i

11

mm

SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE.

DISCUSSION

MAGNETIC AND METEOROLOGICAL OBSERVATIONS

MADE AT THE GIRAED COLLEGE OBSERVATORY, PHILADELPHIA,
IN 1840, 1841, 1842, 1843, 1844, AND 1845.

PART II.

INVESTIGATION OF THE SOLAR DIURNAL VARIATION IN THE MAGNETIC DECLINATION AND ITS

ANNUAL INEQUALITY.

BY

A. D. BACHE, LL. D.

[ACCEPTED FOR PUBLICATION, SEPTEMBER, I860.]

COLLIKS, PBINTEB.
PHILADELPHIA.

INVESTIGATION

SOLAR-DIURNAL VARIATION OF THE MAGNETIC DECLINATION,
AND ITS ANNUAL INEQUALITY.

HAVING discussed, in Part I, the eleven-year period in the amplitude of the
solar-diurnal variation, as well as in the disturbances of the magnetic declination,
I now proceed to the analysis of the annual inequality of the solar-diurnal
variation.

To obviate the difficulty which would occur in cases of months of unusal dis-
turbance, if the crude observations were used, the normals or means freed from the
disturbances have been employed in the discussion. This mode of proceeding not
only obviates the necessity for rejecting the observations of particular months, but
brings out the most consistent results which the observations can furnish, for both
diurnal and annual variation. It is the course adopted by General Sabine in the
third volume of his discussion of the Toronto observations.1

Returning, then, to the hourly normals, they are rearranged in the tables which
follow, according to the different months of the year. The normals for 1840 are
corrected for the index error by the addition of 93.3 scale divisions. All correc-
tions for referring the partial monthly readings to the annual mean are, of course,
omitted.

1 Table LXVI, of this volume, exhibits the solar-diurnal variation of the declination after the separa-
tion and omission of the larger disturbances ; whereas Table VII, of the preceding volume, similar in
form, differs from the latter, being derived from all the observations including the disturbances.

AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

HOURLY DECLINATION. NORMALS FOR JANUARY.*
Observations 19J minutes later than indicated. Valne of one scale division = 0'.453.
Increase of scale readings corresponds to a decrease of westerly declination.

TEAR.

Oh.

lh.

2h.

3h.

4h.

5b.

6k.

7h.

gh.

9h.

10h.

llh.

1840
1841
1842
1843
1844
1845

d.

579.3
564.3

558.6
530.9

d.

558'.2
531.3

d.

577.0
563.8

d.

d.

578'.6
565.3

d.

d.

576'.9
565.9

d.

d.

d.

d.

d.

...

580.7
570.9

...

581.9
566.4

...

558*4
531.1

559.2
531.5

558.9
533.0

558.8
531.6

559.7
532.9

561.2
535.2

562.9
535.8

563.3
533.8

559.1
530.2

555.9
526.7

Mean1

558.28

...

557.57

...

558.95

...

558.85

...

562.57! ...

559.40

...

Same refer'd
to its mean
epoch'

L565.25

564.80

564.35

565.62

565.70

564.66

565.47

567.74

569.27

569.51

566.65

561.88

TEAK.

Noon.

13h.

14h.

15i>.

16h.

17h.

18».

19h.

20h.

21h.

22h.

23h.

1840
1841
1842
1843
1844
1845

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

570.0
556.7

552.9
524.2

552.4
525.2

568.8
556.0
555.4
553.2
526.2

570.3
562.9

...

574.2
563.2

559.2
532.8

578.0
566.1

559.5
533.3

560.9
533.0

580.1

567.8

56o'.8
532.4

559.6
532.0

554.1
528.0

556.3
530.1

556.9
531.8

557.8
532.7

Mean'

550.95

...

551.92

554.90

...

556.97

...

559.22

...

560.27

...

Same refer'd
to its mean
epoch'

1557.72

557.31

557.55

558.97

561.20

562.41

563.38

564.82

565.90

567.00

567.20

566.35

1 The hours refer to mean local time, reckoned from midnight to 24 hours.

* The mean given is the simple mean of the four readings, and at 14h- of five readings, and is here inserted for
comparison with the corrected mean in the line below, which would have been obtained if there had been no omis-
sions in the observations.

' To obtain the normals referring to January of the mean year, the readings for the defective years 1840 and 1843
have been interpolated in the following manner : 1. For the even hours. — The normals for any two consecutive years
differ simply by the annual effect of the secular change, which may be regarded as uniform when the same hours
and months are compared, as in the present case. The values derived from the comparison of the several months
of any two years differ, however, by the accidental errors of the observations ; thus, taking the difference of the
normals for 1840 and 1841, we obtain for the several mouths the values —

June
July .
August

20.5
18.5

September

October

November

12.7

17.5

December

+20'J.0

Mean

16.86

Which mean corresponds exactly to the difference of the constant terms in Part I, for 1840 and 1841. By adding,
therefore, 16.9 scale divisions to the normals for 1841, we obtain interpolated values for 1840. The values from
January to May, 1840, were thus supplied. The normals for 1843 were supplied in a different manner, by making
use of the readings at 2 P. M., which were taken for the purpose of keeping up the continuity of the series. Sub-
tracting 0.6 scale division from the hourly readings of 1842, we obtain those for 1843 — this being the difference at
14h- ; in like manner, adding 2.2 scale divisions to the readings of 1844, we obtain a second value for the normals
of 1843. The mean of these two independent determinations has been used in supplying the readings for 1843.
The normals for 1840 and 1843 being thus supplied, the figures in the last line of the preceding table are obtained
by simply taking the mean of the six readings at each even hour. 2. For the odd hours. — The difference in the
mean readings for any given odd hour, in 1844 and 1845, from the two adjacent even hours, was applied to the
normals of these hours, and the mean taken as the normal of the intermediate odd hour. Thus, the mean
reading at noon of 1844 and 1845 is 538.55, at 13h , 538.80, difference +0.25; which, added to the noon normal
557.72, gives 557.97 ; and, in like manner, by comparison with 14h-, the correction to its normal is — 0.90, and the
normal for 13h- becomes 556.65. The mean of the two results, 557.31, is the resulting normal for this hour as given
in the table.

The same principle of interpolation was applied throughout the tables. Due attention must be paid, in the
deductions, for the unequal weight of the normals for the even and odd hours ; these weights being generally as
5 : 2, or proportional to the number of separate readings. The application of a nearly constant quantity to refer
means from a defective number of years to the mean epoch of all the years, is not of much consequence in regard
to the diurnal and annual inequalities, which depend mainly on differences of readings, but it is essential that no
changes should have occurred in the zero of the scale during any interval under discussion.

OF THE MAGNETIC DECLINATION.

HOURLY DECLINATION. NORMALS FOR FEBRUARY.
Observations 19i minutes later than indicated. One division of scale = 0.'453.

TEAR.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7h.

8h.

9h.

10h.

llh.

1840
1841
1842
1843
1844
1845

d.

575.0
564.5

559.1
531.6

d.

558.5
531.1

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

573.2
564.3

559.1
531.0

559.2
532.4

575.6
563.8

559.9
532.3

581.1
533.1

577.8
565.2

560.8
534.7

562.1
535.9

582.1
567.8

562.2
535.7

660.7
535.4

579.5
565.5

557.3
633.0

654.5

528.6

Mean

557.55

556.90

...

557.90

559.62

...

561.95

558.82

Same refer'd
to its mean
epoch

IMS ss

563.10

563.13

563.90

564.23

565.25

565.93

567.88

568.53

567.97

565.42

561.47

TEAR.

Noon.

13h.

14h.

15h.

16h.

17h.

18h.

19h.

20h.

21h.

22h.

23h.

1840
1841
1842
1843
1844
1845

d.

569.5

558.2

d.

d.

566.0
559.9
555.9

d.

d.

d.

d.

d.

d.

d.

d.

d.

569.5
558.0

572.4
561.9

557.6
632.4

558.4
531.3

574.4
565.3

...

575.8
565.5

...

551.1
524.4

551.1
523.0

553.0
525.3

554.7 556.4
527.5 i 529.7

556.6
530.4

559.9
533.6

559.4
534.4

560.1
532.3

559.0
531.9

Mean

550.80

...

552.02

553.40

...

556.07

558.30

558.42

Same refer'd
to its mean
epoch

uftTJS

555.85

557.17

558.30

559.43

560.25

562.13

562.25

564.42

565.02

564.77

564.00

HOURLY DECLINATION. NORMALS FOR MARCH.
Observations 19i minutes later than indicated. One division of •scale = 0'.453.

TEAR.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7h.

8h.

9h.

10h.

llh

1840
1841
1842
1843
1844
1845

d.

577.1
564.8

558.0
532.9

d.

559.0
532.7

d.

577'. 6
564.1

559.2
533.7

J-

d.

d.

d.

d.

d.

d.

d.

d.

557.9
533.6

580.9
565.4

559.8
535.0

...

582.9
566.1

586.8
571.8

564.1
538.6

578.9
565.9

560.3
534.5

554.9
529.4

560.2
533.9

561.3
536.0

663.6
538.8

564.8
539.4

Mean

558.20

558.65

560.27

...

561.58

...

565.70

...

559.90

...

Same refer'd
to its mean
epoch

Ues.eo

565.72

566.03

565.75

567.82

567.53

569.20

572.11

573.37

571.95

567.32

562.02

TEAR.

Noon.

13h.

14l>.

15».

16h.

17*.

18h.

19h.

20h.

2lh.

22h.

23h.

1840
1841
1842
1843
1844
1845

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

569.4
555.6

550.6

524.8

549.4
522.5

567.7
553.9
557.2
549.6
522.8

55 i. 7

524.8

571.8
556.4

553'.0

527.8

...

576.4
560.3

...

577.4
564.5

...

577.7
564.9

...

555.2
529.7

556.6
531.6

558.0
533.0

558.4
533.0

558.2
533.8

558.6
533.5

559.7
534.0

Mean

550.10

550.24

...

552.25

...

556.22

...

558.32

...

558.67

Same refer'd
to its mean
epoch

L557.52

555.75

555.97

557.75

559.63

561.85

563.68

565.31

565.75

566.04

566.08

566.94

AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

HOURLY DECLINATION. NORMALS FOR APRIL.
Observations 19J minutes later than indicated. One division of scale = 0'.453.

TEAS.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7h.

8h.

9h.

10h.

llh.

1840
1841
1842
1843
1844
1845

d.

d.

d.

d.

d.

582.9
566.1
571.0
557.5
529.8

d.

558.4
531.7

d.

585.6
568.5
574.7
561.7
534.0

d.

d.

d.

d.

d.

580.0
563.3
569.7
556.6
529.1

557'.0
528.8

581.9
565.4
570.0
557.2
529.0

556.9
529.2

558.5
535.6

587.6
569.7
576.2
564.4
537.5

56l'.8
535.4

579.4
563.6
566.2
557.1
528.5

552.0
522.5

Hera

559.74

560.70

...

561.46

...

564.90

567.08

...

558.96

Same refer'd
to its mean
epoch

IMS 93

566.42

567.05

567.12

567.85

568.31

571.17

569.90

373.32

570.98

565.18

559.76

TEAR.

Noon.

13h.

14h.

15h.

16h.

17h.

18h.

19h.

20h.

21h.

22h.

23h.

1840
1841
1842
1843
1844
1845

d.

568.8
554.0
557.8
547.4
517.8

d.

545.7
513.9

d.

566.1
552.5
555.7
546.2
514.0

d.

d.

d.

d.

d.

d.

d.

d.

d.

547'. 6
517.2

571.7
555.1
562.6
549.6
521.5

553.4

525.8

576.9
560.6
564.8
553.4

527.8

553.8
527.9

578.0
561.3
568.5
556.2

528.1

555.1

528.5

579.1
563.0
568.7
555.7
528.0

559.3
529.4

Mean

549.16

546.90

552.10

556.70

...

558.42

558.90

Same refer'd
to its mean
epoch

155525

552.54

552.92

555.13

558.18

562.05

562.88

563.16

564.50

564.59

565.08

567.50

HOURLY DECLINATION. NORMALS FOR MAY.
Observations K)J minutes later than indicated. One division of scale = 0'.453.

TEAR.

Oh.

lh.

2h.

3h.

4h.

|k.

6h.

7h-

8h.

9h.

10h.

llh.

1840
1841
1842
1843
1844
1845

d.

579.1
5d3.3
567.0
548.4
529.9

d.

548'.7
531.3

d.

579.8
564.3
567.3
547.8
529.7

d.

547.0
531.7

d.

581.9
566.0
569.6
549.3
533.2

d.

d.

d.

d.

d.

d.

d.

552.5
536.3

587.4
571.2
574.6
555.8
539.3

556.8
541.9

589.1
569.5
575.6
555.1
540.7

552.3
536.0

578.6
560.0
565.7
546.7
528.0

542.2
522.6

Mean

557.54

557.78

...

560.00

565.66

566.00

...

555.80

Samer fer'd
to its mean
epoch

Ussgs

565.16

564.27

564.72

566.47

569.28

572.10

574.01

572.67

569.07

562.42

557.72

TEAR. Noon.

13».

14h.

15h.

16h.

17h-

18h.

19h.

20h.

21h.

22h.

23h.

1840
1841
1842
1S43
1844
1845

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

547.8
530.3

569.4
552.6
556.0
538.3

517.1

535.8
516.8

567.9
552.3
556.2
536.5
518.9

I88.J

522.1

573.6
557.7
562.2
542.1
526.7

545.1
529.3

577.4
560.8
566.4
545.2
529.6

546.5
530.4

578.5
561.8
566.9
546.3
529.7

547.3
530.3

580.1
562.3
567.3
547.3
530.5

Mean j 546.68

546.36

552.46

...

555.88

556.64

557.50

Same refer'd ]
to its mean s-553.28
epoch

551.62

552.77

555.23

558.80

561.94

562.28

563.44

563.10

563.94

564.09

564.04

OF THE MAGNETIC DECLINATION.

HOURLY DECLINATION. NORMALS FOR JUNE.

Observations 19j minutes later than indicated. One division of scale = 0'.453.

YEAR.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7h.

8i>.

9h.

10h.

111".

1840
1841
1842
1843
1844
1845

d.

587.7
571.7
564.6
566.0
548.7
531.5

d.

549.0
531.7

d.

588.3
572.2
563.7
565.6
549.3
531.6

d.

549.1
532.0

d.

590.8
574.7
567.2
568.4
551.6
534.8

d.

553.9
537.9

d.

597.3
583.3
573.7
574.1
557.6
541.9

d.

559.1
543.5

d.
596.0
582.6
573.0
573.9
558.2
542.5

d.

554.3
538.6

d.
587.1
571.1
565.2
564.8
547.9
532.2

d.

541.8
524.9

Mean

561.70

561.78

564.58

571.32

...

571.03

561.38

Same refer'd
to its mean
epoch

}-

561.81

...

561.91

...

567.38

...

572.42

...

567.46

555.22

YEAR.

Noon.

13h.

14h.

15h.

16h.

17h.

18h.

19h.

20k

21k-

22h.

23h.

1840
1841
1842
1843
1844
1845

d.

578.8
561.6
555.1
556.4
537.4
521.3

d.

535.0
519.6

d.

576.7
560.3
552.5
556 0
537.3
520.0

d.

540.0
522.1

d.
581.2
565.0
558.3
561.1
542.4
525.4

d.

545.2
528.9

d.
586.1
570.1
561.8
564.3
545.6
530.3

d.

546.2
530.7

d.
585.8
570.9
563.7
564.0
546.5
530.1

d.

546.8
530.7

d.
586.9
570.8
f-64.1
565.6
548.0
530.3

d.

548.5
531.4

Mean

551.77

550.47

...

555.57

...

559.70 ...

560.17

...

560.95

...

Same refer'd
to its mean
epoch

}-

549.42

...

552.80

558.76

560.26

...

560.58

...

561.65

HOURLY DECLINATION. NORMALS FOR JULY.
Observations 19J minutes later than indicated. One division of scale = 0'.453.

YEAR.

Oh.

]h.

2h.

3h.

4h.

5h.

gh.

7h.

8h.

9h.

10h.

llh.

1840
1841
1842
1843
1844
1845

d.
590.6
569.9
566.0
566.9
549.0

d.

550.5

d

590.5
568.5
566.0
565.9
548.4

d.
549.4

d.

592.2
571.6
568.4
568.2
551.0

d.
554.3

d.

598.0
578.4
576.6
574.2
556.9

d.
559.8

d.

598.8
581.2
576.4
574.6
558.6

d.
554.8

d.

588.7
571.8
565.8
564.5
548.0

d.

540.8

Mean

568.48

567.86

570.28

576.82

...

577.92

567.76

Same refer'd
to its mean
epoch

Uei.77

563.26

561.15

562.07

563.60

567.16

570.02

572.67

571.23

567.61

561.00

535.47

»

YEAR.

Noon.

13h.

14h.

15h.

16l>-

17*.

18h.

19h.

20h.

21h.

22h-

23h.

1840

1841
1842
1843
1841
1845

d.
577.8
558.9
550.3
555.1
538.3

d.

535.5

d.

577.3
557.3
553.8
554.1
536.3

d.

53&'.8

d.

582.0
562.3
558.5
559.5
541.9

d.
544'. 5

d.

586.6
567.2
562.4
563.6
545.8

d.
546.2

d.
588.8
568.8
564.2
563.8
546.6

d.

547'.4

d.

589.6
568.6
567.1
565.6
5J8.8

d.

549.3

Mean

557.28

555.76

560.84

565.12

566.44

567.94

Same refer'd "I
to its mean j-550 65
epoch

548.05

549.05

551.33

554.22

556.98

1
558.43

t

559.05

559.67

560.18

561.28

561.97

AMPLITUDE OF THE S OL A Il-DI U II N A L VARIATION

HOURLY DECLINATION. NORMALS FOR AUGUST.
Observations 19J minutes later than indicated. One division of scale = 0'.453.

YEAR.

Oh.

lh.

2h.

3t>.

4h.

M

6l>.

7h.

8h.

9h.

iou.

llh.

1840
1841
1842
1843

1844
1845

d.

588.6
568.4
564.8
564.2
548.6

d.

547'. 8

d.
589.0
570.3
566.0
564.5
547.3

d.
547.4

d.
592.1
571.6

568.5
267.2
550.9

d.
552'.4

d.
599.7
580.1
573.7
573.5
557.5

d.
560.3

d.
602.4
583.9
575.0

572.7
558.2

d.

ss'i'.s

582'.7
568.9
560.0
560.5
543.3

d.

536.4

Mean

566.92

567.42

...

570.06

576.90

578.44

563.08

Same refer'd
to its mean
epoch

1560.40

559.85

560.60

560.80

563.40

565.00

570.20

573.35

571.60

565.01

556.32

549.14

YEAR.

Noon.

13h.

14h.

15h.

16''.

17h.

18h.

19h.

20t.

21h.

22'i.

23ii.

1840
1841
1842
1843
1844
1845

d.
573.8
558.3
552.3
555.1
531.8

a.
532.0

d.

575.2
556.9
553.7
554.6
534.3

d.
538'. 7

d.

581.5
564.0
561.5
561.2
542.1

d.
544.3

d.

586.5
566.8
562.2
563.6
546.0

d.

546.5

d.
588.2
568.6
564.1
562.3
546.7

d.
546.6

a,

589.4
568.9
564.5
564.2
547.8

d.

547.7

Mean

554.26

-

554.94

562.06

...

565.02

...

565.98

...

566.96

...

Same refer'd
to its mean
epoch

1547 05

546.49

548.03

552.15

555.27

557.12

558.38

558.99

559.30

559.15

560.30

559.85

HOURLY DECLINATION NORMALS FOR SEPTEMBER.
Observations 19J minutes later than indicated. One division of scale = 0'.453.

YEAR.

Oh

lh.

2h.

3h.

4h.

|k.

6h.

7h.

8h.

9h.

10h.

llh.

1840
1841
1842
1843
1844
1845

d.

585.8
565.1
567.4
5B0.4
543.3

d.

543.1

d
588.5
564.5
567.8
560.4
544.1

d.
546.0

d.
590.2
565.5
570.0
560.3
546.5

d.

547.1

d.
596.5
569.4
576.8
565.7
550.0

d.
552'.9

d.
595.8
571.1
574.9
566.6
552.4

d.

545.8

d.
584.1
564.1
561.2
554.6
538.3

d.
532.5

Mean

564.40

565.06

...

566.50

...

571.68

...

572.16

...

660.46

Same refer'd
to its mean
epoch

L557 42

557.16

558.10

559.60

559.70

561.00

564.60

566.70

565.40

559.80

553.30

547.47

YEAR.

Noon.

13h.

14h.

15>i.

16h-

17h.

18i>.

19''.

20h.

21h.

22h.

23i».

1840
1841
1842
1843
1844
1845

d.
570.6
553.6
556.0
547.5
529.3

d.
530.0

d.
572.8
554.5
555.4
550.5
534.1

d.

538.3

d.
581.7
559.5
562.0
556.8
539.4

d.
541.9

d.
58:3.2
562.9
565.7
558.0
542.4

d.

541.9

d.

586.6
563.8
566.7
560.0
543.0

• d.
544-. 6

d.

585.9
564.0
566.6
558.7
543.7

d.

543'. 3

Mean

551.40

...

553.46

559.88

562.44

...

564.02

563.78

Same refer'd
to its mean
epoch

[544.25

543.81

546.77

551.44

553.00

555.31

555.63

556.04

557.05

558.26

556.97

557.00

OF THE MAGNETIC DECLINATION.

HOURLY DECLINATION. NORMALS FOR OCTOBER.

Observations 19J minutes later than indicated. One division of scale = 0'.453.

TEAR.

Oh-

lh.

2h.

3i>-

4h.

5h.

6h.

7h.

8h.

9".

lOti.

Hh.

1840
1841
1842
1843
1844
1845

d.

585.8
566.8
563.1
559.6
545.1

d.

560.2
545.3

d.

583.7
566.3
563.1
559.6
544.2

d.

559.1
546.1

d.
584.4
565.5
564.4
559.9
545.8

d.

560.6
544.4

d.
582.4
567.6
566.0
562.1
548.6

d.

565.1
550.9

d.
582.5
569.4
568.8
566.0
551.5

d.

565.0
548.7

d.

577.4
568.2
564.0
560.8
545.3

d.

556.5
540.8

Mean

564.08

...

563.38

564.00

...

565.34

567.64

563.14

...

Samerefer'd
to its mean
epoch

155745

557.71

556.72

557.33

557.50

556.67

559.08

561.23

561.48

560.04

556.70

552.36

TEAR.

Noon.

13h-

14h.

15h.

16h.

17h.

18h-

19h.

20h.

2lh.

22h.

23h.

1840
1841
1842
1843
1844
1845

d.

571.7
564.0
556.0
553.6
541.1

d.

552.6
539.5

d.
570.6
562.3
555.0
552.7
541.4

d.

554'. 2
544.0

d.
575.2
564.7
558.2
556.2
545.7

d.

557.0
545.4

d.

579.6
573.5
564.3

558.2
545.6

d.

559.7
545.0

d.
579.0
568.6
565.0
560.1
544.9

d.

561.1
544.6

d.

586.4
569.3
565.3
559.7
544.5

d.

560.7
544.6

...

...

Mean

557.28

...

556.40

...

560.00

...

564.24

...

563.56

...

565.04

...

Same refer'd
to its mean
epoch

L551.12

549.62

550.43

552.39

554.15

555.68

557.67

557.47

556.98

558.12

558.15

558.22

HOURLY DECLINATION. NORMALS FOR NOVEMBER.

Observations 19J minutes later than indicated. One division of scale = 0'.453.

YEAR.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7"-

8h.

9h.

10h.

lib.

1840
1841
.1842
1843
1844
1845

d.
574.4
557.2
564.2
556.3
546.8

d.

556.7
546.8

573.9
558.5
563.8
556.6
548.3

d.

556.6
548.6

576'.2
558.5
565.6
557.4
547.4

d.

557.4
548.5

d.

577.0
557.6
566.9
559.1
551.5

d.

sei.s

549.2

d.

579.7
561.7
569.2
561.3

548.4

d.

560.1
547.9

d.
575.0
557.1
563.3
556.2
546.2

d.

552.6
542.8

Mean

559.78

...

560.22

...

561.02

...

562.42

564.06

...

559.56

...

Same refer'd
to its mean
epoch

L554.15

554.21

554.77

555.20

555.28

555.30

557.13

557.98

557.98

556.90

553.87

550.00

TEAK.

Noon.

13h.

14h.

15h-

16h.

17h.

18i».

19t>.

2Qh.

21h.

22h.

23k.

1840
1841
1842
1843
1844
1845

567.5
551.8
556.6
550.4
542.8

3.

550.0
541.7

d.

565.8
549.9
557.3
551.1
544.5

d.

552.6
546.1

d.
570.8
553.4
561.2
553.8
545.6

d.

554.9
547.9

d.
574.1
554.9
564.0
556.3
548.8

d.

fl57'.5
548.2

d.

576.9
558.0
565.5
557.5
548.3

d.

557'. 7
549.6

d.
576.0
558.6
565.0
557.3
548.0

d.

557.4
548.0

Mean

553.82

...

553.72

...

556.96

...

559.'62

561.24

...

560.98

Samerefer'd
to its mean
epoch

1.548.52

547.32

548.72

550.76

551.60

553.25

554.35

555.26

555.62

556.36

555.35

555.35

8

AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

HOURLY DECLINATION. NORMALS FOR DECEMBER.
Observations 19J minutes later than indicated. One division of scale = 0'.453.

YEAR.

Oh-

lh.

£h.

gb.

4h.

5h.

6h.

7h.

gh.

»k.

10h.

Hh.

1840
1841
1842
1843
1844
1845

d.
571.2
560.1
561.7
559.0
536.1

d.

558'.!
535.8

d.

568.5
559.3
560.7
557.4
535.4

d.

558.2
535.9

d.

573.1
560.5
562.1
557.8
536.8

d.

558.8
537.3

d.

572.8
559.6
562.7
560.0
537.2

d.

560.8
536.8

d.

573.8
560.1
565.5
561.2
537.9

d.

561.9
539.3

d.

573.9
558.1
564.2
559.9
536.1

d.

556.7
532.9

Mean

557.62

556.26

...

558.06

...

558.46

...

559.70

...

558.44

...

Same refer'd
to its mean
epoch

1550 57

549.92

549.32

550.38

551.05

551.35

551.45

551.75

552.60

553.75

551.25

547.78

TEAK.

Noon.

13h.

14h.

15k.

16t.

17h.

18k-

191-.

20h.

2lh.

22h.

23i>.

1840
1841
1842
1843
1844
1845

d.
564.0
552.9
556.6
552.9
530.6

d.

551.4
529.3

564^9
551.7
556.2
550.9
529.4

d.

553.1
532.1

d.
566.0
555.8
560.1
554.6
533.2

d.

557.5
534.8

d.

571.8
559.6
562.0
558.2
535.9

d.

558.9
537.0

d.

572.3
563.3
563.5
559.6
536.8

d.

560.0
537.4

d.
574.5
561.6
563.8
559.9
537.8

d.

559.5
537.1

Mean

551.40

...

550.62

...

553.94

557.50

...

559.10

...

559.52

...

Same refer'd
to its mean
epoch

L544.47

543.45

543.62

546.35

547.02

549.40

550.43

551.50

551.92

552.35

552.43

551.60

The following table contains the recapitulation of the monthly normals for each
hour of the day, and for the mean epoch 1842 to 1843, and forms the basis for the
discussion of the diurnal variation and its annual inequality. The table exhibits
at one view the mean hourly readings for each month, unaffected by the larger dis-
turbances.

OF THE MAGNETIC DECLINATION.

RECAPITULATION. — MONTHLY DECLINATION- NORMALS FOR EACH HOUR OF THE DAY, AND FOR THE

MEAN EPOCH 1842-43.

Increasing scale divisions

denote

an easterly movement of the north end of the magnet. The readings belong

to an hour 19J minutes

later than indicated by the figures at the head of the columns. Value of a scale

division = 0'.453. Readings derived from five years of observation between 1840 and 1845.

PHILADELPHIA MEAN TIME.

MEAN EPOCH
J842-13.

Oh.

lh.

2h.

3i.

4h.

5h.

61-

7h.

8*-

9h-

10t>-

Hh.

d.

d.

A

d.

d.

d.

d.

d.

d.

d.

d.

d.

January

565.25 564.80

564.

35

565.62

565.70

564.66

565.47

567.74

569.27

569.51

566.65

561.88

February

563.88 563.10

563.

13

563.90

564.23

565.25

565.93

567.88

568.53

567.97

565.42

561.47

March

565.60 . 565.72

566.

C3

565.75

567.82

567.53

569.20

572.11

573.37

571.95

567.32

562.02

April

565.93 566.42

567.

OS

567.12

567.85

568.31

571.17-

569.90

573.32

570.98

565.18

559.76

May

563.95 565.16

564.

•11

564.72

566.47

569.28

572.10

574.01

572.67

569.07

562.42

557.72

June

561.70 561.81

561.

78

561.91

564.58

567.38

571.32

572.42

571.03

567.46

561.38

555.22

July

561.77 : 563.26

561.

15

562.07

563.60

567.16

570.02

572.67

571.23

567.61

561.00

553.47

August

560.40 559.85

560.

60

560.80

563.40

565.00

570.20

573.35

571.60

565.01

556.32

549.14

September

557.42 557.16

558.

10

559.60

559.70

561.00

564.60

566.70

565.40

559.HO

553.30

547.47

October

557.45 557.71

556.

7:2

557.33

557.50

556.67

559.08

561.23

561.48

560.04

556.70

552.36

November

554.15 554.21

454.

77

555.20

555.28

555.30

557.13

557.98

557.98

556.90

553.87

550.00

December

550.57 549.92

549.

32

550.38

551.05

551.35

551.45

551.75

552.60

553.75

551.25

547.78

JlEAS EPOCH
1842-43.

Noon.

131'.

14h.

15h.

16h.

17h.

18*.

19h.

20t>-

21h.

22h.

23h.

Mean.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d

January

557.72

557.31

557.55

558.97

561.20

562.41

563.38

564.82

565.90

567.00

567.20

566.35

564.20

February

557.33

555.85

557.17

558.30

559.43

560.25

562.13

562.25

564.42 565.02

564.77 564.00

562.98

March

557.52

555.75

555.97

557.75

559.63

561.85

563.68

565.31

565.75 566.04

566.08 566.94

564.86

April

555.25

552.54

552.92

555.13

558.18

562.05

562.88

563.16

564.50 564.59

565.08 567.50

564.03

May

553.28

551.62

552.77

555.23

558.80

561.94

562.28

563.44

563.10

563.94

564.09

564.04

563.18

June

551.77

549.42

550.47

552.80

555.57

558.76

559.70

560.26

560.17

560.58

560.95

561.65

560.84

July

550.65

548.05

549.05

551.33

554.22

556.98

558.43

559.05

559.67

560.18 561.28 561.97

560.24

August

547.05

546.49

548.03

552.15

555.27

557.12

558.38

558.99

559.30

559.15 560.30 i 559.85

559.07

September

544.25 543.81

546.77

551.44

553.00

555.31

555.63

556.04

557.05

558.26 1-556.97 ' 557.00

556.07

October 551.12 549.62

550.43

552.39

554.15

555.68

557.67

557.47

556.98

558.12 558.15 558.22

556.43

November 548.52;547.32

548.72

550.76

551.60

553.25

554.35

555.26

555.62

556.36 555.35

555.35

553.97

December

544.47 543.45

543.62

546.35

547.02

549.40

550.43

551.50

551.92

552.35

552.43

551.60

549.82

Mean

559.64

This table shows plainly the relation of the mean hourly position of the magnet
of each month to its general mean position, after the separation of the larger dis-
turbances, and also, by running the eye along any horizontal line, the solar-diurnal
variation for each month. It does not, however, show distinctly the annual in-
equality, on account of the changes in the numbers by the secular change. To
eliminate the effect of this change, each hourly normal has been compared, in the
following table, with the corresponding mean monthly value, as given in the last
right-hand column ; the sign + indicating a westerly direction, and — an easterly
direction,1 of the- north end of the magnet from the mean monthly position. The
scale divisions have been converted into minutes of arc.

1 The sign -f being generally taken to signify west declination, it has been retained to indicate a
movement of the north end of the magnet to the west.

10

AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

TABLE OF

THE SOLAR DIURNAL VARIATION or THE MAGNETIC DECLINATION FOR EACH MONTH OF

THE YEAR, SHOWING THE ANNUAL INEQUALITY.

Observations 19} minutes later than indicated in the headings.

PHILADELPHIA MEAN TIME.

MKAK EPOCH
1842-43.

Oh.

lh.

2h.

3h.

4h.

5h-

6h.

7V

gk.

9h.

10*-

llh.

January

— 0'.47

— 0'.27 — 0'.07

— 0'.64

— 0'.68

— 0'.21

— 0'.57

— I'.ei

— 2'.29

— 2'.40

— I'.ll

+1'.06

February

—0.41

—0.06

—0.07

—0.42

—0.56

—1.03

—1.34

—2.22

—2.51

—2.26

—1.11

+0.68

March

—0.34

—0.39

—0.53

—0.40

—1.35

—1.21

—1.97

—3.28

—3.85

—3.21

—1.12

+1.29

April

—0.86

—1.09

—1.37

—1.40

—1.73

—1.94

—3.24

—2.65

—4.21

—3.15

—0.50

+1.93

May

—0.35

—0.90

—0.49

—0.70

—1.49

-2.77

—4.04

—4.90

—4.30

—2.66

+0.35

+2.47

June

—0.39

—0.44

—0.43

—0.48

—1.70

—2.97

—4.75

—5.25

—4.62

—3.00

—0.25

+2.54

July

—0.68

—1.37

—0.41

—0.82

—1.53

—3.18

—4.44

—5.63

—4.98

—3.34

—0.35

+3.07

August

—0.60

—0.36

—0.69

—0.78

—1.96

—2.68

—5.03

—6.47

—5.68

—2.69

+1.25

+4.50

September

—0.61

—0.49

—0.92

—1.60

—1.64

—2.23

—3.86

—4.81

—4.23

—1.69

+1.26

+3.89

October

—0.46

—0.58

—0.13

—0.41

—0.48

—0.10

—1.20

—2.17

—2.28

—1.63

—0.12

+1.84

November

—0.09

—0.11

—0.36

—0.55

—0.59

—0.60

—1.44

—1.81

—1.81

—1.33

+0.05

+1.80

December

—0.34

—0.05

+0.23

—0.26

—0.55

—0.69

—0.73

—0.87

—1.27

—1.78

—0.64

+0.93

Summer

—0.58

—0.78

—0.72

—0.96

—1.68

—2.63

—4.23

—4.95

—4.67

—2.76

+0.29

+3.07

Winter

—0.35

—0.24

—0.16

—0.45

—0.70

—0.64

—1.22

—1.99

—2.33

—2.10

—0.67

+1.27

Year

—0.47

—0.51

—0.44

—0.71

—1.19

—1.64

—2.72

—3.47

—3.50

—2.43

—0.19

+2.17

MEAW EPOCH
1812-43.

Noon.

13h.

14h.

15h-

161".

17h.

18k.

19ii.

20h.

21h.

22h.

23t>-

January

+2'.94

+3'.12

+3'.01

+2'.36

+ 1'.36

+0'.81

+0'.37

— 0'.28

— 0'.77

— 1'.27

— 1'.36

— 0'.98

February

+2.55

+3.23

+2.62

+2.12

+1.61

+1.24

+0.38

+0.33

—0.65

—0.93

—0.81

—0.46

March

+3.33

+4.13

+3.02

+3.22

+2.36

+1.36

+0.53

—0.20

—0.40

—0.54

—0.55

—0.95

April

+3.98

+5.20

+5.02

+4.03

+2.64

+0.90

+0.52

+0.39

—0.21

—0.26

—0.47

—1.57

May

+4.49

+5.24

+4.71

+3.60

+1.99

+0.56

+0.41

—0.12

+0.04

—0.35

—0.41

—0.39

June

+4.11

+5.16

+4.70

+3.64

+2.38

+0.95

+0.51

+0.27

+0.30

+0.12

—0.05

—0.36

July

+4.35

+5.53

+5.07

+4.03

+2.73

+1.47

+0.81

+0.53

+0.26

+0.03

—0.47

—0.78

August

-5.45

+5.71

+5.00

+3.14

+1.72

+0.88

+0.32

+0.04

—0.10

—0.04

—0.56

—0.36

September

-5.35

+5.56

+4.17

+2.09

+ 1.39

+0.35

+0.20

+0.01

—0.45

—1.00

—0.41

—0.42

October

-2.40

+8.08

+2.72

+1.83

+ 1.04

+0.35

—0.56

—0.47

—0.25

—0.76

—0.78

—0.81

November

-2.46

+3.01

+2.37

+1.45

+1.08

+0.33

—0.18

—0.59

—0.74

—1.09

—0.63

—0.63

December

+2.42

+2.89

+2.81

+1.57

+1.27

+0.19

—0.27

—0.76

—0.96

—1.15

—1.18

—0.81

Summer

+4.62

+5.40

+4.78 ! +3.42

+2.14

+0.85

+0.46

+0.19

—0.03

—0.25

—0.40

—0.65

Winter

+2.68

+3.24

+2.76 +2.09

+1.46

+0.71

+0.05

—0.33

—0.63

—0.95

—0.88

—0.77

Year

+3.65

+4.32

+3.77 +2.76

+1.80

+0.78

+0.25

—0.07

—0.33

—0.60

—0.64

—0.71

The distinctive features of the above table are next to be considered analytically
as well as graphically. The inequality in the diurnal variation is most conspicuous
when the tabular numbers in the horizontal lines for the months of February and
August are compared. The annual variation appears plainest by carrying the eye
over the vertical column at the hours 6 or 7 A. M. The annual variation depends
on the earth's position in its orbit ; the diurnal variation being subject to an in-
equality depending on the sun's declination. The diurnal range is greater when
the sun has north declination, and smaller when south declination ; the pheno-
menon passing from one state to the other about the time of the equinoxes. To
show the diurnal variation at these periods, the summer and winter means, as well
as the annual means, were tabulated. The months from April to September (in-
clusive) comprise the summer period, and from October to March (inclusive) the
winter period. The first diagram (A) shows this variation, and contains the type
curves for these half yearly periods. We find for the summer months a diurnal
range of nearly lOi minutes, and for the winter months of but 5i minutes. These
and other curves will be further analyzed hereafter.

OF THE MAGNETIC DECLINATION.

11

(A). — MEAN SOLAR-DIURNAL VARIATION OP THE DECLINATION POB SUMMER, WINTER, AND THE WHOLE YEAH.
West /v

JJ/ — j • i i i i • i -A ' ii

4
3
2
1
0
1
2
3
4

-i — i — r

**
Normal fine of

in, a

-r

£///

w

II [the declination.

East Oh- 1 2 3 4 5 6 7 8 9 10 11 N'n 13 14 15 16 17 18 19 20 21 22 23 42t>.

Philadelphia mean time.

The second diagram (B) exhibits the same phenomenon in a different way ; the
yearly curve of the first diagram being straightened out and forming the axis of
the second diagram, which thus shows the deviations from the annual mean value
for the two seasons when the sun has north and south declination. The ordinates
are obtained by subtracting the annual mean from either the summer or winter
mean in the preceding table. This diagram exhibits, in quite a characteristic
manner, the course of the annual variation at the different hours of the day, at

(B). — SEMI-ANNUAL IBREOULABITIES OP THE SOLAB-DIUKNAL VARIATION OF THE DECLINATION.

a
West

-

^

-

: <

r\

•

1

1

\

/— ' \

4 /

\

i

\

: 4Jy

\

1

\

.

mear/n. \

f/Mrtial varA

ffo\/'~

"v-

N v

J

/X--

— -*w.-^'"

- \

!/

V. \

/

-

1

\ //

S

itw£./

-

East

i,ii

, , , ,

r f i i

1 1 1 1

Philadelphia mean time.

12

AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

the season for which the diagram is constructed. Thus, at the hour of 6 or 7 in
the morning, the annual variation is a maximum, disappearing at a quarter before
10 A. M., and reaching a second (secondary) maximum value at 1 P. M. It
almost disappears soon after 5 P. M., and a third still smaller maximum is reached
after 9 P. M. Half an hour before midnight, the annual variation again disap-
pears. At (and before and after) the principal maximum, between 6 and 7 in the
morning, the annual variation causes the north end of the magnet to be deflected
to the east in summer and to the west in winter; at 1 P. M., the deflections are to
the west in summer and to the east in winter. The range of the diurnal motion
is thus increased in summer and diminished in winter ; the magnet being deflected
in summer more to the east in the morning hours, and more to the west in the
afternoon hours, or having greater elongations than it would have if the sun moved
in the equator. In winter, the converse is the case. The range of the annual
variation from summer to winter is about 3'.0, and its daily range about 2'.6 at
Philadelphia.

(C). — COMPARATIVE DIAGRAM OF THE SEMI-ANNUAL DEFLECTION OF THE SOLAK-DIURNAL VARIATION.

9 Noon 15
Mean local time.

21 24h. Oh.

9 Noon 15
Mean local time.

18 21 24t.

The next diagram (C) has been projected in order to illustrate the semi-annual
inequality of the diurnal variation at four principal magnetic stations.1 The
general features of the Philadelphia curve most nearly resemble those exhibited
in the St. Helena curve ; and, relatively, the Toronto and Hobarton curves appear
to represent rather extreme than normal shapes. The Philadelphia and St. Helena

1 The annual variation of the diurnal motion has been made the subject of a particular discussion by
General Sabine, in papers presented to the British Association and the Royal Society. See Reports of
the British Association, 1854, pp. 355-368, and Transactions of Royal Society, May 18, 1854, pp.
67-82; also, article XXVIII, Philosophical Transactions, 1851.

OF THE MAGNETIC D INCLINATION.

13

curves have another feature in common : the amplitude at its maximum value,
shortly after 6 A. M., is less than the amplitude at Toronto and Hobarton ; and,
upon the whole, the Philadelphia type confirms the idea that all forms partake of
the same general character, more or less affected by incidental irregularities.

In reference to the annual variation, General Sabine, in the "rectifications and
additions" to the last volume of Hurnboldt's Cosmos, expresses himself as follows:
"Thus, in each hemisphere, the semi-annual deflections concur with those of the
mean annual variation for half the year, and consequently augment them, and oppose
and diminish them in the other half. At the magnetic equator, there is no mean
diurnal variation, but in each half year the alternate phases of the sun's annual in-
equality constitutes a diurnal variation, of which the range in each day is about 3'
or 4', taking place every day in the year except about the equinoxes ; the march of
this diurnal variation being from east in the forenoon to west in the afternoon,
when the sun has north declination, and the reverse when south declination."
According to the same authority, the annual variation is the same in both hemi-
spheres, the north end of the 'magnet being deflected to the east in the forenoon,
the sun having north declination; when in the diurnal variation, the north end of
the magnet at that time of the day is deflected to the east in the northern hemi-
sphere and to the west in the southern hemisphere. In other words, in regard to
direction, the law of the annual variation is the same, and that of the diurnal
variation the opposite, in passing from the northern to the southern magnetic
hemisphere.

I next proceed to consider more in detail the annual variation at the hours of
6 and 7 in the morning and of 1 and 2 in the afternoon, these being the hours of
the principal and secondary maxima respectively. By subtracting the annual
mean from each monthly value at the respective hours, we obtain from the preced-
ing general table the following columns : —

ANNUAL VARIATION AT THE HOURS OF THE PRINCIPAL AND SECONDARY MAXIMA OF RANGE.
' 1 indicates j ™^ 1 deflection from the mean annual position.

6h. A. M.

7h- A. M.

Mean.

lh- P. M.

2h. p. M.

Mean.

+2'.15
+1.38
+0.75
—0.52
—1.32
—2.03
—1.72
—2.31
—1.14
+1.52
+1.28
+1.99

+1'.86
+1.25
+0.19
+0.82
—1.43
—1.78
—2.16
—3.00
—1.34
+1.30
+1.66
+2.60

+2'.01
+1.31
+0.47
+0.15
—1.38
—1.90
—1.94
—2.66
—1.24
+1.41
+1.47
+2.30

— 1'.20
—1.09
—0.19
+0.88
+0.92
+0.84
+1.21
+1.39
+1.24
—1.24
—1.31
—1.43

-0'.76
—1.15
—0.75
+1.25
+0.94
+0.93
+1.30
+1.23
+ 0.40
—1.05
—1.40
—0.96

— 0'.98
—1.12
—0.47
+1.06
+0.93
+0.89
+1.25
+1.31
+0.82
—1.14
—1.35
—1.20

May

July

Maximum range at the above hours,
5'.0 ; the easterly deflection being greater
by 0'.4 than the westft-ly.

Range at the hours 1 and 2 P. M., 2'. 7 ;
the eastern and western deflections being
equal.

A general inspection of the above columns containing the mean values shows
that, approximately, the solstices are the turning epochs of this annual variation,

14 AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

the signs changing at the time of the equinoxes. To ascertain how nearly this is
true, and in order to obtain a more precise expression, the means of the two columns
(after changing the signs in the second) for each month respectively, were put into
an analytical form, using Bessel's well-known formula for periodic functions —

Aa = +l'.78 sin (e + 90°) + 0'.32 sin (29 + 180°) ;
or, Aa = -f 1'.78 cos e — 0'.32 sin 29 ;
the angle 6 counting from January 1st.

The maximum values will occur on the first of January and the first of July;
and the transition from a positive to a negative value, and the reverse, will take
place on the first of April and the first of October, the equation 1.78 cos 6 = 0.32
sin 2 S, being only satisfied for 0 = 90° and 270°. That the angles <7, and Ca
should be exactly 90° and 180° is remarkable. The monthly values are satisfied
as follows : —

Middle of By observation. By calculation.

January + 1'.50 + 1'.56

February +1.22 +0.94

March +0.47 +0.30

April —0.46 —0.30

May . . . . . . . . —1.16 —0.94

June —1.40 —1.56

July —1.59 —1.56

August — 2.00 — 0.94

September — 1.03 — 0.30

October +1.28 +0.30

November +1.41 +0.94

December +1.76 +1.56

The regular progression of the monthly values is a feature of the annual varia-
tion deserving particular notice. There is no sudden transition from the positive
to the negative side, or vice versd, at or near the time of the equinoxes (certainly
not at the vernal equinox) ; on the contrary, the annual variation seems to be
regular in its progressive changes. The method here pursued is entirely different
from that employed by General Sabine for the same end, but the results are, never-
theless, in close accordance. He remarks (in the British Association report above
cited): "When a mean is taken corresponding to the 10th or llth day after the
equinox, the transition from the character of the preceding six months has already
commenced and advanced very far towards its completion, and, by the middle of
October, is quite complete; apparently, the progress of the change is somewhat
more tardy in the March than in the September equinox." From the above an-
alysis, we have found that the transition took place ten days after either equinox,
and also that the turning points occur ten days after the solstices.

For the more precise determination of the law of the phenomenon, and in order to
render the results of similar investigations comparable with one another, the regular
solar-diurnal variation is now to be expressed as a function of the time. The pre-
ceding tabular values, given in minutes of arc, when treated as required by Bessel's1
periodic function, furnish the following expressions for each month of the year: —

1 For another development of the formula, see Rev. Dr. H. Lloyd, " On the Mean Results of Obser-
vations," Transactions Royal Irish Academy, 1848, Vol. XXII, Part I. Dublin, 1849.

OF THE MAGNETIC DECLINATION. 15

For January, Ad = + 1'.423 sin (15 n + 225° 09') + 1'.491 sin (30 n + 16° 38')

+ 0'.579 sin (45 n + 220° 23') + 0'.548 sin (60 n + 53° . . )
For February, A<J = +1'.469 sin (15 n + 211° 09') + 1'.456 sin (30 n + 20° 50')

+ 0'.472 sin (45 n + 231° 59') + 0'.352 sin (60 n + 60° . . )
For March, A<J = + 2'.093 sin (15 n + 206° 46') + 1'.827 sin (30 n + 26° 34')

-f 0'.693 sin (45 n + 230° 10') + 0'.413 sin (60 n + 84° . . )
For April, Ad = + 2'.906 sin (15 n + 213° 21') + 2'.001 sin (30 n + 34° 01')

-f 0'.926 sin (45 n + 223° 29') + 0'.245 sin (60 n + 80° . . )
For May, A<J = +2'. 746 sin (15 n + 210° 38') + 2'.377 sin (30 n + 45° 50')

+ 0'.970 sin (45 n + 251° 57') + O'.IOO sin (60 n +161° . . )
For June, Ad = + 2'.883 sin (15 n + 204° 09') + 2'.438 sin (30 n + 44° 15')

+ 0'.94l sin (45n + 254° 03') + 0'.216 sin (60n +114° . . )
For July, Ad = +3'.310 sin (15 n + 204° 19') + 2'.465 sin (30 n + 38° 48')

+ 1'.047 sin (45 n + 251° 38') + 0'.092 sin (60 n +176°. . )
For August, Ad = +3'.161 sin (15 n + 211° 37') + 2'.849 sin (30 n + 52° 16')

+ 1'.375 sin (45 n + 265° 49') + 0'.201 sin (60 n + 51° . . )
For September, A<J = +2'.706 sin (15 n + 220° 05') + 2'.372 sin (30 n + 55° 54'>

+ l'.126sin(45n + 261° 14') + 0'.414 sin (60n + 115° .. )
For October, Ad = +1'.271 sin (15 n + 226° 29') + 1'.325 sin (30 n + 33° 12')

+ 0'.727 sin (45 n + 230° 52') + OM50 sin (60 n -f 47° . . )
For November, Ad = +1'.259 sin (15 n -f 229° 06') + 1'.257 sin (30 n + 39° 15')

+ 0'.390 sin (45 n + 236° 30') + 0'.242 sin (60 n + 87° . . )
For December, Ad = + 1'.212 sin (15 n + 231° 46') + 1'.321 sin (30 n -f 23° 34')

+ 0'.367 sin (45 n + 205° 46') + 0'.418 sin (60 n + 32° . . )

In like manner, we obtain for the summer half-year (from April to September
inclusive), for the winter half-year (from October to March inclusive), and for the
whole year, the following expressions for the diurnal variation : —

For summer half-year, Ad = +2'.936 sin (15 n -f 210° 36') + 2'.404 sin (30 n + 46° 07')

+ 1'.031 sin (45 n + 253° 37') -f OM78 sin (60 n + 132° 20')

For winter half-year, Ad = +1'.420 sin (15 n + 220° 41') + 1'.399 sin (30 n + 26° 39') '

+ 0'.520 sin (45 n + 227° 26') + 0'.310 sin (60 n + 61° 17')

For the whole year,1 Ad = +2'. 167 sin (15 n + 213° 55') + 1'.875 sin (30 n + 38° 52')

-f 0'.759 sin (45 n + 244° 40') + 0'.198 sin (60 n + 83° 05')

1 For the purpose of showing the correspondence when the above equation is deduced independently,
from the observations at the even and odd hours, I add here the values for the two cases: —

From even hours, Ad = +2'.170 sin (15 n + 213° 27') + K888 sin (30 n + 38° 59')
+0'.729 sm (45 n + 244° 57') + 0'.183 sin (60 n + 83° 26')

From odd hours, Ad = +2M59 sin (15 n + 215° 19') + 1'.835 sin (30 n -f 38° 31')
+0'.848 sin (45 n + 243° 49') + 0'.242 sm (60 n + 82° 01')

The relative weights of the results by the even hours and the odd hours are as 3 : 1.

If, for the purpose of comparison with the previous results in Part I of this discussion, and with
other similar expressions, we change the angles Gv C3, C3, Gv by 180°, which is equivalent to an easterly
deviation from the mean for positive results and to a westerly deviation for negative results, we find —

For Philadelphia, A<j = +2M67 sm ( 0 -f ^3° 55') -f K875 sm (2fl + 218° 52')
+0'.759 sm (38 + 64° 40') + 0'.198 sm (40 + 263° 05')

For Dublin, Ad = +3'.519 sm ( 6 + 64° 18')+ 2'.127 sm (28 + 225° 22')

+0'.688 sm (38 + 70° 40') + 0'.322 sm (4 0 + 242° 27')

This latter expression is copied from the Rev. H. Lloyd's discussion of the Dublin observations in
1840-'43.

For a comparison of the monthly equations, the reader may also consult similar expressions obtained

16

AMPLITUDE OF THE SOLAR-DIURNAL VARIATION

In determining the least square coefficients in these equations, allowance has
been made for the different weights due to the readings at the even and odd hours.
0 is reckoned from midnight at the rate of 15° an hour. To compare the numerical
quantities of the angles Cl} C2, Cs, Ct, in the general expression —

Ad = Sl sin (0 + Ci) + A *in (20 + CJ + B3 sin (30 + Q + B, sin (40 + C74),
with the same quantities in the formula of the diurnal variation (pp. 8 and 9 of
Part I), 180° must first be added or subtracted from each angle given there; since,
in the discussion of Part I, increasing numbers correspond to a decrease of western
declination, the scale being thus graduated, whereas, in the present case, increasing
positive numbers correspond to an increase of western declination, as stated above.

The following table exhibits the close correspondence of the computed and ob-
served mean annual value of the regular solar-diurnal variation : —

*

DIURNAL VARIATIOH.

DIURNAL VARIATION.

Philadelphia

C— 0.

Philadelphia

C— 0.

Computed.

Observed.

Computed.

Observed.

Oh. 19$™.

— 0'.49

— 0'.47

— 0'.02

Noon 1 9

m.

+3'.69

-3'.65

+0'.04

1 19$

—0.48

—0.51

+0.03

1311.19,

+4.28

-4.32

—0.04

2 19i

—0.51

—0.44

—0.07

14 19i

+3.81

-3.77

+0.04

3 19ir

—0.67

—0.71

+0.04

15 19i

+2.77

-2.76

+0.01

4 19!

—1.09

—1.19

+0.10

16 19i

+1.71

+1.80

—0.09

5 19i

—1.82

—1.64

—0.18

17 19;

+0.88

+0.78

+0.10

6 19]

—2.77

—2.72

—0.05

18 19i

+0.33

+0.25

+0.08

7 19r

—3.49

—3.47

—0.02

19 19;

—0.07

—0.07

0.00

8 19$

—3.44

—3.50

+0.06

20 19;

—0.38

—0.33

—0.05

9 19$

—2.29

—2.43

+0.14

21 191

—0.57

—0.60

+0.03

10 19$

—0.24

—0.19

—0.05

22 19$

—0.62

—0.64

+0.02

11 19$

+2.03

+2.17

—0.14

23 19$

—0.57

—0.71

+0.14

The maximum difference at anyone hour is less than 11", and the probable error
of "any single hourly result is + 0'.05. The probable error of any single computed
value from a monthly expression is +OM9.

By means of the preceding equations, the hourly values of the diurnal variation
for each month of the year have been computed ; and the results, projected in
curves, are given in Diagrams D and E. The first contains the curves for the
six months of the summer half-year, and the second those of the winter half-year.
Positive ordinates correspond to a westerly movement, and negative ordinates to
an easterly movement, of the north end of the magnet. The diagram following
(F) contains the type curves for summer, winter, and the whole year, all being
upon the same scale.

by Mr. Karl Kreil from his discussion of declinometer observations at Prague, extending over ten con-
secutive years (1840-'49), and selected from a thirteen years' series, in order to obtain mean results
unaffected by the smaller inequality of the te»or eleven year period with which our results are still
affected. Part I of the present discussion, however, affords ready means of changing slightly the numeri-
cal values of the coefficients Bt, Bs, B.,, Bt, in our equations, in order to obtain the values we would have
obtained, had we discussed a consecutive eleven year series of observations or one extending over a series
of years corresponding to the actual length of the solar period then observed. Mr. Kreil's discussion
will be found in Vol. VIII of the proceedings of the mathematical and physical section of the Imperial
Academy of Sciences at Vienna (1854).

OF THE MAGNETIC DECLINATION.

17

REGULAR SOLAR-DIURNAL VARIATION OF THE MAGNETIC DECLISATION, SUMMKB HALF YEAB.

April,

May,

June,

July,

August,

September,

6'
5
4

2

1

0

—1

--2

C'

&

4
3
2
1
0

—1

—2

—3

6' —4

5 —5'

4
3
2
1

0
— 1

_2

—3

—4 1

-5 0

—6' —1

—2

—3

—4

—5

—6'

5'

4

3

2

1

0

-1

-2

-3

-5

-G'

V

G

4
3

2

1

0
-1
-2
-3
-4

Oh. 2

8 10 Noon 14 16
Philadelphia mean time.

18 20 22 24h.

18

SOLAR-DIURNAL VARIATION

REGULAR SOLAR-DIURNAL VARIATION OP THE MAGNETIC DECLINATION, WINTER HALF YEAR.

October,

November,

December,

January,

February,

March,

Oh.

4 - 6

8 10 Noon 14 16
Philadelphia mean time.

18 20 22 24''-

OF THE MAGNETIC DECLINATION.

TyPB-CuEVBS OP THE REGULAB SoLAB-DlUHHAL VARIATION OP THE DECLINATION.

19

Summer

Year

Winter

tiit

i i i i i i i i

6'
5
4
3
2
1
0

— 1
—2
—3
—4
—5'

3'
2
1
0

—1
—2
—3'

4'
3

2

1

0

-1

-2

-3

2 4 6 8 10 Noon 14 16 18 20 22 24h.
Philadelphia mean time.

REGULAR SOLAR-DIURNAL VARIATION OF THE MAGNETIC 'DECLINATION, COMPUTED FOR EVERY

MONTH OF THE YEAR, AND FOR THE PRINCIPAL SEASONS.

MEAN EPOCH
1842-43.

Oh-

lh.

2h.

3h.

4h.

5h.

(b.

7h.

8h-

9H.

10h-

Hh.

January

— 0'.52 ! — 0'.24

— O'.SO

— 0'.48

— 0'.48

— 0'.38

— 0'.55

— 1'.24

— 2M2

— 2'.45

— 1'.59

+0'.26

February

—0.30

—0.09

—0.14

—0.32

—0.49

—0.71

—1.18

—1.90

—2.52

—2.49

—1.49

+0.24

March

—0.25

—0.32

—0.55

—0.71

—0.81

—1.09

—1.84

—2.93

—3.67

—3.40

—1.81

+0.55

April

—0.88

—1.14

—1.34

—1.44

—1.54

—1.88

—2.64

—3.55

—4.02

—3.42

—1.54

+1.11

May

—0.58

—0.59

—0.50

—0.59

—1.18

—2.32

—3.75

— 4.74

—4.66

—3.24

—0.81

+1.93

June

—0.19

—0.28

—0.41

—0.69

—1.32

— 2.45

—3.87

—5.02

—5.13

—3.80

—1.23

+1.69

July

—0.80

—0.82

—0.67

—0.72

—1.34

—2.62

—4.22

—5.42

—5.45

—4.04

—1.47

+1.47

Angnst

—0.62

—0.33

—0.21

—0.59

—1.60

—3.09

—4.68

—5.71

—5.48

—3.67

—0.58

+2.87

September

—0.52

—0.72

—0.90

—1.06

—1.42

—2.23

—3.51

—4.55

—4.50

—2.84

+0.11

+3.18

October

—0.44

—0.52

—0.30

—0.20

—0.16

—0.45

—1.33

—1.72

—2.19

—1.92

—0.79

+0.77

November

—0.23

—0.21

—0.32

—0.44

—0.56

—0.75

—1.18

—1.68

—1.91

—1.50

—0.37

+1.11

December

—0.36

+0.01

—0.02

—0.34

—0.60

—0.67

—0.73

—1.00

—1.44

—1.64

—1.09

+0.26

Summer

—0.63

—0.71

—0.71

—0.81

—1.33

—2.43

—3.84

—4.92

—4.91

—3.43

—0.83

+2.12

Winter

—0.41

—0.26

—0.29

—0.42

—0.50

—0.68

—1.09

—1.73

—2.25

—2.15

—1.12

+0.56

Year

—0.49

—0.48

—0.55

—0.62

—0.94

—1.54

—2.41

—3.31

—3.54

—2.80

—1.02

+1.32

MEAN EPOCH
1842-13.

Noon.

13>>.

14h.

15h-

16b.

17*.

18h.

19k

2Qh.

21 h.

22h.

23ii.

January

+2'.26

+3'.40

+3'. 34

+2'.46

+1'.52

+0'.92

+0'.57

+0'.08

— 0'.64

— 1'.29

— 1'.45

— I'.OS

February

+1.96

+2.97

+3.02

+2.42

+1.71

+1.17

+0.76

+0.26

—0.36

—0.85

—0.97

—0.70

March

+2.71

+3.86

-+3.85

+3.17

+2.33

+1.65

+1.02

+0.35

—0.31

—0.70

—0.67

—0.43

April

+3.60

+5.06

+ 5.18

+4.28

+2.98

+1.76

+0.88

+0.27

—0.14

—0.38

—0.54

—0.67

May

+4.06

+5.07

+4.88

+3.85

+2.48

+1.22

+0.39

—0.02

—0.12

—0.14

—0.21

—0.43

June

+3.99

+5.00

+4.79

+3.79

+2.60

+1.59

+0.87

+0.38

+0.07

—0.10

—0.13

—0.15

July

+3.90

+5.26

+5.37

+4.54

+3.28

+2.04

+1.16

+0.66

+0.39

+0.18

—0.15

—0.53

August

+5.44

+6.35

+5.55

+3.75

+1.98

+0.87

+0.50

+0.45

+0.26

—0.13

—0.56

—0.77

September

+5.18

+5.54

+4.48

+2.99

+1.68

+0.85

+0.33

—0.11

—0.44

—0.56

—0.55

—0.44

October

+2.60

+3.17

+3.00

+2.20

+1.08

+0.25

—0.39

—0.36

—0.39

—0.52

—0.69

—0.69

November

+2.31

+2.81

+2.58

+1.90

+1.18

+0.57

+0.06

—0.40

—0.59

—0.92

—0.77

—0.49

December

+1.86

+2.95

+3.04

+2.32

+1.34

+0.57

+0.11

—0.28

—0.78

—1.22

— 1^33

—0.96

Summer

+4.35

+5.29

+4.99

+3.89 +2.57

+1.43

+0.64

+0.18

—0.05

—0.17

—0.33

—0.44

Winter

+2.21

+3.12

+3.09

+2.38 +1.52

+0.84

+ 0.37

—0.09

—0.55

—0.89

—0.94

—0.72

Year

+3.25

+4.22

+4.09

+3.14 , +2.06

+1.12

+0.45

+0.05

—0.32

—0.52

—0.58

—0.58

20 SOLAR-DIURNAL VARIATION

In the above table + signifies westerly and — easterly deflection ; it may be
compared with similar tables constructed for Toronto,1 Dublin,2 and Prague.3 It
will be observed that the preceding table, which gives the observed variation, refers
to an epoch 19£ minutes later than the exact local hour (that is, to an exact
Gottingen hour), whereas the computed table refers to the exact Philadelphia hours.

From the computed tabular values, aided by the diagrams, we can now deduce
some of the general features of the diurnal variation and its annual inequality.

The general character of the diurnal motion (see type-curves) is nearly the same
throughout the year; the most eastern deflection is reached a quarter before 8
o'clock in the morning (about a quarter of an hour earlier in summer, and half an
hour later in winter); near this hour the declination is a minimum ; the north
end of the magnet then begins to move westward, and reaches its western elonga-
tion about a quarter after one o'clock in the afternoon (a few minutes earlier in
summer). At this time the declination attains its maximum value. The diurnal
curve presents but a single wave, slightly interrupted by a deviation occurring
during the hours near midnight (from about 10 P. M. to 1 A. M.), when the
magnet has a direct or westerly motion ; shortly after 1 A. M. the magnet again
assumes a retrograde motion, and completes the cycle by arriving at its eastern
elongation shortly before 8 o'clock in the morning. This nocturnal deflection is
well-marked in winter, vanishes in the summer months, and is hardly perceptible
in the annual curve. According to the investigations of General Sabine, it is
probable that, if we had the means of entirely obliterating the effect of disturb-
ances, this small oscillation would almost disappear. In summer, when it has no
existence, the magnet remains nearly stationary between the hours of 8 P. M. and
3 A. M., a feature which is also shown by the annual type-curve.

The two preceding plates show a close general resemblance in the diurnal curves
for the six months when the sun has north declination, and a similar resemblance
in the other six months when it has south declination.

The analytical expressions give the epoch and amount of variation with greater
precision. The hours of minimum and maximum deflection are obtained from the

equation •' , d = o: and the hours of the mean declination, when the curves cross
an

the axis of abscissae, from the condition Ad = o. The following table contains
these results for each month and the two principal seasons of the year, also the
critical interval between the two adjacent hours of the mean position.

1 Vol. III., Table LXVI; compare also with Table VII. of Vol. II.

« Trans. Royal Irish Academy, Vol. XXII., Part I., Table III.

• Academy of Sciences at Vienna, Vol. VIII. of Math. Section, Table II.

OF THE MAGNETIC DECLINATION.

21

Eastern

Western

Critical interval

EPOCH of MEAX DECLIXATIOS.

MO.VTH.

elongation
A. M.

elongation
P.M.

from minimum
to maximum.

Critical
interval.

A. M.

P.M.

January .

8h. 58m.

11'. 27m.

4h. 29m.

10n. 52m.

7h. 08m.

SB. 16m.

February

8 34

1 32

4 58

10 52

7 26

8 34

March

8 07

1 34

5 27

10 46

7 32

8 46

April

8 12

1 27

5 15

10 34

7 40

8 56

May

7 29

1 21

5 52

10 19

6 57

8 38

June

7 33

1 20

5 47

10 25

8 26

10 01

July

7 36

1 28

b 52

10 30

9 32

11 02

August

7 18

1 05

5 47

10 10

8 40

10 30

September

7 30

0 45

5 15

9 58

6 45

8 47

October .

8 00

1 17

5 17

10 30

5 23

6 53

November

7 54

1 08

5 14

10 16

6 08

7 52

December

8 54

1 40

4 46

10 50

6 17

7 27

Summer .

7«- 33m.

1U. 8m.

5h. 35m.

10h. 17m.

7li. 43m.

9h. 26«»-

Winter

8 24

1 25

5 01

10 40

6 49

8 09

Year

7 48

1 16

5 28

10 26

7 08

8 42

We likewise obtain :

and

Secondary minimum of eastern deflection in winter 9h- 42m- P. M. Amount — 0'.97

" maximum of western " " " 1 15 A.M. " — 0.26

Differences: 3h- 33m- 0'.71

Secondary minimum of eastern deflection for the year 10h- llm- P. M. Amount — 0'.62

" maximum of western " " " 1 13 A.M. " —0.47

Differences: 3h- 02m- 0'.15

The effect of the seasons on the critical hours is well marked in the above table.
The eastern elongation occurs earliest between the summer solstice and the autumnal
equinox, and latest about the winter solstice. The western elongation occurs earliest
about the autumnal equinox, and latest about the winter solstice; and the same
holds good for the morning epoch of the mean declination. The afternoon epoch,
however, occurs earliest, shortly after the autumnal equinox, and latest, shortly
after the summer solstice.

The critical hours which vary least during the year are those of the western
elongation and those of the morning mean declination. The extreme difference
between the value for any month and the mean annual value is 31 minutes in the
former and 28 minutes in the latter.

The following graphical representation of three variables (Diagram G) will serve
to show at a glance the various features of the diurnal variation and its annual
inequality: The magnetic surface is formed by contour lines, O.'o apart; the dotted
curves are lines of mean position, the curves represented by dashes correspond to
eastern, and the full curves to western deflection from the normal position. This
diagram, as well as the computed tabular values from which it has been constructed,
serve equally to furnish the correction necessary to reduce any single observation
taken at any hour of the day and month to its mean value. It also enables us in
a measure to dispense with developing the annual variability of the coefficients j5,

2?2 A • • • and Cr Cz C3 (or rather the equivalents a, ^ a2 &2 as ^ from

which they are derived) in the general expression A -f- R^ sin (6 + Ci) + etc. In
most cases either a tabular or graphical interpolation between the two adjacent
monthly values will fully answer the purpose. The diagram also distinctly exhibits

22

SOLAR-DIURNAL VARIATION

the diurnal minima and maxima, the former represented by a valley, the latter by
a ridge in the magnetic surface.

The magnitude of the diurnal range is next to be considered.

DIAGRAM SHOWING THE DEFLECTION (IN MINUTES OF ABC) OF THE NORTH END OF THE MAGNET FROM ITS MONTHLY NORMAL
POSITION FOB EVEEY BODE OF THE DAT AND MONTH OF THE YEAR, DERIVED FROM THE DECLINOMETEB OBSEBVATIONB

AT PHILADELPHIA BETWEEN 1840 AND 1845.

. 1 2345 6

789 10 11 N'n 13 14 15 16 17 18 19 2021 222324''-
Philadelphia mean time.

The following table contains the amount of the deflection at the eastern and
western elongations and the diurnal amplitude of the declination for each month
of the year, derived from the preceding equations : —

DEFLECTIOX AT

Dlnrnal

range.

DEFLECTION AT

Diurnal

range.

E. Elong.

W. Elong.

E. Elong.

W. Elong.

January ....
February . . .
March ....

— 2'.46
—2.64
—3.73
—4.02
—4.89
—5.26

+3'.52
+3.11
+4.03
+5.28
+5.16
+5.06

5'. 98
5.75
7.76
9.30
10.05
10.32

July

— 5 '.5 8
—5.79
—4.71
—2.18
—1.92
—1.65

+ 5'.46

+6.36
+5.60
+3.23
+2.85
+3.14

11'.04
12.15
10.31
5.41
4.77
4.79

August ....
September .
October ....
November . . .
December . .

May

The diurnal range for the summer months is 10'.45, for the winter months 5'.56,

OF THE MAGNETIC DECLINATION.

23

and for the whole year 7'.89; all corresponding to an epoch removed about one
year and a half from the epoch of a minimum of the solar period.

The numbers expressing the diurnal range exhibit three remarkable features,
viz., the maximum value in the month of August, the sudden falling off in the
months of September and October (see the graphical representation), and the

DICBNAI RANGE OP THE DECLINATION.

minimum value in November or December. Otherwise the progression is regular;
the curve is single-crested, a feature equally true for the eastern as well as for the
western deflection when viewed separately. This latter circumstance is of special
importance, since it is probable that it is mostly by the interference of these two
separate curves that we observe at other stations the curve of the diurnal range
at some stations apparently, to be a double-crested one. The curves for Milan, Munich,
Gottingen, Brussels, Greenwich, Dublin, etc., for instance, exhibit two maxima,
one after the vernal equinox, and a second, generally the smaller one, about the
summer solstice, with more or less regularity. The system to which Philadelphia
belongs is exemplified by the annual curve of the diurnal range at Prague and at
some Russian stations, especially at Nertschinsk, but principally at Toronto, for
which last station the curve is shown in the diagram. Neither station appears to
have a tendency to a secondary maximum about the month of April, leaving the
maximum about a month and a half after the summer solstice, a well-marked North
American feature.

Annual Variation of the Declination. — In connection with the preceding discussion
the annual inequality in the magnetic declination next claims attention.

This subject presents greater difficulty, inherent in the observations, than the
diurnal inequality; not so much on account of the length of the period as on
account of the difficulty of keeping the instrument in precisely the same condition
of adjustment throughout the year. In the first part of this discussion I have
already had occasion to refer to this circumstance while investigating the annual
effect of the secular change, and it was there shown that the Philadelphia observa-
tions share in this respect the difficulties of those of other stations,1 in consequence
of which the results must be received with caution.

1 It may be proper to give here, in full, Dr. Lloyd's instructive note on this subject, in his discussion
of the Dublin observations : " The determination of the annual variation is much more difficult than that

24

ANNUAL VARIATION

Returning to the last vertical column in the table, headed " mean," we have
there the monthly values of the declinometer readings (in scale divisions), and in
their differences when compared month for month, the joint effect of the secular
change, and of the annual inequality. To eliminate the effect of the secular
change, we determine its annual amount as follows : Subtracting the mean annual
reading 559.64, corresponding to July 1, from each monthly mean, and putting
x = monthly effect of the secular change (considered as uniform), each monthly
mean reading furnishes an equation for the determination of K, thus : for

January
February
March
April .

4.56 = 5.5 x
3.34 = 4.5 *
5.22 = 3.5 x
4.39 = 2.5 *, etc.,

which, when combined by least squares, give x = ld-.227, hence the annual change
14d .7 or 6'.7 of increasing westerly declination.1

Deducting the effect of the secular change, and comparing the monthly remainders
with their mean values, we obtain the annual inequality of the declination as
follows : —

MO.NTH.

Mean
reading.

Reduction
for sec,
change.

Reduced
reading.

Annual
inequality.

MONTH.

Mean
reading.

Reduction
for sec.
change.

Reduced
reading.

Annual
inequality.

d.

d.

d.

d.

d.

d.

d.

d.

January .

564.20

—6.75

557.45

+2.2

July . .

560.24

+0.61

560.85

—1.2

February

562.98

—5.52

557.46

+2.2

August .

559.07

+1.84

560.91

—1.3

March

564.86

—4.29

560.57

—0.9

September

556.07

+3.07

559.14

+0.5

April . .

564.03

—3.07

560.96

—1.3

October .

556.43

+4.29

560.72

—1.1

May .

563.18

—1.84

561.34

—1.7

November

553.97

+5.52

559.49

+0.2

June .

560.84

—0.61

560.23

—0.6

December

549.82

+6.75

556.57

+3.1

in the annual inequality indicates an f easterly deflection.

The sign f

I + ' I westerly

According to these results the magnet (north end) is deflected to the east of its
mean annual position in summer, and to the west in winter. It is, however,
desirable to test the result by submitting the first and the second 21 years of
observations separately to the same process of investigation. The first 31 months
in the years 1840, '41, and '42, give a result almost identical with that just deduced;

of the diurnal, both on account of the much smaller frequency of the period, and the difficulty of
preserving the instrument in the same unchanged condition during the much longer time, or of determining
and allowing for its changes when they do occur. Accordingly, although the annual period may be
traced in the observations of Gilpin and is decidedly displayed in those of Bowditch, it has evaded the
researches of recent observers. There is but a faint indication of its existence in the Gottingen observa-
tions, which were made at the hours of 8 A. M. and 1 P. M., and Professor Gauss and Dr. Goldschmidt
find, in their analysis of these observations, no important fluctuation dependent on season. A similar
negative result is deduced by Dr. Lament from the Munich observations, which were made twelve times
in the day."

1 This value (+6'. 7), as resulting from a different combination of observed and partly interpolated
values, may not be preferable to that ( + 4'.5) deduced in Part I. of this discussion, but must necessarily
be employed in the present investigation. The most reliable value, +5'.0, was deduced from independent
observations, as already remarked, and lies between the two.

OF THE MAGNETIC DECLINATION.

25

the remaining 27 months in the years 1843, '44, and '45, when discussed in the
same manner, give a rather different result.

Some improvements, however, can be made in the preceding investigation by
omitting the December mean of 1844, which is obviously about 12 scale divisions
too small; the observed value is 535d'.2, and the interpolated value 547d-.0. An
examination of the first series shows a defect in the monthly means of 1841, be-
tween May and June, requiring a constant correction of + 8.0 scale divisions for
the remaining months after May, as may be seen by the following table : —

Year.
1841
1842
1843
1844
1845

Diff.

May.

Jane.

May- Jane.

578.5

571.2?

561.8

563.6

—1.8

566.2

565.0

+ 1.2

546.5

547.5

—1.0

529.7

531.0

—1.3

Computed value for June, 579.2

Mean

—0.7

The following values then remain for the discussion, and they should be con-
sidered as forming the basis from which the legitimate results are to be deduced.
The numbers marked with an asterisk have been increased by 8d .0. Interpolated
values are between brackets, and were obtained by comparing the means of the
remaining months of the year with the corresponding means of every other year ;
by this process several values are obtained for each interpolated number ; the re-
sulting mean is given in the table. The high value of 1841, and the low value of
1844, for the month of May, in some measure compensate.

YEAR.

Jan.

Feb.

March.

April.

May.

Jane.

Jnly.

August.

Sept.

Oct.

NOT.

Dec.

1840
1841
1842
1843

1844
1845

d.
(586.9)
576.3
564.1
(566.5)
558.0
531.0

(585.9)
574.3
563.3
(565.6)
558.0
531.3

d.
(586.3)
577.0
562.0
(565.9)
557.6
532.0

d.

(586.4)
578.1
561.9
567.2
555.2
527.1

d.
(584.1)
578.5
561.8
566.2
546.5
529.7

d.
586.9
*579.2
563.6
565.0
547.5
531.0

d.
588.4
*576.7
565.2
564.7
547.5
(529.9)

d.

587.4
*576.9
563.8
563.6
546.2
(529.0)

d.

585.2
*571.1
566.7
558.3
542.2
(527.0)

d.
579.9
*575.2
562.7
559.0
545.3
(526.2)

d.
573.9
*564.4
563.5
556.1
547.2
(522.7)

d.
570.5
*567.4
561.6
557.6
(547.0)
(522.1)

Means

563.8

563.1

563.5

562.6

561.1

562.2

562.1

561.2

558.4

558.1

554.6

554.4

560.4

Correct'n for
sec. changes

|— 4.4

—3.6

—2.8

—2.0

—1.2

—0.4

+0.4

+1-2

+2.0

+2.8

+3.6

+4.4

Corrected
means

1559.4

559.5

560.7

560.6

559.9

561.8

562.5

562.4

560.4

560.9

558.2

558.8

Annual va-
riation
(in arc)

}+i.o

+0'.5

+0.9
+0'.4

—0.3
— O'.l

—0.2
—O'.l

+0.5
+0'.2

—1.4

— 0'.6

—2.1
— I'.O

—2.0
— 0'.9

—0.0
— O'.O

—0.5
— 0'.2

+2.2
+0'.9

+ 1.6
+0'.7

This last result accords in general with that before deduced, but is much to be
preferred.

From June to October the north end of the magnet is accordingly to the eastward

of the mean annual position (after the elimination of the secular change), and in

the remaining months of the year it is to the westward of this position. From

the vernal equinox till after the summer solstice the motion is to the eastward or

4

26

VARIATION OF THE MAGNETIC DECLINATION.

retrograde in regard to the advance of the secular change (to the westward) ; this
is in conformity with the law as given by Dr. Lloyd in the Dublin discussion, where
the motion of the magnet is to the westward at this period of the year, or the
reverse of the Philadelphia deflection, but the secular change is likewise reversed,
the west declination diminishing at Dublin (at the same time or more accurately
between 1840 and '43).

For further comparison I give here the results deduced from seven years' obser-
vation at Toronto between the years 1845 and '51, a previous working up of a
three years' series (middle year 1846) not being deemed sufficiently distinctive in
its results. The secular change is here 2'.0 per annum, increasing westerly declina-
tion, whereas it was 4'.4 per annum at Philadelphia in 1843; as in the above
result + indicates west, — east deflection.

ANNUAL VARIATION AT TORONTO BETWEEN 1845 AND 1851.

January.

February.

March.

April.

May.

Jane.

July.

August.

September.

October.

November.

December.

+0'.l

— 0'.5

— 0'.2

O'.O

— O'.l

— 0'.5

— 0'.8

— 0'.2

+0'.7

-fl'.O

+0'.3

+0>.3

In regard to the amount of the inequality, the two stations agree remarkably
well, the range remaining slightly below 2' of arc. It has been supposed that this
range at the same station is increasing or diminishing as the secular change increases
or diminishes.

It may further be remarked that the general mean resulting from the above
discussion at Philadelphia, viz., 560.4, is identical with the value given in Part I.
of the discussion, there deduced by an entirely different combination. The annual
effect of the secular change, -f- 4'.4, is likewise in very close conformity with the
value given in Part I., as found by a very different process.

The monthly values of the annual variation may serve to give the corrections
to observed declinations in any month of the year needed to refer the same to the
mean declination of the year, and may also be used in the more refined discussion
of the secular change, in both cases, only, when the greatest accuracy is required.

SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE.

DISCUSSION

MAGNETIC AND METEOROLOGICAL OBSERVATIONS

MADE AT THE GIRARD COLLEGE OBSERVATORY, PHILADELPHIA,
IN 1840, 1841, 1842, 1843, 1844, AND 1845.

PART III.

INVESTIGATION OF THE INFLUENCE OF THE MOON ON THE MAGNETIC DECLINATION.

BY

A. D. BACHE, LL. D.

[ACCEPTED FOE PUBLICATION, SEPTEMBER, I860.]

INVESTIGATION

INFLUENCE OF THE MOON ON THE MAGNETIC DECLINATION.

THE existence of a sensible lunar effect on the magnetic decimation has already
been established by the labors of Broun, Kreil, Sabine, and others. It is never-
theless important to add the weight of new numerical results to those already
obtained.

In the discussions of the Philadelphia observations of magnetic declination,
already presented to the Association, I have shown how the influence of magnetic
disturbances, of the eleven year period of the solar diurnal variation and its annual
inequality, of the secular change, and of the annual variation may be severally
eliminated, leaving residuals from which the lunar influence is to be studied. Each
observation was marked with its corresponding lunar hour and the hourly normals
used for comparison.

This method of treatment of the subject is that followed by General Sabine in
his discussion of the results of the British observations.1

The details of the method will be better understood by an example.

The time of the moon's passage over the meridian of Philadelphia (upper transit)
was obtained from the American Almanac, the small correction for the difference

1 In reference to methods and results, in general, on this subject, the following papers may be consulted :
Observations in Magnetism and Meteorology made at Makerstown, in Scotland, in the observatory of
General Sir Thomas M. Brisbane, Bart., in 1845 and 1846, forming vol. xix., parti, of the Trans. Royal
Society of Edinburgh. By John Allan Broun. Edinburgh, 1849; also vol. xix. part ii., containing
the general results (1850).

Einfluss des Mondes auf die magnetische Declination by Carl Kreil. Vol. iii. of the Proceedings of
the Mathematical and Physical Section of the Imperial Academy of Sciences of Vienna, 1852; also,
vol. v., ibid., 1853.

Philosophical Trans. Royal Society, art. xix., 1853: On the Influence of the Moon on the Magnetic
Declination at Toronto, St. Helena, and Hobarton. By Col. E. Sabine.

Phil. Trans. Royal Society, art. xxii., 1856: On the Lunar-diurnal Magnetic Variation at Toronto.
By Major General E. Sabine. And—

Phil. Trans. Royal Society, art. i., 1857 : On the evidence of the Existence of the Decennial Inequality
in the Solar-diurnal Magnetic Variations and its Non-existence in the Lunar-diurnal Variation, of the
Declination at Hobarton. By Major General E. Sabine.
1

2 LUNAR EFFECT

of longitude being neglected. The observation nearest to the local mean solar
time of the moon's transit was marked with a zero, signifying Oh- of lunar time.
The time of the inferior transit was next obtained; and the observation nearest to
it in time was marked 12h. The greatest difference in interval between the moon's
transit and the time of observation could in no instance exceed half an hour. In
the bi-hourly series, the observations nearest the moon's transit, or to either hour
angle, one hour before or one hour after the transit was marked. The mean of
a number of differences for the same hours thus gave a result corresponding
nearly enough with the hour. The number of observations intermediate between
those marked Oh- and 12h- were marked with the corresponding hour angle by
interpolation, care being taken to note the nearest full hour against each observation
in the bi-hourly series. The hourly series begins with October, 1843. In the case
of thirteen observations within twelve lunar hours, the one nearest midway between
the two consecutive lunar hours was omitted.

In the month of March, 1842, which is selected as an example of the details of
working the bi-hourly series, the number of observations available is 298, of which
148 correspond to western and 150 to eastern hour angles. In the abstract which
follows + indicates a deviation of the north end of the magnet to the west, and
— a deviation to the east of the respective normal position for the hour. The
hourly normals are given in the first part of the discussion. No difference exceeds
eight divisions, this being the limit in number indicated by the criterion.

ON THE MAGNETIC DECLINATION.

LUNAR-DIURNAL VARIATION FROM OBSERVATIONS AT PHILADELPHIA IN MARCH, 1842.

Differences from the hourly normals.

J's Upper transit. Western hour-angles.

Oh.

lh.

2h.

3h-

4h.

5h.

6h-

7h.

8k.

9b.

10h.

llh.

Means

+4.1
—2.5
+3.1
—4.3
—1.9
+6.4
+1.7
—0.7
+0.8
+2.9
—1.7

+6.1
—4.2
—1.4
+4.3
—0.5
+1.0
+3.3
+0.2
—5.1
—2.7
+2.8
—1.3
+2.2

—0.1
+2.0
+4.6
—0.7
+3.9
+3.6
+1.6
—3.2
+3.0
+3.1

—5.0
+1.0
+6.1
+1.8
—1.3
+1.9
—0.9
—0.9
0.0
+1.8
—3.0
—1.9
—1.4
+2.9
+2.1
+1.6

+1.3

+7.2
+1.4
+0.3
—0.6
—4.8
+3.1
+2.9

—0.9
+0.2
+0.9
+1.2
—2.9
+1.3
—2.3
—3.8
—7.2
—3.7
+0.5
+2.9

—0.1
+7.8
—0.6
+2.3
—0.5
—0.1
—1.6
—3.8
—6.3
—2.4
+0.5
—0.2
—5.9
+3.5

+1.0
0.0
—0.5
—3.0
+1.4
+2.1
—6.2
—3.1
—5.9
—4.6
—5.1
-^.6
—4.2
—1.6
+2.0

+2.5
+1.2
+4.2
+1.0
+0.7
—3.3
+2.3
—4.5

+3.1
—2.0
—2.7
+5.2
—1.8
+7.0
—1.1
—5.5
—3.0
+4.4
—2.2
—1.6
—1.9
—1.9

+0.9
+2.1
+1.6
—0.4
—1.1
+1.7
+6.5
—1.9
+2.6
—1.7
—0.9
—0.5
—2.9

—4.1
—1.8
—6.8
—2.0
—5.2
+5.6
+6.6
—1.8
+1.1
+0.7
—1.6

+1.35

— 2.9
—0.8
—0.9

+1-78

+ 04..72

—0.05

— Od..84

—1.15

+0.38

+0.46

—0.53

—0.29

—2.15

+0.30

J's Lower transit. Eastern hour-angles.

12i>.

13t.

14h.

15h.

16h-

17h.

18h.

19h.

20h.

21h.

22h.

23h.

Means

—2.7
—0.2
—1.7
—1.0
+3.2
+0.9
+2.4
+1.9
+7.4
+0.3
+5.3
—1.2

—0.5
—2.4
+3.0
—0.6
—0.2
+2.7
+2.6
+4.9
—0.7
—4.6
—3.5
—0.3

—2.9
—1.9
+ 2.9
+0.5
—5.2
+3.4
+4.5
+5.4
—1.1
+6.4
+1.6
+1.5

+0.5
—0.4
—0.6
—7.2
—0.5
—1.1
+3.4
+4.7
+7.6
+3.4
—0.1

+5.6
—3.4
—2.0
—1.4
—2.3
+ 1.4
+1.0
—1.0
+5.8
+3.0
—0.3
—1.1
+3.7

+ 0.5
—1.7
—0.6
—3.2
—0.4
+2.2
+1.4
+2.3
—0.1
—0.5
—3.0
—1.0

+0.6
—2.8
—1.6
—1.0
—6.0
—3.3
—3.8
+2.9
—0.7
—3.0
+2.5
—0.7
+4.9

-4.1
+1.3
+2.5
—0.6
+0.3
—4.2
—3.3
—0.3
—2.0
+3.6
—6.6
—3.7

+1.6
+6.5
—5.1
—0.6
+0.6
+0.2
—0.7
—3.6
+5.9
—1.0
—1.6
+3.4

—4.9
—5.4
—0.4
+04
+0.7
+0.1
—0.4
—2.2
+1.5
+1.2
—0.8
+5.6

—0.39

+4.4
—0.3
+6.9
—0.9
+1.6
—1.1
—2.8
—1.5
+1.4
+3.0
—0.4
—3.4
—6.5

—4.2
+0.6
—3.1
—0.1
+1.2
+1.7
+1.6
—3.5
—4.0
—3.3
+0.6
+5.1
+2.8

+0.88

+ld.22

+0.20

+1.25

—0.34

—1.43

+0.47

—1.5
+0.6
—1.1

—0.92

+0.03

— Od..35

+0.44

Number of observations or differences at western hour-angles . . 148
" " " " eastern " . . 150

Total 298

The following table contains the number of observations used in the discussion
of the lunar-diurnal variation : —

1840.

1841.

1842.

1843.

1844.

1845.

300
272
269
253
223
271
237

168
263
293
283
276
276
292
262
250
214
230
208

265
257
298
278
285
280
2(>7
254
247
221
289
316

276
309
300
290
244
283
571
590
595

577
571
551
522
596
566
593
541
522
617
517
549

591
535
575
561
603
542

May

July

1825

3075

3257

3458

6622

3407

Total sum

9

1644

LUNAR EFFECT

If divided into western and eastern hour-angles, the annual numbers stand as
follows : —

1840
1841
1842
1843
1844
1845

Western hour-angles.

. 916
. 1523
. 1618
. 1724
. 3288
1700

Eastern hour-angles.

909
1552
1639
1734
3334
1707

Sum

. 10769

10875

The preceding mean results will be found inserted in their proper place in the
following abstract of the mean monthly values for each observing month between
1840 and 1845.

Proceeding in this way the following results are obtained for the different
months discussed.

3>'s Upper transit. Moon's hour-angle.

1840.

Oh.

lh.

2ii.

3ii-

4h.

5h-

gk.

7h.

8h.

91>-

lOli-

111'.

d.

d.

d.

d.

a.

d.

d.

a.

d.

d.

a.

a.

June1

—0.23

—0.25

—1.28

+0.95

—1.09

+0.11

—0.21

+0.30

—1.12

+1.60

—0.02

+0.55

July2

+0.52

+1.87

—0.56

+2.04

—1.98

+1.60

—1.34

+0.40

—0.21

+0.47

+0.11

+0.75

August

—0.71

—0.10

+1.41

+0.73

+1.05

+1.20

—0.50

—0.44

+0.10

+0.86

+0.20

+0.75

September3

+1.74

—0.52

+1.05

—0.87

—0.40

—2.05

—0.67

—1.18

+0.49

+0.28

+0.52

+1.53

October

+0.77

—1.13

+0.37

+0.98

+0.25

+1.23

—0.01

+0.71

—0.78

—0.63

—0.68

—3.61

November4

+1.11

+1.04

+1.21

+0.77

+1.07

+1.44

—0.39

—0.53

—1.44

—2.03

—0.08

—1.61

December

—1.43

+1.14

+0.37

+0.37

+0.16

-0.90

—0.73

—1.44

—1.03

+1.01

—0.81

+1.24

3>'s Lower transit.

1840.

12h.

13ii.

14h.

15k-

16k

17h.

let-

19h.

20ii.

21U.

22U.

231i.

d.

d.

d.

d.

d.

d.

d.

a.

d.

a.

d.

a.

June1

+0.50

+0.75

+0.38

+0.86

+0.19

+1.65

—0.72

+0.68

—1.35

+0.69

—2.30

+0.98

July8

+1.15

—1.08

—0.41

+0.32

—1.71

+1.03

+0.15

—0.18

—0.37

+1.00

—1.38

—0.03

August

+0.18

—1.56

—0.91

—0.65

—1.15

—0.03

+0.06

—2.61

+1.50

—1.30

—1.27

—0.50

September3

+0.64

+0.38

+0.63

+2.25

+0.84

+1.26

—0.61

—0.01

—1.05

—0.61

—0.23

+ 0.20

October

+0.53

—0.59

+0.30

+1.18

—1.19

+0.63

—0.31

—0.99

—0.40

—0.40

+1.51

+1.05

November1

+0.75

—0.62

+0.02

—0.82

—0.49

+0.01

—0.02

+1.09

+0.88

+0.57

+0.14

+0.18

December

+0.91

—0.78

—0.67

—1.82

—0.06

—0.70

—2.57

+1.21

+0.63

+0.86

+0.64

+1.48

' The tabular values for this month are expressed in parts of the new or observatory scale, the quanti-
ties having been converted from parts of the old or college scale into parts of the new scale.

8 The tabular numbers refer to the new scale, the values for the first eighteen days of the month having
been converted as above.

3 Attention was paid to the half-monthly normals for the hour 8h- 19£m- (mean observatory time).

4 The index correction, on and after the twenty-third day of the month, was applied before the
differences were taken.

ON THE MAGNETIC DECLINATION.

D's Upper transit. Moon's hour-angle.

1841.

Oh-

lh.

2h.

3h.

4h.

5h.

6h.

7h.

81>-

9h-

10t.

111,.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

January

+0.86

—1.07

+0.54

+1.39

+0.50

—2.01

+0.89

—0.11

—1.52

+0.48

—0.12

—1.10

February

+1.48

—2.17

+1.12

+0.49

+0.49

+0.10

—0.10

—0.57

—0.38

+0.32 +0.92

+1.40

March

+1.67

+0.82

+0.64

+1.00

+0.61

+0.40

—0.39

—1.07

—1.21

+0.69

—0.65

—0.91

April

+1.57

+ 1.01

+0.45

+0.97

+0.20

+0.12

+0.39

+1.40

—0.27

—1.52

+0.48

—1.43

May

+0.19

+2.11

+0.69

+1.94

—0.05

+0.92

—0.39

—0.60

—0.73

—0.20

—0.94

+1.21

June

—0.56

+1.77

+0.07

+0.45

+2.18

+1.25

—1.15

—0.59

—2.40

—1.13

—0.42

—1.24

July

+0.84

+1.86

+0.46

—1.06

—0.62

—1.52

—0.80

—0.55

—0.88

—1.71

—0.24

+1.63

August

+1.95

+1.31

+1.73

+1.42

—1.17

—1.46

—1.48

—1.39

—2.06

—2.24

—1.72

+0.60

September

+1.05

+0.10

—0.45

—0.17

—3.50

—0.54

—0.55

—0.83

—1.47

+0.86

+1.29

+0.03

October'

—1.15

+0.26

—0.77

—0.06

—1.31

—0.82

—0.66

—0.61

—1.73

+1.73

+0.22

+1.09

November

+0.01

—0.08

+0.02

+0.54

+0.23

—1.08

+1.54

+0.52

+1.39

+0.02

—0.24

—0.06

December

—0.41

+0.10

+0.45

—0.71

—0.94

+0.55

—0.51

+1.09

+0.62

—0.47

+0.48

+0.08

D's Lower transit.

1841.

12b.

131".

14h.

15h-

16h.

17h.

18h.

19h.

20t.

21 h.

22h.

23h.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

January

+1.33

+0.57

—0.04

—0.51

—0.50

+0.21

+0.25

—2.10

—0.21

—1.32

—0.07

0.00

February

—0.03

—1.30

—0.78

—0.30

—1.23

—2.01

—1.12

—1.08

+0.60

+1.30

+0.56

+1.07

March

+0.15

+0.18

+1.05

+0.23

—0.15

—0.59

—0.23

—0.93

—0.47

—0.98

+1.89

+0.35

April

+1.35

—1.05

—0.09

+0.90

—0.02

—1.13

—0.32

—1.67

—0.89

—0.13

—0.63

+0.02

May

+0.42

+1.44

+0.56

+0.24

—1.21

—0.89

—2.64

—0.85

—2.20

—1.09

+0.96

+0.90

June

+0.11

—1.42

—0.13

+0.67

+1.18

—0.53

+0.62

—1.14

+1.79

+0.01

—0.22

+0.80

July

+1.26

+1.50

+1.09

+1.76

+0.32

+0.45

—0.80

+0.01

—0.95

+0.27

—0.87

+0.44

August

+2.28

+0.51

+1.97

4-1.18

+0.62

—1.81

—0.50

—1.07

—0.59

+1.66

+0.06

+1.20

September

+0.37

+0.41

+1.21

+0.95

—1.66

—0.44

—0.25

—0.45

+0.45

+0.19

+0.85

+0.44

October1

—1.73

+1.04

+0.76

+0.34

+0.18

+1.60

+0.97

+ 3.14

+1.30

+3.10

—0.61

—1.54

November

+1.01

+0.03

—1.20

—0.30

—1.89

—1.33

—0.72

—0.49

+0.50

—1.89

+0.79

—0.27

December

+0.73

—0.59

+0.80

—0.49

+0.71

—0.92

—0.67

—1.27

+0.12

+1.21

+1.76

+0.83

3) 's Upper transit. Moon's hour-angle.

1842.

Oh-

lh.

2h.

8k.

4h.

5h.

6i>.

7h.

8h.

9h-

10h.

lib.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

January

—0.30

+0.64

—0.53

+0.02

+0.66

—0.61

+0.14

—1.48

+0.44

—1.20

+0.26

—1.84

February

—0.73

+0.88

+0.36

—0.13

—0.83

+0.67

+0.18

—1.80

—0.92

—0.73

—0.27

+0.04

March

+0.72

+0.38

+1.78

+0.30

+1.35

—1.15

—0.53

—2.15

—0.05

—0.29

+0.46

—0.84

April

—0.77

+0.92

+0.53

+0.37

—0.07

—0.39

—0.20

—1.65

+0.27

—0.42

+1.21

+0.10

May

—0.57

+1.78

+0.01

—0.16

+0.18

—1.01

—1.41

—0.97

— 0.92

+0.08

—0.43

+0.42

June

+0.38

+0.69

—0.95

+1.64

—0.18

+0.77

—0.25

—0.32

+0.76

+1.18

+0.38

—0.74

July

+0.78

+0.16

+0.69

—0.07

+0.60

—0.76

—2.08

+0.08

—1.65

+0.87

—1.04

+3.03

August

+0.88

+0.82

—0.08

—1.03

+1.17

—0.91

—0.95

+0.67

+0.72

—1.24

—0.17

+1.65

September

+0.71

—0.52

—0.13

—0.95

+0.67

+0.96

—0.82

+0.34

+0.82

+0.35

+0.62

+1.36

October

+3.46

+0.38

+0.77

—0.29

+0.06

+0.02

—0.25

—2.21

—0.98

—1.39

+0.52

—1.09

November

—0.05

+0.38

—1.07

—0.48

—0.36

—1.10

—0.53

+0.43

—0.95

+0.54

+0.14

+0.29

December

—0.59

—0.36

—0.34

—1.15

—0.75

+0.26

—0.57

+0.24

+0.39

+0.64

+0.87

+0.16

J's Lower transit.

1842.

12h.

13h.

14h.

15b-

16t.

17h.

18h-

19h-

20h.

21h.

22h.

23fc.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

January

—0.18

—1.19

—0.11

—2.13

+0.17

—0.61

+0.45

+1.05

+0.72

+0.66

—0.12

+0.62

February

—0.91

+0.71

+0.52

+0.40

—0.97

—0.86

—1.11

+0.44

—0.12

+0.14

+0.08

+0.84

March

+1.22

+ 0.20

+1.25

+0.88

+ 0.44

—0.34

—0.92

—1.43

+0.47

—0.39

+0.03

—0.35

April

+ 3.28

—0.86

+0.13

—0.12

—1.05

—1.34

—1.36

+0.15 —1.22

+0.19

—0.94

+1.11

May

+1.13

+1.78

+1.59

+ 1.10

—0.59

—0.52

—0.68

—1.47 —1.05

+0.15

—0.70

+1.01

June

+0.20

—0.82

+1.45

+0.33

+1.73

—1.19

+0.05

—1.36 —1.04

—1.43

—1.35

—1.37

July

—0.32

+1.84

—0.86

—0.72

+0.59

—0.95

—0.27

+0.03

—1.22

+0.09

—0.58

+0.68

August

—0.68

+2.50

—1.34

+0.59

—1.41

—0.67

—0.79

—0.58

—0.96

—0.26

+1.68

+0.81

September

+0.46

+1.11

—1.94

+0.25

+0.99

—0.45

—1.64

+0.10 —1.70

+2.14

+1.50

+0.96

October

+1.31

+1.68

—0.62

+0.74

—1.87

—0.14

+1.08

4-0.43 —0.16

—0.25

+0.71,

—0.56

November

+0.47

+0.40

+0.91

—1.13

+0.02 +0.11

—0.22

—1.46 +0.05

+o.<;s

+0.94

+ 1.58

December

+0.53

+0.35

+0.12

—0.45

—1.12

+0.15

+0.35

+0.54 +0.40 +0.57

+0.21

+0.07

At 14h- 19i'n- (observatory time) the difference from the half-monthly normals was used.

6

LUNAR EFFECT

D's Upper transit. Moon's hour-angle.

IMS.1

Oh.

lh.

2h.

3h.

4h.

6h.

6h.

7h.

8h.

'.HI.

10*.

Ilk.

a.

d.

A.

d.

d.

d.

a.

d.

d.

d.

d.

A.

April

^

-0.87

+ 1.47

+1.06

+0.39

—0.42

—1.30

—2.64

—1.72

—1.99

—0.12

—1.63

—0.48

May

+0.94

+0.89

+ 1.54

+0.45

+0.27

+ 0.38

+0.23

—1.02

—0.79

—1.01

+ 0.47

+1.08

Juno

—0.13

- I/'S

+0.18

—0.81

+0.07

+1.21

—0.31

+0.83

+0.16

+0.01

—0.10

+ 1.3(1

July

+2.10

+ (!.!)]

—0.71

-J-0.05

4-0. iin

+ 0.54

—0.62

+0.50

—0.3!)

—2.29

+1.05

—0.10

August*

—1.66

- (l.sl

—2.28

+1.17

—0.05

—1.12

+0.32

—1.24

+0.20

—0.22

—0.69

+0.46

September

-0.71

+0.26

—0.58

—0.85

—1.08

—0.23

—0.30

+1.74

—0.74

+0.37

—0.42

+ 0.58

October"

+1.06

+0.14

+0.28

+0.17

—0.03

—0.93

+0.19

—0.52

—1.10

+0.27

+ 0.33

+0.88

November

+0.62

+0.10

—0.72

—0.47

—0.80

—0.84

—0.57

—0.72

—0.02

+0.23

—0.17

+0.72

December

—0.41

—0.24

—0.04

—1.15

—0.88

—0.41

+0.07

+0.08

+0.39

+0.99

+1.09

+1.28

D 's Lower transit.

1843.

12h.

13h.

14h.

Ilk.

16h.

17h.

18h.

19».

20h.

21h.

22h.

231'.

d.

d.

d.

d.

.1.

d

d

d.

d.

d.

d.

d.

April

+0.79

+1.92

+0.72

—0.06

+0.53

+o!o5

— l.'lO

—1.06

—0.22

—1.06

—0.56

+1.58

May

+0.07

+0.74

+1.01

—0.58

—1.01

—1.03

—1.43

—0.27

—0.52

—0.49

+0.70

+0.08

Juno

+0.94

+1.46

—0.56

+0.29

— 0.99

—0.05

—0.63

+0.07

—0.38

—0.22

+0.74

—0.20

July

—0.25

+ 0.61

+0.66

+0.60

—0.43

—1.10

—2.00

—1.05

—0.20

—0.06

—0.64

+1.73

August'

+0.91

—0.59

—0.77

+0.59

—1.85

+0.01

—1.00

+1.37

—0.92

+0.74

+0.49

+0.06

September

-

-1.63

+1.85

+0.78

+2.32

+1.15

—0.29

—0.86

+1.08

+0.65

—0.37

—0.90

—0.7S

October1

+0.76

+1.50

+1.30

+0.63

—0.71

—0.92

—1.76

—0.70

—0.08

+0.50

—0.37

+0.78

November

+0.67

+0.45

—0.33

—0.25

—0.54

+0.04

—0.24

+0.17

+1.06

+ 1.00

+0.27

+0.50

December

+0.83

+0.51

+0.60

+0.02

+0.28

—1.14

—0.59

—0.74

—0.46

+0.40

+0.24

—0.42

3>'s Upper transit. Moon's hour-angle.

1844.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7h.

8h.

9h.

10h.

llh.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

January1

—0.79

—0.18

—0.26

+0.07

+0.20

+ 0.94

+0.58

+0.19

+ 0.22

+0.37

—0.46

+0.43

February

+1.43

+0.87

+0.67

—0.52

—0.69

—0.82

—0.56

—0.74

—0.29

+0.77

+1.03

+0.96

Mar eli

+1.10

+1.00

+0.42

+0.04

—0.72

—0.55

—0.69

—0.16

+ 1.18

+0.05

+0.93

—0.02

April

-0.52

+0.08

+0.23

+0.54

+0.09

+0.35

—0.49

—0.12

—0.55

—0.41

+0.16

—0.04

May

-0.76

+1.17

+0.88

+ 0.27

+0.02

—0.49

—0.18

—0.60

—0.35

—0.10

+0.14

+ 0.27

June

-1.11

+0.68

+1.07

+0.44

+0.09

—0.64

—0.24

—1.33

—1.58

—1.47

—0.40

+0.22

July

-1.09

+1.27

+0.78

+0.97

+0.18

—0.73

—1.05

—1.77

—0.17

—0.13

+0.68

+0.37

August

-2.30

+0.93

+0.19

—0.14

—0.16

—1.66

—0.78

—0.69

—0.38

—0.66

+(1.45

+0.45

September

-1.13

+1.47

—0.21

—0.05

—0.61

—1.15

—0.31

+1.05

+1.10

—0.18

+0.12

—0.34

October

—0.22

+0.42

—0.02

+0.22

—0.41

—0.59

—0.78

+0.38

—0.02

+ 1.04

+1.10

+1.01

November

—0.91

—1.12

—0.71

—0.57

—0.76

+0.03

—0.01

+0.45

—0.77

+0.06

+0.02

+2.57

December*

—0.20

—0.74

—0.21

—0.44

—1.14

—0.33

—0.41

—0.18

+0.14

+0.33

+0.30

+0.60

5 's Lower transit.

1844.

12h.

13h.

14h.

15h.

16H.

17h.

18h.

19h.

20h.

21h.

22>>.

231--

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

d.

January4

+ 0.32

+0.10

+0.31

—0.09

—0.61

—0.17

+0.84

+0.95

+0.32

—0.10

—0.80

—0.48

February

+0.44

0.00

+0.64

—0.26

—1.10

—0.49

—1.13

—0.39

—0.02

—0.05

—0.02

+0.84

March

+1.33

+0.62

—0.50

—0.21

—0.21

—0.68

—1.60

—0.50

—0.81

—0.48

+ 0.35

—0.10

April

+0.87

+ 0.70

+0.37

+0.64

—0.22

—0.54

—0.50

+0.05

—0.66

—0.42

— 0.0&

—1.03

May

+0.46

+0.09

+0.74

+0.43

+0.62

+0.00

—0.19

—1.10

—0.85

—1.17

+ 0.10

+0.06

June

+0.19

+0.48

—0.30

—0.36

—0.01

+0.35

+0.31

+0.29

+0.25

+0.20

+0.11

0.00

July

+1.27

+0.36

+0.46

—0.70

—0.51

—0.70

—1.03

—0.13

—0.31

—0.57

—0.12

+0.78

August

-t 0.60

+0.22

+0.84

—0.30

—0.19

—0.77

—1.06

—0.75

—0.34

—0.14

—0.43

+0.76

September

+0.25

+0.04

+0.73

—0.20

—0.03

—1.20

—1.89

—1.27

—1.33

—0.62

+0.13

+1.15

October

+0.66

+1.19

-40.78

—0.10

—0.36

—0.32

—0.03

—0.83

—0.58

—0.55

+ 0.00

-j O.IM;

November

+0.36

+1.09

+0.67

+0.43

+0.06

+0.40

+0.07

—0.77

—0.68

+0.41

+0.15

—0.11

December5

+0.48

+0.64

+1.06

—0.12

—0.12

—0.64

—0.22

+0.23

+0.20

+0.68

+0.17

+.1.42

1 There arc no observations in January, February, and March, of this year.

1 Attention was paid to the shifting of the zero of the scale between tin- 9th and 10th.

* Commencement of the hourly series of observations.

4 Proper attention was paid to the change in the zero of divisions after the 10th.

5 The half-monthly normals were used.

ON THE MAGNETIC DECLINATION.

3>'s Upper transit. Moon's hour-angle.

1815.

Oh-

lh.

2h.

3h-

4h.

5h.

6t>.

JTh.

8k.

9h.

lOt.

lib.

January
February
March.
April
May
Juue

d.
—0.46
—0.13
—0.42
+0.45
+0.53
+1.77

d.
—1.65
+0.48
—0.47
+0.54
+0.49
+1.63

d.
—1.52
—0.26
—0.26
+0.07
+0.01
+0.90

C
—1.65
—1.15
—0.48
+0.52
+0.16
+1.24

d.
—1.63
—0.56
—0.25
—0.21
—0.21
+0.86

d.

—0.24
—0.81
—0.75
—0.47
—0.22
+0.54

d.
+0.11
—0.39
—0.81
—0.27
—0.66
—0.66

d.

+1.41
—0.28
—0.25
—0.07
—0.25
—1.09

A.
+0.96
+0.18
+0.20
—0.25
—0.88
—0.75

d.
+1.83
+1.03
+0.39
—0.03
+0.04
—0.93

d.
+0.91
+0.98
+0.79
+0.27
+0.92
—0.83

d.
+1.11
+1.28
+0.91
+1.08
+0.43
—0.31

D's Lower transit.

1845.

12h.

13h-

14h.

15h.

16h.

17h.

18h.

19h.

20h.

21k-

22h-

23b.

January
February
March
April
May
June

d.
+0.02
+1.70
+1.15
+0.54
+0.53
+0.01

d.
—0.28
+0.67
+0.95
+0.56
+0.03
+0.86

d.

—1.07
—0.13
+1.79
0.00
—0.63
+0.30

d.
—0.60
+0.40
+0.35
+0.76
—0.01
+0.18

d.
—0.30
+0.03
+0.86
+1.01
—0.24
—0.33

d.

+0.14
—0.76
—0.08
—0.30
—0.48
—1.27

+1.09
—0.92
—0.83
—1.00
—0.70
—0.82

+0.29
—1.26
—1.27
—1.67
—0.30
—0.59

+0.'86
—0.46
—0.56
—1.62
—0.40
—0.92

+0.'34
+0.17
+0.37
—0.97
—0.53
+0.05

d.
+0.39
—0.05
—0.39
+0.37
+1.16
+0.74

d.
+0.38
—0.09
—0.73
—0.78
+0.63
+0.64

Value of a scale division 0'.453.

One of the first questions to determine is how many of these residuals must be
used to give a definite result, and another one is whether numbers deduced from
different parts of the series would give harmonious results. To test both of these
the observations were formed into three groups — one containing 4,900 in 19 months
of 1840, '41; another, 6,715 results in 21 months of 1842, '43; and a third, 10,029
results in 18 months of 1844, '45. In all, 21,644 results.

The following table contains the result for each group. Group II includes three
months of the hourly series of observations treated as if only equal in weight to
the bi-hourly series.

The sign 2 indicates the algebraic sum of the values in the preceding tables for
the months comprised in each group, and for every hour-angle of the moon. The
lines headed I, II, III, contain the preceding values divided by their respective
number of months and expressed in minutes of arc, or the lunar diurnal variation.

It's Upper transit. Moon's hour-angle.

Oh.

lh.

2h.

3h.

4h.

5h.

6h.

7h.

8h.

9h.

10h.

llh.

l of group I
I " II
z " III

il.
+10.27
+ 6.59
+ 7.96

d

+8.07
+7.35
+ 6.93

d.

+7.52
—0.23
+1.77

d.
+11.17
— 2.38
— 0.53

d.
—4.32
+0.87
—5.91

d.

—1.46
—5.95

—7.48

d.

— 7.06
—10.90
— 7.60

d.
— 5.49
—10.83
— 4.05

d.

—14.63
— 6.35
— 2.01

d.
—1.61

—2.78
+2.00

d.

—1.70

+2.48
+ 7.77

d.
+ 0.30
+ 7.65
+10.98

I
II
III

+0'.24
+0.14
+0.20

+OM9
+0.16
+0.17

+0'.18
+0.00
+0.05

+0'.27
—0.05
—0.02

— O'.IO
+002
—0.15

— 0'.04
—0.13
—0.19

— 0'.17
—0.24
—0.20

— 0'.13
—0.23
—0.10

— 0'.35
—0.14
—0.05

— 0'.04
—0.06
+0.05

— 0'.04
+0.05
+0.20

+0'.01
+0.16
+0.28

D's Lower transit. Moon's hour- angle.

12h.

13h-

14h.

15h.

16h-

17h.

18h.

19h.

20h.

21h.

22h-

23h.

i of group I
I " II
I " III

d.

+11.91
+13.46
+ 10.98

d.

— 2.18
+16.15
+ 8.22

d.

+4.54
+4.52
+5.96

d.
+6.00
+3.S6
+0.24

d.

—7.22
—6.64
—1.66

d.
— 3.54
—11.24
— 7.45

d.

— 9.43
—14.67
— 9.61

d.

—8.71
—4.68
—9.02

d.

—0.71
—6.90
—7.35

d.
+3.14
+2.79
—3.38

d.

+1.58
+ 1.53
+1.90

d.

+7.60
+ 8.73
+1.80

I
II
III

+0'.29
+0.29
+0.28

— 0'.05
+0.35

+0.21

+0'.ll
+0.10
+0.15

+0'.14
4-0.08

0.00

— 0'.17
—0.14
—0.04

— 0'.09
—0.24
—0.19

— 0'.23
—0.32
—0.24

— 0'.21
—O.ltl
—0.23

— 0'.04
—0.14
—0.19

+0'.08
+0.06
—0.08

+0.04
+0.03
+0.05

+OM8
+0.19
+0.05

+ indicates west, — east, deflection from the normal position.

8

LUNAR EFFECT

These results, I, II, III, when expressed analytically by means of Bessel's form
of periodic functions, and when treated by the method of least squares, are repre-
sented by the following equations, in which the moon's hour-angle 0 is reckoned
from the upper transit westwards at the rate of 15° to each hour. AC represents
the lunar diurnal variation.

Group I, 1840-'41. A^ = -f O'.OOS + 0'.063 sin. (e + 92°) + OM89 sin. (29 + 67°)
" II, 1842-'43. AC = — O'.OOG + O'.OSO sin. (e + 263°) + 0'.282 sin. (29 + 63°)
" III, 1844-M5. AC = O'.OOO + 0'.075 sin. (o + 292°) + 0'.219 sin. (29 + 88°)

The numerical results from these equations are presented graphically on the

following diagram.

LuNAB-DlDRNAL VARIATION OP THE MAGNETIC DECLINATION.

Oh. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24>>.
U. C. L. C. U. C.

from 4,900 observations in 1840, '41.

from 6,715 observations in 1842, '43.

from 10,029 observations in 1844, '45.

The curves all agree in their distinctive characters, and show two east and two
west deflections in a lunar day, the maxima W. and E. occurring about the upper
and lower culminations, and the minima at the intermediate six hours. The total
range hardly reaches 0'.5. These results agree generally with those obtained for
Toronto and Prague.

From 8,000 to 10,000 observations seem to be required to bring out the results
satisfactorily, and the best results are derived from the use of all the groups.

The following table contains annual sums of deflections for each hour, and the
resulting lunar-diurnal variation from the 21,644 observations available for the
purpose : —

ON THE MAGNETIC DECLINATION.

9

Upper curve. Westerly hour-angles.

TEAR.

Oh.

lh.

2h.

3h.

4h.

5h-

6t.

7h.

8i.

9b-

10h-

llh.

I for 1840
1841
1842
1843 (a)
1843 (6)
1844
1845

d.

+1.77
+8.50
+3.92
+1.51
+1.16
+6.22
+1.74

+2.05
+6.02
+6.15
+1.14
+0.06
+5.91
+1.02

d.
+2.57
+4.95
+1.04
—0.19
—1.08
+2.83
—1.06

d.

+4.97
+6.20
—1.93
+1.00
—1.45
+0.83
—1.36

d.

—0.94
—3.38
+2.50
+0.08
—1.71
-3.91
—2.00

d.
+2.63
—4.09
—3.25
—0.52
—2.18
—5.53
—1.95

d.
—3.85
—3.21
—7.27
—3.32
—0.31
—4.92
—2.68

d.
—2.18
—3.31
—8.82
—0.85
—1.16
—3.52
—0.53

d.
—3.99
—10.64
—2.07
—3.49
—0.79
—1.47
—0.54

d.
+1.56
—3.17
—1.61
—2.66
+1.49
—0.33
+2.33

d.

—0.76
—0.94
+2.55
—1.32
+1.25
+4.73
+3.04

d.
—0.40
+0.70
+2.54
+2.78
+2.33
+6.48
+4.50

Mean ^
Same in arc

+0.43
+0'.19

+0.37
+0.17

+0.12
+0.05

+0.08
+0.04

—0.21
—0.10

—0.31
—0.14

—0.42
—0.19

—0.32
—0.14

—0.33
—0.15

+0.01
+0.01

+0.23
+0.10

+0.41
+OM9

Lower curve. Easterly hour-angles.

TEAR.

12h.

13h.

14h.

15h.

16h.

17h.

18t.

19h.

20k

21h.

22h-

23h.

Mos.

1 for 1840
1841
1842
1843 (a)
1843 (6)
1844
" 1845

d.
+4.66
+7.25
+6.51
+4.69
+2.26
+7.03
+3.95

d.

—3.50
+1.32
+7.70
+5.99
+2.46
+5.43
+2.79

d.
—0.66
+5.20
+1.10
+1.85
+1.57
+5.70
+0.26

d.
+1.32
+4.68
—0.26
+3.22
+0.90
—0.84
+1.08

d.

—3.57
—3.65
—3.07
—2.60
—0.97
—2.69
+1.03

d.
+3.85
—7.39
—6.81
—2.41
—202
—4.70
—2.75

d.
—4.02
—5.41
—5.06
—7.02
—2.59
—6.43
—3.18

d.

—0.81
—7.90
—3.56
+0.15
—1.27
— 4.22
—4.80

d.
—0.16
—0.55
—5.83
—1.59
+0.52
-4.25
—3.10

d.
+0.81
+2.33
+2.29
—1.46
+1.96
—2.81
—0.57

d.
—2.89
+4.47
+1.46
—0.07
+0.14
—0.32
+2.22

d.

+3.36
+4.24
+5.40
+2.47
+0.86
+1.75
+0.05

7
12
12
6

3

12
6

Mean ^
Same in arc

+0.63
+0'.29

+0.42
+0.19

+0.29
+0.13

+0.14
+0.06

—0.23
—0.10

—0.40
—0.18

—0.58
—0.26

—0.42
—0.19

—0.27
—0.12

+0.01
+0.01

+0.09
+0.04

+0.26
+OM2

37
21
21

79

The two values for 1843, marked (a) and (&), exhibit the separate sums for the
bi-hourly and the hourly observations, and were required to give proper weights
to each. There are 37 months of bi-hourly, and 21 months of hourly observations
— the latter having double weight, as found from a consideration of the probable
errors derived respectively from all the results of the years 1842 and 1844. The
probable error of any single monthly mean for any hour in the year 1842 was
found = + Od .60, and the same for the year 1844 was = + Odl.40. Hence the
weights for a resulting value in the bi-hourly series is to the weight for a value in
the hourly series nearly as 1:2, or the weights are nearly proportional to the
number of observations — a result which indicates that no constant errors influence
the result. The accordance among themselves of the values for the easterly hour-
angles is somewhat better than the corresponding values for the westerly hour-
angles — a circumstance which seems to connect itself with another phenomenon to
be mentioned presently. Giving, therefore, double weight to months of the hourly
series, the lunar-diurnal variation resulted as given above. When expressed
analytically, it takes the form

Ac = +0'.001 + 0'.029 sin (0 + 295°) + 0'.207 sin (29 + 85°)
which may also be written

AC = 0".0 + 1".7 sin (15n + 295°) + 12".4 sin (30rc + 85°)

where 0 represents the moon's hour-angle, reckoned from the upper culmination,
or n the number of hours after the same epoch : -f indicates west, and — east
deflection.

10

LUNAR EFFECT

The constant in Bessel's formula comes out zero, and hence it is inferred that
the moon has no specific action in deflecting the magnet by a constant quantity.
The coefficient of the first term of the formula is small, and it is from the second
term that the distinctive features of the double-crested curve result. These results
are all represented by curves.

Both the east and west deflections are well marked, those occurring when the
moon is east of the meridian being greater than those when west.

It is not at all necessary to take in the third or higher terms. The progression
of the hourly values is systematic, and the agreement between the computed and
observed values is deemed satisfactory. The following diagram represents the
curve resulting from the above equation, the observed values being indicated by
dots.

LtTNAB-DlURN AL VARIATION.

I

+0'.30
.25
.20
.15
.10
.05
.00
.05
.10
.15
.20
.25

— 0.30

L

-i 1 — i

7

Oh. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24h-
U. C. * L. C. U. C.

From 21,644 observations at Philadelphia, from 1840 to 1845.

The principal western maximum occurs 6 minutes after the lower culmination
of the moon, and amounts to 0'.23. The secondary maximum occurs 14 minutes
after the upper culmination, and amounts to O'.IS. The principal minimum occurs
at 6h- 17m- after the lower culmination, the easterly deflection being 0'.22. The
secondary minimum at 6d 03m- after the upper culmination, with a deflection of
OM9. The greatest range is 27", and the secondary 22". The epochs of the
maxima and minima are found from the formula to be at a mean 10 minutes after
culmination. The probable error of a single computed value of the lunar declina-
tion is +_ 1".32. The Toronto observations gave j+ 1".37 from more than twice the
number of observations, so that the Philadelphia results are worthy of every
confidence.

At Toronto, from the second investigation, embracing about 44,000 observations,
the western and eastern deflections balanced, giving for the range 38".3. The

ON THE MAGNETIC DECLINATION.

11

Prague observations also confirm the nearly equal deflections (mean) to the west
and east. The epochs of the maxima and minima were found from the four roots
of the equation 0 = 0.029 cos (6 + 295°) + 0.414 cos (20 + 85°), which gave 10
minutes as the mean time elapsed between the moon's passing the meridian, and
the time of maxima deflections. If we take the four phases into account, the lunar
action seems to be retarded 10 minutes, which quantity may be termed the lunar-
magnetic interval for the Philadelphia station. At Toronto the intervals are not
so regular.

The secondary range exists at Toronto, and is a marked feature in the Prague
result.

The following table contains the observed and computed values and their dif-
ferences : —

Upper Curve.

Lower Curve.

Observed.

Computed.

Difference.

Observed.

Computed.

Difference.

Oh-

+OM9

+0'.18

+0'.01

12u.

+0'.29

+0'.23

+0'.06

1

+0.17

+0.17

0.00

13

+0.19

+0.21

—0.02

2

+0.05

+0.10

—0.05

14

+0.13

+0.13

0.00

3

+0.04

+0.01

+0.03

15

+0.06

+0.03

+0.03

4

—0.10

—0.09

—0.01

16

—0.10

—0.08

—0.02

5

—0.14

—0.16 .

+0.02

17

—0.18

—0.18

0.00

6

—0.19

—0.19

0.00

18

—0.26

—0.22

—0.04

7

—0.14

—0.17

+0.03

19

—0.19

—0.21

+0.02

8

—0.15

—0.09

—0.06

20

—0.12

—0.14

+0.02

9

+0.01

+0.01

0.00

21

+0.01

—0.05

+0.06

10

+0.10

+0.12

—0.02

22

+0.04

+0.06

—0.02

11

+0.19

+0.20

—0.01

23

+0.12

+0.14

—0.02

The formula or curve enables us to divide the observed curve so as to show the
diurnal and semi-diurnal part of the observed variations. The decomposition of
the curve is made on the diagram where the resulting curve for the diurnal period
is given.

The lunar-diurnal variation seems to be subject to an inequality depending on
the solar year, for the investigation of which the preceding results were rearranged
in two groups, one containing the hourly values for the summer months (April to
September), the other the values for the winter months (October to March). For
the summer season we have 11,087 observations, and for the winter 10,557.

HOURLY SUMS OF THE LUNAR VARIATION FOR THE SUMMER SEASON.
Moon's hour-angle.

Oh.

lh.

2h.

3h.

4h.

5h.

6h-

7h.

8i>.

9h.

10h.

Hh.

I 1840-3
z 1844-5

2
40"
Same in arc

+9.29
+8.62

+0.66
+0'.30

+14.15
+8.26

+0.77
+0.35

+3.45
+3.92

+0.28
+0.13

+7.20
+3.95

+0.38
+0.17

—2.93
+0.05

—0.07
—0.03

—2.23
—4.36

—0.27
—0.13

—15.73
—4.64

—0.63
—0.28

—6.18

—4.87

—0.40
—0.18

—12.04
—3.81

—0.49
—0.22

—4.57
—3.87

—0.31
—0.14

—1.49
+1.51

+0.04
+0.02

+12.38
+2.13

+0.42
+0.19

12h.

13h.

14h.

15h.

16h.

17h-

18k-

19h.

20h.

2lh.

22n-

23h.

Mo's.

z 1840-3
I 1844-5
2
40
Same in arc

+17.02
+4.62

+0.66
+0'.30

+11.44
+3.32

+0.45
+0.20

+5.18
+2.51

+0.26
+0.12

+13.14

+0.44

+0.35
+0.16

—4.94
+0.10

—0.12
—0.05

—7.97
—4.85

—0.44
—0.20

—16.72

—6.88

—0.76
—0.34

—10.27
—5.47

—0.53
—0.24

—12.44
—6.18

—0.62
—0.28

+0.11
—4.17

—0.21
—0.09

—5.49
+2.04

—0.04
—0.02

+10.12
+1.61

+0.33
+0.15

22
9

12

LUNAR EFFECT

HOURLY SUMS OF THE LUNAR VARIATION FOR TUB WINTER SEASON.
Moon's hour-angle.

OU.

lh.

2h.

3h.

4h.

5h.

gh.

7h.

8h.

0k.

10i>.

llh.

z 1840-2
i 1843-5

2
39
Same in arc

+6.42
+0.50

+0.19
+0'.09

+1.21
—1.27

—0.04
—0.02

+4.92
—3.23

—0.04
—0.02

+3.04
—5.93

—0.23
—0.10

+1.19

—7.67

—0.36
—0.16

—3.00
—5.30

—0.35
—0.16

—1.92
—3.27

—0.22
—0.10

—8.98
—0.34

—0.25
—0.11

—8.15
+1.02

—0.16
—0.07

—1.31
+7.36

+0.35
+0.16

+1.02
+7.51

+0.41
+0.18

—6.76
+11.18

+0.40
+0.18

12h.

13i>.

14h.

15l>-

16k

17h.

18h-

19h.

2QU.

21t-

22h-

23h.

Mo's.

z 1840-2
j 1843-5
2
39
Same in arc

+6.09
+8.62

+0.60
+0'.2V

+0.09
+7.34

+0.38
+0.17

+2.31
+5.02

+0.32
+0.14

—4.18
+0.70

—0.07
—0.03

—7.95
—2.73

—0.35
—0.16

—4.79
— 1.62

—0.37
—0.17

—4.79
—5.32

—0.40
—0.18

—1.85
—4.82

—0.29
—0.13

+4.31
—0.65

+0.08
+0.04

+3.86
+2.75

+0.25
+0.11

+8.46
0.00

+0.22
+0.10

+5.35
+1.05

+0.19
+0.09

15
12

Expressed analytically, the lunar-diurnal variation in the two seasons is as
follows : —
In summer,

AC = _0'.006 + 0'.02S sin (e + 18°) + 0'.2T8 (29 + 61°)
In winter,

A<£ = +0'.005 + 0'.058 sin (s + 264°) + 0'.173 (29 + 115°)

The characteristic feature of the annual inequality in the lunar-diurnal variation
is, therefore, a much smaller amplitude in winter than in summer. Kreil, indeed,

Ltrif AB-DIURNAL VARIATION.

In summer

In winter

+0'.30
.25
.20

!• 'II

.05

0.00

.05

; .10

i .15

.20

.25

— 0.30

11,1

O'i. i 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 241'.
U. C. L. C. U. C.

Summer curve from 11,087 observations (.)
Winter " " 111/)".? " (°)

ON THE MAGNETIC DECLINATION. 13

inferred from the ten-year series of the Prague observations, that in winter the
lunar-diurnal variation either disappears, or is entirely concealed by irregular fluc-
tuations, requiring a long series for their diminution. The method of reduction
which he employed was, however, less perfect than that now used. The second
characteristic of the inequality consists in the earlier occurrence of the maxima
and minima in winter than in summer. The winter curve precedes the summer
curve by about one and three-quarter hours. Both these features are well ex-
pressed in the above diagram. At Toronto, the same shifting in the maxima and
minima epochs was notice'd, but the other inequality in the amount of deflection
is not exhibited. It seems probable that the Philadelphia results are more typical
in form than those either of Prague or Toronto. It is also apparent that the
smaller deflection at the upper culmination in the annual mean, when compared
with the deflection at the lower culmination, is entirely produced by the feeble
lunar action in winter. The maximum west deflection in summer occurs actually
near the upper culmination. At the same season the maximum east deflection is
still retained (as in the annual curve) about six hours after the lower culmination.
In the winter season this last mentioned maximum east deflection is actually the
smaller of the two. We have —

Maximum summer range 35".4, Secondary, 31".8

" winter " 25 .2, " 15 .6

Difference 10 .2, 16 .2

At Prague the maximum summer range was 44".

Next I proceed to examine whether the phases of the moon, the declination, or
parallax, have any sensible effect upon the magnetic declination. Mr. Kreil found,
from a ten years' series of observations at Prague, that there was no specific change
in the position of the magnet depending upon the moon's phases and parallax, but
that the declination was 6". 8 greater when the moon was at the greatest northern
declination than when at the greatest southern declination. On the contrary, Mr.
Broun, from the Makerstoun observations, a much shorter series than the one at
Prague, inferred that there was a maximum of declination two days after the full
moon. He also found a maximum corresponding to the greatest northern declina-
tion of the moon, but does not appear to have investigated the effect of distance.
The residuals which we have been treating enable us at once to examine these
several points.

Beginning with the lunar phases, the daily means for the day of full and new
moon, and for two succeeding days, were compared with the monthly mean declina-
tion. In case any of the hours were disturbed, the monthly normal for the hour
was substituted for the disturbed observation before the mean was taken. If one-
half or more of the hourly readings were disturbed, the daily mean was altogether
omitted. Accidental omissions of hourly observations were supplied by the hourly
normal. The half-monthly normals were then compared with the half-monthly
means. In the table of differences thus formed, equal weight is given to the
bi-hourly and hourly observations. The daily mean having been subtracted from the
monthly mean, the positive sign indicates a western deflection, and the negative sign
3

u

LUNAR EFFECT OF THE MAGNETIC DECLINATION.

an eastern one, as compared with the normal position. The following table con-
tains the result : —

Sum of deflections.

Number. Deflection.

Full moon Q
1st day after
2d day after

New moon 9
1st day after
2d day after

+11.6
—7.1
—9.3

52
51

48

+0-I..22
—0.14
—0.19

+OMO
—0.06
—0.08

+0'.07

—11.5
+1.5
+4.4

43
47
49

—0.27
+0.03
+0.09 •

—0.12

+0.01
+0.04

+0'.09

The effect is very small, scarcely much beyond the probable error, but the table
indicates that the north end of the magnet is deflected to the westward O'.l at the
full, and as much to the eastward at the change day, the range between full and
new moon being 0'.2. A more definite result could hardly be expected from a
series of observations extending over but five years.

Treating the subject of the effect of the moon's variation in declination in pre-
cisely the same manner, we obtain the following result : —

Mean deflection.

. — 0'.20
. —0.10
—0.09

One day before .

At moon's max. declination

One day after

Mean .

One day before .

At moon's min. declination

One day after

Mean

from 54 days of observation.
« 53 ,, „

" 55 "

" 162 "

tt

« 54 ,,

" 52
" 52

tt

+ 0'.01

158

These results do not positively fix a deflection of the magnet as depending on
the moon's greatest north and south declination, the amount resulting from the
comparisons being of nearly the same magnitude as its probable error.

A similar investigation, with respect to the moon's distance from the earth, gives

the following results : —

Mean deflection.

One day before .
At moon's perigee
One day after

Mean

One day before .
At moon's apogee
One day after

Mean

— OM8 from 50 days of observation.

—0.18 " 41

0.00 " 59 " "

— C'.12 " 150 "

— 0'.02 " 55 "

—0.20 " 53

—0.13 " 47

— OM2 " 155

The differences being of the same order of magnitude as the probable errors, no
conclusion as to the effect of distance can be drawn from them.

I propose hereafter to extend the discussion of the moon's effect on the declina-
tion to the effect on the earth's magnetic force.

SMITHSONIAN CONTRIBUTIONS TO KNOWLKDGK.

DISCUSSION

MAGNETIC AND METEOROLOGICAL OBSERVATIONS

MADE AT THE GIRARD COLLEGE OBSERVATORY, PHILADELPHIA,

IN 1840, 1841, 184l>, Ie4^, 1844, AND 1845.

SECOND SECTION,

COMPRISING PARTS IT, Y, AXD YI. HORIZONTAL FORCE.

INVESTIGATION OF THE ELEVEN (OR TEN) YEAR PERIOD AND OF THE DISTURBANCES OF THE
HORIZONTAL COMPONENT OF THE MAGNETIC FORCE, WITH AN INVESTIGATION OF THE
SOLAR DIURNAL VARIATION, AND OF THE ANNUAL INEQUALITY OF THE HORI-
ZONTAL FORCE; AND OF THE LUNAR EFFECT ON THE SAME.

BY

A. I). BACHE, LLD,, F.R.S.,

MEM. CORK. ACAD. BC. PARIS ; SUPERINTENDENT U. S. COAST Sl'RVET.

[ACCEPTED FOR PUBLICATION, JUNE, 18C2.]

PART I Y.

INVESTIGATION

OP TUB

ELEVEN (OR TEN) YEAR PERIOD AND OF THE DISTURBANCES OF THE
HORIZONTAL COMPONENT OF THE MAGNETIC FORCE.

(1)

INVESTIGATION

ELEVEN (OR TEN) YEAR PERIOD, AND OF THE DISTURBANCES OF THE HORIZONTAL
COMPONENT OF THE MAGNETIC FORCE.

VOLUME XI of the Smithsonian Contributions to Knowledge contained a discus-
sion, in three parts, of the observations for magnetic declination. The first part
referring to the eleven (or ten) year period in the amplitude of the solar diurnal
variation, and of the disturbances of the magnetic declination ; the second, to the
annual inequality of the solar diurnal variation, and the third, to the influence of
the moon on the magnetic declination. The present discussion refers to the
changes of horizontal force, and will be carried on in the same order as the former,
so as to dispense with explanations in the mode of treatment, unless in those por-
tions involving the peculiarities of the horizontal force instrument and record.
Charles A. Schott, Esq., has rendered me the same assistance in this work, stated
in the introduction to Part I.

The horizontal force instrument was one of Gauss's large bifilar magnetometers,
made by Meyerstein, of Gottingen, the weight of the magnetic bar being about
twenty-five pounds, and its length being thirty-six inches and five-eighths. The
suspension wires were slightly inclined, the smaller distances between them being
above the larger. The value of one division of the scale in parts of the horizontal
force was determined to be : —

in May, 1840, .... 0.000035
in June, 1841, .... 0.000038

The mean, or 0.0000365 is the value used throughout the series. The sensibility
of the instrument was thus very considerable. The instrument having been pro-
perly adjusted with the bar at right angles to the mean magnetic meridian, the
torsion angle Z was found to be 71° 43'. The relation 7c = a cotan. Z expresses
the value of one scale division li in parts of the horizonal force, a being the value
of a scale division in parts of the radius, or 0.00011 = 0'.38, and Z the angle of
torsion. Increase of readings on the scale corresponded to decrease of horizontal
force.

The instruments were placed in position by the equations deduced by Professor
Lloyd, for the case of the declinometer in equilibrium with the horizontal and
vertical force magnetometers, the position of instablc equilibrium being taken

4 DISCUSSION OF THE HORIZONTAL COMPONENT

necessarily from the form and position of the observatory. The effect of the small
vertical force bar at first used, upon the bifilar was quite insensible, and that of
the declinometer bar affected the value of the scale but slightly, the effect of
both instruments changing the value of the scale divisions only in the ratio of 1 to
0.9956.

A thermometer, by Francis, of Philadelphia, divided to half degrees of Fahren-
heit's scale, and easily read to tenths, was placed in the box of the horizontal force
magnetometer and as near as practicable to the bar.

After the bifilar was set up, a motion commenced in the direction indicating
decrease of force ; it was progressive though not steadily so. After a time an extra
scale was required on occasions of auroral, or other disturbances, and finally the
ordinary readings were upon this extra scale. On the occasion of the change of
the vertical force magnetometer, in January, 1841, by the substitution of Saxton's
balance magnetometer for Lloyd's, the magnetism of the horizontal force bar was
examined and found to have sensibly decreased ; its force amounted to 0.9601 of
its original force, in May, 1840. The experiments were made by means of deflec-
tions with a subsidiary declinometer bar, the only means then available. A further
experiment of the loss of force was made in June, 1841, when the instrument was
accidentally disturbed by one of the observers. The loss of magnetism then found,
by means of a new determination of the angle Z, was 0.0314 of its amount in
January, 1841. To ascertain the change of magnetism of the bars of the mag-
netometers, vibrations were also made use of, but they led to no satisfactory result.
The progressive change of the scale readings from the change of the horizontal
force and loss of magnetism of the bar, will be investigated further on.

The observations, between June, 1840, and September, 1843, were made bi-hotirly,
and from October, 1843, to the close of the series, hourly. The series extending
over five years is not quite continuous; no observations were made on eleven
days in January, 1841, on the occasion of the introduction of a new vertical force
magnetometer, and the consequent necessity of readjusting the instruments ; in
January, February, and March, 1843, the work was reduced to but a single reading
a day, by circumstances elsewhere stated ; there are also some minor disturbances
at other times when the difference in the readings, however, were ascertained and
allowed for. Full statements bearing on the continuity of the series will be given
in subsequent pages.

The reduction proper, necessarily commences with the operation of bringing all
the readings to the same standard temperature, to render them comparable among
themselves.

Correction of the Readings of the Bifilar Magnetometer for Changes of Temperature.

The care bestowed on the experiments to ascertain the effect of the temperature
on the instrument, and the perseverance with which they were carried out were
not rewarded with a corresponding degree of agreement in the results obtained, by
the various processes employed. This it will be recollected was also the case at
other observatories. The subject of the co-efficient of temperature for the bifilar
magnet is fully treated in the preface to the three volumes containing the record.

OF THE MAGNETIC FORCE. 5

and it will, therefore, in this place only be necessary to recapitulate in general the
results and to state the nature of the experiments there described.

The first observations for the temperature co-efficient were made on July 16,
1840. Oscillations were observed alternately at the ordinary temperature and near
the freezing point, obtained by surrounding the box containing the magnet with
ice ; at the same time comparative oscillations of a bar in another building were
observed to furnish the necessary data to correct the bifilar results for any change
in the horizontal force during the progress of the experiments. The value deduced
was 2.8 scale divisions for a change of 1° Fahrenheit. No reliance was placed on
this result on account of the comparatively rude indications of the subsidiary
instrument, and also on account of an irregularity at a certain point in the curve
representing the connection of change of force with change of temperature.

The method of deflections was tried, and abandoned on account of the small
amount of deflection at a distance sufficiently great to prevent the chance of per-
manent changes from the mutual action of the bars.

On the 22d of February, 1841, comparisons by vibrations were again resorted to,
but with no better success, the correction for change of force during the interval
being unsatisfactory. The result deduced was 3.0 scale divisions for 1° Fahr.

Applying the results to the readings of the bar when mounted on the bifilar
suspension wires in the observatory, they were so little satisfactory that it was
determined to get the change of intensity of the bar by heating and cooling the
observatory while the bar remained in situ.

In January and February, 1842, a continuous series of observations was made by
allowing the observatory to attain the winter temperature on one day, and obtaining
thus a result by comparison with the preceding and succeeding days, when the
room was artificially warmed. The value found was 1.55 scale divisions for 1°
Fahr. At this time the observatory was warmed by a soap-stone stove with copper
fixtures.

About the close of the year 1842 an efficient set of subsidiary instruments was
mounted in one of the College buildings, the bifilar magnet being about nine inches
in length. After the relative value of the scales of the instruments had been
ascertained, comparative observations were made, six each day, in the morning and
afternoon. These observations and results are given in a table extending over
eleven months, in 1843, and over eleven months, in 1844. The results were fluc-
tuating, and the discrepancies proved conclusively, that other causes were at work
which would not be accounted for. The changes in the force were generally small.
In the course of these experiments I found, beyond a doubt, that instruments of
the same dimensions were required to give comparative results. During an aurora
the small instrument in the College gave by no means the same results as the large
instrument in the observatory; there were numerous comparisons determining this.
I had reason also to believe that the large bar had its induced magnetism easily
disturbed, and not regularly renewing itself, so that the correction for temperature
may be supposed compound, one part permanent and cne part temporary. The
following results were obtained : —

fi DETERMINATION OF THE TEMPERATURE CO-EFFICIENT

Observations between February and June, 1843, 2.50 scale divisions

" July and December, 1843, 2.28 " "

" January and June, 1844, 1.94 "

July and December, 1844, 2.00 "

for 1° Fahr. It may also be stated that no reasonable supposition in regard to
differences of temperature between the indications of the thermometer and mag-
netic bar, or to changes in the co-efficient varying with the temperature, will explain
all the cases of discrepancies. In these comparisons, always near each other in
time, small differences in intensity, as shown by the subsidiary instrument, were
allowed for, but the corrections for temperature of this latter instrument were
neglected, as the changes of temperature in the building where it was placed were
small.

Another method, not quite so unobjectionable as the preceding one, was tried ;
it consisted in taking the results corresponding to the highest temperatures during
each winter, and comparing them with those corresponding to the lowest tempera-
tures, a correction being made to reduce the changes of force by means of the
secondary instrument. These comparisons were liable to be affected by the unequal
distribution of the results used over the different parts of the month. The result
was : for combinations and comparisons, from

January, 1844, to June, 1844, 2.03
July, 1844, to December, 1844, 2.29
scale divisions for each degree of Fahrenheit's scale.

The mean value of all the results obtained by the various processes explained, is
2.6 scale divisions, and as a preliminary measure, it was supposed that the co-effi-
cient was changeable, and hence a correction for change of temperature was applied,
varying from 3.2 scale divisions, in 1840, to 2.0 scale divisions, in 1844.

On resuming the discussion it was thought desirable to deduce a value for this
co-efficient directly from the entire mass of observations, as this could not fail to
satisfy the whole series. For this purpose it was indispensable to make the series
of observations continuous, or, in other words, to refer the readings, extending over
five consecutive years, to the same initial division of the scale. This is, therefore,
a proper place for stating all cases when the instrument suffered any disturbance
and the amount of scale correction required. All necessary explanations are given
in the record.

The first break in the series occurred August 27, 1840, at 12h 22m (Philadelphia
time), when the mirror was accidentally deranged. The observed numbers from
this date to September 22, at 12h 22m have been brought to comparison with former
numbers by the mean position of the bar for six previous days (in some cases
seven) and by the hours, from Oh 22m to 22h 22m inclusive. This correction is
already applied in the record, its probable error is given as 3.3 scale divisions.

On September 22, 1840, the instrument was readjusted.

An interruption of eleven days occurred, in January, 1841, owing to the intro-
duction of a reflecting vertical force magnetometer, and requiring a new arrange-
ment of the instruments. The horizontal force magnetometer was left in its place.
The mean values for January, viz : 944.6 divisions for the bifilar, and 36°.5 for the

OF TIIE HORIZONTAL FORCE. 7

corresponding temperature, as given in volume I of the record, may be reduced to
the true mean by the interpolation of values, between December 31 and January
12. The daily mean (at 32°), on December 31, was 842.3, and on January 12,
913.0, hence, omitting the readings for January 3d, and 10th, as Sundays, the com-
plete monthly mean should be 18.6 divisions less or equal 926.0.

The observations were resumed on the 12th, and continued to February 8th at
221' 49 |m, when the wires were found to have been slightly deranged, two days
previously, February 6, 18h 22m (Philadelphia time), a great change in the position
was noticed ; on re-arranging the instrument it did not return to its former read-
ings. A correction of -f- 116 has been applied (in the record) to the previous mean
readings only in this month, and in consequence + H6 divisions should be added
to each individual reading from the commencement of the series ; but on account
of another disturbance of the instrument, on the 22d, at 16h 22m (Philadelphia time),
a further correction of -f- 92.8 scale divisions should be applied. The total correc-
tion is therefore + 208.8. Besides these corrections the readings on the 22d from
Ou 22m (Philadelphia time) to 10h 22m (Philadelphia time), inclusive, should be
increased by + 25.1 divisions, the alhidade of the instrument having been dis-
turbed.1

On the 2d of June, 1841, the suspension wires were struck accidentally, derang-
ing the instrument ; the readings were then near the end of the subsidiary scale,
and in rearranging the instrument the new readings were brought near the middle
of the scale. The total difference between the old and new scale readings, the
latter commencing with the first of the month, is 900 scale divisions. The means
between June 1st and 5th are already corrected in the record, but the individual
bi-hourly readings require a correction of + 21 32 scale divisions to produce these
means. It was thought best not to apply this correction of — 900 divisions to the
observations between June, 1840, and June, 1841, but simply to state the quantity
since it can be applied easily to any result hereafter.

At the close of 1842 the regular observations were discontinued for three months,
during January, February, and March, 1843; a daily reading was taken at 14h 22m
(Philadelphia time), in order to keep up a continuity in the series. By means of
the reduced readings in the same months in the other years, it was found that a
correction of -- 3d. 4 — 3*. 7 and + ld.5 for January, February, and March, respect-
ively, was required to refer the mean at 14h 22m to the mean of a complete bi-hourly
daily series. Applying these corrections, the corrected monthly means become : —

0

1 The corrected daily means for the month of February, 1841, should, therefore, read as follows: —

1st ... 1163.5

10th

1131.1

19th

1127.9

2cl ... 1144.8

llth

1103.8

20th .

1130.0

3d ... 1141.9

12th

1082.5

22d

1182.9

4th . . . 1133.0

13th

1083.5

23d

1182.6

5th . . . 1138.1

15th

1100.0

24th

1128.0

6th . . . 1138.G

16th

1122.1

25th

1107.7

8th . . . 1181.2

17th

1139.7

26th

1144.6

9th ... 1150.0

18th

1137.0

27th

1162.3

Mean 1135.7

Fur the first day only + 142, according to the mean in the record.

8 DETERMINATION OF THE TEMPERATURE CO-EFFICIENT

For January, 1843, .
For February, 1843,
For March, 1843, .

803". 1 at 59°.2
798".9at51°.9
815". 1 at 48°. 1

On the 15th of April, 1843, the instrument was carefully examined and found in
adjustment.

At 61' 50m on May 4, 1843, the bifilar was disturbed, but readjusted on May 5,
before the regular observation at 2h 21™ P. M. A correction of — 16 divisions
during the interval is to be applied to the readings. After this date the instrument
remained undisturbed.

We have, therefore, for discussion the following continuous series of monthly
means of the readings of the bifilar magnetometer with its corresponding mean
temperature. The series extends over five years and one month. To obtain a
better view of the series, the correction of — 900 divisions for the first twelve
months has been applied, it gives a negative value to the June mean of 1840.

TABLE I. — RECAPITULATION OF MONTHLY MEAN READINGS OF THE BIFILAR MAGNETOMETER,

CORRECTED so AS TO PRESENT A CONTINUOUS SERIES.

1840-41.

1841-42.

1842-43.

1843-44.

1844-45.

June . .

— 85.4

+432.3

+663.5

+901.0

+1092.0

July . .

+ 90.1

463.9

710.2

946.5

1126.6

August

146.2

511.6

718.1

956.3

1149.5

September

162.1

537.9

740.3

985.4

1124.8

October

149.4

515.6

768.8

988.6

1140.7

November

136.8

503.1

777.8

983.7

1135.1

December

156.0

535.4

775.9

986.1

1191.3

January .

234.8

561.0

803.7

988.3

1227.2

February .

235.7

576.4

798.9

1018.1

1221.6

March . .

248.9

572.1

815.1

1052.1

1235.3

April . .

266.5

606.7

869.5

1067.6

1257.3

May . .

307.8

625.1

873.6

1072.4

1250.8

June . .

...

...

...

1291.7

Temperature of the bifilar magnet.

June . .

+720.1

+740.1

+710.3

+75.1

+72.9

July . .

75.6

77.3

76.8

76.8

77.8

August

75.5

75.4

74,7

77.2

75.8

September

65.0

70.6

72.5

73.1

71.5

October

58.7

53.7

67.9

66.3

68.8

November

47.4

47.1

61.8

60.5

61.5

December

35.7

55.4

57.3

57.7

57.4

January .

36.5

61.5

59.2

51.7

58.8

February .

34.7

60.5

51.9

54.6

53.6

March . .

43.5

64.1

48.7

62.8

58.2

April . .

50.5

65.5

67.4

63.8

64.1

May . .

60.3

68.3

68.4

68.9

64.3

June . .

• •*

• .*

...

• ••

74.8

Under the supposition of a uniform progression in the change of the mean
monthly readings (due to change in the horizontal force and loss of magnetism of
the bar) the bifilar readings for a given period may be represented by the form :—

B = Bm + Ae x + A* y

where Bm a mean bifilar reading for the period.
x the change during a period.
y the change in the reading due to a change of 1° Fahr.

OF THE HORIZONTAL FORCE.

9

Ae — difference between any single period and the mean epoch.
A< — " " any temperature and the mean temperature.

The formula was first applied to the monthly means resulting from five years of
observation ; it gave y = + 1.0 scale division ; but the remaining differences showed
that the irregular changes between June and July, and December and January, of
the years 1840-41, had an undue effect on the result, the first year's observations
were, therefore, omitted, and the process repeated for the remaining four years.
The twelve conditional equations gave the normal equations : —

+ 2143.15 = + 143a; — 200.4 y.
— 2549.73 = — 200.4x+ 71 1.1 y.
whence x= monthly effect of the progression = + 16.5 scale divisions.

y— temperature correction for 1° Fahr. = + 1.8 " "

An examination of the observed and computed values showed that the introduc-
tion of a term Ae22 Avould improve the agreement, solving the three normal equa-
tions we found

x= + 17.6
y= + 1.62
• --• 0.31

The following table shows the comparison of the observed and computed monthly
mean readings of the bifilar : —

1841-1845.

Mean temperature.

Mean observed bifilar
reading.

Mean computed.

Difference c. — o.

C. — 0. +3.5.

June

73.3

772.2

779.2

+ 7.0

+10.5

July . .

77.2

811.8

806.2

— 5.6

— 2.1

August

76.5

833.9

824.7

— 9.2

— 5.7

September

71.9

847.1

837.0

—10.1

— 6.6

October

64.2

853.4

843.3

—10.1

— 6.6

November

57.7

849.9

851.4

+ 1.5

+ 5.0

December .

57.0

872.2

867.8

— 4.4

— 0,9

January .

57.8

895.0

886.0

— 9.0

— 5.5

February .

55.2

903.8

897.9

— 5.9

— 2.4

March . .

58.5

918.6

919.3

+ 0.7

-f 4.2

April . .

65.2

950.3

945.4

— 4.9

— 1.4

May

67.5

955.5

963.5

+ 8.0

+11.5

Mean

65.17

872.0

Adding + 3.5 scale divisions to the mean value of Bm the above differences will
balance. According to the above results, the annual progressive change is + 17.6 x
12= 211.2 scale divisions, and the change in magnetic moment of the bar for a
change of 1° Fahr. in the temperature, or q = + 1.62 x 0.0000365 = 0.0000591.
This agrees with the best direct determination, being the one in which the observa-
tory was alternately heated and cooled.

To test these results, a combination of the six warmest months with the six
coldest months, by alternate means furnished several values for q depending
merely on the assumption of a gradual regular progressive change during each year
and a half, for which separate results were deduced ; this series commences with
May, 1841, and ends with April, 1845, and contains, therefore, the same number
of months as the first combination, excluding at the same time the two defective
portions noticed above. This combination also possesses the advantage of showing
the variations in the values of q.

10

DISCUSSION OF THE HORIZONTAL COMPONENT

COMBINATION BY ALTERNATE MEANS OP THE WARMER MONTHS, FROM MAY TO OCTOBER INCLU-

SIVE, WITH THE COLDER MONTHS, FROM NOVEMBER TO APRIL INCLUSIVE.

Bifllar.

Temperature.

Alternate Means.

Ad

At

'/ in scalo
divisions.

May, 1841 to Oct., 1841

461.5

68.57

Nov., 1841 to April, 1842

559.1

59.05

582.9

70.25

23.8

11.20

+2.1

May, 1842 to Oct., 1842

704.3

71.92

683.0

58.38

21.3

13.54

+1.6

Nov., 1842 to April, 1843

806.8

57.72

823.1

72.37

16.3

14.65

+1.1

May, 1843 to Oct., 1843

941.9

72.82

911.4

58.12

30.5

14.70

+2.1

Nov., 1843 to April, 1844

1016.0

58.52

1029.8

72.72

13.8

14.20

+1.0

May, 1844 to Oct., 1844

1117.7

72.62

1113.6

58.72

4.1

13.90

+0.3

Nov., 1844 to April, 1845

1211.3

58.93

Sum

109.8

82.19

+1.3

The result from this combination + 1.3 confirms the preceding value, the result,
according to weight or + 1.5 scale divisions or 5=0.0000548 in parts of the hori-
zontal force has, therefore, been adopted in the reduction of the bifilar readings to
a standard temperature, for which + 63°.0 Fahr. has been determined upon as the
mean temperature of the magnetic bar during the five years series of observations.

The difference in the resulting value for q, when obtained from deflections or
vibrations, and from combinations of the bifilar readings themselves, has been re-
marked before, and no satisfactory explanation has as yet been given of it. Thus,
for instance, at Toronto, the two respective values were 2.69 and 1.63 scale divi-
sions, as shown in General Sabine's remarks (Vol. III.) The existence of a similar
discrepancy in the case of the Makerstoun bifilar has been detected by Mr. Broun.
Whatever may be the cause of the difference, there can be no hesitation in saying
that the result derived from the bifilar observations themselves is the one to be pre-
ferred. At St. Helena (Vol. II., London, 1860), the two values were 1.45 and 0.98,
the half yearly comparisons at this station even show a less value, viz., 0.88 scale
divisions; 0.98 (for convenience 1.0) was adopted hi the reduction. Dr. Lamont,
in his Handbook of Terrestrial Magnetism (p. 206, edition of 1849), says: " It de-
serves to be remarked that the value obtained by comparing monthly mean readings
of the bifilar at high and low temperatures is smaller than that obtained by direct
observation."

In the present discussion the value ? = _!—

k 0.0000365

1.5 has been adopted. At

Toronto this va!uo was? , °™ _ 1.63, and at St. Ho.cna f-£^ - 1.0.

It will be seen from these values that the Philadelphia bifilar magnetometer was
very sensitive; its scale value in parts of the horizontal force is but four-tenths of
the Toronto value, and only two-tenths of that of the St. Helena instrument.

In the computations which follow the tenths of scale readings have been omitted
(keeping only the nearest unit) as contributing nothing to the accuracy of the results,
and merely increasing the labor of reduction. The uncertainty in the readings
arising from the uncertainty in the value of q probably affects the units, and the
same may be said of the declination changes, so that in extreme (individual) cases
the next higher figure may be affected.

OF THE MAGNETIC FORCE.

11

The next step of the reduction consisted in transcribing the whole body of the
observations after correcting them individually for differences of temperature; the
adopted standard temperature being 63° Fahr.

The following table contains the monthly means of the bifilar readings reduced
to the standard temperature; the series has been made continuous by the application
of certain corrections explained before.

The readings are in scale divisions of 0.0000365 parts of the horizontal force;
increasing numbers denote decrease of force. The time is Observatory mean time,
counted to twenty-four hours for convenience sake.

TABLE II. — MONTHLY MEANS OF THE BIFILAR READINGS TAKEN AT INTERVALS OF TWO HOURS

AND REDUCED TO THE STANDARD TEMPERATURE 63° FAHRENHEIT.

Philadelphia time (A. M.) (P, M.)

0" 22"

2" 22-

4>> 22™

6" 22'°

8" 22">

10" 22"'

12" 22"

14" 22°>

16" 22°"

18" 22-"

20" 22">

22" 22"

1840. Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Juno

—96

—98 —101

—113

— 102

— 79

— 94

—115

—117

— 96

— 88

— 90

July

+74

+67

+ C3

+ 60

+ 86

+100

+ 81

+ 52

+ 41

+ 74

+ 79

+ 79

August

129

117

117

113

14(1

157

137

113

110

129

126

133

Sept.

158

147

143

138

169

201

183

157

152

153

157

153

October

155

149

137

140

153

179

177

161

155

157

158

152

Nov.

160

157

149

141

153

171

179

165

167

159

160

164

Dec.

203

192

184

178

184

210

218

206

192

196

202

202

1841. . 0" 22™

2" 22'"

4h 22'»

61' 22™

8h 22">

10" 22'"

12" 22"> 14" 22'°

16" 22'"

18° 22°> 20" 22™

22" 22-"

"January

296

287

286

276

272

294

322

306

289

298

294

298

Feb.

279

270

265

256

261

286

303

295

276

283

289

275

tt*roh

27 1>

273

267

260

272

298

299

272

279

281

282

280

April

285

278

268

265

287

312

314

282

273

280

289

286

May

311

312

311

303

318

335

323

304

298

307

312

315

June

420

417

414

405

418

427

406

402

408

416

426

427

July

444

440

435

436

447

457

449

429

430

442

453

448

August

490

490

485

481

499

515

500

479

481

496

501

497

Sept.

517

520

517

514

534

561

538

522

521

528

523

524

October

528

520

517

518

532

540

545

535

529

530

531

530

Nov.

528

529

522

515

525

535

539

525

523

525

528

529

Dec.

545

541

537

534

539

551

562

550

547

553

553

551

1842.

Oh21J"'

2" 21j»

4h 21 Jm

6" 21 j™

8" 21J-

10"21J">

12>>21J"Vl4"21i™

16"21J°'

18"21J°'201'2]J"

22"21J"

January

560

558

557

554

553

575

579

564

559

568

565

565

Feb.

582

576

574

568

570

580

593

582

578

583

589

582

March

573

564

561

561

567

580

577

567

568

574

576

577

April

605

599

598

593

601

618

612

596

592

605

007

607

May

618

614

609

609

624

632

622

607

609

618

620

622

June

652

655

649

641

652

664

654

642

639

652

655

656

July

G84

689

682

683

695

710

698

681

674

687

693

697

August

702

695

695

693

712

722

703

689

690

700

704

703

Sept.

721

723

719

712

732

746

734

722

718

729

730

727

October

757

750

747

747

755

774

778

772

766

764

765

762

Nov.

780

774

772

769

778

791

786

782

778

778

781

785

Dec. 783

780

778

776

779

793

800

791

780

781

784

785

1843.

0" 21j"

2" 21 i"'

4" 21 i"1 6h 21i»

8" 2LJ'"

10''21j™

12"21.i»>14"21i'"

16"21i"'

18''21i'»20''212l'»

22" 21 i"'

January

813

Feb.

819

March

835

April

860

859

853

853

867

880

875

860

859

863

866

859

May

866

8U4

862

860

875

877

862

855

856

863

873

8',0

June

884

883

879

876

886

898

887

873

873

884

887

888

July

924

921

921

920

933

MO

932

920

916

921

931

1 929

August

932

931

931

928

950

9.r>7

944

924

925

930

936

935

Sfpi.

968

907

962

957

977

990

981

96«

968

970

970

966

DISCUSSION OF T II E II O K I Z O N T A L COMPONENT

Hourly Series.

0" 21 i"

1" 21}"-

2" 21i™

3" 21J™

41. 21J»

5" 21 J»

6" 211™

7" 21j»

8" 21 i"

9" 214m

10" 211"

11"21J'°

1843.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

October
Nov. •
Deo.

983
988
996

978
987
994

980
986
993

978
984
992

976
983
990

978
981
988

977
981
988

980

984
988

984
988
992

987
992
992

991
994
993

992
994
998

12" 214-"

13h21j»14h21J'"

15" 214"-

i6»2ij">

17h21Jn

18"21JI"

19"213°>

20" 21 $"

21" 21 J"

22"21£"

23" 21 4»'

October
Nov.
Dec.

991
992
1000

989
990
999

985
•988
997

983
987
994

983
985
992

983
986
991

985
987
993

985
987
996

985
988
996

984
988
996

983

989
998

984
989
999

1844.

0" 21 J™

1" 21£°> 2h 21 J-

3" 21i™ 4" 21J-

5" 21J°

6h 21 J»

7" 2H°>

8" 214°'

9" 21j">

10h2]4°>

11"214'»

January
Feb.
March
April
May
June
July
August
Sept.
October
Nov.
Deo.

1009
1031
1050
1067
1066
1080
1103
1129
1108
]132
1136
1203

1007
1031
1048
1066
1066
1079
1104
1130
1108
1128
1135
1201

1006
1031
1047
1065
1064
1078
1106
1130
1108
1127
1133
1198

1004
1029
1046
1062
1063
1079
1107
1130
1109
1123
1132
1196

1002
1026
1P45
1059
1063
1079
1107
1129
1105
1122
1131
1194

1002
1026
1044
1059
1062
1077
1106
1127
1107
1124
1127
1192

1001
1026
1045
1062
1062
1075
1105
1126
•1106
1125
1128
1188

1001
1028
1046
1062
1065
1079
1105
1131
1113
1130
1129
1191

1004
1029
1051
1067
1069
1082
1110
1139
1123
1137
1134
1192

1007
1030
1058
1075
1075
1084
1117
1148
1129
1143
1141
1196

1010
1034
1060
1079
1076
1086
1119
1149
1133
1146
1147
1207

1013
1036
1062
1079
1071
1083
1115
1143
1129
1141
1149
1215

12»2U'»

13"21J"

14"21J-

15h21J»16h21j°'

17"21im

18"21j°>

19"21J°>

20" 21 i«

21''21J">

22»21J"'

23"2U/"

January
"Feb.
March
April
May
June
July
August
Sept.
October
Nov.
Dec.

1011
1035
1067
1074
1065
1079
1107
1134
1119
1139
1146
1215

1008
1032
1063
1069
1058
1074
1101
1125
1108
1134
1145
1210

1005
1028
1056
1063
1054
1069
1097
1117
1102
1128
1139
1205

1001
1028
1049
1059
1054
1067
1094
1115
1100
1129
1137
1200

1000
1032
1052
1061
1052
1067
1093
1117
1101
1128
1138
1195

1002
1031
1054
1059
1055
1069
1094
1123
1105
1132
1138
1196

1004
1032
1054
10U5
1060
1073
1097
1130
1108
1133
1138
1197

1005
1033
1053
1067
1064
1075
1100
1131
1110
1133
1143
1197

1005
1034
1051
10(i8
1065
H'77
1102
1132
1111
1135
1141
1197

1006
1033
1052
10i;9
1065
1079
1103
1131
1111
1132
1138
1201

1007
1034
1052
1066
1064
1079
1104
1132
1112
1133
1135
1201

1009
1033
1051
1069
1064
1080
1108
1131
1116
1130
1139
1201

1845.

0" 21 }•»

l"21J-»

2>> 21 j"

3" 21 J"

4" 21j">

5" 21 J«

6h 21J"

7" 21 j™

8" 21.1"'

9" 21 >

10'' 21 J'"

11" 21V"

January
Feb.
March
April
May
June

1233
1232
1237
1253
1249
1274

1230
1234
1237
1250
1248
1274

1231
1232
1235
1249
1246
1274

1229
1230
1236
1247
1245
1273

1227
1230
1235
1245
1241
1268

1225
1227
1235
1243
1238
1267

1224
1224
1231
1241
1235
1262

1226
1228
1234
1247
1242
1266

1230
1234
1242
1255
1254
1273

1238
1238
1250
1270
1264
1284

1244
1246
1256
1280
1265
1290

1248
1249
1202
1279
1263
1289

12"2li™ 13" 21}°'

14h21}"»

15"21j">

16"21j"'

17"2U°'

18" 21.]"'

19"21J-»20"2n°>

21 "214"'

22" 215™

23" 211"'

January
Feb.
March
April
May
June

1245
1251
1261
1271
1256
1282

1241
1247
1254
1267

1248
1278

1238
1240
1246
1255
1242
1269

1235
1236
1240
1253
1242
1267

1233
1235
1241
1249
1242
1266

1236
1233
1243
1251
1246
1269

1237
1234
1245
1254
1251
1274

1233
123ii
1242
1257
1251
1278

1232
1236
1241
1257
1251
1277

1231
1232
1238
1254
1253
1276

1231
1232
1241
1251
1251
1275

1229
1233
1240
1252
1245
1275

OF THE MAGNETIC FORCE.
The monthly means are contained in the following table : —

13

TABLE III. — MONTHLY MEANS OF THE PRECEDING BIFILAR READINGS REDUCED TO THE

STANDARD TEMPERATURE 63° FAHRENHEIT.

1S40-41.

1841-42.

1842-43.

1843-44.

1844-45.

Div's.

Div's.

Div's.

Div's.

Div's.

June .

— 99

July . .

+ 71

443

689

926

1104

August

127

493

701

935

1130

September

159

527

726

970

1112

October .

156

530

761

984

1132

November

160

527

780

987

1138

December

197

547

784

994

1199

January .

'274

563

'808

1008

1233

February .

278

580

»814

1031

1235

March .

278

570

S835

1052

1243

April . .

285

603

863

10 6

1255

May . .

312

617

865

10 4

1249

June .

"415

651

883

10.7

1274

Correction for progressive change in tlie readings. — The observations having been
referred to a uniform temperature, still require a correction for the effect of the
progressive change during each month before Peirce's criterion can be applied for
the purpose of separating the disturbances. We have seen that the mean monthly
value of this change due to loss of magnetism of the bar and to change in the
horizontal force itself, was 17.6 scale divisions; on the average, therefore, a correc-
tion must be applied to the observations on the first and last day of each month of
+ 8.8 and — 8.8 scale divisions, and in proportion for the intermediate days. At
Toronto, also, the progressive change in some months was so great as to present a
practical difficulty by its interference with the proper comparability of the observa-
tions, and in these cases new means at shorter intervals than a month were taken.

1 The actual mean of 17 days was 293 ; to reduce this to the mean of 27 days, 19 scale divisions
were subtracted, resulting from an interpolation between January 1st and January 12th ; the mean
of 7 days preceding and following the gap was made use of.

a Owing to causes already explained, the means of May and June differ so much as to affect the
continuity of the series ; the same is to be said of the differences between June and July, 1840, and
between December, 184ff, and January, 1841 ; the corresponding differences between the same months
in the other four years furnish us with the means of correcting the series for the first year, as will be
seen hereafter; it also appeared advisable to omit the readings in June, 1840, altogether, the instru-
ment not having then been in stable adjustment. «

3 The numbers in table II have been slightly changed, to refer the mean of the hour of observation
to the mean resulting from observation of 12 hours a day. Comparing the mean at 14h 22m in each
month with the respective monthly means in the other four years, the above corrections became — 5,
• — 5 and 0 for January, February, and March.

The bar between September and October, 1843, separates the means from the bi-hourly and the
hourly series.

In the application of the reduction for temperature no attempt whatever has been made at inter-
polation in the magnetic series, but whenever a temperature reading was accidentally omitted, it has
been supplied by comparison witli the observed temperature immediately preceding and following.
No magnetic reading can be supplied by interpolation, however short the interval, as long as the law
of the occurrence of the disturbances remains unknown.

14 DISCUSSION OF THE HORIZONTAL COMPONENT

At Philadelphia the progressive change is so large as to require a systematic correc-
tion throughout the series. In the manuscript tables used for the preparation of
the monthly normals and containing the observations reduced to 63° Fahr., the
readings corrected for progressive change were written in blue ink underneath each
observation. If the monthly differences are taken from Table No. III., it is appa-
rent that the change is irregular, and in three cases at least it is certain that other
causes were in operation, which produced larger monthly differences than coxild be
attributed to the gradual loss of magnetism. These cases are the following (already
noticed in the preceding temperature discussion): between June and July, 1840, a
difference of 170 divisions; between December and January, 1840-41, a difference
of 77; and between May and June, 1841, a difference "of 103 divisions. They
require separate treatment, as will be presently explained. For the correction of
the progressive change the mean reading from one month's series was made out for
the first, middle, and last of each month. By this process of taking the mean from
14 days preceding and 14 days following each of the epochs the lunar effect on the
solar variation is practically eliminated from the resulting mean value.1 These
means corresponding in time to the beginning, the middle, and the end of each
month, furnish the rate of change for the first and second half of the month, and
by simple interpolation give the correction for progressive change for each day.
If the rates for the first and second half of the month are different, the monthly
means of each hour (from the blue figures) will differ by a small but constant quan-
tity from the former monthly means. Thus, for instance, for the month of June,
1842, the monthly mean is 651 divisions, corresponding in time to the middle
of the month, the mean of the readings (at 63°) for the second half of May
and the first half of June is 641, corresponding in time to the first of June, and
the mean of the readings (at 63°) of the second half of June and the first half
of July is 673, corresponding in time to the last of June; the correction applied to
the bi-hourly readings (at 63°) on June 1st was + 10, and to the readings on June
30th was — 22 divisions. At the middle of the month the correction is zero, and
for the intermediate days it is in proportion to their respective distances from the
middle. The algebraic sum of the daily corrections divided by the number of days
of observation is — 3, which gives the new monthly mean 648, as corrected for
irregularity in the progressive change. In the exceptional case of a break, or
beginning and termination, the required rate of change for half the month was
found by a similar process, using half monthly and quarterly means.

The following table, No. IV., contains the monthly means of the bi-honrly and
hourly readings of the bifilar magnetometer referred to a uniform temperature (63°
Fahr.), and corrected for irregularity in the progressive change. It is here inserted
for the purpose of comparing it with the monthly normals, showing the change pro-
duced by the exclusion of the disturbances. The means in the month of June, 1840,
are suppressed, and the readings between June 1 and June 5, 1841, were not used.

1 In connection with this subject, the first part of an interesting paper by Mr. Broun may be
consulted, viz.: "On the lunar diurnal variation of the magnetic declination at the magnetic equator. "
— Proceeding* Hoynl Society, vol. X., No. 39, 1800.

OF THE MAGNETIC FORCE.

15

TABLE IV. — MONTHLY MEANS OF TIIE BI-HOURLY AND HOURLY READINGS OF THE BIFILAR MAG-

NETOMETER, REDUCED TO A UNIFORM TEMPERATURE AND CORRECTED FOR IRREGULARITY IN THE

PROGRESSIVE CHANGE.

Philadelphia time (A. M.) (P. M.)

Oh 22m 2b 22™

41.22°'

61' 22m

8" 22™

10" 22™

12"- 22°

14" 22°

16" 22° 18"'22°

20h 22™

22" 22°'

1840.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

July

90

83

79

76

102

116

97

68

57

90

95

95

August

130

118

118

114

147

158

139

115

112

130

127

134

Sept.

161

150

146

141

172

204

186

160

155

156

160

156

October

153

147

135

138

151

177

175

159

153

155

156

150

Nov.

155

152

144

136

148

166

174

160

162

154

155

159

Dec.

202

191

183

177

183

209

217

205

191

195

201

201

1841.

Oh 22°

2"22»

4h 22^

6" 22°

8h 22°

10" 22°

12h 22°

14" 22°

16h 22°

18" 22°

20" 22°

221' 22™

'January

300

291

290

280

276

298

326

310

293

302

298

302

Feb.

279

270

265

256

261

286

303

295

276

2*>3

289

275

March

276

273

267

260

272

298

299

272

279

281

282

280

April

283

275

265

262

284

309

311

279

270

277

286

283

May

307

308

307

299

314

331

319

300

294

303

308

312

'June

392

390

389

383

400

406

390

380

386

392

402

400

July

445

441

436

437

448

458

450

430

431

443

454

449

August

492

492

487

483

501

517

502

481

483

498

503

499

Sept.

519

522

519

516

536

562

540

524

523

530

525

526

October

527

519

516

517

531

539

544

534

528

529

530

529

Nov.

525

526

519

512

522

532

536

522

520

522

525

526

Dec.

546

542

538

535

540

552

563

551

548

554

554

552

1842.

0" 21i»

2h21J»

4" 21£°

6" 21J">

8" 21 £"'

10>'21£°12"21J°

14" 21^16" 21 j°

18"21Jm

20I>21J»'

22"21j"

January

558

556

555

552

551

573

577

562

557

566

563

563

Feb.

585

579

577

571

573

583

596

585

581

586

592

585

March

569

560

557

557

563

576

573

563

564

570

572

573

April

610

604

603

598

606

623

617

601

597

610

612

612

May

614

610

606

605

621

629

618

604

606

615

617

619

June

C49

652

645

638

649

661

651

639

636

649

652

653

July

687

692

685

686

698

713

700

684

677

690

696

700

August

701

694

695

692

711

721

702

688

689

699

703

702

Sept.

723

725

720

713

734

748

736

724

720

731

732

729

October

761

754

751

751

759

778

782

776

770

768

769

766

Nov.

779

773

771

768

777

790

785

781

777

777

780

784

Dec.

780

777

775

773

776

790

797

788

777

778

781

782

1843.

0"21j"'

2"21i'"

4°21i»

6»21J°

8"21i°

10h21i™

12"21J°

14"21J™

16"21i"'

18" 21$™

20"21<»

22" 2] $"

January

818

Feb.

819

March

831

April

863

862

856

856

870

883

878

863

862

866

869

862

May

865

868

861

859

874

876

861

854

855

862

872

869

June

881

880

876

873

883

892

884

870

870

881

884

885

July

927

924

924

923

936

943

935

923

919

924

934

932

August

931

930

930

927

949

956

943

923

924

929

935

934

Sept.

971

970

965

960

980

993

984

969

971

973

973

969

1 The mean of 17 days is given ; to refer it to a complete month subtract 19 divisions.
* The mean of 19 days is given ; to refer it to a complete month add 8 divisions.

16

DISCUSSION OF THE HORIZONTAL COMPONENT

Hourly Series.

0"21jm

1" 21 }»

2» 214"-

3h 21 jm

4h21£"> 5h21J°>

6"21j»

7h21J™

8"21J»

9h21J"> 10l'21i'"lll'21j'"

1N13.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

October
Nov.
Dec.

983
987
995

978
986
993

980
985
992

978
983
991

976
982
989

978
980
987

977
980
987

980
983
987

984
987
991

987
991
991

991
993
992

992
993
997

12"21$»

13h21j"

14»21j»

IS^IJ"

16h21J-"

17"21J°

18"21J"

19"21J»

201'21J°

2P214"

22" 21 £»

23" 21 4™

October
Nov.
Dec.

991
991
999

989
989
998

985
987
996

983
986
993

983
984
991

983
985
990

985
986
992

985
986
995

985
987
995

984
987
995

983
988
997

984
988
998

1844.

0" 21i°-

l"21Jm

2" 21 J-

3h 21 Jm

4" 21 J-

5" 21J»>

6" 21Jm

7h 21 J-

8" 211'"

9»21£°>

10'>21J"<

ll''21J'"

January
Feb.
March
April
May
June
July
August
Sept.
October
Nov.
Dec.

1007
1031
105)
1070
1065
1078
1102
1133
1102
1136
1132
1205

1005
1031
1049
1069
1065
1077
1103
1134
1102
1132
1131
1203

1004
1031
1048
1068
1063
1076
1105
1134
1102
1131
1129
1200

1002
1029
1047
1065
1062
1077
1106
1134
1103
1127
1128
1198

1000
1026
1046
1062
1062
1077
1106
1133
1099
1126
1127
1196

1000
1026
1045
1062
1061
1075
1105
1131
1101
1128
1123
1194

999
1026
1046
1065
1061
1073
1104
1130
1100
1129
1124
1190

999
1028
1047
1065
1064
1077
1104
1135
1107 '
1134
1125
1193

1002
1029
1052
1070
1068
1080
1109
1143
1117
1141
1130
1194

1005
1030
1059
1078
1074
1082
1116
1152
1123
1147
1137
1198

1008
1034
1061
1082
1075
1084
1118
1153
1127
1150
1143
1209

1011
1036
1063
1082
1070
1081
1114
1147
1123
1145
1145
1217

12»21i">

13"21J">

14h21J">

15"21|'»

16h214">

1V21J™

18" 21^

19"21Jm

20"21£"

21»21Jm

22" 21.,"'

23I'21J"'

January
Feb.
March
April
May
June
July
August
Sept.
October
Nov.
Deo.

1009
1035
1068
1077
1064
1077
1106
1138
1113
1143
1142
1217

1006
1032
1064
1072
1057
1072
1100
1129
1102
1138
1141
1212

1003
1028
1057
1066
1053
1067
1096
1121
1096
1132
1135
1207

999
1028
1050
1062
1053
1065
1093
1119
1094
1133
1133
1202

998
1032
1053
1064
1051
1065
1092
1121
1095
1132
1134
1197

1000
1031
1055
1062
1054
1067
1093
1127
1099
1136
1134
1198

1002
1032
1055
1068
1059
1071
109(5
1134
1102
1137
1134
1199

1003
1033
1054
1070
1063
1073
1099
1135
1104
1137
1139
1199

1003
1034
1052
1071
1064
1075
1101
1136
1105
1139
1137
1199

1004
1033
1053
1072
1064
1077
1102
1135
1105
1136
1134
1203

1005
1034
1053
1069
1063
1077
1103
1136
1106
1137
1131
1203

1007
1033
1052
1072
1063
1078
1104
1135
1110
1134
1135
1203

1845.

0" 214"

Ih2!f°

2" 214-°

3"21J°'

4" 21 J™

5* 211*

6"21^

7"21j">

8" 21 i«'

9" 21 j"

10" 21 2"'

11" 21 ja-

January
Feb.
March
April
May
June

1234
1231
1236
1255
1244
1281

1231
1233
1236
1252
1243
1281

1232
1231
1234
1251
1241
1281

1230
1229
1235
1249
1240
1280

1228
1229
1234
1247
1236
1275

1226
1226
1234
1245
1233
1274

1225
1223
1230
1243
1230
1269

1227
1227
1233
1249
1237
1273

1231
1233
1241
1257
1249
1280

1239
1237
1249
1272
1259
1291

1245
1245
1255
1282
1260
1297

il 249
1248
1261
1281
1258
1296

12" 2 li-

13"21i»

14"21J»

15h21Jm

16h214"

17" 214°'

18h21j°>

19*21$*

20"21£m

21''21jm

22I>21J°>

23" 21 £m

January
Feb.
March
April
May
June

me
1250
1260
1273
1251
1289

1242
1246
1253
1269
1243
1285

1239
1239
1245
1257
1237
127(5

1236
1235
1239
1255
1237
1274

1234
1234
1240
1251
1237
1273

1237
1232
1242
1253
1241
1276

1238
1233
1244
1256
1246
1281

1234
1235
1241
1259
1246
1285

1233
1235
1240
1259
1246
1284

1232
1231
1237
1256
1248
1283

1232
1231
1240
1253
124i)
12H2

1230
1232
1239
1254
1240
1282

OF THE MAGNETIC FORCE.

TABLE V. — MONTHLY MEANS OF THE PRECEDING BIFILAR READINGS REFERRED TO A UNIFORM

TEMPERATURE AND CORRECTED FOR IRREGULARITY IN

THE PROGRESSIVE CHANGE.

The column 1840-41 contains a double set of figures, the first are the

monthly means directly obtained from

Table IV, the second contains the means when the series is made

continuous for the two breaks already

noticed. The mean difference between May and June (from four years) is 25 scale divisions, and between

December and January it is 22 scale divisions ; these corrections were applied in

the second set of figures.

1840-1841.

1841-1842.

1842-1843.

1843-1844.

1841-1845.

Monthly Meant

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

of Series.

July

87

215

444

692

929

1103

677

August

128

256

495

700

934

1134

704

September

162

290

529

728

973

1106

725

October

154

282

529

765

984

1136

739

November

155

283

524

779

986

1134

741

December

196

324

548

781

993

1201

769

January

297—19

346 561

813

1003

1234

791

February

278

346 583

814

1031

1234

802

March

278

346 566

831

1053

1242

808

April

282

350 608

866

1069

1257

830

May

308

376

614

864

1063

1244

832

June

393-f-8

401 648

880

1075

1281

857

Annual Means

•318

554

793

1008

1192

773

The differences in the successive annual means indicate that the progressive
change may be assumed to have been uniform from year to year, and applying the
usual method we find an annual progressive change of 220 scale divisions.

Introduction of the Horizontal Intensity in absolute measure and separation of the
effect of the loss of Magnetism of tJie Bifilar bar from the effect due to the secular
change of tJie Horizontal Intensity. — Although some experiments were made to
determine the gradual loss of magnetism of the bar, as, for instance, in January,
1841, when the amount was found to be 0.9601 of the force in May, 1840, and
again in June, 1841, when the amount was 0.9686 of its amount in January, 1841,
yet the experiments do not extend over the whole period of observation, and con-
sequently we are obliged to deduce the effect of the secular change of the horizontal
intensity from other independent means, and, after converting it into scale divisions,
we can assign the proper proportion of what is due to secular change and to loss
of magnetism, in the whole progressive change of 220 scale divisions in a year.

In connection with the operations of the U. S. Coast Survey, Assistant Schott has
investigated1 the secular change of the horizontal intensity at a number of stations
on the Atlantic and Pacific coasts. At several stations the results were subsequently
improved by a discussion of my observations for intensity, made in part in connection
with a magnetic survey of Pennsylvania, and also extending into adjoining States,
and, in one of the journeys, into Canada. From the complete material the values
in the following table of observed horizontal and total intensities have been collected.
The horizontal intensity X and the total intensity <p are expressed in absolute mea-
sure (grains and feet).

Report to Superintendent, dated January 19, 1861.

18

DISCUSSION OF THE HORIZONTAL COMPONENT

No.

Year.

Observer.

Reference from which the valuer were
derived or taken.

X.

t-

1

1835.0

Bache and Courtenay.

Trans. Amer. Phil. Soc., Vol. V, 1837.

4.198

13.58

2

1836.7

Bache.

4.159

13.4G

3

1839.5

Loomis.

Trans. Amer. Phil. Soc., Vol. VIII.

4.149

13.41

4

1840.9

Bache.

13.41

5

1841.5

Locke.

Phil. Trans. Roy. Soc., 1846.

4.172

13.51

g

1841.8

Bache.

13.46

7

1842.5

Locke.

Phil. Trans. Roy. Soc., 1846.

4.174

13.52

8

1842.8

Lefroy.

it tt it it it

4.176

13.50

9

1843.6

Bache.

4.172

13.46

10

1844.5

Locke.

Phil. Trans. Roy. Soc., 1846.

4.162

13.47

11

1846.4

Locke.

U. S. Coast Survey Records.

4.143

13.42

12

1855.7

Schott.

tt tt it ' tt

4.226

13.89

'13

1862.6

Schott.

tt tt it tt

4.088

13.30

The first three observations were not made at the Girard College grounds ; and
it appears from Prof. Loomis' observation when compared with Dr. Locke's, that a
correction of 0.023 in the value of X should be added to these; to the twelfth observa-
tion I have assigned only half weight ; it was probably made during a disturbance.
From the general discussion an annual diminution in the horizontal force of 0.0011
parts was deduced for a number of stations on the Atlantic coast. At Toronto (vol.
Ill of General Sabine's Discussion) the annual decrease was found 0.0010 in parts
of the horizontal force. Being somewhat guided by these results, after several
trials, the following combination of the results in the table has been adopted, as
perhaps best representing the values for the time during which the Girard College
observations were made, these latter being merely of a differential character: —

Combination.
1, 2, 3
5, 1, S, 9
10, 11, 12, 13

Mean epoch.
1837.1
1842.6
1852.3

Mean horiz'l int. X.
4.191
4.174
4.145

The annual diminution of X is 0.0030, or, when expressed in parts of the hori-
zontal force, = 0.0007; its equivalent in scale divisions is 19.2. The total annual
change was found to be 220 scale divisions ; hence, 200.8 scale divisions of annual
change is due to loss of magnetism of the bar.

The mean epoch is 1844.0, and the corresponding mean X = 4.170; the mean
epoch of the observation taken at the Girard College, is January, 1843, for which,
therefore, the mean value of X = 4.173. This value has been adopted whenever
it was desirable to introduce the horizontal force in absolute measure.

Separation of the Larger Disturbances. — The observations having been referred
to a uniform temperature, and corrected for progressive change, Peirce's criterion
was applied separately to each month. For this purpose, a systematic application
was made extending over the whole series of observations, commencing with the
hour 0 and the month of July, next with the hour 2 and August, followed by hour
4 and September, and so on in regular progression. This process eliminates from
the result the diurnal variation and the annual variation of the disturbances them-
selves. The value for Ob in July, 1840, was omitted as affected by two very large
disturbances. The following table shows the limiting value of difference from the

1 Added while this paper is passing through the press.

OF THE MAGNETIC FORCE.

19

mean (the monthly mean for the respective hour), also the number of observations
in each year subjected to the process: —

LIMITS OF REJECTION BY PEIRCE'S CRITERION.
Div's.

1840-41 ex = 53 ?i = 241

1841-42 " 44 312

1842-43 " 37 309

1843-44 28 313

1844-45 " 33 313

Mean value 39 Sum 1488

The limiting value derived from nearly 1,500 observations is 39 scale divisions,
and the separate annual values show plainly the effect of the eleven (ten 1) year
period, the year 1843-4 being a minimum year. Certain limits in the adoption of
a separating value are allowable, and upon trial as to the actual number of disturb-
ances separated, the value 33 scale divisions was finally adopted. Any observation
differing 33 divisions or more from its respective monthly mean, was therefore
marked and excluded from the mean. 33 divisions equal 0.0012 parts of the hori-
zontal force, and in the value of the absolute scale it amounts to 0.005. At Toronto
the limiting value was 14 divisions, = 0.0012 parts of the horizontal force, equal
to 0.004 in the absolute scale. (Vol. Ill of the Toronto Obser's.)

. TABLE VI. — SHOWS THE NUMBER OF OBSERVATIONS AND THE NUMBER OF THE LARGER DIS-

TURBANCES SEPARATED BY THE VALUE 33, AS THE LIMIT, FOR EACH MONTH, YEAR, AND THE

WHOLE PERIOD.

^

1S40— 1841.

1811—1842.

1842-1843.

1843—1844.

1844—1843.

MOUTH.

Obser's.

Dial's.

Obser's.

Dist's.

Obser's.

Dist's.

Obser's.

Dist's.

Obser's.

Dist's.

July . . 323

165

323

26

308

24

312

15

648

0

August .

308

73

312

17

321

3

324

11

648

4

September

312

54

310

41

308

44

312

16

600

27

October .

323

68

308

28

310

53

624

3

648

32

November

293

49

312

32

312

15

624

1

624

42

December

321

120

323

26

323

5

624

0

624 • 46

January .

201'

23

311

14

263

0

646

3

648 27

February

288

50

287

37

24'

1

600

5

57ti

18

March

320

62

323

26

27s

1

624

29

624

3

April . .

3U9

48

309

38

300

14

624

16

624

33

May . .

310

46

300

29

324

25

648

3

648

19

June . .

2252

13

311

16

312

4

600

0

600

56

Sums ....

3533

770

3729

330

2895

189

C562

102

7512

307

Ratio ....

1 dist. in 4.6 ob's.

Idist. in 11.3 ob's.

1 dist. in 15.3 ob's.

1 dist. in 64.3 ob's.

1 dist. in 24.4 ob's.

Total number of observations
Total number of disturbances

24,231
1,698

The limiting value separated, therefore, one in every 14.3 observations.
Toronto one in every 12.5 was marked as a disturbance.

At

1 In 17 days.
1 In 19 days.

' One observation a day.
• One observation a day.

* One observation a day.

DISCUSSION OF THE HORIZON T A L C O M P 0 X K N T

The larger disturbances having been excluded, new monthly means were taken,
and the process was repeated several times, when required, until all readings differ-
ing 33 scale divisions or more had been excluded ; the final means constitute the
normals as given in the following table: —

TABLE VII. — MONTHLY NORMAL OF THE BI-HOURLY AND HOURLY READINGS OF THE BIFILAR

MAGNETOMETER REDUCED TO A NORMAL TEMPERATURE AND CORRECTED FOR IRREGULARITY IN

THE PROGRESSIVE CHANGE.

Philadelphia time (A. M.) (P. M.)

0.22- 2' 22°

4"22»

6" 22°

8" 22""

10" 22"

12" 22™

14" 22™ 16" 22™

18" 22°

20" 22°>

22" 22°'

1840.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

July

113

97

89

50

112

116

94

59

52

92

93

108

August

108

112

117

106

138

153

134

103

111

114

121

126

September

155

147

139

141

180

202

177

155

153

158

157

150

October

142

137

122

138

153

166

159

158

148

140

148

151

November

155

150

144

133

144

154

175

157

151

148

144

160

December

190

188

176

166

178

208

217

193

182

185

200

194

1841.

0" 22 »

2" 22™

4" 22m

6" 22™

8" 22™

10" 22°

12" 22'°

14" 22»

16" 22™

18" 22"' 20" 22"

22" 22°'

January1

298

300

294

284

281

302

326

311

289

296

301

302

February

269

261

264

257

265

288

297

289

275

274

275

272

March

268

272

267

257

271

294

286

267

266

282

264

272

April

273

271

262

262

283

317

315

279

268

271

283

280

May

311

305

306

297

306

323

313

301

294

306

309

313

June1

392

390

392

386

400 401

395

382

385

392

402

392

July

442

442

435

435

447 458

449

428

430

444

448

439

August

490

494

487

482

501 518

502

483

483

497

500

495

September

510

514

515

508

531

542

537

516

519

520

515

515

October

521

517

518

514

526 537

547

530

525

527

529

528

November

519

517

515

509

518 529

531

514

518

513

516

518

December

546

541

538

535

537

548

562

549

545

547

550

552

1842.

0" 21 J"1

2" 22]°

4" 21$'°

6" 21 i™

8" 213°>

10"21j"> 12-21 j»

14''21J'«16h21J»

18"21Jm'20"211»

22-214-

January

561

556

555

558

553

573

577

559

554

564 503

504

February

580

573

572

567

568

582

589

578

578

580 590

578

March

565

559

557

554

563

574

575

561

565

571 507

506

April

595

598

597

594

604

620

618

603

598

tit '7 608

611

May

614

610

611

605

621

630

622

600

607

615 i 618

619

June

649

652

646

638

649

659

650 639

638 649

648 650

July

692

686

682

678

695

708

700

680

677 690

694 700

August

699

694

695

692

711

721

700

688

689

701

703 702

September

726

733

722

717

739

750

737

730

727

737

737 734

October

764

759

757

757

764

781

783

776

776

768

769 764

November

774

770

771

768

777

789

787

781

778

775

776

776

December

780

777

775

773

776 790

795

786

773

776

781 782

1843.

0" 21 J°

2" 21J°

4" 21 £•"

6" 21^' 8" Zl!2"

10-21J- 12-21 4-;i4"211-

16"2U"

18h21{-»

20-214-22-21J-

January

818

1

February

817

March

829

April

861

861

854

854

868

883

878

863

860

801

865

859

May

864

862

858

857

875

872

864

855

856

862

867

803

June

881

879

876

873

883

894

884 870

870

881

881 885

July

927

924

924

923

935

94]

934 923

916

221

928

931

August

931

930

931

927

947

9f,4

938 921

924

829

932

933

September

974

907

905

960

980 992

985

972

972

975

974

973

i The mean of 17 Jays,

The mean of 19 days.

OP THE MAGNETIC FORCE.

•21

Hourly Series.

Oh 214°-

1" 214™

2" 214™

3h 21 J°-

4" 214™

5" 214-° 6* 21 j"'' 7* 21J""

8" 214"

9* 21 J"

10*214""

11*21J°

1843.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

October
November
December

983
987
995

978
986
993

983
985
992

978
983
991

976
982
989

978
980
987

977
980
987

980
983

987

983
987
991

987
991
991

991
992
992

992
993
997

i2*2i4-»

13*214'''

14*21 4"'

15*214-"

16h214°>

17*214""

18*214"" 19*214»

20*214"" 21*2H">

22*21 J"

23"21j"

October
November
December

991
991
999

989
989
998

985
987
996

983
986
993

983
984
991

983
985
990

985
986
992

985
986
995

985
987
995

986
987
995

983
988
997

984
988
998

1844.

0&31J-

1" 214"'

2" 214™

3* 21 J»

4" 214™

5" 214™

6" 214-"

7" 21 J»

8" 21 4"'

9" 21 4»

10*214-"

11*21J"

January
February
March
April
May
June
July
August
September
October
November
December

1006
1031
1048
1070
1065
1078
1102
1133
1106
1133
1131
1213

1005
1031
1047
1069
1065
1077
1103
1134
1104
1132
1130
1202

1004
1031
1046
1068
1063
1076
1105
1134
1107
1131
1127
1200

1002
1029
1046
1065
1062
1077
1106
1133
1105
1127
1126
1198

1000
1026
1046
1063
1062
3077
1106
1133
1101
1124
1125
1196

1000
1026
1043
1062
1061
1075
1105
1131
1101
1125
1123
1194

999
1026
1043
1064
1061
1073
1104
1130
1100
1129
1122
1190

999
1028
1047
1061
1064
1077
1104
1135
1107
1134
1125
1193

1002
1029
1050
1067
1068
1080
1109
1143
1117
1141
1130
1194

1005
1030
1054
1074
1076
1082
1116
1152
1125
1149
1135
1197

1008
1034
1057
1078
1077
1084
1118
1153
1128
1152
1138
1209

1011
1034
1063
1078
1070
1081
1114
1147
1125
1145
1142
1217

12*214°"

13"21j»"

14*21 j"»

15*21J"'

16*21J°" 17*214-" 18"214°

19*21 J-"

20*21 J">

21*214'"

22"21J°"

23*21 J"

January
February
March
April
May
June
July
August
September
October
November
December

1009
1035
1063
1077
1064
1077
1106
1138
1115
1145
1136
1220

1006
1032
1061
1071
1057
1072
1100
1129
1104
1137
1133
1212

1003
1028
1057
1066
1053
1067
1096
1121
1097
1134
1129
1209

999
1028
1050
1062
1053
1065
1093
1119
1095
1130
1127
1202

998
1030
1051
1064
1051
10G5
1092
1121
1095
1132
1124
1201

1000
1031
1050
1062
1054
1067
1093
1127
1100
1134
1131
1201

1002
1032
1050
1068
1059
1071
1096
1134
1102
1135
1128
1203

1003
1033
1052
1068
1063
1073
1099
1135
1104
1137
1129
1198

1003
1034
1050
1071
1064
1075
1101
1135
1104
1138
1130
1200

1004
1033
1048
1071
1064
1077
1102
1134
1108
1134
1130
1204

1004
1032
1050
1068
1065
1077
1103
1135
1107
1137
1131
1206

1005
1030
1048
1069
1063
1078
1104
1135
1108
1135
1131
1206

1845.

0" 214"' I1' 214™

2h 21J°' 3h 21^°"

4" 21 J-"

5" 214"'

6" 214"-

7" 21 i"

8" 21 j-»

9" 21J"" 10*214°"

11°21J»

January
February
March
April
May
June

1233
1230
1236
1252
1244
1280

1228
1230
1236
1250
1243
1281

1281
1231
1234
1249
1241
1281

1230
1229
1235
1247
1239
1281

1228
1229
1234
1245
1236
1275

1226
1226
1234
1243
1233
1271

1225
1223
1231
1241
1229
1266

1226
1227
1233
1244
1236
1273

1231
1231
1241
1253
1251
1282

1241
1236
1249
1268
1261
1293

1248
1243
1255
1278
1262
1295

1252
1244
1261
1281
1258
1292

12*214'"

13*21J"'14"21J">

15"2]^

16*214-

17*214°"

18*214°"

19*21]""

20*21 4»>

21*21j">

22*214™

23*21 J°'

January
February
March
April
May
June

1249
1250
1260
1258
1253
1286

1242
1242
1253
1267
1244
1280

1239
1238
1245
1255
1238
1272

1233
1231
1239
1252
1236
1269

1229
1233
1240
1248
1237
1269

1230
1229
1242
1253
1239
1273

1233
1231
1244
1256
1245
1278

1231
1233
1240
1254
1246
1281

1230
1235
1239
1254
1246
1280

1230
1231
1237
1253
1248
1277

1229
1231
1240
1250
1247
1279

1229
1232
1239
1254
1242
1280

Increase of scale readings corresponds to decrease of force. Value of one divi-
sion of the scale = 0.0000365 parts of the horizontal force, or in the absolute scale
equal to 0.0001523.

Investigation of tfie Eleven Year (a/so called Ten Year) Period, as sliaum in the
< '/Hinges of tlie Amplitude of the Solar Diurnal Variation of the Horizontal Force. —
The variation in the amplitude of the diurnal motion of the horizontal force is

22

DISCUSSION OF THE HORIZONTAL COMPONENT

subject to the same inequality of about eleven years as the declination, and tin-
means of investigation will be analogous to those used in Part I of this discussion.
For greater convenience, the preceding monthly normals were united into annual
means and the results put into an analytical form, using Bessel's function applicable
to periodical phenomena, and determining the numerical quantity by the application
of the method of least squares.

In the following table of the regular solar diurnal variation of the horizontal force
the means for 1842-43 depend only on nine months of observation; the correction
given to refer them to twelve months of observation depends on the mean difference
between the results of the same nine months and twelve months of the preceding
and following year ; this correction is nearly constant and the same within one scale
division for the adjacent years. In the second corrected column for 1842-43 the
effect of the annual inequality is thus eliminated. In the year 1843-44 the results
from nine months of observation at the odd hours were reduced to twelve months
by means of corresponding differences in the series of even hours ; thus (omitting
the minutes) at hour 2, mean of 12 months = 1006, mean of 9 months = 1028; at
hour 3 for the same 9 months, mean = 1026, or 2 divisions less; at hour 3 for
12 months the mean is therefore 1004, and the same result is found by comparing
with the following hour 4 ; the mean is given in case of a difference in the two
results.

TABLE VIII. — REGULAR SOLAR DIURNAL VARIATION OF THE HORIZONTAL FORCE FOR EACH

YEAR OF OBSERVATION EXPRESSED IN SCALE DIVISIONS.

Increased numbers indicate decrease of force. The minutes at the head of each column are to bo added to

the hours given in the first vertical column. Kach year commences with the month of July.

184O-41.

1841-42.

1842-43 (9 m'ths).

Correc-

1842-43.

1843-44.

1844-4."..

Hour of the

22™

21f-

21j°-

tion.

21^»

nj»

21 J'"

d»y.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

Div's.

0 (A. M.)

223

549

782

+c

788

1008

1191

1

1007

1189

2

219

648

780

+e

780

1006

1189

3

1004

1188

4

214

545

777

+ 6

783

1003

1186

5

1002

1184

6

206

542

774

+6

780

1002

1182

7

1005

1186

8

226

552

788

+5

793

1010

1194

9

1013

1202

10

244

564

799

+5

804

1017

1206

11

1(116

1207

12 (P.M.)

241

563

792

+ 6

798

1014

1202

13

1010

1 1 !I5

14

221

547

781

+ 7

788

1110!)

1189

15

1002

1186

16

215

547

778

+7

785

1(102

1185

17

1004

1188

18

222

553

783

+7

790

1006

1190

19

1008

1191

20

225

554

786

+7

793

1008

1191

21

1009

1191

22

227

553

785

+ 6

791

1008

1191

23

1008

1191

Mean.

223.5

551.5

789.9

1007.4

1191.4

(Philadelphia local time, counted from midnight to midnight, 24 hours.)

OF THE MAGNETIC FORCE.

23

The preceding mean diurnal variations were put in the following analytical form,
in which the angle 6 counts from midnight at the rate of 15° an hour.

Year 1840-41 H = 223d.5 + 5".98 sin (fl + 252° 14') + 1K68 sin (28 + 121° 16') + 5*.89 sin (38 + 314° 42')

" 1841^*2 H = 551.5 + 4.03 sin (fl + 244 07 ) + 6.58 sin (2 9+131 32 ) + 4.48 sin (3 fl + 312 19 )

" 1842-43 H = 789.9 + 4.14 sin (fl + 250 06 ) + 7.07 sin (2 fl + 132 24 ) + 3.74 sin (38 + 323 06 )

" 1843-44 H = 1007.4 + 2.14 sin (8 + 273 65 )+ 5.09 sin (20 + 128 58 ) + 2.35 sin (38 + 317 58 )

" 1844-45 H = 1191.4 + 4.40 sin (fl + 271 13 ) + 6.86 sin (2 fl + 123 25 ) + 4.11 sin (38 + 321 26 )

To show the degree of correspondence hi the formula when deduced from the
observations of the even and odd hours separately, the results for the last year have
been added, viz: —

Even hours II = 1191d.3 + 4«.20 sin (fl + 271° 28') + 6d.98 sin (28+ 122° 36') + 4d.ll sin (3 fl + 322° 35')
Odd hours H = 1191.5 + 4.60 sin (fl + 270 59 ) + 6.73 sin (2 8 + 124 13 ) + 4.12 sin (38 + 320 17 )

The close agreement between the observed and computed values is shown gene-
rally in the annexed diagram.

(A). — IHBQDALITY IN THE DICKNAL VARIATION OP THE HORIZONTAL INTENSITY.

1840-41.

1841-42.

1842-43.

1843-44.

1844-45.

Oh 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
A. M. P. M.

Philadelphia local time.

The following table exhibits the differences for the year 1842-43, as an example
of the numerical correspondence.

DISCUSSION OF THE HORIZONTAL COMPONENT

A 51

Computed.

Observed.

C— O. ' P.M. Computed. <ih>erved.

C— 0.

0™ 21$"

788.7

788

+0.7

12"> 21£» 799.5 7U8

+ 1.5

2 "

786.6

786

+0.6

14 " 787.6 7s8

—0.4

4 "

781.3

783

—1.7

16 " 784.5 785

—0.5

6 "

781.2

780

+1.2

18 " 790.2 790

+ 0.2

8 "

792.5

793

—0.5

20 " 792.9 793

—0.1

10 "

803.3

804

—0.7

22 " 720.5 791

—05

The differences, using three terms in the equations, are within the uncertainty
of the observed values. The probable error of a single representation is _+_ 0.6 scale
divisions, or _+_ 0.00009 in the absolute scale.

The curves show a double progression in the daily motion, with a principal
maximum of horizontal force in the morning, a principal minimum before noon,
and a secondary maximum in the afternoon ; the precise epochs (to the nearest five
minutes) and extreme values were computed by means of the preceding formula?.

Tear.

Principal A. M. Maxi-
mum of hor. force.

Principal A. M. mini-
mum of hor. force.

Diurnal range in

Secondary P. M. maxi- i
mum of hor. force. Less than

From July to
July.

A. M

max. by

Epoch.

Amount.

Epoch.

Amount.

Scale

Parts of hori-

Value in

Epochs.

Amount.

div'e.

Div's.

DIY'B.

div's.

zontal force.

absol. scale.

Div's.

1840-41

6"45m

207.3

11" 0-»

246.1

38.8

0.00142

0.0059

4h 05m

213.5

6.2

1841-42

5 50

541.7

11 5

565.5

23.8

0.00087

0.0036

3 50

545.1

3.4

1842-43

5 30

779.8

10 55

803.9

24.1

0.00088

0.0037

3 50

784.0

4.2

1843-44

5 40

1001.7

10 50

1016.9

15.2

0.00055

0.0023

4 0

1002.0

0.3

1844-45

5 40

1182.4

10 50

1206.6

24.2

0.00088

0.0:J37

4 0

1184.8

2.4

Mean

5 41

10 56

0.0038

3 57

The secondary maximum is reached about 8h 30m P. M. with a comparatively
small range.

The mean value of the force is attained about 7h 55m A. M., and again about
lh 55m P. M., with considerable regularity ; it is again reached at 6|h and ll|h P. M.,
though with less regularity.

At Toronto (see Vol. II. of the Toronto Observations) the diurnal variation of
the horizontal force has a principal maximum at a little after 4 P. M., and a prin-
cipal minimum at 10 or 11 A. M.; the secondary maximum occurs about 6 A. M.
There is, therefore, this specific difference in the diurnal motion at these two
stations : in that at Philadelphia the morning maximum is the higher of the two,
while at Toronto it is the afternoon maximum. The difference between the two
maxima, as shown above, is almost nothing in the minimum year 1843-44, but
increases before (and after) this epoch in proportion to the interval. At Toronto
the daily range seems to be slightly greater. The secondary minimum at Toronto
occurs about 2 or 3 A. M., or about six hours later than at Philadelphia ; this is a
second though less significant point of difference.

The minimum daily range occurs in 1 843-44 ; its value is then less than one-half
what it was in 1840-41.

The following equation expresses the mean diurnal range in scale divisions: —

R = + 19.68 — 3.78 (t — 1843) + 2.77 (/ — 1843)2.
It represents the observed values as follows: —

OF THE MAGNETIC FORCE. 25

Observed range. Computed range.

January, 1841 38.8 38.3

1842 . 23.8 26.2

1843 . 24.1 19.7

1844 . .... 15.2 18.7
1845 24.2 23.2

The minimum range as given by the formula is in September, 1843. In Part I.
of the discussion we found the minimum range of the declination in May, 1843,
and the minimum from the disturbances of the declination in August, 1843.

Before proceeding to the discussion of the disturbances in the horizontal force,
the formulae given for the diurnal variation require to be put in a different form for
future use and for convenience of comparison with other places.

The scale divisions were multiplied by the value of one division of the scale
(0.0000365), and again by the value of A' found for the year; the numerical constant
was replaced by JTand the angular quantities were changed by 180° so as to make
increasing numbers correspond to increase of force ; we then obtain in absolute
measure the following expressions for the regular solar-diurnal variation of the
horizontal force at the Girard College: —

Year 1840-41 H = 4.178 + 0.00091 sin (9 + 723 14') + 0.00178 sin (28 + 301° 16') + 0.00090 sin (38 + 134° 42')
" 1841-12 H = 4.175 + 0.000(51 sin (9+64 07 ) + 0.00100 sin (2 8 + 311 32 ) + 0.00069 sin (3 8 + 132 19 )
" 1842-43 H = 4.173 + 0.00063 sin (8+70 06 ) + 0.00108 sin (2 0 + 312 24 ) + 0.00057 sin (38 + 143 06 )
" 1843-44 H = 4.170 + 0.00033 sin (8 + 93 55 ) + 0.00078 sin (28 + 308 58 ) + 0.00036 sin (38 + 137 58 )
" 1844-45 H = 4.168 + 0.00067 sin (8+91 13 )+ 0.00104 sin (2 8 + 303 25 ) + 0.00063 sin (38 + 141 26 )
The angle 9 counts from midnight ; the middle epoch to which each equation refers is January.

Investigation of the Eleven (Ten?) Year Inequality in tlie Disturbances of the
Horizontal Magnetic Force. — In Table VI. the number of disturbances in each month
has been given as found from the observations ; these numbers are, however, not
directly comparable with one another, first, on account of some omissions in the
record, and secondly, on account of the change from a bi-hourly to an hourly series.
For any incomplete month the number of disturbances for the whole month is
obtained by simple proportion from the number during the part of the month re-
corded; for January, 1841, the total number becomes 35, for June, 1841 the total
number is 18. For January, February, and March, 1843, the mean total number
of the disturbances, as found in the same months in the preceding and follow-
ing year, was substituted ; this mean gave 8, 20, and 20, respectively. The num-
ber of disturbances after October, 1843, were halved to make them comparable
with the bi-hourly series. There were two anomalous months, July and December,
1840, in which the disturbances amount to 165 and 120, with an annual mean of
64, whereas in the same months in the following year they only amount to 26 and
26 respectively, with an annual mean of 27 ; the mean annual difference 37 was
applied to the numbers found in 1841, which give 63 and 63 as a substitute for the
anomalous values in July and December, 1840. This anomaly does not exist in
the phenomenon itself, but is unquestionably due to the irregularity in the pro-
gressive change.

Table IX. contains the number of disturbances as distributed over the several
years and months, all referred to a uniform series of bi-hourly observations. To

•26

DISCUSSION OF THE DISTURBANCES

this table the monthly means and their ratio, when compared with the annual mean,
have been added ; also, for comparison, the corresponding ratios found in Part I. of
the discussion of the disturbances of the declination.

MONTH.

1840-41.

1841-42.

1842-43.

1843-44.

1844-45.

Mean.

Hor. force.
Katio.

Declination.
Ratio.

July

C63")

26

24

15

o

26

1 09

0 86

73

17

3

11

2

21

0 8Q

1 riQ

54

41

44

16

13

34

1 43*

1 <*(»

68

28

53

2

16

33

1 39

21 9*

49

32

15

0

21

24

1 00

1 08

(63)

26

5

0

23

2^

ft Q7

i on

35

14

g

1

13

14

0 59

07T

50

37

20

3

g

24

1 00

0 ^9

61

25

20

14

2

25

1 06

0 fiR

48

38

14

g

16

25

1 06

0 91

46

30

25

2

10

23

0 97

ft t\&

18

16

4

o

28

13

0 55*

OV4*

Sums

628

830

235

72

153

285

12.00

12.00

Mean

52

28

20

6

13

24

Observed N.

Computed N.

52

54

. 28

29

20

14

6

9

13

13

In the columns of ratios the principal maxima and minima are indicated by an asterisk.

The annual means exhibit plainly the eleven year inequality; they have been
represented by the formula : —

N = + 14.4 — 10.2 (t — 1843) + 4.8 (t — 1843)2.

January, 1841
1842
1843

" 1844
1845
According to the formula, the minimum occurs in January, 1844.

We have next to consider the eleven year inequality in the magnitude of the
disturbances of the horizontal force. Table X. contains the aggregate amount
of the disturbances expressed in scale divisions, and also their mean amount obtained
by application of the number of disturbances already given in Table VI.

For reasons already explained, the amount of disturbances in July, 1840, equal
to 10761 scale divisions, has been diminished in the ratio of 165 : 63. The ratio of
each monthly mean to the mean amount of the year is also given, together with a
column of corresponding ratios derived from the disturbances of the declination, as
made out in Part I. of the discussion.

OF THE HORIZONTAL FORCE.

27

TABLE X. — AGGREGATE AND MEAN AMOUNT OF THE DISTURBANCES OF THE HORIZONTAL FORCE.
EXPRESSED IN SCALE DIVISIONS.

MOSTH.

1840-41.

1841-42.

1842-43.

1843-44.

1844-45.

Mean
Amount.

Hor. force.
Ratio.

Declination.
Ratio.

Jnly

(4089)
4084
3092
3720
2390
6515
1186
2664
3112
2138
2456
560

1157
755
3075
1284
1991
1225
601
1822
1176
2075
1211
794

1295
131
2099
2399
915
239
0
44
39
676
1187
164

6S9

471
660
169
34
0
111
200
1412
861
131
0

0

142

1228
1412
2173
2283
1402
806
127
1604
789
2390

56
52
56
49
54
52
49
50
49
49
47
44

1.10
1.03
1.11*
0.97
1.06
1.03
0.97
0.99
0.97
0.97
0.93
0.87*

0.87
1.61
1.56
2.06*
1.06
1.00
0.72
0.54
0.66
0.94
0.66
0.42*

April

May

Mean amount

53.9

52.0

48.6

46.3

46.8 50.6 i 1.00 1.00

Maxima and minima in the columns of ratios are marked with an asterisk.

The inequality in the mean amount of the horizontal force disturbances in each
year, indicates the year 1843-44 as the minimum year.

From the preceding results, we may assume the month of November, 1843, as
the epoch for the minimum of the eleven (ten ?) year inequality, as far as indicated
by the differential observations of the horizontal force.

Further Analysis of t7te Disturbances of the Horizontal 'Force. — The distribution
of the disturbances in number and mean amount over the several months of the
year has been given in Tables IX. and X. From Table IX. we learn that the
disturbances are greatest in number in September and March or April, or about the
time of the equinoxes, and least in number about January and June, or about the
time of the solstices. At the autumnal equinox the numbers exceed those of the
vernal equinox ; the same law was found at Toronto ; also the numbers are smaller
at the summer solstice than at the winter solstice, in perfect accordance with the
result found at Toronto. These results are shown graphically on the annexed dia-
gram, which contains also the ratio of the disturbances for the declination in which
the same law is apparent.

(B). — DISTRIBUTION OF THB NUMBER OF DISTURBANCES is THE SEVERAL MONTHS OF THE YEAK.
Full line for horizontal force. Dotted line for declination.

»r £ .a" - - - -s-

**» JT* o r_J *~ » i_fc • ' » • •* ^>

Illllltllllll

28

DISCUSSION OF THE DISTURBANCES

Table X. shows that, in reference to the average magnitude of the disturb-
ances, the same law holds good, viz : the greatest relative magnitude occurring
about the time of the equinoxes ; the greatest amount corresponding to the autumnal
equinox, and the least to about the time of the solstices, the smaller amount occur-
ring near the summer solstice. The average magnitude of the disturbances of the
declination was found subject to the same law.

If we separate the disturbances which increase the force from those which decrease
it, we may form the two following tables of the distribution of the disturbances in
number and average amount over the several months of the years.

TABLE XI. — ANNUAL INEQUALITY IN THE NUMBER OF DISTURBANCES, INCREASING AND

DECREASING THE HORIZONTAL FORCE.

1840-41.

1841-42.

1843-43.

1843-44.

1S44-45.

Sum.

Ratios.

Inc.

Dec.

Inc.

Dec.

Inc.

DM.

Inc.

Dec

Inc.

Dec.

Inc.

Dec.

Inc.

Dec.

July

(38)

(25)

6

20

5

19

1

14

0

0

50

78

1.2

1.0

August

18

55

6

11

1

2

2

9

0

2

27

79

0.7

1.0

September

25

29

5

36

38

6

11

5

9

4

88

80

2.1*

1.1

October

18

50

11

17

37

16

1

1

8

8

75

92

1.8

1.2

November

13

36

1

31

4

11

0

0

0

21

18

99

0.4

1.3*

December

(25)

(38)

8

18

0

5

0

0

15

8

48

69

1.1

0.9

January

19

16

6

8

3

5

0

1

3

10

31

40

0.8

0.6

February

15

35

4

33

2

18

0

3

0

9

21

98

0.5

1.2

March

17

44

10

16

3

17

0

14

1

1

31

92

0.8

1.2

April

18

30

14

24--

1

13

1

7

0

16

34

90

0.8

1.3

May

24

22

16

13

10

15

1

1

5

5

56

56

1.3

0.7

June

9

9

6

10 1

3 j 0

0

7

21

23

43 0.5*

0.6*

Sum

239

389

93

237

105

130

17

55

48

105 ; 502

916 12.0

12.0

In each year the number of disturbances increasing the force is less than the
number which decreases it; the numbers of increase are to the numbers of decrease
as 1 : 1.8. The numbers of the monthly ratio for the increasing disturbances exhibit
the same law as found in Table IX. : with respect to the numbers for the
decreasing force the law is apparently less distinctly marked ; the maximum seems
to occur about two months later (before the winter solstice), at a time when the
number for increasing force is apparently at its minimum. This indistinctness in
the law may possibly be due to an irregular distribution in reference to the hours
of the day, and could only disappear through a longer series of observations.

OF THE HORIZONTAL FORCE.

29

TABLE XII. — ANNUAL INEQUALITY IN THE MEAN AMOUNT OP THE DISTURBANCES OF THE HORI-

ZONTAL FORCE. AGGREGATE AMOUNT FOR INCREASING AND DECREASING DISTURBANCES, EX-

PRESSED IN SCALE DIVISIONS.

1840-41.

1841-42.

1S43-43. 1843-44.

1844-45.

1840-45.

Aver. am't.

Ratios.

Inc.

Dec.

Inc.

Dec.

Inc. Dec. Inc.

Dec.

Inc.

Dec. ; Inc.

Dec.

Inc. | Dec.

Inc.

Dec

July

(2202)

(1887)

214

943

292 1003

41

628

0

0 ; 2749

4461

55d

57"

1.2

1.1

August

794

3290

261

494

51

80

69

402

0

142

1175

4408

44

54

1.0

1.0

Sept.

1082

2010

186

2889

1857

242

452

208

873

355

4450

5704

45

56

1.0

1.1

October

726

2994

421

863

1685

714

128

41

691

721

3651

5333

44

S3

1.0

1.0

Nov.

520

1870

35

1956

185

730

0

34

0

2173

740

6763

41

56

0.9

1.1

Deo.

2204

4311

289

936

0

239

0

0

1483

800

3976

6286

47

56

1.0

1.1

January

723

463

231

370

0

0

0

111

302

1100

1256

2044

48

60

1.1

0.8

Feb.

649

2015

140

1682

0

44

0

200

0

806

789

4747

42

52

1.0

1.0

March

643

2469

415

761

0

39

0

1412

37

90

1095

4771

39

52

0.9

1.0

April

732

1406

550

1525

54

622

75

786

41

1563

1452

5902

40

52

0.9

1.0

May

1000

1456

696

515

412

775

83

48

398

391

2589

3185

42

52

1.0

1.0

June

307

253

284

510

50

114

0

0

604 1786

1245

2663

44

44

1.0

0.8

Sum 11582

24424

3722

13444

4586

4602

848

3870

4429

9927 25167

56267

12.0

12.0

Number

254

414

93

237

97

92

20

82

96

211 ! 560

1036

Mean

46

59

40

57

47

50

42

47

46

47

45

54

The average amount of a disturbance increasing the horizontal force is 45 scale
divisions, or 0.0069 in absolute measure ; the average amount of a disturbance
decreasing the same is 54 scale divisions, or 0.0082 in absolute value. The ratio
of these numbers is as 1 : 1.2, whereas at Toronto the ratio is 1 : 6.4.

The law of the monthly inequality for amount of increasing or decreasing dis-
turbances is, as in the preceding case, very indistinct and further obscured by the
small absolute amount of variation.

In the following Table, XIII., the larger disturbances have been distributed
over the different hours of their occurrence; in this combination the bi-hourly series
(of the even hours) of observation has been used throughout.

Hour.

Aggregate amount in
sc. dlr.

Number of occur-
rence.

Average amount.

Ratio of numbers.

0 (Midnight)

8116

142

57

1.12

2

5967

109

55

0.86

4

4961

93

53

0.73*

6

4751*

94

51

0.74

8

5562

104

53

0.83

10

7721*

146

53

1.15

12 (Noon)

6825

161

42

1.27*

14

6636

127

52

1.00

16

6634

135

49

1.07

18

6894

132

52

1.05

20

7574

139

55

1.09

22 7358

139

53

1.09

Directing our attention to the columns of aggregate amount and of ratios of
number of occurrence, we find a principal maximum about 11 A. M., which seems
to correspond to the secondary maximum of corresponding ratios at Toronto occur-
ring about three hours earlier; the principal minimum occurs about 5 A. M., which
corresponds to the secondary minimum at Toronto occurring between 5 and 6 A.
M. ; again, at Philadelphia, the secondary maximum at midnight is about two hours
earlier than the principal maximum at Toronto, and the secondary minimum about

30

DISCUSSION OF THE DISTURBANCES

4 P. M. corresponds in time to the /in'/id/ml minimum at Toronto occurring between
2 and 6 P. M. Thus, the curves at the two stations, representing the diurnal vari-
ation of the disturbances (irrespective of increase or decrease) of the horizontal
force, is double crested with an exchange of the principal and secondary maximum
and also of the principal and secondary minimum.

In the next Table, XIV., the diurnal variation of the disturbances is exhibited
separately for disturbances increasing and disturbances decreasing the horizontal
force.

DISTURBANCES INCREASING HORIZONTAL FORCE.

DisrrRBA.iCES DECREASING HORIZONTAL FORCE.

Excess of aggregate

Hour.

decrease over

Number of
occurrences.

Aggregate
amount.

Batio.

Number of
occurrences.

Aggregate
amount.

Katio.

aggregate increase.

0 (Midn't)

57

2878

1.28

85

5238

1.21

2360

2

44

2173

0.97

65

3794

0.87

1621

4

42

1998

0.89

51

2963*

0.68

965

6

28

1213*

0.54

66

3538

0.81

2325

8

48

2345

1.04

56

3217

0.74

872

10

61

2732

1.22

85

4989

1.15

2257

12 (Noon)

74

3134*

1.39

87

3691

0.85

557

14

48

2239

1.00

79

4397

1.01

2158

16

49

2200

0.98

86

4434

1.03

2234

18

45

2005

0.89

87

4889

1.13

2884

20

39

1758

0.78

100

5816*

1.34

4058

22

50

2296

1.02

89

5062

1.18

2766

Sums.

585

26971

12.00

936

52028

12.00

25057

The disturbances increasing and those decreasing the horizontal force evidently
follow different laws; at Toronto they were found completely opposed; they are less
so at Philadelphia. The principal maximum of increasing disturbances (at noon)
seem to be contemporaneous with a secondary minimum of the decreasing disturb-
ances ; again the principal maximum of the decreasing disturbances (at 8 P. M.)
corresponds to a secondary minimum of the increasing disturbances. In reference
to the main feature, the maximum disturbance of those increasing the force and of
those decreasing the force, the Philadelphia ratios show even a greater resemblance
to the results at St. Helena and the Cape of Good Hope than to those at Toronto.
At the two southern stations the maximum in the disturbances which increase
occurs at 11 A. M. and the maximum in the disturbances which decrease occurs
about 6 or 7 P. M. (See Vol. II. of the St. Helena Observations.)

Table XIV. contains also the hourly excess of the aggregate amount of the dis-
turbances which decrease the horizontal force over those which increase the same.
If we divide the numbers by the whole number of days of observation (nearly 1500)
we obtain the diurnal disturbance variation expressed in scale divisions.

TABLE XV. — DIURNAL DISTURBANCE VARIATION.

Hour.

S. D.

In absolute measure.

Hour.

S. D.

In absolute measure.

0 (Midn't)

1.6

0.00024

12 (Noon)

0.4

0.00006

2

1.1

17

14

1.4

21

4

0.7

11

16

1.5

23

6

1.6

24

18

2.0

30

8

0.6

09

20

2.8

43

10

1.5

23

22

1.9

29

OP THE HORIZONTAL FORCE.

31

The average amount by which the disturbances tend to decrease the diurnal
variation of the horizontal force is 1.4 scale divisions or 0.00021 in the absolute
scale. The maximum eifect takes place at 8 P. M., at exactly the same hour when
the declination disturbances reach their greatest effect.

In the preceding Tables, XIII., XIV., and XV., to the hours indicated 21 g
minutes should be added, the observations being made so much later than the even
hours.

The preceding discussion shows that for two stations, even at a comparatively
short distance, as for Philadelphia and Toronto, there are, generally speaking, some
close coincidences in the laws derived from independent observations ; but there
are also certain differences in other results ; yet it must not be forgotten that for a
strict comparability we require, if not simultaneous observations, at least observa-
tions extending over similar parts or the whole of an eleven year period. The
Philadelphia series includes a minimum year of that inequality, with the greater
extent of observations before that epoch, whereas at Toronto the series begins after
the minimum epoch and barely extends to a maximum year.

For the purpose of obtaining a better view of the absolute amount of the disturb-
ances and their frequency of occurrence,1 they were classified in nine groups of equal
differences of 20 scale divisions ; the number of disturbances in each was found as
follows : —

LIMITS ADOPTED.

In scale divisions.

In parts of horizontal force.

Iu the absolute scale.

33 to 53

0.0012 to 0.0019

0.005 to 0.008

1159

53

' 73

19

27

08

11

348

73

' 93

27

34

11

14

93

93

113

34

41

14

17

45

113

133

41

48

17

20

27

133

153

48

55

20

23

14

153

173

55

62

23

26

4

173

193

62

70

26

29

6

193

213

0.0070

0.0077

0.029

0.032

2

Beyond.

0

The numbers in the last column cannot be considered as entirely independent
of the eleven year period, and in attempting to apply the theory of probabilities in

1 A table analogous to that given above, showing the distribution of the disturbances in declina-
tion, is here added for comparison : — •

Lmmi ADOPTED.

V tuv nf rliodirlia nfaa

In scale divisions.

In minutes of arc.

8 to

16 3'.6

to 7'.2

1856

16

24 7.2

10.8

333

24

32 10.8

14.4

105

32

40

14.4

18.1

42

40

48

18.1

21.7

16

48

56

21.7

25.3

2

56

64

25.3

29.0

2

64

72

29.0

32.6

1

Bpyond

0

3'2 DISTURBANCES OF THE HORIZONTAL FORCE, ETC.

reference to the number of disturbances which ought to occur between the assigned
limits, it became apparent that the larger disturbances greatly preponderate, a fact
no doubt intimately connected with the difficulty in correctly allowing for the pro-
gressive change during the first year of observation.

PART V .

INVESTIGATION

OP THE

SOLAR-DIURNAL VARIATION AND OF THE ANNUAL INEQUALITY OF THE
HORIZONTAL COMPONENT OF THE MAGNETIC FORCE.

(33)

INVESTIGATION

SOLAR-DIURNAL VARIATION, AND OF THE ANNUAL INEQUALITY OF THE
HORIZONTAL COMPONENT OF THE MAGNETIC FORCE.

THE discussion of the diurnal and annual variations of the horizontal force is
based on the resulting montlily normal values for each observation hour as given in
the preceding part (IV.), in which the horizontal force has been discussed in relation
to the ten or eleven year period, and which also contains the investigation of the
disturbances; in the same part all necessary statements are given relating to the
instrumental data and the absolute values of the horizontal force.

The normals, as has been shown, are referred to a uniform standard temperature ;
they are corrected for irregularity in the progressive change, and are necessarily
freed from all the larger disturbances. The use of the normals instead of the sim-
ple means of the readings (corrected for difference of temperature) will insure
greater regularity in the variations of the horizontal force, now under consideration.

The diurnal variation requires an arrangement of the five year series of monthly
normals according to the months of the year and hours of the day; in general, the
method of interpolation for an occasional omission in either a month or hour, is the
same as that used in Part II. of the discussion of the Girard College observations ;
there is, however, this difference in the tabulation of the monthly values, that in
the present case the results are consolidated in a five years' arrangement, and in
consequence the year commences with the month of July. This arrangement was
preferred, particularly since it was found desirable to make no use of the observa-
tions in the first month of the series.

Tabulation of monthly normals for each observing hour and each observing year,
beginning and ending with July. The individual values are taken from Table
VII. of the preceding Part IV.

After applying the corrections of — 19 scale divisions to the normals for January,
1841, and of +8 scale divisions to those of June, 1841, to allow for defective num-
ber of observations in these months, a further correction of + 68 scale divisions was
applied to all values between July, 1840, and May, 1841, inclusive, and of + 60 to
all values between July, 1840, and December, 1840, inclusive, to allow for defects
in the regularity of the progressive change, thus making the total correction for
the latter months = 128 scale divisions. The above corrections, when divided by 5,

(35)

86 DISCUSSION OF THE HORIZONTAL COMPONENT

in order to give the correction to the means derived from five years, become, there
fore: for months between July and December inclusive, + 26; for January + 10;
for February, March, April, and May +14; for June + 2. These corrections are
constant for each hour of the day in any one month, and consequently do not affect
the diurnal variation; but they have nevertheless been applied at once to facilitate
subsequent deductions. Their origin has also been explained in the remarks accom-
panying Table V. of the preceding part.

The following example of the process of interpolation for the odd hour values
will suffice for all similar cases: Required the mean normal from the 5 year series
for 5h 21 |m A. M. in June (see tabular values and results below). The mean nor-
mals for the two last years at 4h 21 |m, 5h 21 lm, and 6h 21 im, are 1176, 1173, and
1169 respectively; the mean at 5h 21^m is therefore 3 divisions less than the mean
at 4h 21 |m, and since the mean of the 5 year series at 4h 21 |m is 853, the result for
5h 21 |m becomes 849; again, adding 4 divisions to 847, the mean at 6h 21 |m, we
find 851; the mean of the two values, or 850, is that given in the table, to which
+ 2 has been added, making the final result 852. The means of the odd hours, thus
found from the adjacent even hours, in general, do not differ by as much as a scale
division.

The time given in the tables of the normals is mean local time, counting from
midnight to midnight to twenty-four hours. The observations were taken (on the
average) 21 1 minutes after the full hours, as indicated in the tables. Increase of
scale readings indicates decrease of horizontal force; the value of a scale division
equals 0.0000365 parts of the horizontal force, or 0.0001523 in absolute measure,
the mean horizontal force being 4.173 (in absolute measure). Proper weights have
been given to the normals of the even and odd hours, in proportion to the number
of observations, as will be seen hereafter. Other special remarks will be found at
the end of the month to which they refer.

Tabulation of the hourly normals for each month and the mean of the five year
series, expressed in scale division readings and reduced to the standard temperature
of 63° (Fahrenheit's scale), also corrected for all irregularities in the progressive
change. The regular progressive and secular change, therefore, remains in the
tabular quantities.

OF THE MAGNETIC FORCE.

37

NORMALS OF TUB HORIZONTAL FORCE FOR JULY.

Year.

O1"

1"

2"

3"

41,

5"

6"

7"

8"

9" 10"

11"

+ 21 i"

1840

113

442
692
927
1102

1103

97
442
686
924
1105 1106

89
435
682
924
1106

1105

50
435
678
923
1104

1104

112
447
695
935
1109

1116

116

458
708
941
1118

1114

1841

1842

1843

1844

605

653

651

649

647

642

638

647

660

666

6i:8

664

Referred mean ....

Constant correction -(- 26

681

679

677

675

673

668

664

673

686

692

694

690

Year.

12"

Noon.

13"

14"

15»

16»

17"

18"

19"

20"

21"

22"

23"

+ 21J»

1840

94
449
700
934
1106

1100

59
428
680
923
1096

1093

52
430
677
916
1092

1093

92
444
690
921
1096

1099

93
448
694
928
1101

1102

108
439
700
931
1103

1104

1841

1842

1843

1844

657

646

637

634

633

640

649

651

653

655

656

657

Referred mean ....

Constant correction -|- 26
Normals

683

672

663

660

659

666

675

677

679

681

682

683

Monthly mean normal from the even hours f-f- 21£m) 676.3, weight 5.
" " " odd " " 676.3, " 1.

NORMALS OF THE HORIZONTAL FORCE FOR AUGUST.

Year.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10"

11"

+ 21$-»

1840

108
490
699
931
1133

1134

112
494
694
930
1134

1133

117
487
695
931
1133

1131

106
482
692
927
1130

1135

138
501
711
947
1143

1152

153

518
721
954
1153

700

1147

692

1841

1842

1843

1844

672

673

673

672

673

669

667

676

688

698

Referred mean ....

Constant correction -t- 26

698

699

699

698

699

695

693

702

714

724

726

718

Year.

12h

Noon.

13"

14"

15"

16"

17"

18"

19"

20*

21"

22"

23"

+ 21j»

1S40

134
502
700
938
1138

1129

103
483
688
921
1121

1119

111
483
689
924
1121

1127

114
497
701
929
1134

1135

121
500
703
932
1135

1134
677

126
495
702
933
1135

1135

1841

1842

1843

1844

Mean

682

672

663

662

666

670

075

677

678

678

676

Referred mean ....

Constant correction -f- 26

708

698

689

688

692

696

701

703

704

703

704

702

Monthly mean normal from the even hours (+ 2Um) 702.2, weight 5.
" " " odd "- " 702.2, " 1.

38

DISCUSSION OF THE HORIZONTAL C O M I' 0 N E NT

NORMALS OF THE HORIZONTAL FORCE FOR SK.I»TKMKKB.

Year.

0" 1» 2"

3" 4"

6"

7"

8"

!)>>

10"

11" +21$"'

1840

155
510
726
974
1106

1104

147
514
733
967
1107

1105

139
515
722
965
1101

1101

141
508
717
960
1100

1107

18d
531
739
980
1117

1125

202
542
750
992
1128

1125

1841 .... . .

1842

1843

1844 .... . .

694

694
692

688
692

687

685

695

709

718

723

720

Referred mean ....

Constant correction •+- 26

720

718

720

718 714

713

711

721

735

744

749

746

Year.

12"

Noon.

13h

14"

15"

16" 17" 18"

19h

20"

21"

22"

23"

+ 211"

1840

177
537
737
985
1115

1104

155
516
730
972
1097

1095

153
519
727
972
1095

1100

158
520
737
975
1102

1104

157
515
737
974
1104

1108

150
515
734
973
1107

1108

1841

1842

1843

1844

710

700

694

692

693

697

698

699

697

699

696

696

Referred mean ....

Constant correction + 26
Normals

736

726

720

718

719

723

724

725

723

725

722

722

Monthly mean normal from the even hours (+ 21im) 724.4, weight 5.
" " " odd " " 724.9, " 1.

NORMALS OF THE HORIZONTAL FORCE FOR OCTOBER.

Year.

0" 1"

2"

3h

4h

5*

6><

7"

8"

9"

10"

11"

+ 21 A"

1840

142
521
764
983
1133

978
1132

137
517
759
983
1131

978
1127

122
518
757
976
1124

978
1125

138
514
757
977
1129

980
1134

153
526
764
983
1141

787
1149

166
537
781
991
1152

992

1145

1841

7842

1843

1844

709
705

705

701

699

702

703

708

713 725
720

724

Referred mean ....

Constant correction + 26

735 ; 731

731

727

725

728

729

734

739

746 751

750

Year.

12"
Noon.

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+ 2H°

1840

159
547
783
991
1145

989
1137

158
530
776
985
1134

983
1130

148
525
776
983
1132

983
1134

146
527
768
985
1135

985
1137

148
529
769
985
1138

986
1134

151
528
764
983
1137

984
1135

1841 .......

1842

1843

1844 .

725

721

717

714

713

713

712

713

714

713
713

712

Referred mean ....

Constant correction -f- 26
Normals

751

747

743 740

739

739

738

739

740

739

739

738

Monthly mean normal from the even hours (+ 21Jm) 738.3, weight 5.
" " " odd " " 738.2, " 2.

OF THE MAGNETIC FORCE.

NORMALS OP THE HORIZONTAL FORCE FOR NOVEMBER.

Year.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10'' 11" + 21J"

1840

155
519
774
987
1131

986
1130

150
517

770
985
1127

983
1126

144
515
771
982
1125

980
1123

133
509

768
980
1122

983
1125

144

518
777
987
1130

991
1135

154

529
789
992 993
1138 1142

1841

1842

1843

1844

713

712

710

708

707

704

702

706

711

717

720

725

Referred mean ....

Constant correction 4- 2(i

739

738

736

734

733

730

728

732

737

743

746

751

-

Year. l 12" ! 13"

Noou.

14"

15''

16"

17"

18"

19"

20"

21"

22"

23"

4- 21J"

1840

175
531

787
991
1136

989
1133

157
514
781
987
1129

986
1127

151
518
778
984
1124

985
1131

148
513
775
986
1128

986
1129

144
516
776
987
1130

987
1130

160
518
776
988
1131

988
1131

1841

1842

1843

1844

724

720

714

712

711

713

710
710

711

713

715

714

Referred mean ....

Constant correction + 20

750

I
74« 740

7"s

737

739

736

736

737

739

741

740

Monthly mean normal from the even hours (-(-
" " " odd "

21$") 738.3, weight 5.
" 738.8 " 2.

NORMALS OF THE HORIZONTAL FORCE FOR DECEMBER.

Year.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10"

11" -f 21 i»

1840

196
546
780
995
1213

993
1202

188
541
777
992
1200

991
1198

176
538
775
989
1196

987
1194

166
535
773
987
1190

987
1193

178
537
776
991
1194

991
1197

208
548
790
992
1209

997
1217

1841

1842

1843

1844

746

741

740

738

735

733

730

732

735

740

749

757

Referred mean ....

Constant correction -\- 26

772

7C7

766

764

761

759

756

758

761

766

775

783

Year.

12"

Noou.

13"

14"

15"

16"

17"

18"

19"

20"

21" ' 22"

23"

+ 214"

1840

217
562
795
999
1220

998
1212

393
549
786
996
1209

993
1202

182
545
773
991
1201

990
1201

185
547
776
992
1203

995
1198

200
550
781
995
1200

995
1204

194

552
782
997
1206

998
1206

1841

1842

1843

1844

759

752

747

742

738

739

741

742

745

746

746

745

Referred mean ....

Constant correction -f Hi!

785

778

773

768

7C4

765

767

768

771

772

772

771

Monthly mean normal from the even hours (4- 211m) 768.6, weight 5.
" " " odd " " 768.2, " 2.

40

DISCUSSION OF THE HORIZONTAL COMPONENT

NORMALS OF THE HORIZONTAL FORCE FOR JANUARY.

Year.

0"

1"

2"

3"

41,

5"

6"

7"

8"

9"

10"

IP

+ 21J"

1841

298
561
(820)
1006
1233

1005
1228

300
556
(817)
1004
1231

1002
1230

294
555
(814)
1000
1228

1000
1226

284
558
(815)
999
1225

999
1226

281
553
(814)
1002
1231

1005
1241

302
573
(827)
1008
1248

1011
1252

1842

1843 .

1844

1845

784

782

782

780

778

777

776

774

776

785

792

798

Referred mean ....

Constant correction + 10

794

792

792

790

788

787

786

784

786

795

802

808

Year.

12"

Noon.

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+ 21*".

1841

326
577
(830)
1009
1249

1006
1242

311
559
818
1003
1239

999
1233

289
554
(813)
998
1229

1000
1230

296
564
(820)
1002
1233

1003
1231

301
563
(820)
1003
1230

1004
1230

302
5G4
(821)
1004
1229

1005
1229

1842

1843

1844

1845

798

791

786

780

777

780

783

784

783

784

784

786

Referred mean ....

Constant correction + 10

808

801

796

790

787

790

793

794

793

794

794

796

Monthly mean normal from the even hours 793.3, weight 4.
" " " odd " 793.4, " 2.

The values for 1843 within brackets are interpolated by means of the continued
readings at 14b 21 |m; at this hour the difference of reading from the preceding
year is 259, which added to the values of 1842 gave resulting normals for 1843; in
the same manner the reading in 1843 at 14h 21 |m when compared with the reading
in the following year (1844) leaves the difference 185, which quantity when sub-
tracted from each hourly value in 1844 gives a second determination for the year
1843; the mean of the two determinations for each hour has been inserted above.

OF T 11 E M A G N E T 1C FORCE.

41

NORMALS OF THE HORIZONTAL FORCE FOR FEBRUARY.

Year.

Oh

1"

2"

3"

4"

5"

6"

7h

8"

9"

10"

11"

+ 21 4"

1S41

2U9
580
(820)
1031
1230

1031
1230

261
573
(816)
1031
1231

1029
1229

264
572
(813)
1026
1229

1026
1226

257
567
(810)
1026
1223

1028
1227

265
568
(812)
1029
1231

1030
1236

288
582
(822)
1034
1243

1034
1244

1842

1843

1844

1S45

786

784

782

782

781

779

777

779

781

786

794
808

796
810

Referred moan ....

Constant correction -|- 14

800

798

796

796

795

793

791

793

795

800

Year.

12"

Noon.

297
589
(826)
1035
1250

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+ 21 J»

1841

1032
1242

289
578
817
1028
1238

1028
1231

275
578
(818)
1030
1233

1031
1229

274
580
(820)
1032
1231

1033
1233

275
590
(826)
1034
1235

1033
1231

272
578
(819)
1032
1231

786

1030
1232

1842

1843 . .

1844

1845

799

794

790

786

787

786

787

790

792

788

78«

Referred mean ....

Constant correction + 14
Normals

813

808

804

800

801

800

801

804

806

802

800 ; 800

Monthly mean normal from even hours (-(- 21 jm) 800.8, weight 4.
" " " odd " " 800.4, " 2.

The values of 1843 inclosed in brackets are derived from the reading at 14h 21 1'
in the same manner as explained in the preceding month.

DISCUSSION OF THE HORIZONTAL COM J' 0 N K N T

NORMALS OF THE HORIZONTAL FORCE FOR MARCH.

Year.

0*

P

»

3»

4"

5"

6"

7"

8*

91'

10"

11"

+ 21i-

1841

268
565
(827)
1048
1236

1047
1236

272
559
(823)
1046
1234

1046
1235

267
557
(822)
1046
1234

1043
1234

257
554
(819)
1043
1231

1047
1233

271
563
(827)
1050
1241

1054
1249

294
574
(836)
1057
1255

1063
1261

1842

1843

1844

1845

789

788

787

786

785

783

781

785

790

798

803

808

Referred mean ....

Constant correction + 14

803

802

801

800

799

797

795

799

804

812

817

822

Year.

12*

Noon.

13"

14"

15"

16"

17"

18*

19*

20h

21"

22*

23'' + 21 J"

1841 ....

286
575
(839)
1063
1260

1061
1253

267
561
829
1057
1245

1050
1239

266
565
(828)
1051
1240

1050
1242

282
571
(831)
1050
1244

1052
1240

264
567
(828)
1050
1239

1048
1237

272
566
(828)
1050
1240

1048
1239

1842

1843

1844

1845

805

800

792

787

790

793

796

794

790

789

791

790

Referred mean ....

Constant correction -f- 14
Normals

819

814

806

801

804

807

810

808

804

803

805

804

Monthly mean normal from the even hours (-)- 21jm) 805.6, weight 4.
" " " " " odd " " 805.8, " 2.

The values for 1843 are interpolated as in the preceding two months

NORMALS OF THE HORIZONTAL FORCE FOR APRIL.

Year.

0" -

1*

2*

3"

4"

5*

6*

7*

8*

9"

10"

11*

+ 21*"

1841

273
595
861
1070
1252

1069
1250

271
598
861
1068
1249

1065
1247

262
597
854
1063
1245

1062
1243

262
594
854
1064
1241

1061
1244

283
604
868
1067
1253

1074
1268

317

620

883
1078
1278

1078
1281

1842

1843

1844

1845 .......

Mean
Referred mean ....

810

809

809

806

804

803

803

806

815

827

835

837

Constant correction + 14

824

823

823

820

818

817

817

820

829

841

849

851

Year.

12"

Noon.

13"

14"

16*

16*

17*

18*

19*

20"

21*

22*

23*

+ 21 J»

1841

315
618

878
1077
1268

1071
1267

279
603
863
1066
1255

1062
1252

268
598
860
1064
1248

1062
1253

271
607
861
1068
1256

1068
1254

283
608
865
1071
1254

1071
1253

280
611
859
1068
1250

1069
1254

1842

1843

1844

1845

831

825

813

810

808

808

813

813

816

816

814

813

Referred mean ....

Constant correction + 14
Normals

845

839

827

824

822

822

827

827

830

830

828

827

Monthly mean normal from the even hours (+ 21 J"1) 828.2, weight 5.
odd " " 828.4, " 2.

OF THE MAGNETIC FORCE.

43

NORMALS OF THE HORIZONTAL FORCE FOR MAY.

Year.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10*

11*

+ 21J-

1841

311
614

864
1065
1244

1065
1243

305
610
862
1063
1241

1062
1239

306
611
858
1062
1236

1061
1233

297
605
857
1061
1229

1064
1236

306
621
875
1068
1251

1076
1261

323
630
872
1077
1262

1070
1258

1842

1843

1844

1845

820

819

816

815

815

812

810

815

824

832

833

829

Referred mean ....

Constant correction -f- 14

834

833

830

829

829

826

824

829

838

846

847

843

Year

12*

Noon.

13h

14"

15"

16"

17"

18"

19"

20"

21"

22*

23*

+ 21J-"

1841

313
622
864
1064
1253

1057
1244

301
606
855
1053
1238

1053
1236

294
607
856
1051
1237

1054
1239

306
615
862
1059
1245

1063
1246

309
618
867
1064
1246

1064

1248

313
619
863
1065
1247

1063
1242

1842

1843

1844

1845

823

816

811

810

809

811

817

818

821

822

821

818

Referred mean ....

Constant correction -f- 14
Normals

837

830

825

824

823

825

831

832

835

836

835

832

Monthly mean normal from the even hours (+ 21Jm) 832.3, weight 5.
" " " " " odd " " 832.1, " 2.

NORMALS OF THE HORIZONTAL FORCE FOR JUNE.

Year.

0*

1"

2*

3"

4"

5*

6*

7*

8*

9*

10*

11*

+ 21i">

1841

392
649
881
1078
1280

1077
1281

390
652
879
1076
1281

1077
1281

392
646
876
1077
1275

1075
1271

386
638
873
1073
1266

1077
1273

400
649
883
1080
1282

1082
1293

401
659
894
1084
1295

1081
1292

1842

1843

1844

1845

856

856

856

856

853

850

847

853

859

865

867

864

Referred mean ....

Constant correction + 2

858

858

858

858

855

852

849

855

861

867

869

866

Year.

12*

Noon.

13*

14"

15"

16*

17*

18*

19*

20"

21*

22*

23"

+ 21J-

1841

395
650
884
1077
1286

1072
1280

382
639
870
1067
1272

1065
1269

385
638
870
1065
1269

1067
1273

392
649
881
1071
1278

1073
1281

402
648
881
1075
1280

1077
1277

392
650
885
1077
1279

1078
1280

1842

1843

1844

1845

858

853

846

845

845
849

854

856

857

856

857

857

Referred mean ....

Constant correction -f- 2

860

ff.r,

848

847

847

851

856

858

859

858

859 859

Monthly mean normal from the even hours (4- 21 j1") 856.6, weight 5.
" " " odd " " 857.0, " 2.

44

D 1 S C V S S I 0 N OK T II K II O U I X O N T A L C' O .M 1' O X E N T

TABLE I. — RECAPITULATION OF THE HOURLY NORMALS OF THE HORIZONTAL FORCE (EXPRESSED

IN SCALE DIVISIONS) FOR EACH MONTH OF THE YEAR.

Increase of scale readings denotes decrease of force.

1840-1845.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10"

11"

+ 21$"'

July .

681

679

677

675

673

668

664

673

686

692

694

690

August .

698

699

699

698

699

695

693

702

714

724

726

718

September

720

718

720

718

714

713

711

721

735

744

749

746

October

735

731

731

727

725

728

729

734

739

746

751

750

November

739

738

736

734

733

730

728

732

737

743

746

751

December

772

767

766

764

761

759

756

758

761

766

775

783

January

794

792

792

790

788 '

787

786

784

786

795

802

808

February

-800

798

796

796

795

793

791

793

795

800

808

810

March .

803

802

801

800

799

797

795

799

804

812

817

822

April

824

823

823

820

818

817

817

820

829

841

849

851

May .

834

833

830

829

829

826

824

829

838

846

847

843

June

858

858

858

858

855

852

849

855

861

867

869

866

Year .

771.5

769.8

769.1 767.4

765.7

763.7

761.9

766.7

773.7

781.3

786.1

786.5 j

Summer

769.2

768.3

767.8 ! 766.3

764.7

761.8

759.7

766.7

777.2

785.7

789.0

785.7

Winter .

773.8

771.3

770.3

768.5

766.8

765.7

764.2

766.7

770.3

777.0

783.2

787.3

1840-1845.

12"

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23" + 21j°>

Noon.

July . .

683

672

663

660

659

666

675

677

679

681

682

683

August . .

708

698

689

688

692

696

701

703

704

703

704

702

September

736

726

720

718

719

723

724

725

723

725

722

722

October

751

747

743

740

739

739

738

739

740

739

739

738

November .

750

746

740

738

737

739

736

736

737

739

741

740

December .

785

778

773

768

764

765

767

768

771

772

772

771

January

808

801

796

790

787

790

793

794

793

794

794

796

February .

813

808

804

800

801

800

801

804

806

802

800

800

March .

819

814

806

801

804

807

810

808

804

803

805

804

April . .

845

839

827

824

822

822

827

827

830

830

828

827

May . . .

837

830

825

824

823 ' 825

831

832

835

836

835

832

June

860

855

848

847

847 851

856

858

859

858

859

859

Year . .

782.9 776.2

769.5 766.5

766.2 768.6

771.6

772.6

773.4

773.5

773.4 772.8

Summer

778.2 770.0

762.0 760.2

760.3 763.8

769.0

770.3

771.7

772.2

771.7 770.8

Winter . .

787.7 782.3

777.0

772.8

772.0 773.3

774.2

774.8

775.2

774.8

775.2; 774.8

In the preceding table the normals for the summer half year comprise the months
between April and September inclusive ; those for the winter half year comprise
the months between October and March inclusive.

The following table contains the mean values of the normals for each month and
season.

TABLE

II.

1840-1844.

Normal.

1841-1845.

Normal.

1840-1 845.

Normal.

July . .

676.3

793.3

Year

772 1

August

702.2

February

800.6

Summer ....

770.1

September

724.6

March .

805.7

Winter ....

774.1

October .

738.2

April .

828.3

November

738.5

May .

8322

December .

768.4

June .

856.8

Regular Solar-Diurnal Variation of the Horizontal Force. — If we subtract the
hourly normals of Table I. from their respective monthly mean value as given in
Table II., the difference (in scale divisions) will represent the regular solar-diurnal

OF THE MAGNETIC FORCE.

45

variation for each mouth in the year. In like manner we obtain the diurnal varia-
tion of the horizontal force — free of the larger disturbances — for the summer and
winter half, and for the whole year. Table III. will exhibit these differences
after their conversion from scale divisions into parts of the horizontal force (one
scale division equalling 0.0000365 parts of the horizontal force). The tabular
numbers are expressed in units of the sixth place of decimals. A plus sign indi-
cates a greater force, a minus sign a less force than the mean value. Casting the
eye over the vertical columns, we obtain also a view of the annual inequality of the
diurnal variation, which will be examined further on.

TABLE III. — REGULAR SOLAR-DIUHNAL VARIATION OF THE HORIZONTAL COMPONENT OF THE

MAGNETIC FORCE EXPRESSED IN PARTS OF THE HORIZONTAL FORCE.

A plus sign indicates greater force than the mean. For convenience sake, the first three decimals (0.000)

have been placed on the side of the tahle.

1840-1845.

0"

I*

2h

3" 4"

5" 6"

7"

8"

9"

10"

11"

+ 21J-

July

—171

—098

—025 +047 +120 +303 +449

+120

—353

—572

—646

—499

August

+153

+116

+116

+153 +116

+262 +335

+007

—430

—795

—868

—576

September

+168

+241

+168+241 +387

+423 : +481

+131

—380

—708

—891

—781

October

+116

+262

+262 +408 +481

+372 +335

+153 —029

—284 —467

—430

November

—018

+018

+091 +164

+200

+310 +383

+237 +054

—164 —273

—456

! December

—131

+051

+088 +161

+270 +343 +453

+380

+270

+088 —241

—533

5 January

—025

+047

+047 +120 +193 +230

+266

+339

+266

—061 ; —318

—536

"•2 February

+022

+095

+146 ' +168 +204 +277

+350 1 +277

+204

+022 —270

—343

o

March

+098

+134 +171 +207

+244 +317

+390

+244

+061

—230 —412

—595

April

+157

+193 +193 ! +303

+376 +412

+412

+303

—025

— 4ti3 —755

—828

May

—065

—029 +080

+116

+116 1 +226

+299

+116

—211

—503 —540

—394

June

—043

—043 —043 —043

+065 +175

+284

+065

—153

—372 —445

—335

Year

+022

+082 +108 +170 +231 +304

4-370

+198

—060

—337 —511

—526

Summer

+033

+063 +082 +136

+197

+300

+377

+127

—259

—570 —691

—569

Winter

+010

+ 101 +134

+205

+265

+308

+363

+272

+138

—105 —330

— 482

1840-1845. 12"

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+ 21J-

Noon.

July

—244

+157

+485

+595

+631

+376

+047

—025

—098

—171

—244

—244

August

—211

+153

+481

+518

+372

+226

+043

—029

—065

—029

—065

+007

September

—416

—051

+168

+241

+204

+058

+022

—015

+058

—015

+095

+095

October

—467

—321

—175

—065

—029

—029 +007

—029

—065

i— 029

—029

+007

November

—419

—273

—054

+018

+054

—018 +091

+091

+054

—018

—091

—054

December

—600

—350

—168

+015

+161

+ 124 +051

+015

—095

—131

—131

—095

o

January

—536

—317

—098

+120

+230

+120

+011

—025

+011

—025

—025

—098

February

—453

—270

—124

+022

—015

+022

—015

—124

—197

—051

+022

+022

o

March

—485 i —303

—Oil

+171

+061

—047

—157

—088

+061

+098

+025

+061

April

—609

—390

+047

+157

+230

+230

+047

+047

—061

—061

+011

'+047

May

—175

+080

+262

+ 299

+335

+262

+043

+007

—102

—138

—102

+007

June

—116

+065

+321

+357

+357

+211

+029

—043

—080

—043

—080

—080

Year

—395

—152

+095

+204

+216

+128

+018

—019

—049

;—051

—051

—027

Summer — 290

+002

+294

+361

+355

+227

+037

—009

—058

—076

—064

—028

Winter

—494

—306

—105

+047

+077

+029

—002

—027

—039

—026

—038

—026

46

DISCUSSION OF THE HORIZONTAL COMPONENT

TABLE IV.

Table IV. is derived from Table III. by multiplication with the absolute value of the horizontal force (4.173) ;

it contains, therefore, the regular solar-diurnal variation of the horizontal force in absolute measure.

A plus sign indicates greater force than the mean. Two places of decimals have been placed on the side

of the table.

1840-1845.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10"

11"

+ 21J"'

July

—071

—041

—010

+020 +050

+127

+188

+050

—147

—239

—270

—208

August

+064

+048

+048

+064 : +048

+109

+140

+003

—180

—332

—362

—241

September

+070

+101

+070

+101 +162

+177

+201

+055

—159

—296

—372

—326

October

+048

+109

+109

+170 +201

+155

+140

+064

—012

—119 — 1!)5

—180

November

—008

+008

+038

+068 +083

+129

+160

+099

+022

—068 —114

—190

December

—055

+021

+037

+067 +113

+143

+189

+159

+113

+037 —101

—223

S~

January

—010

+020

+020

+050 +081

+096 +111

+141

+111

—025 —132

—224

February

+009

+040

+061

+070

+085

+ 116! +146

+116

+085

+009 —113

—143

March

+041

+056

+071

+086

+102

+132

+163

+102

+025

— 096

—172

—248

April

+066

+081

+081

+127 ' +157

+172 +172

+127

—010

—193

—315

—346

May

—027

—012

+033

+048

+048

+094

+125

+048

—088

—210

—226

—165

June

—018

—018

—018

—018

+027

+073

+119

+027

—064

—155

—186 —140

Year

+009

+034

+045

+071

+096

+127

+155

+083

—025

—141

—213

—220

Summer

+014

+026

+034

+057

+082

+125

+157

+053

—108

—238

—289

—238

Winter

+004

+042

+056

+086

+111

+ 129

+152

+114

+058

—044 —138

—201

1840-1845.

12"

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+ 2U1"

Noon.

July —102 +065

+203

+248 +263

+157

+020

_010 ' —041

—071

—102 —102

August

—088 +064

+201

+216

+155

+094

+018

—012 ! —027

—012

—027

+003

September

_174 _021

+070

+ 101

+085

+024

+009

—006

+024

—006 +040

+040

October

—195 —134

—073

—027

—012

—012

+003

—012

—027

—012

—012

+003

November

—175 —114

—022

+008

+022

—008

+038

+038

+022

—008

—038

—022

December

—253 —146

—070

+006

+067

+052

+021

+006

—040

—055

—055

—040

8

January

—224 —132

—041

+050

+096

+050

+005

—010

+005

—010

—010

—041

February

—189 —113

—052

+009

—006

+009

—006

—052

—082

—021

+ 009

r009

March

—203 —127

—005

+071

+025

—020

—065

—037

+025

+041

+010

-025

April

—254 —163

+020 +065

+096

+096

+020

+020

—025

—025

+005

-020

May

—073 +033

+109 +125

-J-140

+109

+018

+003

—043

—058

—043

-003

June —048 +027

+134

+149

+149

+088

+012

—018

—033

—018

—033

—033

Year —165 —063

+040

+085

+090

+053

+008 —008

—020

—021

—021

—Oil

Summer —123 ; +001

+123

+151

+ 148 +095

+015 1 —004

—024

—032

—027

—012

Winter 1—206 —128

—044 +020

+032 +012

—000 —Oil

—016

—Oil

—016

—010

Annual Inequality in tJie Diurnal Variation of tlie Horizontal Force. — The dis-
tinctive feature of the diurnal variation is shown in the annexed diagram (A),
constructed from the mean annual and half-yearly values given in the preceding
table, IV. It exhibits in the annual mean, as its characteristic type, a maximum
value about 6 A. M., a minimum value about 11 A. M., a secondary maximum value
about 3| P. M., and a secondary minimum about 9 P. M. For the half year when
the sun has north decimation, the morning minimum becomes smaller and the
afternoon maximum larger, thus increasing the diurnal range ; the converse takes
place in the other half of the year, when the sun has south declination. The 6
A. M. maximum remains nearly unchanged throughout the year. The average
summer range (April to September inclusive) is 0.0046, and the average winter
range (October to March inclusive) is 0.0025, both expressed in absolute measure.
The range between the morning maximum and the morning minimum is 0.0045 in
summer and 0.0036 in winter, as will be explained further on.

O F T HE MAGNETIC F O R C K .

(A.) — DIURNAL VARIATION OP THE HORIZONTAL FOBCE IN SUMMEK, WINTER, AND FOB THE WHOLE YKAII.

47

9

"o

£

+0.00180

SUMMER

1

120

./

/

\
\

090
060
030

0 00000

.

xr

ftS

\\ \

'• \ >

If

YEAH \
WINTER^^N^

•

030

\\\
• \ *

1 /

%

^^-•'•^ •

060

,

\\

1 1 1

090

-

\ \

/ / /

•

120

u '

III

•

150

! / j

180

\\

\j/i

-

210

\

— /

240

\

•

270

\

/

•

—0.00300

1 . 1 1

1 . 1 1

' iiii

0" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
A. M. P. M.

Philadelphia mean time.

This semi-annual change in the diurnal amplitude is more conspicuously repre-
sented in the annexed diagram (B), derived from diagram (A) by straightening out
the annual curve and using it as an axis of abscissae for laying off the differences
between the annual values and the summer and winter values at the same respective
hours of the day.

(B.) — SEMI-ANNUAL INEQUALITY IN THE DIURNAL VARIATION OP THE HORIZONTAL FORCE.

+0.00090

/\

-

75
60

7

\ / "

\.

-

45
30

i!

/

\ /

\^

-

15

• j

\l

^

0.00000
15

"\

A

/^

30

/ \

ft

•

45
60

*"\

i/ \ '

S

-

75
—0.00090

-

III!

v

\/

III!

iiii

C

h 1 2 3 4 I
A.M.

67891

0 11 12 13 14 1
P.M.

5 16 17 18 19 2

0 21 22 23 24*

Philadelphia mean time.

This diagram (B) may, with advantage, be compared with the analogous one
representing the annual change of the diurnal variation of the declination as given
in Part II. of this discussion. The construction is the same in either case.

At 6 A. M. there is hardly any change throughout the year. The maximum
variation, in the course of a year, takes place at 9 A. M. (range 0.00194 in absolute
measure); about 11| A. M. there is an epoch of no variation ; at 2 P. M. a second
maximum is reached (range 0.00107); again at 7| and IIP. M. points of no

48

DISCUSSION OF T II K II O K 1 X O X T A 1. C' O M PONE N T

variation are reached. Owing to the prominent annual variation near 2 P. M., the
range of the diurnal variation between the morning minimum at 11 A. M. and the
afternoon maximum at 3| P. M. is of more interest in the discussion of the diurnal
fluctuation of the horizontal force than the 6 A. M. and 1 1 A. M. range, which
latter range, as we have seen, is slightly greater than the first one.

To find the turning epochs of the annual variation, the monthly values for the
hours 9 A. M. and 2 P. M., when it is best developed, were taken from Table IV.,
and each value was again compared with its annual mean.

TABLE V. — ANNUAL VARIATION AT THE HOURS 9 A. M.

AND 2 P. M.

MONTH.

9 A. M.

0.00

Differences.
0.00

2 P. M.
0.00

Differences.

0.00

Mean difference.

0.00

January ....
February ....

—025
+009
—096
—193
—210
—155
—239
—332
—296
—119
—068
+037

+ 116
+ 150

+045
—052
—009
—014
—098
—191
—155
+022
+073
+178

—041
—052
—005
+020
+109
+ 134
+ 203
+201
+070
—073
—022
—070

—081
—092
—045
—020
+069
+094
+ 103
+ 161
+030
—113
—062
—110

+099
+121

+045
—016
—069
—054
—130

— n<;

—092
+046
+ 068
+ 144

Auril

May

•July .
August
September
October
November
December

Mean

—141

+040

Casting the eye over the columns headed "differences," we see by the change of
sign and the magnitude of the values that the transition from a positive to a nega-
tive value occurs some time after the equinoxes, and that the maximum variation
is reached about the time of the solstices — a result in close correspondence with the
conclusions reached in the discussion of the annual inequality in the diurnal varia-
tion of the declination (Part II. of the discussion). For convenience in the analy-
tical treatment, a column headed "mean difference" has been added to Table V.,
obtained by changing the signs of the 2 P. M. differences (the annual variation
being then opposite to the morning values), and taking the mean of the 9 A. M.
and 2 P. M. differences. The values in this column are tolerably well represented
by the following formula: —

Aa= +0.00129 tin (6 + 79°) + 0.00018 *m (20 + 191°),

the angle 6 counting from January 1, at the rate of 30° a month. Accordingly, we
find the transition to take place shortly before the middle of April and October, or
about twenty-two days after the equinoxes. This is about twelve days later than
the epoch found in Part II. for the declination.

Analysis of the Solar-Diurnal Variation of the Horizontal Force. — For convenience
of investigation and proper comparison with similar results at other localities, the
values given in Table I. have been put in an analytical form, and are represented
by the following expressions. It will be seen that the difference between any
monthly normal mean and the corresponding mean in Table V. of Part IV., which
latter mean is affected with the disturbances, does not exceed 2^ scale divisions.
Tins small difference includes also a small effect due to the necessity of different

OF T1IE MAGNETIC FORCE. 49

methods of interpolation in the construction of the two tables. In the determination
of the numerical quantities (by application of the method of least squares) in the
monthly equations, due attention was paid to the relative weights of the values for
the even and odd hours. The coefficients are expressed in scale divisions (increasing
numbers denoting decrease of force), and the angle 6 counts from midnight at the
rate of 15° an hour.

For January, AA = + 793d.3 + 3d.77 sin ( 0 + 236° 52') + 6d.56 sin (2 9 + 96° 52')

+ 3d.99 sin. (3 6 + 282° 13') + 2d.OO sin (49+ 91° )
For February, A4 = + 800d.6 + 5d.50 sin ( 9 + 218° 26') + 4d.57 sin (29 + 102° 29')

+ 3d.27 sin (3 e + 282° 40') + ld.66 sin (49 + 121° )
For March, A4 = + 805". 7 + 6d.56 sin ( e + 243° 31') + 5d.35 sin (29+114° 14')

+ 4d.23 sin (39 + 316° 04') + ld.91 sin (49 + 113° )
For April, AA = + 828d.3 + 7d.G5 sin ( 9 + 257° 37') + 9d.55 sin (29+ 123° 06')

+ 5d.15 sin (39 + 306° 44') + ld.18 sin (49 + 163° )
For May, A* = + 832d.2 + 2d.24 sin ( 9 + 314° 31') + 7d.81 sin (29 + 140° 53')

+ 4". 40 sin (3 0 + 330° 05') + ld.34 sin (49 + 214° )
For June, A4 = + 856d.8 + 2d.12 sin ( 9 + 356° 03') + 6d.40 sin (29 + 140° 32')

+ 4d.48 sin (39+ 327° 14') + Od.92 sin (49 + 216° )

For July, AA = + G7Cd.3 + 3d.42 sin ( e + 4° ll') + lld.50 sin (2 9 + 139° 14')

+ 6d.14 sin (3 o + 330° 15') + Od.78 sin (4 9 + 210° )
For August, A» = + 702d.2 + 5d.32 sin ( 9 + 310° 58') + 10d.37 sin (29 + 153° 46')

+ 6d.79 sin (39 + 335° 55') + 2d.88 sin (49 + 203° )
For September, A4 = + 724d.6 + 8d.02 sin ( 0 + 271° 57') + 9d.59 sin (29+ 137° 25')

+ 7d.08 sin (39 + 345° 17') + ld.99 sin (49 + 215° )
For October, A» = + 738*.2 + 8d.06 sin ( 9 + 237° 57') + 6d.40 sin (29+ 123° 37')

+ ld.34 sin (39 + 325° 20') + 0".29 sin (49+ 174° )
For November, AA = + 738d.5 + 4d.13 sin ( e + 237° 36') + 6d.08 sin (29 + 100° 01')

+ ld.93 sin (39 + 310° 45') + Od.46 sin (49 + 211° )
For December, AA = + 7C8d. 1 + 5d.03 sin ( o + 212° 48') + 8d.07 sin (29+ 94° 14')

+ 3".98 sin (3 o + 269° 17') + ld.31 sin (49+ 88° )

We have also: For summer half year (April to September inclusive), for winter
half year (October to March inclusive), and for the whole year, the following
expressions for the regular solar diurnal variations: —

For summer, A4 = + 770d.l + 3d. 7 9 sin ( o + 293° 49') + 9".ll sin (29 + 139° 10')

+ 5d.36 sin (3 e + 329° 17') + ld.42 sin (4 e + 202° )

For winter, A» = + 774d.l + 5d.36 sin ( 0 + 231° 36') + 6d.04 sin (29 + 104° 46')

+ 2d.88 sin (3 0 + 293° 54') + ld.ll sin (49+ 108° )

For year, AA = + 772d. 1 + 3d.95 sin ( e + 256° 19') + 7".25 sin (29 + 125° 05')

+ 3d.96 sin (39 + 317° 31') + Od.86 sin (4 9 + 165° )

The following expressions for January may serve as specimens of the agreement
of the result derived from the even and odd hours independently: —

From even hours, A» = 793d.3 + 3d.81 sin ( 9 + 238° 01') + 6d.56 sin (2 o + 94° 32')

+ 4d.10 sin (39 + 280° 19') + 2d.08 sin (4 9+86° )

From odd hours, A» = 7 93d. 4 + 3d.71 sin ( 9 + 234° 35') + 6a.56 sin (29+ 101° 32')

+ 3d. 7 6 sin (:i 9 + 286° 00') + ld.85 sin (4 9 + 119° )

giving to the first equation the weight 2 and to the second the weight 1, we obtain
the equation as given above.

50

DISCUSSION OF THE DIURNAL VARIATION

The following comparison will show the agreement of the observed and computed
values we have for August: —

(A. M.)

Computed.

Observed.

A

(P. M.)

Computed.

Observed.

A

(VZIJ"'

698.3

698

0

12»21J'"

707.7

708

0

1 "

698.3

699

—1

13

695.1

698

—3

2 "

699.6

699

+1

14

688.4

689

1

3 «

699.7

698

+2

15

888.7

688

+1

4 "

697.6

699

—i

16

692.5

692

0

5 "

694.3

695

—i

17

607.1

696

+1

6 "

694.5

693

+1

18

700.3

701

7 "

701.2

702

—i

19

702.6

703

0

8 "

712.7

714

—i

20

704.5

704

0

9 "

723.6

724

0

21

704.8

703

+2

10 "

7271

726

+1

22

703.3

704

11 "

720.4

718

+2

23

700.6

702

—1

Diagrams C and D exhibit the regular solar-diurnal variation of the horizontal
force ; the dots represent the observations directly taken from Table 1 ; the curves
give the computed values from the preceding equations. These diagrams also
exhibit the general agreement between the observed and computed values. The
summer months are represented on diagram C, the winter months on diagram D;
their comparison shows plainly the much greater range of the diurnal variation
when the sun is north of the equator than when south of it, as was also the case
with the magnetic decimation.

OF THE HORIZONTAL FORCE.

51

Scale

(C.)— SOLAR-DIURNAL VARIATION OP THE HORIZONTAL FORCE; APRIL TO SEPTEMBER, 1840 TO 1845.
divisions. I* _ 0.0000365 parts of the horizontal foice.

Angn«t.

September.

23456

7 8 9 10 11 N. 13 14 15 16 17 18 19 20 21 22 23 24"
Philadelphia mean time.

DISCUSSION U F T H E I) I I II N A L V A 111 A T I O X

Scale

-SolAR-DIURXAL VARIATION OP THE HORIZONTAL FORCE ; OCTOBER TO MARCH, 1840 TO 1845.

V = 0.0000365 parts of the horizontal force.

October.

November.

December

January.

rVbrnary.

1234567

8 9 10 11 N. 13 14 15 16 17 18 19 20 21 22 23 24h
Philadelphia mean time.

Table VI. contains the coefficients Bl B2 B% Z?4 of the general equation: —
Ah --= A + Bl sin (0 + (7,) + B2 sin (26+ C2) + Ii3 Kin (3 0 + Cs) + B4 sin (40+ Q
expressed in parts of the horizontal force, by multiplying the corresponding quan-
tities in the preceding equations with the value of a scale division. The angles
(7, C2 C3 C4 will be found in Table VII.; they are the same as given before,
increased by 180°, so as to make a corresponding change in the direction of the
scale readings; increasing numbers will now indicate increasing force.

OF THE HORIZONTAL FORCE. 53

The first three decimals (0.000) have been placed in front of the table.

TABLE VI

MONTH.

B,

B2

B3

B4

January
February
March ....

138
202
239

239

lt>7
195

146
119

154

073
060
070

April

279

349

188

043

082

285

161

049

9

077

234

164

034

July

o

125

420

224

029

0

194

379

248

105

September ....

295
291

350
234

258
048

073

on

November ....
December

151
184

222
295

071
145

017
048

138

333

196

052

Winter

19ti

220

1(15

040

Year

144

265

145

031

In Table VII. the same quantities are given in absolute measure ; the first two
places of decimals (0.00) are placed at the head of the columns. (Increasing num-
bers denote increase of force.) The numerical values of A will be found in con-
nection with the discussion of the annual variation of the horizontal force.

TABLE

YII.

MONTH.

B,

0.00

c,

B2

0.00

c,

B3

0.00

C3

B4

0.00

C4

January ....
February ....

057
084
100

560 52'
38 26
63 31

100
070

082

2760 52'
282 29
294 14

061
050
064

1020 13'
102 40
136 04

030
025
029

2770
301
293

117

77 37

146

303 06

079

126 44

018

343

034

134 31

119

320 53

067

150 05

020

34

032

176 03

098

320 32

068

147 14

014

36

July

052

184 11

175

319 14

094

150 15

012

30

August
September
October .
November
December

081
122
123
063

077

130 58
91 57
57 57
57 36
32 48

158
146
098
093
123

333 46
317 25
303 37
280 01
274 14

104
108
020
029
061

155 55
165 17
145 20
130 45
89 17

044
030
005
007
020

23

35
354
31

2«8

Summer .
Winter
Year

058
082
060

113 49
51 36
76 19

139
092
111

319 10

284 46
305 05

082
044
060

149 17
113 54
137 31

022
017
013

22
288
345

On diagram E the average value of the diurnal variation throughout the year,
together with the summer and winter value, has been represented as resulting from
the numerical quantities in the above table. It exhibits the noticeable feature in
the annual curve of a greater morning maximum (about 6 A. M.) than afternoon
maximum (about 3| P. M.), whereas in the summer curve it is the afternoon maxi-
mum which is the greater of the two.1 In the winter season the contrast is more

1 The same is the case at Prague ; in May, June, and July, the afternoon maximum was the greater
of the two. Karl Kreil, in vol. VIII. Proceedings of the Academy of Sciences of Vienna, 1855:
"Resultate aus den magnetischen Beobaclitungen zu Prag."

54

DISCUSSION OF THE DIURNAL VARIATION

marked, the morning maximum being considerably greater. These curves also show
the gradual shifting of the maxima and minimum to a later hour in winter than in
summer, a phenomenon also well exhibited in the preceding diagrams C and D.
The numerical values of this change of hours will be given in tabular form further
on. The small afternoon minimum about 9 P. M. is less distinctly marked than
any other feature of the diurnal curve.

(E.) — REGULAR SOLAR-DIURNAL VARIATION OF THE HORIZONTAL FORCB TOR SUMMER, WINTER, AND WHOLE YEAR.

(In absolute measure.)

.

.

Ull^
55C

- X

•— \

\

/

\

-

510
4G4
419

41 7T71

4.17.r>29
483

\

A

\

327

437

.

/£

.

282

391

S

r

' "x^

-

23U

346

^^

If /

X,

-

190
144

254

\v

J 1

~"

099

209

A

_

3G4

103

^,^

\\

A

•

318

117

417O71

-/

\\

iCNa,

-

273
4 17227

\»^ /

•^

• — •"**

.

\

//

.

181
13G

-

090

V /-&

-

044

1 ° 1 1

998

0" 1 2 3 4 5 6 7 8 9 10 11 N'nl 2 3 4 5 0 7 8 9 10 11 12"
A. M. P. M.

Philadelphia mean time.

Table VIII. contains the computed values of the time and amount of the morning
maximum and minimum, and of the afternoon maximum. The values for the
secondary afternoon minimum are taken from the diagrams. The time of the A. M.
maximum and minimum is within the nearest eighth minute ; that of the P. M.
maximum within the nearest tenth minute. The time for the P. M. secondary
minimum is within the nearest hour. The amount of change of horizontal force is
expressed in scale divisions.

OF THE HORIZONTAL FORCE.

55

TABLE VIII.

MONTH.

Morning maximum.

Morning minimum.

Afternoon maximum.

Secondary after-
noon minimum.

Interval

A.. M miu to
I>. M. max.

January . . .
February .

Jl.'uvh
April . .

7h10m

7 15
6 15
6 00
5 50
5 50
5 35
5 55
5 35
5 00
6 00
7 05

— 9"».2
— 9.6
— 9.2
—12.3
— 7.9
— 6.3
— 9.9
— 8.5
—14.9
—12.6
— 9.8
—12.1

ll"50m
11 40
11 30
11 20
10 25
10 30
10 30
10 10
10 20
11 15
11 25
12 05

+15d.7
+12.7
+16.4
+22.5
+15.5
+12.5
+19.3
+24.8
+25.9
+13.7
+11.0
+16.1

4i,10m
4 00
3 20
3 55
3 10
3 20
3 25
2 45
3 05
5 10
5 15
4 35

— 5".3

— 0.9
— 2.3
— 6.6
— 9.8
—10.4
—17.5
—14.2
— 6.7
— 0.1
— 3.0
— 5.1

11"

7
6
9
|

8
9
9
7
9
11
10

+2<
+2
+3
+3
+4
+3
+6
+3
—1
+2
+0
+4

4h20m
4 20
3 50
4 35
4 45
4 50
4 55
4 35
4 45
5 55
5 50
4 30

June . . .
July . . .
August
September . . .
October
November . .
December .

Summer
Winter ....
Year . . .

5 50
6 15
5 55

— 9.8
— 9.4
— 9.6

10 30
11 45
11 00

+19.6
+13.9
+15.6

3 25
4 10
3 35

—10.5
— 2.2
— 6.0

20J
21
20|

+3
+2
+2.5

4 55
4 25
4 35

The extreme variation in the epoch of the A. M. maximum is therefore 2h 15m;
the variation for the A. M. minimum is lh 55m; for the P. M. maximum it is 2h 30m,
and for the secondary afternoon minimum between 3 and 4 hours. In all cases, the
earlier hours occur in the summer season.

Table IX. shows the diurnal range, expressed hi scale divisions, parts of the
horizontal force and in absolute measure. In the second column the range between
the A. M. maximum and minimum is given; in the third column that between the
A. M. minimum and the P. M. maximum. These two amplitudes for A. M., and
for A. M. and P. M., are further illustrated in diagram F, which shows the curve
to be double crested, with maxima near the time of the equinoxes, and the greater
of these near the autumnal equinox.

TABLE IX. — AMPLITUDE OF THE DIUKNAL VARIATION OF THE HORIZONTAL FORCE.

MONTH.

For A. M.

For
A. M. and P. M.

For A. M.

For
A. M. and P. M.

For A. M.

For
A. M. and P. M.

24*. 9

22.3
25.6
34.8
23.4
18.8
29.2
33.3
40.8
26.3
20.8
28.2

21d.O
13.6

18.7
29.1
25.3
22.9
36.8
39.0
32.6
13.6
14.0
21.2

0.00091
081
093
127
085
069
106
122
149
096
076
0.00103

0.00077
050
068
106
092
084
134
142
119
050
051
077

0.0038
34
39
63
36
29
45
51
62
40
32
0.0043

0.0032
21

29
45
38
35
56
59
50
21
21
0.0032

May

July

September ....

29.4
23.3
25.2

30.1
16.1
21.6

0.00107
0.00085
0.00092

0.00110
0.00059
0.00079

0.0045
0.0036
0.0038

0.0046
0.0025
0.0033

Winter

Year . ...

In scale division*.

In parts of the horiiontal force.

Ln absolute measure.

56

DISCUSSION OF THE DIURNAL V A K I A T ION

(K.) — SoLAK-DlUKKAL RAXOB Or THE HORIZONTAL FORCE FOR EACU MoXTU OF TUB YEAR.

1. scale.
0.0060
56
52
48
44
40
36
32
28
24
0.0020

The next table contains the epochs when the mean horizontal force is reached in
each day, as computed by the preceding formula?. The diurnal curves intersect
the axis of abscissa) four times, of which the table contains only the A. M. and
first P. M. intersection: those later in the afternoon and near midnight occur in
summer, winter, and whole year at 7 P. M., 5| P. M., and 6| P. M. respectively,
and at 11| P. M., 12 P. M., and llf P. M. respectively.

TABLE X. — rmNciPAL EPOCHS OF MEAN HORIZONTAL FORCE.

MONTH.

A. M.

P. M.

January
February
March

9" 20'°
9 23
8 42

2>>36»
2 58
2 28

April
May
June

8 14
7 44

7 47

2 19
0 59
0 48

July
August
September
October

7 57
7 28
7 42
8 08

0 53
0 44
1 29
5 00

November

8 40

3 28

December

9 34

3 03

Summer .

7"4.V»

Ih12"

Winter .

9 00

3 07

Year

8 14

1 54

The above times are generally correct within two minutes (according to the
formulae). The morning hour of average daily horizontal force is less variable in
the course of a year than the afternoon hour.

The following table contains the computed diurnal variation of the horizontal
force. The values have been expressed in absolute measure. It compares directly
with Table IV., which contains the observed values. It will be useful for the
interpolation of observations, or for their reduction to the mean value of the day
from observations taken at irregular hours. The table also forms the basis for the
construction of diagram G.

OF THE HORIZONTAL FORCE.

57

TABLE XI. — COMPUTED SOLAR-DIURNAL VARIATION OF THE HORIZONTAL FORCE IN ABSOLUTE

MEASURE.

The first two places of decimals (0.00) are placed in front of the table.

1840-1845.

0"

1"

2"

3"

4"

5"

6"

7"

8"

9"

10"

11"

+2H'"

July

—061

—061

—030

+015

+091

+137

+137

+046

—107 ! —244

—290

—244

August

+122

+061

+030

+030

+061

+122

+122

+015

—167

— 33E

—381

—274

September

+061

+061

+061

+107

+ 182

+229

+198

+061

—152

—320

—381

—320

October

+046

+091

+122

+ 167

+182

+182

+137

+076

—030

—122

—182

—213

November

000

+015

+030

+061

+107

+152

+152

+122

+030

—061

—137

—167

§

December

—046

000

+030

+061

+091

+137

+167

+182

+122

+ 015

—122

—229

d

January

—030

000

+030

+046

+061

+091

+107

+122

+091

—015

—137

—229

February

+030

+061

+076

+076

+091

+107

+137

+152

+137

+015

—107

—182

March

+046

+061

+076

+107

+107

+137

+137

+122

+030

—076

—198

—244

April

+061

+076

+091

+107

+137

+167

+182

+122

—015

—198

—320

—351

May

000

000

000

+030

+061

+107

+107

+046

—076

—198

—244

—182

June

—015

—030

—030

000

+046

+091

+091

+046

—061

—152

—182

—305

1840-1845.

12"

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+21J-

Noon.

July

—091

+076

+213

+259

+229

+ 152

+046

—015

—061

—091

—076

—076

August

—091

+107

+213

+198

+152

+076

+030

—015

—030

—046

—015

+015

September

—152

—015

+091

+107

+076

+046

+015

000

+030

+030

+046

+076

October

—182

—137

—076

—030

—015

000

000

—015

—015

—030

—015

+015

—

November

—137

—091

—046

000

+030

+ 046

+046

+030

+015

000

—015

—015

^ December

—244

—182

—076

+015

+061

+ 061

+015

—015

—046

—061

—076

—061

o

January

—229

—137

—030

+061

+076

+046

+015

—015

—030

—015

—015

—030

February

—182

—107

—030

+015

+015

—015

—030

—030

—030

—015

—015

000

March

—198

—107

000

+046

+015

—015

—046

—030

+015

+046

+046

+046

April

—274

—137

000

+076

+091

+061

+030

000

—030

—030

000

+030

May

—076

+046

+ 122

+152

+ 122

+076

+030

—015

—046

—061

—046

—015

June

—046

+061

+ 137

+167

+ 137

+076

+030

—015

—030

—046

—030

—015

Diagram G exhibits the changes in the horizontal force (in absolute measure)
from the monthly normal value for each hour of the day and for each month of the
year. The three variables are: the hour of the day, the month of the year, and
the difference of the horizontal force from the normal. The contour lines of the
magnetic surface differ 0.0005 of horizontal force in absolute m'easure. Full lines
indicate greater value, lines of dashes less value than the mean; dotted lines repre-
sent the normal value.

DISCUSSION OF THE HORIZON T A L C O M P O N H N T

I OF T11E IIoEIZOXTAL FORCE FROM ITS NoKMAL VALUE, FOR EACU Hoi'K Of THE L>AY AM) MoliTU OF

TUB YICAK. Expressed iu absolute measure.
0.00

(II.

123
A. M.

4567

10 11 N. 1 2 3 4 5
P.M.

Philadelphia mean time.

6 7 8 9 10 11 12"

Annual Variation of tfte Horizontal Force. — For the discussion of the annual
variation we make use of the monthly normal readings of the horizontal force as
given in Table II. If m equals the monthly effect of the total progressive change,
we obtain from the twelve equations by the usual method the value m = + 15.49,
and the correction for progressive change for July and June, for instance, becomes
+ 5.5 m and — 5.5 in respectively. The following table contains the monthly
normals unconnected and corrected for progressive change; also the differences from
the mean for each month, constituting the annual variation.

OF THE MAGNETIC fOR CE.

TABLE XII.

Difference**, or annual variation.

MONTH.

Normals.

progressive change.

n»rm;iiv

0.000

0.00

July ....

676 3

+85.2

761.5

+10.6

+39

+16

7d2.2

+ 69.7

771.9

+ 0.2

+01

+00

September

724 ti

-f 54.2

778.8

— 6.7

—24

—10

( Irtoher

738.2

4-38.7

776.9

— 4.8

—17

—07

November

738.5

4-23.2

761.7

(+10.4)

(+38)

(4-ie)

December

768.4

4- 7.7

776.1

— 4.0

—15

—06

.January

793.3

— 7.7

785.6

—13.5

—49

—20

February

800.6

—23.2

777.4

— 5.3

—19

—08

March .

805.7

—38.7

767.0

+ 5.1

+19

+08

April

828.3

—54.2

774.1

— 2.0

— 7

—03

May

8322

— G9.7

762.5

+ 9.6

+35

+15

June

856.8

—85.2

771.6

+ 0.5

+02

+01

Mean ....

772.1

0.0

772.1

In i In ]>;n t> of the

In absolute

scale divisions, .horizoutal force.

measure.

i

With the exception of the month of November, the values given above for the
annual variation are tolerably regular in their progression, and considering the
delicacy of the test applied to the observations in deducing the annual variation,
this exceptional irregularity in the November value will not affect the general
conclusion. We have as the general result: a greater horizontal force in summer
(from April to August), and a smaller horizontal force in winter (from September
to March) than the average annual value. The maximum occurs in July (at
Toronto in June), and the minimum in January (at Toronto in December).
For Toronto we have the expression for the annual variation: —

3.531 + 0.002 sin (0 + 312°).
For Philadelphia (omitting the November value):

4.176 + 0.001 m'n (0 + 306°);
the angle 9 in both equations counting from January 15th.

The annual range is 0.0021 (in absolute measure). The transition appears to
take place about the time of the equinoxes or a short time before.

Table XIII. contains the monthly normal values of the horizontal force in abso-
lute measure, obtained by adding (algebraically) 4.1730 to the values in the last
column of Table XII. These numbers, it will be observed, are corrected for secular
change; if we apply the same we obtain the resulting monthly mean values of the
horizontal force answering to the epoch January, 1843. The quantity A, mentioned
in the explanatory remarks to Table VII., is given in the last column of Table XIII.

60 DISCUSSION OF THE HORIZONTAL COMPONENT, ETC.

TABLE ]

OIL

MONTH.

Normals corrected
for secular change.

Monthly means
(affected with
secular change).

July

4.1746
4.1730

4.1759
4.1740

September
October .
November
December
January .
February

4.1720
4.1723
4.1746
4.1724
4.1710
4.1722
4 1738

4.1727

4.1728
4.1749
4.1725
4.1709

4.1719
4 1733

April
May ....

4.1727
4 1745

4.1720
4 1735

4 1731

4 1718

Mean .....

4.1730

4.1730

PART VI.

INVESTIGATION

LUNAR INFLUENCE ON THE MAGNETIC HORIZONTAL FORCE.

(61)

INVESTIGATION

OF THE MOON OX THE MAGNETIC HORIZONTAL FORCE.

THE method pursued in the investigation of the lunar effect on the horizontal
force is, in general, the same as that explained in Part III. of the discussions of
the Girard College observations. The process may be briefly recapitulated as fol-
lows : Each horizontal force observation, after it had been corrected for the effect
of difference from the standard temperature and for progressive change, the dis-
turbed readings being omitted (as fully explained in Part IV.), was marked with
its corresponding lunar hour; the observation nearest to the time of the moon's
upper transit over the true meridian of the observatory was marked 0\ that nearest
to the lower transit was marked l'2\ and the observations between, for western and
eastern hour angles of the moon, were marked with the proper lunar hour by inter-
polation. In the hourly series where thirteen observations are recorded in twelve
lunar hours, that observation which is nearest midway between any two consecutive
lunar hours was omitted. Each observation and reduced reading thus marked with
its corresponding lunar hour was subtracted from the monthly normal belonging to
its respective hour, and these differences wen- set down in tabular form, arranged
according to lunar hours and keeping each monthly result separate for future com-
bination. Let n = any normal belonging to any reduced reading r, the following
tables contain the mean monthly values of the differences n — r; a positive sign,
therefore, indicates greater force, a negative sign less force than the normal. It
need hardly be repeated that in the original record of the horizontal force increasing
numbers denote a decrease of the force. The greatest possible difference is 33, the
number of scale divisions, which, according to the criterion, separates a disturbed
from an undisturbed observation. For the formation of these differences which
amount to more than '2'2,000, the manuscript tables of the reduced record were
used: these tables have already been referred to in the preceding Part IV.

The units in which the differences » — r are expressed are scale divisions, one
division being equal 0.0000:>(>"> parts of the horizontal force, or equal to 0.0001. VJ
in absolute measure, the mean A" being = 4.173 (in units of grains and feet).

The lunar effect on terrestrial magnetism being exceedingly minute, the pr<>> n
required tor its elucidation is proportionally delicate; all the regular and irregular

(63)

64

DISCUSSION OF THE INFLUENCE OF THE MOON

deviations arising from other sources must first be eliminated. In the method, as
indicated above, the magnetic disturbances (as far as they could be recognized as
such), the diurnal and annual solar variation, as well as the eleven (or ten) year
inequality and secular change, are all eliminated, leaving numbers fitted for the
lunar research.

The readings taken in the month of June, 1840, have not been used in this
discussion (these had likewise been rejected in the two preceding parts), on account
of the imperfect manner in which the allowance for the progressive change could
only be made at that time. For the lunar hour 21 in July, 1840, the number of
differences is so small that the mean had necessarily to be reduced; one-fourth of
its amount was set down in the table. In January, February, and March, 1843,
the observations were discontinued, excepting a single daily reading. These months,
therefore, do not occur in the lunar discussion.

The number of observations used are distributed over the several months and
years, as shown in the following table.

TABLE I. — NUMBER OF OBSERVATIONS FOR LUNAR DISCUSSION.

MONTH.

1840-1841.

1841-1842.

1842-1843.

1843-1844.

1644-1843.

Sum.

July

157
235
258
255
245
199

179
238
260
262 •
264
212

297

295
269
281
279
297
298
250
297
271
271
295

284
318
265
257
297
318

286
299
309

294
313
296
*602
603
603
. 621
575
576
586
623
579

627
622
» 556
' 597
564
559
601
541
601
575
612
522

1659
1783
1644
1992
1988
1976
1699
1604
1734
1980
2069
1917

August
September
October
November
December

January
February
March
April .
May .
June .

Sum .....

2764

3400

2633

6271

6977

22045

TABLE II. — DISTRIBUTION OF THE NUMBER OF

OBSERVATIONS ACCORDING TO WESTERN AND

EASTERN HOUR ANGLES OF THE MOON.

YEAR.

Western hour angles. Enntern hour iuiple«

1840-41
1841-42
1842-43
1843-14
1844-45

1371
1688
1320
3138
3499

139:3
1712
1313
3133
3478

Sum

11016

11029

Tables III., IV., V., VI. and VII. contain the monthly and annual means of the
lunar diurnal variation for the years 1840 to 1845. The numbers arc expressed in
scale divisions.

* Commencement of the hourly series.

ON Till: MAliNKTIC HORIZONTAL FORCE.

65

TABLE III. — DIFFERENCES FKO.M THE MONTHLY NORMALS, 1840-41, WESTERN HOUR ANGLES

OF THE MOON.

1840-41.

0"
Up. cnl.

1"

2"

3"

4"

5''

6"

7"

8"

9"

10"

11"

July
August
September
October
November
December

+2
0
—2
—3
—6
—4

+1

+v

—4
0
+3

J

+ 1

0
—1
+3
—3

+3
+5
+4
+6
—3
—5

+3
+3
+ 8
— 1
0
+3
—1
0
+1
+1
+1
0

—9
—5
+1
•fJ

—4

-M

+3
+6
0
—2
—1
—3

+3
+6
0
0
+1
+2
—7
—3
+3
—2
—8
+4

+7
+2
—4
—4
—5
—7
+3
+4
+3
—1
+2
+4

-1
—4
—5
—4
+4
—5

—8
—2
—7
—1
—1
+5

—17
— 4
+ 2
+ 1
— 4
— 3

+ 1
0
j

+ 3
— 1

+ 8

+12
— 2
— 4
— 7
— 4
0
— 9
— 4
+ 8
— 1
— 6
— 1

—4
+2
—7
+7
+1
+3
—4
0

+1

—2
0

+1

—3
+5
+8
+4
+6
—8

0
—2
+3
+1

+2

— 8
— 1
+ 4
+10

+ 9
+ 2
0
— 2
— 1
— 5
— 8

January
February
March
April
May
June

Mean

—0.4

+0.5

+1.5

—0.3

—0.1

+0.3

—2.4

— 1.3

— 1.5

—0.2

+1.3

- 0.1

1840-41.

12h

Low. cnl.

13"

14"

15"

16"

17"

18»

19"

20"

21"

22"

23"

July
August
September
October
November
December

+11
+ 7

— 2

—16
— 2
+ 6
— 2
— 5
— 4
— 1
+ 8
+ 8

— 9
+ 6
— 1
+14
+ 1
+ 9
— 4
+ 4
0
— 3

— 3

4

—5
+9
+2
—9

—1
+2

+3
—4
—5

+3

0

+ «

I!

+ 6
+ 4
+ 4
+10
— 1
— 7
+ 2
— 8
— 3
— 5

+6
+5
+5
—7
—6
—3

+1
—6
—1
—3

0

+7

0
+2
+4
+3
0
+2

1

+5
+4
—4
0

—8

— 2

tl

—10

+ 1
— 6

+ 4
+ 1
—10
0

— 2

— 5

— 5
— 3

+ 1
— 2
— 1
—12
— 2
+ 2
+ 2
+ 3
+ 8
— 7

+ 6
+5
—2
—1
+4
—3

—2
+1
—2
—2
+3
0

— 5
—11
— 3
+ 6
+ 6
— 6

+ 1
— 5
— 2

+ 2
— 2
— 7

—4
0
—1
—3
+1
+3
+3
+3
+2
+4
—2
+1

— 2
— 2
— 2
+ 5
+ 5
+ 5
+ 7
+ 4
+ 2
+ 2
+ 2
—11

January
February
March
April
May
June

Mean + 1.0

+0.8

+0.1 + 0.4

—0.2 +0.61 — 2.3 —1.3! +0.6 !— 2.1 +0.6

+ 1.2

DISCUSSION OF T1IK INFLUENCE OF Till] .MOON

TABLE IV. — DIFFERENCES FROM THE MONTHLY NORMALS, 1841-42, WESTERN HOUR ANGLES

OF THE MOON.

1841-42.

0"
Up. cul.

l»

2"

3"

4"

5"

6"

7"

8"

9"

10h

11"

July
August
September
October
November
December

+4
—1
—3

+7
0
+8
—2
—5
+4
0
0
+1

+5
0
+8

+6
—4

+8
+1
+3
0
—2
0

0
— 2

ts

— 3

+ 12
+ 2

+ 2
+ 1
+10
+ 3

+8
+2

+4
+1
—2

+2
—3
—1
0

+1

0

—4
+2
0
0
—7
—1
1

+4
+2
0

+5
+4

0
+3
—1

+1
0
—3

+7
+2
—1
+4
+4
—3

0
+3
— 5
^

—3

+2
0
+4
+2
+1
+6
—1

—2
0
—3

+4

—3

+3
—7
0
+3
—4
—3

0
—5
+1
+1
+6
—2

—2
—5
—1
+2
+ 5
—5

—8
0
0
—2
+3

+1
+5

—1

—7

——y

+2
+ 1
—3
0
+1
—3

+ 5
0
—2
0
—3
0

0
+ 5
+10
+ 1
+ 3
0
0
+ 2
— 3
+ 1
— 4
— 3

January
February
March
April
May
June

Meau

+1.1

+2.0

+ 2.5

+0.9

+0.3

+1.1

+0.7

—1.1

—0.4

—1.3

—0.2

+ 1.0

1841-42.

12"
Low. cul.

13»

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

July
August
September
October
November
December

+3
+1
+3'

+3
1

—1

+4
+7
—2

+1
0
—4

—5
+3
+2
—1
+4
0

—2
+1
+3
+1
—5
—2

+3
0
+2
—3
+3
—1

—2

+1

—2

+3
—3

—4

+ 5
+2
—6
—5
—6
+2
—4
—2
0
—3
—3
+2

+1
+1
+5

—1

—4
—1
—3
—6
+1
+4
0

—1
—5
—1
—3
—5
—3
—5
0
—1
1

—6
+2

—8
I

—5

+7
+1

—3
—8
0
—3

+6

+2

—4
+3
—2
—3
—2
+1
—3

+6
—2

+2
—4
+6

+1
—4

+1
—1
0
+1
+5
—7
—1
—5
0
+ 6

—1
—3
+4
—3
—3
+1
0

%

—3
+3

—2

I

—5

—5
—1
—4
+6
—3
+3
—6
—2
+4
+2

+3

+6

+1
3

+1

+2
+2

^

+1
+2
+4

January
February
March
April
May
June

Mean

+1.2

—o.i ; —0.2

—1.5

—0.6 —2.4

—1.1

—0.2

—0.3

—0.3

—1.0

+ 1.4

ON THE MAGNETIC HORIZONTAL FORCE.

67

TABLE V. — DIFFERENCES FROM THE MONTHLY NORMALS, 1842-43, WESTERN HOUR ANGLES

OF THE MOON.

1842-43. 0"
i Hp. cnl.

1"

2ii 311 4h

5h

6"

7"

8"

9L

10" ll"

July
August
September
October
November
December

+3
+3
+ 3
+2
+1
—2

—3

+ 1
—6
—7
+3
—3

+2
—3
—1
0
—1
—6

— 1
0
+ 9
+ 1
+ 2
+ 1

+1

+4
—6

+ 1
—5

0
4

—1
+3

*}

+7
—3
+7

0
—2

+2
+4
+1
+3
—2
0

0
+2
0
—3

—2
+1

—4
+ 1
+ 2
+5

—1

+ 1
+1
— 3
—3
—4
+ 5

—8
+3
0
+2
+1
0

January
February
March
April
May
June

—1

+3

—6

+2

—2
+ 7

0
+2

—4

+ 10
+ 5

+4
+3
0

+9
+4
+2

—1
—1

0

+1

+9

—3
—1
—5

—1

+ 1

+4

+1
—6

1

—4

43
+3

Mean

+0.7

—0.9

—1.0

+ 2.9

+0.1

+1.6

+0.7 +1.9

—1.2

+0.7

—1.0

0.0

1842-43.

12"
Low. cul.

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

July
xAugust
September
October
November
December

+1

—2
+6
—7
—2
+3

+1
+1

—3

—2
+3

+4
+1

—1
+2

+2

—2
+2
—8
—1
—3
+1

+4
+2
—3

s

+3

—3
—4
—1
0
+4
0

—4
+ 3
—4
—1
—1
+1

1

—5
—1
+4
+6
+2

0
—1

—2
+4
0

—2

—2
+2
—7
—3
+1
+4

+ 3 -1
+ 2 -2
+ 1 —6
+11 j +3
+ 1 ! +2
— 3 +3

January
February
March
April
May
June

+2
0
0

—2

+1

+3

+3
+4

+2
0

+4

0

1 ±2

—2
—4

+ 2

—5
—3
—3

0
1

—3

—3
—1

+2

—2
—1

+1

+1

—7

—1
—2
+4

Mean

+O.li 40.1 +1.4 1 —0.6 +0.8 —0.9 —1.9

+0.1 —0.3 1 —0.8

+0.9 0.0

68

DISCUSSION OF THE INFLUENCE OF T 11 E MOON

TABLE VI. — DIFFERENCES FROM THE MONTHLY NORMALS, 1843-44, WESTERN HOUR ANGLES

OF THE MOON.

1843-44.

0"
Up. cut.

1"

2"

3"

4"

5h

6h

7"

8h

9"

10" llh

July
August
September
October
November
December

+ «
+2
+ 1
—1

+1
+ 2

+1
— 1
—1
+2
—2
0

44
+2
—1
+4
+1
+ 1
0
1 —1
—3
+2
—2
—2

+2
0
—3
+3
0
+2
0
+ 1
+1
+3
0
0

+4

—1

+6
+ 5
0
0
0
+2
+1
+2
—1
0

+ 5
+2
0
+2
0
0

—1

+1

+1

0
—2

+ 2

—4

+ 1
—2
+3
0

—2

—1
1

+ 1
0
0
+2

+3
—3
—1
+2
0
—1

+1
0
+2
+1
—1
+2

+ 1
+4

—4

+ 1
—2
—1

+ 1
0
+2
-LI
—l
+ 2

+1
0
—1
0
0

—1

+1

+3
0
—1

—2
+1

2

—1
0
—2
0
—2
0
0
+2
—2
—1
—1

—5
—2
—2
—1
+ 1
+ 1
—1
1

+1
—3

0 *
—2

—2
o

0
—3

+ 1
1

0
+2
+1
—2
—1
0

January

February
March
April
May
June

Mean

+0.9

+0.4

+0.8

+1.5

+0.9

—0.8

+0.4

+0.3

+0.1

-0.8

—1.2

—0.6

1843-44.

12"

Low. cul

13"

14"

15"

16"

17"

18h

19"

20" 21»

22"

23"

July
August
September
October
November
December

—2
+4
+3
—3
+1
0

+1
+2
+1
—4
0
0

—7
0
0
—4
+2
+ 1
+2
+1
0
0
0
+2

—2
+2
+3
—2
+2
+ 1

—1

+1
—1
0

—2
+ 1

—3
—1
+3

+2
0
I

+2
0
0
0
+3

+3
—2
+8
—2
+2
+1
—1
+2
0
+2
0
+2

j
0
+2
0
0
—1
—2
—3
0
0
—2
0

+4
+2
—6
0
—1
—3
0
—2
—1
0
—3
—1

—2

|

3
±1

+1
+1

0

+1
+1

-1

-\

+1
—2

-o

+0

—1
—2
—3

+1
—1
—3

+ 2
—1
—1
0

+1
—1

+2
+4
—2
—2
0
—2

+1
—1

+1
—1
+ 2
—2

+2
0
0

—1
—1

0

+2
—2
—3
0
+1
0

January
February
March
April
May
June

Mean

+0.3

—0.2

+0.2

+0.3

+1.3

—0.6

—0.9

—0.7 —0.9

—0.8 0.0

—0.2

Equal weight has been given to each monthly result in the formation of the
annual mean.

OX Tlin MA (INK TIC HORIZONTAL FORCE.

Gi)

TAHI.E VII. — DIFFERENCES FROM THE MONTHLY NORMALS, 1844-45, WESTERN HOUR ANGLES
op THE MOON.

1844^5.

0"
I'p. ml.

1*

2"

3"

4"

5"

6"

7"

8"

9"

10"

11"

July
August
September
October
November
December

0
—3
—2
0
—1
—1

+1
4-1
4-1

—4

4-2
-5

4-1
4-1

0

4-4
+3
(i

4-2
4-1

—3

4-2
0
—4

+ 1
—1
—1

+ 5

4-1
4-4

0
—3

4-2
4-2

O

4-1

0
0

4-2
4-2

0
—2
0
—3

4-2
4-2
—1

0

4-2

—2

4-3
4-1

—2

—3
4-1

0
0
0

o

4-1

(1

+2

4-4
4-3
—3

—4

4-1

0

4-2

—2

4-3

+2
4-1

0

4-2
4-3

—3
—1

4-1
4-1
0
0

4-1

4-2
4-3
4-3

0

4-3

—2
—3
4-2
41
4-2
—1
4-1

0

$

0
+3
—1

0
—1

0
—2
—2
+1

+1
—3

4-2
-t-i
4-3
—1

—1

—2
4-1

—2
—2
0

0

—2

4-2

—3

4-2
4-1
4-4

0

41
—i

±\

—2
+1
44
0
—1
— 1

42
+ 4
0
— 1
0
—4

January
February
March
April
May
June

Mean —0.9

+0.6 +0.5

+0.3 0.0 +0.6 +0.6

+0.9

+0.1

—0.3 0.0

+ 0.2

1844-45.

12"
Low. cnl.

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

July
A .must
September
October
November
December

0
+3
4-2
+1

+ 1
4-4
4-1
4-1
—2

+1
+1

0
4-2
4-3
4-2

—4

0
0

4-2
4-2
4-1

—2

—1

+1
4-3
4-1
4-1

0

—i

4-2
4-1
—i

0
—2

4-1

0
—1

4-1

4-2

—2

4-2
—1
—1

0
0

—2
4-2

—1
0
—1
0
0
0
—5
—3

4-4
4-1

—2
—1

0
—2
—2
—2
0

4-2

—4
—1

4-3
4-1

0

4-4

0
0
—3
—2
—3

4-2
—4
—2
4-2
4-3
—1
4-4

0
0
—3
—4
—2
+1
—4
—1

4-1
—l
0
+ 3

—2
—3
—4
—4
—1
0
0
—5
—3
—3
+1

4-2

—2
—3
—3
—5

4-1
4-3

4-2
—1

—2

—4
—3
4-2

—2
0
—4

0

—4
+ 2

4-1
—i
—i

—3
0
0

—3
2
—4
—2
—3
0

4-2
—1

—3
—4
42

1

— 1.0

January
February
March
April
May
June

Mean

+1.0 +0.4 +0.5

0.0

—0.7

—0.1 —0.3

—0.8

—1.8 —1.2

—1.0

TABLE VIII. — RECAPITULATION OP THE ANNUAL MEANS EXHIBITING THE LUNAR-DIURNAL
VARIATION, FROM 22,045 OBSERVATIONS BETWEEN 1840 AND 1845, EXPRESSED IN SCALE
DIVISIONS.

July to July.

0"
I'p. ml.

1"

2"

3"

4"

5"

6"

7"

8"

9"

10"

11"

1840-41
1841-42
1842-43
1843-44
1844-45

—0.4

4-1-1
+0.7
+0.0
—0.9

+0.5
+2.0
— 0.9
+0.4
+0.6

+1.5
+2.5
—1.0
+0.8
+0.5

—0.3
+0.9
+2.9
+1.5
+0.3

—0.1
+0.3
+0.1
+ 0.9
0.0

+0.3
+1.1
+1.6
—0.3
+0.6

—2.4
+0.7
+0.7
+0.4
+0.6

—1.3
—1.1
+1.9
+0.3
+0.9

—1.5
—0.4
—1.2
+0.1
+0.1

—0.2
—1.3
+0.7
—0.8
—0.3

+1.3
—0.2
—1.0
—1.2
0.0

—0.1
+ 1.0
0.0
—0.6
+0.2

HMM

+0.3

+0.5

+0.9

+1.1

+0.2

+0.7

0.0

+0.1

—0.6

—0.4

—0.2 i +0.1

July to July.

12"
Low. cnl.

13"

14"

15"

16"

17"

18"

19"

20"

21"

22"

23"

+1.2
+ 1.4
00
—0.2
—1.6

1840-41
1811-42
1842-43
1843-44
1844-45

+ 1.0
+1.2
+0.1
+ 0.3
+1.0

+ 0.8
—0.1
+0.1
—0.2
+0.4

+0.1
—0.2
+ 1.4
+0.2
+0.5

+0.4
—1.5
—0.6
+0.3

0.0

—0.2
—0.8

+0.8
+1.3

—0.7

+0.6
—2.4
—0.9
—0.6

—0.1

—2.3
—1.1
—1.9
—0.9
—0.3

—1.3
—0.2
+0.1
—0.7
—0.8

+0.6
—0.3
—0.3
—0.9
—1.8

—2.1
—0.3
—0.8
—0.8
—1.2

+ 0.6
—1.0
+ 0.9
0.0
—1.0

Mean +0.7

+ 0.2

+0.4

—0.3

+ 0.1

—0.7

—1.3

—0.6

—0.5

—1.0

—0.1 +0.2

70 DISCUSSION OF T II H I N K L T K N (' !•: OF THE MOON

If AVC give Aveight to the annual means according to the number of observations,
they Avould be; one for the first and second year, three-fourths for the third year,
one and three-fourths for the next year, and tAvo for the last year: a general exam-
ination, hoAvever, shoAVS that, owing to the disturbing effect of the progressive
change, the monthly means are very nearly of equal A'alue, derived either from the
In-hourly or the hourly series. It Avill also be shown in the sequel that the lunar
diurnal variation is nearly the same in. the summer and Avinter seasons; the means
of Table V. and the final means of Table VIII. have therefore been adopted with-
out reference to combinations or AA'cights.

A comparison of the values of Table VIII. among themselves shows them to be
very irregular, although derived from many thousand obserA'ations ; afiA'e year scries
of observations seems barely sufficient to exhibit a tolerably regular progression.
In the folloAving table tAvo groups have been formed, one of results from three
years, 1840 to 1843, comprising 8,797 observations, the other from the remaining
tAvo years comprising 13,248 observations. From these it appears that the lunar
diurnal variation during these tAvo periods exhibits the same general character.

LUNAR-DlURNAL VARIATION DURING THE PERIODS 1840-43 AND 1843-45.

Groups.

0"

1"

2"

3"

4"

5"

G"

7"

8"

9"

10"

11"

184(1-43
1843-45

+0.5
0.0

+0.5
+0.5

+1.0
+0.7

+ 1.2
+0.9

+0.1
+0.4

+ 1.0
+0.3

—0.3
+0.5

—0.2
+0.6

—1.0
+0.1

—0.3
—0.6

0.0
—0.6

+0.3
—0.2

Oroups. 12h

13"

14"

15"

1G"

17"

18"

19"

20"

21"

22"

23"

1840-43

1843-45

+0.8
+0.7

+0.3 , +0.4
+ 0.1 +0.4

—0.6
+0.2

0.0
+0.3

—0.9
—0.4

—1.8 —0.5
— 0.6 — 0.7

0.0
—1.3

—1.2
—1.0

+ 0.2
—0.5

+ 0.9
—0.9

Before proceeding to the analysis of the final result of Table VIII. the separate
results have been combined into summer and winter groups ; the first group com-
prising the months from April to September, the second group the months from
October to March.

Table IX. exhibits the lunar diurnal variation of the horizontal force during the
summer and winter seasons.

ON TILE MAGNETIC HORIZONTAL FORCE.

71

TABLK IX. — LUNAR-DIURNAL VARIATION IN SUMMER.
(In scale divisions.)

Apr. to Sept.

0"
Up. cul.

1" 2"

3"

4" 5h

6" 7" 8"

9"

10"

11"

—3.2
+1.5
—0.5
—1.2
—0.3

1840-41
1841-42

1S42^3
1843-44

1844-45

+0.7
+0.2
+0.8
+1.5
—2.0

— 0.9
+1.8
—0.2
+ 0.5
0.0

+2.7
+2.3
—0.7
+0.3
0.0

—3.2
+ 1.7
+3.6
+1-7
+0.7

+0.5
+1.2
+ 1.8
+ 1.2
0.0

+1-7
+ 1.2
+ 1.7
—0.5
+1.0

—1.1

+0.7

+ 1.5
+0.2
+0.7

—1.5 —0.3
—1.5 —0.3
+2.7 —1.2
+0.5 —0.3
+1.7 0.0

—1.7 ' +2.0
—3.5 —0.5
+0.5 —1.2
—1.2 —2.3
—0.7 —0.8

Mcuu

+0.2

+0.2

+0.9

+0.9

+0.9

+ 1.0

+0.4

+ 0.4 —0.4

—1.3

—0.6 —0.7

13»

13"

I4h

15"

16"

17h

18"

•

19"

20"

21"

22"

23"

1S4H-41
1841-42
1-42-43
1843-44
1844-45

+ 5.8
+0.7
+ 1.2
+0.2
+0.8

—2.3
—1.0
+0.5
—0.8
+0.5

+2.5
+0.2
+1.7
+0.3
+0.7

—1.2
—0.5
—0.3
+0.3
0.0

+3.2
+2.0
+0.3
+2.2
—0.7

—1.0
—2.0
-2.0
—0.2
+0.2

—1.3
—1.5

—2.7
—0.7
+0.5

—0.5
+0.2
—1.8
0.0
—0.2

+ 1-7
—0.2
—0.8
—0.5
—1.5

—4.3
—0.3
—1.5
—1.0
—2.2

—0.3
—1.2
—0.2
+ 0.5
—1.5

—2.2
+2.5
—1.3
+ 0.5
—2.0

Mean

+1.7

— 0.6

+1.1

—0.3

+1.4 —1.0

—1.1

—0.5

—0.3

—1.9

—0.5

—0.5

LUNAR-DlURNAL VARIATION IN WINTER.
(In scale divisions.)

Oct. to Mar.

0"
Up. cul.

1"

2" 3"

4" •

5"

6"

7"

8"

9"

10"

11"

1840-41
1841-12
1842-43
1843-44
1844-45

— 1.5
+2.0
+0.3
+0.2
+0.2

+1.8
+2.2
—2.3
+0.3
+ 1.2

+0.3
+2.7
—2.3
+1.2
+1.0

+2.5
+0.2
+1.3
+1.3
—0.2

—0.7
—0.5
—3.3
+0.5
0.0

—1.0
+1.0
1.3
+0.0
+0.2

—3.7
+0.7
—1.0
+0.7
+0.5

—1.0
—0.7
+0.3
+0.2
+0.2

—2.7
—0.5
—1.3
+0.5
+0.2

+1.3
+0.8
+1.0
—0.3
+0.2

+0.5
+0.2
—0.7
0.0
+0.8

+3.0
+0.5
+1.0
0.0
+0.7

Mean

+0.2

+0.6

+0.6

+1.0

—0.8

+0.3

—0.6

—0.2

—0.8

+0.6

+0.2

+1.0

12"

13"

14"

15"

16"

17"

18"

19*

20"

21"

22"

23"

1840-41
1841-42
1842-43
1843-44
1844-45

—3.8
+1.7
—2.0
+0.3
+1.2

+4.0
+0.8
—0.7
+0.3
+0.3

—2.3
—0.7
+1.0
0.0
+0.3

+2.0
—2.5
—1.0
+0.3
0.0

—3.7
—3.2
+1-7
+0.3
—0.7

+2.2
—2.8
+1.3
—1.0
—0.3

—3.3
—0.7
—0.3
—1.2
—1.2

—2.2
—0.5
+4.0
—1.3
—1.5

—0.5
—0.5
+0.7
—1.3
—2.2

0.0
—0.3
+0.7
—0.5
—0.3

+1.5
—0.8
+3.0
—0.5
—0.7

+4.7
+0.3
+2.3
—0.8
—1.2

Mean

—0.5

+0.9

—0.3

—0.2 —1.1

—0.1

—1.3

—0.3

—0.8

—0.1

+0.5

+1.1

The results arc exhibited in the annexed diagram. The number of observations
(about 11,000 for each group) is evidently too small to eliminate the greater irregu-
larities.

72

DISCUSSION OF THE I X F I. F K N (' K OK T II K MOON

(A.)

+1.5
+1.0
+0.5

a

0

— 0.5

— LuXAR-DlCRXAL VARIATION OF THE HORIZONTAL FORCE IN Sl'MMKK AM) \V INTER.

I 1 1 r~

—2.0

\

0" 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24h
U. C. (Western hour angles of the moon.) L. C. (Eastern hour angles of the rnoou.) U. C.

-- summer deflection.
- ...... winter deflection.

If there is any marked difference in the lunar diurnal variation in the summer
and winter season, the summer range is slightly greater than the winter range; as
to the epoch, there is no doubt that in winter the lunar maxima and minima are
earlier than in summer. It is a remarkable fact that we have found the same fea-
tures in the lunar effect on the declination, viz., a greater amplitude in summer and
an earlier occurrence of the maxima and minima in winter; the amount of the
shifting of the two curves appears to be nearly the same. From the ten year series
of observations at Prague (1840-49) Mr. Karl Kreil found a larger lunar effect in
the summer months than in the winter months.

Recurring to the final values of the lunar-diurnal variation of the horizontal force,
as given in Table VIII., they can be represented by the usual Bcsselian form of
periodic functions.

The angle 6 counts from the moon's upper culmination westward at the rate of
15° to an hour; a + sign indicated greater, a — sign, less force than the average
normal. The observed values are represented by the following expression: —
HZ = — 0.01 + 0.40 ain (6 + 13° 29') + 0.60 sin (26 + 38° 43') + 0.155 sin (3 6

+ 244° 31').

The three coefficients arc expressed in scale divisions; if expressed in parts of the
horizontal force the equation may be written as follows: (M signifies millionth parts
of the force.)

MM M M

//c = _ ().3f> + U.60 sin (0 + 13°.o) + 21.90 .sin (2 0 + 38°. 7) + 5.64 sin (3 0 +

If expressed in absolute measure and if n = number of hours after the upper cul-
mination, it may be written

MM M M

— 1.5 + 61.0 ain (15 n + 13°.5) + 91.5 ain (30 n + 39°) + 23.6 sin (45 n +

244°.5.)

ON THE MAGNETIC HORIZONTAL FORCE.

73

The curve is double-crested and is exhibited, together with the observed values,
in the annexed diagram. It presents two maxima and two minima, which are found
from the equation

^= - 0 = + 0.40 cos (6 + 13°) + 1.20 cos (2 0 + 39°) + 0.45 cos (30 + 245°).

The lunar effect on the declination we have found likewise to present two maxima
and two minima. (Sec Part III. of the discussion.)

(B.) — LUNAR-DIURNAL VARIATION OF THE HORIZONTAL FoRCE OBSERVED AND COMPUTED.

+1.5
+ 1.0

+0.5

m

I °'°

*53

'•5 —0.5

j»

"3

=c —1.0
—1.5

—2.0

23456 7

Wo find

0" 1

U. C. L. C.

Principal maximum 2h 52m after Upper Culmination

9 10 11 12 13 14 15 lli 17 18 19 20 21 22 23 24"

D. C.

+ 0.87 scale divisions.

Secondary " 17" Lower
Principal minimum 6 41 " "
Secondary " 8 19 " Upper

+ 0.51

— 0.87

— 0.45

The epoch of the horizontal force tide for the high values is nearly 2 hours after
the culminations, and for the low values it is 7| hours after the same phases.

For Makerstoun, in Scotland, at General Sir Thomas M. Brisbane's observatory,
in 1843-46, Mr. J. A. Broun found (Trans. Eoyal Society of Edinburgh, Vol.
XIX. p. 11, 1849) the smaller maximum of the horizontal force 2 hours after
upper culmination, the greater maximum 1| hours after the lower culmination, the
smaller minimum 8 hours after the upper culmination, and the greater minimum 9
hours after the lower culmination.

At Prague all extremes appear from 2 to 3 hours later. Mr. Karl Kreil (Dcnk-
schriften of the Imperial Academy of Sciences, at Vienna, Vol. V. 1853), found
from the ten year series at Prague (1840 — 49) maxima of horizontal force between
four and five hours after the upper and lower culminations, the latter being the
greater of the two ; and minima between ten and eleven hours after the same
epoch, that after the upper culmination being the greater of the two.

From the Toronto observations, continued for five years, Major-Gencral Sabine
deduced the formula (see Vol. III. of the Toronto Magnetical and Meteorological
Observations, London, 1857).

A,. - + 0.05 + 0.215 ein (n + 353°.6) + 0.3324 sin (2 a + 13°.5).

10

74

DISCUSSION OF THE INFLUENCE OF THE MOON

The coefficients are in decimals of scale divisions (1 div. — 0.000087) parts of the
horizontal force) ; the angle a counts from the superior culmination, giving a curve
of which the general features are in exact accordance with those deduced from the
Philadelphia observations, viz : a principal maximum after Upper Culmination, fol-
lowed by the secondary minimum ; the secondary maximum after the Lower Cul-
mination, followed by a principal minimum. The times and amount of these values
are compared in the following Table X.

TABLE X. — COMPARISON or THE LUNAR-DIURNAL VARIATION OP THE HORIZONTAL COMPONENT
OF THE MAGNETIC FORCE AS DEDUCED FROM 22,045 OBSERVATIONS BETWEEN 1840 AND 1845
AT PHILADELPHIA, AND AS DEDUCED FROM 34,303 OBSERVATIONS BETWEEN 1844 AND 1848
(A FIVE YEAR SERIES) AT TORONTO, CANADA.

Philadelphia.

Toronto.

2h.9 after up. cul.
8 3 " "
1.1 " low. cul.
6.7 " "

3h after up. cul.
9 " "
2 " low. cul.
8" " "

In parts of horizontal force.

+0.000032
—0.000016
+0.000019
—0.000032

+0.000046
—0.000010
+0.000024
—0.000041

In absolute measure.

+0.000133
—0.000068
+0.000078
—0.000133

Probable error of any single representation of the Philadelphia values = + Od.25
= +_ 0.000009 parts of the horizontal force = + 0.000038 in absolute measure.

Investigation of the Horizontal Force in Reference to the Lunar Phases. — The fol-
lowing process of reduction has been adopted : After marking the days of the full
and new moon, and also the days preceding and following, the daily means of the
horizontal force readings were taken (already corrected for difference of tempera-
ture and progressive change.) In the place of any disturbed observation, the
monthly normal, belonging to the respective hour, was substituted before taking
the daily mean. All accidental omissions in the record of the hourly or bi-hourly
series were supplied by the hourly normal of the month. The means thus obtained
are independent of the solar diurnal variation. The monthly normal was next
compared with each daily mean and the differences (normal minus mean) were
tabulated.

A positive sign signifies a greater ; a negative sign, a less force than the normal
value. As the results deduced from a single year are yet too much affected by the
incidental irregularities of the observations, the collective results from the five
year series (1840-45) are herewith presented.

ON THE MAGNETIC HORIZONTAL FORCE.

75

TABLE XI. — INFLUENCE OF THE LUNAR PHASES ON THE HORIZONTAL FORCE.

Scale divisions.

Parts of the hor. force.

In absolute measure.

—1.0
—1.5
—0.2

+0.0
+2.4
+0.9

3.9

—0.00003(5
— 0.000055
—0.000007

+o.onoono

+0.000091
+ 0.000033

0.000146

—0.00015
—0.00023
—0.00003

+0.00000
+0.00038
+0.00014

O.OOOG1

The average number of observations from which any one of the above six means
were deduced, is over 800, and the probable error, in scale divisions, of any one of
the results is +_ 0.7 (nearly).

From the Makerstoun observations, Broun found for the years 1843-46, a
minimum at the time of the full moon, and a maximum at the time of the new
moon; Kreil, from the Prague observations, between 1843-46, found the same
result, all in accordance with the Philadelphia results, as given above. It must be
remarked, however, that after the year 1848, Kreil found that the signs were
reversed and consequently it appears that the lunar influence on the horizontal
force is subject to a cycle of short perjod. This last remark does not apply to the
effect of the moon's declination and variations in distance.

Influence of the Moon's Changes of Declination on the Horizontal Force. — The
method of investigation is precisely the same as that adopted for the phases. We
find :—

TABLE XII.

One day before the greatest north declination
On the day of " " " "
One day after " " " "
Two days after " " " "

Scale divisions.
+0.8
+0.6
+2.2
+0.9

;- Mean +1.1.

On the day of the moon's crossing the equator

—1.2

Probable error of any one result 40.9.

One day before the greatest south declination
On the day of " " " "
One day after " " " "
Two days after " " "

—3.4
—0.9
+0.9
+1.0

> Mean — 0.6.

It seems probable that the greatest effect takes place rather a day after than on
the day of the moon's greatest declination. Taking means, as indicated in the
above table, we find about the time of the maximum north declination an increase
of horizontal force of 1.1 scale divisions (or 0.000040 parts of the horizontal force) ;
at the time of the moon's crossing the equator the force is decreased 1.2 scale divi-
sions (or 0.000044 parts of the horizontal force) ; the horizontal force also appears
decreased about the time of the moon's greatest south declination ; the amount is
about half that of the other two cases, and is somewhat doubtful, from an fipparcntly
excessive value on the preceding day.

76

DISCUSSION OF THE INFLUENCE OF T II E M O O N

According to Broun, there is at Makerstoun a maximum horizontal force at the
time of the moon's greatest north and south declination, with a minimum force at
the time of her crossing the equator; in two cases, therefore, viz: for north decli-
nation and no declination, the Makerstoun and Philadelphia results agree; while
in the third case they disagree or remain doubtful. Kreil's results, from the Prague
observations, do not appear to me sufficiently decisive and regular to admit of com-
parison.

Influence of the Moon's Variation in Distance on ilic. Horizontal Force. — By a
process of reduction similar to that followed in the preceding investigation we
find:—

TABLE XIII.

Scale ilivisiuu.-.
—1.5
—1.9
—2.0

+2.3
+2.3
+2.7

1

!

». d.
Mean —1.8.

Mean —2.4.

On the day of " ......
One day after "

The probable error of any one result is about the same as in the preceding re-
sults (Tables XI. and XII.). The results for variation in the moon's distance are
more consistent and satisfactory than those depending on the phases and declination
changes. The lunar effect is to diminish the horizontal force by its 0.000066 part
in perigee, and to increase it by its 0.000088 part when she is in apogee.

The Prague results are the same, viz: a greater horizontal force at and after the
moon's apogee than at and after her perigee ; a three years' series of observations
at Milan, however, do not agree therewith.

In no branch of magnetic research would additional results from independent
observations, particularly at stations widely apart, be more acceptable and valuable
than in the study of the lunar effect in its various manifestations.

PUBLISHED BY THE SMITHSONIAN INSTITUTION,
WASHINGTON CITY,

NOVEMBER, 1 S 6 2 .

I