mm

The, mean and extreme daily Temperatures in St. Louis
for forty-seven years, as calculated from daily obser-
vations.

Bv Dr. GEORGE ENGELMANN.

The Evolution of the amepj'^an Trotting-Horse.

By FRANCIS E. in J ''HER.

Magnetic Survey of Missouri. 5th Annual Report.

By FRANCIS E. NIPHER. '

On the Expression of Electrical Resistance in
Terms of a Velocity.

By FRANCIS E. NIPHER.

F'rom the Trans, of the. St. Louis Acad, of Science. Vol, IV., JVo. 3.
March, 1884.

COMPLIMENTS OF

Francis E. JSripher.

Digitized by tine Internet Arciiive

in 2009 witii funding from

Boston Library Consortium IVIember Libraries

http://www.archive.org/details/meanextremedailyOOenge

--

Jnnufirv. /■'e/sriiorv. Narrh.

,„ ,^ in .r .„ ^ a ,t /I JA / e II JS X Jt '3

"^

Apri

X /a IS !

7 '

D JS M

May , ' JuTie. ' July ' August. ' September ' October Naverrber ' I)prcmbc'r

90-

70-

-T"

1

...

1

LV^

, 1

■"

1

'

1

^

^

\^

■

1

—

^

^^

(-J

\

■^

_\

■

"

-A

1

\-.

^

,

;

X

—

—

—

—

—

-

^

-

-

—

f

\

—

i

r

f

^

^

—

—

—

—

—

—

—

—

xir

—

—

—

—

—

-

—

—

—

—

'

t

—

—

—

-

—

—

—

~]

'

^

s

h

^

h

-

-

-

—

—

—

-

—

-

-

-

—

^=^H

—

—

—

-

—

—

—

—

r~~

J

_

_„

"--.

—

,.

~

!

-TO

,

,

-T'

^

—

—

—

1 —

—

—

—

—

—

— H

—

—

—

^

—

—

—

—

—

—

—

—

V-

—

—

_

_

—

—

—

—

T

=:7

—

' —

—

—

—

—

—

—

—

—

—

—

—

—

— '

—

^

\-

—

—

~

—

—

—

— '

1

—

-

—

-

—

—

\

^.^

V

—

H

^

"

fciii

\

"

_ 1

/

7^

"

!■=>,

1

^

\ ■ /

^

f-

-^

\

/\

/

^

\ '/

!^

1

1

vJ

.\

/

K

—

7^>^ . Ji.1'"

^ff

"

1

'./

1

/

^

/

i^-l'

■y' 1

T~

__

^

_

__

A

V

1

u

\

/

1,^ '''

1

1

^

\.

1

1

'' 1

1

'^

/T.

—

--

—

—^

w

1

-^

-

—

—

-

-

-

~-

■S.

' ti^'J:

-

---

r

-

-

-

-

s.

""

I

-J

_._

1

—

K

/

\

^

— 1

^ — 1

I

'

s

^

1

-H

~

/^'

^

N

s

\

;

/■■

^

\

^^>..

-"^

1

/

N

r

^

:

'■■■

i /

\ /

\!

1 K

1

^■

1

i\

\

-*o

■»«

/^

1 1

/

\,

■\!

/,o-

, i

.-/'

J^\

i

/

)

\

s

i

>-

~y

l.;-

^<^■

r

1

K

.

1

/■P

.s("^

.If''

1

/

\

1

-U

i

^

_/

' .nsj-lviae''

1

^

-\

-.' :■> . JrW'r;..nir'-

1

y

N-.

1

-N

/x^

' \/ -vne':..t«'T , i

f

\ 1

I

1

1

'^

\'V

^

-,1

H^d^V 1 1 1 i

:

/

^

S,

1

; 1 .

r.

wr

'. i

i

\

^-

t,"-; '

1

1

■

\,

^0-
0-

1

/

1

V

1

1

/

/

1

\

!

!

y

V

-le

j

\

1

1

\

\

/

v^

1

/

,

1

■^

\

A

f

\

1

\

/

\

-e

/v/

^^'

N

1

/ ' 1 .•

<>^

^

' !

jL ' ii^

L\

r

■ 1

r

7t^

<K

\

1

A ■ ! !'"

\/

\,

1

/! : '/

, «'■

\/

^ :\ J \.<:

-

-20

/

: / 1,^

r

-

^0-

/

' I'

V

■

\

r

/

\\l \

/

1 \l

1

Diagram represenlinq the results (fDrEngelmanrCs .

1

fhcrm obs in SrT.ouis from lfi36to IRKZincL

1 i 1

1 1

1

L_

1_

1_

__

_J

1

.

__

_

1

'

THANS. ST. LOUIS ACAD. SCIENCE. 496

Tlie mean and extreme daily Temperatures in St.
Louis during forty seven years, as calculated from
daily observations,

Bj Dr. George Engelmann.

Half a century has passed since I began to study the meteor-
ology and climatology of this neighborhood, and since the year
1836 I have made regular meteorological observations, first on
temperature, the winds and the condition of the sky, and soon
afterwards on atmospheric pressure, rainfall and humidity.

I give here the results of my thermometrical observations,
which I consider as the most important and most interesting of
the series. They comprise, to be sure, only forty-seven years, and
I might have waited until at least half a century was completed ;
but the results would scarcely have been different, and the task
then perhaps problematical of accomplishment.

The observations were made within the city of St. Louis, and
can thus not claim precision for this whole region. St. Louis,
to be sure, was, when they commenced, a small town of perhaps
15,000 inhabitants, while now, at their completion, it is a large
city of probably 400,000, with the necessary accompaniment of
brick and stone, and especially with the smoke of thousands of
chimneys, furnaces and factories, and the almost total absence of
verdure. It has been held by some, that these influences had
little effect on temperature, but that brisk breezes would soon dis-
pel smoke and equalize temperature. This, however, is not quite
so, and direct thermometrical comparisons prove that the extreme
temperatures, and, remarkably enough, even the extreme heat,
are less marked in the city than in the country, and that the mean
temperature is higher in the city than in the country (Trans,,
vol. ii., p. yo) ; but, aside from instrumental observation, the
state of the vegetation proves it every spring and fall, when we
find in our city gardens the plants uninjured on mornings when
in the country they have suffered from late or early frosts.

St. Louis lies very nearly in the centre of the Mississippi Valley,
600 miles north of the Gulf of Mexico and just as far south of Lake
Superior, about 500 miles west of the Alleghanies and 800 miles
east of the Rocky Mountains ; its Washington University, one

497 ENGELMANN MEAN & EXTREME TEMPERAT'e IN ST, LOUIS.

mile west of the river, lies in Lat. 38° 38' 03" and Long. 90° 12'
15'' ; the low-water mark of the Mississippi is 379 feet above the
Gulf, and the foot of Market street (City Directrix) is 413 feet
above the same.

My observations were made in the first twelve years on the
south-east corner of Second and Chestnut streets, only two blocks
from the river and 75 feet above low-water mark of 1863 ; for the
next 22 years on the south-west corner of Fifth and Elm streets,
five blocks from the river and 1 10 feet above low-water mark ;
and for the last 13 years on the north-west corner of Thirtieth and
Locust streets, two miles from the river and 177 f"2et above low-
water mark. When 1 was absent from the city Dr. A. Wislize-
nus and lately Mr. B. D. Kribben have kindly filled the gaps.

My instruments were at first such as could then be obtained
here ; soon I imported correct thermometers from Europe, and for
nearly 40 years I used those made by Jas. Green, then of Balti-
more, and soon afterwards of New York.

For many years the observations were made at different peri-
ods of the day, and especially at hours when the extremes might
be expected to occur, viz. at sunrise and at 3 p.m. ; and the maxi-
mums and minimums were selected from all of them, often eight
in a day, at whatever hour of the day they were found. Differ-
ential thermometers were observed only since the last i 2 years.
Thus I may not always have noted the absolute extremes of each
day, and my tables can claim only approximate reliability ; I
give them for what they may be worth, but I can assure my
readers that they furnish a record elaborated with zeal, conscien-
tiousness, care and assiduity, and for a length of time such as
probably few others, if any, exist in this valley.

The arrangement of the tables explains itself The first two
columns represent the means of the 47 minimum and of the 47
maximum observations made on each day of the year, and the
third column the mean calculated from the two former. The next
^'Min." column gives the lowest and the "Max." column the high-
est temperature ever observed on that day ; the column of years
next to these gives the year in which these extremes did occur.
The last column represents a supposed — or estimated — true mean
for the day after eliminating excessive extremes.

The year has been divided into 73 periods of 5 days each, the

TRANS. ST. LOUIS ACAD. SCIENCE. 498

means of which are printed in full-face type, to distinguish them.
It will be seen, however, that the means of these periods do not
progress, rise and fall, much more evenly than the single daily
means; compare, e.g., the mean of Jan. 31st to Feb. 4th, which
is so much lower than the mean of the foregoing or the following
five da3' s that one might suspect a regular and normal decline of
temperature in these days, and not a mere accident.

A few facts must strike every one who examines the ta-
bles. The first is, that a time even as long as 47 3'ears fails to
give us anything approaching absolute and reliable means ; and
we come to the painful conclusion, that observations even contin-
ued for double that time, or for a century, may not yet obtain that
desirable object. It seems that the excessive extremes of one or of
a few days such as we often observe in our climate of extremes,
especially in the winter season, will influence — or, I may say,
vitiate — the means of a long series of observations ; and the ques-
tion with me arises, whether such extremes ought not to be elim-
inated from the series, and thus truer means be obtained. At the
same time we may justly be astonished that from such heteroge-
neous data so much order and system result — which gives us
hope that we cannot be quite on the wrong track.

Another fact, which strikes us in looking over the tables, is
that the mean temperatures do not increase and decrease evenly,
but sometimes quite rapidly, and at other times they may become
almost stationary for a time. These points come out most strik-
ingly on a diagram which embodies the essential parts of the
results and shows the daily progress of the temperature. Thus
we find very little change from the middle of December to the
first part of February, though the temperature proves to be low-
est from January 4th to 13th ; then we notice a rapid rise from
Feb. 6th to 20th, a slower rise to the middle of March, then a
rapid one to the end of the month ; in the forepart of April a slow
and after the middle of that month a very marked one ; then fol-
lows a tolerably even, at last quite slows rise to July 9th, when
between this date and the iSth the greatest elevation of the curve
is obtained. After that the mean temperature falls slowly to the
middle of August, followed by a more rapid decline to the end
of September ; after a slight pause in the first week in October,
a more rapid fall takes place for the following two weeks and a

499

ENGKLMANN MEAN & EXTREME TEMPERAT E IN ST. LOUIS.

slighter one in the two weeks succeeding them. After that the
temperature sinks rapidly to about Dec. loth, from which time
till the beginning of February the changes are not very marked.

The mean temperature of April 17th to 19th and from October
1 2th to 17th correspond with the mean of the year.

The tables, and still more distinctly the diagram, show us also
that the extreme highest and lowest temperatures diverge most in
winter and least in summer, and that their values are much more
variable in the former than in the latter season. The possibilities
of range from the middle of December to the iniddle of March are
80 to 95 degrees, while in June and July they amount only to 40
or 45 degrees.

The same law is found when we compare the actually ob-
served lowest minimum and highest maximum of every month ;
their divergence is greatest in January, and least, not much more
than half, in July.

Min, Max. Range.

January —22.5 72.0 94.5

February .... —15.0 76.0 91.0

March 0.0 ■ 86.0 86.0

April 18.0 99.0 81.0

May 29.0 97 5 68.5

June 43.0 101.5 58.5

Min.

July 53.0

August 45.0

September ... 35.0

October 19.5

November — 0.5

December — 19 . 5

Max. Range.

104.0 51.0

104.0 59.0

102.0 67.0

91 0 71.5

81.5 82.0

72.5 92.0

Nearly the reverse is the case — i.e. the range in winter is much
smaller than that in summer — if we compare the difference of the
average daily minima and maxima for each month :

January.. 13.27
February. 14.72
March.... 16.40

April 18.29

May 18.77

June 18.14

July 18.24

August... 17.75
September 19.05

October .. 18.00
November 14.06
December. 11.97

The range, it will be seen, is, on the whole, least in the cooler
and greatest in the warmer months of the year ; but this differ-
ence is not due to the lower or higher temperatures of those
months, for it will be seen that in December the range is the
smallest (smaller than in January) and in September greatest
(greater than in July). This variation in the range of maxima
and minima is undoubtedly owing to the condition of the sky in
the different months. Gloomy weather prevails in the beginning
of winter, and a clear sky with abundant evaporation, and thus
a reduction of night temperature, in the autumn. The little table
can give us an indication of the prevailing weather in the differ-
ent months. Thus the difference, and its cause, the clearness of

TRANS. ST. LOUIS ACAD. SCIENCE.

500

the sky, rises from December gradually till May, falls a little in
June and July and more in August, rises to its highest point in
September, is yet high in October and then falls rapidly till De-
cember, to rise again in January.

The temperature of our continental locality shows a great dif-
ference from that of the western coast of Europe ; as a convenient
example we may refer to the temperature of London. Their win-
ters are warmer from the latter part of November until the begin-
ning of March, and their summers much cooler from this period to
the latter third of November ; and the mean is much higher here.

Whole
Jan. Feb. Mar. Apr. May. June. July.. Aug. Sept. Oct. Nov. Dec. year.

St. Louis.. 31.8 35.4 43.7 56.2 66.3 74.7 79.2 76.8 69.0 56.1 42.8 33.4 55.4
London... 37.2 39.3 42.7 48.1 54.5 60.8 68.6 62.0 57.6 50.4 42.7 39.7 49.9
Difference. -+5.4 +3.9 — LO —8.1 -11.8 -13.9 —15.6 -14.8 -11.4 -5.7 -0.1 +6.3 -5.5

MEAN AND EXTREME TEMPERATURES IN ST. LOUIS FROM 1836 to 188?.

Mean Values for each

Extreme Maxima and Minima observed i

Sup-
posed
true

1836-1882

Day.

on each Day

3f the Year. |

Min. 1 Max. 1 Mean.

Min.

Year.

Max.

Year.

Mean,

Jan. 1

23.55 36.77

30.16

—22.5

1864

68.0

1876

31.5

2

25.35

37.97

31.66

—13.0

1879

65.5

1855

31.3

3

25.54

38.55

32.04

—15.5

(1

66.5

1874, 1880

31.0

4

23.95

35.82

29.88

— 6.0

(<

63.5

1880

30.5

5

23.45

39.22

31.33

— 8.5

1864

62.0

1876

i 30.2

24.36 37.66 31.01

— 13.1

65.1

30.9

6

23.76

37.63 1 30.69

— 9.0

1879

64.0

1880

30.0

7

22.33

33.95 28.14

— 1.0

1881

64.0

1839

29.4

8

22.75

.34.61 28.68

— 6.0

1877

68.0

1876

29.0

9

22.65

35.48 29.06

—18.0

1875

65.5

((

29.0

10

22.67

34.82 28.74

—11.0

1881

70.0

1839

29.5

22.83

35.29 29.06

-9.0

66.3

29.4

11

25.42

39.20 32.31

— 1.0

1881

71.0

1839

i 30.0

12

26.69

39.27 32.98

— 2.0

1852

65.0

1863

i 30.2

13

24.61

36.81 30.71

0.0

<(

59.0

i(

30.6

14

25.61

38.11 31 86

—12.5

1881

64.0

1848

31.0

15

L'6.71

39.67 33.19

— 2.5

1875

66.0

1847

31.4

25.80

38.61 32.21

— 60

65.0

30.6

16

24.03

36.27 30.15

2.0

1841

63.0

1845

31.8

17

21.09

34.27 1 27.68

—11.0

(1

64.0

1842

32.0

18

21 .65

34.32 27.98

—12.5

1857

66.0

((

32.0

19

23.63

38.09 30.86

—12.0

1852

61.0

1843

32,0

20

27.83

39.-54 33.68

— 1.5

1866

64.0

11

32.0

23.64

36.49 30.07

— 7.0

63.6

31.9

21

25.97

.88.79 32.38

— 3.0

1854

67.0

1843

1 32.0

22

23.84

39.19 31. .52

— 2.5

1857

62.0

1858

32.0

23

24.63

38.36 31.49

0.0

1854

62.0

1864

32.0

24

25.57

39.64 32.60

2.0

1873

65.0

1860

32.2

25

27.26

41.63 34.44

— 55

1840

65.0

1864

1 32.4

2o.4o

39.52

32.48

— 1.8

64.2

32.1

50I ENGELMANX —

-MEAN

i- EXTR

.EME TEMP

ERAT

E IN ST. I.

UUIS.

Mean Value for each

Extreme Maxima and

Minima observed

1 Sup.

1836-1882

Day.

on each Day of the Year.

i posed

Min.

Max. 1 Mean.

Min.

Year.

Max.

Year.

Mean

Jan. 26

26.76

40.36 .

33.56

1.0

1865

71.5

1843

: 32.6

27

26.96

39.53

33.24

— 0.5

1873

72.0

1864

32.6

28

24.85

39.15

32.00

— 6.5

((

67.0

i(

' 82.7

29

25.32

39 30

32.31

—23.0

C(

64.5

1852

32.8

30

24.79

41.09

32.94

— 2.0

1856

64.5

1842

32.8

25.73

39.88

32.81

-6.2

67.8

32.7

31

24.96

38.20

31.58

2.0

1875

65.5

1877

32.8

Feb. 1

23.32

37.20

30.26

— 8.5 1

1836

70.0

1854

32.8

2

23.55

35.77

29.66

— 3.5 i

1873

56.0

1846

32.9

3

21.71

35.72

28.72

—15.0 1

1856

62.5

1852

1 32.9

4

22.01

36.51

29.26

—11.0

II

61.0

1837

1 33.0

23.11

36.68

29.89

-7.2

63.0

32.9

5

24.67

39.29

31.98

— 3.5

1856

61.0

1837

i! 33.0

6

26.00

41 04

33.52

3.0

1843

67.0

1855

33.1

7

26.08

41.19

33.63

— 3.5

1872, 1875

65.0

1851

33.1

8

24.74

39.98

32.36

2.0

1842

66.0

1847

i 33.2

9

24.37

40.05

32.21

— 5.0

1875

72.0

1876

I 33.3

26.17

40.31

32.47

-1.4

66.2

133.1

10

25.92

41.56

33.74

1.0

1841

73.0

1876

■ 33.5

11

29.98

43.93

36.95

2.0

((

73.0

1845

33.7

12

29.00

43.44

36.22

2.0

II

70.5

1882

33.9

13

29.06

40.41

34.73

4.5

1838

69.0

1867

34.0

14

24.71

39.38

32.04

— 3.5

1866

64.0

1857

34.1

27.73

41.74

34.73

1.2

69.9

33.8

15

26.53

41.09

33.81

— 9.5

1866

68.0

1848

34.2

16

26.07

42.59

34.33

— 5.0

[1

63.5

1857

34.4

17

28.03

41.18

34.60

— 4.0

1838

74.5

11

34.6

18

28.05

42.39

35.22

— 2.5

1849

65.5

1873

34.8

19

30.26

44.57

37.41

5.0

1838

76.0

1859

35.0

27.79

42.36

35.07

- 3.2

69.5

34.6

20

31.83

45.80

38.81

— 3.5

1870

68.5

1850

35.5

21

30.33

45.27

37.80

— 4.5

1838

68.0

1836

36.0

22

31.82

46.97

39.39

1.5

1858

68.5

1861

36.5

23

30.11

44.71

37.41

0.0

1 .

69.5

1851

37.0

24

29.38

I 45.91

37.64

6.0

1873

69.0

1880

37.5

30.69

45.73

38.21

-0.1

68.7

36.6

25

31.02

1 46.05

38.53

7.0

1855

67.0

1876

;i 38.0

26

31.68

48.91

40.29

2.0

1846

68.5

1880

11 38.5

27

30.58

45.46

38.02

5.0

1836

73.5

1876

38.7

28' 30.47

47.02

38.74

10.5

1836, 1869

74.0

1861

39.0

Mar. ll 32.35

49.02

40.68

10.0

1843

79.5

(1

39.2

31.22

47.29

39.25

6.9

72.5

38.7

2

31.36

45.97

38.66

8.0

1843

76.0

1861

39.8

3

29.29

43.89

36.59

0.0

1848

78.0

1842

40.0

4

29.50

44.54

37.02

6.0

1875

75.5

1882

40.5

5

30.62

47.38

39.00

8.0

1848

71.0

1855

, 40.8

6

34.94

49.20

42.07

i 4.5

1869

76.5

1860

41.0

31.14

46.19

38.67

1 5.3

75.4

40.4

1

34.88

! 51.60

43.24

10.5

1857

77.0

1853, 187J

) 41.2

i

i 34.49

1 50.31

42.40

13.5

1875

77.0

1879

41.4

i

> 35.01

i 48.18

41.59

6.0

1877

78.5

1842

1 41.6

1(

) 33.22

49.52

41.37

10.0

1856

79.5

1279

1 41.8

11

34.55

! 49.67

42.11

7.0

1836

69.0

1848

42.0

34.4?

5 49.85

42.14

7.4

76.0

41.6

TRANS. ST. LOUIS ACAD. SCIENCE.

502

j Mean Value for each

1 Extreme Maxima and Minima observed 1

Sup-

1836-1882 '^^y-

for each Day

3f the Year. |

posed

Min. Max.

Mean.

Min.

11.5

Year.

Max.

Year.

Mean

Mar 12 34.82

50.86

42.84

1836, 1857

71.0

1839, 1861 :

42.2

13 U.2i

50.64

42.44

5.0

1867

75.0

1850 1

42.4

14 34.51

50.55

42.53

j 1.0

ti

76.5

1875

42.5

15 33.87

48.89

41.38

7.5

1870

80.5

1854

42.6

16 34.14 50.03

42.08

9.0

1843

77.5

1868

42.8

34.3150.19

42.25

6.8

76.1

42.5

17 33.49

52.07

42.78

10.5

1879 .

79.0

1842

43.0

18 34.86

52.32

43.59

15.0

(<

84.0

II

43.5

19 36.09

54.82

45.45

18.5

1875

84.0

II

44.0

20 36.91

52.52

44.71

14.0

1855

84.0

11

44.5

21 34.21

50.68

42.44

7.0

1876

76.0

1878

44.8

35.11

52.48

43.79

13.0

81.4

43.9

22 35.56

54.04

44.80

13.0

1843

76.0

1857

45.0

23 37.09

55.48

46.28

7.5

II

82.5

1868

45.2

24 36.90

54.30

45.60

1 12.0

11

83.0

1842 i

45.4

25 37.21 53.76

45.48

1 13.0

11

82.5

1852

45.6

26 37.69

54.92

46.30

! 13.5

1873

78.5

1838

46.0

36.89

54.50

45.69

11.8

80.5

'

45.4

27 39.16

56.81

47.98

23.5

1850

85.0

1838 i

46.5

28 39.77 57.31 48.54

18.0

1855

83.5

1879 i

47.0

29 40.42 58.31

49.36

23.5

1876

86.0

1842

47.5

30 41.07 57.91

49.49

28.0

<i

84.0

1838

48.0

31 40.35 57.34

48.84

25.5

1856

84.0

11

48.5

40.15 57.53 48.84

23.7

84.5

47.5

Apr. 1 39.70 57.25 48.47

24.0

1881

81.5

1882

49.5

2 40.92 61.12 51.02

24.0

(1

85.0

II

50.0

3 44.66 62.44

53.55

24.5

1879

86.0

II

51.0

4 44.00 59.67

51.83

23.0

11

85.0

11

51.5

5 42.79 60.82

51.80

22.5

1857

88.5

1871

52.0

42.41 60.26

51.33

23.6

85.2

50.8

6 43.61

62.89

53.25

18.0

1857

89.0

1871

52.5

7 44.77

63.98 54.37

29.0

1880

85.5

1860

53.0

8 45.59

60.96 53.28

24.0

1845

82.5

1836

53.0

9 43.84

61.86 52.85

27.0

1857

84.0

1844

53.2

10 45.07

61.94 53.50

28.5

1836, 1874

87.0

II

53.4

44.57

62.33 53.45

25.3

85.6

53.0

11 43.81

62.53 53.17

27.0

1857

83.0

1842

53.6

12 45.35

62.44 53.89

26.0

II

84 0

1856

53.8

13 45.33

63.59 54.46

32.0

11

88.0

1845

54.0

14 45.03

63 26 54.14

28.5

11

84.0

'■•

54.2

15 44.52

62.02 53.27

23.0

1850

82.0

1856

54.4

44 81

62.7 7

53.79

27.3

84.2

54.0

16 45.62

62.26

53.94

26.5

1875

91.0

1845

54.6

17 45.11

h4.55

54.83

20.5

11

93.0

1855

55.0

18 45.78 64.34

55.06

26.0

11

99.0

II

56.0

19 47.20

66.47

56.83

29.0

1857

83.0

1847

57.0

20 48.47

67.92

58.19

34.0

II

85.0

1836

58.0

46.43

65.11

55.77

27.2

90.2

56.1

21 49 76

69.01

59.38

36.0

1857, 1875

85.0

1867

59.0

22 51.37

69.70

60.53

i 31.5

1875

87.5

1842

60.0

23 49.88

69.90

59.89

i 31.5

1865

87.0

1842, 1854

60.0

24 50.24

68.92

59.58

34.0

] 1874

88.5

1854

60.0

25 51.89

70.82

61.35

33.5

1874, 1875

93 0

1813, 1855

60.0

50.63

69.67

60.15

33.3

88.2

59.8

503 ENGELMANN MEAN & EXTREME TEMPERAT E IN ST. LOUIS.

Mean Values for each \

Extreme Maxima and Minima observed

Sup-

1836 1882

Day.

on each Day

3f the Year.

posed

Min.

Max.

Mean. 1

Min.

Year.

Max.

Year.

Mean

Ap. 26

51.20

70.53

60.86

33.5

1873

88.0

1872

60.0

27

50.63

69.98

60.30

37.0

1857

93.0

1838

60.0

28

51.21

68.71

59.96

34.0

1854

83.5

1845

60.0

29

50.87

69.15

60.01

33.0

1874

89.5

i<

60.0

30

50.68

69.07

59.87

32.0

1877

92.5

1855

60.0

50.92

69.49

60.20

33.9

89.3

60.0

May 1

50.53

69.72

60.12

35.5

1877

91.5

1836

60.0

2

51.06

68.34

59.70

29.0

1851

87.0

a

60.2

8

51.05

69.67

60.36

38.0

1841

88.5

1849

60.4

4

53.60

71.04

62.32

37.0

1877

89.0

1860

61.0

5

53.72

71.88

62.80

37.0

1851

91.5

u

6i.4

51.99

70.13

61.06

35.3

89.5

60.6

6

52.85

71.47

62.16

37.5

1863

88.0

1872

61.8

7

53.77

73 49

63.63

35.0

1867

88.0

11

62.0

8

54.05

72.56

63.30

38.0

1855

88.0

((

62.5

9

54.40

73.21

63.80

39.0

u

88.0

If

63.0

10

53.37

73.16

63.26

40.0

1838, 1871

89.5

1844, 1863

63.5

53.68

72.78

63.23

37.9

88.3

62.5

11

54.12

72.78

63.45

39.0

1864

91.5

1844

64.0

12

55.17

74.79

64.98

39.5

1857

91.5

1836

64.5

13

56.34

75.17

65.75

, 41.5

1878

90.0

1862

65.0

14

56.72

74.75

65.73

42.0

u

97.5

1836

65.5

15

55.61

75.53

65.57

40.5

11

93.0

(1

66.0

55.59

74.60

65.051

40.5

92.7

65.0

16

56.73

75.52

66.12

40.0

1837, 1875

92.0

1851

66.5

17

56.01

73.47

64.74

42.0

1857

91.0

1853

67.0

18

55.19

75.27

65.23

1 42.0

"

87.0

1836, 1870

67.5

19

57.24

77.30

67.27

43.0

1853

89.5

1871

68.0

20

57.61

77.34

67.47

42.0

1852

90.5

1836

68.2

56.55

75.78

66.17

41.8

90.0

67.4

21

58.76

76.31

67.53

43.0

1857

96.0

1870

68.4

22

58.53

78.02

68.27

40.0

1838

97.0

(1

68.6

23

59.26

77.68

68.47

44.0

1867, 1876

90.0

1839, 1856

68.8

24

59.66

78.80

69.23

45.0

1851

92.5

1873, 1879

69.0

25

60.21

77.40

68.80

44.0

1845

93.0

1860

69.5

59.28

77.64

68.46

43.2

93.7

68.8

26

60.46

81.00

70.73

48.0

1853

93.0

1860

70.0

27

60.33

79.37

69.85

48.0

( (

94.0

1874

70.2

28

eo.46

80.59

70.52

45.0

1838

91 0

1848, 1851

70.4

29

61.08

79.24

70.16

44.0

1866

91.0

1852, 1879

70.6

30

61.68

79.94

70.81

44.0

1845

90.0

1841, 1854

70.8

60.80

80.02

70.41

45.8

91.8

70.4

31

62.14

79.25

70.69

52.0

1856

97.0

1871

71.0

June 1

61.49

79.78

70.63

49.0

1843

91.0

1845, 1852

71.0

2

62.39

80.70

71.54

49.0

1838

94.0

1852

i 71.2

3

62.44

80.12

71.28

47.5

1879

93.0

1856

71.4

4

62.05

79.06

70.55

44.0

1859

94.0

1841

71.6

62.10

79.78

70.94

49.3

93.8

71.2

5

61.36

79.45

70.40

43.0

1839

93.0

1871

71.8

6

62.57

81.88

72.22

43.0

183S

93.0

1836. 1874

72.0

7

62.18

81.34

71.73

50.0

1854

95.0

1874

72.2

8

63.83

81.95

72.89

49.0

u

96.0

1836

72.4

9

63.62

81.18

72.40

51.5

1852, 1877

99.5

((

! 72.6

62.71

81.16

71.93

47.3

95.3

72.2

TRANS. SI . LOUIS ACAD. SCIENCE.

504

Mean Values for each

Extreme Maxima an

d Minima observed 1

Sup-

1836-1882

Day.

on each Day of the Year.

posed
true

Min.

Max.

Mean.

Min.

Year.

Max.

Year.

Mean

Jun.lO

62.65

81.90

72.27

46.5

1877

97.5

1836

72.8

11

61.90

79.38

70'.64

45.0

1842

94.0

1841

73.0

12

63.32

81.59 1 72.45

50.0

1858

94.5

lh53

73.2

13

64.87

83.82

74.34

50.0

K

94.5

"

73.4

14

65.01 83.84

74.42

51.0

1856

96.0

1879

73.6

63.55 82.10

72.82:

48.5

95.3

73.2

15

65.11 83.79

74.45

49.0

1869

96.5

1868

73.8

16

65.26 82.32

73.79

53.0

1841

98.5

u

74.0

17

65.56 82.60

74.08

51.5

1876

98.5

(1

74.3

18

65.78 83.97

74.87

49.5

u

99.0

n

74.6

19

65.59 84.37

74.98

52.0

1866

96.0

1853, 1869

74.8

65.46 83.41

74.431

51.0

97.7

74.3

20

65.92 83.96

74.94

52.0

1862

98.0

1861

75.0

21

65.57 83.52 74.54

49.0

1863

97.0

1853

75.3

22

65.64 85.82

75.73

50.0

1868

99.0

1871

75.6

23

67.06 84.58

75.82

53.0

u

101.5

((

76.0

24

66.91 85.11

76.01

55.5

1853

97.5

1870

76.5

66.22 84.60

75.41

51.9

98.6

75.7

25

68.13 86.54

77.33

56.0

1852

98.0

1870, 1882

77.0

26

68.73 87.88

78.30

55.0

1865

98.5

1870

77.5

27

70.26 87.21

78.73

59.0

1836

97.0

1854

78.0

28

69.36 87.48

78.42

i 55.5

1866

100.0

1870

78.0

29

69.26 86.08

77.67

51.0

u

101.5

11

78.0

69.15 87.04

78.09

55.3

99.0

77.7

30

69.23 86.95

78.09

56.0

1871

101.5

1870

78.0

July 1

68.39 85.91

77.1fc

54.0

1851

98.0

1854

78.0

2

68.06 85.60

76.83

54.0

1861

98.5

1858

78.0

3

68.42 ■ 87.10

77.76

56.0

1857

99.5

1856

78.1

4

68.71 87.89

78.30

53.0

1859

100.5

1868

78.2

68.56 86.69

7 7.62

54.6

99.6

78.1

5

69.24 87.39

78.32

56.5

1882

98.5

1870

78.3

6

70.11 88.05

79.08

54.0

1842

97.0

1868

78.6

7

70.20 87.84

79.02

58.0

t(

98.0

1874

79.0

8

70.55 87.97

79.26

58.0

1870

97.0

1J:54, 1879

79.0

9

71.05 89.15

80.10

57.0

1842

99.0

1858

79.2

70.23 88.08

79.15

56.7

97.9

78.8

10

71.46 87.84

79.65

61.0

1836

101.5

1881

79.2

11

70.35 86.99

78.67

58.0

1854, 1873

100.0

1841

79.4

12

70.64 87.50

79.07

58.0

1863

100.0

u

79.4

13

69.99

88.61

79.30

57.0

1861

100.6

1862

79.6

14

70.69

88.66

79.67

56.5

1882

100.5

1868

79.6

70.62

87.92

79.27

58.1

100.5

79.4

15

71.44

89.38

80.41

58.0

1842

100.0

1856

80.0

16

71.42

89.02

80.22

55.0

1863

100.0

1870

80.0

17

70.66

90.07

80.36

56.0

u

102.5

1856

80.0

18

70.77

88.73

79.75

58.0

1846

101.5

1868

79.6

19

70.44

87.70

79.07

1 58.0

1878

100.0

1854

79.4

70.94

88.98

79.96

57.0

100.8

79.8

20

69.94

86.92

78.43

57.0

1873

100.5

1854, 1860

79.2

21

69.08

86.42

77.13

57.0

1869

104.0

1860

79.0

22

68.63

85.63

77.94

57.0

1864

101.5

1870

79.0

23

68.72

87.16

78.01

55.0

1861

98.5

((

79.0

24

69.01

87.86

78.43

56.0

11

101.0

((

78.8

69.07

86.79

77.93

56.4

101.1

79.0

505 ENGELMANN-

-MEAN

r & EXTREME TEMPERAT E IN ST. LC

)UIS.

Mean Values for each

Extreme Maxima and Minima observed |

Sup.

1836-1882

Day.

on each Day

of the Year. j

posed

Min.

Max.

Mean.

Min.

Year.

Max.

Year.

Mean.

Jul. 25

70.24

88.38

79.31

59.0'

1876

100.0

1870

78.6

26

70.73

88.27

79.50

58.0 1

1853

99.5'

u

78.4

27

70.38

87.58

78.98

56.0 i

n

101.5

It

78 2

28

70.23

87.80

79.01 1

56.0

(1

100.0

1838

78.0

29

70.58

87.58

79.08 1

61.0 '

1853, 1865

101.0 1

1854

78.0

70.43

87.92

79.17

58.0

100.4

78.2

30

68.52

85.57

77.04

55.0

1847

101.0

1838

77.8

31

67.96

86.47

77.21

550

1849

100.0

1854 ;

77.8-

Aug.l

68.38

87.33

77.85

52.0

1842

101.0

i<

77.5

2

68.25

86.95

77.60

52.0

u

99.0

1861 !

77.5

3

68.61

86.59

77.60

55.0 !

u

101.0

"

77.5

68.34

86.58

77.46

53.8

100.4

77.6

4

68.40

85.51

76.95

54.0

1880

101.5

1861 1

77.5

5

68.50

86.01

77.25

58.0

(c

97.5

1858

77.5

6

68.97

87.18

78.07 ;

58.0 '

1842

98.5

1838

77.5-

7

69.11

87.07

78.09

57.5

1852

100.0

1861

77.4

8

68.96

87.09

78.02

56.0

1869

99.0

1850 I

77.4

68.79

86.57

77.68'

56.7

99.3

1

77.4

9

68.94

85.14

77.04 ;

58.0

1879

104.0

1881

77.4

10

69.07

83.39

76.23

55.5

1882

98.0

1

77.4

11

69.37

86.44

77.90

57.0

(f

100.5

If

77.4

12

68.38

86.47

77.42 1

56.0

1868

105.0

u

77.2

13

68.72

86.08

77.40 '

57.0

1860

101.5

1850

77.0'

68.89

85.50

77.19

56.7

101.8

77.3

14

68.49

85.30

76.89

56.5

1861

98.5

1857

77.0

15

68.52

85.39

76.95 \

59.5

a

97.0

1841

76.9

16

67.48

86.22

76.89

57.0

1866 '

96.0

1860

76.8.

17

67.94

85.54

76.74

54.0

1855

97.0

1843, 1860 1

76.7

18

68.03

86.27

77.15

56.0

1855, 1866

99.5

1850

76.5

68.09

85.74

76.91

56.6

97.6

176.8

19

68.19

85.25

76.72

56.0

1855

99.5

1850

76.4

20

66.88

85.72

76.30

1 52.0

1836

99.0

u

76.3

21

67.87

85.71

76.79

, 59.0

1864

97.0

1869

76.2

22

67.29

84.67

75.98

51.0

1837

97.5

1872

76.0

23

66.31

84.09

75.20

52.0

1866

97.5

1869

76.0'

67.31

85.09

76.20

54.0

98.1

76.2

24

66.63

85.29

75.96

49.0

1866

97.0

1872

75.8.

25

66.38

84.42

75.40

50.5

a

100.0

ii

, 75.5

26

67.02

84.94

75.98

49.0

1863

98.5

u

, 75.3

27

65.88

84.11

74.99

54.0

1856

97.5

1838

1 75.0'

28

65.37

82.98

74.17

51.0

1844

97.5

1881

■ 74.8

66.25

84.35

75.30

50.7

98.1

75.8

29

64.80

83.05

73.92

' 49.0

1863

99.5

1881

74.5

30

64.55

84.34

74.44

1 45.0

u

100.5

1854

74.3

31

65.45

82.96

74.20

48.5

li

99.0

1854, 1873

74.2

Sept. 1

64.75

83.69

74.22

50.0

1849

98.5

1854

74.0

2

65.08

82.80

73.94

51.5

1850

102.0

1864

74.0

64.93

83.37

74.15

48.8

99.9

74.2

3

64.54

83.00

73.77

51.0

1863

102.0

1864

74.0

4

65.10

83.59

74.34

1 51.0

1868

100.0

1881

74.0

5

65.33

82.15

73.74

1 50.0

1859

100.0

u

73.8

6

64.98

81.84

73.41

51.5

1848

97.0

u

73.6

7

65.61

83.17

74.39

52.0

1849

97.0

iC

73.4

65.11

82.75

73.93

51.1

99.2

73.7

TRANS. ST

. LOUIS

ACAD. SCT

ENCK.

5ot>

Mean "Values for each

Extreme Maxima an

d Minima observed 1

Sup-

1836-1882

Day.

on each Day of the Year. |

posed
true

Min.

Max. Mean.

Min.

Year.

Max.

Year.

Mean

Sept. 8

64.48

83.47 73.97

49.5

1849

99.5

1854

73.0

9!

63.79

80.63 72.21

50.0

1847, 1869

93.5

1841

72.0

10

62.r>9

79.95 71.27

46.5

1880

96.5

1842

71.0

11

61.01

78.90 69.95

47.5

1878

94.0

" 1

70.2

12

60.69 ,

77.79 69.24

46.0

1839, 1878

92.0

1865

70.0

62.51

80.15 71.33

47.9

95.1

71.2

13

60.27 I

77.85 69.06

47.0

1839, 1878

93.0

1851, 1864

70.0

14

60.37

79.16 69.76

43.5

1873

93.0

1846

69.5

15

60.51

77.88 69.19

47.5

1880

88.0

1849, 1862 !

69.0

16

60.76

79.34 70.05

47.0

1842

91.5

1857

69.0

17

60.54 1

77.72 69.13

40.5

1868

93.0

1843, 1857

68.5

60.49

78.39 69.44

45.1

91.7

69.2

18

60.08

78.29 69.18

42.0

1863

92.5

1867

68.0

19

57.74

75.91 66.82

44.5

((

92.0

u

67.0

20

55.76

73.68 64.72

39.0

1875

93.5

1881

66.0

21

55.50

73.29 64.39 |

39.5

1866

95.0

1872 1

66.0

22

55.39

73.69 64.54 ;

39.0

1875

92.0

1881 '

65.8

56.89

74.96 65.93

40.8

93.0

66.5

23

58.17

76.82 67.49

36.0

1856

92.0

1881

65.5

24

58.15

76.23 67.19

37.0

(1

92.5

" i

65.0

25

57.09

75.37 66.23 :

42.0

1879

91.5

1850

64.8

26

54.61

73.81 64.21 j

40.0

1875

92.0

1847

64.5

27

54.87

73.82 64.34 |

41.5

1871

88.0

1854

64.3

56.58

75.21 65.89;

39.3

91.2

64.8

28

54.37

73.53 63.95

36.0

1839

90.5

1867

64.0

29

54.17

71.87 63.02

35.5

1846

93.0

1858

63.5

30

52.59

71.53 62.06

35.0

1851

90.0

a

63.0

Oct. 1

54.64

73.37 64.00

36.5

1856

87.0

1856 !

63.0

2

54.68

73.74 64.21 i

38.5

u

91.0

1867

63.0

54.09

72.81

63.45}

36.3

90.3

63.1

3

54.52

73.55

64.03

33.0

1840

89.0

1872

62.5

4i 52.29

70.59

61.44

31.0

1836

88.5

((

62.0

5 52.18

70.36

61.27

34.0

a

88.0

1879

1 61.5

6

52.52

70.03

61.27

34.0

1855

88.5

1852

' 61.5

7

51.93

70.62

61.27

34.0

1873

87.0

1860

i 61.0

52.69

71.03

61.86

33.2

88.2

61.7

8

51.70

71.14

61.42

31.5

1868

85.0

1856

i 60.5

9

51.49

70.66

61.07

36.5

1842, 1864

87.0

1879

i 60.0

10

51.26

69.91

60.58

37.0

1849

86.0

11

59.5

11

49.98

67.14

58.56

31.5

1872

86.0

a

59.0

12

48.73

64.91

56.82

30.0

1875

87.0

a

58.5

50.63

68.75

59.69

33.1

86.2

59.5

13

45.99

65.96

55.97

29.5

1860

81.5

1879

58.0

14

1 47.20

65.24

56.22

29.5

1872

84.0

1878 •

57.5

15

I 46 88

65.82

56.35

28.0

1845

84.5

1881 •

57.0

16

47.34

65.64

56.49

27.0

1838

83.0

1842 :

56.0

17

46.80

65.42

56.11

31.0

1836, 1868

83.0

1839, 1842

55.0

46.84

65.61

56.23

29.0

83.2

56.7

18

44.64

60.55

52.59

34.5

1875

82.5

1867

54.5

19

' 42.70

61.62

52.16

30.0

1846

84.0

1837

! 54.0

20

42.75

62.31

52.53

24.0

1836

83.0

1843

53.5

21

1 44.60

62.47

53.53

25.0

<(

84.0

1837

53.0

22

44.15

61.47

52.81

30.0

1869

85.0

a

52.5

43.77

61.68

52.72

28.7

83.7

53.5

507 ENGE MANN — -MEAN cV EXTREME TEMPERAT'e IN ST. LOUIS.

Mean Values for each

Extreme Maxima an

d Minima observed

Sup-

1836-1882

Day.

on each Day-

Df the Year. ]
Max. Year.

posed
true

Min.

Max.

Mean.

Min,

Year.

Mean

Oct. 23

43.41

61.54

52.47

20.0

1863

79.5

1839

52.0

24

44.32

60.64

52.48 ;

20.0

u

78.0

1875

51.8

25

42.51

59.96

51.23

22.0

1841

78.5

1882

51.6

26

43.64

60.56

52.10

21.5

1862

81.5

1874

51.4

27

42.15

61.11 51.63

26.0

1869

81.5

1870

51.0

43.20

60.76 51.98

21.9

79.8

51.5

28

43.54

60.56

52.05

27.0

1873, 1878

80.5

1874

51.0

29

43.71

60.77

52.24

22.0

1873

81.5

1875

50.5

30

42.34

57.28

49.81

26.5

1863

81.5

1876

50.5

31

39.75

56.66

48.20

19.5

a

80.0

(f

50.0

Nov. 1

42.01 1 59.97

50.99

22.0

1873

78.0

1842, 1876

50.0

42.27

59.05

50.66

23.4

80.5

50.4

2

43.20

58.00

50.60

30.5

1848

77.0

1847

60.0

3

41.11

56.59

48.85

25.5

1879

75.5

1859

49.8

4

42.01

58.66

50.33

23.0

11

80.0

1850

49.4

5

41.23

55.70

48.46

25.0

1865

72.5

1874

49.0

6

38.91

55.29

47.10 1

23.5

1877

73.0

1874, 1878

48.5

41.2956.85

49.07

25.5

75.6

49.3

7

40.78

57.55

49.16

24.0

1856

77.0

1874

48.0

8

40.30

55.78

48.04 '

11.0

1838

75.5

1868

47.0

9

37.43

51.88

44.66

16.0

1 1

75.0

1844

46.0

10

39.03

52.71

45.87

20.0

li

76.0

'<

45.5

11

40.23

53.53

46.88

26.5

1869

81.5

1837

45.0

39.55

54.29

46.92

19.5

7 7.0

46.3

12

36.93

51.66

44.29 1

17.0

1859

71.5

1879

44.5

13

36.66

52.82

44.74

15.0

IC

79.0

11

44.0

14

36.67

51.86

44.26

20.0

1872

71.5

1855

43.5

15

35.18

50.01

42.59

18.0

1838

72.0

1873 1

43.0

16

36.11 49.60

42.85 !

10.0

u

69.0

1865

42.0

36.31

51.19

43.75

16.0

72.6

43.4

17

35.55

47.80

41.67

12.0

1838

69.0

1853

41.0

18

33.62

45.58

39.60

6.0

1880

72.0

(1

40.5

19

31 .60 45.03

38.31

7.5

u

71.0

II

40.0

20

32.59 45.11

38,85

9.5

1872

72.5

1837

39.5

21

33.09 : 45.84

39.46

10.5

1880

69.0

1841

39.0

33.2945.87

39.58

9.1

70.7

40.0

22

32.28 ' 45.92

39.10

6.5

1880

71.0

1843

38.5

23

32.14 43.97

38.05

9.5

1871

69.0

1867

38.0

24

29.85 41.93

35.89

5.5

I860

65.5

1850

37.8

25

29.83 : 41.92

35.87

0.0

1839

64.5

1856

37.6

26

31.25 i 44.06

37.65

14.0

II

65.0

1850

37.4

31.07

43.5637.31

7.1

67.0

■

37.6

27

31.44

43.22

37.33

5.0

1845

67.0

1870 i

37.0

28

31.64

44.05

37.84

— 0.5

u

72.0

1864

36.8

29

29.04

42.76

35.90

2.0

1872

76.5

II

36.4

30

28.55

42.98

35.76

6.5

1845

72.5

1837

36.0

Dec. 1

30.33 45.57

37.95

— 1.0

1.

72.5

II

36.0

30.30 43.71

36.95

2.4

72.1

36.4

2

31.06

44.95

38.00

4.0

1876

72.0

1864

35.8

3

30.61

43.00

36.80

8.0

1859

61.0

1842, 1873

35.6

4

30.75

42.18

36.46

— 2.5

1871

59.0

1877

35.4

5

29.45

41.33

35.39

2.5

((

61.0

1879

35.2

6

29.56

41.88

35.72

3.5

1859

«)2.0

1861

35.0

30.28

42.67

36.47

3.1

63.0

35.4

;oS

TRANS. ST, LOUIS ACAD. SCIENCE.

Mean Values for each

Extreme Maxima an

d Minima observed

Sup-

1836 1882

Day.

on each Day of the Year.

posed
true

Min.
"28.00

Max.

40.23

Mean.

34.11

Min.

Year.

Max.

Year.

Mean

Dec. 7

—11.0

1882

63To"

1851

34.0

8

27.79

39.11

33.49

— 4.0

i(

65.0

1861

33.5

9

25.07

35.35

30.21

— 5.0

1876

74.5

((

83.0

10

23.89

36.06

29.97

0.0

1868

68.0

K

32.5

11

28.19

37.61

32.90

—11.0

u

68.0

1873

32.0

26.59

37.67

32.13

— 6.2

67.7

33.0

12

25.54

37.15

31.34

— 0.5

1868

68.5

1877

31.8

13

26.25

36.70

31.47 !

4.0

1865

62.5

1881

31.6

14

23.46

33.79

28.62 ;

— 1.0

a

59.0

1861

31.4

15

23. .57

33.46

28.51 :

— 2.5

1851

67.5

1877

31.2

16

24.29

34.83

29.56

— 0.5

i(

62.0

u

31.0

24.62

35.18

29.90

-0.1

63.9

31.4

17

25.10

36.91

31.00

— 2.5

1875

67.0

1877 :

31.0

18

25.76

38.87

32.31

1.0

1876

69.0

(1

30.8

19

26.37

38 10

32.23

0.5

1863

67.5

" 1

30.6

20

23 51

35.84

29.67

— 2.0

1871

65.0

ti

30.4

21

24.84

36.97

30.90

— 2.0

1865

66.0

'(

30.0

25.11

37.34

31.22

— 1.0

66.9

30.5

22

22.64

33.86

28.25

—14.0

1872

62.0

1877

yo.o

23

22.51

35.34

28.92

— 7.0

1870

61.0

1875

30.2

24

23.90

36.62

30.26

—19.5

1872

66.0

(1

30.5

25

25.42

37.95

31.68

—11.0

u

70.0

1867

31.0

26

25.63

38.06

31.84

— 5.0

<(

65.0

1875

31.2

24.02

36.36

30.19

—11.3

64.8

30.6

27

26.47

38.41

32.-14

— 6.0

1872

65.0

1846

31.3

28

26.34

37.80

32.07

— 6.0

1880

59.0

1862

31.5

29

25.83

37.49

31.66

—18.0

i(

64.0

1851

31.5

30

23.26

36.73

29.99

— 8.0

<(

66.0

1875

31.5

31

24.25

38.43

31. '!4

—10.5

1863

73.5

it

31.5

25.23 37.77

31.50,

1 — 9.7

65.5

1

31.5

The annexed diagram, for the construction of which I am in-
debted to Dr. G. Hambach, represents the principal resuhs of
these tables. The perpendicular lines divide the year into 73
periods of 5 days each, while the horizontal ones mark the de-
grees. The central full-faced curve indicates the Mean Tempera-
ture of the penthemeral periods of the 47 years, as actually found,
while the dotted line represents the supposed real Mean Temper-
ature as suggested in the last column of these tables. The upper-
most curve shows the Highest Temperatures and the lowest curve
the Lowest Temperatures observed in those same penthemeral
periods within the s ime number of years. It will be noticed that
while the points of Mean Temperature occupy the centre of each
period, the Maxima and Minima do not show in the middle of the
spaces, but on that one of the 5 days of the period on which they
actually did occur.

—■■I

■■■■■■■■■■■■■■■■■■■■■I

IBUHBIIBIBillBSBnHBaiBBI&Sl
■■■■■■■■.^1

■

■■^■■■■■■■■■■■■■■■i

■!■■■■■■■■■■■■■■■
_ KaBHiMRBBnUBIH

BBWl—IMMI

12

■■■Mil

IMBil —■■■■■■■■■■■

■■■■HHHHIHBBHBaBi

■■■■■■■■■■■■■■HiiaB

■■■■■■ilHHHiBaHliiin

ummmmmssmamammmm

■■■■■■■■■■^■■■■■■H
■■—■■■■■■■■■MB

■■■^■■■■■■■■■■HBaH

IhSSHIEBIIBBII

NIPHER EVOLUTION OF THE AM. TROTTING-HORSE.

509

The Etiolution of the American Trotting- Horse. '^

By Francis E. Nipher.

In the American Journal of Science for April, 1883, Prof. W.
H. Brewer has furnished data for the discussion of the change in
speed of the American trotting-horse. His table is here repro-
duced.

TABLE SHOWING THE NUMBER OF HORSES UNDER THE RESPECTIVE

RECORDS.

Prof. Brewer states that the data for the speeds 2 130 and 2 127
are very unsatisfactory, but for all the others are reasonably
correct.

On taking the logarithms of all the numbers A^of horses capa-
ble of trotting a mile in 5 seconds, it results that the plotted val-
ues of log. A'^ for their proper dates give a straight line for each
value of s. For the speeds 5 of 2 :30 and 2 127 these lines are
parallel to each other, and the lines representing the remaining

* Read May 7th, 18S3.

:io

TRANS. ST. LOUIS ACAD. SCIENCE.

speeds are also parallel to each other, but the two groups are not
parallel.

For the first set, the lines can be represented by the equation

log iV-=^' +0.0,5^,
where y4' is a function of .y, and 7" is estimated in years from any
-arbitrarily assumed date.
For the second group.

It is apparent that for the speed of 2 130 and 2 127 the values
of N are too small, for the reason perhaps that in earlier years,
when this was called good time, less general attention was paid
to the breeding of trotters, while in later years, as this became a
common speed, a constantly increasing number of horses of this
grade have been used as roadsters and remained undiscovered in
private hands.

These plotted lines are shown in Fig. i. It is clear that the
intersection of any one of these lines with the time axis determines
the date when this speed may be supposed to have originated,
or when N= i, and that this determination of the date, based as
it is upon a number of observations running through a series of
years, is much more reliable than the date when some accident-
ally arranged trotting match revealed the fact that the horse
capable of making this speed had already come.

The dates for the origin of the speeds of 2 :i3 and 2:11 cannot
yet be determined very accurately, and this fact is to be remem-
bered in considering the discussion which follows.

The following table gives the values of s in seconds and the
dates for the origin of these speeds, determined as before ex-
plained. The third column contains the change in speed per
3ear, calculated in a well known manner from alternate differ-
ences in the two previous columns.

ds

5.

YEAR.

dT

1 45

1854-0

143

1857-4

0-571

141

1861.0'

0-547

139

1864.7

0- 500

137

1869.0

O-506

13s

1872. G

O-430

133

1878.3

0-476

131

188I.0

NIPHKR EVOLUTION OF THE AM. TROTTING-HORSE. 51I

When the vakies of --^ are plotted with the simultaneous val-
ues of s, we get a somewhat irregular series of points shown in
Fig 2, and represented fairly well by the equation

The constants A and B can be determined graphically with
as great precision as the nature of the data will warrant.
The values are found to be

A = 1. 00

^ = +0-0110.

and the differential equation (i) becomes

^= — i-oo+o-oiio^ - - (2)

This equation being put into the form

,_QO =0-oiio ^^^

S 9U. g

it admits of direct integration as follows,

n

/df

■ 0 1 1 0 /
5-90.9 -^

So T

on performing the indicated operations

/(5— 90.9) =/(i-o_90.9) H-o-oiio 7"o_o.oiio 7;
where s^ and 7^q are simultaneous values at any assumed date.
Placing the initial values in a single term, we have

/(5-9o.,)= c-^r - - (3)

or for the primitive equation

C-BT

s = 90-9 + e - - (4)

where e is the Naperian base.

It thus appears that the limiting speed of which the trotting-
horse is capable, which he will continually approximate and
never reach, is 1:31. This follows from (2) by making — ^ = o,
or from (3) and (4) by making T= 00 .

/

ds ^ Q /dT

512

TRANS. ST. LOUIS ACAD. SCIENCE.

The constants B and C are best determined by taking the lo-
garithms of (^_9i) for the vaiious vakies of 5, and plotting
them on the time axis. These values are given in the following
table :

5.

5 — 91.

log (5—91)

YEAR.

T.

5 calc.

DIFF.

1 45

54

1-732

1854-0

— 6.0

144.8

— 0.2

143

52

1. 716

IS.S7-4

— 2.6

142.9

— CI

141

50

1.699

1861.0

I.O

140.9

— Q. I

'39

48

1.6S1

1864.7

--4-7
--9.0

139.2

+0.2

137

i^6

1.663

1 869 . 0

137-2

4-0.2

135

44

1-643

1872.6

--12.0

135-2

-|-0.2

133

42

1.623

1878.3

-18.3

132.6

-0.4

131

40

1.602

1881 -o

— 21.0

131-4

+0.4

The constants are determined by well known graphical meth-
ods, and it is thus found that the observations are represented by
the equation

log (.s_9i) = 1.703 - O-0046 ^' - (5)

where the logarithms are common, and T is estimated in years
from i860. Substituting in (4) the values of T for the dates of
the above table, the values of s and their differences from the ob-
served values of s have been determined and are given in the
final column. These differences are seen to be greatest for the
later dates, where the possible errors are known to be greatest ;
but the error in 5- even here coriesponds to an error of only a
year in date, which is certainly within the error of observation.

From (5) it is easy to determine the date when the horse will
have reached within one second of the limiting speed. Making
s = 92, this value of 2" turns out to be 370 years. By the close
of the present century the time of trotting a mile will be reduced
to 2 :o4, and the time of 3 :oo will be reached in the year 191 2.
But they indicate that the trotting-horse will finally be able to
make his mile in a time not differing materially from the time
of the running-horse, which is at present about 100 seconds.
Whether or not the trotting-horse will finally beat the running-
horse, as the present results seem to indicate, it is perhaps not
possible to decide at present with the insufficient data at our
command. A weighty consideration is found in the fact that a
well trained trotter carries his body more steadily, or with less of
rise and fall, than the racer, and this may possibly result to the

NIPHER EVOLUTION OF THE AM. TROTTING-HORSE.

513

final advantage of the trotting-horse after the process of develop-
ing and adjusting of his muscles and chest shall have been suffi-
ciently carried on, so that the contest between the trotter and the
racer shall have been reduced to a matter of muscular capacity.

It is w^ell known that some herds of wild horses on the Texas
plains were natural pacers, and even when pushed to the utmost,
and for days together, by the best running-horses, the greater por-
tion of them held to their gait. One large white pacer became
widely known and his capture was often attempted, but he al-
ways proved more than a match for the best horses that could be
brought against him.

Whatever may be said about the particular numerical results
of this discussion, it is clear that the trotting-horse is very likely
to reach a much higher speed than has been heretofore thought
possible.

Added Nov. 7, 1883.

In the November number of the American Journal of Science
Mr. W. H. Pickering has criticised the method of reduction used
in the present paper (which had been printed from advance
sheets in the July number of that journal), and has reached a very
different conclusion from that reached in the present paper.

Mr. Pickering thinks that it is objectionable to determine the
value of — ^ by taking the alternate differences in s and 7^, and
he has reduced the observations by taking differences between
consecutive values in the table. In this way he gets the values of
the third column in the table below.

s.

\

YEAR.

ds
'dT'

ds ,

dT ^^^''^

e.

145
143
141

139

^37
135

131

1854.0

1857-4
1861.O
1864.7
1869.0
1872.6
1878.3
1881.O

0-59
0-55
0-54
0.46

0-55
0-35
0-7.5

0-59
0.56

0.54
0.51
0.49
0.46
0.44

0.0

— 0.1
0.0

-0.4
+ 0.4

— 1-4

+ 1.8

ds

Plotting these values of ~y=r and the corresponding values of s,
he then goes on to say that the points so determined may be rep-

ds

resented by a curve, such that the value of --tt^- increases as s

dT

514 TRANS. ST. I.OUIS ACAD. SCIENCE.

diminishes, and thus indicating disturbing causes not easily dis-
cussed. Assuming that a straight line will represent the values,
he determines the value of the constants, and finds that the line
intersects the axis of ^ at a point where the value of 5 is — 25.
This would mean that the limiting speed of the trotter is 25 sec-
onds less than no time at all.

When making his first discussion of the subject, the writer con-

ds
sidered the propriety of determining the value of -,„ by means

of consecutive differences, and unfortunately rejected the method
without even giving it a trial, for the reason that the dates iSSi.^
and 1878.3, corresponding to the values 131 and 133 of s. were
very imperfectly determined. It was clear that the additional
point thus secured would deserve very little weight. It was
thought to diminish the irregvilarity of the line by combining these
with previous and better determined dates. Mr. Pickering has
not only used this method (which properly used is capable of
yielding good results), but he has given equal weights to the val-
ues of -7!, for all the dates in the table. This is the fatal defect

which entirely vitiates the conclusion reached by him. A refer-
ence to Fig. I of this paper will show that for the earlier dates
from 1854.0 down to 1872.5 the graphically determined dates dif-
fer from the real dates when the record was actually lowered by
from one to two years.

It will also be seen that the dates 1S78.3 and i88i.(, are subject
to errors which may be as great as two years. After having made
a preliminary examination, these dates might indeed have been
"adjusted" so as to make them agree better with the others, but
they now stand exactly as they did when first made and before
any other work had been done. It is clear that the most weight
should be given to the earlier dates. I have therefore plotted the
new values of ^|r with the values of 5, and have drawn the line
representing the values so as to give most weight to the best de-
termined values. The equation of this line is

^ = — 1-24 +O-0 127 •^- - - - (6)

From this equation the values of -^ were calculated as given

in the fourth column of the last table. The fifth column, headed

e, gives the time in years by which the corresponding time in-

NIPHER — EVOLUTION OF THE AM. TROTTING HORSE. 515

tervals dT must be increased in order to bring Mr. Pickering's

values of — ^^ into accordance with the values calculated from
dT

the above equation. In this case the intervals are supposed to be
separately adjusted. If the later dates were simultaneously ad-
justed or changed by intervals ranging from two-tenths to three-
fourths of a year, the values of -^ , which Mr. Pickering pre-
fers to use, would agree exactly with the values calculated from
the last equation. Now it is perfectly clear that these later dates,
and particularly the last two, are subject to just such errors as this.

Whatever these values of -j=- may be said to prove, they cer-
tainly do not prove that my results as before published are absurd,
and they do not indicate a limiting speed of _ 25 seconds. If
--^= o, the limiting speed of the horse is found to be 98 seconds.

I desire to express my thanks to Mr. Pickering for his criti-
cisms and suggestions, as he has corrected a tendency which I
had begun to feel, to attach too much importance to the numeri-
cal result reached ; but I maintain that his method, correctly ap-
plied, gives in general, substantially, the same result as my own.
It is not necessary to assert that this result is really correct if any
person feels inclined to doubt it, because at present it is not pos-
sible to demonstrate it more fully than has been done in the pres-
ent paper. I only insist that it is not wholly unwarranted by the
facts which we now know.

Most horsemen seem to think that the limiting speed of the
trotting-horse will be somewhere near a mile in 120 seconds. If
this were true, the differential equation could hardly be a linear
one. The equation

ds

where /& is a constant and L is the limiting speed, would how-
ever be in harmony with this view. But this equation gives on
integration an equation of the form

V-y - Z = C—A T . . . - (8)

According to this equation the horse would absolutely reach
the limiting speed L in a finite time, — . Practically this may be
true, as is in fact shown by my own equation (4), so that some
such equation might really represent the results sufficiently rear

5l6 TRANS, ST. LOUIS ACAD. SCIENCE.

for all practical purposes. But the relation is not a rational one,
since it cannot be supposed that the horse will really attain his
limiting speed in a finite time. After he had come within a
thousandth of a second, it would take a great interval of time to
compass the next millionth of a second. Furthermore, this equa-
tion could not hold for values of Z" greater than 2^, as the value
of s would then begin to increase according to equation (8). I
therefore claim that equation (4), in all probability, represents
the relation between the values o( s and T, and that the constants
in the equation will be determined with greater and greater pre-
cision as the data becomes more and more complete.

Magnetic Survey of Missouri. Fifth Annual Report.

By Francis E. Nipher.

During the summer of 1882 the survey was continued under
the same auspices as in the previous year. The friend who fur-
nished the entire means for conducting the work enlarged upon
his former bounty, and furnished the party with two fine spring-
wagons designed with reference to the needs of camp life, and
provided with all needed conveniences. Two paid assistants,
Messrs. Joseph Cunningham and Albert Meyer, were also sent
with the expedition, and Mr. Frank Ringling of the Sophomore
class accompanied the expedition as volunteer assistant, paying
his own expenses.

The work of the summer was interfered with in a serious man-
ner by the sickness of the horses, and more particularly by the
horrible condition of the roads, due to heavy and long-continued
rains. During the entire summer we were compelled to improve
roads and fords, and to build bridges, and this frequently took
up a quarter of our time during an entire week. This made it
impossible to make complete observations after Aug. 7th, as we
were obliged to travel every day in order to reach St. Louis with-
in the time which could be devoted to the survey. After the
above date, therefore, only declination observations were made,
the magnetic meridian being determined from the morning elonga-

NIPHER 5*'^ ANN. REP. MAGNETIC SURVEY OF xMISSOURI. 517

tion as explained in the previous report.* The true meridian
was in nearly all cases obtained by pole-star observations, but the
great number of cloudy nights made it necessary in some cases
to observe at other times than at elongation.

A description of the stations where observations were made
is here given, the numbers being continued from the previous
report.

Station \o\ — Kirk-wood, St. Louis Co. Lat. 38° 36'; Ion. 90° 24' .
In the orchard of H. W. Leffingwell, 128 feet from the street fence on
the south, and 150 feet from that on the east. Polaris observation on
elongation.

Station 102 — Gray's Summit., Franklifi Co. Lat. 38° 29'; Ion. 40°
49'. On the Union road about half a mile to the S.W. from the railroad
crossing, and in the second depression, 20 ft. from the road, and on the
N.W. side. Polaris obs. on elongation.

Station iot^— Newport, Franklin Co. Lat. 38° 36'; Ion. 91° 06'. In
the "old town" on the summit of a small ridge, 128 ft. N.W. from the N.W.
corner of the church. A large elm to the N.W. across the small water-
course is said to be at, or very near, the N.W. corner of the S.E. qr. of
sec. II, tp. 44, r. 2 W. Polaris obs. on elongation.

Station 104 — On the farm of August Goebel, near Newport. Lat. 38°
34'; Ion. 91° 06' . The station was within a few feet of the middle point
of the line dividing the E. half of the S.W. qr. from the W. half of the S.E.
qr. of sec. 15, tp. 44, r. 2 W. Polaris obs. on elongation. In this imme-
diate vicinity Dr. Goebel, grandfather of the present owner of the farm,
had established two magnetic stations, where he made extended and care-
ful observations. The original records of this work were given to the U. S.
Coast Survey some years since by his son, Mr. Gert Goebel.

The earlier station of Goebel is found by going from our station in a
line bearing S. 93° 34'.5, E. 255 ft. and thence N. 83 ft. This station of
Goebel's is 61 ft. W. and 14 ft. N. of the S.W. corner of the house of Au-
gust Goebel. The observations here were made in the year 1839. The
declination was 9° 21' E.

The other station of Dr. Goebel was occupied in the year 1849. ^t is at
the S. window of a now abandoned stone house, the N.W. corner of which
is 158 ft. W. and 193 ft. S. of our station. The house is a one-story struc-
ture, having the dimensions of N. and S. sides 18 ft., and E. and W. sides
24 ft. The window where his observations were made is in the middle ot
the S. side. His value for declination in 18^9 was 9° 05' E. Our value
determined June 22d, 1882, was 7° 36' .

Station 105 — In Franklin Co. Lat. 38° 41'; Ion. 91° 20'. The sta-
tion is on timber land of Elijah Ruck, 315 ft. N. and 15 E. of the well in

* Trans, iv, 3, p. 454.

5l8 TRANS. ST. LOUIS ACAD. SCIENCE.

front of the house of John Bedts, and about 325 ft. from the line between
Franklin and Gasconade counties. The station was said to be in sec. 10,
tp. 45, r. 4 W. Polaris obs. on elongation.

Station ig6 — /w Gascovade Co. Lat. 38° 37'; Ion. 91° 29'. On the
land belonging to Fred. Bruhns. a quarter of a mile N. and 260 ft. E. of
the S.W. corner of sec. 19. tp. 45, r. 5 W. The station is on the bank of
First creek. The value for declination here was very much smaller than
at surrounding stations, but no error could be detected in our work.
Whether the discrepancy was due to some minute local effect or not, we
could not remain to determine, as sickness at home made it desirable to
reach the telegraph as soon as possible. This is the only case of the kind
so far reached, excepting in the Iron Mountain region. Two Polaris ob-
servations were made on elongation.

Station 107— /« Osage Co. Lat. 38° 28'; Ion. 91° 41'. On the land
of Fritz Kaldeweiher, near the centre of the S.E. qr. of the S.W. qr. of
sec. 9, tp. 43. r. 7 W. The station was 50 ft. N. and 33 ft. W. of the N.W.
corner of Kaldeweiher 's house. Polaris obs. on elongation.

Station ic8 — Z/w«, Osage Co. Lat. 38° 28' ; Ion. 91° 50' . Station
on L'Ours creek* on the Jefferson city road, about half a mile from town.
The S.E. corner of James N. Clark's yard is 72 ft. W. and 68 ft. S. of the
station. Polaris obs. on elongation.

Station 109— /« Crt//rtway Co. Lat. 38° 43' ; Ion. 92° 01' . On Little
Auxvasse creek at the crossing of the New Bloomfield and Fulton road,
about 40 rods S.W. of the N.E. corner of sec. 28, tp. 46, r. 10 W. A spring
across the creek and just at the ford lies N. 65° E. 165 ft. Polaris obs. on
elongation.

Station no— Near Stffhen.'C Store, Boone Co. Lat. 38*^ 58' ; Ion. 92°
05'. About one half mile S. of the village. The old Fulton road is 12 ft.
W. and the bank of Cedar creek is 105 ft. N. Polaris obs. on elongation.

Station hi — Cetiiralia, Boone Co. Lat. 39° 13'; Ion. 92° 05'. The
station was on a vacant lot 48 ft. W. of the centre of the street leading
directly S. to the depot and crossing of the Chicago & Alton R.R., which
is about a square and a half distant. The centre of the street to the N. is
distant 77 ft. and leads E. to a flouring mill, the smokestack of which bears
S. 90° 44'. 1 E. Polaris obs. on elongation.

Station 112 — In Monroe Co. Lat. 39° 24'; Ion. 92° 10'. On the S.
bank of the Long Branch of Salt river. The station was 150 ft. from the
creek and midway between the road and the W. fence. The station is on
the W. line of sec. 20, tp. 53. r. ii- W., and about 120yds. from the middle
of this line. Polaris obs. on elongation. — Some years since the county
surveyor of Audrain Co. called my attention to this region as showing

* Named after the first (French) settler on its bunks. A postoffice ne.ir the stream was
afterwards named " Loose Creek" P. O. by some poor speller, and this official name has
since been applied to the stream, which appears on some maps as " Loose Creek."

NIPHER 5'^'^ ANN. REP. MAGNETIC SURVEY OF MISSOURI. 519

marked local effects. The region is level prairie, and long N. and S. lines
run bj compass aregreatlj and uniformly curved, showing an abnormally
great easterly declination. This station and station No. 144, about 12
miles E., show an area of abnormal easterly declination. The disturbed
region extends over an area of many miles.

Station iiT^—Moberly, Randolph Co. Lat. 39° 26'; Ion. 92° 26'. On
the fair grounds 184 ft. E. and 2S9 ft. S. of the W. entrance. Polaris obs.
on elongation.

Station 114 — Macon, Macon Co. Lat. 39° 46'; Ion. 92° 30'. In the
stock-yard of O. S. Bearce, directly in front of his barn and 20 ft. from the
Vine-st. fence. The city school-house is one square W. and one square N.
Polaris obs. on elongation.

Station 115 — In Macon Co. Lat. 39° 48'; Ion. 92° 37' On the farm
of Isaiah Lewis, which is the N. halfof N.E. qr. of sec. 21, tp. 58, r. 15 W.
The station was in front of the house, and midway between the road and
the yard fence. Polaris obs. on elongation.

Station 116 — Near Mercy ville, Macon Co. Lat. 39° 57'; Ion. 92° 42'.
About half a mile N. of town. A corner-stone in the road, a quarter of a
mile S. of the middle point of the N. line of sec. 35, tp. 60, r. 16 W., bears
S. 3° 23' W. 589 ft. Polaris o-bs. on elongation.

Station 117 — In Linn Co. Lat. 39° 54'; Ion. 93° 07', In the bottom
of the west branch of Yellow creek. The station is within a few feet of
the corner, a quarter of a mile due E. of the middle point of the E. line of
sec. 22, tp. 59, r. 19 W. A large white-oak tree stands 20 ft. W. , and the
east end of the bridge is 261 ft. distant. The mark used was an iron rod
on the bridge, 11 ft. west of the centre of the bridge. Polaris obs. on
elongation.

Station 118 — Linnczus, Linn Co. Lat. 39° 51'; Ion. 93° 13'. On a
vacant lot on the summit of the hill E. of the Burlington & South-western
R.R. depot. The S. line of the yard of Chas. B. Purdin lies 166 ft. N., the
N. line of the farm of Joel Wilkinson lies 166 ft. S., while the field to the
E. across the road is 237 ft. distant. The court-house spire was used as a
mark. Two polaris observations on elongation.

Station 119 — Near Laclede, Linn Co. Lat. 39° 47'; Ion. 93° 17'.
Station one mile W. of town, on the E. side of Muddy creek; about 350 ft.
E. of the bridge and 20 ft. N. of the road centre. The station is said to be
on the S E. qr. of sec. 36, tp. 58, r. 21 W. Polaris obs. on elongation.

Station 120 — /« Livingston Co. Lat. 39° 38'; Ion. 93° 45' . On the
farm of Wm. E. Wolfort, in the N.E. qr. of the S.E. qr. of sec. 33, tp. 56, r.
25 W. The station was in the cattle-yard 25 ft. from the road fence to the
east (the road being on the section line), and 40 ft. N. of the door-yard
fence. The middle line of the section is in the E. and W. road perhaps,
100 ft. N. Polaris obs. on elongation.

Station 121 — Kingston, Caldwell Co. Lat. 39° 41'; Ion. 94° 04'. The
station will be found by going from the S.W. corner of the court-house

520 TRANS. ST. I.OUIS ACAD. SCIENCE.

square W. 1646 ft., and S. from the middle of the road 62 ft. It lies 91 ft,
E. of the summit of the small ridge. Polaris obs. on elongation.

Station 122 — /« Caldwell Co. -Lat. 39° 39'; Ion. 94° 11'. On land
of Christian Smitt, 50 ft. W. and 212 ft. N. of the middle of sec. 29, tp. 56,
r. 29 W. Polaris obs on elongation.

Station i2-x,—Maysville, DeKalb Co. Lat. 39° 43'; Ion. 94° 24'. On
the grounds of the public school building, 65 ft. W. and 21 ft. N. of the
N.W. corner of the building. Polaris obs. on elongation.

Station 124— /« DeKalb Co. Lat. 40° 01' ; Ion. 94° 23'. On land of
Harvey Johnson, 50 ft. S. and 206 ft. E. of the middle of the N. line of sec.
14, tp. 60, r. 31 W. Polaris obs. on elongation.

Station 125 — Albany., Getiiry Co. Lat. 40° 15'; Ion. 94° 21 ' . The
station is 979 ft. E. of the N.E. corner of the court-house square and 8 ft.
S., these measurements being along the streets. The station is 11 ft. W.
and 8 ft. S. of the N.E. corner of lot 2, block 5, of Hundley's second addi-
tion. Polaris obs. on elongation.

Station 126— /« Getitry Co. Lat. 40° 16'; Ion. 94° 17'. The fence
E. on the E. edge of sec. 15, tp- 63, r. 30 W., is 107 ft. distant. The fence
S , which is the S. line of the N. half of the N.E. qr. of the section, is 193
ft. distant. There appears to be a double corner here. The evening-mark
reading was missed, but the station was on raw prairie and the instrument
was certainly not disturbed between the star observation and the morn-
ing mark reading. Polaris was observed on elongation.

Station 127 — Bethany, Harrisofi Co. Lat. 40° 16'; Ion. 94° 03'. On
a vacant lot of Mrs. R. J. Turner, 365 ft. E. of the N.E. cornerof her house.
The station is about 320 ft. S. of the N. line and 346 ft. W. of the E. line of
sec. 15, tp. 63, r. 28 W. The line fence of T. B. Shearer's yard is loi ft.
E. Polaris obs, on elongation.

Station 128 — Farm of John Honafi, in Harrison Co. Lat. 40° 08' ;
Ion. 93° 56'. The station was in the meadow, 133 ft. S. and 289 ft. W. of
the N.E. corner of sec. 36, tp. 62, r. 27 W. Meridian determined by equal
altitudes of the sun. Small cumulus clouds cut oft" five observations out of
a series of seven. The two differed 1 ' .

Station i2()— In Daviess Co. Lat. 40° 04'; Ion. 93° 53'. The station
was in the road about midway between the track and the S. fence, and 334
ft. E. of the N.W. corner of the S. half of the S.W. qr. of sec. 28, tp. 61,
r. 26 W. By reason of a very heavy rain which came up while the camp
was being made it was impossible to get an evening-mark reading. The
rain lasted until 9:15 p.m., and then a small patch of sky cleared around
polaris for about half an hour, and a pole-star observation was made.l

When the star-observation was made the whole hillside was covered
with a sheet of water three to four inches inches in depth, which filled the
trenches around the tent and ran through the tent in a torrent. The
ground was however firm, and the tripod was as usual mounted firmly on

NIPHER 5"' AW. REP. MAGNETIC SURVEY OF MISSOURI. 52I

large stakes driven eight to ten inches into the ground. The observation
was therefore deemed entirely satisfactory. At the next station on the
next night an observation was made the same interval before elongation,
and the difierence between the azimuth of the star and that of elongation
agreed within a quarter of a minute with that at Station 129.

Station 130 — Trenton^ Grufidy Co. Lat. 40°03'; Ion. 93° 39' . Sta-
tion in a grove of Dr. Harris, in the east part of town. The station is
found by starting at the front (S.) fence of the door-yard and measuring
S. along the centre of the road 112 ft., thence E. 415 ft. Polaris obs. on
elongation.

Station 131 — In Grundy Co. Lat. 40° 13'; Ion. 93° 38'. Station in
the road about midway between the track and theE. fence, and 150 ft. S.W.
from the front gate of the farm of Faust Amick. The station is near the
S.E. corner of the N.E. qr. of N.E. qr. of sec. 34, tp. 63, r. 24 W. Po-
laris was observed before elongation, and its azimuth calculated as before
described.

Station 132 — Princeton. Mercer Co. Lat. 40° 24' ; Ion. 93° 39' . The
station is at the base of the bluff, 395 ft. W. of the W. side of Lincoln st.
and 563 ft. N. of the centre of Hickland st. Polaris observations were
made at 9 and I2h. 30 m.

Station 133 — In Putnajn Co. Lat. 40° 27'; Ion. 93° 21'. On land of
Joseph Williams, about a quarter of a mile W. of the centre of sec. 7, tp,
65, r. 21 W. The station was about 20 ft. N. of the centre of the road, and
250 ft. E. of the front gate of the house of Crede Yocum. Polaris obs. on
elongation.

Station 134 — Iti Putnam Co. Lat. 40° 27'; Ion. 93° 21'. Station in
a lane near the house of Joseph Ward, in sec. 12, tp. 65, r. 20 W. The
middle stone of the S. line of the section is 1S9 ft. S. of the station. Pola.
ris observed at 11 o'clock p.m.

Station 135 — Unionville., Putnam Co. Lat. 40° 29'; Ion. 93° 03'. The
station is on an open square 562 ft. N.W. of the W. corner of the court-
house square and 150 ft. N.W. of the same. These measurements are
made along the streets which lie diagonally in reference to the points of
the compass. The sky was again cloudy at elongation, and polaris was
observed at 9 h. 11 m. and 10 h. 46 m.

Station 136 — In Sullivan Co. Lat. 40° 19'; Ion. 93° 07'. On the
farm of Nathan Bankes, on the N.E. qr. of the S.E. qr. of sec. 28, tp. 64,
r. 19 W. The station is in the meadow 26 ft. S. of the S.W. corner of
Bankes' house and 249 ft. W. of the middle of the road. Polaris obs. on
elongation.

Station 137 — Milan, Sullivan Co. Lat. 40° 12' ; Ion. 93° 11'. On
the common, 160 ft. S. of the S.W. corner of the public school building.
Polaris obs. on elongation.

522 TKANS. ST. LOUIS ACAD. SCIENCE.

Station 138 — Stickhrville, Sullivan Co. Lat. 40° 09' ; Ion. 92° 58';
Near the S.W. corner of the N.W. qr. of sec. 22, tp. 62, r. 18 W. The N.
W. corner of the church bears S. 31° 15' W., and is distant 731 ft. The
same corner of the church is 137 ft. S.E. of the qr. sec. corner before men-
tioned. Polaris obs. not at elongation.

Station 139 — Kirksville^ Adair Co. Lat. 40° 12' ; Ion. 92° 37'. In
a vacant lot, owned by Dr. Hurley, on the S.W. corner of Fifth and Fill-
more sts., 76 ft. from the centre of the latter and 83 ft. from the centre of
the former street. The left side of the tower of the State Normal school
building bears S. 69° 02'. 5 E. Polaris obs. on elongation.

Station 140 — La Plata, Macon Co. Lat. 40° 00' ; Ion. 92° 34' . Sta-
tion in the street about midway between the track and the N. fence. The
middle, E. and W. line of sec. 7, tp. 60, r. 14 W., is 486 ft. N., and the E.
line of the section is 637 ft. E. These distances were measured along the
streets. The house of B. F. Bragg is on the S. side of the street, a little E.
of the station. Polaris obs. on elongation.

Station 141 — In Macon Co. Lat. 39° 53' ; Ion. 92° 22'. Station on
Bear creek bottom, 304 ft. N. and 832 ft. E. of the middle of the S line of
sec. 23, tp. 59, r. 13 W. , near Harris's farm. Some error was made in
reading the verniers in the star observation. It is conjectured that the
altitude was read too high by lo'. This conjecture is baesd on observa-
tions at the next station, made at elongation and an equal interval after
elongation, allowance being made for the change in latitude.

In the magnetic determination on the morning of the 12th marked dis-
turbances of the needle were observed. The declination diminished 9'
between 6 and 7 o'clock.

Station 142 — In Shelby Co., 3 miles S. of Shelby ville. Lat. 39° 44' ;
Ion. 92° 04'. The middle stone on the N. line of sec. 5, tp. 57, r. 10 W.,
bears N. 4°, 50' E., and is distant 910 ft. Polaris obs. on elongation.

Station 143 — In Monroe Co., on the farm of Henry Winkler, 40 ft. E.
of the centre of the road, and 669 ft. N. of the S. line of sec. 35, tp. 56, r.
10 W. The road, which runs N. and S., divides the S.W. qr. of the sec-
tion in halves. Polaris obs. on elongation.

Station 144 — In Monroe Co. Lat. 39° 22' ; Ion. 91° 59'. On the
summit of the S. bluff of Long Branch of Salt river, W. of the road, on
land of B. F. Dowell. The land is in sec. 30, tp. 53, r. 9 W. The station
was about 75 ft. W. of the road, which is on the E. line of the section.
The Baptist church across the road is about 50 ft. farther S. than the sta-
tion. These measurements were forgotten, and the distances were esti-
mated the same day after having left the locality. Polaris observation on
elongation.

Station 145 — Montgomery City, Lat. 39° 00' ; Ion. 91° 30' . The sta-
tion is 105 ft. W. of the middle (N. and S.) line of the S.E. qr. of sec. 32,
tp. 49, r. 5 W., and a perpendicular laid off to the track of the Wabash-

NIPHER 5^'' ANN. REP. MAGNETIC SURVEY OF MISSOURI. 523

Pacific R.R. track measures 200 ft. Passing freight trains caused the nee-
dle to swing through 2'. Polaris obs. on elongation.

Station 146 — Warrenton, Warren Co. Lat. 38° 46' ; Ion. 91° 08' .
The station is at theW. end of town, about a mile from the station of 1881.
Starting at the creek bridge W. of the court-house, the station will be found
bj going along the road westwardlj 705 ft., thence southwardly at right
angles to the road a distance of 45 ft. The court-house spire bears S. 79°
14.3' E. Polaris obs. on elongation.

Station 147— /« St. Charles Co. Lat. 38° 43'; Ion. 90° 40'. The sta-
tion is in the Booneslick road about midway between the track and the S.
fence, and almost due south of O'Fallon.* The O'Fallon road is 250 ft. E.
The house of D. Heald lies a few rods to the W. Polaris observation on
elongation.

Station 148—/// St. Louis Co. Lat. 38° 41'; Ion. 90° 21'. On the St.
■Charles rock road. The station was in a gap in the fence opposite the
grounds of J. B. Lucas. From the station to the centre of the road the
distance is 30 ft. From thence along the road to a point opposite the gate
is 165 ft., while the distance in the opposite direction to a point opposite
the S.E. corner of the Lucas grounds is 158 ft. Polaris observation on
elongation.

Station 149 — Near Atalissa, Muscatine Co., Iowa, on the farm of Mrs.
Grace Aikins, on the N.E. qr. of the N.W. qr. of sec. 3, tp. 78, r. 3 W.
The station is on the front path, exactly between the front gate and the
house. This station is a mile west of station 33 in the report of i88o.t
Polaris obs.

Station 34 — This station was occupied in 1880, and is described in the
report for that year. Polaris obs. on elongation.

At six of the stations of the summer deflection determinations
were made with the University magnetometer, with magnet Cg
deflecting and Cj^ deflected, and these observations have been
used in determining the value of P., and in calculating the mag-
netic moment of Cg for the summer. The latter was sensibly
constant, the observed diflerence between the extreme value
observed and the mean of all being about o.^q^j, of the average
moment. In the reduction of the work the magnetic moment
was therefore assumed to be constant. The calculations for P
and for the magnetic moment are given in the adjoining tables.

* In the report for iSSo the Ion. of O'Fallon should be 99' 40'.

t Station 33 is on the N.E. qr. of the N.W. qr. of sec. 2, and not N.E. qr. of N.E. qr.
as was given in the report of 1 5S0.

524

TRANS. ST. LOUIS ACAD. SCIENCE.

CN

00

00

<4-

o

w

0)

§

E

S

E

h

3

1^

C/)

tf

<D

<i

0

j_

o

^

h-l

1:0 rH Oi M OO O
iO Oi QO r- 1 CD Oi
OS 30 (M O I— I Tt<
O O O O >-< O

000000
1+1 I++

^1^

00 00 00 GC 00 GO

a,?;

55, a. s

s

<M

1—1

lO

rM

(M

(M

T

-^'

00

I— 1

-M T+>

'^

<M

0 00

1^^

-t

CO

'^

CO

CO

t^

r^

m

CO

CO 00 Tt^

Tj"

0

r^

t^ CO

lO

t^

t^

^ •

CO

(M

00 CD

t^ CD

s

00 0

1^

iM

1^

1—

c

1—

0

r-^

'+

CO

r^

0

0

T-^

(M

(M

CN

0

0

0 0

0

0

K

Oi

Oi Oi Oi Oi Oi

(M 0 T# 0 -f

l-H

on

CS5

1-

CO

r^

1— 1

on

1—1

co 00

CO

0

cS

on

00

C5

0 0

(—1

00

00

00 Ci 02

Ci

k

00

00

00

00

QO

00

0 Oi

lO

CO ~f*

CO

'jO cr.

00

CO

00

00

c

1^ CO

t-- <0 Oi

CO

cS

or.

(/;

05

y^-i

0

1-H

't

'*

-f

lO

0

>o

\

Oi Oi ■^ Oi Oi Gi

00 CD O CO O t^
OC 05 00 CO QO -^
CD CO 00 O lO (Kl
05 00 C5 — I O -^
Tf -^ -^ O -x: lO

0:> Oi Oi Oi Gi Oi

«.5 ^

o

fe <u .^ J^ t?

'T aj c r^ c

.t; c (u .s •"

+

SS Si, g S Si, ?i,

l-H ^ t~ Oi 1-1 0
CO 00 C^l — 1 lO CO

0 oi O' CO t^ 0

00 -^^ CD 00 CO 03
Oi 01 rfi 0 0 CO

00 00' 06 i>^ oi oi

c

S S S S S S

1— 1 t^ 00 CO 1— 1 (M
1— 1 lO lO Ci l^ '-^
(M 0 00 CO CO CO

CO 00 1-^ 05 0 0

CO CO CO CO -H -*

a;

CJ

bfl

CD Ttl T^ 1— 1 -^

.—1 — ^

1—1

1 (M

t^ 00 0 00 CO CD

CO

•^

CO Tt< CO CO

0
eg

-rOO'M'OOOIMdO^

1 CO

OiOiOCO-tOOOOOO

I— 1

1— lOOCOO— OOiOtO

1 —'

oocr>c20000

C<I

00000000

0

00000000

0

M 1 l + l I+' 1

8

THOi-^iO-fooi— (1— 1

en

be

OCO'ThCDt— OiCOCO

s

0

00000000

3

en

II 1

00000000

00000000

^S

00000000

+++1+1 1+

CDMCCi— l(M0i0iO5

1

CM M r-i .—

1

"«

1 1 H-++++1

•sXBa

O-^OOt^OOtOiOiO

CD

1— < !M (M CO -^ -^

(M

I— ICO-^Oi— ICOCD':*^

>o

^ I- 1^ 00 -t ■ r cc

I— 1

§

■^COCC-^COiO'^CC

^

bo

CDCOCOCDCDCDCDCD

CD

OOOOOOOOOnOOGOGC

O:i0iaiC:>GiO:>0i0i

02

OlOI~00»OCOOO

II

Ho

05CD'-t^C0C0I:^-*^-

§

s

c^ii— i-^ioio-ti-^c;

COCDCOCOCOCOCDCD

be

OC cyj GO 00 QC 00 CC 00

bJD

0

Oi^GiOiCiaiO'^Oi

^

--^ — ' -+ W CD 1— CO -f

''. \ ' — ' 'M -^ t^ CO 0 1 — '

be <»

-~ o-i cr. oi 1 000

0 1

0 -CriOiOlOOC

0 0 02 C7j 0 0 0 0

+

0 0 01 03 CJ-.' 0 0 C

i

1^

lOi— 'CD(Mt-0OCOI-

0

CO

CDOCO-^Oi— lOO

I— 1 1— 1

1

++i 1 I++-+

-

lOOOi—iiCOiOO-*

t^

%;»

COO>t^COO(M — I— 1

0

QOO^-l^t^OOOOOC

do

t^w lO'^lON 1-1 iH

CC

1-1 N b, i-i N

c

JJ >, u

C3

1)

Q

3. ^ <

^

d

0

13

Is

i4C

)Uh-

Mi-

NIPHKR — 5*'' ANN. REP. MAGNETIC SURVEY OF MISSOURI. 525

The value of P^ as determined in the first of the tables, gives
p
for the value of i ^ the values

P ,

I — ^ = 0.9946 log = 9-99765

_ ^ — 1 —

I /j \2 — 0.9930 ^^^ 9*9 96 9 5

These values were used in the reduction of the deflection series
made for the determination of the magnetic moment of magnet

In the second table, the decrease (a) in the value of log m is
determined, and it is found that for the summer of 1882, and at
a temperature of 80.7, the value of {a) is

'^•000,009'
20 32

or \o^m = 9.86415 + O-000,009 ^'

where d is estimated in days from July 13. The value of log m

was therefore considered constant during the summer.

In all of the intensity determinations the time of vibration was
determined by means of a Waltham watch belonging to Mr.
Ringling. This watch had been cleaned just before leaving St.
Louis, but it had not been rated. The error of the watch was
determined, at intervals during the summer, by comparison with
clock-beats from the observatory of Washington University,
transmitted daily to the telegraph lines of various railways in the
State. Its rate during the summer was a loss of 20 seconds per
day, fluctuating however between 17 and 22 seconds. The cor-
rection on the time of vibration was -(- o.qqj6 second at all the
stations, the time of vibration at the stations not varying suffi-
ciently to change the value of this correction. The effect of
neglecting this correction altogether would be equivalent to the
effect of an error of half a degree in temperature.

The intensity determinations were all made with magnet Cg in
the University declinometer, C j 7 being used as a deflected mag-
net. The moment of inertia of Cg was obtained from the table
given in the 4th report.* The values for H ?lx& not corrected for

* Trans, vol. iv. No. 3, p. 468.

526

TRANS. ST. LOUIS ACAD. SCIENCE.

the effect of magnetic brass-work of the magnetometer. This
correction is given in the 4th report, p. 472.

The observations for inclination were not very satisfactory, as
the axes of the needles were both bent during the early part of
the summer.

The following observations for meridian, by equal altitudes of
the sun, were made. The method of reduction has been ex-
plained in previous reports.

Sun Observations for Meridian.

Station.

Date.

X3
0

0

6

Mean Time of Series.

i.

}i(A+A').

A. M.

p. M.

Little Auxvasse Cr.
Honan's

June 30
July 30

5
2

k. m. s.

9 36 58
9 38 25

A. m. s.

2 32 40
2 23 18

deg. m.

37 03.7

35 42-5

deg. m.

244 56.7
176 38.5

log A d".

a. c. log cos

a.c. log sin t

Cor.

South reads

Mark reads

Az. of Mark.

I.67112
2.23805

0.10777
0.11660

0.21992
0.23384

4-o'.8
+ 3-2

244°57'-5
176 41 .7

l80°02^0
180 01 .2

S.64°55-5E.
S. 3 19.5 W.

Polaris Observations for Meridian.

Station.

Daviess Co., Sta. 129.
Amick's

Princeton

Ward's . . . .
Unionville.

Sticklerville
Harris's . . . .

Lat. <p.

40'=' 04'
40 13

40 24

((

40 27
40 29

40 09
39 53

Alt. /^.*

39° 42'' -5

39 34 -o

39 46 .0

39 58

40 05
40 48
40 12
40 45
39 37 -o

39 46 -5

40 25 .of

Polar D./.

19^-3

^ Sum =S.

40° 32/. 9

40 33-1
40 39 .2
40 50 .6
40 54 .2
17 .2

41

41 00

41 16

40 32

40 37

40 48 .6

* The altitudes are all corrected for refraction.

f This altitude was recorded 40'' 36'. o. It should have been 40* 26I , as was deter-
mined at the next station (Shelbyville) by an observation made the same time interval after
elongation.

NIPUER 5^'^ ANN. REP. MAGNETIC SURVEY OF MISSOURI. 537

J3

o

JO

o

CL

-o

03

<

O CS

^ C4
O <0

CO

^

0
u

T'

u

ci

CS

'/i

0

u

CA!

^

^

^

^

^'

^

^

^

^"

0

"

m::

t^

"

(-»

-:

\o

VD

to

in

GO

LO

OS

1-

CO

LO

CO

LO

ro

ro

LO

LO

0

2

ro

ro

^

CO

73

cri

Cfi

c/j

c/3

73

7J

73

O I-" "

i-i M On

On \0 «

O i-i f^

vO \0 ^ vO

C» 11 I-

« OS -

^ ;S

528

TRANS. SI . LOUIS ACAD. SCIENCE.

to

'-0

CT5

lac

"3

be

O On ■^ 'i- >o lo OnOO i-> as0>-'000\OrO>')0N0iO ^VD O On

00 VO 00 M 00 u^ ro fOOO \0 "~.00 lo I>.v£) Ov N 00 M N Th m t>.VO

J>.w00 >OM lotoM O -^^ O "^ u-00 rooo O O O O 00 vO lo
f< CT> O On lo U-) ro lo\0 ''lONt-rO'-' ON'^O '^r ^\0 vD ON^O

Mr)«OM:^P<Mc^Nir^O'*-OOi-ii-i>J^. ■^rOfOi-iONOON

wi-cMOi-ii-ii-'i-iMi-iMMrororofOrorocorotnMrOM
o

O

O

O

O

lyj t^ vo U-) O

tr!*o M

li-jC^t^O t^N loioioo

t^ >o

00 t^ O J>--*t^i:^rOMvO00 M t^t^ON^hONN N n n OOOVO

OOt^N t^O O N l>.t^t^tot^i:^l>M M l>.t^rj t^O t^t^t>.

s

■O D
fe « 2 "a; ^"=

U

■J- f*

^ (U '

ji > .;.- ^ >, • • = U

NIPHER 5^*^ ANN. REP. MAGNETIC SUHVEY OF MISSOURI. 529

1) -

H..E
o o

000

t>.00 \0 t- LO

ww^uw :

0 On ^ LO 10 •

o\^oo

r, 0 0

so 'I-OOVO r-
fO - L1-, 0 fN

M ro ro -^ '^-

uo c) 10 0 r> •

') Th « OS 0\ •
- vO rosOOO •

00 Os^
rn-i- >-<

(M 10 On

On I- !>•

LO t^ 0\

CO 0 "

1^00 0

NO NO

Tj- t^ - NO ON ^nO OnO — CJnO ttloO O S. Onh-
■^00 O LO t^ - NO '^ t^ONt^OO CTs -^00 00 CO \o
MMi-chi — MtT) 1-11-1 (S « —

t^ !>.»>• O LO

(U to

> O
Ml tn

10 10 LO r> O

ii c; lu c —

U

— ■ OS) v '

OOi-iroONOLo-^»-<r- lonO OnOnn r^Q O lolo

00 f^NO On ■^00 N "^00 On OnOO 00 M '^h OnCO CO 00 On
On '^go ONLot^ — NO r»NO00t^l>>ON^i>-t^ ir^NO >o

0

10 tJ- Tt- LO

Tt- 0 CO

OsCO LO 1-1 00

^0

t^ t^ t^ 0

0

NO

rorOfOrOi^-^'^fOrOfOfOrO'N r» f» 1-1 m — vO

'l-'!^T^T^Tt-Tr't-•'r^■^T^Tt-■^T^•^Tl-Tf't■Tl-

0

10 LO t--.VO

0 LO (S

0 LO 0 !>. t^ ro r>

0 t^ t^>0 LO

530

TRANS. ST. LOUIS ACAD. SCIENCE.

(0

>

O

sz
o

_c
"o

o

a ■3'g

3 +J tfl

c ——.- — - ^^ - , ^,

H- > "^^

Tt- Th ONCO M M rj-vo lAvO l>.vO OS OVOO t^vo VO >^ O C N

O

vo vO ^ !>• t^vO !>• t^ t^ t^ t^CO J>- 1^ t^OO CO t>. t^OO 00 On

M loO rO" ■*t^ON'^J>-i-i LO\0 Ol^-O'-'^Mt-Oi-'

M N l>.\0 0\0 N Ti-rO'^tO'^l:^ t^\0 10 "*• '^ r^OO 00 O

o

\0 VO >0 t^ »>.\0 t^ !>. !>- 1^ t--00 t- t>. t^oO 00 t^ t^OO 00 OS

00 OsvO Os t~-VO rOOO <-i MOO -^t^i-it^w-iroN O m •- I>.

OWO On\0 rovO 10 1- 0\vO -^O) >^.vO lt, u-.oO CO OS Ost^ -^
QwiociLOTi-Mro'Ocq'^tsooi-iOrODrii-iiy-.ro
o

t^MCO ^^ n u-,n O •^^ O 10 LT-.OO rooo O O O O 00 \0
■^ Jr^ M t^OO t^" ro-^rot^ioiorO — so msDsO -^CO I>.

0000>-oNr«ioi>'MP< t>.vO t^t>.0 O N N «ol>-t^t>.

O\i-i's«0i-ii-''-'0i-in0'-i0i-'N0roi-'>-i000
voOOOOOOOOOOOOOOOOOOOOo

OsOOOOOOOOOOOOOMOOOOOOO
»^00 CX)0000COCOCO0O0O0000CC0000COO0CO000OO0O0

Cr5^Ml-ll-lh«-^WWWI-l-H>Hl-ll-(H«l-llHl-lMM

OS -^so ^ <X> OVO t^LOOsOsOsrow ■^lo t(-oo m CC >-. 00

1-1 OssD rO M t^ t^sO M O OSN fOrOM O fS M rit^tort-
roO LoO -^r^Loo "-tjO roroO O ►-' CH loc^ n n ro-^
o

roco U-) ro O N O\00 o ThoO pO rOSO msCOOOOCOOO Ir^io
10 t^ roCO 0\C0 " PO "-o -^ r^sO sO -^Ni— (NvosO Th osoo

t^O >^OCO00 M loO X>.00 O "J-'M toJr^trjM t^O t^l>-

CJN rooo ThN j>.i-i t-i-H 000 MIX Tt-roOS'^r< Thw ir-.vo
(siwioO'^roOOLoOrorO'^. O'-'i-'LoNDrorO'^
o

rOOO 10 CO O N O 00 M ■^00 fODsO i-isOOOCOOOOOJ^-lo
LO !>. roOO OsOO N fO Lo ■^ t^vo SO -^rir^oivo^ ■^ OsOO
MM MHiMroMMCOMtr) Mi-ii-it-i M M

NSO Osoo O 00 so 00 Lo N >-i OsOO H-i woo i-i\0 lOMVD OS

MfOi-iOOOroOi-iO'-i--i-i-<>HOMOMroOi-i

+ i I I II !+++++! I + 1 + 1 I I I

^N M N M c> r< N OsosOsOsCTsOsOsOsOsw >-i — w '^

§)00oocooocoooco t^t^t^t^t^j^-t^t^ t^co co 00 00 00

I I I ^1 — ji ^1 I I II — ^1 ^1 ^1 ^1 — II ii I 1 ^1 II II I

crj fO M 00 M 00 fOOO t^ O lo OS -"^ PO ro roOO lOCO ■^00 11

"osSO t^ J>-00 1>.\0 t~-00 00 00 00 O t^ t^OO so 00 so so i^ t>.

__ -_

ri wirj OS Os-^«o "^ co t^co ■<i-0

_3* ••* •** •••* .** .* ..* ..
vo •<j- Lo Trh vo -"^ Th t^ vo loco Th CO

"1 O CO c« OSOO O 10 -^sO loso mOOnioncoi-'MN

73 3

3 ,"= ci J<

B^
^

.i^t^uoncts.S.-tliiwoOcsraj-^^c

NIPHER — 5*J' ANN. KEP. MAGNETIC SURVEY OF MISSOURI.
TO Tj- tcvc t^OO O - " <■) ro ^ i^ ^■■O t^CO ON O " N ro 't- Lo t^CO «^ O ^ t-. O^

5, J

0\OMOM"-. OfOO-^ •^00 wOOOOOO OnO io<^ CnO >^00 m CO -^ ro "H CO -^

\D 00 rO'O fO rOOO VO m fO l^CO O ro t^ l-^ t^ f i VO CT\0 t^ -^ OMr~ f~0VO CO N 00 CO

On 0\ OnOO OOOOCOCOOOCCOOOOCOOO t^OD COOOOOCO i>.t^t^t^ t^MD MD NO t>- *>• t^
ONOf<Oc)i^OroOS'^ Tj-00 wCOOOCJO 0\0 "OCS OnO logo i-i CO -^ ro M CO ■<*■

row rOCJ fO-^'^Tt-O (S -rt-cots O'orO'-i •^m O ro■^■^'J^O rO-^O M m •<*•
OS On OnOO COOOOOOOOOOOOOOOOOOO t^OO OOOOCOOOt^t^t^t^ t^vO VO VO t^ t^ t^
VO O <^ rO -^00 t^ Ov Ov t>- ^OvO 00 -OvOO O t--vb M 6 OwO On i-< >-o ro O O »^ J>.VO
M Tt-\o MJ:^Oi-OOM^»^^'f»|-'i-iJ>-OM'* 'i-vo vO O O '- >^OvOM:-»tr""

loOO POVO OS J>-vO 00 -^00 CO CO 00 O O <■> ■^CO Ov On O CO CO <N "^ O\C0 OO CO CO Ov
i^M(-i t^Tj-t^LT-. ro'd-'NLot--r^X:^CVThTi- T^^o ro lo lo r^vO w-, lo lo tt -^ t^
M M r>r)i-irOfO""fO" MrO'-'Cirii-.rofON r<roror<(S«

t^t^ioOV" t^DTJ ■^I>- J>-T3 O Ov O 00 lo t^ LT) UTO M O ^oT! • '^ t^-vO
<U • • • (U 1) ...(Ij....

en tc tc <"■___

00>-"0'^0V"300'-ia MOrOCNO">-ii-i3 "-03 'OOQ

OOOOLoioO OCO iOOO^oOOOO ::ooo •ooo

ooooroovocoooc oooovooooc ooon -ooo
00 00 00 00 >-■ r^co o(»oooo5 000000 t^co cococoS cocoooo -oooooo

to C "2 fOVO ro t-» r) CO "^bW- 0\ 1--VO OOVOvOt^-P) OvO 'S- O^ >-< -^ t^vo lO Q

t>. O I>-vO 00 D t^ioOst^O OvOvrOt^'N t^DOO " " " rO t^vO t- ro lo t^ "^00
rO-^-^Hwiy^csOri^LO-^rO'-'O'^fO'Oi-iroi-HVoOrO'-i'^OMf^MM

^ J>. N Tj-oo u^vor^fSVOvOvOvOOOCO — rivOJ>" t^OO "~.vO O " lo^O-^ioiot^
LorirO"-OOi':oo ^loro COt^-t^O"". ^o^^r^ro CO t^vo vO vO "^' "OOO

ri r> cirii-i rO">- <-> rOfOi-ir<t^" P» nrOfONt^M

t^O^o^^Ot^i^Ot^O Oio (^ n 6 i^O t~-0 r^iot^LoLoiot^c^t^M i>.io

O 0\ l>.vO 0'N0O000"0M"0"-'00r0'-'')0M'"it^ 'i-vO "^ -"t-OO r) m
rfrO'^ts M LoroO N LOioi^-^-M i- roroio^-) rO" >00 ro— ■^O M M N ro

T^t^!^ tJ-oO inuiO pJvOvOvOvOCOOO ■-' fjvo t^ t>.00 vovO O w inioThtoiot»
lo M fO •- CO w-iCO J>-'*-Loro OOt^t^O'^LO'J^t^rO 00 l>.VO vO vO "1 lOOO

rq M Mts-i rOMM « roPO—onn M NcorOMMi-i

M 1-1 O f< •^Tj-X)0O "-' OV" •-' ro^O'^-rO'^'-i fO^oro— OV'*"" "^ t^vO VO 00 lo

fOi-iOOi-iOP>0"Mi-i>-iMNr<'-iO'-iN>-ii-ii-«oOP>OOQO>-irO

I + I I I I I + 1 I I I + r+ 1 I I I + 1 ++++++ 1 + 1

OvCvOvOvOvOvOvOvOnOvOvOv OvvO vCvOvOvOvOvOvOvOvOvOvOvOvOVOCOOOOO

M ^J1 CnOO N t^i^iOLO-^rorOI>-0vr0f^'i-0 '^OO ro C — CO t^OO O OS ^o t^ O
VO CO t^ t^ t^ t^vO 1^00 vO !>. t^vO CO vO CO t^ t^vo vO 00 t^CO X>-OD t^CO t^t^OOvO

53'

* * * *

***************

Ov O vO OvOvt^CO PI O 1-1 O O ■^ , O O 1-1 t^ ■-' 'o O t^OO lo Th lot-vO M ^O

<u

tn

^

r.

>

o

>^

c

c« J=

U

c « o

lO^i

,<j;z;pqi;QH<l(iH;>:>l^

o

ii • C 0) c

es •- -^ .-. c3 J2 -c S ° 5 ;> ^
pq S w tii hj ffi c/2 ^ h-l 13 ^ K

6 w

■^

B

O

Si

>iT3

a

0

en

532

TRANS. ST. LOUIS ACAD. SCIENCE.

l>-00 00 t-- t>.^0 \0 \0 lO "^ w-)\0 ICVO lO ^O lO lO ID "^ ''^

■+•■^"^■<j-4•■<5-^•4-'^4-'^'^'*-4-TJ-TJ-T^Tl-Ti-■<J-Tt-

vO00"i-ii-iO00O "-.\0 ro ro r» 00 OvO N OO fOOO •*
00 i-i (St^OO ■^Lori OsOfOO ■^vO wi ui -^ -^ O ■^
t^OO CO t^ t^ 1>.\0 \OvD Low-ivO^^ LOU-, ly^LOLow-)!/-,

666666666666d66666666

0\ fO <^ Cs\D CO r^vO N t^\0 (SOO^l^^^O^<00 lOOO
w rovo '-I rO Tj-oo CTn^ fO ro t^ ■^OO m On On OnOO ■<1-00

666666666666666666666

rocororocOi-iMioi-Hi-iOi-iNfONMnM'-ii-r)

M N r) M M (S (N fj n "^i r> n n M M M N M M fs r>
N n M n n (-1 M r« M n n D M r) M n M (S (S N 'I

DvOvOOO rot^roO '-i t-^t^-^O-^i-c w i-i f^ NVOOO 1>.

O >-> rr> rn -^ '^ i/-.\0 t^\0 00 OSMVO i01>.-" ioON'^CT\
VO -^ 1-1 VO ■* rOCO 00 O ro ro On roOO \0 1^.00 00 00 N OO

t- t^ r^ t-^ t^CO CO CO 0\ On OnCO On«) On On On On On O On
VOnOnOnOnOnOnOnOnOnOnOnONOnDnonO^nOnO t^NO

VOOO MNO >-> >^LoOOO t^iow (NVO t^i-< -^00 t--.NO NO
0000 OnOOOI^'- OnOOO n "-,nO 00 rO t^ on "".CO O >^
00 r^ t^co t^OOLri"0'~iO OnCO CTn On On On Q " O^
OnOnOnCJnOnO O OnO O O O C>On-OnOOnOnQ O On
OnOnOnOnOnO u OnO O O O CTnOnOnOnOnOnO O On

OnOnOnOnOnO O OnO O O O OnOnOnOnOnOnO O On

Tt-vo -^D inOnoCO t^M <"» -^nO t^ t(-nO 00 CO to n lo
rO'*-<"Orof^roror< rO'l-rorO-^-f-i roroiN •n mro^)
OOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOQQOOOO
OOOOOOOOOOOOOOOOOOOOO

6666666666666666

o c o o o

NO lo rooo nO^iCOin On'^"'- ONro OnnO r^ r^co t— w On
t^ t^ t^ t^ t^CO C/D ONCO ON ONCO ONCO On On On On On O On
nOnOnOnOnOnOVOnOvDnOnOnOnOnOnOnOVOnOnC 1>.\0

a,

lOOO NOOMi-iOMLo<^ONIOMJ>.m Ot^ LONO O

O tc
O ^
fe 1)

^■^ C

u iJ c
•- o ^

UC/3

<u » rt

> J- i aj

.= o.i: 3 iJ 53 o
W O -I < c« U S

> 3

o :;:

^ c -

' ' u o

i::; "C >^ cs r; c
o c ^£ i; (u

^ S S < mi^

o :?

^ u

C.2

ANN. REP. MAGNETIC SUKVEY OF MISSOURI. 533

00 -H

O <M

C» 00

'rt CD
lO CO

C-l CO 05 LTi

r-l 1-H I— 1— I ^^ (M <M

(M

O
(M

00

o

OiOiGidOiOiOiOiOiOiOiOi

en «

a

<
o
o

•u

Oi

rr,

,,

an

__

-+

r^

-M

,-,

CO

00

(M

w .

00

00

i~

1-

CM

Cvl

t^

I—

0

t^

0 «

t--

00

0

t-

lO

QC

1^

r^.

(M

0

a

■*

IJ -

00

iC

00

■ re

rr.

CO

0

00

0

00

0

00

u Hi

lO

t^

lO

t^

0

'^

CO

t--

CO

t^

CO

t^

0 -^

00

00

00

00

00

OD

00

OC'

00

00

00

00

0

-t

»o

«o

■^

"*

Tf

-+1

0

(M

0

r-

■*s|S

oo

t^

t^

05

a

05

05

t^

lO

r~

t^

c

-— .

0

0

0

0

0

0

0

0

0

0

+

0

(-%

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

M

0

0

0

0

0

0

0

0

0

0

0

0

CO
CO

CO

o

01

o ?o

C5 (M

O CO

-^ O

1— lO

CO 00

00

00

(^ lO o o
O l^ O I—

tO o
1^ o

lO o
I- o

iC o
I- o

(M 1— 1 C<l

CO

CO

-H

0

00

CO

(M

oc

Tt^

I— 1

r— 1

QO

rr?

CO

0

0

t—

1— 1

lO

'^

-^

t-

^

ire

00

00

Oi

as

r-

00

t-

t^

t^

l^

00

i^ ^_ 1— I -^ lO ic

^ __ (M (M

-a
o
o

o

a

w

0

c

0

■^

0

T)

<C s.

-fj

S

b!) ^

a

<-

a

0)

A

y

cH

534

TRANS. ST. LOUIS ACAD. SCIENCE.

INCLINATION, OR DIP.

Needle No 2.

STATION.

Marked End.

North.

South.

Means by Polarities.

Series I. Series II.

Resulting
Dip.

Date.

Kirkwood*..

Goebel's

Linn

Little Anxvasse Cr'k

Centralia

Moberly

Mercyville

Linneus

Wolfort's*

Kingston ■

Maysville

Albany

Bethany

Trenton

Princeton

Unionville

Milan

68^59;. 9

66^44;. 9

68 53

.4

69 18 .1

68 35

.0

68 58 .8

68 50

.6

69 19 ,5

69 26

.2

69 48 .2

65 25

.2

69 45 .4

69 54

.4

70 07 .5

69 51

.4

70 10 .0

70 41

.2

71 07 .4

70 04

.8

70 15 .4

69 34

.4

69 51 .9

70 04

•6

70 25 .4

70 04

.9

70 29 .0

70 04

.8

70 24 .8

70 13

.6

70 30 .0

70 23

.6

70 05 .4

70 05

.8

70 27 .9

G9°01;,
68 58 ,
68 39

68 54

69 44
69 30 .
69 .57

69 53

70 34
70 05

69 33

70 08 ,
70 12
70 04
70 16
70 20
70 10

r66°48;,8

6 69 12 .8

0'68 54 .7

5 69 15 .6

6 69 29 .6
l!69 37 .8
0 70 04 .8
0 70 08 .5
9 71 13 .7

70 14 .8

69 52 .5

70 21 .2
70 21 .9
70 25 .2
70 27 .4
70 08 .4
70 23 .4

67^52 i
69 05

68 46

69 05
69 37

69 35

70 00
70 00
70 54
70 10

69 43

70 15
70 16
70 14
70 21
70 14
70 16

June 17
" 22

" 27

'' 3a

July 5

" 7

" 11

" 15

" 20

" 22

" 24

" 26

" 27
.8 'Aug. 1

.8! " 2

.5 " 5

.8, " 8

* Some error.

Needle No.

STATION.

Marked End.

Means by

Polarities.

Resulting
Dip.

North.

South.

Series 1.

Series II.

69«34».7

69^^15 ;. 7 70 39 -.5

68''10;.9

69°25;.2

69 19 .1

68 48 .4 ' 68 15 .8

69 51 .6

69 03 .7

67 34 .8

68 43 .8 68 23 .5

69 55 .1

69 09 .3

69 ,54 .8

69 18 .8 68 44 .3

70 29 .3

69 36 .8

70 24 .6

69 36 .4 69 04 .4

70 56 .6

70 00 .5

70 21 .5

69 45 .2| 69 08 .8

70 57 .8

70 03 .4

70 03 .5

69 30 .5 69 33 .2

70 00 .8

69 47 .0

70 52 .9

69 59 .8 i70 27 .8

70 24 .9

70 26 .4

70 35 .6

69 55 .9

70 07 .4

70 24 .2

70 15 .8

Kirkwood

Goebel's

Little Auxvas.se Cr'k,

Moberly.

Mercyville

Linneus

Maysville

Bethany

Trenton

June 17
" 22
" 30

July 7
"11
" 15
" 24
" 27

Aug. 1

NIPHER EXPRESSION OF ELECTRICAL RESISTANCE, ETC. 535

On the Expression of Electrical Resistance in Terms
of a Velocity.

By Francis E. Nipher.*

If a spherical shell of radius r be charged with Q units of elec-
tricity, the density of electrification being- p ^ the force dF over
any element ds of its surface will be 2 k p^ds. This force is di-
rected radially outward, and is due to the action of the electrifi-
cation Q on the quantity pds upon the element.

If the radius r be diminished to r', the energy of the electri-
fication will increase if Q remains constant, this increase in
energy being due to work done on the sphere by some external
source, causing the sphere to collapse. If the element ds sweeps,
through a distance dr, the stored energy will be

dE = dFdr - - - (i)

in which both dF zxi^ dr are essentially negative.

Substituting in (i) the above value of dF and remembering

that P = — ,

and ds = r^ du ,

where dw is the solid angle subtended by the element ds., we have

dB = ^ ~^du

OTv r^

where one integration is carried over the surface of the sphere,
anJ the other is carried inwards between the limits r and r' .
Performing the integrations, we have

2

I r' r }

I O^
But— — is the energy of a sphere of radius r> ^ charged with

Q units of electricity, and hence the potential of the sphere on
itself between the limits r and r' is equal to the difference in its
initial and final energy.

If the sphere were connected with the ground, by a wire of re-
sistance (/?), the radius (r) might be changed in such a manner

* Read March 17th, 18S4.

r — r

536 TRANS. ST. LOUIS ACAD. SCIENCE.

as to preserve the potential ( F) constant. In this case a current
of constant intensity would flow through the wire, and as F= —
it is clear that r must change at a uniform rate, or

= /'-/ - - - (3)

where t' — / is the duration of the operation. Further,

Q 47rrV

K = -^= = 477r/j

r r

and V .

^^"^^^ dE=dFdr=2TT p2 dsdr= — drdo> ,

or V^ rr V^

B-B' =^jC/drdo>=-^ (r-r') . . (4)

This is the stored energy during the operation. But the energy
of the electrification at first was h r V^, and at the end is 2 r' V^,
so that there has nevertheless been a diminution of energy of

B — B'=~(r—r>) ... (5)

It appears that, under conditions of our experiment, the sphere
has less energy at the close of the experiment than at the begin-
nmg by a quantity — (r — r'), while the equal energy repre.

sented by the potential of the electrification on itself was added.
The total energy lost by the shell was, therefore,

jB = V^{r—r') - . - (6)

The current in the wire was, by Ohm's law,

dq_ F,
^- dt - ^ '
hence ^ ^ V

and hence the energy of the current during the operation was

or by (3), K' r-r' ■ _ _

R V ^''

The expressions (6) and (7) must be equal to each other, and

bence Rv = x , or /? = - ,

where v is the constant velocity of each point in the surface of the
shell during the operation.

i