hydroiodic . Nitric : “ (fuming) Propionic Sulphuric Sulphurous . Valeric . Alcohols: Amyl Butyl Ethyl Octyl Propyl . 3enzene . oe Bromides: Bromoform . Ethyl Ethylene Methyl . Methylene Octyl Propyl . ; : Carbon disulphide . SMITHSONIAN TABLES. Liquids. Verdet’s constant in minutes. Density : Chemical in Pong formula. grammes | jicht. C3H¢O “ CyoH4O2 C4HgO2 CH202 HCl HBr HI HNOgs CsH6O02 H2SO4 H2SOz3 C5Hy002 C5H1,0H C,H )OH C.H;0H “ “ CH3;0H CsH1;,0H CsH;,OH “ “ CoHe “ee “ CHBrg Col {;Br Cok 14 Bre CHsBr CHoBre CgHy7Br Cs3H7br CSe 286 Authority. Jahn. Perkin. Schonrock. Perkin. Becquerel. Perkin. “ “ Becquerel. Perkin. Becquerel. “ee Perkin. Becquerel. Jahn. | “ Becquerel. Quincke. Jahn. Perkin. Schonrock. Quincke. Jahn. Becquerel. Perkin. Schonrock. Perkin. Schénrock. Perkin. Becquerel. Jahn. Jahn. Becquerel. Schonrock. Perkin. “ “ Jahn. Perkin. “ce Quincke. 5 Becquerel, lL 1885. Gordon. Rayleigh. Koepsel. Arons. MACNETO-OPTIC ROTATION Liquids. Densit rs Verdei’s Chemical in ee constant Substance. formula. grammes lich in perc. c. ight. | minutes. Chlorides : Amyl . CHCl 0.8740 | D 0.0140 Arsenic : ; As - if 0.0422 Carbon : ; S - 0.0170 “ bichloride CCl, - i 0.0321 Chloroform CHCls 1.4823 c 0.0164 a . : ; s 1.4990 se 0.0166 Ethyl . . : : CeH;5Cl 0.9169 be 0.0138 Ethylene ‘ CoH4Clo 1.2589 s 0.01606 a - s 1.2561 a 0.0164 Methyl 7 ‘ CH3;Cl - us 0.0170 Methylene . CHeCle 1.3361 s 0.0162 Octyl . . | CgHy7Cl 0.8778 is 0.0141 Phosphorus protochloride pels - se 0.0275 Propyl . | CsH;Cl 0.8922 - 0.0135 Silicon : : SiCl]4 - ‘s 0.0275 Sulphur bichloride S2Cle - ss 0.0393 Tin bichloride : SnCly - & 0.0151 Zinc bichloride ZnCle ~ cs 0.0437 Todides: Ethyl . CoHsI 1.9417 ws 0.0296 Methyl CHsl 2.2832 0.0336 Octyl . CsHy71 1.3395 ce 0.0213 Propy]. CsH71 1.7053 ‘ 0.0271 Nitrates : Ethyl . . | CoHs0.NOe | 1.1149 us 0.0091 Ethylene (nitrogly col) . | CoHg(NOs)e | 1.4948 sé 0.0088 Methyl . . | CHs0.NO9 Te 2S 7 < 0.0078 Propyl . | CsH7;O.NO2 1.0622 < 0.0100 Trinitrin (nitroglycerine) . | CsHs5(NOs)3 | 1.5996 sf 0.0090 Nitro ethane . | CoHsNOg ote ee 0.009 5 Nitro methane . | CHsNOze 1.1432 Uo 0.0084 Nitro propane . | CsHgNOe 1.0100 se 0.0102 Paraffins : Decane - | CyoHee 0.7218 6 0.0128 Heptane . | CrAis 0.6880 se 0.0125 Hexane on le Gein 0.6580 . 0.0122 SS ; nf 0.6743 fe 0.0125 Octane - | CgHis O.701I &§ 0.0128 Pentane - | CsHy2 oO. eee f 0.01 19 Be , : ; : 332 : 0.0118 Phosphorus (melted) pala - ss 0.1316 Sulphur (melted) eS - 5 0.0803 Toluene z . | C;Hg 0.8581 , 0.0269 “ , “ = ‘ 0.0243 | Water . | H2,O 0.9992 X 0.0130 : os 0.995 ‘ 0.0131 se . : = aaeee ‘f 0.01 2 Xylene . - | CgHio = ce 0.0221 sig ke : < 0.8746 e 0.0263 SMITHSONIAN TABLES. 287 Temp. Cc. TABLE 304. Authority. Jahn. Becquerel. “ce Jahn. Perkin. “ce Jahn. Becquerel. Perkin. Becquerel. Perkin. Becquerel. Schoénrock. Perkin. Schonrock. Perkin. Schonrock. “e Perkin. Becquerel. “ Sch6nrock. Becquerel. “ Quincke. Jahn. Becquerel. Schonrock. TaB_Le 305. MACNETO-OPTIC ROTATION. Solutions of Acids and Salts in Water. Density, i Verdet’s grammes ] _ constant perc. c. light. | in minutes. Chemical Substance. raeennine | Acetone . ; : . . | CsHgO 0.9715 0.0129 Acids : Hydrobromic . : , 1.7859 0.0343 a 5 - : 1.6104 0.0304 4 : : 1.3775 0.0244 i. ; : 1.2039 0.0194 Sf : , : 1163 0.0168 Ti: 1.2072 0.022 1.1856 0.0219 1.1573 0.0204 1.1279 0.0193 1.0762 0.0168 1.0323 0.0150 1.0158 0.0140 1.9473 0515 1.9057 0.0499 1.822 0.0468 1.7007 0.0421 1.4495 0.0323 1.2966 0.0255 ; ; : : 1.07 0.0205 Nitric . : ; E on ees 1.5190 0.0010 f 1.3560 0.0105 - 0.0121 0.8918 0.0153 Hydrochloric Sulphuric + 3H2O | Ammonia ; Bromides: Ammonium . - : : 1.2805 0.0226 ss : . : , 1.1576 0.0186 Barium . : : ; abrg 1.5399 0.0215 oe. : : ° : 1.2855 0.0176 Cadmium . - < Sd Brg 1.3291 0.0192 £ ; : - : 1.1608 0.0162 Calcium 2491 0.0189 és -1337 0.0164 -1424 0.0163 0876 O.OISI 1351 0.0165 .0824 0.0152 2901 0.0186 -1416 0.0159 I I Potassium I “ I Sodium : : x : I “ ; : : : I Strontium I “ I 1.1906 0.0140 1.1006 0.0140 1.0564 0.0137 Carbonate of potassium . ae sodium ; . | NagCOg “ “ “ “ Chlorides: Ammonium (sal ammoniac) | NH,Cl Barium ; ; : . | BaClg “ .0718 0.0178 .2897 0.0168 -1338 0.0149 3179 0.0185 2755 0.0179 51782 0.0160 -1531 0.0157 1504 0.0165 “ Cadmium : CdCle CaClg = 0332 0.0152 1049 0.0157 5158 0.0221 2759 0.0186 1330 0.0156 CuCl, I I I I I I I I I I I I I “ SMITHSONIAN TABLES. 288 Temp. Authority. Jahn. Becquerel. Perkin. Sch6nrock. Becquerel. MACNETO-OPTIC ROTATION. Solutions of Acids and Salts in Water. Substance. Chlorides: Iron “ (ferric) Lithium Manganese Mercury Nickel . Potassium “ “ Sodium “c Strontium , “ Pinner “ . “ - Znch “c Chromate of potassium . Bichromate of ‘“ : Cyanide of mercury “ce “ “ “ “ “ Todides: Ammonium. “ Cadmium “ “cs Potassium “ SMITHSONIAN TABLES. Density, Kind Verdet’s Chemical grammes of constant formula. FeCle “ “ FeCle per c. ¢c; light. | in minutes. TaBLe 305. Authority. Becquerel. ‘ Jahn. Becquerel. Schonrock. Becquerel. Jahn. Becquerel. “ Jahn. Jahn. Becquerel. os TABLES 305-307. Substance. Nitrates: Ammonium Potassium Sodium Uranium ae “ “ee Sulphates : Ammonium 4 oe (acid) Barium : “ce Cadmium “ Lithium “ce Manganese . “ Potassium Sodium Substance. Cadmium bromide . o “e | Calcium se i “c Strontium | “ “ Cadmium chloride Strontium ‘“ “e “ce Cadmium iodide “ cas MACNETO-OPTIC ROTATION. TABLE 305.— Solutions of Acids and Salts in Water. Density, grammes perc. c. Chemical formula. NH4NOz KNOg NaNOgs U203.N205 1.2803 1.0634 Tene 2.0267 1.7640 « 1.3865 se 1.1963 1.2286 1.4417 1.1788 1.0938 1.1762 1.0890 1.1762 1.0942 1.2441 1.1416 1.0475 1.0061 (NH 4)2SO4 NH4.HSO, BaSQO, CdSO, LigSO4 MnSO,4 KeSO4 NaSO4 3 Verdet’s Kind | constant . in light. minutes. Density, grammes per c. c. Chemical formula. CdBre “ CaBre “ SrBre “ CdClz SrCle “ Cdle 1.0988 i 0.9484 Verdet’s constant in minutes. TABLE Substance. Antimony trichloride “ “cc Bismuth “ “ SMITHSONIAN TABLES. | Density, grammes per c. c. Chemical formula. 2.4755 1.8573 a 1.5195 sf 1.3420 BiCls 2.0822 s 1.6550 he 1.4156 SbClz 290 Authority. Perkin. Jahn. Becquerel. “ “ Perkin. “ Jahn. “ “ “ “ “ “ “ “ “ Verdet’s constant in minutes. 0.0603 0.0449 0.0347 0.0277 0.0396 0.0359 0.0350 Authority. Becquerel. “ “ Substance. Atmospheric air Carbon dioxide Carbon disulphide . Ethylene - . Nitrogen Nitrous oxide . Oxygen . MACNETO-OPTIC ROTATION. Gases. Pressure. Atmospheric * 74 cms. Atmospheric “ “ “ ‘Temp. Ordinary “ 700. Ordinary “ TABLE 308. Verdet’s constant in minutes. Authority. 6.83 X 10-5 | Becquerel. ii Hore) s Bichat. Becquerel. “ “ “ “cc Sulphur dioxide - i Bichat. 246 cms. Du Bois discusses Kundt’s results and gives additional experiments on nickel and cobalt. He shows that in the case of substances like iron, nickel, and cobalt which have a variable mag- netic susceptibility the expression in Verdet’s equation, which is constant for substances of con- stant susceptibility, requires to be divided by the susceptibility to obtain a constant. For this expression he proposes the name “ Kundt’s constant.” These experiments of Kundt and Du Bois show that it is not the difference of magnetic potential between the two ends of the medium, but the product of the length of the medium and the induction per unit area, which controls the amount of rotation of the beam. TABLE 309. VERDET’S AND KUNDT’S CONSTANTS. The following short table is quoted from Du Bois’ paper. The quantities are stated inc. g. s. measure, circular measure (radians) being used in the expression of “‘ Verdet’s constant ”’? and ‘*‘ Kundt’s constant.” Verdet’s constant. Wave-length of light in cms. Kundt’s constant. Magnetic Name of substance. Sarees inliey. Number. Authority. Cobalt Nickel Iron - Oxygen: I atmo. Sulphur dioxide Water . Nitric acid Alcohol . : Ether . : Arsenic chloride Carbon disulphide . Faraday’s glass Arons Becquerel. De la Rive. — 0.0694 — 0.0633 — 0.0566 — 0.0541 — 0.0876 — 0.0716 — 0.0982 Becquerel. Rayleigh. Becquerel. SMITHSONIAN TABLES. TABLE 310. MAGNETIC SUSCEPTIBILITY OF LIQUIDS AND CASES. The following table gives a comparison by Du Bois* of his own and some other determinations of the magnetic sus- ceptibility of a few standard substances. Verdet’s and Kundt’s constants are in radians for the sodium line D. Werdetie Becquerel’s Wiahner’s value value Substance. constant. EX 108 EX 108 Water . : . S77 One ; —0o.63 —0.536 Alcohol, C2H,O . , : 2:30 —0.49 —o.388 3.1 Ether, CgHypO .. - —o.360 Carbon disulphide : : ’ —o.84 —0.465 Oxygen at I atmosphere. 0.00179 “ ; 0.12 - Air ati1atmosphere . ; 0.00194 “ ! 0.025 Quincke at 20° C. Du Bois at 15° C. Substance. Kundt’s ° r, 6 7 6 Density. k X 10! Density. k X10! ponent Water . . - ; 0.9983 —o.815 0.9992 —0.837 —4.50 Alcohol, C2H.O . . : 0.7929 —o.660 0.7963 —0.694 —4.75 Ether, CBE GO : 0.7152 —0o.607 0.7250 —0.642 —4.91 Carbon disulphide ; 1.2644 —0.724 7 —o.816 | —14.97 Oxygen at 1 atmosphere . - - 0.00135 0.117 0.016 Air at 1 atmosphere . : 0.00123 0.024 0.081 TABLE 311. VALUES OF KERR’S CONSTANT.t Du Bois has-shown that the rotation of the major axis of vibration of radiations normally reflected from a magnet is algebraically equal to the normal component of magnetization multiplied into a constant A. He calls this con- stant, A, Kerr’s constant for the magnetized substance forming the magnet. , Wave- | Kerr’s constant in minutes per c. g. s. unit of magnetization. Spectrum| length ee a line. in cms. X 10% Nickel. Magnetite. Color of light. Red. ; 67.7 —0.0173 +0.0096 Red , ; 62.0 —0.0160 0.0120 Yellow. . 58.9 —0.01 54 +0.0133 Green . s ; 51.7 —0.0159 0.0072 Blue °.5 5 48.6 —0.0163 +0.0026 Violet . : : 43-1 —0.0175 = * “ Wied. Ann.” vol. 35, p. 163. + H. E. J. G. Du Bois, ‘‘ Phil. Mag.” vol. 29. SMITHSONIAN TABLES. 292 TABLES 312, 313. EFFECT OF MACNETIC FIELD ON THE ELECTRIC RE- SISTANCE OF BISMUTH." TABLE 312. —Resistance One Ohm for Zero Field and Various Temperatures, This table gives the resistance to the flow of a steady electric current when conveyed across a magnetic field of the strength in c. g. s. units given in the first column if the wire has a resistance of one ohm at the temperature given at the top of the col- umn when the field is of zero strength. Resistance. TABLE 313. — Resistance One Ohm fee ao Field and Temperature Zero Cen- grade. This table gives the resistance in different magnetic fields and at different temperatures of a wire, the resistance of which is one ohm at 0° C., when the magnetic field is zero. The current is supposed to be steady and to flow across the field. Resistance. 1.072 1.091 1.118 1.162 1.210 1.265 1.327 1.385 1.453 1.515 1.583 1.907 2.243 2.560 ion | * Calculated from the results of J. B. Henderson’s experiments, ‘‘ Phil. Mag.’ vol. 38, p. 488. SMITHSONIAN TABLES. 293 TABLE 314. SPECIFIC HEATS OF VARIOUS SOLIDS AND LIQUIDS.* | SOLIDs. Temperature Substance. in degrees C, Specific heat. Authority. Alloys: Bell metal. : : ; : : ; ; 15-98 0.0858 R Brass, red. : . . : ; : : O 08991 L «yellow . : ; ; : : 2 : oO 08831 ue 80Cu+20Sn . > : : : : : 14-98 0862 R 88.7 Cu + 11.3 Al : ; : , : ; 20-100 -10432 Ln German silver . ; ; ; : : : 0-100 09464 alt Lipowitz alloy: 24.97 Pb + 10.13 Cd + 50.66 Bi | + 14.24 Sn ; ‘ : ; ; 2 ; 5-50 0345 M ditto ; : , ; : 2 . : 100-1 50 .0426 g Rose’s alloy : 275 Pb + 48.9 Bi + 23.6Sn . ; —77-20 0356 ditto z : : z . ; : . 20-89 0552 < W oo0d’s alloy : 25-85 Pb + 6.99 Cd + 52.43 Bi + 14.73Sn_. . : . . ° : : 5-50 0352 ditto (fluid) . ; , : 2 ; : : 100-150 .0426 Miscellaneous alloys : 17-5 Sb + een Pee TOs oan ; ‘ 20-99 05657 R 37-1 Sb + 62.9 Pb : : 10-98 03880 ss | 39.9 Pb + 60.1 Bi . ; : . , : . 16-99 03165 iB ditto (fluid) . 2 : ; : . : : 144-358 -03500 is 63.7 Pb + 36.3Sn. 7 ; : ; : : 12-99 04073 46.7 Pb + 53.3Sn. ; : ; , ° : 10-99 04507 Hy 63.8 Bi + 36.2Sn . ; : 7 : : . 20-99 04001 & 46.9 Bi + 53 ISn. , ; ; : : . 20-99 -04504 : CdSnz . ; : - : . . - | —77-20 -05537 as Basalt 5 : ; , : ; : ; 20-100 -20-.24 - | Calcspar . - ; = ‘ ‘ A : ‘ 16-48 .206 K | Diamond . : ; : , - . ; ; —50.5 .0635 H W ; ; A ; 4 606.7 .4408 % we : = : ; : ; : ; : 985 -4589 a | Gascoal . : : : s 5 ; : . 20-1040 -3145 - Glass, crown. : : : ; : : : 10-50 -161 HM eeu : : . . , : : : 10-50 “L7 . “mirror. : : : : , ; : 10-50 186 ss Gneiss : : ; : : ; ; : : —19-20 .1726 RNY, ‘ ° . : : : . . : : 17-213 +2143 o Granite. : ; . : ; : ; : 0-100 -I19-.20 J&B Graphite . ; : : ; ; . . : —50.3 1138 H W ss : ; ; ; : ; ; ; : 10.8 1604 g ‘ : ° : , : : : : : 138.5 +2542 “ “ : : ; ; : . : . ; 201.6 2906 S “ ; : : ; : : : : : 641.9 4450 s aS : ; : : , , : : , 977.0 .4670 = a : : : Z ; ; : ; 16-1040 310 D REFERENCES. A M =A. M. Mayer. B = Batelli. D = Dewar. E = Emo. G & T=Gee & Terry. H & D= De Heen & Deruyts. H M= H. Meyer. H W =H. F. Weber. J & B= Joly & Bartoli. K = Kopp. L. = Lorenz. Ln = Luginin. M = Mazotto. Ma = Marignac. P= Person, Pa = Pagliani. Pn = Pionchon. R = Regnault. R W=R. Weber. T =H. Tomlinson. Th = Thomsen. W = Wachsmuth. * Condensed from more extensive tables given in Landolt and Boérnstein’s ‘‘ Phys. Chem. Tab.”’ SMITHSONIAN TABLES. 204 TABLE 314, SPECIFIC HEATS OF VARIOUS SOLIDS AND LIQUIDS. Gypsum Jeemars “ Substance. India rubber (Para) . Marble, white “ gray Paraffin . fluid Quartz ac o Sulphur, cryst. : Vulcanite . ; Alcohol, ethyl “ methyl Benzene “ Ethyl ether Glycerine . | Oils, castor “citron “ olive . «sesame “turpentine Petroleum CuSOg + 50 He 0 + 200 H.O NaOH + 50 He 20 = 100 HO a. 10 H.O + 200 H2O Sea water: density “ce “cs vie Einav — te Orenz. P = Person. RW=R. Weber. SMITHSONIAN TABLES. A. M. Mayer. G & T=Gee & Terry. EB Weber: LIQUIDs. I (0043 1.0235 (about normal) 1.0463 : : REFERENCES. D = Dewar. H & D=De Heen & Deruyts. J & B= Joly & Bartoli. M = Mazotto. Pn = Pionchon. Th= Thomsen. B = Batelli. Ln = Luginin. Pa = Pagliani. T =H. Tomlinson. 295 Temperature in Specific degrees C. heat. Authority. 16-46 —78-0 —2I-I ?-100 16-98 23-98 —20-3 —19-20 0-20 35-40 60-63 ° 350 400-1200 17-45 20-100 E = Emo. H M = H. Meyer. K = Kopp. Ma = Marignac. R = Regnault. W = Wachsmuth. TABLE 315. SPECIFIC HEAT OF METALS.* 2 5 Temperature Specific — Temperature Specifi = ; in Metal. in peas 2 pe degrees C. heat. = degrees C. heat. = < < Aluminium . . 20 0.2135 Manganese . . 14-97 0.1217 R kc Ho 100 2211 Mercury: solid .|—78 to—4o0] .03192 | “ s oie 200 .2306 " uae 20-50 .03312 | W cs ae 300 -2401 ss 54 e Oo 03337 | N Antimony. . . 15 .04890 g ae 100 .03284 | “ a pees 100 05031 fs eaters 200 03235 | “ as Aer coe 200 05198 as SFr 250 03212 || “ “ + OF 300 05306 Nickel one 14-97 -Iog16 | R Bismuth . . . ° 03013 Spe: ene 100 11283 | Pn se ene 20-84 .0305 Soebe: ets 300 14029 | “ “« fluid. .| 280-380 .0363 See ake 500 12988 | “ | Cadmium. . . 2ni 0551 s Seeman 800 1484 | “ « woe & 100 0570 § & OD .OeaC 1000 -16075 | “ cs pac 200 +0594 Palladium. . . 0-100 S050 25a av ac eee 300 0617 ut Pd 0-1265 0714 s Caleiumiae- a.) a: 0-100 1804 Platinum . . .| —78-20 .03037 | S Chromium (?) . 22-51 0997 5 S ao O-I00 0323 Cobaltv.m-meme 9-97 10674 i coe 0-784 eRe. || & s eee 500 14516 i . eee ttreeeeeeesssses++207 | Formule, dimension (see also Units) . .Xvii-xxix SOlAST ees eee ACs edocs 216 | Force, conversion FACEONS POP arc inc ois\0 i SE Cyclic magnetization, dissipation of energy Force de cheval, definition of............... 19 LIL «sie aranw vatente bmi ated eet +++++..--280-283 | Fraunhofer lines, wave-lengths of..........175 Freezing mixtures 01 + sists siete Feieie ue'sieisinie~ TOO Freezing-point, lowering of, by salts ..... ..192 Friction, coefficients OL ais + 2:4 veel ninice tale LSS Functions, hyperbolic tee e tees eee ee 28-35 GAMMA... see eee e cere nnsesscceeeee ZO Fundamental anitsst.ecr: a: 1.0 eee eee eee Fusion, Jatent heat/ofsrs:.s.. Juses senor Declination, magnetic..........2.+2+.IL3-118 Densities, of air, values of 2/760...... mee eo? alcoholenavce aiekelareloe eee ees seeee+ 90-98 alloys and other solids./5..S-cs< =.= 285 aqueous SOLWHONS =). s)si-' (o's sb ee ='vie wale OO BASES ss oo cs ae dee n'e sine selsisiale visits « se ee OQ iqadsyn 5 sanclice ea cee ee eee MA CL CUNY Hai eisiciotal oYetoleistateite jetta bie eee 95 Gamma FUNCHONS»\... wi sss nciccisesle eames eas mctalseere cee eee vis ssleteene Gases, absorption by liquids ..............125 organic compounds ..................212 colhpressibility of s2e.c0 eae -79-81 WALT osc oie Sivininin sla'eioicinivaisie'e bieia/o's « e O2=OU. critical temperatures of...............200 WOOUS? aint ce tas tenes slalatotetetoleob een 7 density and specific gravity Of; s. tae BO Density, conversion factors for............ “23 expansion Of «os 0. lers's ue eee ee Dew-points, table for calculating: jnader 158 magnetic susceptibility of............ -292 Diamonds, unit of weight for .......... poeais magneto-optic rotation in.............201 Dielectric strength...... hope itches oo 0-244, 245 refractive “indices of. .2 60.1 ee eee 190 Diffusion of gases and vapors............. 149 Specific heat of J<.m.0 essen eee -224 liquids and solutions ............. Bais ALA, thermal conductivity of............... 198 Dilution of solution, contraction due to .... 34 VISCOSILY/ Of sn). ace tee oe eee 145, 146 Dimension formule (see also Onits).......XVii volume of perfect (values of r++ 00367 #) Daip,macneticny..) oe. Bicester pepe ec 164-168 Dynamic units, dimension formulz of......xvii Galuges; Wire i.iac.cch pee eo ee . 58-68 formulz for conversion of ...... +++++-2 | Geometric units, conversion formulz for .... a2 Dynamical equivalent of thermal unit ..... -219 | Glass, electric resistance Of .............. -270 indices of refraction for ........¢. 178, 179 Gravity, force Obra jen leo werloe eee melOe toe Earth, miscellaneous data concerning ......106 Hlashieity, moduli of. ce pe ae -74-78 Electric conductivity of alloys......... 251, 252 otumetals eee sie el eloicielstereje ere 25S relation toithermals4,... 68 soe 271 constants of wires..............58-68, 254 displacement ....0. 2.20... ...00ce0 000.25 potential, conversion factors for....... S27 resistance, conversion factors for .......2 resistance, effect of elongation on..... -258 units, conversion factors for............ 3 Harmonics, ZONAL ..:s:s/s neice a slelee See EAS Heat, conversion factors for quantities of... 24 Jatent heat offusion.. o< 9.2) aeeeae as latent heat of vaporization........... +204 mechanical equivalent of..............220 units, conversion factors for........... .24 dimension formule for ..........xxiii formulz for conversion factors of... 33 Heats of combustion and combination... 201, 202 units, dimension formulz........... --xxv | Heights, determination by barometer....... 169 Electrochemical equivalents and atomic Humidity, rélativeldos.. spc. ene een oe WEISS ens eer steerer eeeeeeeeeee+-272 | Hydrogen thermometer stein eleietaldlsfosteysielsielte 38 of solutions ....... fetes eeee cee e eee 259 | Hyperbolic cosines settee eect e cree ee ee 2Q-3I Electrolytes, conductivities of ............ - 269, | ELyperbolic functionssa..msse eee ee ee - 28-35 Electrolytic deposition, conversion factors for. 24 | Hyperbolic sines ........... eee «+ .28-30 Electromagnetic system of units.......... xxix | Hysteresis, magnetic ...........+.++.+.280-2 3 Electromotive force of battery cells....246, 247 Electrostatic system of units .............XXVi Electrostatic unit of electricity, ratio of, to Iceland spar, refractive index of.......... 185 electromagnetics. sense cesta eee -243 | Indices of refraction for alums............2180 Plliptic integrals. ..)¥ essen ee aleielelesieie setoAS CLYStalS'o.5 vioidinia's cop ora mint g Shae enero aE Oe Elongation, effect on resistance of wires.... 258 Huor spar’... scmeinoss nee ener Emissivity .......... aie jesehokelnioret state +++ +234, 235 gases and vapors mc). ep sk pasiees ons LEGO Energy, conversion factors for........ see ZOnol G1aS8 sais haere eee - .178, 179 Equivalent, electrochemical............... 22 Iceland SPA. eeeeeeecsecceeeeeceeees IOS electrochemical of solutions.......... +259 liquids; various a7 sae pee sine ansite 189 mechanical, of heat ..................220 metals and metallic oxides ............181 Expansion, ‘thermal’. .\j., ge. eae -214, 218 monorefringent solids... cc)iccoscuce .184 INDEX. 299 Indices of refraction for alums (covtinued). Melting-points (continued). Quartz ..eeceseeeeeec ees ee sense eens 0186 of mixtures and alloyS...++eeereeeeeee 211 FOCK Salt...ceeeeccersececesees Siivcee aloe of organic compounds.....-.++-+ at pious @ke solutions of salts........+sseeeeee+e+ +188 | Mercury, density of PA eins colitis ctaign ee SylVine....-seveeeseeceeeeneeesecees 182 electric resistance of ....--+-- 2060255, 250 Inductance, mutual ......ee eee ee eee eee ee G2 index of refraction.......++-- eigtaiweie ais 181 Integrals, elliptic .......- Rae doeminaiices as 5 specific heat Of ....+e+eeeeererees ace Intensity, horizontal, of earth’s magnetic field strength of...... atetatetnlatvints araiclaneis Peo O 112 | Metals, density of.....---- eielctois stelereisiatne’ exe « 86 total, of earth’s magnetic field.......+-110 electric resistance of....-- sone cs en 254—250 Iron, elasticity and strength of .....++++++++72 specific heat of ....- iulg late en ctvisees alain ZOO hysteresis in...-.+.+-- eieie ate .- «280-283 thermal conductivity Of......+++++2++> 197 magnetic properties OE sepsieieiele 274-283, 292 | Metals and metallic oxides, indices of refrac- Tsotonic coefficients ......eeeeeereeeee res 0150 CLOQULOM a eines ara erete olee St ahascoelaieraviersisiais,ate 181 Metre, definition of.......--++--++ Shee otat ones xvi Metric weights and measures — Jewels, unit of weight for..... peehcetersfeleccieyal > 13 equivalents in British ....++++++++e+0r+ 5 Joule’s equivalent......+++sseeeeeeerereee 220 equivalents in United States ....--.-+++ 10 Mixtures, freezing.....-.-- iereiskoreeste eis Heonae 199 Moduli of elasticity ......-++--+ atareeeiee 74-78 Kerr’s constant, definition and table of..... 292 | Molecular conductivities......++++++- .261, 262 Kilogramme, definition of.....-+++++ _.....Xvi | Moments of inertia, conversion factors for. ..13 Kundt’s constants .....-- Meee etclepeleretetsies A: 291 | Moment of momentum, conversion factor definition Of. .....-++-+++++e- sooncansey FOP re ise aintey Seton ais eiclat rials Soe Momentum, conversion factors for....- AS Mutual inductance, table for calculating.....42 Matent heat.......>+<« Eratehets tie keto reknere 204, 206 Least squares, various tables for ....---- 35, 37 Legalization of practical electric units... .XXXIV Length, conversion factors LOTS cfeievaters 150 density of ....--+++++++5 Ressieletertacl- soo magneto-optic rotation in.....---- 286, 287 magnetic susceptibility ...-.-++++++++- 292 | Pearls, unit of weight fONie ce slevereteiel-l= Braise hist refractive indices Of.......-- eet TSO} Peltier effect... . 274-280 thermal expansion of.......--- .ee-e-217 | Photometric standards .......+-------ee=> 176 Lowering of freezing-point by salts ...---+-192 Planets, miscellaneous data concerning. ...- 106 Poisson’s ratio ....--sccce creer eserrsseces 76 Polarized light, rotation of the plane Obs sLOL Magnetic field, effect of, in resistance of bis- Potential, contact difference of ....-.------ 268 AULT eee es seiets ote. im ctsievo le sieelstarerares= 293 difference of, between metals in solu- moment, conversion factors for......--+- 27 TOTS i slakoe oie Seinielsloreteie letter olan 269 permeability ......-++s+eeeeeees . 274-280 electric, conversion factors for..-..-.-+- 27 properties of cobalt, manganese steel, Pound, definition Of ......+-+eeeeeeeeeeees xvi magnetite and nickel...-.----+++-+-- 279 | Power, conversion factors LOL elas sores J. LO; 120 properties of iron and Steeler itecte shletat: 276 | Practical electrical LUTE Pfc chelstcer veneers: Xxxiii saturation values for steel.....---+-++-- 279 | Pressure, barometric, for different boiling- susceptibility of liquids and gases ..... 292 points of water .....-- Srarestes store seal Osu units, conversion formule for......----- 8 critical, of ZaSES «1+ eeeeeeee reer errs 200 dimension formule for.....---.-- XXV effect on radiation .....22-++-eeeeeees 236 Magnetism, conversion factors for surface of aqueous Vapor ..----++eee reer 151-154 density .........--- Bete ste feteiicieietasleteicic.= 26 at low temperatures....---+-+---+++> 156 terrestrial ....... Bee oc cacine sta cts 110-118 in the atmosphere....---+++++e++: 157 Magnetization, conversion factors for inten- of mercury column.....-++++eeeereeee 119 SIG ohare tetas ae peietn nia = shelsien a isin diel» soonest) OSMOTIC. se oie\e «1 sie'e:ciere\wlecermie)s' s1/+l aimee 150 Magnetite, Kerr’s constant for ....-- Sere 292 Of VAPOIS 2... sere sere eee reese 126, 225-227 magnetic properties Of......+.++++++++279 OF WING 6 00 eee ciceee voce seeeers soe Seis LOO Magneto-optic rotation, general reference to Probability, table for calculating......++-+-- 36 284 tables Of.......- Hau DCROODBOS «2 6. 205-291 Masses, conversion factors for ...-.--++++++ 13 | Quartz, fibres, strength of .......-- Saab seo Materials, strength of .....--++++++ee+e- 70-73 refractive index Of .....++seeeeeeerees 186 Measurement, units Of ....--+-+ee eer reece XV Mechanical equivalent of heat..... Bele ieisieies 220 Melting-points of chemical elements ....--- 207 | Radiation, effect of pressure On ....++++++ 236 of inorganic compounds Sundae ce cee +208 | Relative humidity... 0s -0ccssssseusceres 161 300 Resistance (see also Conductivity), electric. of alloys...... date s\ereie tes 251 25GN 2h O27 of electrolytes........ stots teitc= “20 0259 of plass and porcelain . 5... cc02-5< 293270 of metals and metallic wires...... «254-257 of wires, effect of elongation on....... 2 Rigidity, modulus defined: «so. cn ec - see ns 74 OF metals xer-).rctw’os eter te Selelatsterctelale vais eee variation of, with temperature..........76 Rotation, magneto-optic..... Belsialelecee 2O4—201 Saturation values, magnetic, for steel...... 279 Seconds pendulum, length of..........104, 105 Secondary batteries........... Saeieteettere 247 Sections of wires ......... oeeee 044-54, 58-68 Sheet metal, weight of ........ miayaietelcdaorsy SOsus 7 Soaring of planes, data for....... si efaieisie eleva LOO) Solar, Constantecaceasenie deste « patel eae Solar spectrum, wave-length in............ 172 Solids, compressibility and bulk moduli of. ...83 densitylot ee meena fae efetelotetatetataterersio magneto-optic rotation in..... eee 284 Solution, contraction produced by..... 131-134 Solutions, aqueous, boiling-points of ....... 196 CONSE VIOR aericiters eect tere terre go magneto-optic rotation in......... 288-290 Fema chive sn ICES Ome ysl itete eer stekele ere 183 specific heat Of =:...1-\-\..6 Bee eters aatateretee Sound, velocity/Ofimialtgte ce o1-)s seletl- ile - «99 ID) Las estan deliquids 7. cre ijtsteretses ers stette = IOI MUSH 6 So Gedagecconnces Ree eee 100 Specific electrical resistance, conversion fac- LOTS HOD er ngcler err eieleraleiere nice its 23, 254-256 Specific gravity (see also Dezsity). of aqueous ethyl alcohol........... SA Dck\e) methyl-alcoholl® secretes esti 97 Gli LANES: somcudoocesccucgdénave eee OO Speciicwheatiof air-- jc. +s ee sieielelaieteteie 223 Ol PASS ANG WADOTS i isieieieieeielcteieial stots 22 Obmetals: sme eset meeiieinie seine ier 296 of solids and liquids ..... selehlnees 20451205 Ob Wallonia rterrette ice maleleieterletoleretote erere of: water, formule for <1 ccieoe 6 ce se ete 222 Specific inductive capacity............263-265 viscosity, aqueous solutions........... 144 OUS cyopteieicieteyielosets Bolofarcieleheletetey tetra) WW ALC Veste tele elotateNalotclatete taster eV -telet tetaraiets 136 Spectra, wave-lengths.in arc and solar ..... 172 Standardicellss7scrariss cate tlateels sitet accel 247 wave-lengths of light......... sitorstel ke G7 Standards; pHOtOmeLtriC: ... . cielei\e.s c/o eievelei='e 176 Steel, physical properties of........... dinietsior/id Steam, properties of saturated ........ sisieei237) Steinmetz, constants for hysteresis of ...... 251 stone; 'Strenpth Ob jus cis-ic)s'-10 Sfetoreleiateteietertstrer= 70 thermal conductivity of.............. - 197 Cielectric <2 -1..% Dtelereeterets cers shee ae 244 Strength of materials............ eth On7 5 Stress, conversion factors for ........... 19, 22 Surface-tension, constants of.......... 128, 129 conversion factors fOr «simile sie cierere 20, 22 Sylvine, refractive index of..............2- 182 Temperature, conversion factors for........ 25 critical, of gasesicn sani eetete 200 Terrestrial magnetism, agonic lines ........117 declination, data for maximum east at various stations dip and its secular variation for differ- ent latitudes and longitudes.........-111 INDEX. Terrestrial magnetism (continued). horizontal intensity and its secular varia- tion for different latitudes and longi- tudes ieee eee ovesceccovcceseslIZ secular variation of declination ....113-116 Thermal conductivities..............-197, 198 relation to electrical. ....:scess.= age expansion, coefficients of ..... + 214-218 units, dynamic equivalent of ..... «eee 219 Thermoelectricity-.-tcscn.+--vass-+- 220250 Thermometer. see Mercury im Glassen ee Pee eer zero change due to heating............229 zero, change of, with time........... - -230 ‘Timber, strength oft oetas «2 2: meee oe Time, unit of, defined...... ots eter Jepoc ot xvii Times, conversion factors for Transformers, permeability of iron in.. Units of measurement ........ Balete atereiete eter dimension formule for dynamic......xviii electric and magnetic : clectromasnetich misters ElectrOstaticee = oieleanelcisisiasieieitettate XXvi fundamentalsisce eel siovalaters heatejjess oes sie eee eee oo ete ROXIE practical, legalization of electric ..... XXxili ratio of electrostatic to electromagnetic 24 United States weights and measures in : MEIC eevee eet ae Vapor, density of aqueous...............-155 cifitisLOny Ofer easier eee SetetelteaG) pressure Of ...... ave ciotoetets 126, 225-227 pressure of aqueous.......... +++ -ISI-154 WaluesO110:378\ esse itete estate 160 pressure of, for aqueous solutions. .....194 refractive indices for...... crolstelelelstatelara LOO Specitic heatsiOl sey -perlereieieeisterieeeeieeiete 224 Vaporization; latent heatioter ce eeeeretenee 204 Velocity, angular and linear, conversion fac- LOTS SLO Dyeretetepstetetetetets afolot eset: olteteierate tote teletete 15 OL MIphtss: Asc ertereetsrieiaete eee So tigkey 27.12% OL SOUNC ernie refer reretelatelot-tieielels Q9, 101 Verdet’s constants for alcoholic solution of SalltS/ererleteteieteettere ea cefelyeerier eet *va|0/e2Q0 aqueous solutions of salts ........ 287 GASES Oairesiehe water -isrepee ete ter eet -291 hydrochloric acid solutions of salts 290 liquids and solids......... - » -285-287 and Kundt’s constants ......... meeaZ Oe Viscosity, coefficient, definition of......... 136 coefficient of, for aqueous alcohol .....137 POY, SASES seis, ccicis elutes ate eee 146 for, lignicds) citer ole e aXe temperature effect on, for liquids ..... SPECHIC; LON OllS).cle ayant ee eee ee ay, for water Volumes, conversion factors for...........-. 12 critical, of gases. -j.1' sc eretererettere ere 200) Water, boiling-point for various barometric PLESSULES leer cee eee reser 170, 171 Gensity (Ofer Selenite eee 92-94 SPECIICMCALOL 1ci9'e1sesisidleieis's sel CoC Water (continued). thermal conductivity of............... 198 IRIE OM ally ces nec siu'e edna nwue eh 136 Wave-lengths of Fraunhofer lines ......... 175 standard for arc and solar spectrum... .172 Weights and measures — British Imperial to Metric............ 7,8 Metric to British Imperial............ 5, 6 Metco; Umlted States... crew e enews 10 UWinttegustates to Metric ....2..5..-..ee 9 Weights of Sheet metal .............«.. 56, 57 Weights Of Wires ..........csaveccseses 44-54 INDEX. 301 Wind, pressure Of... s.0<0sss Sr 1 Sarat rate 108 Wie; PAULCS ss 2. cnr ev eiee's rile eine ns 55-67 WiOOdS: CensitieSObnececrse se aies'e sie eiecatcln s)e1s 85 Work, conversion factors for...........20, 21 Ward, degnition of \scccinessevots vest ox bs xvi Woung’s modula jo) cijee s:aapere qrareterstriaatn esac 75 modulus, definition of............-..+- 75 Zonal harmonics ice sale area eealy epee oes awsome 40 SMITHSONIAN wv TIT LIBRARIES IMP TINV 3 9088 01421 4266 hed pe ihe etek any, pears St es Lalal peresorat) Pita saraiee he, he eters PT ea aes rary Noire teael A re eee ekg | pis eee Hi ete ers ea erate) Chub nd ce t i Ne So f ; Mes Ute erty ert ala Ot Prat Bd art ets ee ‘ veh Li i Acure’ f $0 if « Ty H ot - i ray tt AH iaentttte Uta fie , is ith ‘herdart! ae be . a rey eet : etd get yy wath ra aaa if é ri Rat is ee at Maite o o BH vi ae uit Ge Re id . 2 ria’ yearn rt inne mn ie 4 { c i 4 ta i J si ehh ‘ : is eet ae tt if \F rate Nerd eC ee y Dt Mita uh eh a hs f wie i 1 ase ate f gah aye te etek ns i i rat mete i Y iad Phe ; aa A Coin nae ua te A 4 hits) iar a Tyan ree ie rat mg ty Osh piles; ; i hale eae i { bys + att u Pt fe 0 one i a ae a! a ate Caetarrathaa ttt vp nites ae yi r th Oty) is ere aes add [esiraae 4 oe. eerieratn we