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GIFT OF
ASTRONOMICAL SOCIETY OF THE

PACIFIC




St. S




METEOROLOGICAL TABLES



SMITHSONIAN MISCELLANEOUS COLLECTIONS.



1032




SMITHSONIAN



METEOROLOGICAL TABLES



[BASED ON GUYOT S METEOROLOGICAL AND PHYSICAL TABLES.]
(REVISED EDITION)







CITY OF WASHINGTON:

PUBLISHED BY THE SMITHSONIAN INSTITUTION.
I 896







PRINTED FOR THE SMITHSONIAN INSTITUTION
BY W. F. ROBERTS, WASHINGTON



I8Q6



6 C * 73



*stron. Dept*






PREFACE TO REVISED EDITION.



The original edition of Smithsonian Meteorological Tables, issued in
1893, having become exhausted, necessitating a second edition, a care
ful examination of the original work has been made, at my request, by
Mr. Alexander McAdie, of the United States Weather Bureau.

All errata thus far detected have been corrected upon the plates,
and a few slight changes have been made. The International Meteoro
logical Symbols and an Index have been added.

S. P. I;ANGLEY,

Secretary.

SMITHSONIAN INSTITUTION,

February 15, 1896.



iii

701401



PREFACE



In connection with the system of meteorological observations estab
lished by the Smithsonian Institution about 1850, a collection of
meteorological tables was compiled by Dr. ARNOLD GUYOT, at the
request of Secretary HENRY, and published in 1852 as a volume of the
Miscellaneous Collections.

Five years later, in 1857, a second edition was published after
careful revision by the author, and the various series of tables were
so enlarged as to extend the work from 212 to over 600 pages.

In 1859 a third edition was published, with further amendments.

Although designed primarily for the meteorological observers report
ing to the Smithsonian Institution, the tables obtained a much wider
circulation, and were extensively used by meteorologists and physicists
in Europe and in the United States.

After twenty-five years of valuable service, the work was again
revised by the author ; and the fourth edition, containing over 700
pages, was published in 1884. Before finishing the last few tables,
Dr. GUYOT died, and the completion of the work was intrusted to his
assistant, Prof. WM. LIBBEY, JR., who executed the duties of final editor.

In a few years the demand for the tables exhausted the edition,
and thereupon it appeared desirable to recast entirely the work. After
very careful consideration, I decided to publish the new tables in
three parts: METEOROLOGICAL TABLES, GEOGRAPHICAL TABLES, and
PHYSICAL TABLES, each representative of the latest knowledge in its
field, and independent of the others ; but the three forming a homo
geneous series.

Although thus historically related to Dr. Guy of s Tables, the present
work is so substantially changed with respect to material, arrange
ment, and presentation that it is not a fifth edition of the older tables,
but essentially a new publication.



Vlii TABLE OF CONTENTS.

BAROMETRICAL TABLES. Continued.
TABLE PAGE

Determination of heights by the barometer English measures.

20 Values of 60368 [i + 0.0010195 x 36] log 100

21 Term for temperature 104

22 Correction for latitude and weight of mercury 106

23 Correction for an average degree of humidity 108

24 Correction for the variation of gravity with altitude . . . 109
Determination of heights by the barometer Metric measures.

25 Values of 18400 log no

>

26 Term for temperature in

27 Correction for humidity . 112

28 Correction for latitude and weight of mercury 114

29 Correction for the variation of gravity with altitude . . . 115

30 Difference of height corresponding to a change of o. i inch in the

barometer English measures 116

3 1 Difference of height corresponding to a change of i millimetre in

the barometer Metric measures 117

Determination of heights by the barometer.

32 Formula of Babinet 118

Barometric pressures corresponding to the temperature of the

boiling point of water

33 English measures 119

34 Metric measures 119



HYGROMETRICAL TABLES.

Pressure of aqueous vapor (Brock)
35 English measures 122

> Metric measures \

43 / I 142

37 Pressure of aqueous vapor at low temperatures (C. F. Marvin)

English and Metric measures 13

38 Weight of aqueous vapor in a cubic foot of saturated air

English measures I3 2

39 Weight of aqueous vapor in a cubic metre of saturated air

Metric measures 133

Reduction of psychrometric observations English measures.

40 Pressure of aqueous vapor J 34

X f f \

41 Values of 0.000367 B (//,)( l H ) l ^

42 Relative humidity Temperature Fahrenheit 138



OF CONTENTS. ix

HYGROMETRICAL TABLES. Continued.

TABLE PAGE

Reduction of psychrometric observations Metric measures.

43 Pressure of aqueous vapor 142

44 Values of 0.000660 B (t t^) ( i + ^J 143

8 73 /

45 Relative humidity Temperature Centigrade 144

Reduction of snowfall measurements.

46 Depth of water corresponding to the weight of snow (or rain)

collected in an 8-inch gage 146

47 Rate of decrease of vapor pressure with altitude 146

WIND TABLES.

Mean direction of the wind by Lambert s formula

48 Multiples of cos 45 ; form and example of computation . . 148

49 Values of the mean direction (a) or its complement (go a.) 149

50 Synoptic conversion of velocities 154

5! Miles per hour into feet per second 155

52 Feet per second into miles per hour 155

53 Metres per second into miles per hour 156

54 Miles per hour into metres per second 157

55 Metres per second into kilometres per hour 158

56 Kilometres per hour into metres per second , . 159

57 Beaufort wind scale and its conversion into velocity 160



GEODETICAL TABLES.

58 Relative acceleration of gravity at different latitudes .... 162

59 Length of one degree of the meridian at different latitudes . . 164

60 Length of one degree of the parallel at different latitudes . . . 165

61 Duration of sunshine at different latitudes t . . . 166

62 Declination of the sun for the year 1894 177

63 Relative intensity of solar radiation at different latitudes . . . 178

CONVERSION OF LINEAR MEASURES.

64 Inches into millimetres 180

65 Millimetres into inches 187

66 Feet into metres . . 200

67 Metres into feet 202

68 Miles into kilometres 204

69 Kilometres into miles 206

70 Interconversion of nautical and statute miles ...*... 208

71 Continental measures of length with their metric and English

equivalents 208



X TABLE OP CONTENTS.

CONVERSION OF MEASURES OF TIME AND ANGLE.

TABLE PAGE

72 Arc into time 210

73 Time into arc 211

74 Days into decimals of a year and angle 212

75 Hours, minutes and seconds into decimals of a day 216

76 Decimals of a day into hours, minutes and seconds 216

77 Minutes and seconds into decimals of an hour 217

78 Mean time at apparent noon , . . 217

79 Sidereal time into mean solar time 218

80 Mean solar time into sidereal time 218

MISCELLANEOUS TABLES.

81 Density of air at different temperatures Fahrenheit . . . . 220
Density of air at different humidities and pressures English

measures.

82 Term for humidity: auxiliary to Table 83 221

h b o.^jSe

83 Values of = 222

29.921 29.921

84 Density of air at different temperatures Centigrade 224

Density of air at different humidities and pressures Metric

measures.

85 Term for humidity : auxiliary to Table 86 225

86 Values of ^-=*-; 378g . ... 326

70O 70O

87 Conversion of avoirdupois pounds and ounces into kilogrammes . 226

88 Conversion of kilogrammes into avoirdupois pounds and ounces 230

89 Conversion of grains into grammes . 230

90 Conversion of grammes into grains . . . 231

91 Conversion of units of magnetic intensity 231

92 Quantity of water corresponding to given depths of rainfall . . 232

93 Dates of Dove s pentades 232

94 Division by 28 of numbers from 28 to 867 972 233

95 Division by 29 of numbers from 29 to 898971 234

96 Division by 31 of numbers from 31 to 960969 235

97 Natural sines and cosines 236

98 Natural tangents and cotangents 238

99 Logarithms of numbers 240

100 LIST OF METEOROLOGICAL STATIONS 243

APPENDIX.

Constants 258

Synoptic conversion of English and metric units 260

Dimensions of physical quantities 262

International Meteorological Symbols ... 263



INTRODUCTION.

DESCRIPTION AND USE OF THE TABLES.



THERMOMETRICAI, TABLES.

COMPARISON OF THERMOMKTRIC SCALES.

Conversion of readings of the Reaumur thermometer to readings
of the Fahrenheit and Centigrade thermometers.

The argument is given for every Reaumur degree from -f 80 to 40
Reaumur, and the corresponding readings Fahrenheit and Centigrade are
given to hundredths of a degree, permitting the exact values to be
expressed. A column of proportional parts gives the values corresponding
to tenths of a Reaumur degree. By the help of the column of proportional
parts, the table is also conveniently used for converting Fahrenheit to
Centigrade and Reaumur, and Centigrade to Fahrenheit and Reaumur
throughout the thermometric scale from the boiling point of water to
60 F. or 51 C.

The formulae expressing the relation between the different scales are
given at the bottom of the table, where

F = Temperature Fahrenheit.

C = Temperature Centigrade.

R = Temperature Reaumur.

Examples :

To convert i8?3 Reaumur to Fahrenheit and Centigrade.

From the table, i8.o R. = 72:50 F. = 22*50 C.

From column Prop. Parts, 0.3 = 0.675 = 0.375



18:3 R. = 73.2 F. = 22.9 C.
To convert i47-7 Fahrenheit to Centigrade and Reaumur.

From the table, 146:75 F. = 63:75 C. = 5i.o R.

From column Prop. Parts, 0.95 = 0.53 = 0.4



i 4 77 F. = 64:3 C. = 5i4 ^-
To convert i6.9 Centigrade to Fahrenheit and Reaumur.

From the table, 16:25 C = 6i2sF. = 13:0^?.

From column Prop. Parts, 0.65 = 1.17 = 0.5

16:9 C. = 62. 4 F. = i3.5^.
xi



xii INTRODUCTION .

TABLE 2. Conversion of readings of the Fahrenheit thermometer to readings
Centigrade.

The conversion of Fahrenheit temperatures to Centigrade temperatures
is given for every tenth of a degree from -f- 1 3o.9 F. to 7o.9 F. The
side argument is the whole number of degrees Fahrenheit, and the top
argument, tenths of a degree Fahrenheit ; interpolation to hundredths of a
degree, when desired, is readily effected mentally. The tabular values are
given to hundredths of a degree Centigrade.

The formula for conversion is



where F is a given temperature Fahrenheit, and C the corresponding
temperature Centigrade.

Example :

To convert 79-7 Fahrenheit to Centigrade.
The table gives directly 26.5O C.

For conversions of temperatures above 13 1 / 7 , use Table i.

TABLE 3. Conversion of readings of the Centigrade thermometer to readings
Fahrenheit.

The conversion of Centigrade temperatures to Fahrenheit temperatures
is given for every tenth of a degree Centigrade from + 5o.9 to 50^9 C.
The tabular values are expressed in hundredths of a degree Fahrenheit.

The formula for conversion is

F= 9C + 3 2-



where C is a given temperature Centigrade, and F the corresponding
temperature Fahrenheit.

For conversions of temperatures above the upper limit of the table,
use Tables i and 4.

TABLE 4. Conversion of readings of the Centigrade thermometer near the
boiling point to readings Fahrenheit.

This is an extension of Table 3 from 90^0 to ioo.9 Centigrade.
Example :

To convert 95^74 Centigrade to Fahrenheit.

From the table, 95-7 C. 204*26 F.

By interpolation, 0.04 = 0.07

95-74 C. = 204^33 F.



THERMOMETRICAI, TABLES. Xlii

Conversion of differences Fahrenheit to differences Centigrade. TABLE 5.

The table gives for every tenth of a degree from o to 2og F. the
corresponding lengths of the Centigrade scale.

Conversion of differences Centigrade to differences Fahrenheit. TABLE 6.

The table gives for every tenth of a degree from o to g.g C. the corre
sponding lengths of the Fahrenheit scale.

Example :

To find the equivalent difference in Fahrenheit degrees for a difference

of 4.72 Centigrade.

From the table, 4.7o C. = 8:46 F.

From the table by moving the decimal point for 0.2, 0.02 = 0.04

4 .72 C. = 8^50 F.



REDUCTION OF TEMPERATURE TO SEA

English Measures. TABLE 7.

Metric Measures. TABLE 8.

These tables give for different altitudes and for different uniform rates
of decrease of temperature with altitude, the amount in hundredths of a
degree Fahrenheit and Centigrade, which must be added to observed tem
peratures in order to reduce them to sea level.

The rate of decrease of temperature with altitude varies from one
region to another, and in the same region varies according to the season
and the meteorological conditions ; being in general greater in warm lati
tudes than in cold ones, greater in summer than in winter, and greater
in cyclones than in anti-cyclones. For continental plateau regions, the
reduction often becomes fictitious or illusory. The use of the tables there
fore requires experience and judgment in selecting the rate of decrease
of temperature to be used.

The tables are given in order to facilitate the reduction of temperature
either upwards or downwards in special investigations, but the reduction is
not ordinarily applied to meteorological observations.

The tables, 7 and 8, are computed for rates of temperature change
ranging from i Fahrenheit in 200 feet to i Fahrenheit in 900 feet, and
from i Centigrade in 100 metres to i Centigrade in 500 metres ; and
for altitudes up to 5,000 feet and 3,000 metres respectively.

Example, Table 7 :

Observed temperature at an elevation of 2,500 feet, 52. 5 F.

Reduction to sea level for an assumed decrease in tem
perature of iF. for every 300 feet,

Temperature reduced to sea level,




XIV INTRODUCTION.

Example, Table 8 :

Observed temperature at an elevation of 500 metres, 12. "5 C.
Reduction to sea level for an assumed decrease in tempera
ture of i C. for every 200 metres, + 25



Temperature reduced to sea level, i5o C.

CORRECTION FOR THE TEMPERATURE) OF THE MERCURY IN THE THER

MOMETER STEM.

TABLES. Fahrenheit thermometers ; Centigrade thermometers.

When the temperature of the thermometer stem is materially differ
ent from that of the bulb, a correction needs to be applied to the observed
reading in order to correct it for the difference in the length of the mer
cury column caused by this difference in its temperature. This correction
frequently becomes necessary in physical experiments where the bulb only
is immersed in a bath whose temperature is to be determined, and in
meteorological observations it may become appreciable in wet-bulb, dew
point, and solar radiation thermometers, when the temperature of the bulb
is considerably above or below the air temperature.

If t be the average temperature of the mercury column, t the observed
reading of the thermometer, n the length of mercury in the stem in scale
degrees, and a the apparent expansion of mercury in glass for i, the
correction is given by the expression



in which, for Centigrade temperatures, a = 0.000154 or 0.000155.

The average temperature of the mercury column can not be directly
observed and is difficult to determine, for it differs from the temperature
of the glass stem by an amount depending on the conduction of heat
between the bulb and the mercury column. Practically however it is
possible to use the actually observed temperature of the glass stem as the
value of / by making a small compensating change in the value of a,
and this appears to be the simplest method that has been proposed. Mr.
T. K. Thorpe (Journal of the Chemical Society, vol. 37, 1880, p. 160) has
determined by a series of experiments that the proper thermometric cor
rections will be obtained by this method if 0.000143 be used as a coefficient
(for Centigrade temperatures) instead of the value of a given above, and
this value has been adopted in the present tables.

The correction formulae are, then,

T= t 0.0000795 n (f t*) Temperature Fahrenheit.
7"= t 0.000143 n (t t} Temperature Centigrade.
in which T = Corrected temperature.
t = Observed temperature.
t = Mean temperature of the glass stem.
n = Length of mercury in the stem in scale degrees.



BAROMETRICAL TABLES. XV



When f is ss 1 " j than /, the numerical correction is to be

Example :



The observed temperature of a black bulb thermometer is i2o.4 F., the
temperature of the glass stem is 55.2 F. and the length of mercury
in the stem is 130 F. To find the corrected temperature.

With n = 130 F. and / /= [ ] 65 F., as arguments, the table gives
the correction o.7 F. , which by the above rule is to be added to the
observed temperature. The corrected temperature is therefore 1 2 1 . i F.



BAROMETRICAL TABLES.

REDUCTION TO A STANDARD TEMPERATURE OF OBSERVATIONS MADE
WITH BAROMETERS HAVING BRASS SCALES.

The indicated height of the mercurial column in a barometer varies not
only with changes of atmospheric pressure, but also with variations of the
temperature of the mercury and of the scale. It is evident therefore that
if the height of the barometric column is to be a true relative measure of
atmospheric pressure, the observed readings must be reduced to the values
they would have if the mercury and scale were maintained at a constant
standard temperature.

This reduction is known as the reduction for temperature, and combines
both the correction for the expansion of the mercury and that for the expan
sion of the scale, on the assumption that the attached thermometer gives the
temperature both of the mercury and of the scale.

The freezing point is universally adopted as the standard temperature
of the mercury, to which all readings are to be reduced. The temperature
to which the scale is reduced is che normal or standard temperature of the
adopted standard of length. For English scales, which depend upon the
English yard, this is 62 Fahrenheit. For metric scales, which depend
upon the metre, it is o Centigrade.

As thus reduced, observations made with English and metric barometers
become perfectly comparable when converted by the ordinary tables of linear
conversion, viz.: millimetres to inches and inches to millimetres (see Tables
64, 65), for these conversions refer to the metre at o Centigrade and the
English yard at 62 Fahrenheit.

The general formula for reducing barometric readings to a standard tem
perature is

m(t-T] -l(t-0)
i+m(t-T}



XVI INTRODUCTION.

in which C = Correction for temperature.

B = Observed height of the barometric column.
t = Temperature of the attached thermometer.
T= Standard temperature of the mercury.
m = Coefficient of expansion of mercury.
/ = Coefficient of linear expansion of brass.
= Standard temperature of the scale.

The accepted determination of the coefficient of expansion of mercury
is that given by Broch s reduction of Regnault s experiments, viz :

m (for iC) = 10-9(181792 + 0.175/4- 0.0351 16/ 2 ).
As a sufficiently accurate approximation, the intermediate value

m = 0.0001818

has been adopted uniformly for all temperatures in conformity with the usage
of the International Meteorological Tables.

Various specimens of brass scales made of alloys of different com
position show differences in their coefficients of expansion amounting to
eight and sometimes ten per cent, of the total amount. The Smithsonian
Tables prepared by Prof. Guyot were computed with the average value
/(for i C) =0.0000188 ; for the sake of uniformity with the International
Meteorological Tables, the value

/= 0.0000 1 84

has been used in the present volume. For any individual scale, either value
may easily be in error by four per cent.

A small portion of the tables has been independently computed, but the
larger part of the values have been copied from the International Meteoro
logical Tables, one inaccuracy having been found and corrected.

TABLE 10. Reduction of the barometer to standard temperature English
measures.

For the English barometer the formula for reducing observed readings
to a standard temperature becomes






!+*(/- 32)

in which B = Observed height of the barometer in English inches.

t = Temperature of attached thermometer in degrees Fahrenheit.

m = 0.0001818 X | = o.oooioi
/ 0.0000184 X | = 0.0000102

The combined reduction of the mercury to the freezing point and of the
scale to 62 Fahrenheit brings the point of no correction to approximately



BAROMETRICAL TABLES. XV11

28.5 Fahrenheit, and this is therefore the standard temperature to which
all readings are reduced. For temperatures above 28. 5 Fahrenheit, the
correction is subtractive, and for temperatures below 28. 5 Fahrenheit, the
correction is additive, as indicated by the signs ( + ) and ( ) inserted
throughout the table.

The table gives the corrections for every half degree Fahrenheit from
o to ioo. The limits of pressure are 19 and 31.6 inches, the corrections
being computed for every half inch from 19 to 24 inches, and for every
two- tenths of an inch from 24 to 31.6 inches.

Example :

Observed height of barometer
Attached thermometer, 545 F.
Reduction for temperature

Barometric reading corrected for temperature = 29.075



TABLE 11.

TABLE 11. Reduction of the barometer to standard temperature Metric
measures.

For the metric barometer the formula for reducing observed readings to
the standard temperature, o C, becomes




i + mt

in which C and B are expressed in millimetres and t in Centigrade
degrees.

m = 0.0001818 ; / = 0.0000184.

In the tables, the limits adopted for the pressure are 440 and 795 mil
limetres, the intervals being 10 millimetres between 440 and 600 milli
metres, and 5 millimetres between 600 and 795 millimetres

The limits adopted for the temperature are o + and + 35^8, the
intervals being 0^5 and ifo from 440 to 560 millimetres, and o.2 from 560
to 795 millimetres.

For temperatures above o Centigrade the correction is negative , and
hence is to be subtracted from the observed readings.

For temperatures below o Centigrade the correction is positive, and
from o C. down to 20 C. the numerical values thereof, for ordinary baro
metric work, do not materially differ from the values for the corresponding
temperatures above o C. Thus the correction for 9 C. is numerically
the same as for + 9 C. and is taken from the table. In physical work of
extreme precision, the numerical values given for positive temperatures may
be used for temperatures below o C. by applying to them the following
corrections :



XV111



INTRODUCTION.



Corrections to be applied to the tabular values of Table 1 1 in order to use them
when the temperature of the attached thermometer is below o Centigrade.



Temper
ature.


PRESSURE IN MILLIMETRES.


450


500


550


600


650


700


750


800


C.


mm.


mm.


mm.


mm.


mm.


mm.


mm.


mm.


- i


O.OO


0.00


0.00


O.OO


0.00 0.00


0.00


O.OO


- 9


.OO


.00


.00


.00


.00


.00


.00


.00


10


O.OO


0.00


0.00


O.OO


O.OO


+ O.OI


+ 0.01


+ 0.01


n


.OO


.00


.00


.00


+ 0.01


.OI


.01


.01


12


.00


.00


.00


+ 0.01


.01


.01


.01


.01


13


.00


.00


+ 0.01


.01


.01


.01


.01


.01


-14


.00


+ 0.01


.01


.01


.01


.01


.01


.01


-15


+ 0.01


+ 0.01


+ 0.01


+ 0.01


+ 0.01


+ 0.01


+ 0.01


+ 0.01


16


.01


.01


.01


.01


.01


.01


.01


.01


17


.01


.01


.01


.01


.01


.01


.01


.02


18


.01


.01


.01


.01


.01


.01


.01


.02


-19


.01


.01


.01


.01


.01


.01


.02


.02


20


+ 0.01


+ O.OI


+ O.OI


+ 0.01


+ 0.01


+ 0.02


+ 0.02


+ O.O2


21


.01


.01


.01


.02


.02


.02


.02


.02


22


.01


.01


.02


.02


.02


.02


.02


.02


23


.01


.02


.02


.02


.02


.02


.02


.02


-24


.01


.02


.02


.02


.02


.02


.02


03



Example :

Observed height of barometer, 763. 17**-:

attached thermometer, 12 C.
Numerical value of the reduction for + 12 C.
Correction for temperature below o C.

Reduction for 12 C.
Observed height of barometer

Barometer corrected for temperature



Temperature of the




= 764.68



REDUCTION OF THE BAROMETER TO STANDARD GRAVITY
AT LATITUDE 45

The atmospheric pressure is measured by the weight of the mer
curial column of the barometer, but by common usage the pressures are
expressed in terms of the height of the barometric column instead of by
its weight. The observed height however is not a true measure of the
pressure, because it changes with the temperature of the mercury and
with the variations in the value of gravity. Therefore to obtain a height
that shall be a true relative measure of the atmospheric pressure, the ob



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