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
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Diagram represenlinq the results (fDrEngelmanrCs .
1
fhcrm obs in SrT.ouis from lfi36to IRKZincL
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'
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.
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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
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TRANS. SI . LOUIS ACAD. SCIENCE.
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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
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