UC-NRLF SB EM p&fflft$ft '/A! tik i\t^ LIBRARY UNIVERSITY OF CALIFORNIA QIF S T OF Class \J A COLLECTION OF MATHEMATICAL AND PHYSICAL TABLES FROM A COURSE OF EXPERIMENTS IN PHYSICAL MEASUREMENT. BY HAROLD WHITING, PH.D., ASSISTANT PROFESSOR OF PHYSICS IN THE UNIVERSITY OF CALIFORNIA. BOSTON, U.S.A. D. C. HEATH AND CO., PUBLISHERS. 1900. A COLLECTION OF MATHEMATICAL AND PHYSICAL TABLES FROM A COURSE OF EXPERIMENTS IN PHYSICAL MEASUREMENT. BY HAROLD WHITING, Pn.IX, ASSISTANT PROFESSOR OF PHYSICS IN THE UNIVERSITY OF CALIFORNIA. BOSTON, U.S.A. D. C. HEATH AND CO., PUBLISHERS. 1900. Copyright, BY HAROLD WHITING. JOHN WILSON AND SON, CAMBRIDGE, U.S.A. PREFACE. THESE mathematical and physical tables with their explanations have been reprinted from plates of a work on " Physical Measurement " (pages 761-900, Part III.) , prepared by the author while holding the position of Instructor in Physics at Harvard Univer- sity. In accordance with a practical suggestion con- tained in a review of this work, 1 four-place tables of logarithms and antilogarithms were subsequently introduced (pages 821 a, b, c, d) ; but it was not thought desirable to omit the five-place tables, which are preferred by many persons even for rough and rapid work. It will be noticed that the most important mathe- matical tables extend from 1 to 11 units, instead of stopping in the usual manner at 10. By this slight extension ten-fold accuracy becomes attainable in the use of factors between 1.0 and 1.1, which are of com- paratively frequent occurrence in physical calculations. The physical tables are arranged especially for scientific use, and are expressed accordingly in the Metric, or, more precisely, in the Centimetre-Gram- Second (C. G. S.) system, now widely adopted by 1 " Philosophical Magazine," October, 1891, page 396. 116 iv PREFACE. scientific men. This system has one great advantage over all others, in that it is the only one system which has been consistently applied to all branches of physics. Feet and pounds are, it is true, more com- monly employed by English-speaking people than metres and grams ; but the volt, ohm, and ampere are familiar to every electrician, while the corresponding units of the English system are practically unheard of. The Metric system is preferred also by many persons on account of the facility of the reductions from absolute to practical units, or the reverse, which in the Metric system consist simply in moving a decimal point. The necessary decimal multipliers are generally given in connection with each value or column of values contained in the tables. Engineers will find factors for reducing English to Metric values, or the reverse, on the last three pages, and will note that a single setting of a " slide rule " is sufficient for the rapid conversion of a long series of data. The author has sought to embrace in the physical tables all the properties of substances about which sufficient information could be obtained. To make this possible, it was found necessary to employ a con- densed arrangement (see pages 843-863), whereby a dozen or more properties of a given substance could be represented in a single line. It was not thought desirable to include in the tables rare substances, or those of variable or uncertain composition, unless in addition to densities, boiling-points, etc., necessary to identify such substances, a determination of at least two other physical properties could be found. PREFACE. V Various sources of authority for the values con- tained in these tables are mentioned on pages 794- 795. Care has been taken to give all figures in regard to which different physicists were found to agree, and in general one and only one additional figure, express- ing some more or less probable mean among the several determinations. Attention is called to the fact that in this respect the author has departed from the usual misleading custom of appending two or more insignificant figures to results (see page 796), and that most of the differences which will be found between values quoted in this book and those given elsewhere are due to this departure. It is hoped, accordingly, that throughout the physical tables, in the absence of any special warning to the contrary, it may be reasonably safe to count upon the accuracy of every figure except the last. BERKELEY, March 11, 1892. TABLE OF CONTENTS. MATHEMATICAL AND PHYSICAL TABLES. PAGE EXPLANATION OF TABLES 761 SOURCES OF AUTHORITY 794 MATHEMATICAL TABLES. TABLE 1. PROPORTIONAL PARTS 797 2. POWERS, CIRCULAR PROPERTIES, ETC 798 3. TRIGONOMETRIC FUNCTIONS (S-PLACE) 800 3A. RECIPROCALS . . 802 3C. SQUARES . 804 3D. CUBES 806 3F. CIRCUMFERENCES OF CIRCLES 808 3G. AREAS OF CIRCLES 810 3H. VOLUMES OF SPHERES 812 4. NATURAL SINES 814 4A. LOGARITHMIC SINES 816 5. NATURAL TANGENTS 818 5A. LOGARITHMIC TANGENTS 820 5B. ANTILOGARITHMS 821a 5C. LOGARITHMS (4-PLACE) 821c viii TABLE OF CONTENTS. 6. LOGARITHMS (5-PLACE) 822 7. PROBABILITY OF ERRORS . . 842 PHYSICAL TABLES. GENERAL PROPERTIES OF SOLIDS, LIQUIDS, AND GASES. 8. PROPERTIES OF ELEMENTARY SUBSTANCES . . . 843 9. PROPERTIES OF SOLIDS BUILDING MATERIALS, ETC. 846 9a. PROPERTIES OF SOLIDS CHEMICAL MATERIALS, ETC 848 10. PROPERTIES OF SOLIDS OPTICAL MATERIALS, ETC 852 11. PROPERTIES OF LIQUIDS 856 12. PROPERTIES OF GASES AND VAPORS ... . 861 HYPSOMETRIC, HYGROMETRIC, AND BAROMETRIC TABLES. 13a. MAXIMUM PRESSURE OF VAPORS 864 14. BOILING POINTS OF WATER, 68 CM. TO 80 CM. . 867 14A. DEW-POINT, TEMPERATURE, AND HUMIDITY . . 867 15. HYGROMETRIC TABLE .868 15A. SPECIFIC HEAT OF MOIST AIR 868 15B. VELOCITY OF SOUND 869 15C. COEFFICIENTS OF INTERDIFFUSION OF GASES . . 869 16. REDUCTION OF BAROMETRIC RKADTNGS TO CM. . 870 16 A. (REDUCTION OF BAROMETRIC READINGS ) G = 980 871 16B. j TO MEGADYNES PER SQ. CM. . . j G = 981 871 17. ESTIMATION OF HEIGHTS BY THK BAROMETER . 871 17A. CORRECTION FOR TEMPERATURE IN TABLE 17 . 871 17B. CORRECTION FOR HUMIDITY JN TABLE 17 ... 871 18a. BAROMETRIC CORRECTIONS FOR EXPANSION . . 872 ISb. BAROMETRIC CORRECTIONS FOR CAPILLARITY. . 872 18c. BAROMETRIC CORRECTIONS FOR MERCURIAL VAPOR 872 18d. REDUCTIONS OF DENSITY TO 76 CM 873 18e. REDUCTIONS OF DENSITY TO 873 18f. REDUCTIONS OF VOLUME TO 76 CM 873 18g. REDUCTIONS OF VOLUME TO 873 TABLE OF CONTENTS. ix REDUCTION OF WEIGHINGS TO VACUO. 19. DENSITY OF AIR (0- 30; 72-77 CM.) .... 874 20. CORRECTIONS *OK HUMIDITY IN TABLE 19 . . 874 20A. BUOYANCY OF AIR ON BRASS WEIGHTS . . . 874 21. REDUCTION OF APPARENT WEIGHINGS TO VACUO 875 SPECIFIC VOLUMES AND DENSITIES. 22. APPARENT SPECIFIC VOLUMES OF WATER . . . 875 23. TRUE SPECIFIC VOLUME OF WATER 876 23A. TRUE SPECIFIC VOLUME OF MERCURY .... 876 23B. APPARENT SPECIFIC VOLUME OF MERCURY . . 876 2t. DENSITY OF MERCURY 877 25. DENSITY OF WATER 877 26. DENSITY OF COMMERCIAL GLYCERINE . 877 PROPERTIES OF SOLUTIONS DEPENDING UPON THEIR STRENGTH. 27. DENSITY OF ALCOHOL (0%-1 00%; 15-22) . . 878 28. DENSITY OF ACIDS AND SOLUTIONS AT 15 . . 880 29. BOILING-POINTS OF SOLUTIONS 882 30 SPECIFIC HEATS OF SOLUTIONS 883 31A. ELECTRICAL CONDUCTIVITY OF SOLUTIONS AT 18 884 31 B. REFRACTIVE INDICES OF SOLUTIONS 885 310. TABLE FOR MIXING SOLUTIONS 885 31 D. COEFFICIENTS OF SALINE DIFFUSION 885 31 K. ( ROTATION OF THK PLANE OF ) IN SOLUTIONS . 886 31 F. ( POLARIZATION, LINES A-H i IN SOLIDS . . 886 MISCELLANEOUS DATA. 31G. MAGNETIC ROTATION OF POLARIZATION. ... 887 31H. MAGNETIC SUSCEPTIBILITY, ETC 887 311. COEFFICIENTS OF HYDRAULIC FRICTION ... 887 31J. COEFFICIENTS OF FRICTION BETWEEN SOLIDS. . 887 31K. RELATIVE RADIATION, ABSORPTION, ETC. . . . 887 31L. CONSTANTS OF RADIATION . 887 32a. HEATS OF COMBUSTION IN OXYGEN 808 32b. HEATS OF COMBUSTION IN CHLORINE .... 888 33. HEATS OF COMBINATION 888 TABLE OF CONTENTS. ELECTROMOTIVE FORCE AND RESISTANCE. 34. CONTACT DIFFERENCES OF POTENTIAL .... 889 35. ELECTROMOTIVE FORCES OF VOLTAIC CELLS . . 890 36. ELECTROMOTIVE FORCE AND LENGTH OF SPARK . 890 37a. SPECIFIC RESISTANCES OF CONDUCTORS .... 891 37b. SPECIFIC RESISTANCES OF INSULATORS .... 891 38. SPECIFIC RESISTANCES OF ELECTROLYTES . . . 891 ARBITRARY SCALES. 39. FAHRENHEIT AND CENTIGRADE THERMOMETERS 892 40. HYDROMETER SCALES 892 41. WAVE-LENGTHS 892 42a. BOARD OF TRADE (IMPERIAL) WIRE GAUGE . . 893 42b. BIRMINGHAM WIRE GAUGE 893 43. MUSICAL PITCH 893 ASTRONOMICAL AND GEOGRAPHICAL TABLES. 44 A. REDUCTION OF (') AND (") TO () 894 44B. EQUATION OF DATHS IN DIFFERENT YEARS . . 894 44C. GAIN OF SIDEREAL TIME . 894 44D. SIDEREAL TIME AT GREENWICH, NOON .... 894 44E. SEMI-DIAMETER OF THE SUN 894 44F. DECLINATION OF THE SUN 895 44G. EQUATION OF TIME 895 44H. THE SOLAR SYSTEM 896 45. RIGHT ASCENSIONS AND DECLINATIONS OF STARS 896 46. GEOGRAPHICAL LATITUDES, LONGITUDES, AND ELEVATIONS 897 47. ACCELERATION OF GRAVITY 897 48. LENGTHS OF SECONDS PENDULA . ... 897 REDUCTION OF MEASURES TO AND FROM THE C. G. S. SYSTEM. 49a. REDUCTIONS INDEPENDENT OF "G" 898 49b. REDUCTIONS FOR "G"=980 AND "G"=981 899 50. CONSTANTS FREQUENTLY REQUIRED 900 USE AND EXPLANATION OF MATHEMATI- CAL AND PHYSICAL TABLES. TABLE 1 consists of products obtained by multiply- ing any of the whole numbers (from 1 to 100) in the left-hand column of either half of the table by the decimals .1, .2, .3, .4, .5, .6, .7, .8, .9 at the head of the table. The decimal part of the product is rejected in every case, the units being increased by 1 if the frac- tion is .5 or more. The table is useful in dividing differences into parts proportional to the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, whence the name of the table. It may be used in connection with any of the tables which follow. Let us suppose that it is required to find the sine of 12.34 in Table 4, page 814. We find the sine of 12. 3 (in the line with 12 and in the col- umn with .3) to be .2130, while the sine of 12.4 is .2147. The first number (.2130) is too small ; the second (.2147) is too great. The difference between them is .0017, or 17 units in the last place, as indi- cated by the nearest number in the column of differ- ences. If 0.l makes a difference of 17 units, 0.04 should make a difference of .04 -5- 0.1 X 17, that is, 6.8 or (nearly) 7 units in the last place. The xante result may be found by seeking in Table 1 a number 12 762 EXPLANATION OF TABLES. [No. 1. opposite the difference (17) and under the figure (4) for which the interpolation takes place. The result (7 units in the last place) is to be added to the sine of 12.3, because the sines increase when the angles increase in other words, because the differences are positive. The sine of 12.34 is accordingly 0.2130 + .0007 = 0.2137. Again, to find the reciprocal of 6.789, by Table 3 A, page 802, we observe that the reciprocal of 6.78 is .14749, while that of 6.79 is .14728. The difference between these reciprocals is .00021, because the re- ciprocals decrease as the numbers increase. Opposite 21 and under .9 in Table 1 we find 19 ; hence the answer is .14749 00019 = .14730. If we had used the nearest number (22) in the column of differences of Table 3 A., instead of the actual difference (21), we should have found similarly .14729 instead of 14730. The true reciprocal happens to lie between these two values. Table 1 can be used also in inverse processes. Let us suppose that it is required to find the cube root of 800, by Table 3 D, page 806. We notice that the cube of 9.28 is 799.2, just below 800, while the cube of 9.29 is -801.8, just above 800; the differ- ence being 26 units in the last place. The difference between 799.2 and 800.0 is 8 units in the last place. In line with the number 26 in the left-hand column of Table 1, and over the number 8, 1 we find .3. We see 1 When the exact number cannot be found amongst the propor- tional parts we choose the one nearest to it. No. 2.] MATHEMATICAL TABLES. 763 therefore that the cube of 9.283 would be 800.0 ; hence, conversely, 9.283 is the cube root of 800. The use of proportional parts is especially recom- mended when accuracy in the last figure is important. The tables which follow have, however, been con- structed with such fulness that interpolation will generally be unnecessary, or readily carried on in the head. TABLE 2 contains several functions often needed, and is intended for rough and rapid work. More exact values of the functions will be found in Tables 3 A 3 H, which follow. Column a contains the "reciprocals" of the num- bers in the first column from 1 to 100. The recipro- cal of a number is defined as the quotient obtained when unity is divided by the number in question. Example : the reciprocal of 30 is .0333. Column b contains the square roots of numbers from 1 to 100. The square root of a number is de- fined as a number which multiplied by itself would give a product equal to the original number. Ex- ample : the square root of 49 is 7.00. Column c contains the squares of numbers from 1 to 100 ; that is, the products obtained when each number is multiplied by itself. Example : the square of 40 is 1600. Column d contains the cubes of numbers from 1 to 100. The cube of a number is defined as the result of multiplying that number by the square of that num- ber ; or as the result of multiplying that number three times into unity. Example : the cube of 5 is 125. 764 EXPLANATION OF TABLES. [No. 3. Column e contains three-place logarithms (see under Table 6) from 0.1 to 10.0. Example : the logarithm of 2 is 0.301, correct to 3 places of decimals. Column f contains the circumferences of circles having diameters from .1 to 10.0. The circumference is given in the same units as the diameter. Example : given the diameter 2.0 cm., the circumference is 6.28 cm. Column g contains the areas of circles having diam- eters from .1 to 10.0. The area is given in units cor- responding to the unit of length employed in meas- uring the diameter. Example : given the diameter 2.0 cm., the area of the circle is 3.14 sq. cm. Column h contains the volumes of spheres having diameters from .1 to 10.0. The volume is given in units corresponding to the unit of length employed in measuring the diameter. Example: given the diameter 2.0 cm., the volume of the sphere is 4.19 cu. cm. TABLE 3 contains principally 3-place trigonometric functions, and is, like Table 2, intended for rough and rapid work. Column a contains angles from to 90 ; covering in all a right-angle. Column b contains the tangents of angles. The tangent of an (acute) angle is denned, with reference to a right-angled triangle, as the ratio of the side opposite it to the (shorter) adjacent side. Example : the tangent of 15 is 0.268. Column c contains " arcs ; " that is, in a circle of radius unity, the length of the arcs intercepted by No. 3.] MATHEMATICAL TABLES. 765 angles with their vertices at the centre of the circle. "Arcs" are also called the "circular measures" of angles. Example: 15 is equal to 0.262 -in circular measure ; or the arc of 15 is 0.262. Column d contains the " chords " of angles. The chord of an angle is defined, with reference to an isosceles triangle, as the ratio of the side opposite the vertical angle to either of the two equal sides. Ex- ample : the chord of 15 is 0.261. Column e contains natural sines. The sine of an angle is defined, with respect to a right-angled tri- angle, as the ratio of the side opposite that angle to the longest side, or hypothenuse. Example : the sine of 15 is 0.259. Column f contains natural cosines. The cosine of an angle is defined as the sine of the complement of that angle (see i). Example : the cosine of 15 is 0.966. Column g contains rates of vibration corresponding to different arcs from to 45, through which for in- stance a pendulum is vibrating. The arcs are meas- ured from one side of the vertical to the other.. The rate of vibration in a very small arc is taken as 1. Example I. : if a pendulum vibrates once a second in a very small arc, it will vibrate .99893 times a second in an arc of 15 (i, e. 7J on each side of the verti- cal). Example II. : given the time of oscillation of a magnet equal to 10 seconds in an arc of 45 ; re- quired its time of oscillation in a very small arc. Answer, 10 X .99037 = 9.9037 sec. Column g con- tains also cover sines from 45 to 90. 766 EXPLANATION OF TABLES. [No. 3. The coversine of an angle is defined as unity less the sine of the angle. It is the same thing as the versine of the complement of the angle. Versines and coversines measure various errors introduced into physical measurement when two lines which ought to be parallel or perpendicular are inclined at a given angle. The inclination of the two lines is to be found in column a or in column i as the case may be. Example I. : the shaft of a cathetometer (^f 262) makes an angle of 89 with the horizon ; required the error introduced in the measurement of vertical distances. Answer, .00015 parts in 1, or ^f Q of 1 %. Example II. : a magnet which should be horizontal dips 10; required the error in estimating its mag- netism. Answer, .0152, or 1 ffa oj . Column h contains secants, or the reciprocals of cosines. Example : the secant of 15 is 1.035. Column i contains the complements of the angles contained in column a , that is, the results of sub- tracting these angles from 90. Example : the com- plement of 15 is 75. It may be remarked that the cotangent of an angle is the tangent of its complement ; the cochord of an angle is the chord of its complement ; the cosecant of an angle is the secant of its complement. These may all be found, accordingly, by Table 3. Examples : The cotangent of 15 = tangent of 75 = 3.732 The cochord of 15 = chord of 75 = 1.218 The cosecant of 15 = secant of 75 = 3.864 To find any function of the complement of an angle, No. 3F.] MATHEMATICAL TABLES. 767 we have only to look up that angle in column i, in- stead of in column a. TABLE 3 A is essentially a 4-place table of recipro- cals from 1.00 to 11.09, carried out, however, to 5 places between 6.00 and 9.99. Examples: the re- ciprocal of 2.73 is .3663 ; the reciprocal of 273 is .003663. TABLE 3 C is a 4-place table of squares from 1.00 to 9.99, carried out to 5 places between 10.0 and 11.09. Examples : the square of 3.14 is 9.860 ; the square of 31.4 is 986.0. The square root of 1.25 is is 1.12 nearly, or more exactly, 1.118 (see under Table 1). TABLE 3 D is a 4-place table of cubes from 1.00 to 9.99, carried out to 5 places from 10.0 to 11.09. Ex- amples : the cube of 5.55 is 171.0 ; the cube of .555 is .1710. The cube root of 800 .is 9.283 (see under Table 1). TABLE 3 F contains the circumferences of circles with diameters (diam.) varying from 1000 to 10090 by 10 units at a time. The results are carried out to units. The differences in this table are either 31 or 32, from beginning to end. The mean difference is 31.416. Proportional parts corresponding to this mean difference are printed at the bottom of the table. The circumference is given in units of the same magnitude as the diameter. Example I.: the circumference of a circle 3600 cm. in diameter is 11310 cm. Example II. : given a circumference 10,000 metres, the diameter is 3180 metres, nearly ; or more exactly, 3183 metres (see under Table 1). 768 EXPLANATION OF TABLES. [No. 4 A. TABLE 3 G is a 4-place table containing the areas of circles corresponding to diameters (diam.) from 10.0 to 100.9. The area is given in units correspond- ing to the unit of length in which the diameter is measured. Example I. : diameter = 15.0 cm., area 176.7 sq. cm. Example II. : diameter = 55.5 mm., area = 2419 sq. mm. 24.19 sq. cm. Example III. : area = 4000 sq. cm., diameter = 71.4 cm., nearly ; more exactly, 71.36 cm. (see under Table 1). TABLE 3 H contains the volumes of spheres cor- responding to diameters from 1.00 to 10.09. The volume is given in units corresponding to the unit of length in which the diameter is measured. Example I. : diameter = 11.1 mm. = 1.11 cm. : volume .539 cu. cm. = 539 cu. mm. Example II. : volume = 35.00 cu. cm., diameter = 4.06 cm., nearly ; or more exactly, 4.058 cm. (see under Table 1). TABLE 4 is a 4-place table giving the natural sines of angles from 0.0 to 89.9. when interpreted in the ordinary manner by means of the argument at the left and at the top of the page. Natural cosines may also be found by means of this table, by using the argument at the right and at the bottom of the page. Example I. : the sine of 30.0 is 0.5000. Example II. : the cosine of 30.0 is .8660. TABLE 4 A is a 4-place table giving the logarithmic sines (that is the logarithms of the sines) of angles from 0.0 to 89. 9, when read in the ordinary way. Logarithmic cosines may be found through the ar- gument at the right and bottom of the page. Ex- ample I.: the logarithm of the sine -of 30 is 1.6990. No. 6.J LOGARITHMS. 769 Example II. : the logarithm of the cosine of 30 is 1.9375. TABLE 5 contains the natural tangents of angles from 0.0 to 89.9. Natural cotangents from 45.0 to 89. 9 may also be found by using the argument at the right and bottom of the first half of the table. Below this limit, they are not given ; but they may be found by calculating the complement of the angle and looking up its tangent. Example I. : the tan- gent of 30 is 0.5774. Example II. : the cotangent of 22.5 = tangent of 77.5 = 4.511. TABLE 5 A is a 4-place table giving the loga- rithmic tangents (that is, the logarithms of the tan- gents) of angles when read in the ordinary way. Logarithmic cotangents may also be found by using the argument at the right and at the bottom of the page. Example I. : the logarithm of the tangent of 30.0 is 1.7614. Example II. : the logarithm of the cotangent of 30 is 0.2386. TABLE 6 is a 5-place table of the logarithms of numbers from 1,000 to 11,009. A decimal point is understood after the first figure of each number and before the first figure of each logarithm. Ex- ample : the logarithm of 2.000 is .30103. When the decimal point of a number does not follow the first figure, the corresponding logarithm consists of two parts. The first part is a whole number called the u characteristic " of the logarithm ; the second or decimal part is called the " mantissa." The " characteristic " of a logarithm is not to be found in Table 6, but is to be supplied by inspection. 770 EXPLANATION OF TABLES. [No. 6. Its numerical value is equal to the number of figures between the decimal point of the argument and the space following the first figure of the argument. Thus the logarithm of the number 1.11 has the characteristic 0; while the characteristics of 11.1 and 111 are 1 and 2 respectively. The sign of the characteristic is positive if the decimal point is at the right of the first figure of the argument ; if it is at the left, the sign is negative. Thus the characteris- tic of the logarithm of .1111 is 1., the character- istic of the logarithm of .01111 is 2., &c. The negative sign is in practice written over the char- acteristic, as it affects this characteristic alone. It is a peculiarity of logarithms that the "man- tissa " is not affected by the location of the decimal point in the original number. The logarithm of 1.111 (namely, 0.04571) is, for instance, the same as the logarithm of 1,111. (namely, 3.04571), as far as the mantissa is concerned. The mantissa or decimal part of the logarithm of any number may be found, accordingly, by Table 6, by considering only the fig- ures of which the number is composed. Initial and final ciphers may be thrown off ad libi- tum in this process ; but ciphers in the middle of a number form an essential part of it. Thus in finding the decimal part of the logarithm of .000,100,100, we need to consider only the figures 1001, since these are preceded and followed only by ciphers ; but the ciphers between the first and last figures cannot be neglected. The following logarithms from Table 6 may also serve as examples : No. 6.] LOGARITHMS. 771 The logarithm of 3.1416 is 0.49715 " " " 980 u 2.99123 " u 41,700,000 " 7.62014 " .00367 " 3.56467 Conversely, in finding the number corresponding to a a given logarithm, we first obtain the figures of which the number is composed by considering simply the mantissa, or decimal part of the logarithm, and to these figures we add as many initial or final ciphers as may be needed ; then starting with the space at the right of the first figure (disregarding initial ciphers) we count off to the right if the characteristic of the logarithm is positive (or to the left if negative) a number of spaces equal to the characteristic in ques- tion, in order to locate the decimal point. In any case the number of figures between the decimal point and the space following the first figure of the answer must be equal to the characteristic of the logarithm. Example I. : given the logarithm 0.14860, the fig- ures of the corresponding number are 1408 ; the char- acteristic of the logarithm being 0, the answer is 1.408. Example II. : given the logarithm 3.14860, the man- tissa being .14860 as before, we find the same figures, 1408. Since the characteristic (3) is positive, the decimal point is at the right of the first figure, and since 3 figures must come between the decimal point and the space following the first figure, the answer is 1,408. 772 EXPLANATION OP TABLES. [No. 6. The following rules embody the most important applications of logarithms, namely, to problems of multiplication and division. Rule 1. To multiply two or more numbers to- gether, find the logarithm of each and add the loga- rithms together. The number corresponding to their sum is the required product. Example : to multi- ply 2X4. The logarithm of 2 is 0.30103 " u " 4 is 0.60206 The sum of these logarithms is 0.90309, which is the logarithm of 8, the answer. Numbers involving more than 3 significant figures may be mul- tiplied together by the aid of logarithms with greater ease than by arithmetical processes. Rule 2. To divide one number by another, find the logarithm of the first, subtract the logarithm of the second ; the remainder is the logarithm of the answer. Example : to divide 4 by 8, The logarithm of 4 is 0.60206 " " " 8 " 0.90309 The difference is T.69997, which is the logarithm of 0.5, the answer. Rule 3. To find the value of a fraction with sev- eral factors, find the logarithm of each factor in the numerator, and add the logarithms together. Then find the logarithm of each term in the denominator, and add these logarithms together. Subtract the No. 7.] LOGARITHMS. 773 latter sum from the former sum. The remainder is the logarithm of the answer. Example : to find the value of the fraction .2345 X 45.67 x 6,789 wefind _ 1.234 X 34,56 X 567.8' (1) log. .2345 = 1.37014 (5) log. 1.234 = 0.09132 (2) " 45.67 = 1.65963 (6) 34.56 = 1.53857 (3) " 6789 = 3.83181 (7) " 567.8 = 2.75420 (4). sum = 4.86158 (8) sum = 4.38409 (9) subtract 4.38409 (10) remainder^ 0.47749 = log. 3.002 +, ans. Rule 4. To raise a number to any power, find its logarithm, multiply by the power, and the product is the logarithm of the answer. Example : to find the 4th power of 2. The logarithm of 2 is 0.30103; which multiplied by 4 gives 1.20412. This is the logarithm of 16, the answer. Rule 5. To extract any root of a number, find the logarithm of the number and divide by the root in question ; the quotient is the logarithm of the answer. Example : to find the 12th root of 2. The logarithm of 2 is 0.30103 ; this divided by 12 gives .02509, which is the logarithm of 1.0595, the answer. (This is the value of the interval called 1 semitone on the tempered scale.) TABLE 7 contains the probability of an error's ex- ceeding limits bearing to the " probable error " ( 50) the ratios represented in the left-hand column. The probability is expressed as so many chances in 1. Example I. : the probable error of a weighing is 1 774 EXPLANATION OF TABLES. [Nos. 8-12. centigram ; what are the chances of an error greater than 1 centigram? Answer, by definition, an even chance or 0.50000. Example II. : under the same circumstances, what are the chances of an error's ex- ceeding 2 centigrams? Answer, 0.17734, i. e. 17,734 chances in 100,000,. or about 1 chance in 6. Exam- ple III. : under the same circumstances, what are the chances of an error's exceeding 5 centigrams ? Answer, 0.00075, or less than 1 in 1000. 1 TABLES 8, 9, 10, 11, and 12 contain (1) the names, (2) the chemical symbols, and (3) the atomic weights of various substances, and deal with the following physical properties : (4) the specific gravity ( 69) of gases and vapors referred to hydrogen at the same temperature and pressure ; (5) the density ( 15) of substances at under the ordinary atmospheric pressure ; (6) the " viscosity " of liquids at about 20, or the force in dynes required to maintain a relative velocity of 1 cm. per sec. between two sur- faces 1 cm. square and 1 cm. apart ; (7) the " surface tension " of liquids (^ 169) at about 20, or the force in dynes with which each surface of a liquid film 1 cm. broad tends to contract ; (8) the " breaking strength " of solids, or the force in kilo-megadynes 2 required to break a wire 1 sq. cm. in cross section ; (9) the " crushing strength " of solids, or the force in kilo-megadynes required to crush a block 1 sq. cm. 1 The chances relate only to "accidental errors" ( 24). The chances of " mistakes " are not included. 2 1 kilo-megadyne = 1 02 " tonne weight," or 1 English ton weight, nearly Nos. 8-12.] GENERAL PROPERTIES. 775 in cross section ; (10) the " shearing strength " of solids, or the force in kilo-megadynes required to cut a wire 1 sq. cm. in cross section; (11) the "hard- ness " of -solids according to Mohs' arbitrary scale (page 587) ; (12) the " simple rigidity " of solids, or the force in kilo-megadynes required to make two surfaces 1 cm. square and 1 cm. apart move parallel to one another through a thousandth of a centimetre (.001 cm) , (13) " Young's modulus," or the force in kilo-megadynes required to pull two such surfaces apart through one thousandth of a centimetre (.001 cm) ; (14) the " resilience of volume " or the" pres- sure in kilo-megadynes required to compress a centi- metre cube by one cubic millimetre ; (15) the average cubical " coefficient of expansion" of substances 1 ( 83) between and 100 under a constant pres- sure of 76 cm. of mercury ; (16) the " melting-point " of solids, or the "freezing-point" of liquids on the Centigrade scale : (17) the u boiling-point " of liq- uids, or the " temperature of condensation " of vapors at the atmospheric pressure ; (18) the " criti- cal temperature" of liquids and vapors, that is, the temperature at which the properties of the liquid and its vapor become indistinguishable ; (19) the " criti- cal pressure " of liquids and vapors, that is the pres- sure of the vapor of a liquid at the critical tempera- ture in megadynes per sq. cm.; (20) the "pressure 1 When a change of state takes place between and 100, the averages in question refer only to that part of the interval (0 to 100) in which the substance exists in the state named at the head of the table. 776 EXPLANATION OF TABLES. [Xos. 8-12. of vapors " at 20, in megadynes per sq. cm. ; (21) the average specific heat of substances 1 ( 86) be- tween and 100, under the " constant pressure " of 76 cm. of mercury; (22) the average specific heat of substances 1 between and 100, when pre- vented from expanding ; that is, confined to a " con- stant volume; " (23) the " latent heat of melting " of solids, or the "latent heat of liquefaction" of liquids; that is, the number of units of heat required to con- vert 1 gram of a solid, at its melting-point, into a liquid at the same temperature under a pressure of 1 atmos- phere ; (24) the " latent heat of vaporization " of liq- uids, or the " latent heat of condensation'' of vapors ; that is, the number of units of heat required to con- vert 1 gram of a liquid at the boiling-point into vapor at the same temperature under the atmospheric pressure ; (25) the " heat conductivity" of substances, or the number of units of heat conducted in one second between two opposing faces of a centimetre cube differing 1 in temperature ; (26) the " electri- cal conductivity" of substances, or the current in amperes flowing between two opposing faces of a cen- timetre cube differing 1 microvolt (.000,001 volt) in electrical potential ( 139) ; (27) the " thermo-elec- tric heights" of conductors, or the electromotive force in microvolts developed by a thermo-electric junction of which one element is lead, corresponding to a dif- ference of temperature of 1 ; (28) u electro-chemical equivalents," or the weight in milligrams of various 1 See footnote, page 775. Nos. 8-12.] GENERAL PROPERTIES. 777 elementary substances affected by a current of 10 am- pres in 1 second ; (29) the specific inductive capacity of substances determined by currents alternating several hundred times per second (^[ 256) ; (30) the minimum " extraordinary index of refraction " of opti- cal materials ; (31) the "ordinary index of refraction" of uniaxial crystals, or the " medium'' index of refrac- tion of biaxial crystals ; (32) the maximum " extraor- dinary index of refraction " of different substances these three indices referring to the sodium (D) line ; (33) the ordinary (or medium) " index of disper- sion," or the difference between the ordinary (or medium) indices of refraction for the lines A and H of the solar spectrum ; and finally (34) the solubility of solids in water, expressed in per-cents by weight, and the solubility of gases, also in per-cents by weight, under a pressure of 1 atmosphere. The first line of each table contains factors by which the values given in the column below them may be reduced to the c. G. s. system. Thus the co- efficient of resilience of aluminum (Table 8) is 0.5 (?) X 10 12 = 500,000,000,000(7), and the thermo-electric height of copper is about 4 x 100 = 400 absolute units. TABLE 8 contains the properties of elementary substances. TABLE 9 contains the properties of solids remark- able especially for their strength or for other proper- ties rendering them suitable for building materials or for the construction of machines. 778 EXPLANATION OF TABLES. [No, 14 A. TABLE 9 A contains the properties of certain chemical salts and other substances in ordinary use. TABLE 10 contains the properties of solids remark- able for their optical or other allied properties. TABLE 11 contains properties of liquids. TABLE 12 contains properties of gases and vapors. TABLES 13 A, B, and C, give the (maximum) pres- sure in megadynes per sq. cm. of the vapor arising from various liquids at different temperatures. TABLE 13 A contains substances which are for the most part gaseous at ordinary temperatures. TABLE 13 B contains more or less volatile liquids. TABLE 13 C gives the pressure of the vapor of mercury, sulphur, and water, including the vapor of water arising from sulphuric acid of different strengths. TABLE 13 D contains the " density of steam," or the maximum density of aqueous vapor at different temperatures. TABLE 14 gives the boiling-points of water corres- ponding to different barometric pressures from 68.0 to 77.9 centimetres of mercury reduced to latitude 45 (see Landolt and Bornstein, Table 20). Exam- ple : when the barometer stands at 75.0 cm., water boils at 99.63. TABLE 14 A gives dew-points (calculated from Regnault's data) corresponding to different degrees of temperature and " relative humidity." The ''dew- point" means that temperature at which moisture would (barely) be precipitated out of the air (as when dew is formed) ; the " relative humidity " is the No. 16 A.] METEOROLOGICAL DATA. 779 proportion which the moisture contained in the air at a given temperature bears to the maximum possible amount which it can hold at that temperature. Ex- ample I. : the air of a room at 20 is half saturated with moisture (i. e. the relative humidity = 50 %); required the dew-point. Answer, 9 Centigrade by Table 14 A. Example II. : sea air saturated at 9 with moisture is warmed to 20 ; required the rela- tive humidity. Answer, 50 %. TABLE 15 shows at a given temperature (T) the maximum pressure (P) of aqueous vapor in centi- metres of mercury, the maximum density (D) of aqueous vapor, and the factor (F) by which the differ- ence between the readings of a wet and a dry bulb thermometer must be multiplied in order to find the difference between the dew-point and the tempera- ture (T) of the air. The data have been taken from Kohlrausch, Table 13, Landolt and Bornstein, Tables 18 a and 23, and from Everett's " Units and Physical Constants," Art. 124. The first three columns are an amplification of results contained in Table 13. The last column is useful in hygrometry. Example : if the dry-bulb thermometer reads 20, and the wet-bulb thermometer reads 15, so that the difference be- tween them is 5, we have (since F = 1.8), 5 X 1.8 = 9, which subtracted from 20 gives 11 for the dew-point. TABLE 16 A gives the specific heat of moist air at about 50, corresponding to different dew-points un- der a constant pressure of 76 cm. of mercury. The specific h,eat of dry air at (.2383) is the mean be- 780 EXPLANATION OF TABLES. [No. 16 B. tween the results obtained by Regnault and E. Wiedemann. The other specific heats have been cal- * culated by interpolation between the specific heats of air and of steam (.4805). ' TABLE 15 B gives the velocity of sound in atmos- pheric air, calculated for different degrees of temper- ature and relative humidity, allowing for the effect of moisture on the density of air and on the ratio of the two specific heats of air under constant pressure and under constant volume. The barometric pressure (which has hardly a perceptible influence on the re- sult) was assumed to be 76 cm. of mercury. TABLE 15 C contains coefficients of interdiffusion of gases. The values (due to Maxwell) are taken from Everett's "Units and Physical Constants" (Art. 131). If two reservoirs filled with different gases are connected by a tube 1 cm. long, the numbers in Table 15 C show the mean velocity in cm. per sec. wi'th which a stream of gas flows through the tube from each reservoir into the other. TABLE 16 is intended for the reduction of baro- metric readings, when given in inches, to centimetres. The last line of the table contains " proportional parts" (see under Table 1). TABLES 16 A and B are intended for the reduction of barometric readings in cm. of mercury at to meg- adynes per sq. cm. A is calculated for a value of the acceleration of gravity (#) equal to 980 cm. per sec. per sec. ; B for the value g = 981. The two tables differ by about 10 units in the last place. For values of g between 980 and 981, or just outside of these limits, No. 18 a.] BAROMETRIC TABLES. 781 results may be easily obtained by interpolation. Ex- ample : g = 980.4 ; required the value of 1 atmos- phere (76 cm.) in megadynes per sq. cm. Answer, 1.0126 + 11 x -4 = 1.0130 megadynes per sq. cm. Table 17 gives the elevation in metres above 'the sea-level corresponding to different barometric pres- sures at 10 Centigrade. It has been calculated for dry air in latitude 45 by the formula h = 190790 (log. 76 log. p) (1 + .000,0001 A). It is used in estimating heights by the barometer. Example I. : the mean barometric pressure is 70.0 cm. at the top of a hill rising out of the sea, the sides of the hill having a mean temperature of about 10 ; required the height of the hill. Answer, about 681 metres. Example II. : the barometric pressures at a given instant are 75.1 cm at the foot of a hill, and 74.2 cm. at the top of the hill, the mean temperature being about 10 ; required the height of the hill. Answer, 199 99 = 100 metres. TABLES 17 A and 17 B give corrections in per cent to be added to or subtracted from the results of Table 17, according to the mean temperature and dew-point between the observing stations. Thus for a mean temperature 23 and the dew-point + 8 add 4.6 + 0.4 5.0 % to all results. This would make the height of the hill in Example II., 105 (instead of 100) metres. TABLE 18 a gives the correction in centimetres to be subtracted (on account of expansion) from the reading of 1 a mercurial barometer provided with a 782 EXPLANATION OF TABLES. No. 18 c,J brass scale reaching from its zero in the surface of mercury in the reservoir to the free surface of mer- cury in the tube. In calculating this table, the coeffi- cient of expansion of mercury was assumed to be .000180 + .000,000,036*; the value .000019 was taken for the coefficient of expansion of brass. Ex- ample I. : the mercurial column is 76 cm. long, meas- ured by a brass scale, its temperature is 20, we subtract 0.245 cm., and find 75.755 cm. for the value at 0. Example II. : same as I. except that a glass scale is used ; corrected value the same less .016 cm. T that is, 75.739 cm. TABLE 18 b gives the mean correction to be added to the apparent height of the mercurial column on ac- count of " capillarity," that is, the tendency of capil- lary or in general small tubes to depress a mercurial column (see Everett, 46 A, and Pickering, Table 12) The correction depends, however, not only upon the internal diameter of the barometer tube at the point where the mercury stands, but also upon the height of the " meniscus," which is different according to the direction in which the mercurial column has been moving. Corrections corresponding to differ- ent heights of the meniscus are taken from Kohl- rausch, Table 15, 6th ed. The results in this table differ widely from those quoted in the 2d edition. TABLE 18 c contains corrections for the pressure of mercurial vapor. They have been obtained by aver- aging the results of Regnault, Hagen, and Hertz, quoted in Landolt and Bornstein, Table 27. The [No. 20. DENSITY OF GASES. 783 results in question differ in some cases even in regard to the position of the decimal point. On account of the great discrepancy between the results obtained by different observers, barometric readings, even when corrected by Tables 18 a, 18 6, and 18 0, are significant only as far as hundredths of a centimetre. TABLES 18 d, 18 e, 18 /, and 18 #, contain factors for the reduction of either the density or the volume of a gas to or to 76 cm. Example I. : the density of coal-gas being .0005 at 20 and 75.0 cm., required its density at and 76 cm. Answer, .0005 X 1.0734 X 1.0133 = .00054+. Example II. : the volume of a gas at 20 and 75 cm. is 100 cu. cm. ; required its volume at and 76 cm. Answer, 100 X 0.9316 X 0.9868 = 91.9 cu. cm. If the gas were collected over water at 20 we should subtract 1.74 cm. (see Table 15) from the apparent pressure (75 cm.) and find 73.26 cm. for the pressure of the gas. This would give a factor .9640 instead of .9868, and a result 89.8 cu. cm. in the example above. TABLE 19 contains the density (or weight of 1 cu. cm..) of air corresponding to different tempera- tures and pressures, and has been taken from Kohl- rausch, 2d ed., Table 6. It was calculated from Regnault's observations for latitude 45. TABLE 20 contains corrections for the results in Table 19 to be applied on account of moisture. Ex- ample : required the density of air at 20 and 76 cm. pressure when the dew-point is + 4 Centigrade. Answer, .001204 .000004 = .001200. 784 EXPLANATION OF TABLES. [No. 23. TABLE 20 A contains the weight of air displaced by 1 gram of brass of the density 8.4, and is useful in calculating effective weights ( 64). Example: a body is balanced by 100 grams of brass in air of the density .001200 ; required the effective weight of the body. Answer, 100 grams minus 100 X 0.000143 grams, or 99.9857 grams. TABLE 21 contains factors for reducing apparent weighings with brass weights to vacuo. The factors correspond to different densities of the substance weighed, as well as of the air in which the weighing takes place. Example: a piece of glass of the den- sity 2.5 is balanced by 100 grams of brass, in air of the density .00120 ; required its true weight in vacuo. Answer, 100 X 1.00034 = 100.034 grams. TABLE 22 contains " apparent specific volumes " of water; that is, the space in cubic centimetres occupied by a quantity of water weighing apparently 1 gram when counterpoised in air with brass weights of the density 8.4. The apparent specific volumes corres- pond to different temperatures and different condi- tions of atmospheric density, and are useful especially in calculations of volume or capacity in h} r drostatics. Example : a flask holds apparently 1000 grams (1 litre, nearly) of water at 20, when weighed in air of the density .00120 ; required the capacity of the flask. Answer, 1000 X 1.00279 = 1002.79 cu. cm. TABLE 23 contains true " specific volumes " of water ; that is, the space in cubic centimetres occu- pied at various temperatures by a quantity of water weighing actually 1 gram in vacuo. These values No. 26.] DENSITY OF LIQUIDS. 785 are reciprocals of those in Table 24, and are to be used for the calculation of volumes corresponding to true weights in vacuo. Example : a piece of steel displaces 100 grams of boiling water; required its volume. Answer, 100 X 1.04311 = 104.311 cu. cm. TABLE 23 A gives the true specific volume of mer- cury at different temperatures, and is used like Table 23. In calculating this table Regnault's value (13.596) for the density of mercury at was used, and a coefficient of expansion .000180 + .000,000,036 t. TABLE 23 B gives apparent specific volumes of mercury when balanced by brass weights of the den- sity 8.4 in air of the density .0012. It is used, like Table 22, to calculate volumes and capacities. Exam- ple : the apparent weight of mercury required to fill a tube at 20 is 100 grams; required the capacity of the tube. Answer, 100 X 0.073812 = 7.3812 cu. cm. TABLE 24 contains the density of mercury at dif- ferent temperatures. The values are reciprocals of those contained in Table 23 A. TABLE 25 contains the density of water at differ- ent temperatures. A mean value, 1.00001, was taken for the maximum density of water (Kupffer's value is 1.000013). The relative densities lie between the estimates of Rossetti and Volkmann, founded upon observations by Despretz, Hagen, Jolly, Kopp, Matthiessen, Pierre, and Rossetti. TABLE 26 contains the density of commercial glycerine, calculated from observations made in the Jefferson Physical Laboratory. 786 EXPLANATION OF TABLES. [No. 31 A. TABLE 27 contains the density of dilute alcohol corresponding to different temperatures and different strengths. The values are a mean between results obtained by numerous observers. TABLE 28 gives the density, at 15, of acids and saline solutions corresponding to various strengths, and is useful in making tests with a densimeter. See Storer's " Dictionary of Solubilities." Example : the density of some sulphuric acid is 1.807 at (about) 15 ; required its strength. Answer (about) 88 o/ . TABLE 29 gives the boiling-points of solutions of various strengths estimated by interpolation from data contained in Storer's " Dictionary of Solubilities." It furnishes an independent (and in processes of con- centration by boiling a very convenient) method of estimating the strength of such solutions. Thus a solution of hydrate of sodium boiling at 120 is known to have a strength of about 40 %. TABLE 30 gives the specific heats of solutions of different strengths at about 20. It is useful in cer- tain processes in calorimetry (see ^f^[ 99-100). The numbers were obtained by interpolation from results contained in Landolt and .Bb'rnstein, Tables 71 and 72. Those nearest the observed values are printed in heavier type. TABLE 31 A gives the electrical conductivity of solutions at about 18. It shows the current in am- peres which an electromotive force of one volt would cause to flow through a metre-cube of the solutions in question, or through a voltameter with plates 1 deci- metre square and 1 cm. apart, filled with these solu- tfo. 31 F.] PROPERTIES OF SOLUTIONS. 787 tions, neglecting the effects of polarization. The re- sults must be multiplied by 10- 11 (.000,000,000,01) to reduce them to the c. G. s. system. The relative values of different results are probably accurate within 5 or 10 per cent, but their absolute values are much less reliable. TABLE 31 B gives Refractive and Dispersive in- dices corresponding to the sodium (D) line for solu- tions of different strengths, and was obtained by interpolation from results quoted by Landolt and Bornstein. TABLE 31 C is intended to facilitate the preparation of solutions of any desired strength, and for the cal- culation of per cent contents from the ratio of two constituents. Example : how many parts of salt must be added to 100 of water to make a 20 % solu- tion ? Let A = salt ; B = water, the answer is 25 parts. Example II. : a solution contains 100 parts of sulphuric acid to 150 of water; required its strength. Let A = water, B = sulphuric acid ; the -answer is : 60 % water, 40 % sulphuric acid. TABLE 31 D gives coefficients of diffusion of saline solutions in water at about 20. The values were calculated from Graham's data quoted in Cooke's " Chemical Physics." Example : how much common salt would escape by diffusion into pure water from a 20 / solution in 600,000 seconds through a layer 1.2 cm. thick and 8 sq. cm. in cross section ? Answer, 20 % of 600,000 X 8 X .000,0046 -*- 1.2 = 3.68 grams. TABLES 31 E and F give the rotation in degrees of the plane 'of polarization of different kinds of light 788 EXPLANATION OF TABLES. [No. 31 L. corresponding to the Fraunhofer lines A to H. E re- fers to dilute solutions having such a depth that a beam of light passing through an orifice 1 cm. square meets just one gram of the dissolved substance. 1 F refers to the effect of plates 1 cm. thick. TABLE 31 G relates to the effect of a magnetic field in rotating the plane of polarization of light parallel to the lines of force. TABLE 31 H relates to (1) Magnetic Susceptibil- ity, (2) Saturation, and (3) Permanent Magnetism, that is, the magnetic moment of a unit cube of differ- ent materials (1) in a unit magnetic field, (2) in an infinite magnetic field, and (3) in space after the magnetizing influence has been removed. The re- sults are taken from Everett, and Ganot. TABLE 31 I contains some of Weisbach's results for the coefficient of friction of water moving with dif- ferent velocities through tubes not far from 1 cm. in diameter. The results have been reduced to the the c. G. s. system. TABLE 31 J gives coefficients of friction of solids on solids, taken from De Laharpe's " Notes et Form- ules de 1'Inge'nieur." TABLE 31 K contains coefficients of reflection, ab- sorption, and transmission of radiant heat, from Ganot's Physics. TABLE 31 L contains estimates (by the author) < f the heat radiated at different temperatures by 1 sq. 1 The rotation is proportional, within more or less narrow limits,, to the strength of the solution; but may vary widely outside of these limits. Cases of reversal even occur. See Landolt and Bornstein. No. 33.] HEAT OF COMBUSTION. 78$ cm. of blackened or perfectly radiating surface sur- rounded by perfectly absorbing walls, or space at 0. The table was calculated by the formula q = log.- 1 (.0013 X (t + 273) 1.8249) .034, which was found to reconcile various well-known facts. Example : how much heat is required to main- tain 1 sq. cm. of platinum at its melting-point (1900) for 1 sec. ? Answer, 10 (?) units. 1 TABLES 32 A and 32 B give heats of combustion 2 in oxygen and in chlorine respectively, from data quoted by Everett, by Landolt and Bornstein, and by other authorities. The chemical reactions are not in all cases such as actually take place ; but the table gives the heat which it is supposed would be developed if the reactions did take place. The last column gives the electromotive forces developed by or neces- sary to undo some of the reactions. Example : 2 grams of hydrogen uniting with 16.0 grams of oxy- gen give out 69,000 units of heat, or 34.500 units per gram of hydrogen. This is equivalent to 1440 megergs per mgr. of hydrogen consumed. To de- compose water, an electromotive force of 1.49 volts is required. TABLE 33 gives " heats of combination " involving more complicated chemical reactions than those which take place in simple combustion. 1 This corresponds to 8 + volt-amperes per candle-power. 2 The heat of combustion of many substances can be inferred onl^r from indirect processes. See experiment 38. 790 EXPLANATION OF TABLES. [No. 38. TABLE 34 gives contact differences of electrical po- tential in volts. The data are taken from Everett's "Units and Physical Constants," Art. 206. Example : a piece of zinc is brought into contact with a piece of copper ; required the difference of electrical potential. Answer, the zinc is positively electrified with respect to the copper; the difference of potential is 0.750 volts. TABLE 35 gives the electromotive force in volts of voltaic cells of various sorts. TABLE 36 gives the relation between electromotive forces and the length in mm. of the spark which they produce in ordinary atmospheric air, calculated from Everett, Art. 192. Example: an induction machine produces sparks 2.5 mm. long ; required the difference of potential between its poles at the in- stant. Answer, 9000 volts. Only the first two fig- ures are significant in this answer. TABLES 37 a and b give specific resistances of con- ductors and insulators at 0. The last column gives the per cent of increase of all these resistances due to a rise of temperature of 1 Centigrade. TABLE 38 gives the specific resistances of electro- lytes corresponding to various strengths. The resist- ances are in ohms, and apply to a centimetre cube of the liquid. The probable error of the results is about 10 %. Relative values are probably not so inaccurate. Example : required the resistance of a cubical Dan- iell cell, with a plate of copper 10 X 10 cm., separated lay a layer of 20 % (crystallized) sulphate of copper -5 cm. deep, and by a layer of 20 % (crystallized) sul- ffo. 43.] ARBITRARY SCALES. 791 phate of zinc, also 5 cm. deep, from a plate of zinc 10 X 10 cm. Answer : the resistance of the copper so- lution is 20 X 5 -^- (10 X 10) = 1 ohm ; that of the zinc solution is the same ; hence the resistance of the battery is 2 ohms. TABLE 39 gives a comparison between the Fahren- heit and Centigrade thermometers. Example: 98. 6, F = 37.0, C. TABLE 40 (Pickering, Table 14) gives a comparison of hydrometer scales. Example : 40 Beaum6 for liquids lighter than water corresponds to the density 0.830. TABLE 41 gives lengths of waves of light in air, intermediate between the numerous results quoted by Landolt and Bornstein. The probable error is about 1 unit in the last figure. Example : the Fraun- hofer lines Di and D 2 , together designated ^ (or D), are due to sodium (symbol, Na) and occur in t^g yellow of the spectrum. They correspond to numSlr 50 on Bunsen's scale, to numbers 1003 and 1007 on (Bun- sen and) KirchofFs scale, and have the wave-lengths 0.00005896 cm. and 0.00005890 cm. respectively. TABLE 42 A refers to the imperial wire gauge adopt- ed by the Board of Trade (Stewart & Gee, I. B.). TABLE 42 B gives the Birmingham wire gauge (B. w. G.). The results are intermediate between those quoted in English, French, and German books. The probable error is about 1 unit in the last figure. TABLE 43 gives the number of vibrations corres- ponding to a series of musical notes on the tempered or isotonic 'scale, one half of a semitone apart. The 792 EXPLANATION OF TABLES. [No. 44 C- designation of some of these notes is given in the left-hand or in the right-hand column. The former is to be used for "physical pitch," in which all powers of the number 2 represent the note C ; the right-hand column may be used for notes given by American instruments tuned to " concert pitch. " The numbers between those corresponding to a given note in the first and last columns may be taken to represent the same note according to the old Stutt- gart standard of pitch (A = 440, C = 264). Ex- ample : the " middle C " of. an American piano (in the little octave), makes about 135.6 vibrations per second, and corresponds to C# physical pitch. TABLE 44 A gives reductions of minutes and seconds to thousandths of a degree. The num- ber of minutes is first sought ; the tenths of a degree will be found next to it. Then in the same section of the table (there are 6 sections) the nearest number of seconds is found, and next to it the hundredths and thousandths of a degree. Ex- ample : 2327'13 // = 23. + 0.4 + 0.054, nearly, or 23.454. TABLE 44 B gives the correction to be added to dates in different years to compare them with the year 1891. Thus, Jan. 1, IGh. Om. Os., A. M., 1899; corresponds to Jan. 1, lOh. Om. Os. + Ih. 29m. 28s. A.M. = Jan. 1, llh. 29m. 28s. A.M. 1891. The dec- lination of the sun and the equation of time will, for instance, be the same on these two dates. TABLE 44 C gives the gain of sidereal over mean solar time. No. 50.] ASTRONOMICAL TABLES, ETC. 793 TABLE 44 D gives the sidereal time at Greenwich mean noon for the 10th, 20th, and last day of every month of the year 1891. TABLE 44 E gives the semidiameter of the sun at different times in the year. TABLE 44 F gives the declination of the sun at Greenwich mean noon for the year 1891. The sign of the declination is to be found at the head of the several columns (+ north, south). TABLE 44 G gives the " equation of time " at Greenwich mean noon for the year 1891. The signs + and at the head of the columns and elsewhere show whether the sun is "fast" or "'slow" respect- ively ; + indicates that the sun passes the meridian before noon; after noon. TABLE 44 H gives certain astronomical data relat- ing to the solar system. TABLE 45 gives the Right Ascension and Declina- tion of some of the most important stars. TABLE 46 gives latitudes, longitudes, and eleva- tions of certain important places. TABLES 47 and 48 give respectively the acceleration of gravity and the length of the seconds pendulum corresponding to different latitudes. Example : since the latitude of the Jefferson Physical Laboratory of Harvard College is 4222|' or 42.38, the acceleration of gravity is 980.37 cm. per sec. per sec. TABLE 49 A and 49 B relate to the reduction of measures to and from the c. G. s. system. TABLE 50 contains mathematical and physical con- stants in frequent use. 14 SOURCES OF AUTHORITY. TABLES 1-3 H were prepared, in so far as possible, from existing tables, by rejecting decimal places when necessary. More than 3,000 values (including all doubtful cases) were confirmed or determined by an independent calculation. The results were printed with the ordinary precautions to avoid typographical errors. Tables 4-5 A were obtained by transposing Pickering's tables 6-9. The logarithms of numbers from 1,000 to 10,000, in Table 6, were printed directly from a copy of the tables arranged by Mr. Oliver Whipple Huntington, of Harvard College. The proofs were compared with Bowditch's 5-place tables (Government Printing- office, Washington, 1882). The logarithms of num- bers from 10,000 to 11,000 were obtained by rejecting figures in Chamber's 7-8-place tables. A special in- vestigation was made in cases where the rejected figures were 50 or 500. Stereotype-proofs of all the logarithms were compared with the tables of Gauss. The table of probabilities as far as 5.0 is due to Chauvenet. The remainder of the table was the result of special calculation. SOURCES OF AUTHORITY. 795 The physical tables (Nos. 8 to 50) were compiled for the most part by the aid of results contained in Landolt and Bornstein's "Physico-Chemical Tables," 1 to which the reader is referred for a full exposition of the evidence upon which the selection of values has been made. The author wishes to thank Professors Landolt and Bornstein for looking over his manu- script, for several useful suggestions, and for their kind permission to utilize their results. The author has quoted numerous data from Ever- ett's " Units and Physical Constants " (Macmillan, 1886). He has also made use of information given by Professor Everett in choosing the unusually low value (4.17 X 10 7 ) for the mechanical equivalent of heat. Among other books from which results have been taken are the following : Cooke's Chemical Philos- ophy, Deschanel's Natural Philosophy, Ganot's Phy- sics, Hoffmann's Tabellen fiir Chemiker, Kohlrausch's Leitfaden der Praktischen Physik, das Nautisches Jahrbuch, 1891, Pickering's Physical Manipulation, Stewart and Gee's Practical Physics, Storer's Dic- tionary of Solubilities, Trowbridge's New Physics, and Weisbach's Mechanics. These and other sources of authority have been acknowledged in connection with the explanation of the tables above , but it was found impossible, in the limited space which could be devoted to the tables, to give authority for the separate data. It was, 1 Physikahsch-Chemische Tabellen von Dr H. Landolt und Dr. Richard Bornstein, Professoren. Verlag von Julius Springer, Montbi- jou Platz 3, Berlin. 796 SOURCES OF AUTHORITY. moreover, considered inexpedient to present to stu- dents, who would naturally be unaccustomed to weighing evidence, the conflicting statements from which the probable values of many of the physical constants have to be estimated by scientific men. Care has been taken, in all such cases, to give re- sults intermediate between those obtained by different observers. To do this, a considerable number of figures was sometimes required ; but the use of fig- ures, not really significant, has been in so far as pos- sible avoided. The last figure quoted in the results is in general the only one in regard to which a differ- ence of opinion was found to exist. It is regretted that, owing to the necessity of entrusting the composition to foreign printers, obvi- ous imperfections of type will be found, especially in the mathematical tables. In the expectation of re- printing these tables at no distant date, corrections and suggestions will be most gladly received. Table i. Proportional Parts. 797 iflV * *- 4* 4CT /ur 50 5 10 15 20 25 30 35 4045 1 1 1 1 1 1 51 5 10 15 20 26 31 36 41 46 2 1 1 1 1 1 2 2 52 5 10 16 21 26 31 36 42 47 3 1 1 1 2 2 2 2 3 53 5 11 16 21 27 32 37 42 48 4 1 1 2 2 2 3 3 4 54 5 11 16 22 27 32 38 43 49 5 1 2 2 3 3 4 4 5 55 6 11 17 22 28 33 39 44 50 6 1 2 2 3 4 4 5 5 56 6 11 17 22 28 34 39 45 50 7 1 2 3 4 4 5 6 6 57 6 11 17 23 29 34 40 46 51 8 2 2 3 4 5 6 6 7 58 6 12 17 23 29 35 41 46 52 9 2 3 4 5 5 6 7 8 59 6 12 18 24 30 35 41 47 53 10 2 3 4 5 6 7 8 9 60 6 12 18 24 30 36 42 48 54 11 2 3 4 6 7 8 9 10 61 6 12 18 24 31 37 43 49 55 12 2 4 5 6 7 8 10 11 62 6 12 19 25 31 37 43 50 56 13 3 4 5 7 8 9 10 12 63 6 13 19 25 32 38 44 50 57 14 3 4 6 7 8 10 11 13 64 6 13 19 26 32 38 45 51 58 15 2 3 5 6 8 9 11 12 14 65 7 13 20 26 33 39 46 52 59 16 2 3 5 6 8 10 11 13 14 66 7 13 20 26 33 40 46 53 59 17 2 3 5 7 9 10 12 14 15 67 7 13 20 27 34 40 47 54 60 18 2 4 5 7 9 11 13 14 16 68 7 14 20 27 34 41 48 54 61 19 2 4 6 8 10 11 13 15 17 69 7 14 21 28 35 41 48 55 62 20 2 4 6 8 10 12 14 16 18 70 7 14 21 28 35 42 49 56 63 21 2 4 6 8 11 13 15 17 19 71 7 14 21 28 36 43 50 57 64 22 2 4 7 9 11 13 15 18 20 72 7 14 22 29 36 43 50 58 65 23 2 5 7 9 12 14 16 18 21 73 7 15 22 29 37 44 51 58 66 24 2 5 7 10 12 14 17 19 22 74 7 15 22 30 37 44 52 59 67 25 3 5 8 10 13 15 18 20 23 75 8 15 23 30 38 45 53 60 68 26 3 5 8 10 13 16 18 21 23 76 8 15 23 30 38 46 53 61 68 27 3 5 8 11 14 16 19 22 24 77 8 15 23 31 39 46 54 62 69 28 3 6 8 11 14 17 20 22 25 78 8 16 23 31 39 47 55 62 70 29 3 6 9 12 15 17 20 23 26 79 8 16 24 32 40 47 55 63 71 30 3 6 9 12 15 18 21 24 27 80 8 16 24 32 40 48 56 64 72 31 3 6 9 12 16 19 22 25 28 81 8 16 24 32 41 49 57 65 73 32 3 6 10 13 16 19 22 26 29 82 8 16 25 33 41 49 57 66 74 33 ^ 7 10 13 17 20 23 26 30 83 8 17 25 33 42 50 58 66 75 34 3 7 10 14 17 20 24 27 31 84 8 17 25 34 42 50 59 67 76 35 4 7 11 14 18 21 25 28 32 85 9 17 26 34 43 51 60 68 77 36 4 7 11 14 18 22 25 29 32 86 9 17 26 34 43 52 60 69 77 37 4 7 11 15 19 22 26 30 33 87 9 17 26 35 44 52 61 70 78 38 4 8 11 15 19 23 27 30 34 88 9 18 26 35 44 53 62 70 79 39 4 8 12 16 20 23 27 31 35 89 9 18 27 36 45 53 62 71 80 40 4 8 12 16 20 24 28 32 36 90 9 18 27 36 45 54 63 72 81 41 4 8 12 16 21 25 29 33 37 91 9 18 27 36 46 55 64 73 82 42 4 8 13 17 21 25 29 34 38 92 9 18 28 37 46 55 64 74 83 43 4 9 13 17 22 26 30 34 39 93 9 19 28 37 47 56 65 74 84 44 4 9 13 18 22 26 31 35 40 94 9 19 28 38 47 56 66 75 85 45 5 9 14 18 23 27 32 36 41 95 10 19 29 38 48 57 67 76 86 46 5 9 14 18 23 28 32 37 41 96 10 19 29 38 48 58 67 77 86 47 5 9 14 19 24 28 33 38 42 97 10 19 29 39 49 58 68 78 87 48 5 10 14 19 24 29 34 38 43 98 10 20 29 39 49 59 69 78 88 49 5 10 15 20 25 29 34 39 44 99 10 20 30 40 50 59 69 79 89 50 5 10 15 20 25 30 35 40 45 100 10 20 30 40 50 60 70 80 90 798 Powers. Table 2. so. a - f R n e r c a r'- re <*' *** .r., a. Recip- 6. Square - , p . flO, rocaj Root c. Square 4. Cubi CO 0.00 50 .0200 7.07 2500 125000 1 1.000 1.00 1 1 51 196 7.14 2601 132651 2 0.500 1.41 4 8 52 192 7.21 2704 140608 3 333 1.73 9 27 53 189 7.2S 2809 148877 4 250 2.00 16 64 54 185 7.35 2916 157464 5 0.200 2.24 25 125 55 .0182 7.42 3025 166375 6 167 2.45 36 216 56 179 7.48 3136 175616 7 143 2.65 49 343 57 175 7.55 3249 185193 8 125 2.83 64 512 58 172 7.62 3364 195112 9 111 3.00 81 729 59 169 7.68 3481 205379 10 0.100 3.16 100 1000 60 .0167 7.75 3600 21COOO 11 .0909 3.32 121 1331 61 164 7.81 3721 220981 12 833 346 144 1728 62 161 7.87 3844 238328 13 769 3.61 169 2197 63 159 7.94 3969 250047 14 714 3.74 196 2744 64 156 8.00 4096 262144 15 .0607 3.87 225 3375 65 .0154 8.06 4225 274625 16 625 4.00 256 4096 66 152 8.12 4356 287496 17 588 4.12 289 4913 67 149 8.19 4489 300763 18 556 4.24 324 5832 68 147 8.25 4624 314432 19 526 4.36 361 6859 69 145 8.31 4761 328509 20 .0500 4.47 400 8000 70 .0143 8.37 4900 343000 21 476 4.58 441 9261 71 141 8.43 5041 357911 22 455 4.69 484 10648 72 139 8.49 5184 373248 23 435 4.80 529 12167 73 137 8.54 5329 389017 24 417 4.90 576 13824 74 135 860 5476 405224 25 .0400 5.00 625 15625 75 0133 8.66 5625 421875 26 385 5.10 676 17576 76 132 8.72 5776 438976 27 370 5.20 729 19683 77 130 8.77 5929 456533 28 357 5.29 784 21952 78 128 883 6084 474552 29 345 5.39 841 24389 79 127 8.89 6241 493039 30 .0333 5.48 900 27000 80 .0125 8.94 6400 512000 31 323 5.57 961 29791 81 123 9.00 6561 531441 32 313 5.66 1024 32768 82 122 9.06 6724 551368 33 303 5.74 1089 35937 83 120 9.11 6889 571787 34 294 5.83 1156 39304 84 119 9.17 7056 592704 35 .0286 5.92 1225 42875 85 .0118 9.22 7225 614125 36 278 6.00 1296 40656 86 116 9.27 7396 63.6056 37 270 6.08 1369 50653 87 115 9.33 7569 658503 38 263 6.16 1444 54872 88 114 9.38 7744 681472 39 256 6.24 1521 59319 89 112 9.43 7921 704969 40 .0250 6.32 1600 64000 90 .0111 9.49 8100 729000 41 244 640 1681 68921 91 110 9.54 8281 753571 42 238 6.48 1764 74088 92 109 9.59 8464 778688 43 233 6.56 1849 79507 93 m 9.64 8649 804357 44 227 6.63 1936 85184 94 106 9.70 8836 830584 45 .0222 6.71 2025 91125 95 .0105 9.75 9025 857375 46 217 6.78 2116 97336 96 104 9.80 9216 884736 47 213 6.86 2209 103823 97 103 9.85 9409 912673 48 208 6.93 2304 110592 98 102 9.90 9604 941192 49 204 7.00 2401 117649 99 101 9.95 9301 970299 50 .0200 7.07 2500 125000 100 .0100 10.00 10000 1000000 Table 2. Circles, etc. 799 Diam- eter ..Log- arithm /. Circum- ference g. Area of Circle h. Volume of Sphere Diam- eter e. Log- arithm f. Ciroum- ference g. Area h. of Circle of Volume Sphere .0 CO 0.00 0.00 .000 5.0 0.699 15.71 19.6 65 .1 rooo 31 01 .001 5.1 708 16.02 20.4 69 .2 301 63 03 .004 5.2 716 16.34 21.2 74 .3 477 94 07 .014 5.3 724 16.65 22.1 78 .4 602 1.26 13 .034 5.4 732 16.96 22.9 82 .5 T.699 1-57 0.20 .065 5.5 0.740 17.28 23.8 87 .6 778 1.88 28 .113 5.6 748 17.59 24.6 92 .7 845 2.20 38 .180 5.7 756 17.91 25.5 97 .8 903 2.51 50 .268 5.8 763 18.22 26.4 102 .9 954 2.83 64 .382 5.9 771 18.54 27.3 108 1.0 0.000 3.14 0.79 0.52 6.0 0.778 18.85 28.3 113 M 041 3.46 0.95 70 6.1 785 19.16 29,2 119 1.2 079 3.77 1.13 90 6.2 792 19.48 30.2 125 1.3 114 4.08 1.33 1.15 6.3 799 19.79 31.2 131 1.4 146 4.40 1.54 1.44 6.4 806 20.11 32.2 137 1.5 0.176 4.71 1.77 1.77 6.5 0.813 20.42 33.2 144 1.6 204 5.03 2.01 2.14 6.6 820 20.73 34.2 151 1.7 230 5.34 2.27 2.57 6.7 826 21.05 35.3 157 1.8 255 5.65 2.54 3.05 6.8 833 21.36 36.3 165 1.9 279 5.97 2.81 3.59 6.9 839 21.68 37.4 172 2.0 0.301 6.28 3.14 4.19 7.0 0.845 21.99 38.5 180 2.1 322 6.60 3.46 4.85 7.1 851 22.31 39.6 187 2.2 342 6.91 3.80 5.58 7.2 857 22.62 40.7 195 2.3 362 7.23 4.15 6.37 73 863 22.93 41.9 204 2.4 380 7.54 4.52 7.24 7.4 869 23.25 43.0 212 2.5 0.398 7.85 4.91 8.2 7.5 0.875 23.56 44.2 221 2.6 415 8.17 5.31 9.2 7.6 881 23.88 45.4 230 2.7 431 8.48 5.73 10.3 7.7 886 24.19 46.6 239 2.8 447 8.80 6.16 11.5 7.8 892 24.50 47.8 248 2.9 462 9.11 661 12.8 7.9 898 2482 49.0 258 3.0 0.477 9.42 7.C7 14.1 8.0 0.903 25.13 50.3 268 3.1 491 9.74 7.55 15.6 81 908 25.45 51.5 278 3.2 505 10.05 8.04 17.2 8.2 914 25.76 52.8 289 3.3 519 10.37 8,55 18.8 8.3 919 26.08 541 299 3.4 531 10.68 9.08 20.6 8.4 924 2639 55.4 310 3.5 0.544 11.00 9.6 22.4 8.5 0.929 26.70 56.7 322 3.6 556 11.31 102 24.4 8.6 934 27.02 58.1 333 3.7 568 11.62 10.8 26.5 8.7 940 27,33 59.4 345 3.8 580 11.94 11.3 28.7 8.8 944 27.65 60.8 357 3.9 591 12.25 11.9 31.1 8.9 949 27.96 62.2 369 4.0 0.602 12.57 12.6 33.5 9.0 0.954 28.27 63.6 382 4.1 613 12.88 13.2 36.1 9.1 959 28.59 65.0 395 4.2 623 13.19 13.9 38.8 9.2 964 28.90 66.5 408 4.3 633 13.51' 14.5 41.6 9.3 968 29.22 67.9 421 4.4 643 13.82 15.2 44.6 9.4 973 29.53 69.4 435 4.5 0.653 14.14 15.9 47.7 9.5 0.978 29.85 70.9 449 4.6 663 14.45 16.6 51.0 9.6 982 30.16 72.4 463 4.7 672 14.77 173 54.4 9.7 987 30.47 73.9 478 4.8 681 15.08 18.1 57.9 9.8 991 30.79 75.4 493 4.9 690 15.39 18.9 61.6 99 996 31.10 77.0 508 5.0 0.699 15.71 19.6 65.4 10.0 1.000 31.42 78.5 524 800 Trigonometric Functions. Tables. o. Angle. 6. Tangent, e. Arc. d. Chord, e. Sim. /".Cosine. g. Rate of h. Secant, i. Compli- Vibration. oient. 0.000 0.000 0.000 0.000 1.000 1.00000 1.000 90 1 017 017 017 017 1.000 1.00000 1,000 89 2 035 035 035 035 0.999 0.99998 1.001 88 3 052 052 052 052 999 99996 1.001 87 4 070 070 070 070 998 99992 1.002 86 5 0.087 0.087 0.087 0.087 0.996 0.99988 1.004 85 6 105 105 105 105 995 99983 1.006 84 7 123 122 122 122 993 99977 1.008 83 8 141 140 140 139 990 99970 1.010 82 9 158 157 157 156 988 99961 L012 81 10 0.176 0.175 0.174 0.174 0.985 0.99952 1.015 80 11 194 192 192 191 982 99942 1.019 79 12 213 209 209 208 978 99931 1.022 78 13 231 227 226 225 974 99920 1.026 77 14 249 244 244 242 970 99907 1.031 76 15 0.268 0.262 0.261 0.259 0.966 0.99893 1.035 75 16 287 279 278 3,76 961 99878 1.040 74 17 306 297 296 292 956 99862 1.046 73 18 325 314 313 309 951 99846 1.051 72 19 344 332 330 326 946 99828 1.058 71 20 0.364 0.349 0.347 0.342 0.940 0.99810 1.064 70 21 384 367 364 35JS 954 99790 1.071 69 22 404 384 382 3/5 927 99770 1-079 68 2S 424 401 399 391 921 99749 1.086 67 24 445 419 416 407 914 99726 1.095 66 25 0.466 0.436 0.433 0.423 0.906 0.99703 1.103 65 26 488 454 450 438 899 99678 1.113 64 27 no 471 467 454 891 99653 1.122 63 28 532 489 484 469 883 99627 1.133 62 29 554 506 501 485 875 99600 1.143 61 30 0.577 0.524 0.518 0.500 0.866 0.99572 1.155 60 31 601 541 534 515 857 99543 1.167 59 32 625 559 551 530 848 99513 1.179 58 33 649 576 568 545 839 99482 1.192 57 34 675 593 585 559 829 99450 1.206 56 35 0.700 0.611 0.601 0.574 0.819 0.99417 1.221 55 36 727 628 618 588 809 99384 1.236 54 37 754 646 635 602 799 99349 1.252 53 38 781 663 651 616 788 99314 1.269 52 39 810 681 668 629 777 99277 1.287 51 40 0.839 0.698 0.684 0.643 0.766 0.99239 1.305 50 41 869 716 700 656 755 99200 1.325 49 42 900 733 717 669 743 99161 1.346 48 43 933 750 733 682 731 99121 1.367 47 44 966 768 749 695 719 99079 1,390 46 45 1.000 0.785 0.765 0.707 0.707 0,99037 1.414 45* fable 3. Trigonometric Functions. 801 a. Angli. 6. Tangent. t. Are. d. Chord. e. Sill. f. Cosini. g. Coversini h. Secant. . Compli- ment. 45 1.000 0.785 0.765 0.707 0.707 0.293 1.414 45 46 1.036 0.803 781 719 695 281 1.440 44 47 1.072 0,820 797 731 682 269 1.466 43 48 1.111 0.838 813 743 669 257 1.494 42 49 1.150 0.855 829 755 656 245 1.524 41 50 1.192 0.873 0.845 0.766 0.643 0.234 1.556 40 51 1.235 0.890 861 777 629 223 1.589 39 52 1.280 0.908 877 788 616 212 1.624 38 53 1.327 0,925 892 799 602 201 1.662 37 54 1.376 0.942 908 809 588 191 1.701 36 55 1.428 0.960 0.923 0.819 0.574 0.181 1.743 35 56 1.483 0.977 939 829 559 171 1.788 34 57 1.540 0,995 954 839 545 161 1.836 33 58 1.600 1.012 970 848 530 152 1.887 32 59 1.664 1.030 985 857 515 143 1942 31 60 1.732 1.047 1.000 0.866 0.500 0.134 2.000 30 61 1.804 1.065 1.015 875 485 125 2.003 29 62 1.881 1.082 1.030 883 469 117 2.130 28 63 1.963 1.100 1.045 891 454 109 2.203 27 64 2.050 1.117 1.060 899 438 101 2.281 26 65 2.145 1.134 1.075 0.906 0.423 0.094 2.366 25 66 2.246 1.152 1.089 914 407 086 2.459 24 67 2.356 1.169 1.104 921 391 079 2-559 23 68 2.475 1.187 1.118 927 375 073 2.669 22 69 2.605 1.204 1.133 934 358 066 2.790 21 70 2.747 1.222 1.147 0.940 0.342 0.060 2.924 20 71 2.904 1.239 1.161 946 326 054 3.072 19 72 3.078 1.257 1.176 951 309 049 3.236 18 73 3.271 1.274 1.190 956 292 044 3.420 17 74 3.487 1.292 1.204 961 276 039 3.628 16 75 3.732 1.309 1218 0.966 0.259 0.034 3.864 15 76 4.011 1.326 1.231 970 242 030 4.134 14 77 4.331 1.344 1.245 974 225 026 4.445 13 78 4,705 1.361 1.259 978 208 022 4.810 12 79 5.145 1.379 1.272 982 191 01S 5.241 11 80 5.671 1.396 1.286 0985 0.174 0.0152 5.759 10 81 6.314 1414 1299 988 156 0123 6.392 9 82 7.115 1.431 1.312 990 139 0097 7.185 8 83 8.144 1.449 1.325 993 122 0075 8.206 7 84 9.514 1.466 1.338 995 105 0055 9.567 6 85 11.43 1.484 1.351 0.996 0.087 0.00381 11.47 5 86 14.30 1.501 1364 998 070 00244 14.34 4 87 19.08 1.518 1.377 999 052 00137 19.11 3 88 28.64 1.536 1.389 999 035 00061 28.65 2 89 57.29 1.553 1402 1.000 017 00015 57.30 1 90 00 1.571 1.414 1.000 0.000 0.00000 00 802 Reciprocals. Table 3, A. M 128456789 Bit. 1.0 1.0000 9901 9804 9709 9615 9524 9434 9346 9259 9174 1.1 0.9091 9009 8929 8850 8772 8696 8621 8547 8475 8403 76 1.2 8333 8264 8197 8130 8065 8000 7937 7874 7813 7752 6b 1.3 7692 7634 7576 7519 7463 7407 7353 7299 7246 7194 1.4 7143 7092 7042 6993 6944 6897 6849 6803 6757 6711 1.5 0.6667 6623 6579 6536 6494- 6452 6410 6369 6329 6289 " 1.6 6250 6211 6173 6135 6098 6061 6024 5988 5952 5917 1.7 5882 5848 5814 5780 5747 5714 5682 5650 5618 5587 1.8 5556 5525 5495 5464 5435 5405 5376 5348 5319 5291 1.9 5263 5236 5208 5181 5155 5128 5102 5076 5051 5025 2.0 0.5000 4975 4950 4926 4902 4878 4854 4831 4808 4785 " 2.1 4762 4739 4717 4695 4673 4651 4630 4608 4587 4566 " 2.2 4545 4525 4505 4484 4464 4444 4425 4405 4386 4367 80 2.3 4348 4329 4310 4292 4274 4255 4237 4219 4202 4184 18 2.4 4167 4149 4132 4115 4098 4082 4065 4049 4032 4016 1T 2.5 0.4000 3984 3968 3953 3937 3922 3906 3891 3876 3861 w 2.6 3846 3831 3817 3802 3788 3774 3759 3745 3731 3717 " 2.7 3704 3690 3676 3663 3650 3636 3623 3610 3597 3584 13 2.8 8571 3559 3546 3534 3521 3509 3496 3484 3472 3460 " 2.9 3448 3436 3425 3413 3401 3390 3378 3367 3356 3344 3.0 0.3333 3322 3311 3300 3289 3279 3268 3257 3247 3236 " 3.1 3226 3215 3205 3195 3185 3175 3165 3155 3145 3135 3.2 3125 3115 3106 3096 3086 3077 3067 3058 3049 3040 * 3.3 3030 3021 3012 3003 2994 2985 2976 2967 2959 2950 3.4 2941 2933 2924 2915 2907 2899 2890 2882 2874 2865 3.5 0.2857 2849 2841 2833 2825 2817 2809 2801 2793 2786 8 3.6 2778 2770 2762 2755 2747 2740 2732 2725 2717 2710 3.7 2703 2695 2688 2681 2674 2667 2660 2653 2646 2639 7 3.8 2632 2625 2618 2611 2604 2597 2591 2584 2577 2571 3.9 2564 2558 2551 2545 2538 2532 2525 2519 2513 2506 4.0 0.2500 2494 2488 2481 2475 2469 2463 2457 2451 2445 6 4.1 2439 2433 2427 2421 2415 2410 2404 2398 2392 2387 4.2 2381 2375 2370 2364 2358 2353 2347 2342 2336 2331 4.3 2326 2320 2315 2309 2304 2299 2294 2288 2283 2278 4.4 2273 2268 2262 2257 2252 2247 2242 2237 2232 2227 * 4.5 0.2222 2217 2212 2208 2203 2198 2193 2188 2183 2179 4.6 2174 2169 2165 2160 2155 2151 2146 2141 2137 2132 4.7 2128 2123 2119 2114 2110 2105 2101 2096 2092 2088 4.8 2083 2079 2075 2070 2066 2062 2058 2053 2049 2045 4.Q 2041 2037 2033 2028 2024 2020 2016 2012 2008 2004 5.0 0.2000 1996 1992 1988 1984 1980 1976 1972 1969 1965 * 5.1 1961 1957 1953 1949 1946 1942 1638 1934 1931 1927 5.2 1923 1919 1916 1912 1908 1905 1901 1898 1894 1890 5.3 1887 1883 1880 1876 1873 1869 1866 1862 1859 1855 5.4 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 5.5 0.1818 1815 1812 1808 1805 1802 1799 1795 1792 1789 5.6 1786 1783 1779 1776 1773 1770 1767 1764 1761 1757 5.7 1754 1751 1748 1745 1742 1739 1736 1733 1730 1727 5.8 1724 1721 1718 1715 1712 1709 1706 1704 1701 1698 5.9 1695 1692 1689 1686 1684 1681 1678 1C75 1672 1669 <>.0 0.1667 1664 1661 1658 1656 1653 1650 1647 1645 1642 Table s, A. Reciprocals. 803 M 0123456789 6.0 0.16667 16639 16611 16584 16556 16529 16502 16474 16447 16420 27 6.1 16393 16367 16340 16313 16287 16260 16234 16207 16181 16155 26 6.2 16129 16103 16077 16051 16026 16000 15974 15949 15924 15898 8e 6.3 15873 15848 15823 15798 15773 15748 15723 15699 15674 15649 25 6.4 15625 15601 15576 15552 15528 15504 15480 15456 15432 15408 24 6.5 0.15385 J5361 15337 15314 15291 15267 15244 15221 15198 15175 23 6.6 15152 15129 15106 15083 15060 15038 15015 14992 14970 14948 23 6.7 14925 14903 14881 14859 14837 14815 14793 14771 14749 14728 22 6.8 14706 14684 14663 14641 14620 14599 14577 14556 14535 14514 21 6.9 14493 14472 14451 14430 14409 14388 14368 14347 14327 14306 21 7.0 0.14286 14265 14245 14225 14205 14184 14164 14144 14124 14104 20 7.1 14085 14065 14045 14025 14006 13986 13966 13947 13928 13908 7.2 13889 13870 13850 13831 13812 13793 13774 13755 13736 13717 19 7.3 13699 13680 13661 13643 13624 13605 13587 13569 13550 13532 7.4 13514 13495 13477 13459 13441 13423 13405 13387 13369 13351 18 7.5 0.13333 13316 13298 13280 13263 13245 13228 13210 13193 13175 7.6 13158 13141 13123 13106 13089 13072 13055 13038 13021 13004 " 7.7 12987 12970 12953 12937 12920 12903 12887 12870 12853 12837 7.8 12821 12804 12788 12771 12755 12739 12723 12706 12690 12674 l6 7.9 12658 12642 12626 12610 12594 12579 12563 12547 12531 12516 8.0 0.12500 12484 12469 12453 12438 12422 12407 12392 12376 12361 8.1 12346 12330 12315 12300 12285 12270 12255 12240 12225 12210 I5 8.2 12195 12180 12165 12151 12136 12121 12107 12092 12077 12063 8.3 12048 12034 12019 12005 11990 11976 11962 11947 11933 11919 8.4 11905 11891 11876 11862 11848 11834 11820 11806 11792 11779 " 8.5 0.11765 11751 11737 11723 11710 11696 11682 11669 11655 11641 8.6 11628 11614 11601 11587 11574 11561 11547 11534 11521 11507 8.7 11494 11481 11468 11455 11442 11429 11416 11403 11390 11377 13 8.8 11364 11351 11338 11325 11312 11299 11287 11274 11261 11249 8.9 11236 11223 11211 11198 11186 11173 11161 11148 11136 11123 900.11111 11099 11086 11074 11062 11050 11038 11025 11013 11001 9.1 10989 10977 10965 10953 10941 10929 W917 10905 10893 10881 12 9.2 10870 10858 10846 10834 10823 10811 / 10799 10787 10776 10764 9.3 10753 10741 10730 10718 10707 10695 10684 10672 10661 10650 94 10638 10627 10616 10604 10593 10582 10571 10560 10549 10537 9.5 0.10526 10515 10504 10493 10482 10471 10460 10449 10438 10428 9.6 10417 10406 10395 10384 10373 10363 10352 10341 10331 10320 97 10309 10299 10288 10277 10267 10256 10246 10235 10225 10215 9.8 10204 10194 10183 10173 10163 10152 10142 10132 10121 10111 99 10101 10091 10081 10070 10060 10050 10040 10030 10020 10010 10.00.10000.09990 9980 9970 9960 9950 9940 9930 9921 9911 10.1 .09901 9891 9881 9872 9862 9852 9843 9833 9823 9814 10.2 9804 9794 9785 9775 9766 9756 9747 9737 9728 9718 10.3 9709 9699 9690 9681 9671 9662 9653 9643 9634 9625 10.4 9615 9606 9597 9588 9579 9569 9560 9551 9542 9533 10.50.09524 9515 9506 9497 9488 9479 9470 9461 9452 9443 10.6 9434 9425 9416 9407 9398 9390 9381 9372 9363 9355 10.7 9348 9337 9328 9320 9311 9302 9294 9285 9276 9268 10.8 9259 9251 9242 9234 9225 9217 9208 9200 9191 9183 10.9 9174 9166 9158 9149 9141 9132 9124 9116 9107 9099 11.00.09091 9083 9074 9066 9058 9050 9042 9033 9025 9017 804 Squares. Table a. c, J\s 1 2 34 567 89 . 1.0 1.000 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 21 1.1 1.210 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.2 1.440 1.464 1.488 1.513 1.538 1.563 1.588 1.613 1.688 1.664* 1.3 1.690 1.716 1.742 1.769 1.796 1.823 1.850 1.877 1.904 1.932 " 1.4 1.960 1.988 2.016 2.045 2.074 2.103 2.132 2.161 2.190 2.2*20 3S 1.5 2.250 2.280 2.310 2.341 2.372 2.403 2-434 2.465 2.496 2.528 81 1.6 2.560 2 592 2.624 2.657 2.690 2.723 2.756 2.789 2.822 2.856 88 1> 2.890 2.924 2.958 2.993 3.028 3.063 3.098 3.133 3.168 3.204 * 1.8 3.240 3.276 3.312 3.349 3.386 3.423 3.460 3.497 3.534 3.572 87 1.0 3.610 3.64$ 1686 3.725 3.764 3.803 3.842 3.881 3.920 3.960 89 2.0 4.000 4.040 4.080 4.121 4.162 4.203 4.244 4.285 4.326 4.368 tt 2.1 4.410 4.452 4.494 4.537 4.580 4.623 4.666 4.709 4.752 4.796 4| 2.2 4.840 4.884 4.928 4.973 5.018 5.063 5.108 5.153 5.198 5.244 2.3 5.290 5.336 5.382 5.429 5.476 5.523 5.570 5.617 5.664 5.712* 2.4 5.760 5.808 5.856 5.905 5.954 6.003 6.052 6.101 6.150 6.200 2.5 6.250 6.300 6.350 6.401 6.452 6.503 6.554 6.605 6.656 6.708 M 2.6 6.760 6.812 6.864 6.917 6.970 7.023 7.076 7.129 7.182 7 236 63 2.7 7.290 7.344 7.398 7.453 7.508 7.563 7.618 7.673 7.728 7.784" 2.8 7.840 7.896 7.952 8.009 8.066 8.123 8,180 8.237 8.294 8 352 67 2.9 8.410 8.468 8.526 8.585 8.644 8.703 8.762 8.821 8.880 8.940 69 3.0 9.000 9.060 9.120 9.181 9.242 9.303 9.364 9.425 9.486 9.548 61 3.1 9.610 9.672 9.734 9.797 9.860 9.923 9.986 10.05 10.11 10.18- 3.2 10.24 10.30 10.37 10.43 10.50 10.56 10.63 10.69 10.76 10.82 3.3 10.89 10.96 11.02 11.09 11.16 11.22 11.29 11.36 11.42 11.49 3.4 11.56 11.63 11.70 11.76 11.83 11.90 11.97 12.04 12.11 12.18 3.5 12.25 12.32 12.39 12.46 12.53 12.60 12.67 12.74 12.82 12.89 7 3.6 12.96 13.03 13.10 13.18 13.25 13.32 13.40 13.47 13.54 13.62 3.7 13.69 13.76 13.84 13.91 13.99 14.06 14.14 14.21 14.29 14.36 3.8 14.44 14.52 14.59 14.67 1475 14.82 14.90 14.98 15.05 15.13 3.0 15.21 15.29 15.37 15.44 15.52 15.60 15.68 15.76 15.84 15.92 4.0 16.00 16.08 16.16 16.24 16.32 16.40 16.48 16.56 16.65 16.73 8 4.1 16.81 16.89 16.97 17.06 17.14 17.22 17.31 17.39 17.47 17.56 4.2 17.64 17.72 17.81 17,89 17.98 18.06 18.15 18.23 18.32 18.40 4.3 18.49 18.58 18.66 18.75 18.84 18.92 19.01 19.10 19.18 19.27 4.4 19.36 19.45 19.54 19.62 19.71 19.80 19.89 19.98 20.07 20.16 4.5 20.25 20.34 20.43 20.52 20.61 20.70 20.79 20.88 20.98 21.07 9 4.6 21.16 21.25 21.34 21.44 21.53 21.62 21.72 21.81 21.90 22.00 4.7 22.09 22.18 22.28 2237 22.47 22.56 22.66 22.75 22.85 22.94 4.8 23.04 23.14 23.23 23.33 23.43 23.52 23.62 23.72 23.81 23.91 4.9 24.01 24.11 24.21 24.30 2440 24.50 24.60 24.70 24.80 24.90 5.0 25.00 25.JO 25.20 25.30 25.40 25.50 25.60 25.70 25.81 25.91 *> 5.1 26.01 26.11 26.21 26.32 26.42 26.52 26.63 26.73 26.83 26.94 5.2 27.04 27.14 27.25 27.35 27.46 27.56 27.67 27.77 27.88 27.98 5.3 28.09 28.20 28.30 28.41 28.52 28.62 28.73 28.84 28.94 29.0c 5.4 29.16 29.27 29.38 29.48 29.59 29.70 29.81 29.92 30.03 30.14 5.5 30.25 30.36 30.47 30.58 30.69 30.80 30.91 31.02 31.14 31.25 5.6 31.36 31.47 31.58 31.70 31.81 31.92 324)4 32.15 32.26 32.38 5.7 32.49 32.60 32.72 32.83 32.95 33.06 33.18 33.29 33.41 33.52 5.8 33.64 33.76 33.87 33.99 34.11 34.22 34.34 34.46 34.57 34.69 59 34.81 34.93 35.05 35,16 35.28 35.40 35.52 35.64 35.76 35.88 6(1 36.00 36.12 66.24 36.36 36.48 36.60 3672 36.84 56.97 3709 Tables, C. Squares. 3456 8 805 9 on. 6.0 36.00 3612 36.24 3636 36.48 36.60 36.72 36.84 36.97 37.09 1 6.1 37.21 37.33 37.45 37.58 37.70 37.82 37.95 38.07 38.19 38.32 6.2 38.44 38.56 38.69 38.81 38.94 39.06 39.19 39.31 39.44 39.56 6.3 39.69 39.82 39.94 40.07 40.20 40.32 40.45 40.58 40.70 40.83 6.4 40.96 41.09 41.22 41.34 41.47 41.60 41.73 41.86 41.99 42.12 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 85 86 8.7 88 8.9 9.0 91 9.2 9.3 9.4 42.25 42.38 43.56 43.69 44.89 45.02 46.24 46.38 47.61 47.75 42.51 43.82 45.16 46.51 47.89 49.00 49.14 49.28 50.41 50.55 50.69 51.84 51.08 52.13 53.29 53.44 53.58 54.76 54.91 55.06 42.64 43.96 45.29 46.65 48.02 49.42 50.84 52.27 53.73 55.20 42.77 44.09 45.43 46.79 48.16 49.56 50.98 52.42 53.88 55.35 56.25 57.76 59.29 60.84 62.41 64.00 65.61 67.24 68.89 70.56 72.25 73.96 75.69 77.44 79.21 56.40 56.55.56.70 56.85 57.91 58.06 58.22 58.37 59.44 59.60 59.75 59.91 61.00 61.15 61.31 61.47 62.57 62.73 62.88 63.04 64.16 64.32 64.48 64.64 65.77 65.93 66.10 66.26 67.40 67.57 67.73 67.90 6906 69.22 69.39 69.56 7073 70.90 71.06 71.23 72.42 74.13 75.86 77.62 79.39 81.00 81.18 82.81 82.99 84.64 84.82 86.49 86.68 88.36 88.55 72.59 74.30 76.04 77.79 79.57 81.36 83.17 85.01 86.86 88.74 72.76 74.48 76.21 77.97 79.74 81.54 83.36 85.19 87.05 88.92 72.93 74.65 76.39 78.15 79.92 81.72 83.54 85.38 87.24 89.11 42.90 44.22 45.56 46.92 48.30 49.70 51.12 52.56 5402 55.50 57.00 58.52 60.06 61.62 63.20 64.80 6642 68.06 69.72 71.40 73.10 74.82 76.56 78.32 80.10 81.90 83.72 85.56 87.42 89.30 43.03 44.36 45.70 47.06 48.44 49.84 51.27 52.71 54.17 55.65 57.15 58.68 60.22 61.78 63.36 64.96 66.59 68.23 69.89 71.57 43.16 44.49 45.83 47.20 48.58 49.98 51.41 52.85 54.32 55.80 57.30 58.83 60.37 61.94 63.52 65.12 66.75 68.39 70.06 71.74 43.30 44.62 45.97 47.33 48.72 50.13 51.55 53.00 54.46 55.95 57.46 58.98 60.53 62.09 63.68 65.29 66.91 68.56 70.22 71.91 43.43 1 44.76 46.10 47.47 48.86 50.27 u 51.70 53.14 54.61 56.10 57.61* 59.14 60.68 62.25 63.84 6545 16 - 67.08 68.72 70.39 72.08 73.27 73.44 75.0(f 75.17 76.74 76.91 78.50 78.68 80.28 80.46 73.62 73.79 1T 75.34 75.52 77.09 77.26 78.85 79.03 80.64 80.82 82.08 83.91 85,75 87.61 89.49 82.26 84.09 85.93 87.80 89.68 82.45 84.27 86.12 87.98 89.87 82.63 84.46 86.30 88.17 90.06 9.5 90.25 90.44 90.63 90.82 91.01 91.20 91.39 91.58 91.78 91,97 1 9.6 92.16 92.35 92.54 92.74 92.93 93.12 93.32 93.51 93.70 93.90 9.7 9409 94.28 94.48 94.67 94.87 95.06 95.26 95.45 95.65 95.84 9.8 96.04 96.24 96.43 96.63 96.83 97.02 97.22 97.42 97.61 97.81 9.9 98.01 98.21 98.41 98.60 98.80 99.00 99.20 99.40 99.60 99.80 10.0100.00 100.20 100.40 100.60 100.80 101.00 101.20 101.40 101.61 101.81 20 10.1 102.01 102 21 102.41 102.62 102.82 103.02 103.23 103.43 103.63 103.84 10.2 104.04 104.24 104.45 104 65 104.86 105.06 105.27 105.47 105.68 105.88 10.3 106.09 106.30 106.50 106-71 106.92 107.12 107.33 107.54 107.74 107.95 10.4108.16 108.37 108.58 108-78 108.99 109.20 109.41 109.62 109.83 110.04 10.5 110.25 110.46 110.67 110.88 111.09 111,30 111.51 111.72 111.94 112.15* 10.6112.36 112.57 112.78 113.00 113.21 113.42 113.64 113.85 114.06 114.28 10.7 114.49 114.70 114.92 115.13 115 35 115.56 115.78 115.99 116 21 116.42 10.8116.64 116.86 117.07 117.29 117.51 117.72 117.94 118.16 118.37 118.59 10.9 118.81 119.03 119.25 119.46 119.68 119.90 120.12 120.34 120.56 120.78 11.0 121.00 121.22 121.44 121.66 121.88 122.10 122,32 122.54 122.77 122.99" 806 M 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.000 1.331 1.728 2.197 2.744 3.375 4.096 4.913 5.832 6.859 1 1.030 1.368 1.772 2,248 2.803 3.443 4.173 5.000 5.930 6.968 2 1.061 1.405 1.816 2.300 2.863 3.512 4.252 5.088 6.029 7.078 3 1.093 1.443 1.861 2.353 2.924 3.582 4.331 5.178 6.128 7.189 Cubes. 4 5 1.125 1.158 1.482 1.521 1.907 1.953 2.406 2.460 2.986 3.049 3.652 3.724 4.411 4492 5.268 5.359 6.230 6.332 7.301 7,415 6 1.191 1.561 2.000 2.515 3.112 3.796 4.574 5.452 6.435 7.530 7 1.225 1.602 2.048 2.571 3.177 3.870 4.657 5.545 6.539 7.645 Table 3, 8 9 1.260 1.295 1.643 1.655 2.097 2.147 2.628 2686 3.242 3.308 3.944 4.020 4.742 4.827 5.640 5.735 6.645 6.761 7.762 7.881 D. 33 CL> 47 H n TS M Oi 101 1H 2.0 8.000 8.121 8.242 8.365 8.490 8.615 8.742 8.870 8.999 9.120 m 2.1 9.261 9.394 9.528 9.664 9,800 9.938 10.08 10.22 10.36 10.50 - 2.2 10.65 10.79 10.94 11.09 11.24 11.39 1154 11.70 11.85 12.01 15 2.3 12.17 12.33 12.49 12.65 12.81 12.98 13.14 13.31 13.48 13.65 16 2.4 13.82 14.00 14.17 14.35 14.53 14.71 14.89 15.07 15.25 15.44 18 2.5 15.63 15.81 16.00 16.19 16.39 16.58 16.78 16.97 17.17 17.37 l9 2.6 17.58 17.78 17.98 18.19 18.40 18.61 18.82 19.03 19.25 19.47 8t 2.7 19.68 19.90 20.12 20.35 20.57 20.80 21.02 21.25 21.48 21.72 22 2.8 21.95 22.19 22.43 22.67 22.91 23.15 23.39 23.64 23.89 24.14 a * 2.9 24.39 24.64 24.90 25.15 25.41 25.67 25.93 26.20 26.46 26.73 * 6 8.0 27.00 27.27 27.54 27.82 28.09 28.37 28.65 28.93 29.22 29.50 28 3.1 29.79 30.08 30.37 30.66 30.96 31.26 31.55 31.86 32.16 32.46 80 3.2 32.77 33.08 33.39 33.70 34.01 34.33 34.65 34.97 35.29 35.61 82 3.3 35.94 36.26 36.59 36.93 37.26 37.60 37.93 38.27 38.61 38.96 84 3.4 39,30 39.65 40.00 40.35 40.71 41.06 41.42 41.78 42.14 42.51 86 3.5 4288 43.24 43.61 43.99 44.36 44.74 45.12 45.50 45.88 46.27 38 3.6 46.66 47.05 47.44 47.83 48.23 48.63 49.03 49.43 49.84 50.24 40 3.7 50.65 51.06 51.48 51.90 52.31 52.73 63.16 53.58 54.01 54.44 * 2 3.8 54.87 55.31 55.74 56.18 56.62 57.07 57.51 57.96 58.41 58.86 " 3.9 59.32 59.78 60.24 60.70 61.16 61.63 62.10 62.57 63.04 63.52 47 4.0 64,00 64.48 6496 65.45 65.94 66.43 66.92 67.42 67.92 68.42 49 4.1 68.92 69.43 69.93 70.44 70.96 71.47 71.99 72.51 73.03 73.56 52 4.2 74.09 74.62 75.15 75.69 76.23 76.77 77.31 77.85 78.40 78.95 8 * 4.3 79.51 80.06 80.62 81.18 81,75 82.31 82.88 83.45 84.03 84.60 67 4.4 85.18 85.77 86.35 86.94 87.53 88.12 88.72 89.31 89.92 90.52 60 4.5 91.13 91.73 92.35 92.96 93.58 94.20 94.82 95.44 96.07 96.70 M 4.6 97.34 97.97 98.61 99.25 99.90 100.6 101.2 101.8 102.5 103.2 4.7 103.8 104.5 105,2 105.8 106.5 107.2 107.9 108.5 109,2 109.9 4.8 110.6 111.3 112.0 112.7 113.4 114.1 114.8 115.5 1162 116.9 4.9 117.6 118.4 119.1 119.8 120.6 121.3 122.0 122.8 123.5 124.3 5.0 125.0 125.8 126.5 127.3 128.0 128.8 129.6 130.3 131.1 131.9 5.1 132.7 133.4 134.2 135.0 135.8 136.6 137.4 138.2 139.0 139.8 5.2 140.6 141.4 142.2 143.1 143.9 144.7 145.5 146.4 147.2 148.0 5,3 148.9 149.7 150.6 151.4 152.3 153.1 154.0 154.9 155.7 156.6 5.4 157.5 158.3 159.2 160.1 161.0 161.9 162.8 163.7 164.6 165.5 9 6.5 166.4 167.3 168.2 169.1 170.0 171.0 171.9 172.8 173.7 174.7 ? 5.6 175.6 176.6 177.5 178.5 179.4 180.4 181.3 182.3 183.3 184.2 10 5.7 185.2 186.2 187.1 188.1 189.1 190.1 191.1 192.1 193.1 194.1 10 5.8 195.1 196.1 197.1 198.2 199.2 200.2 201.2 202.3 203.3 204.3 10 5.9 205.4 206.4 207.5 208.5 209.6 210.6 211.7 212.8 213.8 214.9 11 6.0 216.0 217.1 218.2 219.3 220.3 221.4 222.5 223.6 224.8 225.9 ki Table 3, D. Cubes. SOT I 23 45 6 789 ML 6.0 216.0 217.1 218.2 219.3 220.3 221.4 222.5 223.6 224.8 225.9 " .1 227.0 228.1 229.2 230.3 231.5 232.6 233.7 234.9 236.0 237.2 6.2 238.3 239.5 240.6 241.8 243.0 244.1 245.3 246.5 247.7 248.9 12 C.3 250.0 251.2 252.4 253.6 254.8 256.0 257.3 258.5 259.7 260.9 l2 6.4 262.1 263.4 264.6 265.8 267.1 268.3 269.6 270.8 272.1 273.4 ia 6.5 274.6 275.9 277.2 278.4 279.7 281.0 282.3 283.6 284.9 286.2 6.6 287.5 288.8 2901 291.4 292.8 294.1 295.4 296.7 298.1 299.4 l$ 6.7 300.8 302.1 303.5 304.8 306.2 307.5 308.9 310.3 311.7 313.0 " 6.8 314.4 315.8 317.2 318.6 320.0 321.4 322.8 324.2 325.7 327.1 l * 6.9 328.5 329.9 331.4 332.8 334.3 335.7 337.2 338.6 340.1 341.5 " 7.0 343.0 344.5 345.9 347.4 348.9 350.4 351*9 353.4 354.9 356.4" 7.1 357.9 359.4 360.9 362.5 364.0 365.5 367*1 368.6 370.1 371.7 " 7.2 373.2 374.8 376.4 377.9 379.5 381.1 382.7 384.2 385.8 387.4 ie 7.3 389.0 390.6 392.2 393.8 395.4 397.1 398.7 400.3 401.9 403.6 M 7.4 405.2 406.9 408.5 410.2 411.8 413.5 415.2 416.8 418.5 420.2 w 7.5 421.9 423.6 425.3 427.0 428.7 430.4 432.1 433.8 435.5 437.2 7.6 439.0 440.7 442.5 444.2 445.9 447.7 449.5 451.2 453.0 454.8 " 7.7 456.5 458.3 460.1 461.9 463.7 465.5 467.3 469.1 470.9 472.7 7.8 474.6 476.4 478.2 480.0 481.9 483.7 485.6 487.4 489.3 491.2 1$ 7.9 493.0 494.9 496.8 498.7 500.6 502.5 504.4 506.3 508.2 510.1 8.0 512.0 513.9 515.8 517.8 519.7 521.7 523.6 525.6 527.5 529.5 19 8.1 531.4 533.4 535.4 537.4 539.4 541.3 543.3 545.3 547.3 549.4 20 8.2 551.4 553.4 555.4 557.4 559.5 561.5 563.6 565.6 567.7 569.7 20 8.3 571.8 573.9 575.9 578.0 580.1 582.2 584.3 586.4 588.5 590.6 2t 8.4 592.7 594.8 596.9 599.1 601.2 603.4 605.5 607.6 609.8 612.0 21 .5 614,1 616.3 618.5 620.7 622.8 625.0 627.2 629.4 631.6 633.8 22 5.6 636.1 638.3 640.5 642.7 645.0 647.2 649.5 651.7 654.0 656.2 8.7 658.5 660.8 663.1 665.3 667.6 669.9 672.2 674.5 676.8 679.2 2S 8.8 681.5 683.8 686.1 688.5 690.8 693.2 695.5 697.9 700.2 702.6 2S 8.9 705.0 707.3 709.7 712.1 714.5 716.9 719.3 721.7 724.2 726.6" 9.0 729.0 731.4 733.9 736.3 738.8 741.2 743.7 746.1 748.6 751.1 25 9.1 753.6 756.1 758.6 761.0 763.6 766.1 768.6 771.1 773.6 776.2 25 9.2 778.7 781.2 783.8 786.3 788.9 791.5 794.0 796.6 799.2 801.8 M 9.3 804.4 807.0 809.6 812.2 814.8 817.4 820.0 822.7 825.3 827.9 M 9.4 830.6 833.2 835.9 838.6 841.2 843.9 846.6 849.3 852.0 854.7 2T 9.5 857.4 850.1 862.8 865.5 868.3 871.0 873.7 876.5 879.2 882.0 2T 9.6 884.7 887.5 890.3 893.1 895.8 898.6 901.4 904.2 907.0 909.9 M 9.7 912.7 915.5 918.3 921.2 924.0 926.9 929.7 932.6 935.4 938.3 28 9.8 941.2 944.1 947.0 949.9 952.8 955.7 958.6 961.5 964.4 967.4 29 9.9 970.3 973.2 976.2 979.1 982.1 985.1 988.0 991.0 994.0 997.0 3C 10.01000.0 1003.0 1006.0 1009.0 1012.0 1015.1 1018.1 1021.1 1024.2 1027.2 80 10.1 1030.3 1033.4 1036.4 1039.5 1042.6 1045.7 1048.8 1051.9 1055.0 1058.1 3l 10.21061.2 1064.3 1067.5 1070.6 1073.7 107.69 1080.0 1083.2 1086.41089.5 S1 10.3 1092.7 1095.9' 1099.1 1102.3 1105.5 1108.7 1111.9 1115.2 1118.4 1121.6 8 * 10.41124.9 1128.1 1131.4 1134.6 1137.9 1141.2 1144.4 1147.7 1151.0 1154.3 10.5 1157.6 1160.9 1164.3 1167.6 1170.9 1174.2 1177.6 1180.9 1184.3 1187.6 8 * 10.6 1191.0 1194.4 1197.8 1201.2 1204.6 1207.9 1211.4 1214.8 1218.2 1221.6 M 10.7 1225.0 1228.5 1231.9 1235.4 1238.8 1242.3 1245.8 1249.2 1252.7 1256.2 10.81259.7 1263.2 1266.7 1270.2 1273.8 1277.3 1280.8 1284.4 1287.9 1291.5 10.9 1295.0 1298.6 1302.2 1305.8 1309.3 1312.9 1316.5 1320.1 1323.8 1327.4 86 11.0 1331.0 1334.6 1338.3 1341.9 1345.6 1349.2 1352.9 1356.6 1360.3 1363.9 8T 808 Circumferences of Circles. Table 3, F. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 1. 00* 10* 20* 30* 40* 50* 60* 70* 80* 90* 3142 3173 3204 3236 3267 3299 3330 3362 3393 3424 3456 3487 3519 3550 3581 3613 3644 3676 3707 3738 3770 3801 3833 3864 3896 3927 3958 3990 4021 4053 4084 4115 4147 4178 4210 4241 4273 4304 4335 4367 4398 4430 4461 4492 4524 4555 4587 4618 4650 4681 4712 5027 5341 5655 5969 6283 6597 6912 7226 7540 4744 4775 5058 5089 5372 5404 5686 5718 6000 6032 6315 6346 6629 6660 6943 6974 7257 7288 7571 7603 4807 4838 5121 5152 5435 5466 5749 5781 6063 6095 6377 6409 6692 6723 7006 7037 7320 7351 7634 7665 4869 5184 5498 5812 6126 6440 6754 7069 7383 7697 4901 4932 5215 5246 5529 5561 5843 5875 6158 6189 6472 6503 678(5 6817 7100 7131 7414 7446 7728 7760 4964 4995 5278 5309 5592 5623 5906 5938 6220 6252 6535 6566 6849 6880 7163 7194 7477 7508 7791 7823 7854 7885 7917 7948 7980 8011 8042 8074 8105 8137 8168 8200 8231 8262 8294 8325 8357 8388 8419 8451 8482 8514 8545 8577 8608 8639 8671 8702 8734 8765 8796 8828 8859 8891 8922 8954 8985 9016 9048 9079 9111 9142 9173 9205 9236 9268 9299 9331 9362 9393 30 9425 9456 9488 9519 9550 9582 9613 9645 9676 9708 31 9739 9770 9802 9833 9865 9896 9927 9959 9990 10022 32 10053 10085 10116 10147 10179 10210 10242 10273 10304 10336 33 10367 10399 10430 10462 10493 10524 10556 10587 10619 10650 34 10681 10713 10744 10776 10807 10838 10870 10901 10933 10964 85 10996 11027 11058 11090 11121 11153 11184 11215 11247 11278 36 11310 11341 11373 11404 11435 11467 11498 11530 11561 11592 37 11624 11655 11687 11718 11750 11781 11812 11844 11875 11907 38 11938 11969 12001 12032 12064 12095 12127 12158 12189 12221 39 12252 12284 12315 12346 12378 12409 12441 12472 12504 12535 40 12566 12598 12629 12661 12692 12723 12755 12786 12818 12849 41 12881 12912 12943 12975 13006 13038 13069 13100 13132 13163 42 13195 13226 13258 13289 13320 13352 13383 13415 13446 13477 43 13509 13540 13572 13603 13635 13666 13697 13729 13760 13792 44 13823 13854 13886 13917 13949 13980 14012 14043 14074 14106 45 14137 14169 14200 14231 14263 14294 14326 14357 14388 14420 46 14451 14483 14514 14546 14577 14608 14640 14671 14703 14734 47 14765 14797 14828 14860 14891 14923 14954 14985 15017 15048 48 15080 15111 15142 15174 15205 15237 15268 15300 15331 15362 49 15394 15425 15457 15488 15519 15551 15582 15614 15645 15677 50 15708 15739 15771 15802 15834 15865 15896 15928 15959 15991 51 16022 16054 16085 16116 16148 16179 16211 16242 16273 16305 52 16336 16368 16399 16431 16462 16493 16525 16556 16588 16619 53 16650 16682 16713 16745 16776 16808 16839 16870 16902 16933 54 16965 16996 17027 17059 17090 17122 17153 17185 17216 17247 55 17279 17310 17342 17373 17404 17436 17467 17499 17530 17562 fill. (Mean) (i) ft (2) } (4) 13 (5) 16 (6) 19 (7) 22 (8) 25 (9) II iable3,F. Circumferences of Circles. 809 Dial. 00* 10* 20, 30* 40* 50* 60* 70* 80* 90* 55 17279 17310 17342 17373 17404 17436 17467 17499 17530 17562 56 17593 17624 17656 17687 17719 17750 17781 17813 17844 17876 57 17907 17938 17970 18001 18033 18064 18096 18127 18158 18190 58 18221 18253 18284 18315 18347 18378 18410 18441 18473 18504 59 18535 18567 18598 18630 18661 18692 18724 18755 18787 18818 60 18850 18881 18912 18944 18975 19007 19038 19069 19101 19132 61 19164 19195 19227 19258 19289 19321 19352 19384 19415 19446 62 19478 19509 19541 19572 19604 19635 19666 19698 19729 19761 63 19792 19823 19855 19886 19918 19949 19981 20012 20043 20075 64 20106 20138 20169 20200 20232 20263 20295 20326 20358 20389 65 20420 20452 20483 20515 20546 20577 20609 20640 20672 20703 66 20735 20766 20797 20829 20860 20892 20923 20954 20986 21017 67 21049 21080 21112 21143 21174 21206 21237 21269 21300 21331 68 21363 21394 21426 21457 21488 21520 21551 21583 21614 21646 69 21677 21708 21740 21771 21803 21834 21865 21897 21928 21960 70 21991 22023 22054 22085 22117 22148 22180 22211 22242 22274 71 22305 22337 22368 22400 22431 22462 22494 22525 22557 22588 72 22619 22651 22682 22714 22745 22777 22808 22839 22871 22902 73 22934 22965 22996 23028 23059 23091 23122 23154 23185 23216 74 23248 23279 23311 23342 23373 23405 23436 23468 23499 23531 75 23562 76 23876 77 24190 78 24504 79 24819 23593 23625 23908 23939 24222 24253 24536 24567 24850 24881 23656 23688 23970 24002 24285 24316 24599 24630 24913 24944 23719 23750 24033 24065 24347 24379 24662 24693 24976 25007 23782 23813 23845 24096 24127 24159 24410 24442 24473 24724 24756 24787 25038 25070 25101 80 25133 25164 25196 25227 25258 25290 25321 25353 25384 25415 81 25447 25478 25510 25541 25573 25604 25635 25667 25698 25730 82 25761 25792 25824 25855 25887 25918 25950 25981 26012 26044 83 26075 26107 26138 26169 26201 26232 26264 26295 26327 26358 84 26389 26421 26452 26484 26515 26546 26578 26609 26641 26672 85 26704 26735 26766 26798 26829 26861 26892 26923 26955 26986 86 27018 27049 27081 27112 27143 27175 27206 27238 27269 27300 87 27332 27363 27395 27426 27458 27489 27520 27552 27583 27615 88 27646 27677 27709 27740 27772 27803 27835 27866 27897 27929 89 27960 27992 28023 28054 28086 28117 28149 28180 28212 28243 90 28274 28306 28337 28369 28400 28431 28463 28494 28526 28557 91 28588 28620 28651 28683 28714 28746 28777 28808 28840 28871 92 28903 28934 28965 28997 29028 29060 29091 29123 29154 29185 93 29217 29248 29280 29311 29342 29374 29405 29437 29468 29500 94 29531 -29562 29594 29625 29657 29688 29719 29751 29782 29814 95 29845 29877 96 30159 30191 97 30473 30505 98 30788 30819 99 31102 31133 100 31416 31447 29908 30222 30536 30850 31165 31479 Oil, (Mean) 29939 30254 30568 30882 31196 31510 (3) 29971 30002 30285 30316 30599 30631 30913 30945 31227 31259 31542 31573 30034 30065 30348 30379 30662 30693 30976 31008 31290 31322 31604 31636 30096 30128 30411 30442 30725 30756 31039 31070 31353 31385 31667 31699 (4) 13 (5) It (6) 19 (7) (8) 810 Areas of Circles. Table 3, a Diai. *o a s 3 A *5 ,6 .1 ,8 ,9 . 10 78.5 80.1 81.7 83.3 84.9 86.6 88.2 89.9 91.6 93.3 11 95.0 96.8 98.5 100.3 102.1 103.9 105.7 107.5 109.4 111.2 18 12 113.1 115.0 116.9 118.8 120.8 122.7 124.7 126.7 128.7 130.7 20 13 132.7 134.8 136.8 138.9 141.0 143.1 145.3 147.4 149.6 151.7 21 14 153.9 156.1 158.4 160.6 162.9 165.1 167.4 169.7 172.0 174.4 23 15 176.7 179.1 181.5 183.9 1863 188.7 191.1 193.6 196.1 198.6 24 16 201.1 203.6 206.1 208.7 211.2 213.8 216.4 219.0 221.7 224.3 26 17 227.0 229.7 232.4 235.1 237.8 2405 243.3 246.1 248.8 251.6 28 18 254.5 257.3 260.2 263.0 265.9 268.8 271.7 274.6 277.6 2806 2a 19 283.5 286.5 289.5 292.6 295.6 298.6 301.7 304.8 307.9 311.0 " 20 314.2 317.3 320.5 323.7 326.9 330.1 333.3 336.5 339.8 343.1 M 21 346.4 349.7 353.0 356.3 359.7 363.1 366.4 369.8 373.3 376.7 84 22 380.1 383.6 387.1 390.6 394.1 397.6 401.1 404.7 408.3 411.9 M 23 415.5 419.1 422.7 426.4 430.1 433.7 437.4 441.2 444.9 448 6 " 24 452.4 456.2 460.0 4638 467.6 471.4 475.3 479.2 483.1 487.0 38 25 490.9 494.8 498.8 502.7 506.7 510.7 514.7 518.7 522.8 526.9 40 20 530.9 535.0 539.1 543.3 547.4 551.5 555.7 559.9 564.1 568.3 4a 27 572.6 576.8 581.1 585.3 589.6 594.0 598.3 602.6 607.0 611.4 49 28 615.8 620.2 624.6 629.0 633.5 637.9 642.4 646.9 651.4 656.0 43 29 660.5 665.1 669.7 674.3 678.9 683.5 688.1 692.8 697.5 702.2 46 30 706,9 711.6 716.3 721.1 725,8 730.6 735.4 740.2 745.1 749.9 48 31 754.8 759.6 764.5 769.4 774.4 779.3 784.3 789.2 794.2 799.2 50 32 804.2 809.3 814.3 819.4 824.5 829.6 834.7 839.8 845.0 850.1 51 33 855.3 860.5 865.7 870.9 876.2 881.4 886.7 892.0 897.3 902.6 5S 34 907.9 913.3 918.6 924.0 929.4 934.8 940.2 945.7 951.1 956,6 54 35 962 968 973 979 984 990 995 1001 1007 1012 36 1018 1024 1029 1035 1041 1046 1052 1058 1064 1069 37 1075 1081 1087 1093 1099 1104 1110 1116 1122 1128 38 1134 1140 1146 1152 1158 1164 1170 1176 1182 1188 6 39 1195 1201 1207 1213 1219 1225 1232 1238 1244 1250 40 1257 1263 1269 1276 1282 1288 1295 1301 1307 1314 41 1320 1327 1333 1340 1346 1353 1359 1366 1372 1379 42 1385 1392 1399 1405 1412 1419 1425 1432 1439 1445 43 1452 1459 1466 1473 1479 1486 1493 1500 1507 1511 44 1521 1527 1534 1541 1548 1555 1562 1569 1576 1583 45 1590 1598 1605 1612 1619 1626 1633 1640 1647 1655 ' 46 1662 1669 1676 1684 1691 1698 1706 1713 1720 1728 47 1735 1742 1750 1757 1765 1772 1780 1787 1795 1802 48 1810 1817 1825 1832 1840 1847 1855 1863 1870 1878 49 1886 1893 1901 1909 1917 1924 1932 1940 1948 1956 50 1963 1971 1979 1987 1995 2003 2011 2019 2027 2035 51 2043 2051 2059 2067 2075 2083 2091 2099 2107 2116 52 2124 2132 2140 2148 2157 2165 2173 2181 2190 2198 53 2206 2215 2223 2231 2240 2248 2256 2265 2273 2282 54 2290 2299 2307 2316 2324 2333 2341 2350 2359 2367 55 2376 2384 2393 2402 2411 2419 2428 2437 2445 2454 rabie 3, Q. Areas of Circles. 811 Diam, .0 1 ,2 ,3 ,4 5 46 4? 48 49 Dif. 55 2376 2384 2393 2402 2411 2419 2428 2437 2445 2454 56 2463 2472 2481 2489 2498 2507 2516 2525 2534 2543 57 2552 2561 2570 2579 2588 2597 2606 2615 2624 2633 a 58 2642 2651 2660 2669 2679 2688 2697 2706 2715 2725 59 2734 2743 2753 2762 2771 2781 2790 2799 2809 2818 60 2827 2837 2846 2856 2865 2875 2884 2894 2903 2913 61 2922 2932 2942 2951 2961 2971 2980 2990 3000 3009 62 3019 3029 3039 3048 3058 3068 3078 3088 3097 3107 63 3117 3127 3137 3147 3157 3167 3177 3187 3197 3207 64 3217 3227 3237 3247 3257 3267 3278 3288 3298 3308 ia 65 3318 3329 3339 3349 3359 3370 3380 3390 3400 3411 66 3421 3432 3442 3452 3463 3473 3484 3494 3505 3515 67 3526 3536 3547 3557 3568 3578 3589 3GOO 3610 3621 68 3632 3642 3653 3664 3675 3685 3696 3707 3718 3728 69 3739 3750 3761 3772 3783 3794 3805 3816 3826 3837 70 3848 3859 3871 3882 3893 3904 3915 3926 3937 3948" 71 3959 3970 3982 3993 4004 4015 4026 4038 4049 4060 72 4072 4083 4094 4106 4117 4128 4140 4151 4162 4174 73 4185 4197 4208 4220 4231 4243 4254 4266 4278 4289 74 4301 4312 4324 4336 4347 4359 4371 4383 4394 4406 75 4418 4430 4441 4453 4465 4477 4489 4501 4513 4524 76 4536 4548 4560 4572 4584 4596 4608 4620 4632 4645 77 4657 4669 4681 4693 4705 4717 4729 4V42 4754 4766 78 4778 4791 4803 4815 4827 4840 4852 4865 4877 4889 79 4902 4914 4927 4939 4951 4964 4976 4989 5001 5014 80 5027 5039 5052 5064 5077 5090 5102 5115 5128 5140 81 5153 5166 5178 5191 5204 5217 5230 5242 5255 5268 82 5281 5294 5307 5320 5333 5346 5359 5372 5385 5398 1S 83 5411 5424 5437 5450 5463 5476 5489 5502 5515 5529 84 5542 5555 5568 5581 5595 5608 5621 5635 5648 5661 85 5675 5638 5701 5715 5728 5741 5755 5768 5782 5795 86 5809 5822 5836 5849 5863 5877 5890 5904 5917 5931 87 5945 5958 5972 5986 5999 6013 6027 6041 6055 6068 88 6082 6096 6110 6124 6138 6151 6165 6179 6193 6207 89 6221 6235 6249 6263 6277 6291 6305 6319 6333 6348 u 90 6362 6376 6390 6404 6418 6433 6447 6461 6475 6490 91 6504 6518 6533 6547 6561 6576 6590 6604 6619 6633 92 6648 6662 6677 6691 6706 6720 6735 6749 6764 6778 93 6793 6808 6822 6837 6851 6866 6881 6896 6910 6925 94 6940 6955 6969 6984 6999 7014 7029 7044 7058 7073 95 7088 7103 7118 7133 7148 7163 7178 7193 7208 7223 ls 96 7238 7253 7268 7284 7299 7314 7329 7344 7359 7375 97 7390 7405 7420 7436 7451 7466 7482 7497 7512 7528 98 7543 7558 7574 7589 7605 7620 7636 7651 7667 7682 99 7698 7713 7729 7744 7760 7776 7791 7807 7823 7838 100 7854 7870 7885 7901 7917 7933 7949 7964 7980 7996 lfr 812 Volumes of Spheres. Table 3, H. Diam, 1 2 3 4 5 6 7 8 9 Dif. 1.0 .524 .539 .556 .572 .589 .606 .624 .641 .660 .678 17 1.1 .697 .716 .736 .755 .776 .796 .817 .839 .860 ,882 21 1.2 .905 .928 .951 .974 .998 1.023 1.047 1.073 1.098 1.124 26 1.3 1.150 1.177 1.204 1.232 1.260 1.288 1.317 1.346 1.376 1.406 29 1.4 1.437 1.468 1.499 1.531 1.563 1.596 1.630 1.663 1.697 1.732 SS 1.5 1.767 1.803 1.839 1.875 1.912 1.950 1.988 2.026 2.065 2.105 88 1.6 2.145 2.185 2.226 2.268 2.310 2.352 2.395 2.439 2.483 2.527 43 1.7 2.572 2.618 2.664 2.711 2.758 2.806 2.855 2.903 2.953 3.003 18 1.8 3.054 3.105 3.157 3.209 3.262 3.315 3.369 3.424 3.479 3.535 54 1.9 3.591 3.648 3.706 3.764 3.823 3.882 3.942 4.003 4.064 4.126 GO 20 4.189 4.252 4.316 4.380 4.445 4.511 4577 4.644 4.712 4.780 fi6 21 4.849 4.919 4.989 5.060 5.131 5.204 5.277 5.350 5.425 5.500 7', 2.2 5.575 5.652 5.729 5.806 5.885 5.964 6.044 6.125 6.206 6.288 80 2.3 6.371 6.454 6.538 6.623 6.709 6.795 6.882 6.970 7.059 7.148 87 2.4 7.238 7.329 7.421 7.513 7.606 7.700 7.795 7.890 7.986 8.083 94 25 2.6 2.7 2.8 2.9 8.18 8.28 9.20 9.31 10.31 10.42 11.49 11.62 12.77 12.90 8.38 9.42 10.54 11.74 13.04 8.48 9.53 10.65 11.87 13.17 8.5S 9.63 10.77 11.99 13.31 8.68 9.74 10.89 12.12 13.44 8.78 9.85 11.01 12.25 13.58 8.89 9.97 1U3 12.38 13.72 8.99 10.08 11.25 12.51 13.86 9.10 10 10.19 11.87 ia 12.64 ' 8 14.00 u 3.0 14.14 14.28 14.42 14.57 14.71 14.86 15.00 15.15 15.30 15.45 3.1 15.60 15.75 15.90 16.06 16.21 16.37 16.52 16.68 16.84 17.00 3.2 17.16 17.32 17.48 17.64 17.81 17.97 18.14 18.31 18.48 18.65 3.3 18.82 18.99 19.16 19.33 19.51 19.68 19.86 20.04 20.22 20.40 18 3.4 20.58 20.76 20.94 21.13 21.31 21.50 21.69 21.88 22.07 22.26 w 3.5 3.6 3.7 3.8 3.9 22.45 22.64 24.43 24.63 26.52 26.74 28.73 28.96 31.06 31.30 22.84 24.84 26.95 29.19 31.54 23.03 25.04 27.17 29.42 31.78 23.23 23.43 25.25 25.46 27.39 27.61 29.65 29.88 32.02 32.27 23.62 25.67 27.83 30.11 32.52 23.82 25.88 28.06 30.35 32.76 24 02 24.23 20 26.09 26.31 21 28.28 28.50 22 30.58 30.82 28 33.01 33.26 ** 4.0 33.51 33.76 34.02 34.27 34.53 34.78 35.04 35.30 35.56 35.82 M 4.1 36.09 36.35 36.62 36 88 37.15 37.42 37.69 37.97 38.24 38.52 " 4.2 38.79 39.07 39.35 39.63 39.91 40.19 40.48 40.76 41.05 41 34 42.80 43.10 43.40 43.70 44.00 44.30 80 4.3 41.63 41.92 42.21 4.4 44.60 44.91 45.21 42.51 45.52 45,83 46.14 46.45 46.77 47.08 47.40 4.5 47.71 48.03 48.35 48.67 49.00 49.32 49.65 49.97 50.30 50.63 * 4.6 50.97 51.30 51.63 51.97 52.31 52.65 52.99 53.33 53.67 54.02 s * 4.7 54.36 54.71 55.06 55.41 55.76 56.12 56.47 56.83 57.18 57.54 M 4.8 57.91 58.27 58.63 59.00 59.37 59.73 60.10 60.48 60.85 61.22 8T 4.9 61.60 61.98 62.36 62.74 63.12 63.51 63.89 64.28 64.67 65.06 M 5.0 65.45 65.84 6624 66.64 67.03 67.43 67.83 68:24 68.64 69.05 * 5.1 69.46 69.87 70.28 70.69 71.10 71.52 71.94 72.36 72.78 73.20 4t 5.2 73.62 74.05 74.47 74.90 75.33 75.77 76.20 7664 77.07 77.51 * 5.3 77.95 78.39 78.84 79,28 79.73 80.18 80.63 81.08 81.54 81.99 * 5.4 82.45 82.91 83.37 83.83 84.29 84.76 85.23 85.70 86.17 86.64 4T 5.5 87.11 87.59 8807 88.55 89.03 89.51 90.00 90.48 90.97 91.46 a Table 3,H. Volumes of Spheres. 813 Diaa. i 3 3 4 5 6 7 8 9 5.5 87.1 87.6 88.1 88.5 89.0 89.5 90.0 90.5 91.0 91.5Dif. 5.6 92.0 92.4 92.9 93.4 93.9 94.4 94.9 95.4 95.9 96.5 fi 5.7 97.0 97.5 98.0 98.5 99.0 99.5 100.1 100.6 101.1 101.6 5.8 102.2 102.7 103.2 103.8 104.3 104.8 105.4 105.9 106.4 107.0 59 107.5 108.1 108.6 109.2 109.7 110.3 110.9 111.4 112.0 112.5 6.0 113.1 113.7 114.2 1148 115.4 115.9 116.5 117.1 117.7 118.3 6.1 118.8 119.4 120.0 120.6 121.2 121.8 122.4 123.0 123.6 124.2 6.2 124.8 125.4 126.0 126.6 127.2 127.8 128.4 129.1 129.7 130.3 6.3 130.9 131.5 132.2 132.8 133.4 134.1 134.7 135.3 136.0 136.6 6.4 137.3 137.9 138.5 139.2 139.8 140.5 141.2 141.8 142.5 143.1 6.5 143.8 144.5 145.1 145.8 146.5 147.1 147.8 148.5 149 2 149.8 6.6 150.5 151/2 151.9 152.6 153.3 154.0 154.7 155.4 156.1 156.8 - 6.7 157.5 158.2 1589 159.6 160.3 161.0 161.7 162.5 163,2 163.9 6.8 164.6 165.4 166.1 166.8 167.6 168.3 169.0 169.8 170.5 171.3 6.9 172.0 172.8 173.5 174.3 175.0 175.8 176.5 177.3 178.1 178.8 7.0 179.6 180.4 181.1 181.9 182.7 183.5 184.3 185.0 185.8 186.6 7.1 187.4 188.2 189.0 189.8 190.6 191.4 192.2 193.0 193.8 194.6 7.2 195.4 196.2 197.1 197.9 198.7 199.5 200.4 201.2 202.0 202.9 7.3 203.7 204.5 205.4 206.2 207.1 207.9 208.8 209.6 210.5 211.3 7.4 212.2 213.0 213.9 214.8 215.6 216.5 217.4 218.3 219.1 220.0 7.5 220.9 221.8 222.7 223.6 224.4 225.3 226.2 227.1 228.0 228.9 7.6 229.8 230.8 231.7 232.6 233.5 234.4 235.3 236.3 237.2 238.1 7.7 239.0 240.0 240.9 241.8 242.8 243.7 244.7 245.6 246.6 247.5 7.8 248.5 249.4 250.4 251.4 252.3 253.3 254.3 255.2 256.2 257.2 7.9 258.2 259.1 260.1 261.1 262.1 263.1 264.1 265.1 266.1 267.1 8.0 268.1 269.1 270.1 271.1 272.1 273.1 274.2 275.2 276.2 277.2 8.1 278.3 279.3 280.3 281.4 282.4 283.4 284.5 285.5 286.6 287.6 8.2 288.7 289.8 290.8 291.9 292-9 294.0 295.1 296.2 297.2 298.3 8.3 299.4 300.5 301.6 302.6 303.7 304.8 305.9 307.0 308.1 309.2 " 8.4 310.3 311.4 312.6 313.7 314.8 315.9 317.0 318.2 319.3 320.4 8.5 321.6 322.7 323.8 325.0 326.1 327.3 328.4 329.6 330.7 331.9 8.6 333.0 334.2 335.4 336.5 337.7 338.9 340.1 341.2 342.4 343.6 8.7 344.8 346.0 347.2 348.4 349.6 350.8 352.0 353.2 354.4 355.6 18 8.8 356.8 358.0 359.3 360.5 361.7 362.9 364,2 365.4 366.6 367.9 8.9 369.1 370.4 371.6 372.9 374.1 375.4 376.6 377.9 379.2 380.4 9.0 381.7 383.0 384.3 385.5 386.8 388.1 389.4 390.7 392.0 393.3 18 9.1 394.6 395.9 397.2 398.5 399.8 401.1 402.4 403.7 405.1 4064 9.2 407.7 409.1 410.4 411.7 413.1 414.4 415.7 417.1 418.4 419.8 9.3 421.2 422.5 423.9 425.2 426.6 428.0 429.4 430.7 432.1 433.5 9,4434.9 436.3,437.7 439.1 440.5 441.9 443.3 444.7 4461 447.5 M 9.5 448.9 450.3 9.6 463.2 464.7 9.7 477.9 479.4 9.8 492.8 494.3 9.9 508.0 451.8 453.2 454.6 456.0 457*5 4589 460.4 461.8 466.1 467.6 469.1 470.5 472.0 475.5 474.9 476.4 480.8 482.3 483.8 485.3 486.8 488.3 489.8 491.3 495.8 497.3 498.9 500.4 501.9 503.4 505.0 506.5 511.1 512.7 514.2 515.8 5173 518.9 520.5 522.0 10.0 523.6 525.2 526.7 528.3 529.9 531.5 533.1 534.7 536.3 537.9 " 509.6 814 Natural Sines. Table 4. Angle *o ,1 ,2 .3 4 5 *6 .7 8 *9 Complement on. 0.0000 0017 0035 0052 0070 0087 0105 0122 0140 0157 0175 89 1 0175 0192 0209 0227 0244 0262 0279 0297 0314 0332 0349 88 2 0349 0366 0384 0401 0419 0436 0454 0471 0488 0506 0523 87 3 0523 0541 0558 0576 0593 0610 0628 0645 0663 0680 0698 86 4 0698 0715 0732 0750 0767 0785 0802 0819 0837 0854 0872 85 5 0.0872 0889 0906 0924 0941 0958 0976 0993 1011 1028 1045 84 6 1045 1063 1080 1097 1115 1132 1149 1167 1184 1201 1219 83 7 1219 1236 1253 1271 1288 1305 1323 1340 1357 1374 1392 82 8 1392 1409 1426 1444 1461 1478 1495 1513 1530 1547 1564 81 9 1564 1582 1599 1616 1633 1650 1668 1685 1702 1719 1736 80 10 0.1736 1754 1771 1788 1805 1822 1840 1857 1874 1891 1908 79 11 1908 1925 1942 1959 1977 1994 2011 2028 2045 2062 2079 78 12 2079 2096 2113 2130 2147 2164 2181 2198 2215 2233 2250 77 13 2250 2267 2284 2300 2317 2334 2351 2368 2385 2402 2419 76 14 2419 2436 2453 2470 2487 2504 2521 2538 2554 2571 2588 75 15 0.2588 2605 2622 2639 2656 2672 2689 2706 2723 2740 2756 74 16 2756 2773 2790 2807 2823 2840 2857 2874 2890 2907 2924 73 17 2924 2940 2957 2974 2990 3007 3024 3040 3057 3074 3090 72 18 3090 3107 3123 3140 3156 3173 3190 3206 3223 3239 3256 71 19 3256 3272 3289 3305 3322 3338 3355 3371 3387 3404 3420 70 20 0.3420 3437 3453 3469 3486 3502 3518 3535 3551 3567 3584 69 21 3584 3600 3616 3633 3649 3665 3681 3697 3714 3730 3746 68 22 3746 3762 3778 3795 3811 3827 3843 3859 3875 3891 3907 67 23 3907 3923 3939 3955 3971 3987 4003 4019 4035 4051 4067 66 ' 24 4067 4083 4099 4115 4131 4147 4163 4179 4195 4210 4226 65 25 0.4226 4242 4258 4274 4289 4305 4321 4337 4352 4368 4384 64 26 4384 4399 4415 4431 4446 4462 4478 4493 4509 4524 4540 63 27 4540 4555 4571 4586 4602 4617 4633 4648 4664 4679 4695 62 28 4695 4710 4726 4741 4756 4772 4787 4802 4818 4833 4848 61 29 4848 4863 4879 4894 4909 4924 4939 4955 4970 4985 5000 60 30 0.5000 5015 5030 5045 5060 5075 5090 5105 5120 5135 5150 59 31 5150 5165 5180 5195 5210 5225 5240 5255 5270 5284 5299 58 82 5299 5314 5329 5344 5358 5373 5388 5402 5417 5432 5446 57 33 5446 5461 5476 5490 5505 5519 5534 5548 5563 5577 5592 56 34 5592 5606 5621 5635 5650 5664 5678 5693 5707 5721 5736 55 35 0.5736 5750 5764 5779 5793 5807 5821 5835 5850 5864 5878 54 36 5878 5892 5906 5920 5934 5948 5962 5976 5990 6004 6018 53 * 37 6018 6032 6046 6060 6074 6088 6101 6115 6129 6143 6157 52 38 6157 6170 6184 6198 6211 6225 6239 6252 6266 6280 6293 51 39 6293 6307 6320 6334 6347 6361 6374 6388 6401 6414 6428 50 40 0.6428 6441 6455 6468 6481 6494 6508 6521 6534 6547 6561 49 41 6561 6574 6587 6600 6613 6626 6639 6652 "6665 6678 6691 48 42 6691 6704 6717 6730 6743 6756 6769 6782 6794 6807 6820 47 43 6820 6833 6845 6858 6871 6884 6896 6909 6921 6934 6947 46 44 6947 6959 6972 6984 6997 7009 7022 7034 7046 7059 7071 45 9 ,8 .7 .6 ,5 A *3 ,2 1 ,0 Angle Natural Cosines. Table 4. Natural Sines. 815 Aflgle *0 *1 *2 *3 *4 ,5 ,6 .7 *8 *9 Complement Dif. 45 0.7071 7083 7096 7108 7120 7133 7145 7157 7169 7181 7193 44 46 7193 7206 7218 7230 7242 7254 7266 7278 7290 7302 7314 43 I8 47 7314 7325 7337 7349 7361 7373 7385 7396 7408 7420 7431 42 48 7431 7443 7455 7466 7478 7490 7501 7513 7524 7536 7547 41 49 7547 7559 7570 7581 7593 7604 7615 7627 7638 7649 7660 40 50 0.7660 7672 7683 7694 7705 7716 7727 7738 7749 7760 7771 39 51 7771 7782 7793 7804 7815 7826 7837 7848 7859 7869 7880 38 " 52 7880 7891 7902 7912 7923 7934 7944 7955 7965 7976 7986 37 53 7986 7997 8007 8018 8028 8039 8049 8059 8070 8080 8090 36 54 8090 8100 8111 8121 8131 8141 8151 8161 8171 8181 8192 35 55 0.8192 8202 8211 8221 8231 8241 8251 8261 8271 8281 8290 84 56 8290 8300 8310 8320 8329 8339 8348 8358 8368 8377 8387 33 57 8387 8396 8406 8415 8425 8434 8443 8453 8462 8471 8480 32 58 8480 8490 8499 8508 8517 8526 8536 8545 8554 8563 8572 31 59 8572 8581 8590 8599 8607 8616 8625 8634 8643 8652 8660 30 9 60 0.8660 8669 8678 8686 8695 8704 8712 8721 8729 8738 8746 29 61 8746 8755 8763 8771 8780 8788 8796 8805 8813 8821 8829 28 62 8829 8838 8846 8854 8862 8870 8878 8886 8894 8902 8910 27 3 63 8910 8918 8926 8934 8942 8949 8957 8965 8973 8980 8988 26 64 8988 8996 9003 9011 9018 9026 9033 9041 9048 9056 9063 25 65 0.9063 9070 9078 9085 9092 9100 9107 9114 9121 9128 9135 24 66 9135 9143 9150 9157 9164 9171 9178 9184 9191 9198 9205 23 1 67 9205 9212 9219 9225 9232 9239 9245 9252 9259 9265 9272 22 68 9272 9278 9285 9291 9298 9304 9311 9317 9323 9330 9336 21 69 9336 9342 9348 9354 9361 9367 9373 9379 9385 9391 9397 20 8 70 0.9397 9403 9409 9415 9421 9426 9432 9438 9444 9449 9455 19 71 9455 9461 9466 9472 9478 9483 9489 9494 9500 9505 9511 18 72 9511 9516 9521 9527 9532 9537 9542 9548 9553 9558 9563 57 73 9563 9568 9573 9578 9583 9588 9593 9598 9603 9608 9613 16 74 9613 9617 9622 9627 9632 9636 9641 9646 9650 9655 9659 15 75 0.9659 9664 9668 9673 9677 9681 9686 9690 9694 9699 9703 14 76 9703 9707 9711 9715 9720 9724 9728 9732 9736 9740 9744 13 * 77 9744 9748 9751 9755 9759 9763 9767 9770 9774 9778 9781 12 78 9781 9785 9789 9792 9796 9799 9803 9806 9810 9813 9816 11 79 9816 9820 9823 9826 9829 9833 9836 9839 9842 9845 9848 10 80 0.9848 9851 9854 9857 9860 9863 9866 9869 9871 9874 9877 9 81 9877 9880 9882 9885 9888 9890 9893 9895 9898 9900 9903 8 82 9W3 9905 9907 9910 9912 9914 9917 9919 9921 9923 9925 7 83 9925 9928 9930 9932 9934 9936 9938 9940 9942 9943 9945 6 * 84 9945 9947 9949 9951 9952 9954 9956 9957 9959 9960 9962 5 85 0.9962 9963 9965 9966 9968 9969 9971 9972 9973 9974 9976 4 86 9976 9977 9#78 9979 9980 9981 9982 9983 9984 9985 9986 3 > 87 9986 9987 9988 9989 9990 9990 9991 9992 9993 9993 9994 2 88 9994 9995 9995 9996 9996 9997 9997 9997 9998 9998 9998 1 89 9998 9999 9999 9999 9999 1.0000 1-0000 1-0000 1.0000 1.0000 1.0000 9 *8 7 6 4 5 >4 *3 *2 4 4 Angle Natural Cosines. 816 Logarithmic Sines. Table 4. A. ingle .0 .1 J .3 .4 .5 .6 .7 .8 .9 Complement oit. 0l -00 ".2419 ".5429 jT.7190 3.8439 3~9408 2 > .0200 2~.0870 2*.1450 2~.1961 2~.2419 89 1 2*72419 2~.2832 "3210 2T.3558 2~.38SO 2i4179 4459 "f.4723 2~.4971 2~!5206 2^542b 88 2 5428 5640 5842 6035 6220 6397 6567 6731 6889 7041 7188 87 3 7188 7330 7468 7602 7731 7857 7979 8098 8213 8326 8436 86 4 8436 8543 8647 8749 8849 8946 9042 9135 9226 9315 9403 85 5 ".9403 2*9489 ".9573 2**9655 279736 2*9816 2*.9894 2~9970 ".0046 "0120 ".0192 84 T 6 ".0192 T.0264 T.0334 l".0403 T.0472 L0539 T".OG05 ".0670 ".0734 T.0797 f.0859 83 * 7 0859 0920 0981 1040 1099 1157 1214 1271 1326 1381 1436 82 * 8 1436 1489 1542 1594 1648 1697 1747 1797 1847 1895 1943 81 6 9 1943 1991 2038 2085 2131 2176 2221 2266 2310 2353 2397 80 ** 10 ".2397 ".2439 ".2482 ".2524 ".2565 ".2606 ".2647 "2637 "2727 ".2767 ".2806 79 * 11 2806 2845 2883 2921 2959 2997 8034 3070 3107 8143 3179 78 * 12 3179 8214 8249 8284 8319 8353 3387 8421 8455 3488 8521 77 34 13 3521 8554 8586 8618 8650 8682 8713 3745 3775 8806 8837 76 8l 14 8837 8867 8897 3927 8957 8986 4015 4044 4073 4102 4130 75 49 15 ".4130 ".4158 ".4186 ".4214 ".4242 ".4269 T.4296 ".4323 T.4350 ".4377 ".4403 74 27 16 4403 4430 4456 4482 4508 4533 4559 4584 4609 4634 4659 73 26 17 4659 4684 4709 4733 4757 4781 4805 4829 4353 4876 4900 72 2 ' 18 4900 4923 4946 4969 4992 5015 5037 5060 5082 5104 5126 71 2 19 5126 5148 6170 5192 5213 5235 5256 5278 5299 5320 5341 70 22 20 ".5341 ".5361 ".5382 ".5402 ".5423 T.5443 ".5463 ".5484 ".5504 ".5523 ".5543 69 2< 21 5543 5563 5583 5602 5621 5641 5660 5679 5698 5717 5736 68 1! 22 5736 5754 5773 5792 5810 5828 5847 5865 5883 5901 5919 67 * 23 5919 5937 5954 5972 5990 6007 6024 6042 6059 6076 6093 66 1( 24 6093 6110 6127 6144 6161 6177 6194 6210 6227 6243 6259 65 " 25 f.6259 ".6276 ".6292 ".6308 ".6324 ".6340 ".6356 ".6371 ".6387 Jf.6403 ".6418 64 1( 26 6418 6434 6449 6465 6430 6495 6510 6526 6541 6556 6570 63 " 27 6570 6585 6600 6615 6629 6644 6659 6673 6687 6702 6716 62 l * 28 6716 6730 6744 6759 6773 6787 6801 6314 6828 6342 6856 61 M 29 6856 6869 6883 6896 6910 6923 6937 6950 6963 6977 6990 60 30 ".6990 T.7003 T.7016 ".7029 ".7042 ".7055 T.7068 ".7030 ".7093 7.7106 ~7118 59 W 31 7118 7181 7144 7156 7168 7181 7193 7205 7218 7230 7242 58 32 7242 7254 7266 7278 7290 7302 7314 7326 7338 7349 7361 57 ** 33 7361 7373 7384 7396 7407 7419 7430 7442 7453 7464 7476 56 34 7476 7487 7498 7509 7520 7531 7542 7553 7564 7575 7586 55 ll 35 ".7586 "7597 T.7607 ".7618 T.7629 ".7640 T.7650 ".7661 ".7671 ".7682 "f.7692 54 36 7692 7703 7713 7723 7734 7744 7754 7764 7774 7785 7795 53 87 7795 7805 7815 7825 7835 7844 7854 7864 7874 7884 7893 52 10 88 7893 7903 7913 7922 7932 7941 7951 7960 7970 7979 7989 51 39 7989 7998 8007 8017 8026 8035 8044 8053 8063 8072 8081 50 40 ".8081 ".8090 T.8099 ".8108 ".8117 ".8125 ".8134 ".8143 ".8152 ".8161 7.8169 49 ' 41 8169 8178 8187 8195 8204 8213 8221 8230 8238 8247 8255 48 42 8255 8264 8272 8280 8289 8297 8305 8313 8322 8330 8338 47 43 8338 8346 8354 8362 8370 8378 8386 8394 8402 8410 8418 46 44 8418 8426 8433 8441 8449 8457 8464 8472 8480 8437 8495 45 ' Complement .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 Angle Logarithmic Cosines, Table 4. A. Logarithmic Sines. 817 Angle .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Complement on. 45 '.8495 T.S502 ~8510 "8517 "8525 ~8532 ".8540 ".8547 "8555 lts562 ".8569 44 46 8569 8577 8584 8591 8598 8606 8613 8620 8627 8634 8641 43 47 8641 8648 8655 8662 8669 8676 8683 8690 8697 8704 8711 42 7 48 8711 8718 8724 8731 8738 8745 8751 8758 8765 8771 8778 41 49 8778 8784 8791 8797 8804 8810 8317 8823 8830 8836 8843 40 50 ".8843 ".S849 "8855 "8862 "8868 "8874 ~8880 "8887 ".8893 1^8899 L8905 39 51 8905 8911 8917 8923 8929 8935 8941 8947 8953 8959 8965 38 6 52 8965 8971 8977 8983 8989 8995 9000 9006 9012 9018 9023 37 53 9023 9029 9035 9041 9046 9052 9057 9063 9069 9074 9080 36 54 9080 9085 9091 9096 9101 9107 9112 9118 9123 9128 9134 35 55 T.9134 T.9139 T.9144 T.9149 T.9155 ".9160 ".9165 ".9170 ".9175 ".9181 ".9186 34 56 9186 9191 9196 9201 9206 9211 9216 9221 9226 9231 9236 33 5 57 9236 9241 9246 9251 9255 9260 926u 9270 9275 9279 9284 32 58 9284 9289 9294 9298 9303 9308 9312 9317 9322 9326 9331 31 59 9331 9335 9340 9344 9349 9353 9358 9S62 9367 9371 9375 30 60 ".9375 ".9380 ".9384 ".9388 ".9393 ".9397 ".9401 ".9406 T.9410 ".9414 ".9418 29 61 9418 9422 9427 9431 9435 9439 9443 9447 9451 9455 9459 28 62 9459 9463 9467 9471 9475 9479 9483 9487 9491 9495 9499 27 * 63 9499 9503 95o6 9510 9514 9518 9522 9525 9529 9533 9537 26 64 9537 9540 9544 9548 9551 9555 9553 9562 9566 9569 9573 25 65 T.9573 ".9576 ".9580 ".9583 ".9587 T.9590 ".9594 ".9597 ".9601 ".9604 ".9607 24 66 9607 9611 9614 9617 9621 9624 9627 9631 9634 9637 9640 23 67 9640 9643 9647 9650 9653 9656 9659 9662 9665 9669 9672 22 68 9672 9675 9678 9681 9634 9687 9690 9693 9696 9699 9702 21 * 69 9702 9704 9707 9710 9713 9716 9719 9722 9724 9727 9730 20 70 ".9730 ".9733 ".9735 ".9738 ".9741 ".9743 ".9746 ".9749 ".9751 1.9754 ~9757 19 71 9757 9759 9762 9764 9767 9770 9772 9775 9777 9780 9782 18 72 9782 9785 9787 9789 9792 9794 9797 9799 9801 9804 9806 17 73 9806 9808 9811 9813 9815 9817 9820 9S22 9824 9826 9828 16 74 9828 9831 9833 9835 9837 9839 9841 9843 9845 9847 9849 15 75 ".9849 ".9851 ".9853 ".9855 ".9857 ".9859 ".9861 ".9863 ".9865 ".9867 ".9869 14 8 76 9869 9871 9873 9875 9876 9878 9980 9882 9884 9885 9887 13 77 9887 9889 9891 9892 9894 9896 9897 9899 9901 9902 9904 12 78 9904 9906 9907 9909 9910 9912 9913 9915 9916 9918 9919 11 79 9919 9921 9922 9924 9925 9927 9928 9929 9931 9932 9934 10 ".9934 "9935 ".9936 ".9937 T.9939 ".9940 T.9941 F.9943 ~9944 ".9945 L9946 9 81 9946 9947 9949 9950 9951 9952 9953 9954 9955 9956 9953 8 82 9958 9959 9960 9961 9962 9963 9964 9965 9966 9967 9968 7 * 83 9968 9968 9969 9970 9971 9972 9973 9974 9975 9975 9676 6 84 9976 9977 9978 9978 9979 9980 9981 9981 9982 9983 9983 5 85 ".9983 ".9984 "995 ".9985 ".9986 ".9987 ".9987 ".998S "9988 ".9989 7.9989 4 86 9989 9990 9990 9991 9991 9992 9992 9993 9993 9994 9994 3 87 9994 9994 9995 9995 9996 9996 9996 9996 9997 9997 9997 2 88 9997 9998 9998 9998 9998 9999 9999 9999 9999 9999 9999 1 89 9999 9999 0000 0000 0000 0000 0000 0000 0000 0000 0000 Complement .D .8 .7 .6 .5 .4 .3 .2 .1 .0 Angle Logarithmic Cosines. 818 Natural Tangents. Table 5. Angle ,1 ,2 ,3 .4 .5 .6 .7 ,8 .9 Complement IK, 0.0000 0017 0035 0052 0070 0087 0105 0122 0140 0157 0175 89 1 0175 0192 0209 0227 0244 0262 0279 0297 0314 0332 0349 88 2 0349 0367 0384 0402 0419 0437 0454 0472 0489 0507 0524 87 3 0524 0542 0559 0577 0594 0612 0629 0647 0664 0682 0699 86 4 0699 0717 0734 0752 0769 0787 0805 0822 0840 0857 0875 85 5 0.0875 0892 0910 0928 0945 0963 0981 0998 1016 1033 1051 84 6 1051 1069 1086 1104 1122 1139 1157 1175 1192 1210 1228 83 7 1228 1246 1263 1281 1299 1317 1334 1352 1370 1388 1405 82 8 1405 1423 1441 1459 1477 1495 1512 1530 1548 1566 1584 81 9 1584 1602 1620 1638 1655 1673 1691 1709 1727 1745 1763 80 10 0.1763 1781 1799 1817 1835 1853 1871 1890 1908 1926 1944 79 11 1944 1962 1980 1998 2016 2035 2053 2071 2089 2107 2126 78 12 2126 2144 2162 2180 2199 2217 2235 2254 2272 2290 2309 77 13 2309 2327 2345 2364 2382 2401 2419 2438 2456 2475 2493 76 14 2493 2512 2530 2549 2568 2586 2605 2623 2642 2661 2679 75 15 0.2679 2698 2717 2736 2754 2773 2792 2811 2830 2849 2867 74 16 2867 2886 2905 2924 2943 2962 2981 3000 3019 3038 3057 73 u 17 3057 3076 3096 3115 3134 3153 3172 3191 3211 3230 3249 72 18 3249 3269 3288 3307 3327 3346 3365 3385 3404 3424 3443 71 19 3443 3463 3482 3502 3522 3541 3561 3581 3600 3620 3640 70 20 0.3640 3659 3679 3699 3719 3739 3759 3779 3799 3819 3839 69 21 3839 3859 3879 3899 3919 3939 3959 3979 4000 4020 4040 68 22 4040 4061 4081 4101 4122 4142 4163 4183 4204 4224 4245 67 23 4245 4265 4286 4307 4327 4348 4369 4390 4411 4431 4452 66 24 4452 4473 4494 4515 4536 4557 4578 4599 4621 4642 4663 65 " 25 0.4663 4684 4706 4727 4748 4770 4791 4813 4834 4856 4877 64 26 4877 4899 4921 4942 4964 4986 5008 5029 5051 5073 5095 63 27 5095 5117 5139 5161 5184 5206 5228 5250 5272 5295 5317 62 22 28 5317 5340 5362 5384 5407 5430 5452 5475 5498 5520 5543 61 29 5543 5566 5589 5612 5635 5658 5681 5704 5727 5750 5774 60 23 30 0.5774 5797 5820 5844 5867 5890 5914 5938 5961 5985 6009 59 31 6009 6032 6056 6080 6104 6128 6152 6176 6200 6224 6249 58 2 * 32 6249 6273 6297 6322 6346 6371 6395 6420 6445 469 6494 57 33 6494 6519 6544 6569 6594 6619 6644 6669 6694 6720 6745 56 34 6745 6771 6796 6822 6847 6873 6899 6924 6950 6976 7002 55 35 0.7002 7028 7054 7080 7107 7133 7159 7186 7212 7239 7265 54 * 36 7265 7292 7319 7346 7373 7400 7427 7454 7481 7508 7536 53 37 7536 7563 7590 7618 7646 7673 7701 7729 7757 7785 7813 52 * 38 7813 7841 7869 7898 7926 7954 7983 8012 8040 8069 8098 51 M 39 8098 8127 8156 8185 8214 8243 8273 8302 8332 8361 8391 50 29 40 0.8391 8421 8451 8481 8511 8541 8571 8601 8632 8662 8693 49 s * 41 8693 8724 8754 8785 8816 8847 8878 8910 8941 8972 9004 48 M 42 9004 9036 9067 9099 9131 9163 9195 9228 9260 9293 9325 47 M 43 9325 9358 9391 9424 9457 9490 9523 9556 9590 9623 9657 46 M 44 9657 9691 9725 9759 9793 9827 9861 9896 9930 9965 1,0000 45 S4 Complement *9 *8 ,7 ,6 *5 4 4 3 ,2 *i *o Angle Natural Cotangents. 6. Natural Tangents. 819 Angle. 4<> ,f 2 ,3 44 ,5 6 7 *8 ,9 o. 50 1.1918 1.1960 1.2002 1.2045 1.2088 1.2131 1.2174 1.2218 1.2261 1.2305 51 1.2349 1.2393 1.2437 1.2482 1 2527 1.2572 1.2617 1.2662 1.2708 1.2753 46 52 1.2799 1.2846 1.2892 1.2938 1.2985 1.3032 1.3079 1.3127 1.3175 1.3222 47 53 1.3270 1.3319 1.3367 1.3416 1.3465 1.3514 1.3564 1.3613 1.3663 1.3713 49 54 1.3764 1.3814 1.3865 1.3916 U968 1.4019 1.4071 1.4124 1.4176 1.4229 58 55 1.4281 1.4335 1.4388 1.4442 1.4496 1.4550 1.4605 1.4659 1.4715 1.4770 M 56 1.4826 1.4882 1.4938 1.4994 1.5051 1.5108 1.5166 1.5224 1.5282 1.5340 57 57 1.5399 1.5458 1.5517 1.5577 1.5637 1.5697 1.5757 1.5818 1.5880 1.5941 60 58 1.6003 1.6066 1.6128 1.6191 1.6255 1.6319 1.6383 1.6447 1.6512 1.6577 64 59 1.6643 1.6709 1.6775 1.6842 1.6909 1.6977 1.7045 1.7113 1.7182 1.7251 8( 60 1.7321 1.7391 1.7461 1.7532 1.7603 1.7675 1.7747 1.7820 1.7893 1.7966 n 61 1.8040 1.8115 1.8190 1.8265 1.8341 1.8418 1.8495 1.8572 1.8650 1 8728 " 62 1.8807 1.8887 1.8967 1.9047 1.9128 1.9210 1.9292 1.9375 1.9458 1.9542 8a 63 1.9626 1.9711 1.9797 1.9883 1.9970 2.0057 2.0145 2.0233 2.0323 2.0413 ** 64 2.0503 2.0594 2.0686 2.0778 2.0872 2.0965 2.1060 2.1155 2.1251 2.1348 * 65 2.145 2.154 2.164 2.174 2.184 2.194 2.204 2.215 2.225 2.236 10 66 2.246 2.257 2.267 2.278 2.289 2.300 2.311 2.322 2.333 2.344 67 2.356 2.367 2.379 2.391 2.402 2.414 2.426 2.438 2.450 2.463 18 68 2.475 2.488 2.500 2.513 2.526 2.539 2.552 2.565 2.578 2.592 18 69 2.605 2.619 2.633 2.646 2.660 2.675 2.689 2.703 2.718 2.733 U 70 2.747 2.762 2.778 2.793 2.808 2.824 2.840 2.856 2.872 2.888 19 71 2.904 2.921 2.937 2.954 2.971 2.989 3.006 3.024 3.042 3.060 17 72 3.078 3.096 3.115 3.133 3.152 3.172 3.191 3.211 3.230 3.250 19 73 3.271 3.291 3.312 3.333 3.354 3.376 3.398 3.420 3.442 3.465 aa 74 3.487 3.511 3.534 3.558 3.582 3.606 3.630 3.655 3.681 3.706 85 75 3.732 3.758 3.785 3.812 3.839 3.867 3.895 3.923 3.952 3.981 *8 76 4.011 4.041 4.071 4.102 4.134 4.165 4.198 4.230 4.264 4.297 82 77 4.331 4.366 4.402 4,437 4.474 4.511 4.548 4.586 4.625 4.665 87 78 4.705 4.745 4.787 4.829 4.872 4.915 4.959 5.005 5.050 5.097 44 79 5.145 5.193 5.242 5.292 5.343 5.396 5.449 5.503 5.558 5614 61 80 5.67 5.73 5.79 5.85 5.91 5.98 6.04 6.11 6.17 6.24 7 81 6.31 6.39 6.46 6.54 6.61 6.69 6.77 6.85 6.94 7.03 8 82 7.12 7.21 7.30 7.40 7.49 7.60 7.70 7.81 7.92 8.03 10 83 8.14 8.26 8.39 8.51 8.64 8.78 8.92 9.06 9.21 9.36 Id 84 9.51 9.68 9.84 10.0 10.2 10.4 10.6 10.8 11.0 11.2 85 11.4 11.7 11.9 12.2 12.4 12.7 13.0 13.3 13.6 14.0 8 86 14.3 14.7 15.1 15.5 15.9 16.3 16.8 17.3 17.9 18.5 6 87 19.1 19.7 20.4 21.2 22.0 22.9 23.9 24.9 26.0 27.3 88 28.6 30.1 31.8 33.7 35.8 382 40.9 441 47.7 52.1 89 57. 64. 72. 82. 95. 115. 143. 191. 286. 573. ingle. ^O a ,2 .3 .4 4 5 46 47 *3 Natural Tangents. 820 Logarithmic Tangents. fable 5. A. Angle .0 .1 .3 .3 .4 .5 .6 .7 .8 . Complement on 0-<=>o IT.2419 3.5429 3.7190 3.8439 3.9409 2~.0200 2.0870 2~.1450 2".1962 2~.2419 89 1 2".2419 2~.2833 2 > .3211 2".3559 2~.3881 2".4181 2.4461 2.4725 2~.4973 if.5208 .5431 88 2 5431 5643 5S45 6038 6223 6401 6571 6736 6894 704* 7194 87 7194 7337 7475 7609 7739 7865 7988 8107 8223 8336 8446 86 4 8446 8554 8659 8762 8362 8960 9056 9150 9241 9S31 9420 85 5 JT.9420 2*9506 2*9591 2~.9674 2*9756 2*9836 2~.9915 2*9992 1*0068 :T.0143 T.0216 84 80 6 f.0216 T.0289 ~.0360 T.0430 t.0499 ".0567 T.0633 T.0699 1*0764 T.0828 T.0891 83 68 7 0891 0954 1015 1076 1135 1194 1252 1310 1367 1423 1478 82 59 1478 1533 1587 1640 1693 1745 1797 1848 1898 1948 1997 81 M 9 1997 2046 2094 2142 2189 2236 2282 2323 2374 2419 2463 80 48 10 f.2643 1*.2507 ".2551 1*2594 f.2637 T.2680 f.2722 f.2764 7.2805 1*.2846 T.2887 79 4S 11 2887 2927 2967 3006 3046 3085 3123 3162 3200 8237 8275 78 31 12 S275 3312 8349 3385 3422 3453 3493 3529 3564 8599 3634 77 3 13 3634 8668 8702 3736 8770 8804 3837 8870 8903 3935 8968 76 38 14 8968 4000 4032 4064 4095 4127 4158 4189 4220 4250 4281 75 S1 15 T.4281 T.4311 r.4341 5T.4371 7.4400 f.4430 f.4459 T*.4488 T.4517 f.4546 7.4575 74 29 16 4575 4603 4632 4660 4633 4716 4744 4771 4799 4826 4853 73 2I 17 4853 4880 4907 4934 4961 4987 5014 5040 5066 5092 5118 72 27 18 5118 5143 5169 5195 5220 5245 5270 5295 5320 5345 5370 71 2 * 19 5370 5394 5419 5443 5467 5491 5516 5539 5563 6587 5611 70 24 20 7.5611 7.5634 7.5658 7.5681 f.5704 f.5727 f.5750 l".5773 f,5796 T.5819 1*5842 69 28 21 5342 5364 5887 5909 5932 5954 5976 5993 6020 6042 6064 68 2! 22 6064 6086 6103 6129 6151 6172 6194 6215 6236 6257 6279 67 2 23 6279 6300 6321 6341 6362 6383 6404 6424 6445 6465 6486 66 2 24 6486 6506 6527 6547 6567 6587 6607 6627 6647 6667 6687 65 20 25 F.6687 T".6706 f.6726 7.6746 f.6765 1*6785 T.6804 1*6824 7.6848 T.6863 1*.6882 64 26 6882 6901 6920 6939 6958 6977 6996 7015 7034 7053 7072 63 W 27 7072 7090 7109 7128 7146 7165 7183 7202 7220 7238 7257 62 28 7257 7275 7293 7311 7330 7348 7366 7384 7402 7420 7438 61 l * 29 7438 7455 7473 7491 7509 7526 7544 7562 7579 7597 7614 60 30 1*.7614 F.7632 L7649 1*.7667 f.7684 T.7701 T.7719 T*.7736 T.7753 f.7771 l".7788 59 31 7788 7805 7822 7839 7856 7873 7890 7907 7924 7941 7958 58 17 32 7958 7975 7992 8008 8025 8042 8059 8075 8092 8109 8125 57 33 8125 8142 8158 8175 8191 8203 8224 8241 8257 8274 8290 56 34 8290 8306 8323 8339 8355 <*371 838S 8404 8420 8436 8452 55 35 t.8452 l".8468 T.8484 T.8501 T.8517 T.8533 1*8549 T*.8565 T.8581 1*8597 T.8613 54 W 8613 8629 8644 8660 8676 8692 8708 8724 8740 8755 8771 53 37 8771 8787 8803 8818 8834 8350 8865 8881 8897 8912 8928 52 38 8928 8944 8959 8975 8990 9006 9022 9037 9053 9068 9084 51 39 9084 9099 9115 9130 9146 9161 9176 9192 9207 9223 9238 50 40 f.9238 f.9254 lT.9269 t.9284 l".9300 9".9315 T*.9330 t.9346 T.9361 1^9376 T.9392 49 41 9392 9407 9422 9438 9453 9468 9483 9499 9514 9529 9544 48 42 9544 9560 9575 9590 9605 9621 9636 9651 9666 9681 9697 47 43 9697 9712 9727 9742 9757 9772 9788 9803 9S18 9833 9843 46 44 9848 9864 9879 9894 9909 9924 9939 9955 9970 9985 0000 45 1J Complement .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 Angle Logarithmic Cotangents. table 5. A. Logarithmic Tangents. 821 Angle .0 .1 .2 .3 .4 .5 .6 .7 .8 . Complement on. 45 0.0000 0.0015 0.0030 0.0045 0.0061 0.0076 0.0091 0.0106 0.0121 0.0136 0.0152 44 1 46 0152 0167 0182 0197 0212 0223 0243 0258 0273 0288 0303 43 47 OS03 0319 0334 0349 0364 0379 0395 0410 0425 0*40 0456 42 48 0456 0471 0486 0501 0517 0532 0547 0562 057$ 0593 0608 41 49 OG08 0624 0639 0654 0670 0685 0700 0716 0731 0716 0762 40 50 0.0762 0.0777 0.0793 0.0808 0.0824 0.0839 0.0854 0.0870 0.0885 0.090J 0.0916 39 51 0916 0932 0947 0963 0978 0994 1010 1025 1041 1056 1072 38 52 1072 1088 1103 1119 1135 1150 1166 1182 1197 1213 1229 37 53 1229 1245 1260 127C 1292 1308 1324 1340 1356 J371 1387 36 54 1387 1403 1419 1435 1451 1467 1483 1499 1516 1532 1548 35 19 55 0.1548 0.1564 0.1580 0.1596 0.1612 0.1629 0.1645 0.1661 0.1677 0.1694 0.1710 34 56 1710 1726 1743 1759 1776 1792 1809 1825 1842 1858 1875 33 57 1875 1891 1908 1925 1941 1958 1975 1992 2008 2025 2042 32 58 2042 2059 2076 2093 2110 2127 2144 2161 2178 2195 2212 31 tT 59 2212 2229 2247 2264 2281 2299 2316 2333 2351 2368 2386 30 60 0.2386 0.2403 0.2421 0.2438 0.2456 0.2474 0.2491 0.2509 0.2527 0.2545 0-2562 29 61 2562 2580 2598 2616 2634 2652 2670 2689 2707 2725 2743 28 * 62 2743 2762 2780 2798 2817 2835 2854 2872 2891 2910 2928 27 63 2928 2947 2966 2985 3004 3023 3042 3061 3080 3099 3118 26 ** 64 3118 3137 8157 Sl76 3196 3215 3235 3254 3274 3294 3313 25 65 0.3313 0.3333 0.3353 0.3373 0.3393 0.3413 0.3433 0.3453 0.3473 0.3494 0.3514 24 8( 66 3514 3535 3555 3576 8596 3617 3638 3659 3679 .'. 3700 8721 23 2 67 3721 3743 3764 8785 3806 3828 3849 3871 3892 3914 8936 22 2: 68 3936 3958 3980 4002 4024 4046 4068 4091 4113 4136 4158 21 2 69 4158 4181 4204 4227 4250 4273 4296 4319 4342 4366 4389 20 2? ' 70 0.4389 0.4413 0.4437 0.4461 0.4484 0.4509 0.4533 0.4557 0.4581 0.4606 0.4630 19 2l 71 4630 4655 4680 4705 4730 4755 4780 4805 4831 4857 4882 18 2! 72 4882 4908 4934 4960 4986 5013 5039 5066 5093 5120 5147 17 2 73 5147 5174 5201 5229 5256 5284 5312 5340 5368 5397 5425 16 2) 74 5425 5454 5483 5512 5541 5570 5600 5629 5659 ,5689 5719 15 29 75 0.5719 0.5750 0.5780 0.5811 0.5342 0.5873 0.5905 0.5936 0.5968 0.6000 0.6032 14 3 ^ 76 6032 G065 6097 6130 6163 6196 6230 6264 6298 6332 6366 13 8 77 6366 6401 6436 6471 6507 6542 6578 6615 6651 6688 6725 12 3( 78 6725 G763 6800 6838 6877 6915 6954 6994 7033 7073 7113 11 S 79 7113 7154 7195 7236 7278 7320 7363 7406 7449 7493 7537 10 4 * 80 0.7537 0.7581 0.7626 0.7672 0.7718 0.7764 0.7811 0.7858 0.7906 0.7954 0.8003 9 *' 81 8003 8052 8102 8152 8203 8255 8307 8360 8413 8467 8522 8 8 * 82 8522 8577 8633 8690 8748 8806 8865 8924 8985 9046 9109 7 8 83 9109 9172 9236 9301 9367 9433 9501 9570 9640 9711 9784 6 6! 84 9734 9857 9932 1.0008 1.0085 1.0164 1 0244 1.0326 1.0409 1.0494 1.0580 5 * 85 1.0580 1.0669 1.0759 1.0850 1.0944 1.1040 1.1138 1.1238 1.1341 1.1446 1.1554 4 86 1554 1664 1777 1893 2012 2135 2261 2391 2525 2663 2806 3 87 2806 2954 3106 3264 3429 3599 3777 3962 4155 4357 4569 2 88 4569 4792 5027 5275 5539 5819 6119 6441 6789 7167 7581 1 89 7581 8038 8553 9130 9800 2.0591 2.1561 2.2810 2.4571 2.7581 oo Complement .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 Angle Logarithmic Cotangents. .821a Antilogarithras. Table 5 (B). JLogs. O 1 2 3 4 5 6 7 8 9 Dif. .00 1000 1002 1005 1007 1009 1012 1014 1016 1019 1021 .01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 .02 1047 1050 1052 1054 1057 1059 1062 1064 1067 1069 .03 1072 1074 1076 1079 1081 1084 1086 1089 1091 1094 .04 1096 1099 1102 1104 1107 1109 1112 1114 1117 1119 .05 1122 1125 1127 1130 1132 1135 1138 1140 1143 1146 .06 1148 1151 1153 1156 1159 1161 1164 1167 1169 1172 .07 1175 1178 1180 1183 1186 1189 1191 1194 1197 1199 .08 1202 1205 1208 1211 1213 1216 1219 1222 1225 1227 .09 1230 1233 1236 1239 1242 1245 1247 1250 1253 12 F >6 .10 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 .11 1288 1291 1294 1297 1300 1303 1306 1309 1312 1315 .12 1318 1321 1324 1327 1330 1334 1337 1340 1343 1346 3 .13 1349 1352 1355 1358 1361 1365 1368 1371 1374 1377 .14 1380 1384 1387 1390 1393 1396 1400 1403 1406 1409 .15 1413 1416 1419 1422 1426 1429 1432 1435 1439 1442 .16 1445 1449 1452 1455 1459 1462 1466 1469 1472 1476 .17 1479 1483 1486 1489 1493 1496 1500 1503 1507 1510 .18 1514 1517 1521 1524 1528 1531 1535 1538 1542 1545 .19 1549 1552 1556 1560 1563 1567 1570 1574 1578 1581 .20 1585 1589 1592 1596 1600 1603 1607 1611 1614 1618 .21 1622 1626 1629 1633 1637 1641 1644 1648 1652 1656 .22 1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 .23 1698 1702 1706 - 1710 1714 1718 1722 1726 1730 1734 .24 1738 1742 1746 1750 1754 1758 1762 1766 1770 1774 4 .25 1778 1782 1786 1791 1795 1799 1803 1807 1811 1816 .26 1820 1824 1828 1832 1837 1841 1845 1849 1854 1858 .27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 .28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 .29 1950 1954 1959 1963 1968 1972 1977 1982 1986 1991 .30 1995 2000 2004 2009 2014 2018 2023 2028 2032 2037 .31 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 .32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 .33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 5 -34 2188 2193 2198 2203 2208 2213 2218 2223 2228 2234 .35 2239 2244 2249 2254 2259 2265 2270 2275 2280 2286 .36 2291 2296 2301 2307 2312 2317 2323 2328 2333 2339 .37 2344 2350 2355 2360 2366 2371 2377 2382 2388 2393 .38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 ,39 2455 2460 2466 2472 2477 2483 2489 2495 2500 2506 .40 2512 2518 2523 2529 2535 2541 2547 2553 2559 2564 .41 2570 2576 2582 2588 2594 2600 2606 2612 2618 2624 6 .42 2630 2636 2642 2649 2655 2661 2667 2673 2679 2685 ,43 2692 2698 2704 2710 2716 2723 2729 2735 2742 2748 .44 2754 2761 2767 2773 2780 2786 2793 2799 2805 2812 .45 2818 2825 2831 2838 2844 2851 2858 2864 2871 2877 .46 2884 2891 2897 2904 2911 2917 2924 2931 2938 2944 .47 2951 2958 2965 2972 2979 2985 2992 2999 3006 3013 .48 3020 3027 3034 3041 3048 3055 3062 3069 3076 3083 7 ,49 3090 3097 3105 3112 3119 3126 3133 3141 3148 3155 Table 5 (B). Antilogarithms. 8216 Logs. O 1 2 3 4 5 6 7 8 9 Dif. .50 3162 3170 3177 3184 3192 3199 3206 3214 3221 3228 .51 3236 3243 3251 3258 3266 3273 3281 3289 3296 3304 .53 3311 3319 3327 3334 3342 3350 3357 3365 3373 3381 .53 3388 3396 3404 3412 3420 3428 3436 3443 3451 3459 8 .54 3467 3475 3483 3491 3499 3508 3516 3524 3532 3540 .55 3548 3556 3565 3573 3581 3589 3597 3606 3614 3622 .56 3631 3639 3648 .3656 3664 3673 3681 3690 3698 3707 .57 3715 3724 3733 3741 3750 3758 3767 3776 3784 3793 .58 3802 3811 3819 3828 3837 3846 3855 3864 3873 3882 .59 3890 3899 3908 3917 3926 3936 3945 3954 3963 3972 9 .60 3981 3990 3999 4009 4018 4027 4036 4046 4055 4064 .61 4074 4083 4093 4102 4111 4121 4130 4140 4150 4159 .63 4169 4178 4188 4198 4207 4217 4227 4236 4246 4256 .t>3 4266 4276 4285 4295 4305 4315 4325 4335 4345 4355 10 .64 4365 4375 4385 4395 4406 4416 4426 4436 4446 4457 .65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 .66 4571 4581 4592 4603 4613 4624 4634 4645 4656 4667 .67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 11 .68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 .69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 .70 5012 5023 5035 5047 5058 5070 5082 5093 5105 5117 .71 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 12 72 5248 5260 5272 5284 5297 5309 5321 5333 5346 5358 .73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 .74 5495 5508 5521 5534 5546 5559 5572 5585 5598 5610 .75 5623 5636 5649 5662 5675 5689 5702 5715 5728 5741 13 .76 5754 5768 5781 5794 5808 5821 5834 5848 5861 5875 .77 5888 5902 5916 5929 5943 5957 5970 5984 5998 6012 .78 6026 6039 6053 6067 6081 6095 6109 6124 6138 6152 14 .79 6166 6180 6194 6209 6223 6237 6252 6266 6281 6295 .80 6310 6324 6339 6353 6368 6383 6397 6412 6427 6442 .81 6457 6471 6486 6501 6516 6531 6546 6561 6577 6592 15 .82 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 .83 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 84 6918 6934 6950 6966 6982 6998 7015 7031 7047 7063 16 .85 7079 7096 7112 7129 7145 7161 7178 7194 7211 7228 .86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 17 8T 7413 7430 7447 7464 7482 7499 7516 7534 7551 7568 .88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 .89 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 18 .90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 .91 8128 8147' 8166 8185 8204 8222 8241 8260 8279 8299 19 .92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 .93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 .94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 20 .95 8913 8933 8954 8974 8995 9016 9036 9057 9078 9099 21 .96 9120 9141 9162 9183 9204 922^ 9247 9268 9290 9311 21 97 9333 9354 9376 9397 9419 9441 9462 9484 9506 9528 22 98 9550 9572 9594 9616 9638 9661 9683 9705 9727 9750 22 .99 9772 9795 9817 9840 9863 9886 9908 9931 9954 9977 23 821 221 34439 34459 34479 34498 34518 34537 34557 34577 34596 34616 a 222 34635 34655 34674 34694 34713 34733 34753 34772 34792 3481 1 2 4 223 34830 34850 34869 34889 34908 34928 34947 34967 34986 35005 s fl 224 35025 35044 35064 35083 35102 35122 35141 35160 35180 35199* 8 225 35218 35238 35257 35276 35295 35315 35334 35353 35372 35392 51 226 35411 35430 35449 35468 35488 35507 35526 35545 35564 35583 " 227 35603 35622 35641 35660 35679 35698 35717 35736 35755 35774 71S 228 35793 35813 35832 35851 35870 35889 35908 35927 35946 35965 81 229 35984 36003 36021 36040 36059 36078 36097 36116 36135 36154 91T 230 36173 36192 36211 36229 36248 36267 36286 36305 36324 38342 231 36361 36380 36399 36418 36436 36455 36474 36493 36511 36530 232 36549 36568 36586 36605 36624 36642 36661 36680 36698 36717 233 36736 36754 36773 36791 36810 36829 36847 36866 36884 36903 234 36922 36940 36959 36977 36996 37014 37033 37051 37070 37088 235 37107 37125 37144 37162 37181 37199 37218 37236 37254 37273 236 37291 37310 37328 37346 37365 37383 37401 37420 37438 37457 237 37475 37493 37511 37530 37548 37566 37585 37603 37621 37639 238 37658 37676 37694 37712 37731 37749 37767 37785 37803 37822 239 37840 37858 37876 37894 37912 37931 37949 37967 37985 38003 24038021 38039 38057 38075 38093 38112 38130 38148 38166 38184 w 241 38202 38220 38238 38256 38274 38292 38310 38328 38346 38304 1 * 24238382 38399 38417 38435 38453 38471 38489 38507 38525 38543 s * 24338561 38578 38596 38614 38632 38650 38668 38686 38703 38721 s * 244 38739 38757 38775 38792 38810 38828 38846 38863 38881 38899* ' 245 38917 38934 38952 38970 38987 39005 39023 39041 39058 39076 * 246 39094 39111 39129 39146 39164 39182 39199 39217 39235 39252 6 " 247 39270 39287 39305 39322 39340 39358 39375 39393 39410 39428 T W 24839445 39463 39480 39498 39515 39533 39550 39568 39585 39602 81 * 249 39620 39637 39655 39672 39690 39707 39724 39742 39759 39777 9 lfl 250 39794 39811 39829 39846 39863 39881 39898 39915 39933 39950 Table 6. Logarithms. 825 NO. 1 2 3 4 5 6 7 8 9 oif. 250 39794 39811 39829 39846 39863 39881 39898 39915 39983 39950 251 39967 39985 40002 40019 40037 40054 40071 40088 40106 40123 l 2 252 40140 40157 40175 40192 40209 40226 40243 40261 40278 40295 2 3 253 40312 40329 40346 40364 40381 40398 40415 40432 40449 40466 3 5 254 40483 40500 40518 40535 40552 40569 40586 40603 40620 40637 4 7 255 40654 40671 40688 40705 40722 40739 40756 40773 40790 40807 B 9 256 40824 40841 40858 40875 40892 40909 40926 40943 40960 40976 6 10 257 40993 41010 41027 41044 41061 41078 41095 41111 41128 41145 7 12 258 41162 41179 41196 41212 41229 41246 41263 41280 41296 41313 8 14 259 41330 41347 41363 41380 41397 41414 41430 41447 41464 41481 9 15 260 41497 41514 41531 41547 41564 41581 41597 41614 41631 41647 2IM 41664 41681 41697 41714 41731 41747 41764 41780 41797 41814 2(52 41830 41847 41863 41880 41896 41913 41929 41946 41963 41979 203 41996 42012 42029 42045 42062 42078 42095 42111 42127 42144 264 42160 42177 42193 42210 42226 42243 42259 42275 42292 42308 265 42325 42341 42357 42374 42390 42406 42423 42439 42455 42472 266 42488 42504 42521 42537 42553 42570 42586 42602 42619 42635 267 42651 42667 42684 42700 42716 42732 42749 42765 42781 42797 268 42813 42830 42846 42862 42878 42894 42911 42927 42943 42959 269 42975 42991 43008 43024 43040 43056 43072 43088 43104 43120 270 43136 43152 43169 43185 43201 43217 43233 43249 43265 43281 i 271 43297 43313 43329 43345 43361 43377 43393 43409 43425 43441 272 43457 43473 43489 43505 43521 43537 43553 43569 43584 43600 2 8 273 43616 43632 43648 43664 43680 43696 43712 43727 43743 43759 274 43775 43791 43807 43823 43838 43854 43870 43886 43902 43917 275 43933 43949 43965 43981 43996 44012 44028 44044 44059 44075 276 44091 44107 44122 44138 44154 44170 44185 44201 44217 44232 277 44248 44264 44279 44295 44311 44326 44342 44358 44373 44389 278 44404 44420 44436 44451 44467 44483 44498 44514 44529 44545 8 13 279 44560 44576 44592 44607 44623 44638 44654 44669 44685 44700 9 " 280 44716 44731 44747 44762 44778 44793 44809 44824 44840 44855 281 44871 44886 44902 44917 44932 44948 44963 44979 44994 45010 282 45025 45040 45056 45071 45086 45102 45117 45133 45148 45163 283 45179 45194 45209 45225 45240 45255 45271 45286 45301 45317 284 45332 45347 45362 45378 45393 45408 45423 45439 45454 45469 285 45484 45500 45515 45530 45545 45561 45576 45591 45606 45621 286 45637 45652 45667 45682 45697 45712 45728 45743 45758 45773 287 45788 45803 45818 45834 45849 45864 45879 45894 45909 45924 288 45939 45954 45969 45984 46000 46015 46030 46045 46060 46075 289 46090 46105 46120 46135 46150 46165 46180 46195 46210 46225 290 46240 46255 46270 46285 46300 46315 46330 46345 46359 46374 291 46389 46404 46419 46434 46449 46464 46479 46494 46509 46523 l 292 46538 46553 46568 46583 46598 46613 46627 46642 46657 46672 293 46687 46702 46716 46731 46746 46761 46776 46790 46805 46820 294 46835 46850 46864 46879 46894 46909 46923 46938 46953 46967 295 46982 46997 47012 47026 47041 47056 47070 47085 47100 47114 296 47129 47144 47159 47173 47188 47202 47217 47232 47246 47261 297 47276 47290 47305 47319 47334 47349 47363 47378 47392 47407 298 47422 47436 47451 47465 47480 47494 47509 47524 47538 47553 8 12 S99 47567 47582 47596 47611 47625 47640 47654 47669 47683 47698 9 " 300 47712 47727 47741 47756 47770 47784 47799 47813 47828 47842 826 Logarithms. Table 6. Id. 1 2 3 4 5 6 7 8 9 on. 300 47712 47727 47741 47756 47770 47784 47799 47813 47828 47842 u 301 47857 47871 47885 47900 47914 47929 47943 47958 47972 47986 l l 302 48001 48015 48029 48044 48058 48073 48087 48101 48116 48130 303 48144 48159 48173 48187 48202 48216 48230 48244 48259 48273 304 48287 48302 48316 48330 48344 48359 48373 48387 48401 48416 305 48430 48444 48458 48473 48487 48501 48515 48530 48544 48558 306 48572 48586 4S601 48615 48629 48643 48657 48671 48686 48700 307 48714 48728 48742 48756 48770 48785 48799 48813 48827 48841 308 48855 48869 48883 48897 48911 48926 48940 48954 48968 48982 309 48996 49010 49024 49038 49052 49066 49080 49094 49108 49122 310 49136 49150 49164 49178 49192 49206 49220 49234 49248 49262 311 49276 49290 49304 49318 49332 49346 49360 49374 49388 49402 312 49415 49429 49443 49457 49471 49485 49499 49513 49527 49541 313 49554 49568 49582 49596 49610 49624 49638 49651 49665 49679 314 49693 49707 49721 49734 49748 49762 49776 49790 49803 49817 315 49831 49845 49859 49872 49886 49900 49914 49927 49941 49955 316 49969 49982 49996 50010 50024 50037 50051 50065 50079 50092 317 50106 50120 50133 50147 50161 50174 50188 50202 50215 50229 318 50243 50256 50270 50284 50297 50311 50325 50338 50352 50365 319 50379 50393 50406 50420 50433 50447 50461 50474 50488 50501 320 50515 50529 50542 50556 50569 50583 50596 50610 50623 50637 321 50651 50664 50678 50691 50705 50718 50732 50745 50759 50772 322 50786 50799 50813 50826 50840 50853 50866 50880 50893 50907 323 50920 50934 50947 50961 50974 50987 51001 51014 51028 51041 324 51055 51068 51081 51095 51108 51121 51135 51148 51162 51175 325 51188 51202 51215 51228 51242 51255 51268 51282 51295 51308 326 51322 51335 51348 51362 51375 51388 51402 51415 51428 51441 327 51455 51468 51481 51495 51508 51521 51534 51548 51561 51574 328 51587 51601 51614 51627 51640 51654 51667 51680 51693 51706 329 51720 51733 51746 51759 51772 51786 51799 51812 51825 51838 330 51851 51865 51878 51891 51904 51917 51930 51943 51957 51970 is 331 51983 51996 52009 52022 52035 52048 52061 52075 52088 52101 l 1 332 52114 52127 52140 52153 52166 52179 52192 52205 52218 52231 2 8 333 52244 52257 52270 52284 52297 52310 52323 52336 52349 52362 334 52375 52388 52401 52414 52427 52440 52453 52466 52479 52492 335 52504 52517 52530 52543 52556 52569 52582 52595 52608 52621 336 52634 52647 52660 52673 52686 52699 52711 52724 52737 52750 337 52763 52776 52789 52802 52815 52827 52840 52853 52866 52879 338 52892 52905 52917 52930 52943 52956 52969 52982 52994 53007 339 53020 53033 53046 53058 53071 53084 53097 53110 53122 53135 912 340 53148 53161 53173 53186 53199 53212 53224 53237 53250 53263 341 53275 53288 53301 53314 53326 53339 53352 53364 53377 53390 342 53403 53415 53428 53441 53453 53466 53479 53491 53504 53517 343 53529 53542 53555 53567 53580 53593 53605 53618 53631 53643 344 53656 53668 53681 53694 53706 53719 53732 53744 53757 53769 345 53782 53794 53807 53820 53832 53845 53857 53870 53882 53895 346 53908 53920 53933 53945 53958 53970 53983 53995 54008 54020 347 54033 54045 54058 54070 54083 54095 54108 54120 54133 54145 848 54158 54170 54183 54195 54208 54220 54233 54245 54258 54270 :$49 54283 54295 54307 54320 54332 54345 54357 54370 54382 54394 350 54407 54419 54432 54444 54456 54469 54481 54494 54506 54518 Table 6. Logarithms. 827 10. 1 2 8 4 5 6 7 8 9 oir 350 54407 54419 54432 54444 54456 54469 54481 54494 54506 54518 12 351 54531 54543 54555 54568 54580 54593 54605 54617 54630 54642 l 352 54654 54667 54679 54691 54704 54716 54728 54741 54753 54765 2 353 54777 54790 54802 54814 54827 54839 54851 54864 54876 54888 s 354 54900 54913 54925 54937 54949 54962 54974 54986 54998 55011 * 355 55023 55035 55047 55060 55072 55084 55096 55108 55121 55133 5 356 55145 55157 55169 55182 55194 55206 55218 55230 55242 55255 6 857 55267 55279 55291 55303 55315 55328 55340 55352 55364 55376 7 858 55388 55400 55413 55425 55437 55449 55461 55473 55485 55497 8 359 55509 55522 55534 55546 55558 55570 55582 55594 55606 55618 9U 360 55630 55642 55654 55666 55678 55691 55703 55715 55727 55739 361 55751 55763 55775 55787 55799 55811 55823 55835 55847 55859 362 55871 55883 55895 55907 55919 55931 55943 55955 55967 55979 363 55991 56003 56015 56027 56038 56050 56062 56074 56086 56098 364 56110 56122 56134 56146 56158 56170 56182 56194 56205 56217 365 56229 56241 56253 56265 56277 56289 56301 56312 56324 56336 366 56348 56360 56372 56384 56396 56407 56419 56431 56443 56455 367 56467 56478 56490 56502 56514 56526 56538 56549 56561 56573 368 56585 56597 56608 56620 56632 56644 56656 56667 56679 56691 369 56703 56714 56726 56738 56750 56761 56773 56785 56797 56808 370 56820 56832 56844 56855 56867 56879 56891 56902 56914 56926 371 56937 56949 56961 56972 56984 56996 57008 57019 57031 57043 372 57054 57066 57078 57089 57101 57113 57124 57136 57148 57159 373 57171 57183 57194 57206 57217 57229 57241 57252 57264 57276 374 57287 57299 57310 57322 57334 57345 57357 57368 57380 57392 375 57403 57415 57426 57438 57449 57461 57473 57484 57496 57507 376 57519 57530 57542 57553 57565 57576 57588 57600 57611 57623 377 57634 57646 57657 57669 57680 57692 57703 57715 57726 57738 378 57749 57761 57772 57784 57795 57807 57818 57830 57841 57852 379 57864 57875 57887 57898 57910 57921 57933 57944 57955 57967 380 57978 57990 58001 58013 58024 58035 58047 58058 58070 58081 381 58092 58104 58115 58127 58138 58149 58161 58172 58184 58195 382 58206 58218 58229 58240 58252 58263 58274 58286 58297 58309 383 58320 58331 58343 58354 58365 58377 58388 58399 58410 58422 384 58433 58444 58456 58467 58478 58490 58501 58512 58524 58535 385 58546 58557 58569 58580 58591 58602 58614 58625 58636 58647 386 58659 58670 58681 58692 58704 58715 58726 58737 58749 58760 387 58771 58782 58794 58805 58816 58827 58838 58850 58861 58872 388 58883 58894 58906 58917 58928 58939 58950 58961 58973 58984 389 58995 59006 59017 59028 59040 59051 59062 59073 59084 59095 390 59106 59118 59129 59140 59151 59162 59173 59184 59195 59207 391 59218 59229 5940 59251 59262 59273 59284 59295 59306 59318 l 392 59329 59340 59351 59362 59373 59384 59395 59406 59417 59428 2 393 59439 59450 59461 59472 59483 59494 59506 59517 59528 59539 3 394 59550 59561 59572 59583 59594 59605 59616 59627 59638 59649 4 895 59660 59671 59682 59693 59704 59715 59726 59737 59748 59759 5 396 59770 59780 59791 59802 59813 59824 59835 59846 59857 59868 6 397 59879 59890 59901 59912 59923 59934 59945 59956 59966 59977 7 398 59988 59999 60010 60021 60032 60043 60054 60065 60076 60086 8 399 60097 60108 60119 60130 60141 60152 60163 60173 60184 60195 9 400 60206 60217 60228 60239 60249 60260 60271 60282 60293 60304 828 Logarithms. Table 6. JO, 1 2 3 4 5 6 7 8 9 oif. 400 60206 60217 60228 60239 60249 60260 60271 60282 60293 60304 " 401 60314 60325 60336 60347 60358^60369 60379 60390 60401 60412 l * 402 60423 60433 60444 60455 60466 60477 60487 60498 60509 60520 2 403 60531 60541 60552 60563 60574 60584 60595 60606 60617 60627 404 60638 60649 60660 60670 60681 60692 60703 60713 60724 60735 * 405 60746 60756 60767 60778 60788 60799 60810 60821 60831 60842 40(> 60853 60863 60874 60885 60895 60906 60917 60927 60938 60949 407 60959 60970 60981 60991 61002 61013 61023 61034 61045 61055 408 61066 61077 61087 61098 61109 61119 61130 61140 61151 61162 409 61172 61183 61194 61204 61215 61225 61236 61247 61257 61268 410 61278 61289 61300 61310 61321 61331 61342 61352 61363 61374 411 61384 61395 61405 61416 61426 61437 61448 61458 61469 61479 412 61490 61500 61511 61521 61532 61542 61553 61563 61574 61584 413 61595 61606 61616 61627 61637 61648 61658 61669 61679 61690 414 61700 61711 61721 61731 61742 61752 61763 61773 61784 61794 415 61805 61815 61826 61836 61847 61857 61868 61878 61888 61899 416 61909 61920 61930 61941 61951 619&2 61972 61982 61993 62003 417 62014 62024 62034 62045 62055 62066 62076 62086 62097 62107 418 62118 62128 62138 62149 62159 62170 62180 62190 62201 62211 419 62221 62232 62242 62252 62263 62273 62284 62294 62304 62315 420 62325 62335 62346 62356 62366 62377 62387 62397 62408 62418 10 421 62428 62439 62449 62459 62469 62480 62490 62500 62511 62521 1 1 422 62531 62542 62552 62562 62572 62583 62593 62603 62613 62624 2 423 62634 62644 62655 62665 62675 62685 62696 62706 62716 62726 424 62737 62747 62757 62767 62778 62788 62798 62808 62818 62829 425 62839 62849 62859 62870 62880 62890 62900 62910 62921 62931 426 62941 62951 62961 62972 62982 62992 63002 63012 63022 63033 427 63043 63053 63063 63073 63083 63094 63104 63114 63124 63134 428 63144 63155 63165 63175 63185 63195 63205 63215 63225 63236 429 63246 63256 63266 63276 63286 63296 63306 63317 63327 63337 430 63347 63357 63367 63377 63387 63397 63407 63417 63428 63438 431 63448 63458 63468 63478 63488 63498 63508 63518 63528 63538 432 63548 63558 63568 63579 63589 63599 63609 63619 63629 63639 433 63649 63659 63669 63679 63689 63699 63709 63719 63729 63739 434 63749 63759 63769 63779 63789 63799 63809 63819 63829 63839 435 63849 63859 63869 63879 63889 63899 63909 63919 63929 63939 436 63949 63959 63969 63979 63988 63998 64008 64018 64028 64038 437 64048 64058 64068 64078 64088 64098 64108 64118 64128 64137 438 64147 64157 64167 64177 64187 64197 64207 64217 64227 64237 439 64246 64256 64266 64276 64286 64296 64306 64316 64326 64335 440 64345 64355 64365 64375 64385 64395 64404 64414 64424 64434 441 64444 64454 64464 64473 64483 64493 64503 64513 64523 64532 442 64542 64552 64562 64572 64582 64591 64601 64611 64621 64631 443 64640 64650 64660 64670 61680 64689 64699 64709 64719 64729 444 64738 64748 64758 64768 64777 64787 64797 64807 64816 64826 445 64836 64846 64856 64865 64875 64885 64895 64904 64914 64924 446 64933 64943 64953 64963 64972 64982 64992 65002 65011 65021 447 65031 65040 65050 65060 65070 65079 65089 65099 65108 65118 448 65128 65137 65147 65157 65167 65176 65186 65196 65205 65215 449 65225 65234 65244 65254 65263 65273 65283 65292 65302 65312 450 65321 65331 65341 65350 65360 65369 65379 65389 65398 65408 Tables. Logarithms. 829 10. 1 2845 6 7 8 9 Dif. 450 65321 65831 65341 65350 65360 65369 65379 65389 65398 65408 451 65418 65427 65437 65447 65456 65466 65475 65485 65495 65504 452 65514 65523 65533 65543 65552 65562 65571 65581 65591 65600 453 65610 65619 65629 65639 65648 65658 65667 65677 65686 65696 454 65706 65715 65725 65734 65744 65753 65763 65772 65782 65792 455 65801 65811 65820 65830 65839 65849 65858 65868 65877 65887 456 65896 65906 65916 65925 65935 65944 65954 65963 65973 65982 457 65992 66001 66011 66020 66030 66039 66049 66058 66068 66077 458 66087 66096 66106 66115 66124 66134 66143 66153 66162 66172 459 66181 66191 66200 66210 66219 66229 66238 66247 66257 66266 460 66276 66285 66295 66304 66314 66323 66332 66342 66351 66361 461 66370 66380 66389 66398 66408 66417 66427 66436 66445 66455 462 66464 66474 66483 66492 66502 66511 66521 66530 66539 66549 463 66558 66567 66577 66586 66596 66605 66614 66624 6G633 66642 464 66652 66661 66671 66680 66689 66699 66708 66717 66727 66736 465 66745 66755 66764 66773 66783 66792 66801 66811 66820 66829 466 66839 66848 66857 66867 66876 66885 66894 66904 66913 66922 467 66932 66941 66950 66960 66969 66978 66987 66997 67006 67015 468 67025 67034 67043 67052 67062 67071 67080 67089 67099 67108 469 67117 67127 67136 67145 67154 67164 67173 67182 67191 67201 470 67210 67219 67228 67237 67247 67256 67265 67274 67284 67293 9 471 67302 67311 67321 67330 67339 67348 67357 67367 67376 67385 ' ' 472 67394 67403 67413 67422 67431 67440 67449 67459 67468 67477 2 2 473 67486 67495 67504 67514 67523 67532 67541 67550 67560 67569 474 67578 67587 67596 67605 67614 67624 67633 67642 67651 67660 475 67669 67679 67688 67697 67706 67715 67724 67733 67742 67752 476 67761 67770 67779 67788 67797 67806 67815 67825 97834 67843 477 67852 67861 67870 67879 67888 67897 67906 67916 67925 67934 478 67943 67952 67961 67970 67979 67988 67997 68006 68015 68024 479 68034 68043 68052 68061 68070 68079 68088 68097 68106 68115 480 68124 68133 68142 68151 68160 68169 68178 68187 68196 68205 481 68215 68224 68233 68242 68251 68260 68269 68278 68287 68296 482 68305 68314 68323 68332 68341 68350 68359 68368 68377 68386 483 68395 68404 68413 68422 68431 68440 68449 68458 68467 68476 484 68485 68494 68502 68511 68520 68529 68538 68547 68556 68565 485 68574 68583 68592 68601 68610 68619 68628 68637 68646 68655 486 68664 68673 68681 68690 68699 68708 68717 68726 68735 68744 487 68753 68762 68771 68780 68789 68797 68806 68815 68824 68833 488 68842 68851 68860 68869 68878 68886 68895 68904 68913 68922 489 68931 68940 68949 68958 68966 68975 68984 68993 69002 69011 490 69020 69028 69037 69046 69055 69064 69073 69082 69090 69099 491 69108 69117 69126 69135 69144 69152 69161 69170 69179 69188 492 69197 69205 69214 69223 69232 69241 69249 69258 69267 69276 493 69285 69294 69302 69311 69320 69329 69338 69346 69355 69364 494 69373 69381 69390 69399 69408 69417 69425 69434 69443 69452 495 69461 69469 69478 69487 69496 69504 69513 69522 69531 69539 496 69548 69557 69566 69574 69583 69592 69601 69609 69618 69627 497 69636 69644 69653 69662 69671 69679 69688 69697 69705 69714 498 69723 69732 69740 69749 69758 69767 69775 69784 69793 69801 499 69810 69819 69827 69836 69845 69854 69862 69871 69880 69888 500 69897 69906 69914 69923 69932 69940 69949 69958 69966 69975 830 Logarithms. Table 6. 10. I * 3 4 5 6 7 8 9 u 500 69897 69906 69914 69923 69932 69940 69949 69958 69966 69975 501 69984 69992 70001 70010 70018 70027 70036 70044 70053 70062 1 502 70070 70079 70088 70096 70105 70114 70122 70131 70140 70148 2 503 70157 70165 70174 70183 70191 70200 70209 70217 70226 70234 3 504 70243 70252 70260 70269 70278 70286 70295 70303 70312 70321 * 505 70329 70338 70346 70355 70364 70372 70381 70389 70398 70406 8 506 70415 70424 70432 70441 70449 70458 70467 70475 70484 70492 6 507 70501 70509 70518 70526 70535 70544 70552 70561 70569 70578 7 508 70586 70595 70603 70612 70621 70629 7063S 70646 70655 70063 509 70672 70680 70689 70697 70706 70714 70723 70731 70740 70749 9 510 70757 70766 70774 70783 70791 70800 70808 70817 70825 70834 511 70842 70851 70859 70868 70876 70885 70893 70902 70910 70919 512 70927 70935 70944 70952 70961 70969 70978 70986 70995 71003 513 71012 71020 71029 71037 71046 71054 71063 71071 71079 71088 514 71096 71105 71113 71122 71130 71139 71147 71155 71164 71172 515 71181 71189 71198 71206 71214 71223 71231 71240 71248 71257 516 71265 71273 71282 71290 71299 71307 71315 71324 71332 71341 517 71349 71357 71366 71374 71383 71391 71399 71408 71416 71425 518 71433 71441 71450 71458 71466 71475 71483 71492 71500 71508 519 71517 71525 71533 71542 71550 71559 71567 71575 71584 71592 520 71600 71609 71617 71625 71634 71642 71650 71659 71667 71675 i 521 71684 71692 71700 71709 71717 71725 71734 71742 71750 71759 l 522 71767 71775 71784 71792 71800 71809 71817 71825 71834 71842 2 523 71850 71858 71867 71875 71883 71892 71900 71908 71917 71925 3 524 71933 71941 71950 71958 71966 71975 71983 71991 71999 72008 4 525 72016 72024 72032 72041 72049 72057 72066 72074 72082 72090 6 526 72099 72107 72115 72123 72132 72140 72148 72156 72165 72173 6 527 72181 72189 72198 72206 72214 72222 72230 72239 72247 72255 7 528 72263 72272 72280 72288 72296 72304 72313 72321 72329 72337 8 529 72346 72354 72362 72370 72378 72387 72395 72403 72411 72419 530 72428 72436 72444 72452 72460 72469 72477 72485 72493 72501 531 72509 72518 72526 72534 72542 72550 72558 72567 72575 72583 532 72591 72599 72607 72616 72624 72632 72640 72648 72656 72665 533 72673 72681 72689 72697 72705 72713 72722 72730 72738 72746 534 72754 72762 72770 72779 72787 72795 72803 72811 72819 72827 535 72835 72843 72852 72860 72868 72876 72884 72892 72900 72908 536 72916 72925 72933 72941 72949 72957 72965 72973 72981 72989 537 72997 73006 73014 73022 73030 73038 73046 73054 73062 73070 538 73078 73086 73094 73102 73111 73119 73127 73135 73143 73151 539 73159 73167 73175 73183 73191 73199 73207 73215 73223 73231 540 73239 73247 73255 73263 73272 73280 73288 73296 73304 73312 541 73320 73328 73336 73344 73352 73360 73368 73376 73384 73392 542 73400 73408 73416 73424 73432 73440 73448 73456 73464 73472 543 73480 73488 73496 73504 73512 73520 73528 73536 73544 73552 544 73560 73568 73576 73584 73592 73600 73608 73616 73624 73632 545 73640 73648 73656 73664 73672 73679 73687 73695 73703 73711 546 73719 73727 73735 73743 73751 73759 73767 73775 73783 73791 547 73799 73807 73815 73823 73830 73838 73846 73854 73862 73870 548 73878 73886 73894 73902 73910 73918 73926 73933 73941 73949 549 73957 73965 73973 73981 73989 73997 74005 74013 74020 74028 550 74036 74044 74052 74060 74068 74076 74084 74092 74099 74107 Table 6. Logarithms. 831 NO. f 2 8 4 5 6 7 8 9 off 550 74036 74044 74052 74060 74068 74076 74084 74092 74099 74107 531 74115 74123 74131 74139 74147 74155 74162 74170 74178 74186 ll 552 74194 74202 74210 74218 74225 74233 74241 74249 74257 74265 2a 553 74273 74280 74288 74296 74304 74312 74320 74327 74335 74343 8 554 74351 74359 74367 74374 74382 74390 74398 74406 74414 74421 * 8 555 74429 74437 74445 74453 74461 74468 74476 74484 74492 74500 ** 556 74507 74515 74523 74531 74539 74547 74554 74562 74570 74578 e * 557 74586 74593 74601 74609 74617 74624 74632 74640 74648 74656 7 6 558 74663 74671 74679 74687 74695 74702 74710 74718 74726 74733 8 ' 559 74741 74749 74757 74764 74772 74780 74788 74796 74803 74811 9<7 560 74819 74827 74834 74842 74850 74858 74865 74873 74881 74889 561 74896 74904 74912 74920 74927 74935 74943 74950 74958 74966 562 74974 74981 749S9 74997 75005 75012 75020 75028 75035 75043 563 75051 75059 75066 75074 75082 75089 75097 75105 75113 75120 564 75128 75136 75143 75151 75159 75166 75174 75182 75189 75197 565 75205 75213 75220 75228 75236 75243 75251 75259 75266 75274 566 75282 75289 75297 75305 75312 75320 75328 75335 75343 75351 567 75358 75366 75374 75381 75389 75397 75404 75412 75420 75427 568 75435 75442 75450 75458 75465 75473 75481 75488 75496 75504 569 75511 75519 75526 75534 75542 75549 75557 75565 75572 75580 570 75587 75595 75603 75610 75618 75626 75633 75641 75648 75656 571 75664 75671 75679 75686 75694 75702 75709 75717 75724 75732 572 75740 75747 75755 75762 75770 75778 75785 75793 75800 75808 573 75815 75823 75831 75838 75846 75853 75861 75868 75876 75884 574 75891 75899 75906 75914 75921 75929 75937 75944 75952 75959 575 75967 75974 75982 75989 75997 76005 76012 76020 76027 76035 576 76042 76050 76057 76065 76072 76080 76087 76095 76103 76110 577 76118 76125 76133 76140 76148 76155 76163 76170 76178 76185 578 76193 76200 76208 76215 76223 76230 76238 76245 76253 76260 579 76268 76275 76283 76290 76298 76305 76313 76320 76328 76335 580 76343 76350 76358 76365 76373 76380 76388 76395 76403 76410 581 76418 76425 76433 76440 76448 76455 76462 76470 76477 76485 582 76492 76500 76507 76515 76522 76530 76537 76545 76552 76559 583 76567 76574 76582 76589 76597 76604 76612 76619 76626 76634 584 76641 76649 76656 76664 76671 76678 76686 76693 76701 76708 585 76716 76723 76730 76738 76745 76753 76760 76768 76775 76782 586 76790 76797 76805 76812 76819 76827 76834 76842 76849 76856 587 76864 76871 76879 76886 76893 76901 76908 76916 76923 76930 588 76938 76945 76953 76960 76967 76975 76982 76989 76997 77004 589 77012 77019 77026 77034 77041 77048 77056 77063 77070 77078 590 77085 77093 77100 77107 77115 77122 77129 77137 77144 77151 * 591 77159 77166 77173 77181 77188 77195 77203 77210 77217 77225 * 592 77232 77240 77247 77254 77262 77269 77276 77283 77291 77298 2 593 77305 77313 77320 77327 77335 77342 77349 77357 77364 77371 8 594 77379 77386 77393 77401 77408 77415 77422 77430 77437 77444 4 595 77452 77459 77466 77474 77481 77488 77495 77503 77510 77517 5 596 77525 77532 77539 77546 77554 77561 77568 77576 77583 77590 e 597 77597 77605 77612 77619 77627 77634 77641 77648 77656 77663 7 598 77670 77677 77685 77692 77699 77706 77714 77721 77728 77735 8 599 77743 77750 77757 77764 77772 77779 77786 77793 77801 77808 9 600 77815 77822 77830 77837 77844 77851 77859 77866 77873 77880 832 Logarithms. Tables. 10, a 1 2 3 4 5 6 7 8 9 on 600 77815 77822 77880 77837 77844 77851 77S59 77866 77873 77880 601 77887 77895 77902 77909 77916 77924 77931 77938 77945 77952 602 77960 77967 77974 77981 77988 77996 78003 78010 78017 78025 603 78032 78039 78046 78053 78061 78068 78075 78082 78089 78097 604 78104 78111 78118 78125 78132 78140 78147 78154 78161 78168 605 78176 78183 78190 78197 78204 78211 78219 78226 78233 78240 606 78247 78254 78262 78269 78276 78283 78290 78297 78305 78312 607 78319 78326 78333 78340 78347 78355 78362 78369 78376 78383 608 78390 78398 78405 78412 78419 78426 7843P, 78440 78447 78455 609 78462 78469 78476 78483 78490 78497 78504 78512 78519 78526 610 78533 78540 78547 78554 78561 78569 78576 78583 78590 78597 611 78604 78611 78618 78625 78633 78640 78647 78654 78661 78608 612 78675 78682 78689 78696 78704 78711 78718 78725 78732 78739 613 78746 78753 78760 78767 78774 78781 78789 78796 78803 78810 614 78817 78824 78831 78838 78845 78852 78859 78866 78873 78880 615 78888 78895 78902 78909 78916 78923 78930 78937 78944 78951 616 78958 78965 78972 78979 78986 78993 79000 79007 79014 79021 617 79029 79036 79043 79050 79057 79064 79071 79078 79085 79092 618 79099 79106 79113 79120 79127 79134 79141 79148 79155 79162 619 79169 79176 79183 79190 79197 79204 79211 79218 79225 79232 620 79239 79246 79253 7&260 79267 79274 79281 79288 79295 79302 ? 621 79309 79316 79323 79330 79337 79344 79351 79358 79365 79372 ' ' 622 79379 79386 79393 79400 79407 79414 79421 79428 79435 79442 2 623 79449 79456 79463 79470 79477 79484 79491 79498 79505 79511 32 624 79518 79525 79532 79539 79546 79553 79560 79567 79574 79581 43 625 79588 79595 79602 79609 79616 79623 79630 79637 79644 79650 54 626 79657 79964 79671 79678 79685 79692 79699 79706 79713 79720 64 627 79727 79734 79741 79748 79754 79761 79768 79775 79782 79789 7S 628 79796 79803 79810 79817 79824 79831 79837 79844 79851 79858 86 629 79865 79872 79879 79886 79893 79900 79906 79913 79920 79927 9 630 79934 79941 79948 79955 79962 79969 79975 79982 79989 79996 631 80003 80010 80017 80024 80030 80037 80044 80051 80058 80065 632 80072 80079 80085 80092 80099 80106 80113 80120 80127 80134 633 80140 80147 80154 80161 80168 80175 80182 80188 80195 80202 634 80209 80216 80223 80229 80236 80243 80250 80257 80264 80271 635 80277 80284 80291 80298 80305 80312 80318 80325 80332 80339 636 80346 80353 80359 80366 80373 80380 80387 80393 80400 80407 637 80414 80421 80428 80434 80441 80448 80455 80462 80468 80475 638 80482 80489 80496 80502 80509 80516 80523 80530 80536 80543 639 80550 80557 80561 80570 80577 80584 80591 80598 80604 80611 640 80618 80625 80632 80638 80645 80652 80659 80665 80672 80679 641 80686 80693 80699 80706 80713 80720 80726 80733 80740 80747 642 80754 80760 80767 80774 80781 80787 80794 80801 80808 80814 643 80821 80828 80835 80841 80848 80855 808o2 80868 80875 80882 644 80889 80895 80902 80909 80916 80922 80929 80936 80943 80949 645 80956 80963 80969 80976 80983 80990 80996 81003 81010 81017 646 81023 81030 81037 81043 81050 81057 81064 81070 81077 81084 647 81090 81097 81104 81111 81117 81124 81131 81137 81144 81151 648 81158 81164 81171 81178 81184 81191 81198 81204 81211 81218 649 81224 81231 81238 81245 81251 81258 81265 81271 81278 81285 650 81291 81298 81305 81311 81318 81325 81331 81338 81345 81351 rabies. Logarithms. . 833 FO. f 2 S 4 5 6 7 8 9 oif. 650 8129J 8129$ 81305 81311 81318 81325 81331 81338 81345 81351 ? 651 81358 81365 81371 81378 81385 81391 81398 81405 81411 81418 > ! 652 81425 81431 81438 81445 81451 81458 81465 81471 81478 81485 ~ ' 653 81491 81498 81505 81511 81518 81525 81531 81538 81544 81551 s - 654 81558 81564 81571 81578 81584 81591 81598 81604 81611 81617 48 655 81624 81631 81637 81644 81651 81657 81664 81671 81677 81684 4 656 81690 81697 81704 81710 81717 81723 81730 81737 81743 81750 64 657 81757 81763 81770 81776 81783 81790 81796 81803 81809 81816 7 658 81823 81829 81836 81842 81849 81856 81862 81869 81875 81882 8 6 659 81889 81895 81902 81908 81915 81921 81928 81935 81941 81948 9 e 660 81954 81961 81968 81974 81981 81987 81994 82000 82007 82014 661 82020 82027 82033 82040 82046 82053 82060 82066 82073 82079 662 82086 82092 82099 82105 82112 82119 82125 82132 82138 82145 663 82151 82158 82164 82171 82178 82184 82191 82197 82204 82210 664 82217 82223 82230 82236 82243 82249 82256 82263 82269 82276 665 82282 82289 82295 82302 82308 82315 82321 82328 82334 82341 666 82347 82354 82360 82367 82373 82380 82387 82393 82400 82406 667 82413 82419 82426 82432 82439 82445 82452 82458 82465 82471 668 82478 82484 82491 82497 82504 82510 82517 82523 82530 82536 669 82543 82549 82556 82562 82569 82575 82582 82588 82595 82601 670 82607 82614 82620 82627 82633 82640 82646 82653 82659 82666 671 82672 82679 82685 82692 82698 82705 82711 82718 82724 82730 672 82737 82743 82750 82756 82763 82769 82776 82782 82789 82795 673 82S02 82808 82814 82821 82827 82834 82840 82847 82853 82800 674 82866 82872 82879 82885 82892 82898 82905 82911 82918 82924 675 82930 82937 82943 82950 82956 82963 82969 82975 82982 82988 676 82995 83001 8300S 83014 83020 83027 83033 83040 83046 83052 677 83059 83065 83072 83078 83085 83091 83097 83104 83110 83117 678 83123 83129 83136 83142 83149 83155 83161 83168 83174 83181 679 83187 83193 83200 83206 83213 83219 83225 83232 83238 83245 680 83251 83257 83264 83270 83276 83283 83289 83296 83302 83308 681 83315 83321 83327 83334 83340 83347 83353 83359 83366 83372 682 S3378 833S5 83391 83398 83404 83410 83417 83423 83429 83436 683 83442 83448 83455 83461 83467 83474 83480 83487 83493 83499 684 83506 83512 83518 83525 83531 83537 83544 83550 83556 83563 685 83569 83575 83582 83588 83594 83601 83607 83613 83620 83626 686 83632 83639 83C45 83C51 83658 83664 83670 83677 83683 83689 687 83690 83702 S3708 83715 83721 83727 83734 83740 83746 83753 688 83759 83765 83771 83778 83784 83790 83797 83803 83809 83816 689 SH822 83828 83835 83841 83847 83853 83860 83866 83872 83879 9 * 690 83885 83891 83897 83904 83910 83916 83923 83929 83935 83942 091 83948 83954 83960 83967 83973 83979 83985 83992 83998 84004 692 S4011 84017 84023 84029 84036 84042 84048 84055 84061 84067 693 84073 84080 84086 84092 84098 84105 84111 84117 84123 84130 694 84136 84142 84148 84155 84161 84167 84173 84180 84186 84192 695 84198 84205 84211 84217 84223 84230 84236 84242 84248 84255 696 84261 84267 S4273 84280 84286 84292 84298 84305 84311 84317 697 84323 84330 84336 84342 84348 84354 84361 84367 84373 84379 698 84386 S4392 84398 84404 84410 84417 84423 84429 84435 84442 699 84148 84454 84460 S44G6 8-1473 84479 84485 84491 84497 84504 700 84510 84516 84522 84528 S4535 84541 84547 84553 84559 84566 834 Logarithms. Table6 50. fllt345789 on. 700 84510 84516 84522 84528 84535 84541 84547 84553 84559 84566 701 84572 84578 84584 84590 84597 84603 84609 84615 84621 84628 702 84634 84640 84646 84652 84658 84665 84671 84677 84083 84689 703 84696 84702 84708 84714 84720 84726 84733 84739 84745 84751 704 84757 84763 84770 84776 84782 84788 84794 84800 84807 84813 705 84819 84825 84831 84837 84844 84850 84856 84862 84868 84874 706 84880 84887 84893 84899 84905 84911 84917 84924 84930 84936 707 84942 84948 84954 84960 84967 84973 84979 84985 84991 84997 708 85003 85009 85016 85022 85028 85034 85040 85046 85052 85058 709 85065 85071 85077 85083 85089 85095 85101 85107 85114 85120 710 85126 85132 85138 85144 85150 85156 85163 85169 85175 85181 711 85187 85193 85199 85205 85211 85217 85224 85230 85236 85242 712 85248 85254 85260 85266 85272 85278 85285 85291 85297 85303 713 85309 85315 85321 85327 85333 85339 85345 85352 85358 85364 714 85370 85376 85382 85388 85394 85400 85406 85412 85418 85425 715 85431 85437 85443 85449 85455 85461 85467 85473 85479 85485 717 85491 85497 85503 85509 85516 85522 85528 85534 85540 85546 716 85552 85558 85564 85570 85576 85582 85588 85594 85600 85606 718 85612 85618 85625 85631 85637 85643 85649 85655 85661 85667 719 85673 85679 85685 85691 85697 85703 85709 85715 85721 85727 720 85733 85739 85745 85751 85757 85763 85769 85775 85781 85788 e 721 85794 85800 85806 85812 85818 85824 85830 85836 85842 85848 l 1 722 85854 85860 85866 85872 85878 85884 85890 85896 85902 85908 2 1 723 85914 85920 85926 85932 85938 85944 85950 85956 85962 85968 724 85974 85980 85986 85992 85998 86004 86010 86016 86022 86028 725 86034 86040 86046 86052 86058 86064 86070 86076 86082 86088 726 86094 86100 86106 86112 86118 86124 86130 86136 86141 86147 727 86153 86159 86165 86171 86177 86183 86189 86195 86201 86207 728 86213 86219 86225 86231 86237 86243 86249 86255 86261 86267 729 86273 86279 86285 86291 86297 86303 86308 86314 86320 86326 730 86332 86338 86344 86350 86356 86362 86368 86374 86380 86386 7H1 86392 86398 86404 86410 86415 86421 86427 86433 86439 86446 732 86451 86457 86463 86469 86475 86481 86487 86493 86499 86504 733 86510 86516 86522 86528 86534 86540 86546 86552 86558 86564 734 86570 86576 86581 86587 86593 86599 86605 86611 86617 86623 735 86629 86635 86641 86646 86652 86658 86664 86670 86676 86682 736 86688 86694 86700 86705 86711 86717 86723 86729 86735 86741 737 86747 86753 86759 86764 86770 86776 86782 86788 86794 86800 738 86806 86812 86817 86823 86829 86835 86841 86847 86853 86859 739 86864 86870 86876 86882 86888 86894 86900 86906 86911 86917 740 86923 86929 86935 86941 86947 86953 86958 86964 86970 86976 741 86982 86988 86994 86999 87005 87011 87017 87023 87029 87035 742 87040 87046 87052 87058 87064 87070 87075 87081 87087 87093 743 87099 87105 87111 87116 87122 87128 87134 87140 87146 87151 744 87157 87163 87169 87175 87181 87186 87192 87198 87204 87210 745 87216 87221 87227 87233 87239 87245 87251 87256 87262 87268 746 87274 87280 87286 87291 87297 87303 87309 87315 87320 87326 747 87332 87338 87344 87349 87355 87361 87367 87373 87379 87384 748 87390 87396 87402 87408 87413 87419 87425 87431 87437 87442 749 87448 87454 87460 87466 87471 87477 87483 87489 87495 87500 750 87506 87512 87518 87523 87529 87535 87541 87547 87552 87558 Table 6. Logarithms. 835 10. 0123456780 oif. 750 87506 87512 87518 87523 87529 87535 87541 87547 87552 87558 751 87564 87570 87576 87581 87587 87593 87599 87604 87610 87616 752 87622 87628 87633 87639 87645 87651 87656 87662 87668 87674 753 87679 87685 87691 87697 87703 87708 87714 87720 87726 87731 754 87737 87743 87749 87754 87760 87766 87772 87777 87783 87789 755 87795 87800 87806 87812 87818 87823 87829 87835 87841 87846 756 87852 87858 87864 87869 87875 87881 87887 87892 87898 87904 757 87910 87915 87921 87927 87933 87938 87944 87950 87955 87961 758 87967 87973 87978 87984 87990 87996 88001 88007 88013 88018 750 88024 88030 88036 88041 88047 88053 88058 88064 88070 88076 760 88081 88087 88093 88098 88104 88110 88116 88121 88127 88133 761 88138 88144 88150 88156 88161 88167 88173 88178 88184 88190 762 88195 88201 88207 88213 88218 88224 88230 88235 88241 88247 763 88252 88258 88264 88270 88275 88281 88287 88292 88298 88304 764 88309 88315 88321 88326 88332 88338 88343 88349 88355 88360 765 88366 88372 88377 88383 88389 88395 88400 88406 88412 88417 766 88423 88429 88434 88440 88446 88451 88457 88463 88468 88474 767 88480 88485 88491 88497 88502 88508 88513 88519 88525 88530 768 88536 88542 88547 88553 88559 88564 88570 88576 88581 88587 760 88593 88598 88604 88610 88615 88621 88627 88632 88638 88643 770 88649 88655 88660 88666 88672 88677 88683 88689 88694 88700 e 771 88705 88711 88717 88722 88728 88734 88739 88745 88750 88756 l 772 88762 88767 88773 88779 88784 88790 88795 88801 88807 88812 * 773 88818 88824 88829 88835 88840 88846 88852 88857 88863 88868 3 * 774 88874 88880 88885 88891 88897 88902 88908 88913 88919 88925 4 2 775 88930 88936 88941 88947 88953 88958 88964 88969 88975 88981 5 8 776 88986 88992 38997 89003 89009 89014 89020 89025 89031 89037 e 4 777 89042 89048 89053 89059 89064 89070 89076 89081 89087 89092 7 4 778 89098 8910 i 89109 89115 89120 89126 89131 89137 89143 89148 8 770 89154 89159 89165 89170 89176 89182 89187 89193 89198 89204 9 fi 780 89209 89215 89221 89226 89232 89237 89243 89248 89254 89260 781 89265 89271 89276 89282 89287 89293 89298 89304 89310 89315 782 89321 89326 89332 89337 89343 89348 89354 89360 89365 89371 783 89376 89382 89387 89393 89398 89404 89409 89415 89421 89426 784 89432 89437 89443 89448 89454 89459 89465 89470 89476 89481 785 89487 89492 89498 89504 89509 89515 89520 89526 89531 89537 786 89542 89548 89553 89559 89564 89570 89575 89581 89586 89592 787 89597 89603 89609 89614 89620 89625 89631 89636 89642 89647 788 89653 89658 89664 89669 89675 89680 89686 89691 89697 89702 780 89708 89713 89719 89724 89730 89735 89741 89746 89752 89757 700 89763 89768 89774 89779 89785 89790 89796 89801 89807 89812 701 89818 89823 89829 89834 89840 89845 89851 89856 89862 89867 702 89873 89878 89883 89889 89894 89900 89905 89911 89916 89922 703 89927 89933 89938 89944 89949 89955 89960 89966 89971 89977 704 89982 89988 89993 89998 90004 90009 90015 90020 90026 90031 705 90037 90042 90048 90053 90059 90064 90069 90075 90080 90086 706 90091 90097 90102 90108 90113 90119 90124 90129 90135 90140 797 90146 00151 90157 90162 90168 90173 90179 90184 90189 90195 798 90200 90206 90211 90217 90222 90227 90233 90238 90244 90249 799 90255 90260 90266 90271 90276 90282 90287 90293 90298 90304 800 90309 90314 90320 90325 90331 90336 90342 90347 90352 90358 836 Logarithms. Table 6. 10, OI28456739W. 800 90309 90314 90320 90325 90331 90336 90342 90347 90352 90358 801 90363 90369 90374 90380 90385 90390 90396 90401 90407 90412 802 90417 90423 90428 90434 90439 90445 90450 90455 90461 90466 803 90472 90477 90482 90488 90493 90499 90504 90509 90515 90520 804 90526 90531 90536 90542 90547 90553 90558 90563 90569 90574 805 90580 90585 90590 90596 90601 90607 90612 90617 90623 90628 806 90634 90639 90644 90650 90655 90660 90666 90671 90677 90682 807 90687 90693 90698 90703 90709 90714 90720 90725 90730 90736 808 90741 90747 90752 90757 90763 90768 90773 90779 90784 90789 809 90795 90800 90806 90811 90816 90822 90827 90832 90838 90843 810 90849 90854 90859 90865 90870 90875 90881 90886 90891 90897 811 90902 90907 90913 90918 90924 90929 90934 90940 90945 90950 812 90956 90961 90966 90972 90977 90982 90988 90993 90998 91004 813 91009 91014 91020 91025 91030 91036 91041 91046 91052 91057 814 91062 91068 91073 91078 91084 91089 91094 91100 91105 91110 815 91116 91121 91126 91132 91137 91142 91148 91153 91158 91164 816 91169 91174 91180 91185 91190 91196 91201 91206 91212 91217 817 91222 91228 91233 91238 91243 91249 91254 91259 91265 91270 818 91275 91281 91286 91291 91297 91302 91307 91312 91318 91323 819 91328 91334 91339 91344 91350 91355 91360 91365 91371 91376 820 91381 91387 91392 91397 91403 91408 91413 91418 91424 91429 & 821 91434 91440 91445 91450 91455 91461 91466 91471 91477 91482 * > 822 91487 91492 91498 91503 91508 91514 91519 91524 91529 91535 2 823 91540 91545 91551 91556 91561 91566 91572 91577 91582 91587 8 * 824 91593 91598 91603 91609 91614 91619 91624 91630 91635 91640 4 2 825 91645 91651 91656 91661 91666 91672 91677 91682 91687 91693 6$ 826 91698 91703 91709 91714 91719 91724 91730 91735 91740 91745 6 8 827 91751 91756 91761 91766 91772 91777 91782 91787 91793 91798 7 * 828 91803 91808 91814 91819 91824 91829 91834 91840 91845 91850 84 829 91855 91861 91866 91871 91876 91882 91887 91892 91897 91903 9I 830 91908 91913 91918 91924 91929 91934 91939 91944 91950 91955 831 91960 91965 91971 91976 91981 91986 91991 91997 92002 92007 832 92012 92018 92023 92028 92033 92038 92044 92049 92054 92059 833 92065 92070 92075 92080 92085 92091 92096 92101 92106 92111 834 92117 92122 92127 92132 92137 92143 92148 92153 92158 92163 835 92169 92174 92179 92184 92189 92195 92200 92205 92210 92215 836 92221 92226 92231 92236 92241 92247 92252 92257 92262 92267 837 92273 92278 92283 92288 92293 92298 92304 92309 92314 92319 838 92324 92330 92335 92340 92345 92350 92355 92361 92366 92371 839 92376 92381 92387 92392 92397 92402 92407 92412 92418 92425 840 92428 92433 92438 92443 92449 92454 92459 92464 92469 92474 841 92480 92485 92490 92495 92500 92505 92511 92516 92521 92526 842 92531 92536 92542 92547 92552 92557 92562 92567 92572 92578 843 92583 92588 92593 92598 92603 92609 92614 92619 92624 92629 844 92634 92639 92645 92650 92655 92660 92665 92670 92675 92681 845 92686 92691 92696 92701 92706 92711 92716 92722 92727 92732 846 92737 92742 92747 92752 92758 92763 92768 92773 92778 92783 847 92788 92793 92799 92804 92809 92814 92819 92824 92829 92834 848 92840 92845 92850 92855 92860 92865 92870 92875 92881 92886 849 92891 92896 92901 92906 92911 92916 92921 92927 92932 92937 850 92942 92947 92952 92957 92962 92967 92973 92978 929S3 92988 Table 6. Logarithms. 837 HO. 01 2345 6739 on 850 92942 92947 92952 92957 92962 92967 92973 92978 92983 92988 851 92993 92998 93003 93008 93013 93018 93024 93029 93034 93039 852 93044 93049 93054 93059 93064 93069 93075 93080 93085 93090 853 93095 93100 93105 93110 93115 93120 93125 93131 93136 93141 854 93146 93151 93156 93161 93166 93171 93176 93181 93186 93192 855 93197 93202 93207 93212 93217 93222 93227 93232 93237 93242 850 93247 93252 93258 93263 93268 93273 93278 93283 93288 93293 857 93298 93303 93308 93313 93318 93323 93328 93334 93339 93344 858 93349 93354 93359 93364 93369 93374 93379 93384 93389 93394 859 93399 93404 93409 93414 93420 93425 93430 93435 93440 93445 860 93450 93455 93460 93465 93470 93475 93480 93485 93490 93495 861 93500 93505 93510 93515 93520 93526 93531 93536 93541 93546 862 93551 93556 93561 93566 93571 93576 93581 93586 93591 93596 863 93601 93606 93611 93616 93621 93626 93631 93636 93641 93646 864 93651 93656 93661 93666 93671 93676 93682 93687 93692 93697 865 93702 93707 93712 93717 93722 93727 93732 93737 93742 93747 866 93752 93757 93762 93767 93772 93777 93782 93787 93792 93797 867 93802 93807 93812 93817 93822 93827 93832 93837 93842 93847 868 93852 93857 93862 93867 93872 93877 93882 93887 93892 93897 869 93902 93907 93912 93917 93922 93927 93932 93937 93942 93947 870 93952 93957 93962 93967 93972 93977 93982 93987 93992 93997 * 871 94002 94007 94012 94017 94022 94027 94032 94037 94042 94047 l 872 94052 94057 94062 94067 94072 94077 94082 94086 94091 94096 2 873 94101 94106 94111 94116 94121 94126 94131 94136 94141 9414C 3 874 94151 94156 94161 94166 94171 94176 94181 94186 94191 94190* 875 94201 94206 94211 94216 94221 94226 94231 94236 94240 94245 s 876 94250 94255 94260 94265 94270 94275 94280 94285 94290 94295 6 877 94300 94305 94310 94315 94320 94325 94330 94335 94340 94345 7 * 878 94349 94354 94359 94364 94369 94374 94379 94384 94389 94394 s * 879 94399 94404 94409 94414 94419 94424 94429 94433 94438 94443 9f 880 94448 94453 94458 94463 94468 94473 94478 94483 94488 94493 881 94498 94503 94507 94512 94517 94522 94527 94532 94537 94542 882 94547 94552 94557 94562 94567 94571 94576 94581 94586 94591 883 94596 94601 94606 94611 94616 94621 94626 94630 94635 94640 884 94645 94650 94655 94660 94665 94670 94675 94680 94685 94689 885 94694 94699 94704 94709 94714 94719 94724 94729 94734 94738 886 94743 94748 94753 94758 94763 94768 94773 94778 94783 94787 887 94792 94797 94802 94807 94812 94817 94822 94827 94832 94836 888 94841 94846 94851 94856 94861 94866 94871 94876 94880 94885 889 94890 94895 94900 94905 94910 94915 94919 94924 94929 94934 890 94939 94944 94949 94954 94959 94963 94968 94973 94978 94988 891 94988 94993 94998 95002 95007 95012 95017 95022 95027 95032 892 95036 95041 -95046 95051 95056 95061 95066 95071 95075 95080 893 95085 95090 95095 95100 95105 95109 95114 95119 95124 95129 894 95134 95139 95143 95148 95153 95158 95163 95168 95173 95177 895 95182 95187 95192 95197 95202 95207 95211 95216 95221 95226 896 95231 95236 95240 95245 95250 95255 95260 95265 95270 95274 897 95279 95284 95289 95294 95299' 95303 95308 95313 95318 95323 898 95328 95332 95337 95342 95347 95352 95357 95361 95366 95371 899 95376 95381 95386 95390 95395 95400 95405 95410 95415 95419 900 95424 95429 95434 95439 95444 95448 95453 95458 95463 9546S 838 Logarithms. Table 6. 10, 1 2 3 4 5 6 7 8 9 OK, 900 95424 95429 95434 95439 95444 95448 95453 95158 95463 95468 901 95472 95477 95482 95487 95492 95497 95501 95506 95511 95516 902 95521 95525 95530 95535 95540 95545 95550 95554 95559 95564 903 95569 95574 95578 95583 95588 95593 95598 95602 95607 95612 904 95617 95622 95626 95631 95636 95641 95646 95650 95655 95660 905 95665 95670 95674 95679 95684 95689 95694 95698 95703 95708 906 95713 95718 95722 95727 95732 95737 95742 95746 95751 95756 907 95761 95766 95770 95775 95780 95785 95789 95794 95799 95804 908 95809 95813 95818 95823 95828 95832 95837 95842 95847 95852 909 95856 95861 95866 95871 95875 95880 95885 95890 95895 95899 910 95904 95909 95914 95918 95923 95928 95933 95938 95942 9594V 911 95952 95957 95961 95966 95971 95976 95980 95985 95990 95995 912 95999 96004 96009 96014 96019 96023 96028 96033 96038 96042 913 96047 96052 96057 96061 96066 96071 96076 96080 96085 96090 914 96095 96099 96104 96109 96114 96118 96123 96128 96133 96137 915 96142 96147 96152 96156 96161 96166 96171 96175 96180 96185 916 96190 96194 96199 96204 96209 96213 96218 96223 96227 96232 917 96237 96242 96246 96251 96256 96261 96265 96270 96275 96280 918 96284 96289 96294 96298 96303 96308 96313 96317 96322 96327 919 96332 96336 96341 96346 96350 96355 96360 96365 96369 96374 920 96379 96384 96388 96393 96398 96402 96407 96412 96417 96421 & 921 96426 96431 96435 96440 96445 96450 96454 96459 96464 96468 J > 922 96473 96478 96483 96487 96492 96497 96501 96506 96511 96515 2 l 923 96520 96525 96530 96534 96539 96544 96548 96553 96558 96562 3 2 924 96567 96572 96577 96581 96586 96591 96595 96600 96605 96609 4 2 925 96614 96619 96624 96628 96633 96638 96642 96647 96652 96656 * 926 96661 96666 96670 96675 96680 96685 96689 96694 96699 96703 e 927 96708 96713 96717 96722 96727 96731 96736 96741 96745 96750 7 928 96755 96759 96764 96769 96774 96778 96783 96788 96792 96797 8 929 96802 96806 96811 96816 96820 96825 96830 96834 96839 96844 930 96848 96853 96858 96862 96867 96872 96876 96881 96886 96890 931 96895 96900 96904 96909 96914 96918 96923 96928 96932 96937 932 96942 96946 96951 96956 96960 96965 96970 96974 96979 96984 933 96988 96993 96997 97002 97007 97011 97016 97021 97025 97030 934 97035 97039 97044 97049 97053 97058 97063 97067 97072 97077 935 97081 97086 97090 97095 97100 97104 97109 97114 97118 97123 936 97128 97132 97137 97142 97146 97151 97155 97160 97165 97169 937 97174 97179 97183 97188 97192 97197 97202 97206 97211 97216 938 97220 97225 97230 97234 97239 97243 97248 97253 97257 97262 939 97267 97271 97276 97280 97285 97290 97294 97299 97304 97308 940 97313 97317 97322 97327 97331 97336 97340 97345 97350 97354 941 97359 97364 97368 97373 97377 97382 97387 97391 97396 97400 942 97405 97410 97414 97419 97424 97428 97433 97437 97442 97447 943 97451 97456 97460 97465 97470 97474 97479 97483 97488 97493 944 97497 97502 97506 97511 97516 97520 97525 97529 97534 97539 945 97543 97548 97552 97557 97562 97566 97571 97575 97580 97585 946 97589 97594 97598 97603 97607 97612 97617 97621 97626 97630 947 97635 97640 97644 97649 97653 97658 97663 97667 97672 97676 948 97681 97685 97690 97695 97699 97704 97708 97713 97717 97722 949 97727 97731 97736 97740 97745 97749 97754 97759 97763 97768 950 97772 97777 97782 97786 97791 97795 97800 97804 97809 97813 Table 6. Logarithms. 839 Ko, 1 * 8 4 5 6 7 8 OH. 950 97772 97777 97782 97786 97791 97795 97800 97804 97809 97813 * 951 97818 97823 97827 97832 97836 97841 97845 97850 97855 97859 1 1 952 97864 97868 97873 97877 97882 97886 97891 97896 97900 97905 a l 953 97909 97914 97918 97923 97928 97932 97937 97941 97946 97950 8 * 954 97955 97959 97964 97968 97973 97978 97982 97987 97991 97996 * 2 955 98000 98005 98009 98014 98019 98023 98028 98032 98037 98041 8 * 956 98046 98050 98055 98059 98064 98068 98073 98078 98082 98087 6 * 957 98091 98096 98100 98105 98109 98114 98118 98123 98127 98132 T * 958 98137 98141 98146 98150 98155 98159 98164 98168 98173 98177 8 959 98182 98186 98191 98195 98200 98204 98209 98214 98218 98223 9 * 960 98227 98232 98236 98241 98245 98250 98854 98259 98263 98268 961 98272 98277 98281 98286 98290 98295 98299 98304 98308 98313 962 98318 98322 98327 98331 98336 98340 98345 98349 98354 98358 963 98363 98367 98372 98376 98381 98385 98390 98394 98399 98408 964 98408 98412 98417 98421 98426 98430 98435 98439 98444 98448 965 98453 98457 98462 98466 98471 98475 98480 98484 98489 98493 966 98498 98502 98507 98511 98516 98520 98525 98529 98534 98588 967 98543 98547 98552 98556 98561 98565 98570 98574 98579 98583 968 98588 98592 98597 98601 98605 98610 98614 98619 98623 98628 969 98632 98637 98641 98646 98650 98655 98659 98664 98668 98673 970 98677 98682 98686 98691 98695 98700 98704 98709 98713 98717 971 98722 98726 98731 98735 98740 98744 98749 98753 98758 98762 972 98767 98771 98776 98780 98784 98789 98793 98798 98802 98807 973 98811 98816 98820 98825 98829 98834 98838 98843 98847 98851 974 98856 98860 98865 98869 98874 98878 98883 98887 98892 98896 975 98900 98905 98909 98914 98918 98923 98927 98932 98936 98941 976 98945 98949 98954 98958 98963 98967 98972 98976 98981 98985 977 98989 98994 98998 99003 99007 99012 99016 99021 99025 990&0 978 99034 99038 99043 99047 99052 99056 99061 99065 99069 99074 979 99078 99083 99087 99092 99096 99100 99105 99109 99114 99118 980 99123 99127 99131 99136 99140 99145 99149 99154 99158 99162 981 99167 99171 99176 99180 99185 99189 99193 99198 99202 99207 982 99211 99216 99220 99224 99229 99233 99238 99242 99247 99251 983 99255 99260 99264 99269 99273 99277 99282 99286 99291 99295 984 99300 99304 99308 99313 99317 99322 99326 99330 99335.99339 985 99344 99348 99352 99357 99361 99366 99370 99374 99379 99383 986 99388 99392 99396 99401 99405 99410 99414 99419 99423 99427 987 99432 99436 99441 99445 99449 99454 99458 99463 99467 99471 988 99476 99480 99484 99489 99493 99498 99502 99506 99511 99515 989 99520 99524 99528 99533 99537 99542 99546 99550 99555 99559 990 99564 99568 99572 99577 99581 99585 99590 99594 99599 99603 * 991 99607 99612 99616 99621 99625 99629 99634 99638 99642 99647 lf 992 99651 99656 9&660 99664 99669 99673 99677 99682 99686 99691 993 99695 99699 99704 99708 99712 99717 99721 99726 99730 99734 994 99739 99743 99747 99752 99756 99760 99765 99769 99774 99778 995 99782 99787 99791 99795 99800 99804 99808 99813 99817 99822 996 99826 99830 99835 99839 99843 99848 99852 99856 99861 99865 997 99870 99874 99878 998$3 99887 99891 99896 99900 99904 99909 998 99913 99917 99922 99926 99930 99935 99939 99944 99948 99952 999 99957 99961 99965 99970 99974 99978 99983 99987 99991 99996 1000 00000 00004 00009 00013 00017 00022 00026 00030 00035 00039 840 Logarithms. Table 6. 0133456780 OK 1000 00000 00004 00009 00013 00017 00022 00026 00030 00035 00039 1001 00043 00048 00052 00056 00061 00065 00069 00074 00078 00082 1002 00087 00091 00095 00100 00104 00108 00113 00117 00121 00126 1003 00130 00134 00139 00143 00147 00152 00156 00160 00165 00169 1004 00173 00178 00182 00186 00191 00195 00199 00204 00208 00212 1005 00217 00221 00225 00230 00234 00238 00243 00247 00251 00255 1006 00260 00264 00268 00273 00277 00281 00286 00290 00294 00299 1007 00303 00307 00312 00316 00320 00325 00329 00333 00337 00342 1008 00346 00350 00355 00359 00363 00368 00372 00376 00381 00385 1009 00389 00393 00398 00402 00406 00411 00415 00419 00424 00428 1010 00432 00436 00441 00445 00449 00454 00458 00462 00467 00^71 1011 00475 00479 00484 00488 00492 00497 00501 00505 00509 00514 1012 00518 00522 00527 00531 00535 00540 00544 00548 00552 00557 1013 00561 00565 00570 00574 00578 00582 00587 00591 00595 00600 1014 00604 00608 00612 00617 00621 00625 00629 00634 00638 00642 1015 00647 00651 00655 00659 00664 00668 00672 00677 00681 OOG85 1016 00689 00694 00698 00702 00706 00711 00715-00719 00724 00728 1017 00732 00736 00741 00745 00749 00753 00758 00762 00766 00771 1018 00775 00779 00783 00788 00792 00796 00800 00805 00809 00813 1019 00817 00822 00826 00830 00834 00839 00843 00847 00852 00856 1020 00860 00864 00869 00873 00877 00881 00886 00890 00894 00898 * 1021 00903 00907 00911 00915 00920 00924 00928 00932 00937 00941 l 1022 00945 00949 00954 00958 00962 00966 00971 00975 00979 00983 2 1023 00988 00992 00996 01000 01005 01009 01013 01017 01022 01026 8 ' 1024 01030 01034 01038 01043 01047 01051 01055 01060 01064 01068* 2 1025 01072 01077 01081 01085 01089 01094 01098 01102 01106 01111 52 1026 01115 01119 01123 01127 01132 01136 01140 01144 01149 01153 62 1027 01157 01161 01166 0117001174 01178 01182 01187 01191 01195 73 1028 01199 01204 01208 01212 01216 01220 01225 01229 01233 01237 8 3 1029 01242 01246 01250 01254 01258 01263 01267 01271 01275 01280 9 4 1030 01284 01288 01292 01296 01301 01305 01309 01313 01317 01322 1031 01326 01330 01334 01339 01343 01347 01351 01355 01360 013G4 1032 01368 01372 01376 01381 01385 01389 01393 01397 01402 01406 1033 01410 01414 01418 01423 01427 01431 01435 01439 01444 01448 1034 01452 01456 01460 01465 01469 01473 01477 01481 01486 014CO 1035 01494 01498 01502 01507 01511 01515 01519 01523 01528 01532 1036 01536 01540 01544 01549 01553 01557 01561 01565 01569 01574 1037 01578 01582 01586 01590 01595 01599 01603 01607 01611 01616 1038 01620 01624 01628 01632 01636 01641 01645 01649 01653 01657 1039 01662 01666 01670 01674 01678 01682 01687 01691 01695 01699 1040 01703 01708 01712 01716 01720 01724 01728 01733 01737 01741 1041 01745 01749 01753 01758 01762 01766 01770 01774 01778 01783 1042 01787 01791 01795 01799 01803 01808 01812 01816 01820 01824 1043 01828 01833 01837 01841 01845 01849 01853 01858 01862 01866 1044 01870 01874 01878 01883 01887 01891 01895 01899 01903 01907 1045 01912 01916 01920 01924 01928 01932 01937 01941 01945 01949 1046 01953 01957 01961 01966 01970 01974 01978 01982 01986 01991 1047 01995 01999 02003 02007 02011 02015 02020 02024 02028 02032 1048 02036 02040 02044 02049 02053 02057 02061 02065 02069 02073 1049 02078 02082 02086 02090 02094 02098 02102 02107 02111 02115 1050 02119 02123 02127 02131 02135 02140 02144 02148 02152 02156 6. Logarithms. 841 G f * 3 4 5 6 7 8 9 M. 1050 02119 02123 02127 02181 02135 02140 02144 02148 02152 02156 1051 02100 02164 02169 02173 02177 02181 02185 02189 02193 02197 1052 02202 02206 02210 02214 02218 02222 02226 02230 02235 02239 1053 02243 02247 02251 02255 02259 02263 02268 02272 02276 02280 1054 02284 02288 02292 02296 02301 02305 02309 02313 02317 02321 1055 02325 02329 02333 02338 02342 02346 02350 02354 02358 02362 1056 02366 02371 02375 02379 02383 02387 02391 02395 02399 02403 1057 02407 02412 02416 02420 02424 02428 02432 02436 02440 02444 1058 02449 02453 02457 02461 02465 02469 02473 02477 02481 02485 1059 02490 02494 02498 02502 02506 02510 02514 02518 02522 02526 1060 02531 02535 02539 02543 02547 02551 02555 02559 02563 02567 1061 02572 02576 02580 02584 02588 02592 02596 02600 02604 02608 1062 02612 02617 02621 02625 02629 02633 02637 02641 02645 02649 1063 02653 02657 02661 02666 02670 02674 02678 02682 02686 02690 1064 02694 02698 02702 02706 02710 02715 02719 02723 02727 02731 1065 02735 02739 02743 02747 02751 02755 02759 02763 02768 02772 1066 02776 02780 02784 02788 02792 02796 02800 02804 02808 02812 1067 02816 02821 02825 02829 02833 02837 02841 02845 02849 02853 1068 02857 02861 02865 02869 02873 02877 02882 02886 02890 02894 1069 02898 02902 02906 02910 02914 02918 02922 02926 02930 02934 1070 02938 02942 02946 02951 02955 02959 02963 02967 02971 02975 4 1071 02979 02983 02987 02991 02995 02999 03003 03007 03011 03015 o 1072 03019 03024 03028 03032 03036 03040 03044 03048 03052 03056 1073 03060 03064 03068 03072 03076 03080 03084 03088 03092 03096 1074 03100 03104 03109 03113 03117 03121 03125 03129 03133 03137 1075 03141 03145 03149 03153 03157 03161 03165 03169 03173 03177 1070 03181 03185 03189 03193 03197 03201 03205 03209 03214 03218 1077 03222 03226 03230 03234 03238 03242 03246 03250 03254 03258 1078 03262 03266 03270 03274 03278 03282 03286 03290 03294 03298 1079 03302 03306 03310 03314 03318 03322 03326 03330 03334 03338 1080 03342 03346 03350 03354 03358 03362 03366 03371 03375 03379 1081 03383 03387 03391 03395 03399 03403 03407 03411 03415 03419 1082 03423 03427 03431 03435 03439 03443 03447 03451 03455 03459 1083 03463 03467 03471 03475 03479 03483 03487 03491 03495 03499 1084 03503 03507 03511 03515 03519 03523 03527 03531 03535 03539 1085 03543 03547 03551 03555 03559 03563 03567 03571 03575 03579 1086 03583 03587 03591 03595 03599 03603 03607 03611 03615 03619 1087 03623 03627 03631 03635 03639 03643 03647 03651 03655 03659 1088 03663 03667 03671 03675 03679 03683 03687 03691 03695 03099 1089 03703 03707 03711 03715 03719 03723 03727 03731 03735 03739 1090 03743 03747 03751 03755 03759 03763 03767 03771 03775 03778 1091 03782 03786 03790 03794 03798 03802 03806 03810 03814 03818 1092 03822 03826 03830 03834 03838 03842 03846 03850 03854 03858 1093 03862 03866 03870 03874 03878 03882 03886 03890 03894 03898 1094 03902 03906 03910 03914 03918 03922 03926 03930 03933 03937 1095 03941 03945 03949 03953 03957 03961 03965 03969 03973 03977 1096 03981 03985 03989 03993 03997 04001 04005 04009 04013 04017 1097 04021 04025 04029 04033 04036 04040 04044 04048 04052 04056 1098 04060 04064 04068 04072 04076 04080 04084 04088 04092 04096 1099 04100 04104 04108 04112 04116 04120 04123 04127 04131 04135 1100 04139 04143 04147 04151 04155 04159 04163 04167 04171 04175 842 Probability of Errors. Table 7. >. I I i i I I I i I i i I I I I OOOOO OOOOO OOOOO OOOOO OOOOOO xxxxx xxxxx xxxxx xxxxx xxxxxx CO O0510OS "i-ioorjioi ^H?oco^6 I-NI-* p - wHjcpepq *tH** coo ooooo ooooc kft kA ">** eft eft * sft ? 2^ j>m j~ j<^ ?* a^** 9$ W ^ kO 50 t" I I o I t-^oo^ Oiodsoob s*~iocoiO oso^*^ OOJM 2 OOOOO OOOOO OOOOO OOOOO OOOOOO ._ o* *o" *o* *o' 'o Q. O C L z* o^^w-*a r ^05 (Nwwwwwojcowweowwww o o UU CT^ "^T 1 S^J ^^ STV l.'^ *i" *^^ "^"^ V*- I I ' '^^ v **' "^ *^> ^W 1" ^ -' Wrf T i ^,-vi -^-sfl ai7 cococoo>aT-'O>oi>-iocoi iost^3coi iooo^!Mo>oot>-jLflico 5; W3 iO O IO i rf ^t rf rf ^ CO CO CO CO OO 9Q iM >1 * q\ o* : fO oq o O*^^ \n fo vn ri i . . ,o . I-H- I + + <* '+ ' .00 . ' , O . P SP ! I Q I ' 2" 2? 8 " 2 > q q ro ...N..N....... . . . Q N o + ON o O bo MOro O tl-ir> rnt- fx ^VO f u-ioo N ro xr^oo ir>.oO ^M O O^ c^OO ^Or'OO 1-1 p O "- 1 M - OO O OOO OOt-NO O OO OO *)-'/) OOr~. n ?t^'- 1 NOi_iO OO OO t^ ^ J ro ON p, CB ^ ^ i fi. . o ^ . ^ O - vo r-^ r^oo M oq \r> HH \o c^vq . rJ \o tri ro c* cf. N food i-* HH N vo >-" o oo cj* *** oo* vo 1 ,C v> cxca 2 M fl M f q v oo < 1-4 m & c^.oq r^. q q^ !>. O ^t-vo' O>OO* O' CM- N O* i-I 1-4" \n fi OO" q ^- .rj yj OS 0.-. o II ^^ .si M a 1 1 s .| .s o - 844 Properties of Elementary Substances Table 8, IBOIUI31O -ouusqj, IBOU10313 XjiAipnp 1U3JBT 4 OOI 3 H ogpsdg .0 1 JB3 H psdg uio gL ' O ooi ^o 'iBoiqno aoistiBdxg ssaupJBH oraojuv *ONPO* I""* 1 ! tll 1 ^! . vn ! ... \o* * fo >-< o -< PO >. . . . N- .0 * . t O' . +44-- +-- 5J ' 'S -ffE^ -5 "8 ' '82 , g) ^ vO O i- *O tt- O bb bb q '? 1^ CO.-. q -q q q - q q ^, tr>N fO^O O ^ ^ oo C\ . N M - ' -- o > * O O t*Ni *i A O^ O 3 . . . Q o vo " " 99 ' So |2 JD ' V &?i|| ( |^|l l ' d l' '||| fe _) -j u O O B88 :88 : M 00 O i oo ro t^ N r>. .1-1 . O . O O vo . Q O . ro O fO O O O O O o o o o o t^ i-T ;r^= 3 :- & ii .1 .1 .-K .++....+ .+ CSOs-i*i- O\ s * *? ^ *> 1 "". . ^ 't ^ 1 tA O* M* O i- Tables. Properties of Elementary Substances. 845 -OJ1D313 * oupaig -OU1J31JX CO I A"jiAijonp _ *t" ^O + - 'MD^O'*OO* CN O XjiAijonp -U03 JB3H ~ o OOli-rj-^vO I r^i^>|voooooi/%o 1 t -,0 q q i-. q ro >-^ OOTt-lml TH(S 1 ^f- I rO\O ^-fol ir>| ^\o 1 -^ 1 c-o o o o o'o o o o Stnjiog uio gZ, ' O ooi O o 'iBoiqnf) uoisuBdxg 10 O n . . .00 tx SO - iOiOO O I C*O ' 1 '-' NO*Of^OOMfO sninpoj^ a s t unoA 2 OI09Z,pUB I XJISU3Q ; 4- 5 s M I I O ' *S tl "^ c4 tf 6 O O ^< ^ ' oo oo _l_6 ooiio ooroioosxoo' ^ <> 4- 10 4- <>od r^.fot^.'c^oo' ^-Nao fO O OO O t^. M O M OO fOOO N O fO ++ M l-l I-H H-CJC^|M >-!(< 14 rt O- 846 Properties of Solids. Table 9. 32ja ?+ : f : :: : t't 1: : : T ~T~ PO o o ^ "- 1 ^i ^ q q o XljAipnp j f? -U03 + ' A O* ' c-OOOONOQ-.Q i B9 H *? o * q i N . . . . . q q q q q q oS ':::::::: * POPO N OI ~ i-+_l_ - H. - vn * PO ON O\~T~ *I!I!*IONON***** .5 rj q q q q rj *". ^ H uio gi o o " s^ pioj :g:g::::::::::::::::: 2 JUIOJ QO ,OO . .OO O ,O O^i-.r^O..OO. .O.un t^rJ-NON O\>-| rj- fj OOI O ~P*V> . rt- ** \r>\f dbntreon J^ .... sn l npo K 2 | ^ . . .^ q .^^ ^ tr> . . ^j- r^ vo w> ^ *i . . . ^ ^ I N . ^*" 'f * . " I I "a Slo' 4 r t: 'wo "a "rt^^S'3 '^ 2 E.g-cgg gG&^ijBa -a's u s.s u 3 ,5ci.2 *cfio ^oS-Sfcr ^-s S CQ33aQ CQCQU UUfcC'' Table 9. Building Materials, etc. :+ OUJ0313 O " 1BOUP313 q UI3 9Z, ' OOI JUIOJ uio gZ, ' O ooi O o 'iBoiqno uoisuBdxg IU3IOTJJ303 s.Suno^ 2 gausses 01 3* 30UB1SIS3-SJ ~ sssupjBjj ; 00 ^ * :4 e^. o. --- 1_ ..NN3;. ^ -; -. * 847 4 888t r* HH vo O 8.8 : N : o T*- t^. t^OO I ~i~ ON c^n*- .OO O O W> . POOO O 1 . O * ~ - - f ft? < O * fi M* O o "Ti i- ON O* q O - d N rJ~f~ :tt , .<-^+ 2 ' ^* T .4-| .1? | . OOOOOOONf<) ;s si C/3 CO ^> C3 Cv .i C! "S^ "^ S'l? .'I -tpll ^ oo 848 Properties of Solids. Table 9a, Name Symbol >> 1 ~ c 1? o 8 ts ^o KSr ~_c 0"* |8 c^g Acid Acetic . . . Oxalic . . . Phosphoric . Phosphorous Hypo- Sulphuric (hyd.) Tartaric . . Arsenate of Lead. . . . Potassium . (anhyd.) Borate of Lead . . . Bi-. . Potassium . Bi-. . Sodium . . Bi-. . (Borax) . . Bromide of Lead . . . Potassium . Silver . . . Carbonate of Barium . . Calcium . . Iron . . . Lead . . . Potassium . Sodium . . (acid) . Strontium . Chloral .... Chlorate of Barium . . Potassium . Per- . Sodium . . Chloride of Ammonium. Barium . . ^ >i (Crystals) Calcium . . (crystals) Carbon . . Copper Iron . , HC 2 H 3 2 . . . H 2 C 2 4 .2H 2 0. H 3 PO 4 . . . . i.i 6 . 16 117 . 4 6 44 100 12 IOO 58 70 o + sol sol 47 4 7 0? 39 o 51 20 9 sol 29 7 50 27 26 3i 42 83 c NaC10 3 . . . . H 4 NC1 . 2.3 T r BaCl 2 3 8 BaCl 2 .2H 2 O. 7 n CaCl 2 CaCl 2 .6H 2 O. . C 2 C1 6 . . . . . Cu 2 Cl 2 . . . . FeClo. 2.2 1.6 2.0 3-5 2.S 0006 720 29 187 434 300 187 1000 Table 9a. Chemical Materials. 849 Name Symbol c & Hardness Coefficient Expansion Cubic oioo bo., .S.G !? 'o PH Specific Heat 0100 || If rj !.S "-So 1! Chloride of Lithium . . Magnesium . Mercury . . ,, (calomel) Potassium . & platinum . Rubidium . Silver . . . Sodium . . Strontium . Tin .... (crystals) Zinc . . . Chromate of ,,Lead .. . . Potassium . Sodium . . Bi- . . . Cyanide of ,, Mercury . . Potassium . Ferri-. . Ferro . . Fluoride of ,, Calcium . . Hyposulphite of Barium . . Lead . . . Potassium . Sodium . . ,, ., (crystals) Iodide of Copper . . ,,Lead . . . Mercury . . ,,(mercurous) Potassium . Silver . . . Sodium . . Naphthalene Nitrate of Ammonium. Barium . . ,,Lead .. . . Potassium . PbCl 2 . c 8 2 .000114 .00010 .000121 6OO 700 2 9 730 450 775 850 250 9 00 3 00 625 .067 .282 .194 .067 .052 .172 .112 .0 9 I .214 .120 .IO2 i 45 70? 7 o 26 i 27 35 67? 80? 80 o 39 ii 60? 12 30 25 O o+ sol 41 64 O.I 5? o 59 64 o T 36 24 5 57 35 36 5 o 28 50 45 50 35 55 44 50 o 100 o.5 67? o 76 26 LiCl ...... MgCl s .... HeCl 2 .... $SP. : : : 2.0 2.2 54 I- 1 -> o 3.5 AsCl * 6 NaCl ^ T SrCl 2 .... ? O SnCl 3 .2H a O . ZnCl 2 .... PbCr0 4 . . i. K 2 Cr0 4 . . . K 2 Cr 2 O 7 . ,. . Na z CrO 4 . '. . Na 3 Cr 2 O 7 ... 1 7 2.8 5-9 2-7 2-7 2.7 4.0 T C _ 260 700 .136 !i8y .188 .100 233 >8o K 6 Fe 3 Ci3Ni 2 . K 4 FeC 6 N 5 . 3 H 2 CaF a 1.8 1-9 ? ^ 4 .00004? 900 .212 anh. .163 BaS 2 O 3 .H 3 O . PbS 2 O 3 . . . K 2 S 2 O 3 . . . 34 .00013 .000101 30? 600 380 250 290 640 530 630 80 I CQ 600 34 760 900 350 3 IO 215 .092 .197 .221 445 ,069 .043 .042 .039 .082 .062 .088 455 .150 .114 235 .33 36 49 Na 3 S 3 O 8 . . . Na 3 S 2 O 3 .5H 2 O Cu 2 I 2 . . . . Pbl, . 1-7 tt HgI 2 .... 6 T .000072 .000128 .000004 9-7 3-1 C -7 Nal T ^ H 4 NNO 3 . . . BaN0 6 . . . PbNo0 6 . . . KN0 3 .... 1.7 3-2 44 2.1 2 850 Properties of Solids. Table 9a. Name Symbol >, 1 6 Q Hardness Coefficient Expansion Cubic oioo M ., S c P t! s l Specific Heat 0100 M -i C w J ^ >- f! ">* ^ lEc K Nitrate of Silver . . . Sodium . . Strontium . Oxalate of Potassium . Tetr- . . Oxide of Aluminum . Antimony . Arsenic . . Bismuth . . Boron . . . Calcium . . (hydrate) Chromium Copper . . (cuprous) Iron . . . " k ead ' ' ' Magnesium . (hydrate) Manganese . " *r Pei " ' ' Mercury . . Molybdenum Nitrogen . . Potassium . (hydrate) Silicon . . AsNO 1 ? 7TO T 44 2 7 I8l 2 3 6 283 198 093 .128 .061 .237 6*5 7 47 42 25 5 ' o o-h 2 2 .1 + 90 64 50 40 o 0+ 8? .1 O.I . 1 o o o 04 O.I 70 o 25 NfNo 3 3 : : . SrN 2 O 6 . . . K 2 C20 4 .H 2 . KH 3 C 4 8 .2H2O. A1 3 3 .... Sb 2 O 3 . . 2.2 2. 9 3-9 2 9 310 650 ASoOa ? 7 Bi 2 3 .... BoOq . 8.1 T 8 . . 5^0 7- 2 X 3 CaO .... CaO 2 H 2 . . . 3-1 ? T Cr 2 O 3 .... CuO .... Cu 2 O . . . 5-0 64 60 . . .177 !35 . o o+ o+ o 0.2 FeoO . C "> 5+ .00004 ' . .16 .051 .244 .312 PbO .... MgO .... MeO 9 H . 9-3 3-3 MnO .... MnO 3 .... HsO 5-i 5-0 TT H- . 157 159 MoO 3 . . . NoOs .00004 30 47 .19 77 80? 50 67 o 40- 60 o (?) , 0-f- sol sol 5 20 o K 2 . . . . KOH .... SiO 2 .... 2.6 2.0 7 i . Na 2 O .... ,, (hydrate) Tin . . . . Titanium. . Tungsten. . Zinc . . . Phosphate of Calcium . . Lead . . . Potassium . (acid) . Sodium . . (acid). . Silicate of Al etc. (clay) Calcium . . Zirconium . NaOH. . . . ?. T SnO 2 .... !6.o 6+ .00002 .00003 .091 .172 .085 .125 .199 .082 .191 .208 .228 454 *+ .178 .132 ' : Ti0 2 .... WO 3 .... ZnO .... 4- 6.8 ' 7 CaP 2 O 6 . - . Pb 2 P 2 O 7 . . K4P 2 7 . . . KH 2 PO 4 . . . Na4P 2 7 . . . Na 2 HP0 4 .i2H 2 Al 2 Si 2 O 7 .2H 2 O,etc. CaSiO . . " . 2 -3 2.4 1.5 2. 1 ; .00002? 9 00 36 ZrSi0 4 . . . 7-f . Table 9a Chemical Materials. 851 Name Symbol en C T .128 o 50? , Silver . 7 2-4- 071; o , Tin . . , Bi- ,, Zinc SnS 2 '. '. '. . . '. ZnS ... 5-0 4-5 1 T 4 .000036 . . .084 .119 .122 . o o o Talc 1 7 1 o Tartrate of . . ,, Potass, (acid) KHC 4 H 4 O 6 . 06 6 & sodium KNaC, "-i4O 6 .4H 2 O . 50 33 50? 852 Properties of Solids. Table 10. q ' o jo XjBUIpJQ JO jo xapui : r ro XjISUSQ I M VO l-< NM o* ti Q UUU Table 10. Optical Materials, etc. 853 JHx: O >> -xi C"c> rt - UUUU QWWfc^O O 854 Properties of Soilds. Table 10, UOlSjgdSIQ jo xapui umuiixB^i jo xapuj (Q) jo onpuj AiAipnp -uo'3 JBSH jo OOI-,yO IB3H uio gL 'luioj Sunjog juioj Saiip^j O ooi- o uoisiiBdxg sssupaBH S.5 ^s, O VO o o 5VO m if) ^* * .'> f t ->{SvOO ^- o-i OO 'O C\ t^OO OOO . ^> ^^- vr> ON . . N t : : :-? ro : N CO 2 en c -o O * ' in NO 1 r^ r-^ o w> r^ - ^- O \O &00 C< ^- O N OOO vc LD O N qoq o '^S 1 ^?^ '+ .o .ffi . ilg Sp^ I "ill 3x) J2.S o-H 3 a* IS rtJ3- J . 0)l>OO3c3 vr> i iQ O iJ w ro fO t-I i-I O* . . . . O^ 1 ^ '**" '^ * 'O' fe .N 856 Properties of Liquids. Table 11. H-V tioisjadsiQ jo xapuj (a) jo Dnpupoa BO adg OOI ,0 'JB3R ( OS)JOdB A "o I^vo . iovo t^ r^ t^oo q q * q q q q q q q q * q q ' q q q q q q q rO * ro "3" * rj- Tj- vn ro c*y fO fO w w N *-' ^ '"i-* "* . * j ' i - r * *^ r i vr> . in vo ,vo . vq o * ^ N * i ****>* * *O * * "tO " "5" t* o ' q * q * q ' * q * * q - ? - - 3 UIDO/'lUIOJ Satitog n !c[ 9UIZ30JJ r IB uoisuBdxg 888888888 '88888 ' '8 '88 ' 'O <^5 q . >x:)uoisu3X r- O *O t>.vO ^- O O o) Xji a^o I- to o i-< oo X3 ONOO ON ONOO O O CN C^ N VT _ _ . _ ^ o' o' o' o' o' o i-i i-T o' o' i-T ~ ~ HH* o' o o' -* o' o* o* o . r2 O O rO\O O t^ to u-) ro\O M "-> i-< i-i o a-oo oo o o oo o||fi|lll|g ;|5:|oggg >, C Z* *-< - ' CL.1) aOS ^^L^^. - ! voo -*i^SJP 1 Tabiejt Properties of Liquids. 857 H-y aoisj8dst( jo'xgpuj (a) joBjj JO X3pUJ -no 3 JBSJJ UIlBZUOd -B A poi- o 'JB3H ode J guiipe 8UIZ99JJ JTJ uoistiBdxg jo S ( OZ)UOISU3J, 30BJjng ^-+<^N U->r^ ^-vo CO O t^ t^ vO * >-'vorj-'^-rhn MPO* *n ' "vni-ii-i *I-M oooooo oo * 'o * *ooo *oo ft 1 ! S 1 - - 80000000000 "oo *oooo s q q q q q q q q q q q q q q q q [r>. PO o-\mr^ B : : : : 8 : : : : : : 8 8 : 8 : : : incrvor^ POrh O PO oo O ^ r^ r^vo 00 O OO O H C< *O rt- H- vO O HH" 6 M i-T IM* PO i-T C4 H4* . HH ur> ON ON O in M rJ PO H? O* O* * >-* M * o? -OQ * GO OQPQ CQ 1 |>| tntH^ TOJ3 OQWOQ UU 858 Properties of Liquids. Tablell. H-V UOISJ3dST(J . jo xapiq o w> -' -* d M o H! M M* HH* M M d O u . HP; _ , >> ^ 5 2 fi^ o 2 >, uu Table 11. Properties of Liquids. 859 uoffisdsicj : ~. : ~'~ : : :~ '.^ + &\?*> . ~.& ~.<6 . . . . jo xapiii q q . q q q q q q q q S CO CO c*-* f)^O O *-*"! ^O *O & JO X3PUT * " *?*? <* ? *J- 1? *n i? ' *? " O . . o i . . . . . ; . . . . , *t- ; ro ; M ir> B !! !!!! !! 1 " 1 !!!!! o o o o o o M *0*0* ' O M O* M M fi W* * fO N.* M M O O* O* . e^ - -O . - -ffi 3 . . . .U ^ o O Q *O IC ^,U> " w a . .g .^sou -a ^^ . . . - - :~::'i :- : :! _ [ j j j : : ~ -^ * ^^ _ c ~"o'g : 5 5sr ? J5 5> Cr-; O 860 H-y UOlSJ3dSIQ jo xapu'i led Properties of Liquids. Table 11 jo xspuj JB3H UOlJBZUOdBA 1B9H 'luaiBq * OOI (oOe)JodB^\ o [O 3jnSS3JJ ~ sjnssgjj o uio QZ, JUIOJ 9u;noe UOISUBdXJJ 02)UOtSU3X Xjisoosr^ q o^- ' t-i 10 1-1 Tf 00 OO ^M .g-g *oo ooooc O 1 - 'l MO ^-.O-> CO <^O * <~O _i, O>M (S i-i ^- ri ~ M t- MMM IJ- 1 ' o to CO tj- s-? 88 B^oooSooo ,qqqqqqq oo qq ' 88 ' O | "T txoo o 6 i-" -" d d d d -.* -* t-7 d o* d o* o o o* >- .0 ^ U . *> o *i ' T; _f? *n*r ^^ . M^"^ I! * ' O O cu Table 12. Properties of Gases and Vapors. 861 uio gL ' O oz l -wi"M!% : H-V UOlSJSdSfQ ' jo xspu'i 2 9^ V> I JO 3Aponpui oypsdg XjiAipnp ~ u b' UOllBS ' IBSH ;u3lBq IO A -isu op 0S 1UB1SUO'} osd sanj -J3dUI3X uio gZ, UOT] BSU9PU03 jo -05 jo 3am ' O ooi o uoisuBdxg jo o uio *bs J3d S3UXp 000' 000' I O 'Xj[ 00 5 10 CO ^ PO o o " 43 ^s . VO . O td-O 10 ri o ^ PO CN C4 N M M O vo r-* fooo o M'^cTi^ c? to co CO .00 OO OO . N n o : : : :::::::::: g; ca-o aa 8 8 3 3 * cr 1 I rj- CO O\ O* O ^ -o^ -o u .u rl 5EK O . 21 a .V fl - < cQffl cqu U ~,o- ^S L_ gs Air contains Carbonic A 862 Properties of Gases and Vapors. Table ii uio gL '(joe JSIBAVUI o/ r> o p H-V <| UOlSJSdSIQ 1 jo' xspul 2 uSgz^o : :::::: :S*5 ::< ri? TO vannr *-i ^. ^ Q SAiionp -up'gpsds - ^_ __ -pop iB9H 8 ::::::::: i? : : : : g :::::: o UOIJ -BSU3pU03 BSH'Jpsdg ~t| 'q tj q tj * ^t- 'qq^^ JUBJSUO3 * I'* 5 '^! 'O^OC^^-'fO* '.<*?&' * ! VPOO CT* 3JHSS3JJ -s^ T . .0 . 00 , 3Jn; . ^ o-...pom N- ! O vo t^ m r^ 'G ooo-ooo-i : ::::: :^^ .g&^ s S ) o u ^?o XIISUSQ q^ q q a q q q q q q -3 -OJpXj-I OJ \f) Q LT) * OO ^OO* VT5 I\O .VO If>-'*'O^'l-H^t' &9O 3J Uf) 'dg N l>-00 vQ 0^0 r* POM r< romvo ro ^ o a ^ O (U - o 6 !l"0"ljrtjrfj' 'c?r?^U-? ' c/2 w ""^ *"._'', M _ ^ # o * ' " s ' a - - 5 O "^ C K p ^_i vj Q ^ cx s . * . ^, . .^3 ^ o'o r t-l H-< C - ........ o. 3 3 ^> 3 ^71 % 3 3 "^+3 .73 73 0^2 . Pi ^ .53 4= O 'J'J f -S 864 + +\ + 2 I S- Pressure of Vapors Table 13, A. o - O r^ vo ^ *- 4--.:.Kl O fO .in . 00 M \r> irt ' N PO ~ vo ' _* PO * _I o . . j^ . OO oo . . VO VO ON PO * . . . : j M OO M 00 1 " vo vO vo ri . ON . t>. N r^ PO . o * R. ' ^- 5 oo !? o ! t- ^ S5 M ON VO >- vo ON * M Th PO t^ VO VO vO * M PO ' vo M PO Tj- N C4 I-I . r^- VO 8 ft rf r^- r> vO *4 O n H* PO fNl OO OO VO PO q N ' g VO ' oo 1-4 N PO I-I HH vo* Tf i ON $ 2 S VO PO VO OO VO tf VO ' cS 2 ' r? w ri I-I HH g O eg s c^ O *" vO 2 c? ^ BvO PO 0> N VO 0> '. (S M 1-1 I-I i-i t^ 1-4 N VO CO Tt- t-H O^ vo t^* oo ^~ N ^h PO r^ PO PO 0> ' M ' VO "1 1-4 t-H VO M PO O M 00 ? C? C* c-x o vo PO ^ f^ N O vO C4 oo oo o O vo vO . q oo PO vo vO O M ^J- K- c* o OO OO l> oo rl t*s i- PO CS (M vO * vO M q ^r * '. M t^ Tj- ?s PO 1-1 jj o o VO o 1 o E O oo PO i- PO X E PO O> r^ VO \ OO N PO . q M 00 PO o ^- o ro H* O o o o o q ta vo r^ H- O PO O H4 ON VO PO vo PO PO 00 M 00 O i-i VO 1 1 vO O M o o o HH OO 5 8 - 2 $ O - PO ON s oo vo VO HH vO w, rj- o ! vo t^. vo 1-1 O f q q q r- vo 8. 8 PO vo* q q O vo q q ?vO 5 M . % ? frl PO o q ' sf o > O . N - TJ- ON ri 2 ? 1 O f*O s> s, O t**** oo ^ oo fi 1 8-f II. O oo O ON VO ON Ss | 5 1 O oo oo o 00 t^ vo* "*- vo' t-' O co M O t-^ co O vo o C/D C/3 C/5 C/} Temperature Mercury Hg . Temperature Mercury Hg . Sulphur S. o ffi ffi ffi DC- 3 __o ^o ^o ^o O CD oo t^* vn to q *ppv onnqding ^ g uibjj rt Tables U-14A. Aqueous Vapor. 867 14 Boiling Points of Water cm. .0 .1 .2 .3 68 96.92 96.96 97.00 97.05 g 69 97-33 97.36 97.40 97.44 8 7 9772 9776 97- 8 o 97- 8 4 71 98.11 98.15 98.19 98.23 y 72 98.50 98.54 98.58 98.61 "C 73 98.88 98.92 98.96 98.99 | 74 99 26 99.30 09.33 99.37 5 75 99-63 99.67 99-71 99.74 at Different Pressures (g = .4 .5 .6 .7 97.09 97.13 97.17 97.21 97.48 97.52 97.56 97.60 97.88 97.92 97.96 98.00 98.27 98.31 98.34 98.38 98.65 98.69 98.73 98.77 99.03 99.07 99.11 99.14 99.41 99.44 99.48 99.52 99.78 99.82 99.85 99.89 980-61) .8 97-25 97.64 98.03 98.42 98.80 99.18 99.56 99-93 9 97.29 97.68 98.07 98.46 98.84 99.22 99-59 99.96 76 mo oo 100.04 100.07 100.1 1 100.15 100.18 100.22 100.26 100.29 100.33 ffl 77 100.36 100.40 100.44 100.47 100.51 100.55 100.58 100.62 100.65 100.69 14A. Dew Points corresponding to Different Degrees of Tern perature and Relative Humidity. Relative Humidity of the Air. loO/o 2oO/ 30% 40% 50% 60% 700/0 80% 900/0 100% o .. .. 16 12 9 7 5 3 i o 1 .. .. 1511 8 6 4 2 o 4 i 2 .. 19 14 10 7 5 3 i +i 2 3 18 13 9 6 4 2 o 2 3 ,4 17 12 8 6 -3 i +i 43 +4 5. .. 16 -ii 7 5 2 o 4-2 43 4-5 6 15 10 7 4 i 4i 3 4 6 7.. i59 6 3 2 457 8 149 5 2 4i 3 5 6 9 .. 13 8 -4 -i +2 44 +6 4-7 4 9 , 10 .. 12 7 3 o 43 4-5 4-7 4~ 8 +"> .!: ii ii 6 2 -J-i 3 6 8 9 ii < 12 19 10 5 i 2 4 7 9 10 12 , 13 18 10 4 o 3 5 8 10 ii 13 ^ I4 o _ I? _ 9 _ 3 +! 4.4 _|_6 49 + 11 +12 4H .2387 11 .2403 100 .4805 Tables 15, B C. Aqueous Vapor. 869 15, B Velocity of Sound in centimetres per second through Atmospheric Air at Different Temperatures and under Different Conditions of Relative Humidity. Re- lative Hu- midity o% 2 0/o 40% 60 o/o 800/0 TOO O/o 33,220 33,225 33,231 33,236. 33,242 33,247 1 33,281 33,286 33,292 33,298 33,304 33,310 2 33,34* 33,347 33,353 33,360 33,367 33,373 3 33,402 33,408 33,415 33,422 33,429 33,436 4 33,462 33,469 33,476 33,484 33,491 33,499 5 33,523 33,530 33,538 33,546 33,554 33,562 6 33,583 33,591 33,6oo 33,608 33,6i7 33,625 7 33,643 33,652 33,66i 33,670 33,679 33,689 8 33,703 33,713 33,722 33,732 33,742 33,752 c 9 33,763 33,773 33,784 33,794 33,805 33,815 - 10 33,823 33,834 33,845 33,856 33,867 33,879 < 11 33,882 33,894 33,906 33,9 T 8 33,930 33,942 CD 12? 33,942 33,955 33, ( )67 33,98o 33,993 34,006 5 I3 o 34,001 34,oi5 34,029 34,043 34,056 34,070 34,060 34,075 34,090 34,105 34, TI 9 34,134 o 15 34,120 34,^6 34,151 34,167 34,183 34, T 9 8 o> 16 34,179 34,196 34,2J3 34,229 34,246 34,263 - 17 34,238 34,256 34,274 34,292 34,310 34,328 3 jgo 34,297 34,3i6 34,335 34,354 34,374 34,393 19 34,356 34.376 34,397 34,417 34,438 34,458 S 20 34,415 34,436 34,458 34,480 34,502 34,524 OH 21 34,474 34,496 34,520 34,543 34,566 34,589 E 22 34,532 34,557 34,58i 34,606 34,630 34,655 02 3 34,590 34,6i7 34,643 34,669 34,695 34,722 H2 4 34,649 34,677 34,705 34,732 34,76i 34,789 25 34,707 34J37 34,766 34,796 34,826 34,856 26 34,765 34,797 34,828 34,86o 34,892 34,924 2 7 34,823 34,857 34,890 34,924 34,958 34,992 28 34,881 34,917 34,953 34,988 35,025 35,061 29 34,939 34,977 35, OI 5 35,053 35,092 35,130 30 34,997 35,037 35,077 3^118 35,158 35, T 99 31 35,05 S 35,097 35,139 3^,182 35,225 35,269 32 35, IT 3 35,157 35,202 35,247 35,293 35,340 33 35,170 35,265 35,313 35,362 35,412 15, C. Coefficients of Interdiffusion of Gases. (C. G. SO* Air Car- bonic Oxide Hy- drogen Meth- ane Nitrous Oxide Oxygen Sulphur- ous An- il I'dride CO H, CH 4 N 2 O 9 so a Carbonic Dioxide C O 2 .1423 5614 .1586 .0982 .1409 Hydrogen H 2 .6422 .7214 .4800 Oxygen Os . . .1802 .7214 * See Maxwell's Theory of Heat, 4th Ed. page 332. (Everett Art. 131.) 870 Barometric Tables. Table 16. REDUCTION or INCHES TO CENTIMETRES. Inches. o i 2 3 4 5 6 7 8 9 28.0 71.119 145 .170 .196 .221 .246 .272 297 323 348 28.1 71-373 399 424 450 475 .500 526 551 577 .602 28.2 28.3 71.627 71.881 653 907 .678 932 .704 958 .729 983 754 *oo8 .780 "034 805 *059 % .856 *IIO 28.4 72.135 .161 .186 .212 -37 .262 .288 339 364 28.5 72-389 415 44 .466 .491 .516 542 ii 593 .618 28.6 72-643 .669 694 .720 745 .770 796 .847 .872 28.7 72.897 923 .948 974 999 *024 "050 *75 *IOI *I26 28.8 73.151 .177 .202 .228 253 .278 304 329 355 .380 28.9 73-405 431 456 .482 507 .532 558 583 .609 634 29.0 73-659 685 .710 736 61 .786 .812 837 863 .888 2 9 .I 939 964 .990 *O4O *o66 '091 *n 7 *I 4 2 29.2 74.167 193 .218 244 .269 294 .320 345 371 .396 29-3 74.421 447 .472 498 523 .548 574 599 625 .650 29-4 .701 .726 752 777 .802 .828 853 879 904 29-5 74.929 955 .980 *oo6 "031 '056 *o82 *i33 *i5S 29.6 .209 234 .260 285 .310 336 36? 387 .412 29.7 75-437 463 .488 5 I 4 539 564 590 615 .641 .666 29.8 75-69I .717 .742 .768 793 .818 .844 .869 ; 8 9 5 .920 29.9 75-945 .971 996 *022 *047 "072 '098 -123 *i74 30.0 76.199 .225 .250 .276 .301 326 352 377 403 .428 30.1 76.453 479 504 530 555 .580 .606 .631 657 .682 30.2 76.707 733 758 .809 834 .860 885 .911 ; 93 .001181 .OOlIgS .001214 .001231 .001247 .001263 1G A II 1177 1194 1210 1226 1243 1259 .1 3. 12 1189 1206 1222 1238 1255 .2 9 o 13 1169 1185 1202 1218 1234 1250 .3 5 4) 1 4- 1165 1181 II 9 7 I2I 4 1230 1246 .4 6 1 T -0 .001161 .001177 .001193 .001209 .001225 .001242 .6 8 2 16 1 157 H73 1189 1205 1221 1237 .6 10 2, 17 "53 1169 1185 I2OI 1217 1233 .7 11 a is 1149 1165 1181 1197 1213 1229 .3 13 H J 9 H45 1161 1177 ^93 1209 1224 .9 14 20 .001141 .001157 .001173 .001189 .O01204 .001220 15 21 ' H37 "53 1169 1185 I2OO 1216 .1 22 H33 1149 1165 n8i 1196 1212 .2 23 1130 H45 Ii6t 1177 1192 1208 .3 24 1126 1141 "57 "73 1188 1204 ' 4 25 .001122 .001138 .001153 .001169 .001184 .OOI200 .5 26 1118 H34 1149 1165 n 80 1196 .6 27 III4 1130 H45 1161 1176 1192 .7 10 28 IIIO 1126 1142 1^57 1172 1188 .8 12 2 9 1107 1122 1138 1169 1184 .9 13 30 .001103 ! .001119 .001134 .001149 .001165 .001180 20. Correction for Moisture in Table 19. PoiX Subtl ' act pJJJt Subtract Po'irn Subtract PoiS Subtract 10 .OOO.OO1 o .000,003 --10 .000,006 --20 .OOO,OIO 8 .000,002 6 .000,002 4 .000,002 -f-2 .000,003 -f-4 .000,004 -j-6 .000,004 --I2 .000,006 --I4 .000,007 --16 .000,008 --22 .000,012 --24 .000,013 26 .000,015 2 .OOO,OO3 -j-8 .000,005 --18 .000,009 --28 .000,016 20 A. Weight in grams of air displaced by 1 gram of brass of density 8.4. Density of Air .00110 .00112 .00114 .00116 .00118 .OOI20 Weight Displaced .000131 .000133 .000136 .000138 .000140 .000143 Density of Air .00120 .00122 Weight Displaced .000143 .000145 .00124 .000148 .00126 .000150 .00128 .00130 .0001 52 j. oooi 55 Tables 21,22. Reduction of Apparent Weights. 875 21. Factors for the Reduction of Apparent Weighings in Air with Brass Weights to Vacno. Density of the Air. Density of the Air. .00115. | .00120 .00125 .00115 .001 20 .00125 TJ 0.70 1.00151 LOOT 57 1.00164 J' 2.0 1.00044 1.00046 1.00048 o.75 ] HO 146 ii T 52 2 -5 32 n 34 f, 35 .g>o.8o 130 ,, 136 if HI 3 3-0 fi 2 5 26 ff 27 g 0.85 ! 122 ff I2 7 if 132 > 3-5 19 20 W 2! ^ 0.90 Ir 4 fi "9 124 > 4-0 ! 15 16 16 8 o-95 1G 7 IT2 ii U7 8 4-5 fi I2 I2 T 3 re 1.0 I.OOIOI I.OOI06 1. 00 1 ip 5.0 1.00009 1. 000 TO I.OC-OIO 1 T - r 1.00091 1.00095 1.0009*9 I 6.0 1.00005 1.00006 1.00006 1.2 82 86 89 a 7.0 ff 3 n 3 3 <" 1-3 if 75 f, 78 81 M 8.0 ii i ! if r ^ 1.4 68 ff 71 74 .S 9-0 0.99999 0.99999 0.99999 i-5 1.00063 1.00066 1.00068 I0 0.99998 0.99998 0.99998 o 1.6 58 61 6 3 12 6 n 6 n 5 1-7 54 56 ff 59 >PH ff 5 n 4 4 5 1.8 50 52 55 'co l6 ff 3 ff 3 n 3 5 1.9 ff 47 i) 49 5 1 1.267 8 1.264 13 I.26I 1 8 1.258 23 .255 28 .252 4 1.267 9 1.263 14 1.260 19 1.257 24 .254 29 .251 5 1.266 10 1.263 15 1.260 20 1.257 25 .253 30 .251 878 Density of Alcohol. Table 27. w't VOL. I5| 15 | 16 17 18 19 20 21 22 o.oo .9992 .9990 .9988 .9987 9985 9983 .9981 9979 I 1.26 .9971 .9969 .9967 .9966 .9964 .9962 .9960 9958 2 2.51 9953 9951 9949 9947 9945 9943 9942 9940 3 3-75 9936 9934 9932 9930 .9928 .9926 9924 .9922 4 5.00 .9920 .9918 -9916 .9914 .9912 .9909 .9907 9905 6.24 993 .9901 9899 .9897 9895 .9892 .9890 .9888 5 7-47 .9887 .9885 9883 .9880 .9878 .9876 9874 .9872 7 8.70 .9871 .9869 .9866 .9864 .9861 9859 9857 9855 8 9-93 .9856 9854 .9851 .9849 .9846 .9844 .9842 9839 9 ii. 16 .9842 -9839 9837 9834 .9832 .9829 .9827 .9824 10 12.38 .9828 .9825 9823 .9820 .9817 9815 .9813 .9810 ii f9 .9814 .9811 -9809 .9806 .9803 .9800 .9798 9795 12 . i .9801 .9798 9795 9793 979 9787 .9784 .9781 J 3 16.03 9789 .9786 9783 .9780 9777 9774 .9772 .9769 H 17.24 9777 9774 .9771 .9768 .9765 .9762 9759 9756 15 9765 .9762 9759 9755 9752 9749 .9746 9743 16 19.65 9753 9750 .9746 9743 .9740 .9736 9733 .9730 17 20.85 .9741 9738 9734 973i 9727 .9724 .9721 .9717 18 22.05 9729 .9725 .9722 .9718 9715 .9711 .9708 -9704 IQ 23-25 .9718 .9714 .9711 9707 9703 .9699 .9696 .9692 2O 24-45 .9707 9703 .9699 .9691 .9687 .9683 .9679 21 25.64 .9691 .9687 .9683 .9679 .9674 .9670 .9666 22 26.83 .9683 .9679 .9674 .9670 .9666 .9661 9657 9 6 53 23 28.01 .9671 .9666 .9662 9657 9653 .9648 .9644 9639 24 29.19 9 6 59 9 6 54 .9650 .9645 .9640 .9635 .9631 .9626 25 30.37 .9647 .9642 9637 .9632. .9627 .9621 .9617 .9612 26 3 r .54 .9633 .9628 .9623 .9618 .9613 .9607 .9602 9597 27 .9619 .9614 .9608 .9603 9598 9592 .9587 .9582 28 33*86 .9604 9599 9593 -9588 9583 9577 9571 .9566 29 35.02 .9589 .9583 9578 9572 .9567 .9561 9555 9549 30 36.17 9573 .9567 .9561 9556 9550 9544 .9538 9532 3 1 37.30 9556 9550 -9544 9538 9532 .9526 .9520 95H 32 38.44 9539 9533 9527 .9521 .9515 9508 .9502 .9496 33 39-57 .9522 .9516 9509 9503 9497 .9490 .9484 .9478 34 40.69 .9504 .9498 .9491 .9485 9479 .9472 .9466 9459 35 41.81 .9486 9479 9m .9466 .9460 9453 9447 .9440 36 42.92 .9467 .9460 9454 -9447 .9440 9433 .9427 .9420 37 44.02 .9448 .9441 -9434 .9428 .9421 .9414 .9407 .9400 38 45.12 .9429 .9422 .9415 .9408 .9401 9394 .9388 .9381 39 46.21 .9410 .9403 9396 9389 9382 9375 -9368 .9361 40 47.30 9390 .9383 9376 9369 .9362 9354 9347 9340 48.38 9370 9363 9356 9348 ' 9341 9334 9327 .9320 42 49-45 9349 9342 -9334 9327 .9320 .9312 9305 .9298 43 50.51 .9328 .9321 93 J 3 .9306 .9298 .9291 .9284 .9276 44 51.57 937 .9299 .9292 .9284 9 2 77 .9269 .9262 .9254 45 52.62 .9286 .9278 .9271 .9263 .9256 .9248 .9240 9 2 33 46 53.67 .9265 .9257 .9250 .9242 9234 .9226 .9219 .9211 47 54-7i .9244 .9236 .9229 .9221 .9213 .9205 .9198 .9190 48 55-75 9223 .9215 .9207 .9200 .9192 .9184 .9176 .9168 49 56.78 .9201 9193 .9185 .9178 .9170 .9162 9*54 .9146 50 57.80 9*79 .9171 .9163 9 X 55 .9147 9*39 .9132 .9124 Table 27. Density of Alcohol. 879 w't VOL. 15 15 16 17 18 19 20 21 22 50 57.80 .9179 .9171 .9163 9155 .9147 -9J39 .9132 .9124 5 1 58.81 9157 .9149 .9141 -9J33 .9125 .9117 .9110 9IO2 S 2 59-82 9135 .9127 .9119 .9111 .9103 -9095 .9087 .9079 53 60.82 9 JI 3 .9105 .9097 .9089 .9081 9073 .9065 9057 54 61.82 .9091 .9083 9075 .9067 959 .9050 .9042 934 55 62.81 .9069 .9061 9053 945 937 .9028 .9020 .9012 56 63-79 .9046 .9038 .9030 .9022 .9013 .9005 8997 .8989 57 64.77 .9023 .9015 .9007 .8998 .8990 .8982 8974 .8966 58 65-74 .9000 .8992 .8984 .8975 .8967 .8959 .8951 8943 59 66.70 .8977 .8969 .8961 .8952 .8944 .8936 .8928 .8920 60 67.65 8954 .89^6 -8938 .8929 .8921 .8913 8905 .8897 61 68.60 .8931 .8923 .8914 .8906 .8898 .8890 .8882 .8873 62 69-55 .8908 .8900 .8891 .8883 .8875 .8867 8859 .8850 63 70.49 .8885 .8877 .8868 .8860 .8852 .8844 .8836 .8827 64 71.42 .8862 8854 8845 .8837 .8829 .8821 .8813 .8804 65 7 2 -34 .8838 .8830 .8821 8813 .8805 .8797 .8 7 8 9 .8780 66 73.26 .8815 .8807 .8798 .8790 .8782 8773 .8765 .8756 6? 74.18 .8792 .8784 8775 .8767 8759 .8750 .8742 8733 68 75.08 .8768 .8760 8751 -8743 8735 .8726 .8718 .8709 69 75-98 .8744 .8736 .8727 .8719 .8711 .8702 .8694 .8685 70 76.88 .8721 8713 .8704 .8696 .8688 .8679 .86 7 I .8662 7i 77-77 .8698 .8689 .8681 .8672 .8664 -8655 .8647 .8638 72 78.65 .8674 .8665 .8657 .8648 .8640 .8631 8623 .8614 73 79- 5 J .8649 .8640 .8632 .8623 .8615 .8606 .8598 -8589 74 80.37 .8625 .8616 .8608 8599 .8591 .8582 8574 -8565 75 81.23 .8601 .8592 .8584 8575 .8567 .8558 8550 .8541 76 82.08 .8576 .8567 .8559 8550 .8542 8533 .8525 .8516 77 82.92 -8552 8543 8535 .8526 .8518 .8509 .8501 .8492 78 83-76 .8528 .8519 .8511 .8502 .8494 .8485 .8476 .8468 79 84-59 8503 .8494 .8486 .8477 .8469 .8460 .8451 .8443 80 85-41 .8478 .8469 .8461 .8452 8444 8435 .8426 .8418 81 86.22 8453 .8444 .8436 .8427 .8419 .8410 .8401 -8393 82 87.03 .8428 .8419 .8411 .8402 '8394 8385 .8376 .8368 83 87.84 .8404 .8395 .8387 .8378 .8370 .8361 8352 8344 84 88.63 8379 .8370 .8362 -8353 8345 8336 .8327 .8319 85 89.42 .8354 .8345 -8337 .8328 .8320 .8311 .8302 .8294 86 90.20 .8329 .8320 .8312 8303 .8295 .8286 .8277 .8269 87 90.97 8303 .8294 .8286 .8277 .8269 .8260 .8251 8243 88 91.72 .8277 .8268 .8260 .8251 .8243 8234 .8225 .8217 89 90 92.47 93.22 .8251 .8225 .8242 .8216 .8234 .8208 8225 .8199 .8217 .8190 .8208 .8181 .8l 99 8173 .8191 .8164 9 1 93-96 .8199 .8190 .8182 8i73 .8164 8i55 .8147 .8138 92 94.68 .8172 .8163 -8155 .8146 8i37 .8128 .8120 .8111 93 95-39 .8145 .8136 .8128 .8119 .8110 .8101 .8093 .8084 94 96.09 .8118 .8109 .8101 .8092 .8083 .8074 .8066 .8057 95 96.78 .8090 .8081 .8073 .8064 .8055 .8046 .8038 .8029 96 97-45 .8061 .8052 .8044 8035 .8026 .8017 .8009 .8000 97 98.11 .8032 .8023 .8015 .8006 7997 .7988 .7980 797 1 98 98.75 .8002 7993 7985 .7976 .7967 7958 7950 .7941 99 99-38 797 2 -7963 7955 7946 7937 .7928 .7920 .7911 100 IOO.OO .7941 7932 7924 .7915 .7906 .7897 .7889 .7880 380 Density of Solutions at 15. Table 28. * V. ' .'H -o o "o *0 ftt rt) a "3 6 <0 < *. n i c . w 9J.J, S-2/J? ||8 4ia^ 'C D EZ i'L I-SG 3J 'ii B2o o o |cj 3 ^'v5 w ^O '^JS O ^^o %'jz O J^HH rt*. ^ se 3 OD 3*"^ rt ss'3 .^^Z *5 ^E ^5*^ 2 *~ CO & 00 4 4 1.027 I.O42 I.OI2 1.033 1.028 1.025 1.03 1.023 1.024 1.015 1*009 6 1.042 1.063 I.OI8 1.050 1.043 1.038 1.04 1.035 1.037 1.023 1*015 8 1.057 1.084 1.024 1.067 1.058 I.O52 1.054-1.048 1.051 I.O3I I02I 10 1.072 1. 1 06 1.030 1.085 1.072 1.065 1.07 1. 06 1 1.064 1.039 1.027 12 1.088 I.I28 1.036 1.103 1.088 1.079 i. 08 1.074 1.078 1.047 1.033 H 1.105 I.I5O 1.042 1. 121 1.103 L093 I.IO 1.088 1.091 1.055 1.040 16 1. 121 1.175 1.047 I.I40 1.118 1.107 .102 1.105 1.063 1.047 18 I.I32 1.200 1.053 I.I58 I.I34 1. 121 .116 1. 120 1.072 I.OfJ4 20 I.I55 1.058 LI77 1.150 I-I35 .131 I.I34 l.80 1.062 22 1.173 1.064 LI97 1.167 I.I5O .146 I.I49 1-088 24 I.I92 1.069 I.2I7 1.183 I.I65 .161 1.165 1.096 26 1.075 1-237 1.200 1.181 1.105 28 1.258 1.197 LH3 30 1.278 I.2I4 1-122 882 Boiling Points of Solutions. Table 2 128 , . 134 134 52 118 130 81 . . 115 I 3 I 137 137 54 . . 119 133 81 . . 116 . , 134 . . 140 140 56 ^ t 119 137 81 , , . . . . 138 H3 H3 58 .. 119 139 81 .. .. .. 146 146 60 M 1 20 142 81 .. 1 1 > . 144 , , I 49 149 62 , . 120 145 81 . . 148 . . . . 64 . . 120 150 81 . . 152 . . 66 llg 156 80 t m . . . . 156 . . . . . . 68 .. 116 163 80 .. .. .. 160 .. .. .. 70 >a 170 80 .. t f m . 164 . . . . . . 72 . . . 176 80 . . . . . . 169 . . 74 ^ 183 80 m t . f . 173 , . . . . . 76 ^ 190 80 . , . . 178 . . . . . . 78 198 80 r* 80 IOO? *yw 206 7O 82 /y 7Q 316? 84 225 / 7 70 O 86 / 7 79 )] 316? .. 88 24.8 QO " *>4-J 26O 70 Q2 274 / 7 7Q V 04 288 / V 78 96 40' / 78 ?8 ** T 1 3i8 / 78 ft red red 100 .. . . 333 78 .. . , .. heat heal Table 30. Specific Heat of Solutions. 883 s -^3T vo t>- rt- ro o O O O oooo iOt~ fO 3D -> OO -00 I>.00 .1 <^ O PO ocroo 5^ C^ vo r O ONOO ON rOOO VO qoq 00 Os ON O O ON 00 00 O-OO GO OO ONOO OO *O vO O C^ **OCO ^ ^O^ ^ OO ^C^ H-t H- ^^ ^H ^5^ O OO ' O^oo s * O*^ C^^^ O ^G(D O^ OO OO QO C^ O^^fe C* O^ O^ OO w t^oo i-ifOvnfOvoi-O'-iro O'HO( s ' : IC < ltOijr)p| CJ-OO ON ON ON O O ON ON ON 35 O; O^ ONt ON ON O* CjN q^ q q". q^ ON qo o S ON q ON^C! o ON ^ ro ir^ unco N g-oo roj * * " " l-< l-< CJN * O O ON -^>3D t^ ON HH M O'l O t^*O VO lO f> t~^?O r^OO t> VO \O ^O t^VO ON OM3S ON ON O O ONOi CTv ON q OCt Ox qO5 ON OCi q qOi 0> qv ON3D ON ft H- flj tX3D OO !> C^r>- t^OO hsaD ONOO OO OO fxCO 00 q> 9t ON q q 05 cx^os ONOS ^ qOs ON ON qO5 ON q> q\ q q> q> ON ~O ON O O O O ON ON ON ON30 OO 3D ON ON ON ON ON ON ON c . o :S o o o !-! U y 'tjyjifii.il fij p C0_; - g cS Oi-OOOO OMt w\o_;>-ir< CON*. ON M VO * VO \r> rr> CT> 00 - CTs ^-vO GO ^ OS OD * 10 ONfiO i- vo kO 00 fO ^. 3S i-i r^^H t^ "I vo oo in tx C-*C ^ CO e CO co o ' N *-iH N. rJ-50 iH vo *J- vo O.VO t^ vo M ONOO VO C*> 5.0 vocOvOO NCOVOVOC* o'^G O r< H- coo sc>kO53^CM>c>kaoo;o^**eo^kS9i(NTj<**ei covo rJ- r*- T^- ^-OO VO M O CO fO N N f< C q M - OOOOOCOOOOOOOOOOOOO 00000 000 ^^2 .^ ^ ^ 3 - Sw ^ to e d ' . " t>. * 4 ""'".? i Tables 31, B-D. Refractive Indices, etc. of Solutions. 885 31. B. Refractive and Dispersive Indices of Solutions at about 18. * 2 ^ Name and Symbol Acid, acetic HC2H 3 O2 o 1.333 201.348 It M 40 I362 ft I* 01 '37 * 801.378 v ? v I0 T -374 Hydrochloric,HCl 35 1.413 Nitric, HNO 3 501.401 Sulphuric, H 2 SO 4 01.333 201.358 401.382 601.410 801.434 ioo 1.434? 01.333 40 1.358 ioo 1.360 Name and Symbol Alcohol, (^HgOrf .014 Chloride Amm. H 4 NC1 10 1.351 .016 t t 20 1.370 .018 ,, Calcium CaCl 2 20 1.384 .019 ,, 40 1.441 .023 Sodium NaCl 10 1.350 .016 .017 20 1.368 .018 .023 Zinc ZnCl 2 20 1.370 .018 .024 .014 40 1.410 .021 Hydrate Potas. KOH 40 1.403 .018 . . Sodium,NaOH 10 1.359 .016 .016 20 1.384 .018 , . 3O 1.404 .020 .018 Nitrate Sodium NaNO 3 20 1-355 - OI 7 .017? 4 1.380 .021 .014 Sugar, CiaH^Ou 10 1.348 .015 .015? 20 1.364 .016 .015? 30 1.381 .017 31. C. Table for preparing Mixtures of any Desired Strength. b fc| k k 1| k 3^ os 8 % k lk +J C/3 ,5 4 - PH OH % - 1 PH PH 02 PH & '~ & & ~ O O.OOO IOO 2O 25.000 80 4O 66.667 60 60 1 50.00 40 80 400.00 20 i i.oio 99 21 26.582 79 41 69.492 59 61 156.41 39 81 426.32 19 2 2.041 98 22 28.205 78 42 72.414 58 62 163.16 38 82 455.56 18 3 3.093 97 23 29.870 77 43 75439 57 63 170.27 37 83 488.24 17 4 4.167 96 24 3L579 76 44 78.571 56 64 177.78 36 84 525.00 1 6 5 5-263 95 25 33-333 75 45 81.818 55 65 185.71 35 85 566.67 15 6 6.383 94 26 35.135 74 46 85.185 54 66 104.12 34 86 614.28 14 7 7.527 93 27 36.986 73 47 88.679 53 67 263.03 33 87 669.23 13 8 8.696 92 28 38.889 72 48 92.308 52 68 212.50 32 88 733-33 12 9 9.890 91 29 40.845 71 49 96.078 51 69 222.58 31 89 809.09 1 1 IO II. Ill 90 30 42.857 70 50 100.00 50 70 233.33 30 90 900.00 10 ii 12.360 89 31 44.928 69 51 104.08 49 71 244.83 29 91 1,011.1 9 12 13.636 88 32 47.059 68 52 108.33 48 72 257.14 28 92 1,150.0 8 13 14.943 87 33 49.254 67 53 112.77 47 73 270.37 27 93 1,328.6 7 14 16.279 86 34 5L5I5 66 54 117.39 46 74 284.62 26 94 1,566.7 6 15 17.647 85 35 53.846 65 55 122.22 45 75 300.00 25 95 1,900.0 5 16 19.048 84 36 56.250 64 56 127.27 44 76 316.67 24 96 2,400.0 4 17 20.482 83 37 58.730 63 57 132.56 43 77 334.78 23 97 3,233-3 3 18 21.951 82 38 61.290 62 58 138.10 42 78 354.55 22 98 4,900.0 2 19 23.457 81 39 63.934 61 59 I43.9 4 1 79 376.19 21 99 9,900.0 i '20 25.000 80 40 66.667 60 60 150.00 40 80 400.00 20 IOO 00 31. D. Coefficients Hydrochloric Acid Hydrate of Potassium . . Sulphuric Acid Nitrate of Potassium . . Common Salt . Nitrate of Sodium . , . of Diffusion of Saline Solutions in Water. ooo, o ioo Sulphate of Potassium . .000,0037 .000, 0070 Sulphate of Sodium . . .000, 0030 ooo, 0052 Sulphate of Magnesium . .000, 0020 .000,0052 Sugar ......... 000,0019 ooo, 0046 Gum Arabic ...... ooo, ooio .000, 0040 Albumen ........ ooo, 0002 .... Caramel ........ 000,0001 886 Rotation and Polarization. Tables 31, E-F 31, E. Rotation in degrees of the Plane of Polarization for the Fraunhofer Lines A H, produced by passing through 100 cm, of various solutions, containing in each case 1 gram of a given substance in 100 en. cm. Name and Symbol of Substance Acid. Malic. H 2 C 4 H 4 O 5 -faq Tartaric H 2 C 4 H 4 O 6 +aq -f- Camphor Ci Hi 6 O + alcohol." + Cholesterine C^H^O-}- ether Cinchonidine C 2 o H 24 N 2 O-f- alcohol. . Cinchonine C2oH 2 4N 2 O-f alcohol. . . -f- 24 Glycocol CH 2 NH 2 COOH-f-alcohol. -f Malate of Arnmon(H 4 N) 2 C 4 H 4 O 5 -f-aq. Lithium Salicihe Santonid, para-; Santonine G 15 H 18 O 3 -|- alcohol ..... Sugar (Cane-) C^H^On-f-aq. . . . -- milK maltose .... , lactose ..... -j- 1 inverted .... , 3.04.2 2.02.63.2 ii 24 24 2.22.9 2.2 B IT 3.84.8 C|D ..0.3 12 0.7 I.O 10 10 15 16 6-5 89 16 5.36.65 5 5 8 2,9 3.8 126 4-9 167 22 26 8.5IO.I 6.2 5-7 H 13-215.7 81, F. Rotation in degrees of the Plane of Polarization for Fraunhofer Lines A H produced by plates of various substances 1 cm. thick. Name and Symbol of Substance A B c D E F G H 248 28 Chlorate , NaClOa 24 ^r 40 46 - 6a T^ 3O ? T.V T^ . 168 ? :: J97 146 2 4 6 178 ? ? Hyposulphate of Calcium CaS 2 Og.4H 2 O 21 Lead PbSaOfi^HoO . 41 ce 77 89 Potassium K 2 S2O 6 .2H 2 O . \' m T^ 62 84 / o 105 .7 123 Strontium Sr S 2 O 6 .4H 2 O . t 16 lodate sodium, per- NaIO 4 104 2 33 285 342 471 Nicotine (liquid) CioH^Ng 127 157 108 Z/i 173 ? 16 217 D 275 32 7 425 511 Quartz (ordinary right handed) SiO 2 -f- Strychnine(sulphate)2C 21 H 22 N 2 O 2 .H 2 SO 4 Tartaric Ether (liquid) (C 2 H 5 ) 2 C 4 H 4 O 6 4- Turpentine right handed C 10 Hi 6 ...-)- w (liquid) left handed CioHjg " $ "1 Tables 31, G-L. Miscellaneous Data. 887 81, G. Rotation of the Plane of Polarization caused by a Unit Magnetic Field (C. G. S.) in Unit Thicknesses of Different Substances. Bisulphide of Carbon (sodium light) o.oo7o | Water (white light) .... o.oooi (thallium ) o.oo86 || Coal gas o.ooo,ooo,2 Note. In these, and in nearly all cases, the rotation is with the current producing the magnetic field. A solution of ferric chloride in methyl alcohol is mentioned as one of the exceptions to this rule (Deschanel, 839). 31, H. Magnetic Moment of 1 cu. cm. of various substances (C. G. S.) Name of Substance Magnetization induced by Unit Field Maximum Magnetization Maximum Permanent Magnetization Name of Substance Magnetization induced by Unit Field Iron . 300? 70? 300? 140? 0.2? 1400 1400 800? 500 ' <*8oo Nickel Oxide Water .... Bismuth . . . Phosphorus . + 0.1? o.oi ? 0.01? 0.004 ? Steel Cobalt. . . . Nickel .... Iron Oxide . 81, I. Coefficients of Friction (f) for -water corresponding to Velocities (v) in centimetres per second (From Weisbach). V / V / V / v / V / o 00 100 .00299 200 .00264 300 .00249 400 .00239 IO .00554 no .00293 210 .00262 3IO .00248 410 .00239 20 .00445 I2O .00288 220 .00260 320 .00247 420 .00238 30 .00396 130 .00284 230 .00258 330 .00246 430 .00238 40 .00368 140 .00280 240 .00256 340 .00245 440 .00236 50 .00347 150 .00276 2SO .00255 350 .00244 450 .00236 60 .00333 IOO .00274 200 .00254 360 .00243 460 .00235 TO .00321 170 .OO27I 270 .00253 370 .00242 470 .00235 80 .00312 180 .00269 280 .00251 380 .00241 480 .00234 90 .00305 190 .00266 290 .00250 390 .00240 490 .00234 100 .00299 200 .00264 300 .00249 400 .00239 500 .00233 31, J. Coefficients of Friction of Solids on Solids. Oak Hard Wood India Rubber Leather Hemp. Bronze Iron Cast Iron Oak .2 .5 .38 .% .52 .48 .40 16 .16 ,iq Bronze 48 .20 .18 .21 Iron (cast, smooth) . wet . . . greased . 49 % .20 "i .15 .08 .2 .31 .15 .2 .4 .2 .4 31 15 81, E. Action of Plates (1 cm thick and bounded by plane surfaces) upon nor- mally incident Radiant Heat. Substance Re- flects Ab- sorbs T mi?s S l 'S^stance Re- flects Ab- sorbs Trans- mits 1 '& 1 E tt 55 Lampblack. . . . India Ink Ice . . ^ A. A. O v>rHO rtOOOO OOO O O THOOO O ^t- 10% 10 13 20 21 25? 30 53 20 % 92 QO? 100 QQ.Q8H- Aque ousSolutions Alcohol Ether. . White Lead . . . Glass Oils Chloroform . . . Turpentine. . . . Bisulphide Carbon Shellac Polished Metals . Rock Salt Lampblack. . . . White Lead . . . Ice fShellac. . .... Mercury . . . Polished Metals . Rock Salt . . . . Vapors at i cm . Perm. Gases 76 cm Glass India Ink. . 31, L. Estimates of the number of Units of Heat radiated in 1 sec. by 1 sq. cm. blackened surface in space at 0. Temp.Rad. I Temp.Rad. jTemp. Rad.jTemp. Rad.jTemp. Rad.f Temp. Rad.| Temp. Rad. 273 .oi9?i-Mco-Koi2?*| 500 .1? 2oo .015? 200 .028?*! boo .2? 100 .009? 300 .05?* I 700 .2?' .000 I 400 .08?* I &oo .3?! 900 .5? 1000 .-]> 1100 .g>//\ i 1 200 i. 2? f| I300 2?** 1700 5? I400 2?" 1600 7?' "3? 11900 10? 4? I 2000 13? 2500 60 ?t* 5000 270? f* 3500 1200 ? 000 5400 ?ss * Dark. " "White Heat 11 f Dull red. , it Flame. * "Red Heat". Cherry Red. // Orange. f Yellow f* Voltaic Arc Light. Sunlight 888 Heat of Combustion. Tables 32-33. 32a. Heats of Combustion in Oxygen. Name of Substance Consumed. Chemical Reaction involving 16.0 grams of Oxygen in each case. Grams of Substance consumed. Grams of Product formed. Units of Heat developed. Units of Heat per gram consumed. UH tflli J1I.18 Jj IMI Acetylene. .... 2 Q H a 4- 5 O 2 = 4 CO 2 4- 2 H 2 O C 2 H 6 O4- 3O 2 = 2CO 2 + 3H 2 O As 4 4-30* 2As 2 O 3 As 4 4- 5O 2 = 2As 2 O s 2 Ba 4- O 2 = 2 Ba O Bi 4 4- 30 a = 2Bi a O 3 2Ca 4- O 2 = 2CaO C 4- O= COj 2 CO 4- O,= 2CO 2 2C1, 4- 2 = 2C1.0 4Cu 4- O a = 2Cu,O 2Cu 4- O,= 2CuO 2C 2 H 6 -f- 7O 2 = 4CO 2 4-6H,O C 4 H, O4- 6O 3 = 4CO 2 4-sH 2 O 2C 2 H 4 4- 6O= 4CO 2 4-4H 2 O 2H, 4- O 2 = 2H 2 U 2L 4- 5 a = 21,0, 2Fe 4- O a = 2FeO 3Fe 4- 2O 2 = Fe 3 O 4 2Pb 4- O 2 = 2PbO 2N 2 4- O 2 = 2N 9 O N 2 4- O 2 = 2 NO N a 4- 20 2 = 2 NO, P 4 4- 5 a = 2P 2 5 2K 2 4- O 2 = 2K 2 O Se, 4- 2 2 = 2SeO, 2Ag 2 4- O 2 = 2Ag 2 O 2 Na a 4- O 2 = 2 Na 2 O 2Sr 4- O,= 2SrO CS 2 4- 3O 2 = CO,4-2SOi S, 4- 2O 2 = 2SO a 2T1 2 4- O 2 = 2T1 2 O 2Sn 4- O a = 2SnO 2Sn 4- 2O 2 = 2SnO a C 10 H 16 4-i4O 2 = ioCO 2 4-8H a O 2 Zn 4- O a = 2 Zn O 32b. Heats of Combustion in 5.2 7-7 50.0 30.0 136.8 138.7 39.9 6.0 28.0 70.7 126.3 63.1 ti 4-7 2.0 50.6 55-9 41.9 206.4 24.0 399-6 199-8 4.0 28.0 14.0 7.0 12.4 78.1 39-4 215.4 40.0 87.3 12.7 16.0 408.0 118.0 59-0 4-9 67.9 Chloi 21.2 4 6io 152.8 154.7 55.9 22.0 44.0 86.7 142.2 79.1 20.3 22.2 20.6 18.0 66.6 71.9 57-9 222.4 40.0 415.6 215.8 20.0 44.0 30.0 23.0 28.3 94-1 55-4 231.4 62.0 103.3 28.6 32.0 424.0 134.0 75-0 20.8 80.9 ine. 62,OOO 54,000 44'ooo 130,000 13,300 130,000 48,000 67,000 18,000 40,000 38,000 54,000 50,000 56,000 69.000 9,000 75,000 66,000 50,000 146,000 42,000 30,000 52,000 18,000 22,000 1,000 71,000 136,000 29,000 5,800 152,000 131,000 43,000 36,000 42,400 m 5^000 12,000 7,000 1,030 1,460 950 06 3,28o 8,000 2,400 - 250 12,500 9,000 12,000 34,500 1/7 1350 1575 243 6,100 105 153 13,100 -650 -1550 - 150 5750 1745 730 27 3,3oo 10,300 9,700 1,500 3,400 2,250 104 !575 1,230 10.700 10,500 4,cx 1,300 500 200 40 1 334 100 10 13 25 520 375 505 M40 10 255 44 550 I 240 73 63 142 94 4-3 24 54 1.49 Alcohol Bismuth Carbonic Oxide . oooer Ether Hydrogen. . . . Lead Magnesium .... Methane . . " * Phosphorus. . . . Potassium .... Selenium tilver Spermaceti .... Stearine. trontium ulphideCarbon,Bi- Thallium . Tin Turpentine .... Wax . Wood Zinc Name of Substance Consumed. Chemical Reaction involving 70.7 grams of Chlorine in each case. o-g* w 1, hi i! jit !* M II llfi o S > 14 Units of per gr consurr Antimony As 4 4- 6 Cl a = 4 As C1 3 Cu4- Cl,= CuCl, H 2 4- C1 2 = 2 HC1 2Fe 4-3Cl a = Fe 2 Cl6 K a 4- C1 2 = 2KC1 Sn 4-2Cl t = SnCU Zn 4- C1 2 = ZnCl 2 33. Heats of Combinati 80.7 2.0 59-0 64.9 on. 151.4 57,000) 707 i2o.6| 50,000 904 133.8 oi,ooq 960 72.71 47,000 23,500 io8.0| 65,000 1,750 148.8! 207,000 2,650 129.7) 64,000 i, 080 135.6] 99,000! 1,530 301.23 421.08 401.33 9801.01 73,1.40 110.4.48 451.38 6412.15 Arsenic Hydrogen Iron ... . Potassium .... Tin Zinc Name of Substance Acted upon. Chemical Reaction involving 16.0 grams of Oxygen or its equivalent. 2 c S8 j|j Units of Heat developed. 111 In!! pipjli Copper . . 2 Cu4-O 2 4-2SOo,4-Aq 2CuSO 4 'Aq 63-1 60.0 47.0 04.9 159.1 54,200s 1 86o| 36 Ii.i7 94. d 30,300) 6ooj 25 0.78 63.0 i8,3od qox), ib (0.40 160.9! 108.5001 1.6701 70 12.35 Nitric Oxide . . . Nitrous Acid . . . Zinc Table 34. Electromotive Force. umuijBjj ssBjg UOJJ "O 'O 'S 'X'tV 7 si /o <* %og vn LO r> oo t^ o\^O oo - . O OO I-H O\ t^vO PO M fi ^ >-> * PO ' I 7 I f f I f I 'o^-q *> oo r^.^^-'-' oo N POPOM J_LLIJ_L 2_|i _ OO OO M rorf Cb ^t- o PO O rh O O i-* O t^vO ^ PO - _ _ _ 3-\O OO O <* VO O t^vO ^ POO O i- PO rhirj i-. U JLLLL ' ' ' ' s IT II If ^rTc? ' f r *i- r-^. PO ^ M ^ LOOO o oo ON oo ^- u->o ^-NONMO O 10^ -^ O ~ PO rt t-xOO 00 - CJ I-H PO =* 00 vO ON >O PO ^ t>> oo PO rl 1T5 <- M u-> i-c r-i \o o "- 1 a N O\ OO PO O N ^- 0^0^%- t^flj "c 1 *- ppy ounqd[ns c^ 890 Electromotive Force. Tables 35 3f> SJJOA tn >o ^ JJJ f?00 CO M * r j i_i o i- 1 <^. r> fO 33JOJ 9AIJ -ouioxioafg ON CO rl- 0* o o S" 3 -Sax O #v ft R w> ^-^ R R R R R R R R R R **- fl >> ^ CS 6 G . ;| ^ j .g S R 5 V 3 s i R-P .S > (2 ^ el U 0? . g. , s c3 ^ c3 -"-3 ^s uCO # 1 i CL "I ! 1 h S J Solution next Positive Pole. rmanganates(withM re Nitric Acid 7o ;hromates Iphate of Mercury (] 0, R C R a R o R - c *3 c/D R --5 > /o Nitrate of Coppe Iphate of Mercury (] trie Acid wdered oxides Mang ver Chloride *0 QJ 3 o --5 3 ^\ R S5 J^ S5 ^N ij **5 Q *"^ > eu ex v o OQ C/D ro S>OD Z CL c/D rf S oo | c& e 1 | 85. Electromotive 1 Solution next Negative Pole. rate of Potassium. Sulphuric Acid. 3 NJ co t W Sulphuric Acid. Sulphate of Zinc. > | 1 ? r "."iSJ^ S o rrj o 1?Vs . bb o o .a S| 1 O N o 1 Iff "w ^ R C R ~ ^ ^ a - ~N ' R R S bJQ R R.S re N H 5 57 14 .22 23 .065 32 .023 oooo 1.2 6 53 15 .19 24 .057 33 .021 ooo I.I 7 .48 16 25 .051 34 .018 00 1.0 8 43 17 .15 26 .046 35 .013 o 0.9 9 0-39 18 0.13 27 0.041 36 O.OIO 43. Musical Pitch (Tempered Scale complete Vibrations per second). Physical 32 foot ififoot Great Little 2 foot i foot 6 inch 3 inch t; "^ Pitch Octave Octave Octave Octave Octave Octave Octave Octave G 1 6.0 32.0 64.0 128.0 256.0** 512.0 1024 2048 Jr g I6. 5 32.9 65.9 I3I.8 263.5*'' " 527.0 1054 2108 U~, G# 17.0 33-9 67.8 135-6 271.2** 542.4 1085 2170 G 17.4 34-9 69.8 139.6 279.2 558.3 1117 2233 D 18.0 35-9 71.8* 143.7 287.4| 574-7 1149 2298 c# 18.5 37.0 73-9* 147.9 59L5 1183 2366 D:# 19.0 38.1 76.1* 152.2 3O44J 608.9 1218 2436 D 19.6 39-2 78.3 156.7 3134 626.7 1253 2507 2O.2 40-3 80.6 161.3 322.5 645.1 1290 2580 D# 20.7 41.5 83.0 166.0 332.0 664.0 1328 2656 F 21.4 42.7 854 170.9 34L7 683.4 1367 2734 22.0 44-0 88.0 175.9 35L7 703.5 1407 2814 F# 22.6 45-3 90.5 181.0 362.0 724.1 1448 2896 F 23.3 46.6 93-2 186.3 372.6 745-3 1491 2981 G 24.0 47-9 95-9 191.8 383-6 7 6 7 .i 1534 3068 F# 24.7 49.4 98.7 1974 394-8 789.6* i 1579 3158 G4I 1 25.4 50.8 101.6 203.2 406.4 8i2.8 f 1626 3251 G 26.1 52.3 104.6 209.1 418.3 836.6 1673 3346 A A# 26.9 27.7 28.5 53-8 55-4 57.o 107.6 no. 8 114.0 215-3 221.6 228.1 430.5tf 861.1 443,2ft 886.3 456.1ft 912.3 1722 1773 1825 3444 3545 3649 A 29.3 58.7 117.4 234.8 469.5 939-0 1878 3756 B 30.2 60.4 120.8 241.6 483.3 966.5 1933 3866 A# 3** 1 62.2 124.4 248.7 4974 994.8 1990 3979 32.0 64.0 128.0 256.0 512.0 1024.0 2048 4096 B Note. The Paris Conservatoire standard of pitch, recently adopted by the International Congress at Vienna, is 435 vibrations per second for the note A of the treble staff. This gives C=26i on the natural scale. American instru- ments tuned to Concert Pitch" give C =- 270 -K p. lih^ 6 ,? 1 P of ^ ass Voice< ** Middle C of Piano, f Lowest D of Flute, ft Violin A. Highest G of Treble Voice. 894 Astronomical Tables. Tables M A. E. ' w ^^Erspco 5 Thousandths of degrees. Thousandths of degrees. ,2 Thousandths of degrees. 9&ft3;ft3$^^Sg|&&8 | q\q oo f ovq ejoo ^qvq oq -t-qvq O - Thousandths of degrees. Thousandths of degrees. -' O -I? oooo oooo ts 2 -> f C d ^S^ C 2^ 5-3 rji .- < rj ^-T> S O Thousandths of degrees. ^ 888*8TS^WS^SSrS^rs& 5- qvq: o'ooooooooo --* -., 1 | Tables44,F G. Astronomical Tables. 895 44, F. Declination of the Sun in Degrees at Greenwich Mean Noon for 1891. Day Jan. Feb. March April May June July August Sept, Oct. Nov. Dec, Day 23.091 1 23.01 1 2 22.925 3 22.831 4 22.729 5 22.619 6 22.502 7 22.378 8 22.246 9 22.108 10 21.961 11 21.808 12 21.648 13 21481 14 21.306 15 21.125 16 20.938 17 20.743 18 20.542 19 20.335 20 20.121 21 19.901 22 19.675 23 19443 *24 19.204 25 18.960 26 18.710 27 18455 28 18.194 29 17-927 140 17.653 31 17-378 17-378 -7-958 4-157 17-096 7-579 i6.8og 7.199 4. 16.516 6.816 5.312 16.219 6432 15.918 6.046 6.074 15.611 5-659 6.453 15.301 5.271 6. 14-986 4-8&I 7- 14.666 4-491 7-5 14.343 4/J99 14.016 3.707 8.31 13.684 3-314 13.350 2.920 13.011 2.525 9409 12.669 2.131 9.768 12.324 1.736 10.124 11.975 1.341 i 11.623 0.945 i 11.269 ioii 0.155 10.551 +0.240 10.188 0.635 9.822 1.029 9454 1423 $3 +1.816 .710 2.208 .335 2.600 7.958 2.991 [7-579] 3.3o 3-769 4-157 18.293 18.044 17.790 17.531 17- 2.7Q1 3.l8t) 3.568 3-956 4-343 22.S97 22.806 22.710 22.606 22 22, 22.553 22.000 22.760 22.854 22.941 6.643 7.021 7.398 773 147 18 18.500 18.752 I 19.241 19476 19.706 19.930 20148 20.359 20.565 23-321 23-360 23-393 23419 23-437 12472 12.141 11.806 11468 11.128 10-343 10.701 11.056 II40Q 11.758 20.764 20-957 21.143 21.323 21 21-001 20-953 21.130 21.300 21464 21.623 21.775 21.920 23405 23.376 23.340 23.297 23.247 23.191 21.661 21.820 1 21.972 2 22.nS 3 22.255 4 22.386 5 22.509 6 22.626 7 22.: 0.550 11.175 23.283 15 23.331 16 23.371 17 23.403 18 23.428 19 23.444 20 23453 21 23-454 22 23.447 23 23432 24 23409 25 23-379 26 23-341 27 23.294 28 2^.241 29 23.179 30 23.109 31 44, 6. Equation of Time in Minutes and Seconds at Greenwich Mean Noon for 1891. Day Jan, Feb. March April May June July August Sept, Oct. Nov. Dec, Day 1*6 m s 13 40 m s 12 45 m s H-4 17 in s o - 1 m s -2 35 111 8 3 20 111 8 6 10 m 8 H-o 15 m s 959 m s 16 18 m s II 14 1 345 1348 12 33 359 3 32 6 7 -0 4 10 18 16 20 io 52 1 a 4 13 13 56 12 21 3 4i 3 o 2 lo 3 44 3 23 10 37 16 21 io 29 2 3 4 41 14 2 12 8 323 3 13 2 8 3 55 5 55 042 10 56 16 21 io 5 3 4 5 8 14 8 " 55 3 5 3 19 I 58 4 6 5 54 I I II 14 16 20 941 4 5 535 14 13 II 42 -+-2 48 3 25 - 48 4 17 548 I 21 n 32 16 19 9 17 5 662 -14 18 !I 28 2 30 37 4 27 5 42 1 41 ii 50 16 io 851 6 7 628 14 21 II 14 2 13 3 34 26 4 37 5 35 2 I 12 7 16 13 8 26 7 8 654 9 7 19 14 24 1426 1059 10 44 150 i 39 338 3 41 l \ 447 456 528 520 2 21 242 12 24 12 40 16 9 16 5 7 59 8 733 .0 7 44 1427 10 29 -f-i 23 344 -051 5 5 5 12 -3 3 12 56 15 59 -7 6 10 11 8 8 14 28 10 13 i 7 346 039 5 13 5 3 3 23 13 12 15 53 6 38 11 12 8 32 1427 9 57 o si 348 027 5 21 453 3 44 13 27 1545 6 io 12 13 854 14 20 940 035 349 o 15 5 28 443 4 5 13 41 5 42 13 14 9 17 14 24 924 2O 349 02 5 35 432 427 1355 152? 513 14 15 938 14 22 g 7 +o 5 349 +0 10 5 42 421 -448 14 9 15 19 445 15 16 959 17 10 iq 14 18 14 14 8 50 8 32 o 10 o 24 348 3 47 023 o 36 548 5 53 y 5 9 5 30 14 22 1434 15 8 14 57 4 16 16 346 17 18 10 38 14 9 8 15 o 38 3 45 049 5 58 3 43 14 46 14 44 3 17 18 19 1057 14 3 757 052 343 I 2 6 2 3 30 i 13 1458 14 3i 2 4 7 19 20 n 15 1357 739 - 5 3 40 "*" 1 IS 6 6 3 16 g 34 15 8 14 17 2 18 20 21 n 32 13 50 7 21 18 3 37 I 28 6 9 3 i 6 ss 15 18 14 3 148 21 22 n 48 1343 I 3 30 3 33 I 40 6 12 2 46 716 15 27 13 47 i 78 22 23 12 4 24 12 19 13 20 42 53 329 3 24 6 14 6i5 2 31 2 15 737 758 15 36 15 44 1331 13 13 048 23 o 18 24 25 12 33 13 16 6 8 2 4 3 18 +2 19 6 16 i 59 -8 19 IS 51 12 55 -- o 12 25 26 12 46 27 12 58 13 6 12 56 5 49 53i 2 15 2 2S 3 12 306 231 2 44 6 17 6 16 53 39 8 59 j^57 12 37 12 17 042 26 i 12 27 28 13 10 29 1321 12 45_ [12 33] 5 12 454 234 2 43 2 S9 2 52 256 3 8 6 16 614 i 9 o 51 9 19 9 39 16 12 ii 36 141 28 a n 29 30 13 31 31 13 40 435 4 17 251 2 44 2 35 3 20 6 12 6 10 033 o 15 959 16 15 16 18 ii 14 a 40 30 3Q 31 896 Astronomical Data. 44, H. Solar System. Tables 44 H, 45. Mercury 87.97 .387 0.07? 58. 4.8 0.4? 6.? Venus . 224.70 723 0.8? 1 08. 12.2 5-? 6.? Earth . 365.26 I.OOO 1. 00 149. 12.74 6.1 5-6 Moon . 27.32 .0026* O.OI2 *o.39 348 0.07 3-4 Mars . . 686.98 1.524 O.I I 227. 0.7 4- Jupiter . 4332.53 5.203 310. 777- 142.' 1900. Saturn . 10759.22 9-539 93- 1424. 119. 570. 0.7 Uranus 30686.82 19.18 14. 2864. 50. 85. Neptune 60126.71 30.05 4487. 60. 100. 0.9 * Distance from the Earth. 45. Mean Position of Fixed Stars, Jan. 1891. Names a 0) > i < 1 u Q *E o > > i m s s O Sirrah a Andromedae 2 2 45.2+3.09 4-28.489'- -.0055 Polaris Ursae Minoris 2 I 18 53.4 2.36 +88.727 +.0053 Arietis 2 2 i 1.7 3.37 - 4-22.947- ^.0048 Aldebaran a Tauri I 4 29 39.9 3.44- -(-16.289- -.0021 Capella Rigel Aurigae p Orionis I I 5 5 8 38.2 9 l 7-9 443 - 2.88- -j-45.886- - 8.328- -.00 1 1 -.0012 Beteigeuze Orionis I 5 49 1 6.2 3.25- f 7.386 +.0003 Canopus Sirius a Argus a Canis Majoris I I 6 6 21 31.9 40 20.6 1-33 52.636 .0005 2.64 i6.t;67i .00 u Castor a 2 Geminorum 2-1 7 27 38.7 3.84 - -32.127 .0021 Procyon a Canis Minoris 1 7 33 35-7 3-H - - 5.504 .0025 Pollux p Geminorum 1-2 7 38 38.7 3.68 ;- -28.289' .OO23 Regulus a Leonis I-2;IO 2 34.0 3.20- -12.500 .0049 Denebola p Leonis 2 II 43 30.0, 3.06 - -15.181 .0056 a Crucis I JI2 20 32.6; 3.30 - -62.49 5 -.005 6 Spica a Virginis I 13 19 27.0: 3.15 io.5 9 2|-.oo53 p Centaun 1 J 3 56 8.O| 4.18 59.8471 .0049 Arcturus Bootis a 2 Centauri !-3 10 41.3: 2.73 j- 32 12.5; 4.04 - fi 9 .75o| .0053 60.383 .0042 Antares Vega Altair Deneb Formaihaut Markab Scorpii Lyrae a Aquilae Cygni Piscis Aust. a Pegasi 1-2 I 1-2 2-1 1-2 ^ 16 18 19 20 22 22 22 43.4 3.67 -26.189 .0023 33 14.8 2.03 +38.683 +.0009 45 27.9 2.93 |4- 8.581 +.0026 37 42.9 2.04 +44.89 1 +.0035 *i 37- 6 3-32 i 30.200+0053 59 19.8+2.98 +I 4 .6i 9 +.oo54 Note. Tho yearly precession of the equinoxes is about so".25, or o.oo245-*- The mean (not apparent) obliquity of the ecliptic for 1891 is" about 23, 27', 13"^ or 27.453. The :nean obliquity decreases annually by o".8, or o.ooo2. tables 46 48. Latitude, Longitude and Gravity. 897 46. Latitudes and Longitudes Latitude Longitude Elevation o h ra s Metres Aberdeen . . .057.149 No 8 23 W Amsterdam . . T 52.371 N O 19 39 E Antwerp . . T5I.22I N O 17 37 E Athens. . . 637.972 N I 34 55 E Baltimore . . T 39.298 N 5 628W 55 Belfast. . . 54.66 N02 3 ..W Berlin . . . O 52.505 N O 53 35 E 40 Bonn . . . 50.729 N O 28 23 E 50 Boston. . .T42.358N 44415 W 63 Brussels . . 50.853 N 17 29 E 90 Calcutta . .T 22.557 N 5 53 19 E 39 Cambridge U, S. O 42.380 N 4 44 31 W Cambridge Eng,. 052.215 N O O 23 E CapeofGoodHope O 33-934 S I 13 55 E Christiania . . 059.912 N 042 54 E 42 Copenhagen . . O 55.687 N 50 19 E 53 Cork . . . .T 51,90 No 33 51 W Dublin. . . . 053.387 N 02521 W T 24 Edinboro . . . O 55.956 N O 12 43 W Tl39 Geneva .... 46.200 N O 24 37 E Genoa . . . . T444I9 N 35 41 E Glasgow . . . 055.879 N 017 ii W Gottingen . . . 51.530 N O 3946 E 130 Greenwich. . .051.477 No o T 64 Heidelburg . . 49.40 N O 34 32 E IOO Leipzic. . . . 51.335 N o 49 34 E 100 Lisbon . . . . O 38.705 N O 36 34 W Liverpool . . . O 53.401 N O 12 17 W Magnetic Pole . 77.83 N 4 14 W Measured from Greenwich. Latitude Longitude Elevation o h m s Metres 50 663 51.514 N o 023\V O 40.408 N 01445 W 53.48 N o 9.. W 37.83iS 9 39 54 E T 45.52 N 4 54 13 W 48.146 N 04626E O 40.863 N 057 i W T2 9 .963N 6 OHW O 40.730 N 45557 W O 48.836 N o 921 E 44 525 London . Madrid . Manchester Melbourne Montreal . Munich . Naples . New Orleans New York. Paris. . . O 48.836 N O 92iE 60 Philadelphia. T 39.95 3 N 5 o 39 W 50 Quebec . .O 46.805 N 44449X^X108 Queenstown. T 51.85 N 33 6 W Rio deJaneiro O 22.907 S 2 52 41 W T 69 Rome. . . 41.898 N 04954E 29 Rotterdam . T 5 1.908 N o 17 55 E 28 San Francisco O 37.790 N 8 9 43 W Ti 1 1 Savannah. . T 32.081 N 5 24 21 W 42 St.John(N,S.) T 45.262 N 4 24 15 W 38 StPetersburg O 59.942 N 2 I 14 E II Stockholm . O 59.343 N I 12 14 E 20 048.582 N 031 2E 150 033-861810 45oE T 65 045.643 N 055 2E T 17 O 45.430 N 04925E 48.210 N i 532E 182 Strassburg Sydney . Triest. . Venice . Vienna . Washington Wellington O38.8 9 4N 5 8i2WT 63 T4I.288S ii 39 ii E T 18 [Note. T = Time Signal. O = Observatory 47. Acceleration of Gravity in Lat. +0 -j-l + 2 +3 978.10 978.10 978.11 978.12 978.25 978.29 978.32 978.36 978.69 978.75 978.81 978.87 979-35 979-43 979.51 979-59 980.17 980.26 980.34 980.43 981.04 981.13 981.21 981.30 981.86 981.93 982.01 982.08 982.52 982.58 982.63 982.68 982.96 982.99 983.01 983.03 10 20 30 40 50 60 70 80 Different Latitudes (cm. per sec. per sec.)-* + 4 +5 -f-6 H-7 +8 +9 Dif 978.13 978.14 978.16 978.18 978.20 978.23 l 978.40 978.44 978.48 978.53 978.58 978.63 4 978.93 979.00 979.06 979.13 979.21 979.28 7 979.67 979.75 979.83 979.9 2 9 8o -00 980.09 3 980.52 980.61 980.69 980.78 980.86 980.95 9 981.38 981.46 981.54 981.62 981.70 981.78 8 982.15 982.21 982.28 982.34 982.41 982.47 7 982.73 982.77 982.82 982.86 982.89 982.93 4 983.05 983.07 983.08 983.09 983.10 983.11 ! Dif 48. Length of Seconds-Pendulum in Different Latitudes (cm.).* Lat. -f +1 -f-2 +3 +4 +5 +6 +7 +8 + 9 99.103 99.103 99.103 99.104 99.105 99.106 99.108 99.110 99.112 99.115 i 10 99.118 99.121 99.125 99.128 99.132 99.137 99.14! 99.146 99.151 99.156 4 20 99.162 99.168 99.174 99.180 99.187 99.193 99.200 99.207 99.214 99.222 30 99.229 99.237 99,245 99.253 99.261 99.269 99.278 99.286 99.295 99.303 40 99.312 99.321 99.330 99.338 99.347 99.356 99.365 99.374 99.383 99.391 9 50 99.400 99.409 99.418 99.426 99.435 99443 99-45 * 99-459 99.467 99-475 s $0 99.483 99.491 99.498 99.505 99.512 99.519 99.526 99.532 99.539 99-545 7 70 99.550 99o56 99.561 99.566 99.571 99.576 99.580 99.584 99.588 99.591 4 80 99.594 99-597 99.600 99.602 99.604 99.606 99.607 99.608 99.609 99.010 i * These values are calculated for the sea level. A deduction of 0.03 % should be made for each kilometre of elevation above the ground and a deduction of 0.02% should be made for each kilometre of elevation of the ground above the sea. 898 Reduction of Measures. Table 49a 49a. Reduction of Measures to and from the C. G. S. System. Lengths in centimetres Equivalent Logarithm Reciprocal inch = 2.53997 0.40483 .393705 link = 7.92 in = 20.1165 1.30355 -0497103 foot = 12 in. . . . . . . = 30.4796 1.48401 .0328088 yard = 3 ft. ....'... = 9M389 1.961 13 .0109363 fathom = 6 ft = 182.878 2.26216 00546813 rod = i6'/8 ft 502.914 2.70149 .00198841 chain = 100 links = 66 ft. . . = 2011.65 3-30355 .000497103 statute mile = 5280 ft. . . . = 160,932 5.20664 6.21378x10-* nautical mile = 185,200(7) 5.2676 5.40x10-6 A eas in square centimetres square inch . . = 6.4514 0.80966 .15500 square foot = 144 sq. in. . . 929.01 2.96802 .0010764 square yard = 9 sq. ft. . . . = 8361.1 3.92226 .00011960 acre = 43,560 sq. ft = 4.0468x10? 7.60711 2.4711x10-8 square mile = 640 acres . . =: 2.5899XI0 10 10.41329 3.8611x10" Vilumea in cubic centimetres cubic inch 16.386 1.21449 .061026 cubic foot = 1728 cu. in. . . = 28316 445203 3.5316x10-5 cubic yard = 27 cu. ft. . . . = 7 6 45 26 5.88339 i 3080x10-6 U. S. pint = 1.043 Ibs. water = 473 2.6750 .002114 U. S. quart = 2 pints . . . . = 946 2.9760 .001057 dry quart = noi 3.0418 .000908 U. S.gallon = 231 cu. in. = 4 qts. = 3785 3-578i .0002642 imperial gallon = 10 Ibs. water = 4541 3.6572 .0002202 Masses in grams grain ; .. = .0647987 2.8115715.4324 ounce (Avoirdupois) = Vie H> = 28.3494 1.45254 .0352741 ounce (Troy) = 480 grams . = 31.1034 1.49281 .0321509 pound (Troy) = 12 oz. Troy. = 373- 2 40 2.57199 .00267924 pound (Avoir) = 7000 grains />a* 453,590 2.65666 2.20463x103 English ton = 2240 Ibs. . . . r 1.01604x10* 6.00691 9.84210x10-7 Times in mean solar seconds year (tropical) = 365.24222 days = 31,556.928 7.49809 3.i6888xio- 8 sidereal year = 365.25637 days = 31,558,150- 7.49811 3.16875x10-* (mean solar) day = 86,400 4.93651 .000011574074 hour = 3,6oo 3-55 6 3o .00027777778 minute = 60 1.77815 .016666667 so-called sidereal second . . = 0.9972695666 .99881 1.0027379091 true sidereal second . . . . = 0.9972696721 1.99881 1.0027378030 Velocities in centimetres per second kilometre per hour = 27.7778 1.4437 .0360000 foot per second 30-479 6 1.48401 .0328088 mile per hour = 44-733 1.65034 .0223696 nautical mile per hour ... = 51.44 1.7113 .01944 kilometre per minute . . . . = 1666.67 3.22185 .0006000000 mile per minute 2682.20 3*42849 .000372827 Accelerations in cm. per sec. per. sec. foot per sec. per sec = 30.4796 1.48401 .0328088 Densities in grams per cu. cm. grain per cubic inch = .0039544 3.59708 252.88 Ib. per cubic foot .....= .016019 2.20463 62.426 Heat TJnits in ergs. unit of heat = i gram-degree G. = 4.T7XIO 7 7.620 2.40x10-8 Ib.-degree Fahrenheit . . . . = i.o5ixio 10 10.022 9.52x10-" i Ib.-degree Centigrade . . . . 1.89X10* 10.277 5.29x10- i Calorie = 1000 g = 4.i7Xio 10 10.620 2.40x10-" Reduction of Measures. Table 49b 49 b. Continuation. Reduction of Measures to and from the C. G. S. System. Values marked with an asterisk (*) are independent of the acceleration of gravity (g). 11H1 _! ^J-O O O O O 99 t^oAAAAA* 899 00 O ^2 it 1 1 - xxxx c, ON O *t- ^1 O O MMO ~ PC l-< r}-OO HH i- OO O ON * oq CJN ^ , M ri rt- 1/> vno f'>vo"vo" < O S VO* t^.C O ^0 OO ONONolar parallax (8" .83?) . . .00245 earths equatorial radius in kilom 6378. " ths polar 6356.+ .31022' .3678794 2.302585 57-2957 3437-747 i 1.0027379 0.0027379 7o 176. 3-74 408. .0001568 .0001573 I.54XIO* .010065 .0010198 1116.1. 11310. 0-99999 1.003 040 .119 .073800 Light. Velocity in cm. per sec 3-ooXio 10 sodium, wave length in air icm.) .00005893 Refractive Index of water for ditto 1.333 Dispersive ., 0.0144- Rotation of ditto by Quartz plate i cm. thick . . . 217 Candle power of i sq. cm. melted platinum (2 Carcels) 20 Heat. Conductivity of Copper C. G. S 0.9+ Coefficient of Expansion of glass (cubical) 000025 steel (linear) .000012 brass .000019 mercury (cubical 20) . .000180-4- gases .00367 Latent Heat of Water 79 Steam (100, 76 cm.) 536 Specific Heat of Brass 0^04 Glass ai9 Water (o 100) i-oos Air (o 100, 76 cm) 0.2383 or. . . 0.238 Gases, (ratio of 2 Sp. Hts.). . . . 1.408 Mechanical Equivalent of i unit of heat (i g) in ergs, 4.166X10' or. 4.i7Xio 7 7.620 i kilogrammetre (lat. 45) 9.8061 Xio 7 7.99149 i foot-pound ( ) i.3557Xio 7 7.13217 Electro-Chemical equivalent of Hydrogen in grams per ampere per sec .00001038 5.0162 i Electrostatic Unit of E. M. F. in volts 300 2477 Electromotive Force of Daniell cell in volts ... i.oto 1.2 0.00 to 0.08 Internal Resistance of Quart ohms ... ito2 0.0 to 0.3 I B. A. unit in legal ohms 0.9889 J-9952 i Siemens ,, 0.0434 1^9747 Specific Electrical Resistance of Mercury (C. G-S.) o.942Xio 5 4.974 Magnetic susceptibility of iron . 'lotal Intensity of Earths Field LStoTS 240X10-8 1.0198x10-8 7.376X10- - 9634 00333 IJO to 08 i .o to .5 I.O1I 1.060 1.061X10 003? 3 to 1.5 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS OVERDUE. = SEP 12 FEB 26 1935 l ; S:PJ371837 MAR 29 1944 DEC YC I 1 352 v? ft. .