^ LIBRARY REFERENCE. No Division Range Slu-lf Received \ /^yj 187^ 4 - ' -.-.,- ' .',:; • m • PMINTINIi. V A.I,H^ BOOKSELLERS &STAI _ ^'' >l Vltur »1 s SMITHSONIAN CONTKIBUTIONS TO KNOWLEDGE. 175 DISCUSSION OF THE MAGNETIC AND METEOROLOGICAL OBSERVATIONS MADE AT THE GIRARD COLLEGE OBSERVATORY, PHILADELPHIA, IN 1840, 1841, 1842, 1843, 1844, AND 1845. THIRD SECTION, COMPRISING PARTS VII, VIII, AND IX. VERTICAL FORCE. INVESTIGATION OF THE ELEVEN (OE TEN) TEAR PERIOD AND OF THE DISTURBANCES OP THE VERTICAL COMPONENT OF THE MAGNETIC FORCE, AND APPENDIX ON THE MAGNETIC EFFECT OF THE AURORA BOREALIS; WITH AN INVESTIGATION OF THE SOLAR DIURNAL VARIATION, AND OF THE ANNUAL INEQUALITY OF THE VER- TICAL FORCE ; AND OF THE LUNAR EFFECT ON THE VERTICAL FORCE, THE INCLINATION, AND TOTAL FORCE. BY A. D. BACHE, LI.D., F.R.S., HEX. CORE. ACAf). SC. PARIS ; PBBST. NAT. ACAD. SCIENCES; SUPERINTENDENT U. S. COAST SURVEY. [ACCRPTED FOR PUBLICATION, AUGUST, 1863.] PART VII. INVESTIGATION OP THE ELEYEN (OR TEN) YEAR PERIOD, AND OF THE DISTURBANCES OF THE VERTICAL FORCE. (1) INVESTIGATION ELEVEN (OE TEN) YEAR PERIOD, AND OF THE DISTURBANCES OF THE VERTICAL FORCE. THE observations of the vertical component of the magnetic force were com- menced in June, 1840, and continued, with an exception in January, 1841, without interruption to the last of June, 1845. To keep up the continuity of the series, a daily reading was taken at 2h 17m P.M. during the months of January, February, and March, 1843. Up to October, 1843, the observations were bi-hourly, after- wards hourly. Instruments. — From June, 1840, to the end of the year, the observations were made with a balance vertical force magnetometer of Lloyd's pattern. It was at first mounted in the eastern building of the College, but was removed to the obser- vatory in the latter part of July. While in the College an increase of the readings corresponds to a decrease of vertical force ; at the observatory increasing readings denote increasing force. The instrument was made by Robinson, of London ; the magnet, the axis of which was mounted as nearly as possible transversely to the magnetic meridian, was 12 inches in length, having at its ends cross wires set in copper rings. For a full description see Dr. Lloyd's account of the Magnetical Observatory of Dublin, and the preface in volume I, of the record of the Phila- delphia observations. In January, 1841, the Lloyd instrument was replaced by a reflecting vertical force magnetometer, made at my suggestion by Mr. J. Saxton. The bar of this instrument was two feet and one inch in length, two inches wide in the middle, one and a half near the ends, tapering to nothing at the ends, and a quarter of an inch thick. The magnet was of steel and hardened as perfectly as the maker could effect. By means of a ball moving on a fine screw, its equilibrium could be changed. The mirror projected outside the box, and the motion of the bar was observed by means of a telescope. At the top of the box was a piece of plate glass through which a thermometer (of Francis' make) could be read. For further particulars see p. vii, of the preface to volume I of the record. For some time (between three and four months) after being put up, the bar lost considerably of its magnetic force, and after being in use four months, a movement of the adjusting ball upon the screw was required for placing the readings again near the middle of the scale. By this adjustment, the sensibility of the apparatus was not interfered with. The value of a scale division of. the Lloyd instrument, expressed in parts of the vertical force, was carefully determined and found to be =0.0000165, both in the ( 3 ) DISCUSSION OF THE VERTICAL FORCE. College building and at the observatory. This value being known, I considered that the value of the scale of the new reflecting magnetometer could best be ascer- tained by comparison with the former. The result of this, continued at intervals, was, that two divisions of the new scale were equivalent to one of the old, or that a change of one division of the reflecting instrument corresponded to a change of vertical force of 0.000033 parts. This was after the instrument had been finally adjusted. The only disadvantage in the new instrument was the large effect of changes of temperature upon it; by direct observations it was found that a change of 1° (F.) of temperature produced a corresponding change of 13.5 + 0.25 scale readings, whereas in the Lloyd instrument the corresponding change was but 3.12 scale divisions. We have accordingly for the Lloyd instrument 5=0.0000515, and for the reflecting instrument 5— 0.000446. The values actually used in the reduction of the observed reading to a standard temperature will be seen further on. The importance of ascertaining the most correct and suitable coefficients of tem- perature for the two series of observations, demands a more detailed statement and elaborate discussion of the observations themselves independently of the special trials. Experience has shown that the value for q deduced from the differential intensity observations themselves, with the magnet subject generally to gradual and small changes of temperature, is smaller by a considerable fraction than the value found by direct and special observation during which the temperature changes are necessarily more violent. There is no doubt that in the reduction to a standard temperature that value of q should be used which was obtained while the magnet was under its ordinary influences and condition. The same view is taken by Gene- ral Sabine, and was also carried out in the discussion of the horizontal component of the magnetic force; for which see the preceding paper (Part IV). Determination of the Effect of a Change of Temperature on the Readings of the Vertical Force. (A.) Results of special observations made for determining the temperature coeffi- cient. The correction for temperature of the Lloyd vertical force magnetometer was ascertained by the usual method of vibrating the bar when suspended horizontally, and when alternately heated and cooled artificially. The thermometer was placed with its ball near the axis of the magnet. The changes of the horizontal force magnetometer, while these experiments were going on, were noted and allowed for. Date. Feb'y, 1841. Time of 10 oscillations. Temp. (F.) Readings of Horz'l force. Temp. (F.) 9th ii it 87s. 950 87.900 .88.117 37°.2 41.0 94.6 1128.8 1079.3 1139.5 25°. 6 36.5 36.1 Result tt 87.990 88.117 39.1 ) , 94.6 f hence ?= 2 T'2— T2 t'— January 651 651 663 659 657 651 661 648 660 679 674 674 February 705 704 714 714 707 698 704 696 699 714 707 701 March 661 656 662 664 603 662 655 649 655 667 673 666 April 666 655 659 655 653 654 643 643 645 655 667 670 May 6li2 665 657 649 646 647 652 644 647 654 664 665 June 674 6G9 663 658 648 643 639 640 636 652 665 663 July 690 685 675 667 663 656 652 651 656 669 681 684 August 689 687 685 682 675 668 655 655 665 677 684 686 September 698 692 696 689 686 677 671 671 673 679 690 698 October 707 699 703 712 696 709 708 707 707 709 711 706 November 718 710 723 725 713 715 713 713 716 711 718 718 December 708 708 714 709 716 711 709 707 705 710 713 713 Notes to above table: — February 3d, 14h 17^m, the temperature 73°.5 is interpolated. May 9th, 101' 17im, the temperature 59°. 6 is interpolated. June 6th, Oh 17im, 2h 17im, and 18h 17£m, the tem- peratures 70°. 4, 71c.O, and 74°. 4 respectively, were interpolated. August 3d, 12h 17|m; 5th, 22h 17im; Gth, 10h 17£m, and 31st, 14h 17im, the temperatures 69°.0, 73°.7, 76°.0, and 67°.G respectively, were interpolated. September 1st, 22k 17^m, the temperature 77°.0 is interpolated. October 8th, 2h 17|m; 21st, 10" 17im, and 28th, 6" 17^", the temperatures 66°.l, 68°. 1, and 70°.8 respectively, were interpolated. November 3d, 14h173m; an^ I6tn> Gh 17£m, the observations are 6m and 7m late. 10 DISCUSSION OF THE VERTICAL FORCE. TABLE II. — Continued. VERTICAL FORCE READINGS AT (ill0 FAIL 1843. 0" 2 4 6 8 10 Noon. 14 16 18 20 22h +231'" + 17" January 685 February 692 March 676 April 715 713 713 712 708 702 705 687 697 696 706 709 May 698 697 695 690 683 680 677 666 678 679 t-97 690 June 696 691 693 690 677 669 664 660 659 671 681 690 July 692 693 693 689 681 673 664 660 660 667 678 686 August 702 703 707 705 695 682 670 672 672 682 694 698 September 722 - 720 721 716 707 705 694 ti93 694 701 710 70S October 714 708 714 717 704 703 702 703 704 714 719 714 November 740 737 744 744 743 740 734 735 746 750 748 745 December 749 737 740 740 739 728 724 738 755 759 762 754 Additioiial odd hours observed. 1843. 1" 3 5 7 9 11 13 15 17 19 21 23" +23J'» October 710 709 718 712 704 700 701 702 709 717 715 717 November 737 740 745 747 742 735 731 741 750 751 746 747 December 744 738 742 743 738 720 726 747 755 763 756 757 Notes to the above table : — January 4th, February 1st, and Marcli 24th, observations 7m, 7|m, and 20m late, respectively. In April seven readings were supplied by the observers, also one in May and one in June. July 14th, Oh 23^m, observation 6m late. August 10th, 16h 23£m, observation sup- plied by observer. August 29th, Oh 23|m, observation 12m late. September 20th, Oh 23^m, tempera- ture supplied by observer. November, six readings supplied by observers. December 1st, 4h 23im ; December 9th, lh 23£m ; December 12th, 21h 23|m, and December 22d, 5h 23^"', observations 5ra, Gm, 15m, and 8m late, respectively. December 19th, 2h 23^m, a printing error of 200 scale divisions was corrected. December 30th, 9h 23jm, reading supplied by observer. TABLE II. — Continued. VERTICAL FORCE READINGS AT G6° FAIL 1844. 0" 1 2 3 4 5 6 7 8 9 10 11" +23J" January 735 733 731 731 733 736 733 733 731 730 T2G 717 February 736 731 729 730 733 732 733 734 727 725 727 720 March 763 758 758 759 760 762 763 760 755 759 761 762 April 7-6 765 763 765 766 765 763 759 752 751 746 740 May 772 769 766 768 767 764 760 754 749 747 747 744 June 778 776 772 772 771 768 765 7.JO 752 750 749 747 July 809 807 803 802 801 798 794 789 780 779 778 777 August 794 792 788 787 785 783 780 774 768 765 761 759 September • 815 813 811 808 809 807 805 802 796 793 788 783 October 779 776 773 776 778 780 781 782 775 774 775 771 November 775 771 768 769 772 772 771 773 768 772 772 767 December 756 752 753 754 756 757 756 700 752 752 754 749 1844. Noon. 13 14 15 16 17 18 19 20 21 22 23h +23J-" January 717 713 717 724 732 740 743 745 747 748 744 745 February 716 719 720 723 731 735 742 743 743 739 738 737 March 758 751 752 755 752 751 751 749 750 751 759 762 April 739 735 738 744 750 754 758 764 7ti4 762 766 766 May 744 740 740 744 746 748 753 762 7(i5 766 768 772 June 746 745 748 752 754 757 765 772 775 ! 774 775 778 July 776 775 772 778 780 787 795 801 804 804 806 809 August 756 756 752 765 767 769 777 787 788 788 790 793 September 779 111 766 791 790 793 804 810 si)9 810 812 815 October 769 767 771 778 787 789 792 790 7*6 786 782 782 November 766 763 761 758 774 779 777 778 774 770 769 772 December 745 739 740 735 750 756 754 753 753 750 751 754 DISCUSSION OF THE VERTICAL FORCE 11 Notes to preceding table: — January 2d, 10h 23£m, temperature observation 30m late. January 8th, 10h 23^"', instrument disturbed. January 15th, 3h 23|m, temperature 56°. 3 interpolated. February 6th, 4h 23fm, and 13th, 9h 23im, temperature observation 15m and 20m late, respectively, April llth, Oh 23|-m and lh 23£m, readings supplied by observer. July 13th, 12U 23im, observation 36m late. August 26th and 27th, thirteen readings supplied by observers. October 1st, 22h 23^m, observation 8m late. TABLE II. — Continued. VERTICAL FORCE READINGS AT 66° FAH 1845. 0" 1 2 3 4 5 6 7 8 9 10 11" -l-23i" January February March April May Juue 754 761 749 732 722 733 748 756 743 727 720 731 749 753 739 726 718 729 751 757 742 728 721 729 752 759 745 729 718 729 756 760 744 727 717 727 762 763 745 725 715 726 767 764 743 724 711 722 760 756 735 719 707 717 758 756 733 718 704 715 753 752 732 718 702 715 751 749 729 717 701 711 1845. Noon. 13 14 15 16 17 18 19 20 21 22 23" +23J* January February March April May June 752 747 730 716 699 711 748 741 729 713 698 711 749 740 713 715 680 711 739 739 731 724 700 714 754 753 737 726 704 713 759 759 741 723 704 715 756 761 745 732 712 722 753 761 746 737 719 730 748 758 740 735 719 733 746 753 740 729 717 731 746 752 739 726 719 731 753 756 742 728 720 732 Notes to above table: — April 27th, 4h 23^m, reading supplied by observer. April 14th, 2h 23^m, observation 12m late. April 22d, 23d, and 28th, 14" 23|ra ; also April 22d, 15h 23|m, readings sup- plied by observer. April 22d, 16h 23^m, temperature supplied by observer. May 2d, I4h 23£m, reading supplied by observer. May 12th, 4h 23|m, 9m late. June 6th, 5h 23|m, and 28th, Ih 23|m, observations 13m and 9m late, respectively. June 12th, Oh 23^m and lh 23|m, readings supplied by observer. TABLE III. — MEAN MONTHLY READINGS OF THE VERTICAL FORCE REDUCED TO THE TEM- PERATURE op 66° FAH. 1841. 1842. 1843. 1844. 1845. January February March April May June July August September October November December 858 945 993 1022 661 705 661 656 654 654 669 676 686 706 716 710 699 702 684 705 686 678 678 690 708 710 742 744 733 731 757 756 7W 762 792 776 799 779 770 751 752 754 738 725 710 722 631 688 670 648 572 535 603 Mean 679 702 763 The monthly mean for January, February, and March, 1843, was obtained by adding 14, 10, and 8 divisions to the readings at 14h 7m respectively; these corrections were found by comparisons in 1842 and 1844. 12 DISCUSSION OF THE VERTICAL FORCE. Corrections for progressive and irregular changes. — The difficulty of fully elimi- nating all effects of changes of temperature, and adjustment, particularly during the first year (1841), demanded the application of a secondary process analogous to that used in the reduction of the horizontal force for progressive change. The progressive change in the readings of the vertical force is less decided and more fluctuating than in the horizontal force. Half monthly means, and in special cases, means of even less periods of time, have been taken and were compared with the monthly mean, the differences were applied either progressively (increasing or diminishing) or as constants, as the case seemed to demand. Seventeen months required no such correction, and in many months it was applied very sparingly. The process leaves the diurnal variation, relatively, undisturbed, and prepares the series for the application of Peirce's Criterion for the recognition of the disturb- ances. The individual figures thus corrected were inserted in blue ink in the manuscript tables. Recognition and separation of the larger disturbances. — Peirce's Criterion for the recognition of the disturbances was applied to the observations extending over four years, and commencing with July, 1841, in the following order: July Oh, August 2'', September 4h, October 6h, November 8h, December 10h, January (1842) 12h, etc. The odd hours were selected from July, 1844, to the close of the series, thus July lh, August 3h, September 5h, etc. The following limits of separation, in scale divisions, have been found for each year : — July, 1841 — June, 1842, limit, 52 » 1842— " 1843, " 46 " 1843- " 1844, " 40 " 1844— " 1845, " 33 Average limit, 43 As this limit would only separate 1 in every 34 observations, and would not furnish a sufficient number of disturbances to investigate their laws to advantage, it was necessary to contract the above limit, and 30 scale divisions were finaDy selected. There can be no doubt that the limiting number as found by the use of the criterion is too high, owing to the unavoidable presence of irregularities ascrib- able to imperfection in the corrections for temperature in some cases, and in others due to apparently fitful changes in the instrument. 30 scale divisions =0.00099 parts of the vertical force =0.0127' in absolute measure, adopted as limit of devia- tion of any observation from its corresponding mean monthly value for the same hour, will furnish an average value for the ratio of the number of disturbances to the whole number of observations. The ratio of a disturbance to the whole force is also nearly the same for the horizontal and vertical component. All deviations over 30 divisions from the mean were marked, and a new mean was taken, the hourly observations were again compared with this new mean, and 1 The vertical force, in absolute measure, is on the average, between 1841 and 1845, equal to 12.84 (English units), as stated in a subsequent number of this discussion. DISCUSSION OF THE VERTICAL FORCE. 13 the process was repeated, if necessary, until all deviations above 30 had been sepa- rated; the final hourly means for each month, thus, found and known as the " normals," are given in the following tables. TABLE IV. — BI-HOURLY NORMALS OF THE VERTICAL COMPONENT OP THE MAGNETIC FORCE IN 1841. One division of the scale =0.000033 parts of the vertical force. Increasing numbers denote decrease of force. The observations are made 17m after the full hours. 1841. 0" 2 4 6 8 10 Noon. 14 16 18 20 22" February 664 6J4 662 656 654 650 644 648 647 673 668 665 March 670 661 661 655 651 645 643 646 656 665 666 673 April 671 662 658 653 645 646 646 649 656 666 670 676 May 669 665 660 654 647 649 644 646 650 660 674 679 June 646 631 622 617 624 616 603 624 635 650 653 657 July 703 697 687 671 667 664 665 676 680 698 708 706 August 686 680 676 664 662 652 653 662 666 676 689 691 September ert 655 646 647 637 631 627 628 634 645 653 660 October 579 578 573 568 558 556 561 562 571 577 581 583 November 532 537 538 533 526 523 520 521 526 529 531 538 December 597 . 591 590 606 592 598 605 597 607 610 605 604 The normals for February, March, April, and May, have been diminished by 198, 278, 333, and 361 scale divisions respectively; the uncorrected monthly means are 856, 936, 991, and 1019, which can be exactly represented by the expression r— 966 + 54.4 At — 12.8 A<2, where r= monthly reading and t, expressed in units of a month, counts from April 1 as the epoch. It shows that the monthly increase is uniformly retarded. The mean reading from the four succeeding months is 658, the corrections to February, March, April, and May, as applied, will produce the same mean. The rapid change in the monthly means for some adjacent months makes a small correction necessary to the monthly means, viz : of plus one scale division to the February, March, and December means of the hours 0, 2, and 4, and to the Septem- ber and October means at the hours 18, 20, and 22; of minus one scale division to the February, March, and December means at the hours 18, 20, and 22, and to tLe September and October means at the hours 0, 2, and 4. This small correction is included in the above normals. TABLE IV. — Continued. BI-HOURLY NORMALS OF THE VERTICAL COMPONENT IN 1842. The observations are made 17jm after the full hours. 1842. Oh 2 4 6 8 10 Noon. 14 16 18 20 22* Jnmiary (658) 642 656 649 656 653 664 650 663 675 670 663 February 706 701 713 721 699 698 709 692 698 712 723 710 March 655 •43 654 663 657 661 651 650 657 668 673 665 April 668 658 655 655 656 654 657 651 650 660 672 672 May 673 670 661 644 646 647 651 644 645 656 668 670 June 674 669 6f4 658 647 642 635 639 635 653 671 868 July 683 672 664 659 657 650 643 643 647 663 677 682 August 689 689 683 682 679 672 652 659 669 679 688 688 September 692 886 K89 690 681 671 671 673 672 679 687 693 October 7d6 698 702 714 695 708 707 706 706 708 710 709 November 717 713 723 725 712 715 711 713 716 712 • 718 718 December 713 707 709 706 715 711 709 707 706 711 713 713 1 14 DISCUSSION OF THE VERTICAL FORCE. In January at Oh the final mean is 637 which differs so much from the standard value at this hour that it was preferred to substitute the mean of the month (658) as a close approximation. TABLE IV. — Continued. BI-HOURLY NORMAL* OP THE VERTICAL COMPONENT IN 1843. The observations are made 23J'° after the full hours. 1843. 0" 2 4 6 8 10 Noon. 14 16 18 20 22" January 690 February | 697 March 686 April 715 712 717 716 708 702 709 700 696 696 710 709 May 698 099 695 690 682 680 677 668 677 685 691 095 Jane 698 691 693 687 677 668 663 658 659 6G9 681 689 July 691 692 692 686 679 672 662 658 659 666 677 6b5 August 703 703 708 706 698 683 669 671 672 682 695 699 September 721 719 721 716 707 706 693 692 692 703 714 710 October 714 707 712 717 706 703 702 703 704 714 719 714 November 742 745 745 744 742 737 735 731 746 749 749 746 December 752 733 740 740 740 729 727 743 758 767 7G4 754 • Normals at additional odd hours. 1843. 1" 3 ' 5 7 9 11 13 15 17 19 21 23" October 710 713 714 714 704 701 700 701 709 717 715 717 November 740 743 744 748 739 729 731 738 749 751 747 748 December 744 742 742 743 740 720 729 749 760 763 757 757 TABLE IV. — Continued. HOURLY NORMALS OF THE VERTICAL COMPONENT IN 1844. The observations were made 23Jm after the full hours. 1844. 0" 1 2 3 4 5 6 7 8 9 10 11" January 733 739 730 728 732 733 732 732 730 725 720 713 February 734 729 725 726 729 728 729 730 723 724 722 717 March 768 761 763 760 704 762 765 762 758 761 762 764 April 776 773 771 765 766 765 759 755 749 749 744 740 May 772 769 766 768 767 764 700 754 749 747 747 744 June 776 772 767 768 767 764 760 755 747 745 744 744 July 816 811 804 806 805 802 798 793 784 783 782 780 August 794 790 786 781 783 777 776 769 763 760 75« 754 September 816 815 813 812 811 810 809 805 798 795 790 785 October 775 771 769 773 776 779 780 780 774 773 773 770 November 775 772 798 7K9 772 771 770 773 708 772 772 767 December 754 753 754 755 757 756 755 758 749 751 750 740 1844. Noon. 13 14 15 16 17 18 19 20 21 22 23" January 715 708 715 724 737 740 741 743 744 745 744 744 February 718 716 716 720 727 731 738 739 740 787 735 733 March 762 753 758 760 754 757 753 754 752 753 763 764 April 7H7 733 737 . 741 745 744 756 767 768 765 767 775 May 744 740 747 744 746 748 754 763 766 766 768 772 June 742 739 744 747 741) 754 760 769 771 770 771 775 July 780 776 773 781 783 791 799 805 808 809 811 816 August 750 750 746 759 7«4 771 778 789 790 789 792 794 September 780 779 772 794 703 795 806 813 812 812 814 817 October 769 7M 773 777 786 788 791 789 785 785 781 781 November . 7'16 763 762 765 774 779 777 •778 774 770 709 772 December 743 733 736 724 748 757 755 751 751 748 750 750 DISCUSSION OF THE VERTICAL FORCE. 15 TABLE IV. — Continued. HOURLY NORMALS OF THE VERTICAL COMPONENT IN 1845. The observations are made 23im after the full hours. 1845. 0" 1 2 3 4 5 6 7 8 9 10 11" January 754 747 747 752 752 757 763 767 760 758 753 752 February 760 756 752 757 759 760 763 764 756 756 752 749 March 749 741 736 742 746 748 749 746 736 733 732 729 April 732 727 728 729 728 727 725 721 718 715 717 717 May 720 718 717 719 716 715 713 709 705 702 701 699 June 733 731 729 730 729 728 726 722 717 715 715 711 1845. Noon. 13 14 15 16 17 18 19 20 21 22 23" January 751 748 749 742 .753 760 756 753 749 746 747 754 February 747 741 740 744 753 759 761 761 758 753 752 756 March 729 729 713 734 740 747 751 746 741 740 739 743 April 716 713 717 720 724 724 732 737 736 729 726 727 May 6!*7 696 701 698 702 705 710 720 718 717 718 719 June 711 711 713 714 713 714 722 730 735 731 731 733 TABLE V. — NUMBER OF OBSERVATIONS AND LARGER DISTURBANCES IN EACH MONTH. 1841. 1842. 1843. 1844. 1845. Obs. Dis. Obs Dis. Obs. Dis. Obs. Dis. Obs. Dis. January 300 76 26 5 646 81 648 17 February 288 49 284 86 24 3 600 33 576 5 March 321 64 322 36 27 12 624 106 624 68 April 304 46 306 51 300 60 624 83 624 24 May 223 16 293 47 324 36 648 8 64S 28 June 310 91 310 37 312 16 600 52 600 9 July 323 64 305 24 312 4 648 45 August 304 21 318 34 324 10 648 94 September 307 40 303 57 312 20 600 14 October 308 28 310 12 624 '25 648 20 November 312 37 312 13 624 79 624 10 December 323 84 319 15 624 65 624 47 Sum . . . 3323 540 3682 48S 3833 325 7534 593 3720 151 Ratio . . . 1 dis. in 6.2 obs. 1 dis. in 7.5 obs. 1 Uis. in 11.8 obs. 1 dis. in 12.7 oba. Idis.in24.6obs. Total number of observations used, 22092 larger disturbances, 2097 Ratio of disturbances to observations, 1 to 10.5 Investigation of the eleven year (also called ten year] period in the inequality of the amplitude of (lie Diurnal Variation of the Vertical Force. — The preceding monthly means of the bi-hourly and hourly normals were rearranged in four groups of one year each, necessarily omitting the first five months ; the annual means have for their mean epoch, January, as the monthly means were arranged from July to July. The means for the year 1842-43 depend on nine months only, to refer them to the mean of twelve months, the differences for every observing hour, between the same nine months and twelve months for the preceding and following year, were made out and the mean correction, giving the weight two to the following year, as indicated by the readings taken at the hour 14, was applied to the values of 1842-43. 16 DISCUSSION OF THE VERTICAL FORCE. From 9 months. Correction. Annual means. Frniii !1 months. Correction. Annual means 0" 701 +3 704 Noon 682 + 8 890 2 696 +3 699 14 681 +6 687 4 697 +5 702 16 683 +7 690 6 697 +6 703 18 689 +7 696 8 690 + 6 696 20 697 +5 702 10 686 +1 693 22 700 +5 705 The normals for 1843-44 at the even hours are complete, at the odd hours they extend only over nine months. To refer the latter to twelve months, the difference between the means of the same nine months and the annual mean at the even hours was made out and applied as a correction to the means of the odd hours ; the cor- rection thus applied is the mean difference as deduced from the preceding and fol- lowing even hour. Means of 9 months. Correction. Annual means. Means of 9 months. Correction. Annual means. I" 749 —11 738 W 728 —14 714 3 746 —10 736 15 726 —16 720 5 746 —11 735 17 744 —16 728 7 744 —11 733 19 752 —15 737 9 737 —12 725 21 751 —14 737 11 730 —13 717 23 754 —13 741 TABLE VI. — ANNUAL MEANS OF THE BI-IIOUKLY AND HOURLY NORMAL VALUES OF THE REGULAR SOLAR-DIURNAL VARIATION OF THE VERTICAL FORCE. The numbers are expressed in scale divisions, increasing values indicate decrease of force. The minutes at the head of each column are to be added to the hour given in the first column. Each year commences with the month of July. The time is local Philadelphia time counted from midnight to midnight. Hour. 1841-12. 1842-43. 1843-44. 1844-45. +n±~ +20J" +23i- +23i- 0A.M. 650 704 740 765 1 738 761 2 643 699 735 759 3 736 760 4 643 702 737 761 5 735 761 6 640 703 734 761 7 733 759 8 634 696 727 752 9 725 751 10 « 632 693 722 749 11 " 717 747 12P.M. 633 690 717 745 13 " 714 742 14 " 631 687 718 741 15 " 720 746 16 " 636 690 724 753 17 " 728 758 18 " 647 696 732 762 19 " 737 764 20 " 654 702 738 763 21 " 737 761 22 " 652 705 738 761 23 " 741 764 Means 641 697 730 756 DISCUSSION OF THE VERTICAL FORCE. 17 The following formulae of the mean diurnal variation of the vertical force were deduced from the above tabular values. The angle 6 counts from midnight at the rate of 15° an hour. 1841-42 V = 641d + 101" .4 sin (8 + lOtiO 40') + 3\l sin (28 +198° 25') + I4. 7 sin (38 -f- 250°) 1842-43 V=697 + 7.6 «« (9+ 69 17 ) + 2.9 sin (29+196 48)+ 1.3 sin (38 + 195 ) 1843_44 V = 730 + 11.0 sin (9+ 79 54) + 3.4 sin (28+226 29)+ 0.6 sin (39+ 45 ) 1844-45 V = 756 + 9.2 tin (8 + 83 40) + 4.3 «in (28+233 41) + 1.1 sin (38+ 1 ) In the construction of the equation for 1843-44 weighted normals were used, those of the even hours have the weight 4, of the odd hours the weight 3. To show the degree of accordance in the expressions when deduced from the even and odd hours separately, the resulting equations for the last year are added: — Even hours: V = 756 + 9.32 sin (8+ 84O45') + 4.07 sin (28 + 235O17') + 1.2 sin (39 + 353O) Odd " V = 756 + 8.99 sin (8 + 82 36, ) + 4.52 tin (28 + 232 05) + 1.0 sin (38 + 10 ) The observed and computed values compare as follows. The differences, observed less computed, are expressed in scale divisions : — Hour. 1841-42. 1842-43. 1843-44. 1844-45. 0 +2 +2 +1 +3 2 —1 —1 —2 —2 4 0 +1 +1 0 17}, 20J, 23}, and 23} 6 .+1 +1 +1 +2 minutes are to be added 8 0 —1 —2 —3 to the full hours for the 10 0 +1 +1 0 four years respectively. Noon +1 +1 +1 +2 14 —1 +1 —2 16 0 +1 0 +1 18 +1 +1 0 +1 20 0 0 +1 —1 22 —1 0 —1 —1 The graphical representation of the observed and computed values exhibits a maximum of the vertical force between 1 and 2 P. M., and a minimum of force between 83 and 10| A. M. ; the diagrams also show a tendency of a secondary maximum about two hours after midnight followed by a secondary minimum about two hours later, with a range probably less than two scale divisions (0.000066 parts of the force, or 0.00085 in absolute measure). This small nocturnal inequality is only exhibited by one of the formulae, in 1842-43, when it has its greatest value ; in the preceding year there is but a faint trace of it, in the two succeeding years it is indicated in the diagram by dashes. The average diurnal range is nearly 22 scale divisions (0.00073 parts of the vertical force, or 0.00932 in absolute measure). 18 DISCUSSION OF THE VERTICAL FORCE. INEQUALITY IN THE DIURNAL VARIATION OF THE VERTICAL FORCE. 87 89 91 93 95 697 14 99 16 01 18 03 20 05 22 07 24 26 28 40 730 42 32 44 34 46 36 48 38 SO 40 52 42 64 756 68 60 62 64 66 29 31 33 35 37 39 641 43 45 47 49 51 53 55 1841-42. 1842-43. 1843-44. 1844-45. -a Oh 2 4 6 8 10 12 14 16 18 20 22 24" (A.M.) (P.M.) Philadelphia time. EPOCH AND AMOUNT OF THE PRINCIPAL MAXIMUM AND MINIMUM AND AMPLITUDE OF THE DIURNAL INEQUALITY. Year. Mail mum. Minimum. Amplitude. Reading. Epoch. Reading. Epoch. Scale div. la parts of v. f. In absol. mean. 1841-42 1842-43 1843-44 1844-45 G304.9 687.8 715.1 741.8 13" 15" 14 25 13 00 13 10 654'J.5 705.1 739.3 763.8 20" 50m 22 10 23 00 20 30 23'1.6 17.3 24.2 22.0 0.00078 0.00057 0.00080 0.00073 0.01000 0.00733 0.01025 0.00932 Mean j 13} 21 J 21.8 The epochs are given to the nearest quarter of an hour. If we compare the Philadelphia and Toronto curves, we find a general corres- pondence in their form, the early morning secondary in flection being well exhibited at Toronto ; the epochs of the two curves, however, are shifted by nearly three hours, thus: at Toronto principal, maximum at 5 P. M., at Philadelphia \\ P. M. ; DISCUSSION OP THE VERTICAL FORCE 19 principal minimum at Toronto 10 A. M., at Philadelphia 9| A. M. ; the epochs of the early morning inflection are also about 3| hours later at Toronto. The curves exhibit also a difference in the amplitude, at Toronto, Vol. Ill, the diurnal range is 0.00019 parts, whereas at Philadelphia we found it much larger. The special study of the solar diurnal variation of the vertical force is reserved for Part VIII. The minimum diurnal range occurred in 1842-43, on the average, therefore, we may" assume May, 1843, as the epoch of the minimum range in the eleven (or ten) year period, resulting from the discussion of the declination, horizontal and vertical force observations. To facilitate the comparison with similar expressions at other stations, the pre- ceding equations of the diurnal variation are also presented, expressed in parts of the vertical force. The angles have been changed 180° to reverse the order of progression of the scale numbers. 1841-42 V = + 0.00034 sin (9 + 286040') + 0.00010 sin (28 4- ISO 25') + 0.00006 sin (39+70°) 1842-43 V = + 0.00025 sin (8 + 249 17 ) + 0.00010 sin (28 + 16 48 ) + 0.00004 tin (38 + 15 ) 1843-44 V = +0.00036sm (8+259 54) + 0.00011 sin (28+46 29 ) + 0.00002 sin (38+225) 1844-45 V = + 0.00030 sin (8 + 263 40 ) -f 0.00014 sin (28 + 53 41 ) -i- 0.00004 stn (38 + 181) The constant terms and numerical coefficients when expressed in absolute measure (English units) are as follows : — Y Term involving 8 28 38 1841^2 1842-43 1843-44 1844-45 12.85 12.84 12.83 12.83 0.00441 0.00322 0.00468 0.00388 0.00131 0.00123 0.00144 0.00172 0.00072 0.00055 0.00025 0.00047 The angle 0 counts from midnight. Investigation of the Eleven (or ten) Year Inequality in the Disturbances, and General Analysis of the Disturbances of the Vertical Force. — By means of Table V, a new table was formed of the number of disturbances in each month for the years 1841-42, 1842-43, 1843-44, 1844-45, commencing with July, and all referred to a uniform series of bi-hourly observations ; the numbers for and after October, 1 843, were halved. The number of disturbances for January, February, and March, 1843, are the means between the same months in the preceding and following year. The annual means of this Table (VII) are as follows : — In 1841-42 " 1842-43 " 1843-44 " 1844-45 Mean number of Disturbances. . 51 . 34 . 25 16 This seems to indicate the end of the year 1844 as the epoch of the minimum number of disturbances in the eleven year period, taking the numbers collectively for declination, horizontal and vertical force, the minimum probably took place in the spring of 1844. 20 DISCUSSION OF THE VERTICAL FORCE. If we take the monthly aggregate amount of the disturbances, all referred to a uniform series of bi-hourly observations, and form a table of these values for each year (Table VIII), the mean aggregate amount for each year is as follows : — In 1841-42 " 1842-43 " 1843-44 " 1844-45 Mean amount of disturbances. . 2306 div. . 1521 959 636 This again points to the end of the year 1844 for the epoch of the minimum amount of disturbances, and considering the three elements, declination, horizontal and vertical force, the spring of 1844 might be assumed as the time of the minimum magnitude of the magnetic disturbances. Altogether, the inequalities in the diurnal amplitude and in the number and magnitude of the disturbances of the magnetic elements, as observed at Philadelphia, fix the end of the year 1843, or the beginning of 1844, as the epoch of the minimum of the eleven (or ten) year inequality. We now proceed with the analysis of the disturbances, their diurnal and annual inequality in number and amount, and for increasing and decreasing values. Annual Inequality in the number of Disturbances. — The numbers for each month have been referred to a uniform series of bi-hourly observations as explained above. The ratios of the monthly means to the annual means is given, and also, for com- parison, similar ratios found for the horizontal force and declination. TABLE VII. — ANNUAL INEQUALITY IN THE NUMBER or DISTURBANCES. Mean ratio Mean ratio 1841-1842. 1842-1843. 1843-1844. 1844-1845. Means Vert, force Hor. force Declination Vert, force Hor. force and from four ratio. ratio. ratio. hor. force and declination. years. declination. July 64 24 4 22 28 0.9 1.1 0.9 1.0 0.9 August 21 34 10 47 28 0.9 0.9 1.6 1.3 1.1 September 40 57 20 7 31 1.0 1.4 1.4 1.4 1.2 October 28 12 12 10 15 0.5 1.4 2.1 1.7 1.3 November 37 13 40 5 24 0.8 1.0 1.1 1.1 1.0 December 84 15 33 23 39 1.3 1.0 1.0 1.0 1.1 January 76 58 40 9 46 1.5 0.6 0.8 0.7 0.9 February 86 51 16 3 39 1.3 1.0 0.5 0.7 0.9 March 36 44 53 34 42 1.4 1.1 0.7 0.9 1.1 April 51 50 42 12 39 1.3 1.1 0.9 1.0 1.1 May 47 36 4 14 25 0.8 1.0 0.6 0.8 ' 0.8 June 37 16 26 4 21 0.7 0.0 0.5 0.6 0.6 Mean 51 34 25 16 31 The months of maximum disturbance are March and September (the high value in January and the low one in October appear anomalous, and would no doubt dis- appear in a longer series of observations). The minimum occurs in June ; there is no well expressed second minimum. The horizontal force and declination ratios, as well as the ratios of the three elements at Toronto, give the maximum number of disturbances at the equinoxes, and the minimum number at the solstices, and as the winter solstice minimum only is wanting in the Philadelphia vertical force DISCUSSION OF THE VERTICAL FORCE. 21 ratios, it is probably due to the small number of observations, and the difficulty in keeping the instrument in adjustment and allowing for its irregularities. I have, therefore, given the mean ratio of the Philadelphia disturbances in the last column of Table VII, and compared the result, graphically, with those deduced by General Sabine for Toronto.1 ANNUAL INEQUALITY OP DISTURBANCES. Tnrontn. 5 '• 1.6 - - 1.5 I \ _ 1.4 1.3 - ! 1 \ A - 1.2 1.1 If) - / _\ x\ / A\ - .9 .8 - /• \ \ \ ^/ \ \ J - .7 .6 - V J v/ - .5 f V . .4 - - till Illlllll I If we separate the disturbances into two parts, those increasing and those decreasing the force, we obtain the numbers of Table VIII. A positive sign indi- cates disturbances increasing, a negative sign those decreasing the vertical force. The law of the annual variation seems to be the same as shown by the ratios in the last two columns ; this accords with the result at Toronto. TABLE VIII. — ANNUAL INEQUALITY OF DISTURBANCES INCREASING AND DECREASING THE FORCE. 1841-42. 1842-43. 1843-44. 1844-45. Ratios. + — + — + — + — + — July 31 33 8 16 0 4 12 10 0.7 1.1 August 14 7 9 25 8 2 36 11 1.0 0.8 September 22 18 16 41 9 11 5 2 0.7 1.2 October 22 6 8 4 6 6 3 7 0.6 0.4 November 17 20 5 8 14 26 4 1 0.6 1.0 IVc<'inber 51 33 8 7 23 10 13 10 1.4 1.1 January 38 38 32 26 26 14 6 3 1.5 1.5 February 53 33 32 19 11 5 2 1 1.4 1.0 March 16 20 23 21 30 23 23 11 1.3 1.3 April 32 19 30 20 23 19 5 7 1.3 1.1 May 28 19 18 18 3 1 11 3 0.9 0.7 June 23 14 5 11 7 19 3 1 0.6 0.8 » Page Ixx., Vol. III. 22 DISCUSSION OF THE VERTICAL FORCE. TABLE IX. — AGGREGATE AND MEAN AMOUNT OF DISTURBANCES IN EACH MONTH OF THE YEAR. The numbers are expressed in scale divisions and referred to a uniform series of bi-hourly observations. The mean amount or average magnitude is found by dividing the number in the preceding column by 4 and by the number of disturbances found in Table VII. Aggregate amount. Sum of 4 years. Mean amount. 1841-42. 1842-43. 1843-14. 1844-45. July . . 2593 1255 149 784 4781 42 August 791 1323 622 2017 4753 43 September 1612 2798 770 301 5481 44 October . 1216 432 488 438 2574 42 November 1564 503 1504 206 , 3777 40 December 4187 560 831 872 6450 42 January . 3899 2745 1592 314 8550 47 February . 3900 2279 659 109 6947 45 March . . 1672 1898 2125 1245 6940 42 April . . 2324 2111 1642 468 6545 42 May . . 2445 1625 186 704 4960 49 June . . 1472 723 934 168 3297 40 The last column shows that the magnitude of the disturbances is rather irregu- larly distributed over the several months without following any apparent law. TABLE X. — AGGREGATE AND MEAN AMOUNT or DISTURBANCES IN EACH MONTH OF THE YEAR, SEPARATED INTO TWO GROUPS OF INCREASING ( + ) AND DECREASING FORCE ( — ). The mean amount is obtained by means of the numbers of Table VIII. 1841-42. 1842-43. 1843-44. 1844-45. Sum of 4 years. Mean amount. + — + — + — + + — + — July 1130 1463 340 915 0 149 402 382 1872 2909 37 46 August 555 236 359 964 279 343 1568 449 2761 1992 41 45 September 835 777 775 2023 397 373 251 50 2258 3223 43 45 October 999 217 300 132 250 238 128 310 1677 897 43 39 November 653 911 223 280 504 1000 154 52 1534 2243 38 41 December 2745 1442 276 284 508 323 489 383 4018 2432 42 41 January 2126 1771 1589 1156 1050 542 208 106 4975 3575 48 44 February 2615 1235 1538 741 462 197 76 8-1 4691 2256 48 39 March 671 1001 910 988 1149 976 875 370 3605 3335 39 44 April 1471 853 1361 750 853 790 172 296 3856 2689 43 41 May 1535 910 928 697 170 16 598 106 3231 1729 54 42 June 999 473 246 477 246 688 133 35 1624 1673 43 37 Sums 16336 H3H9 8845 9407 5867 5635 5054 2572 36102 2S953 Mean . 43 42 The magnitudes of the disturbances, as before, do not appear to follow any law. The disturbances which increase the force preponderate over those which decrease it ; the ratio of the annual means is 1.3 to 1.0. At Toronto the reverse was found ; the disturbances which decrease the force preponderate over those which increase in the ratio of 1.4 to 1.0. Diurnal Inequality of tTie Disturbances. — In the bi-hourly combination of the disturbances we make use of the series of observations extending from .February, DISCUSSION OF THE VERTICAL FORCE. 23 1841, to June, 1845, omitting only the single daily observation in January, Febru- ary, and March, 1843. Strictly speaking the time is 21 minutes later than indicated in the table. TABLE XI. — DIURNAL INEQUALITY IN THE NUMBER OF DISTURBANCES. The ratios of the three elements have been collected to facilitate comparison. Katios. Number * vertical force. Vertical force. Horizontal force. Declination. 0» 168 1.3 1.1 1.0 2 159 1.2 0.9 1.2 4 156 1.2 0.7 1.0 6 133 1.0 0.7 1.1 8 117 0.9 0.8 1.0 10 115 0.8 1.1 1.1 Noon 131 3.0 1.3 0.9 14 163 1.2 1.0 0.8 16 127 0.9 1.1 0.9 18 116 0.8 1.1 0.9 20 110 0.8 1.1 1.0 22 123 0.9 1.1 1.1 Mean 135 The greatest number of disturbances occur about A. M. (at Toronto at 3 A. M.), with the least number at 10 A. M. (at Toronto at 11 A. M.); the secondary maxi- mum and minimum occur about 2 P. M. and 7 P. M. (at Toronto the hours are 5 P. M. and 9 P. \L). On the average, therefore, the maxima and minima occur lh 40m earlier at Philadelphia than at Toronto. At neither station do the three ele- ments show the same law; they agree only in so far as to exhibit a systematic in- crease and decrease with the solar hours, and in having two maxima and two minima. The diagram shows the law of the disturbances of the vertical force for Phila- delphia and Toronto. DIURNAL VARIATION OF DISTURBANCES. Tnrnntn. B " 1.6 A - 1.5 / - 1.4 \ - 1.3 ». \ 1 - 1.2 1.1 1.0 \\ A / - N[ \ X /; .9 \ \ / / \ J\ - .8 1 ,V ./ N Vy - .7 \ / - .6 - \ / - .5 \ / - .4 \.y " 0" 2 4 6 8 10 a 14 16 18 20 22 24" s R 24 DISCUSSION OF THE VERTICAL FORCE TABLE XII. — CONTAINS THE NUMBER OF DISTURBANCES DISTRIBUTED OVER THE HOURS OF THE DAY, SEPARATED INTO THOSE jviiicii INCREASE ( + ) AND THOSE WHICH DECREASE ( — ) THE VERTICAL FORCE. Number of disturbances. Katies. + — + — V 93 75 1.3 1.2 2 73 86 1.0 1.3 4 69 87 1.0 1.4 6 62 71 0.9 1.1 8 59 58 0.8 0.9 10 63 62 0.8 1.0 Noon 61 70 0.9 1.1 14 96 67 1.3 1.0 16 69 58 1.0 0.9 18 72 44 1.0 0.7 20 67 43 0.9 0.7 22 76 47 1.1 0.7 Mean 71 64 The laws which regulate the diurnal occurrence of the nnmber of disturbances, increasing and decreasing the vertical force, are evidently not the same, yet they are by no means the converse of one another as has been found to be the case in the disturbances of the declination and the horizontal force. At Toronto also, where the horizontal force and declination curves were exactly opposed, that of the vertical force is not so, and at Philadelphia rather favors an agreement between the increasing and decreasing disturbances than an opposition. Principal maximum of increasing disturbances 2 P.M., principal minimum 9 A.M. (at Toronto 5 P. M. and 5 A. M. respectively). Secondary maximum at midnight ; this may possibly be the principal maximum ; secondary minimum at 8 P. M. Principal maximum of decreasing disturbances 4 A. M., principal minimum 8 P. M. (at Toronto 3 A. M. and 6 P. M. respectively). The secondary maximum at noon is less distinctly marked ; secondary minimum at 8 A. M. Thus the epochs of the curves for increasing and decreasing force seem to be 12 hours apart. Diurnal Inequality in the Magnitude of the Disturbances. TABLE XIII. — CONTAINS THE AGGREGATE AMOUNT OF DISTURBANCES AND THEIR AVERAGE MAGNITUDE, THE LATTER FOUND BY MEANS OF TABLE XI. ALL EXPRESSED IN SCALE DIVISIONS. Aggregate amount. D Mean amount. 0" 7049 108 42 2 6876 159 43 4 6480 156 42 6 5418 133 41 8 5022 117 43 10 5096 115 44 Noon 5526 131 42 14 7101 163 44 16 5591 127 44 18 - 5571 116 48 20 4773 110 43 22 5246 123 43 DISCUSSION OF THE VERTICAL FORCE. 25 Average magnitude 43 scale divisions, the disturbances appear to be nearly of the same size at all hours, there is a slight preponderance in magnitude between 10 A. M. and 10 P. M. over the other half of the day. TABLE XIV. — AGGREGATE AMOUNT AND MEAN AMOUNT OP DISTURBANCES, SEPARATED INTO THOSE WHICH INCREASE AND THOSE WHICH DECREASE THE VERTICAL FORCE. Aggregate amount. Mean amount. T»!fF f + — + — aggregate amount. 0" 3737 3312 40 44 + 425 2 3221 3655 44 43 — 434 4 2866 3614 42 42 — 748 6 2577 2841 42 40 — 264 8 2524 2498 43 43 + 26 10 2507 2589 47 42 — 82 Noon 2731 2795 45 40 — 64 14 4456 2645 46 40 +1811 16 2969 2622 43 45 + 347 18 3456 2115 48 48 +1341 20 3003 1770 45 « 41 + 1233 22 . 3258 1988 43 42 +1270 Mean 44.0 42.5 +4861 The magnitude of the disturbances, either increasing or decreasing the force, apparently does not vary with the hours of the day. The disturbances which increase the force preponderate between the hours 2 P. M. and 2 A. M. ; those which decrease the same occur in the other half of the day, the average ratio of the preponderance of increase over decrease is as 4 to 1. Dividing the numbers in the last column of the preceding table, or the excess of the sum of disturbances increasing the force over the sum of those decreasing the same, by the total number of days (1297) of observation, we find the diurnal disturbance variation as follows : — Scale divisions. la parts of vertical force. In absolute measure. 0" 2 +0.3 —0.3 +0.00001 —0.00001 +0.00013 —0.00013 4 —0.6 —0.00002 —0.00025 6 —0.2 —0.00001 —0.00008 8 0.0 0.00000 0.00000 10 —0.1 0.00000 —0.00004 Noon 0.0 0.00000 0.00000 14 16 18 20 22 +1.4 + 0.3 + 1.0 +1.0 +1.0 + 0.00004 +0.00001 +0.00003 +0.00003 +0.00003 +0.00059 +0.00013 +0.00042 +0.00042 +0.00042 Mean +0.3 +0.00001 +0.00013 The value for the hour 14 is evidently anomalous, the mean of the hours 12 and 16 or + Od.2 (0.00001 in parts of force, 0.00008 in absolute measure) should be substituted. The average daily effect of the larger disturbances is therefore to increase the vertical force between 1 P. M. and midnight, and to decrease it 26 DISCUSSION OF THE VERTICAL FORCE. between 1 A. M. and noon, with an amplitude of about 1.6 scale division (0.00005 parts of the force, 0.00067 in absolute measure). The maximum value takes place at. 8 P.M., the same hour at which the horizontal force disturbance is greatest (decreasing that force). The disturbance law at Toronto is nearly the same as at Philadelphia, the dis- turbances increase the force between noon and 9 P. M., and decrease it in the remaining hours of the day ; the range at Toronto appears to be larger. If we classify the disturbances according to their magnitude in eight groups, each differing 25 scale divisions from the preceding, we find the following scale numbers : — Disturbances. In scale divisions. Between limns in parts of the force. Number. 30 and 55 0.00099 a»d 0.00181 1840 55 80 0.00181 " 0.00263 211 80 105 0.002H3 ' 0.00346 28 105 130 0.00346 ' 0.00428 15 130 155 0.00428 ' 0.00511 0 155 180 0.00511 ' 0.00593 2 180 205 0.00593 ' 0.00676 0 205 230 ' 0.00676 ' 0.00759 1 Beyond None. APPENDIX TO PART VII. EFFECT OF THE AURORA BOREALIS ON THE MAGNETIC DECLINATION, AND THE HORIZONTAL AND VERTICAL FORCE AS OBSERVED AT THE GIRARD COLLEGE OBSERVATORY. THERE were in all 22 auroras recorded ; these, however, comprise only the brighter displays. Of those observed, 7 occurred between May 30, 1840, and July 1, 1841 ; 1 occurred between July, 1841, and July, 1842 ; 6 occurred between July, 1842, and July, 1843 ; and 7 between July, 1843, and July, 1844. One is recorded in the last year, ending June 30, 1845. They are distributed over the several months as follows : — January . . . . .2 February . . . . .0 March ...... 1 April 2 May 3 June . 2 July 6 August . . . . .3 September . . . . .2 October 0 November 1 December . . . . .0 In the summer months there were 18, in the winter months 4. In reference to the hours of the night, the phenomenon was visible on the average between 9| P. M. and 11£ P. M. Individual examination of the magnetic record during auroral displays. The time is local time, counted for convenience' sake from midnight to midnight to 24 hours. I. 1840, May 29th — 30th. As the twilight faded an aurora became visible. In the course of the display there were moving pillars, flashes from a low segment of light in the north, and a beautiful arch nearly or quite at right angles to the magnetic meridian. Pillars of aurora from 21h 18m to 22h 2™, varying in brightness and position ; low segment of light to the north, continued throughout the appearances ; at 22h 5m an arch forms from east to west ; streams of light, varying in brightness, fading and reappearing from 22h 20m to about 23h 10m; the brightest flash at 23b 6m. From 18h54m the declination magnet commenced to move eastward (declination decreasing), reaching an extreme position at 20h 34m, difference from average position about 56 divisions or 19' ; the movement then became westerly with smaller fluctuations till 22h 39m, when it reached its westerly extreme of about 71 divisions or 24' from the normal place ; the magnet reached a second easterly extreme at 23h 44m of about 48 divisions or 17', at lh 24ra (30th) again a westerly extreme of about 7', and at 2h 49m an easterly deflection of about 14' ; after this the needle returned gradually to its ordinary position. About the time of the brightest flash the change (easterly motion) was very rapid, no extreme value, however, was reached. When the arch formed, the position was nearly normal. The horizontal force decreased steadily until 22h 42ra, when the readings fell beyond the scale ; a minimum was reached between that time and 22" 52m of at least 0.016 (parts of the force) below the normal force. At the time ot the brightest flash the retrograde movement was in progress. The disturbance of the vertical force commenced before 17h 52m, at which time the force was a maximum; it then decreased very rapidly, and finally moved off the scale after 22h 2™. (The value of a division of the scale was not ascertained.) II. 1840, July 4th. At 20h auroral light in the N. N. W. about 10° aoove the horizon, at 22h very faint aurora still visible in N W. The declination was not at all affected. The horizontal force ( 27 ) 28 APPENDIX. at these hours was 85 divisions (0.003 parts of the force) less than the normal amount. The vertical force is apparently undisturbed ; it is slightly above the normal value. III. 1840, July 6th. An aurora was noticed at Oh 25™ and 2h 25m. The declination was disturbed at Oh 19|m and 2h 19^m; it indicated 50 divisions and 34 divisions, or 17' and 12' of easterly deflection. Jt is likely that there were disturbances two hours preceding and two hours following the above times, as the scale could not be read. The horizontal force was disturbed from midnight till 2 P. M. ; the force was less during this time, and reached its minimum value at 2h 22™ of 130 divisions or 0.005 parts of the force ; between 2 and 8 A. M. the diminution was about 0.004 parts. The vertical force was also less from midnight till after 2'1 17m, the greatest diminution probably took place later as the observations failed at 4h 11™. Minimum value at 2h 17'", 0.004 parts of the force. IV. 1840, July 29th. At 22h 25m a faint aurora. The declination was not disturbed. The hori- zontal force was very slightly affected. At 20h 22m it was 0.001 parts less than the normal, at 22h 22m it was nearly normal, and at, Oh 22m (30th) it was greater by 0.002. There may have been ordinary disturbances not immediately connected with the aurora. At 22h 17m the vertical force was slightly affected, the force decreased 0.002 parts below the normal. V. 1840, August 19th. At 20h 25m auroral light in N. ; 22h 25m aurora continues in X. and N. "W. The declination disturbance commenced at 22h 20m and continued to 2h 20m (20th), west deflection 48 divisions (22'), 10 divisions, and 10 divisions. The horizontal force was disturbed from 16h 22m to 22h 22°", force less 43 divisions, 49, 102, and 85 divisions Cm minimo 0.004 parts of the force). The vertical force seems lower than usual, but hardly reached the limit of a recognized disturbance. VI. 1840, August 28th and 29th. An aurora appeared at 20h 39^m in N. N. E., disappeared at 21h 19Jm, reviving at 21h 59£m ; at 22h 9jm streamers moving from E. to W. ; light continued in N.; streamers again in N. E. at 22h 59^m and lh 14im, after which time the aurora was not observed. An easterly movement of the needle commenced about 20h 19m with a maximum eastern deflection of 125 divisions (or 57') at 21h Om, the westerly motion continued till 21h 55m when the needle was yet 5' east of its normal position; smaller fluctuations were observed till midnight, the deflection was then 19' east; half an hour later it was 20' east; the morning extreme was reached at lh 35m, when the deflection was 25' east ; after this the disturbance gradually subsided. There was a disturbance of the horizontal force about 18h 20m ; from about 21h 52m till 10 the next morning the horizontal force remained below its normal value. At 23h 32m it was 0.009 (parts) below, at 0" 22m it was 0.007, and at lh 22m its minimum value of 0.010 (parts of the force) was reached. The disturbance in the vertical force appears to have commenced about 21h 7m, when the force gradually decreased till 21h 57m when it reached a minimum of about 0.003 (parts) ; after this it gradually increased. VII. l'840, September 21st. At 20h 25m faint aurora, 22h 25m aurora disappeared. Disturbance of the declination commenced at 20h 20m and continued to 4h 20m (22d), deflections 40 divisions (18') W., 10 divisions E., 14 divisions W., and 23 divisions E. The horizontal force disturbance com- menced at 16h 22m and ceased at 4h 22m next day ; force less 69 divisions, 47 divisions, 71 divisions, 42 divisions, 94 divisions, 124 divisions (0.005 parts of the force), and 93 divisions. The vertical orce between 16h and 23h was slightly above the average, but suddenly became much smaller than the normal between midnight and 3 A. M. Minimum about 0.002 parts of the force. VIII. 1842, April 14th. At 22h 40™ appearance of aurora, a bright light in the X. ; at Oh 20ra (15th) an arc of light was visible extending to about 15° above the north horizon. Declination dis- turbed from 22" 20m to 8h 20m (15th), deflections at the regular observing hours 23 divisions W., 39 E., 11, 37, 10, and 14 divisions W. Maximum west deflection at 22h 56m, 58 divisions (2C/), maxi- mum east deflection 39 divisions (18'), derived from the series of extra observations. The horizontal force disturbances commenced at 22h 22m and ceased at 4h 22m, force less 39 divisions, 149 divisions, 37 divisions, and 50 divisions, minimum 279 divisions (0.010 parts of the force) at lh 16m (15th). But one of the 69 extra readings during this aurora shows an increase of force. The vertical force APPENDIX. 29 disturbances commenced at Oh 17^'° (loth) and continued to 6h 17^m; force less 68 divisions, 69 divisions, 59 divisions, and 38 divisions. Minimum value 111 divisions or 0.0037 parts of the force at 1" 24m (15th). IX. 1842, September 2d. At 2h 22m a bright light extending on each side of N. point about 15°, and to about 6° above the horizon ; at 2h 49m light spreading and becoming more faint ; at 3h 12m light faint and gradually subsiding. The declination was very slightly affected, maximum west deflection a,, 3h 26™, 19 divisions (9'). The horizontal force was not disturbed. The vertical force was likewise undisturbed X. 1842, November 21st and 22d. A well developed aurora and the best observed of the series. At 22h 23m a very luminous arc extending to about 15° above the horizon, and about 90° along it in the north ; 22h 38m light slightly increasing; 22h 53m a slight decrease of light; 23h 18m light alter- nately appearing and disappearing ; 23h 33m four streamers of unusual brightness reaching 30° above horizon ; 23h 36m light particularly bright in N. W., whence a large streamer of 20° is shooting, also one due north of 15°; 23h 40m light subsided, no streamers; 23h 43m small streamers appearing; 23h 46ra large streamers attended with great light in N. W. ; 23h 48m the arc still remains about 15° above ho»izon, but has shortened its chord to 30°, no streamers ; 23h 51m arc scarcely visible ; Oh 23m (22d) two arcs visible ; Oh 28m a large streamer of 20° in length ; Ob 36m considerable light without the arc ; lh 08m light very faint ; I1' 23m slight appearances of arc ; lh 33m faint streamer of 10° ; lh 58m faint streamer of 20° ; 2h 48m a large but faint streamer due N. about 20° in length ; light has nearly disappeared ; 3h 3m light scarcely visible ; 3h 33™ no light visible, and readings of instru- ment ordinary. The declination disturbances commenced at 22h 20m, and ceased at 10h 20m (22d) ; deflections 49 divisions W., 20 divisions W., 25, 20, 8, 25, and 16 divisions E. The maximum W. deflection (22') occurred at the commencement, with the appearance of the luminous arc, the needle remained deflected to the westward until towards the end, when there was a smaller easterly deflection. No special effect of the streamers is noticed. The horizontal force disturbances commenced at 16" 22m, and continued to 2h 22m (22d) ; horizontal force less 33 divisions, 68, 82, 183 divisions (0.007 parts of the force) ; this diminution was about the time of the appearance of the arc, 125 divisions and 73 divisions at the last two regular observing times. The streamers did not appear to have any special effect The horizontal force always remained smaller than the normal value at the respective hours. The vertical component was not affected. XI. 1843, May 6th and 7th. At 19" 48m a bright light ; at 2h 18m (7th) light to N. about 23° high, but faint. The declination disturbances commenced at 16h 20m, and continued to about 3b (7th). The deflections at the regular hours were 28, 30, 16 divisions E., 15 divisions W. (20m after midnight), maximum east deflection 18', succeeding maximum west deflection 9', next following maximum east deflection 33', following maximum west deflection 15'. The horizontal force disturbances commenced at the same hour with the declination disturbances, and continued to the end of the series of observations. The change commenced with a violent increase of 113 divisions above the normal value, and increased to 330 divisions (0.012 parts of the force) at 18h 04m, corresponding in time to the first maximum east deflection. The force then decreased, reaching 132 divisions below the normal value, and attaining shortly (16m) after midnight the extraordinary low value 348 divisions (0.013 parts of the force) ; up to the end of the disturbance the force remained below the standard amount. The vertical force was suddenly disturbed, at 18h 23£m it was 161 divisions greater than the mean, and at 22h 23£m bat 41 divisions above the normal. Maximum value 164 divisions (equal to 0.0054 parts of the force) at 18" 12ra. XII. 1843, May 8th. At Oh an aurora visible to north. The declination was but slightly affected ; at 19h 32m there was an easterly deflection of 15 divisions or 7' ; at 20h 26m it was west 4' ; after this there was an easterly motion, changing again to west, which reached an extreme value at 23h 44m of 17 divisions or 8' W. From the commencement of the horizontal force observations (17h 38m) the force was less than the normal ; at 20h 4m the greatest depression was 0.003 (parts of the force). The disturbance continued till 6 A. M., the force being less than the standard value. From 17h 38m, when 30 APPENDIX. tlie vertical force was observed, it was found less than the normal, at 20h 36m depression 20 divisions, at Oh 23m it was 31 divisions or 0.001 parts of the force below the standard value. XIII. 1843, June 21th. At 22b a bright -diffused light to north, particularly bright to N. W., whence streamers are shooting up; general light weakens as it rises at 20b 45m ; at 21h 15m a brilliant light, dark cumulus spots in the bright light, and long streaks of dark clouds to N. Fades at 22h 1 3m, light to N. faint ; dark, fuzzy, low cumuli form and disappear to N. Neither the declination nor the horizontal force was disturbed by this aurora. The vertical force was slightly affected, force less 38 divisions or 0.0012 parts of the force. XIV. 1843, June 30th. At 23h aurora visible to the N. N. E., flaming to about 10°. The declination disturbances commenced at 22h 20m (9 divisions W.), they reach a maximum at Oh 02m (July 1st) of 20 divisions (9'), and gradually disappear, the deflections having been west throughout. The horizontal force is smaller than the normal value, a first minimum is reached about 20h 44m (about 45 divisions), and the principal minimum about Oh 10m (July 1st) of nearly 50 divisions (0.0018 parts of the force). The vertical force remained undisturbed. XV. 1843, July 7th. At 20" 52m very light in the N. N. E. and N. W. The declinatio'n at 18h 20m is deflected 15 divisions E., the motion then became westerly and reached 29 divisions (13') W. at 23" 33m ; at 2h 20m (8th) the deflection is again 16 divisions W. The horizontal force is less than usual, with a minimum value about 20h 52m of 55 divisions (0.002 parts). The force then increases, and about midnight reaches slightly above the normal. The vertical force was not disturbed. XVI. 1843, July 24th and 25th. According to a letter (dated July 25th) from one of the obser- vers, auroral disturbances commenced about 16h (July 24th) and quieted down about 21h. At 16h 20m the declinometer was deflected 15 divisions E., about 4h (25th) the disturbances reappeared deflecting 10 divisions W., and changed to east deflection at 6h 20m, reaching a maximum east of 34 divisions (15') at 13h 20m. At 16h 22m the horizontal force was about 46 divisions less, with dis- turbances reappearing about 8h 22m, reaching at 8h 46m 96 divisions (0.0015 parts of the force) below the normal, and quieting down about one hour after noon. The vertical force was not sensibly disturbed XVII. 1843, July 25th. At 21h 30m (25th) streamers to N., flaming to about 30° ; at 22" streamers very bright, reaching about 40°; At 22h 15m light very faint and gradually disappearing. The declination was disturbed (deflections west) between 20h 20m and 22h 20m reaching a maximum at 21h 58m of 36 divisions (16'). The horizontal force decreased between 18h 22m and 22h 22m,reach- ing at 21h 34m 91 divisions (0.0033 parts) below the normal value. The vertical force apparently undisturbed. XVIII. 1843, August 22d. At 20h 22m there were streamers of 35° in length, bright light in N. Between 14h 20m and 18h 20m there was a small east deflection of the magnet reaching 28 divisions at the latter hour; at 19k 56m it changed to a west deflection of the same amount (13'). At the time of the appearance of the streamers the declination was normal. During the aurora the horizontal force diminished, reaching at 20U 28m 91 divisions (0.0033 parts) brlmv the normal. The low value continued for about two hours after this time. The vertical force was not sensibly affected. XIX. 1844, January 24th and 25th. Aurora visible to N. and N. N. E. at Oh 22m (25th), streamers running up 30°; Oh 33m streamers running up 15° and 20°. During this aurora the horizontal needle was deflected to the westward about 10 divisions, reaching a maximum at 6h 58m of 15 divisions (7') ; at the time of the appearance of the shorter streamers the deflection was near 7', the horizontal force was below the normal value, viz: decrease 36 divisions, 41 and 35 divisions at 22h 22m, 23h 22m, and Oh 22m (25th), minimum 47 divisions (0.0017 parts). At the time of the longer streamers there was an average decrease, and during the continuance of the shorter streamers the horizontal force was APPENDIX. 31 normal. At Ob 23im and 2h 23£m the vertical force was 36 and 32 divisions smaller than the normal. Difference 0.0011 parts of the force. XX. 1844, March 29th. At 16h 51m cloudy, aurora visible. The declination magnet is deflected to the east and west several times in succession; between 16h 20m and 18h 20m about 14 divisions E.( and 16 divisions E. ; the following greatest west deflection of 61 divisions (27') occurred at 20h 10m; the next east deflection reached a maximum at Oh 22m (30th) of 41 divisions; a maximum west deflection was again reached at lh 14™ of 50 divisions (23'). The horizontal force is throughout smaller than the normal value, with differences varying on the average from 50 to 70 divisions. The greatest difference was reached at 20h 2m of nearly 100 divisions (0.0036 parts of the force); at 23k 47m another small value of 90 divisions was observed. The vertical force was disturbed from 21h 23£m to 4h 23im (30th). Force less 49 divisions, 55, 44, 73, 49, 52, 55, and 31 divisions. Minimum value 0.0024 parts of the force. XXI. 1844, April 17th. At 2h 20m, although cloudy, it was very bright at the north; same remark at 22h 20m. The declination disturbances extend nearly over the whole day. The deflection was at first west (between Oh 20m and 4h 20m) with a maximum value of 48 divisions (22') at 3h 10m; it then changed to the east, at 6b 04m it reached 52 divisions (23') ; up to 20h 20m the deflection was slightly to the east. The horizontal force was diminished early in the morning, attaining a first minimum at 2h 40m of 47 divisions; it increased for a short time, reaching at 4h 14m 52 divisions above the normal, the force again decreased and reached at 5k 47m the lowest value of 151 divisions (0.0055 parts); it remained below the normal value for several hours. At 19h 53m the diminution was 41 divisions. Vertical force disturbed from 3b to 8h (+23^m), force less 52 divisions, 58, 61, 66, 53, and 35 divisions. Minimum value 0.0022 parts of the force. XXII. 1845, January 9th. At 17k 20m an aurora visible. The declination magnet is deflected east and west alternately; first maximum east deflection at 16h 32m of 20 divisions ; following maxi- mum west at 17h 02™ of 11 divisions; following east deflection about 20 divisions 12m later; next west deflection at 17h 22m 21 divisions; at 19h 56m the deflection again east 32 divisions; at 21h 38™ it is west 40 divisions (18'), at 22h 20m it is east 33 divisions. The horizontal force between 15k 52m and midnight is considerably smaller than the normal value, a minimum is reached at 17k 16m of 155 divisions (0.0056 parts of the force). The disturbances ceased between 2k and 3k on the morning of the 10th. The vertical force was disturbed at 17h, 20, 22, and 23k ( + 23^™), force greater 44 divisions, 31, 35, and 33 divisions. Average increase 0.0012 parts of the force. From the preceding detailed account of the condition of the declination and of the horizontal and vertical components of the magnetic force during auroral displays, we obtain the following general results : Each of the 22 auroras recorded was accompanied by a corresponding disturbance of the earth's magnetism, at least in one of the three elements; in one case the declination alone was affected, in another case only the horizontal force, and in a third only the vertical force. The latter force was less subject to disturbances than the other two elements. In the following table, showing the condition of the magnetic components during auroras, the first column contains the number of the aurora, the second the amount of declination deflection, the third its direction or the successive large excursions of the north end eastward or westward, the fourth the amount of the horizontal force disturbance expressed in parts of that force (a minus sign indicates less force than the normal belonging to that time, a plus sign indicates the reverse), the last column con- tains the amount of disturbance in the vertical force expressed in parts of that force ; the signs have the same signification as for the horizontal force. 5 32 APPENDIX. Number. Amount of deflection. Direction of deflection and excursions. Excess (-(-) or defect (— ) of horizontal furce. Excess (+) or defect ( — ) of vertical force. 1 24' E. W. E. W. E. —0.016 -(?> 2 —0.003 3 17 E. —0.005 —0.004 4 + 0.002 —0.002 5 22 W. —0.004 6 67 E. —0.010 —0.003 7 18 W. E. W. E. —0.005 —0.002 8 26 W. E. W. —0.010 —0.004 9 9 W. 10 22 W. E. —0.007 11 33 E. W. E. W. + 0.013 +0.005 12 8 E. W. E. W. —0.003 —0.001 13 —0.001 14 9 W. —0.002 15 13 E. W. —0.002 16 15 E. W. E. —0.002 17 16 W. —0.003 18 13 E. W. —0.003 19 7 W. —0.002 —0.001 20 27 E. W. E. W. —0.004 —0.002 21 23 W. E. 5 0.006 —0.002 22 18 E. W. E. W. E. W. E. —0.006 +0.001 The action on the declination magnet appears to be that of alternate deflections either way from the normal position; in 5 cases the deflection was west, in 2 cases east, more frequently there were one or two successions of west and east deflections (or the reverse) in one instance even three ; these alternate excursions appear to be a characteristic sign. In 5 cases the tendency of the deflection was easterly, in 6 cases westerly, and in the remaining 8 cases in both directions. The average amount of deflection is 17'. With but one exception the uniform effect upon the horizontal force was to decrease it. In the exceptional case a decrease followed the increase ; in another case the reverse took place ; during one aurora there was at first a fall in the force, then a rise, and again a fall. The average depression of the horizontal force below the normal value was 0.005 parts of the force (0.021 in absolute measure). The effect upon the vertical force is small ; in 9 cases no disturbance occurred ; in general the force is less than the normal; there are two exceptions to this in the 13 cases. The average depression of the vertical force below its normal was 0.0007 parts of the force (0.009 in abso- lute measure), or irrespective of sign 0.0013 parts of the force. If we wish to compare the tabular differences in declination and horizontal and vertical force with the magnitude of the recognized disturbances, the latter are 4' and 0.001 (parts of the force) for either the horizontal or vertical component. Of the auroras noted, that of May 29, 1840, was in many respects the most remarkable, and the best observed both as to its appearance and as to its magnetic effect ; its study can be recommended to those who have occasion to test their theoretical views in reference to this phenomenon, and to ter- restrial magnetism. Its appearance at New Haven, Conn., has been described by E. C. Herrick (Sill. Jour., 1840, Vol. XXXIX, p. 194). It was seen over a great portion of the United States, in Canada, and England. See, also, description in the volume of the Toronto Observations; also an extract from the proceedings of the British Association (Sill. Jour. Vol. XL, p. 337) ; also (p. 338 ibid.) note on the same by the Astronomer Royal. The total number of auroras which occurred at Philadelphia was much greater than the number given above, as has already been stated. At Toronto the annual distribution of the phenomenon over the same period of time, and for three years beyond the close of the record at Philadelphia, is as follows : — In 1840 (from March) on 23 nights. 1841 1842 1843 1844 1845 1846 1847 1848 36 14 16 20 19 27 29 66 APPENDIX. 33 These figures seem to indicate the existence of a period of frequency, probably of eleven years as conjectured by Prof. Wolf, the least number probably occurred in 1843, if we make an allowance for invisibility of the phenomenon cither by daylight or by cloudy weather. Between June, 1840, and July, 1845 (incl.), there were seen, according to the Toronto record, 109 auroras. The disturbances at Philadelphia on the dates of their appearance have been classified as follows : The numbers give the relative proportion to the total number, which latter is expressed by 1 00 ; the average numbers are given resulting from the examination of the disturbances of the decli- nation, the horizontal and the vertical force. Number of cases. No record at Philadelphia 19 None of the elements disturbed 30 But very few disturbances 20 An ordinary number of disturbances 14 An unusual number of disturbances 17 The number of unusual disturbances is therefore less than one-fifth of the total amount, and in fully one-half of the cases the magnetic elements were either not at all or but very slightly affected. PART VIII. INVESTIGATION SOLAR-DIURNAL VARIATION AND OP THE ANNUAL INEQUALITY OP THE VERTICAL COMPONENT OP THE MAGNETIC FORCE. (35) DISCUSSION SOLAR DIURNAL VARIATION, AND OP THE ANNUAL INEQUALITY OP THE VERTICAL COMPONENT OF THE MAGNETIC FORCE AT PHILADELPHIA. THE necessary data for this investigation are given in the preceding Part (VII), which contains the normals resulting from the reduction of the observations to the same temperature (66° Fah.), from the allowance for irregularity in the progressive change and the exclusion of all recognized disturbances. Owing to the greater irregularity in the indications of the vertical force instru- ment, and the comparatively small number of observations at odd hours, the normals are given for the even hours only ; the observations at odd hours, however, are used to improve those taken at the intermediate even hours by means of a suitable pro- cess of interpolation. The tabular numbers are expressed in scale divisions, one division being equal to 0.000033 parts of the vertical force, or equal to 0.000423 in absolute measure. Increasing numbers denote decrease of force. The hours count from midnight to midnight to 24 hours ; the number of minutes the observations are made later than the full hour are given in the last column for each month. NORMALS OF THE VERTICAL FORCE FOR JULY. Year. 0" 1 2 3 4 5 6 7 8 9 10 11" 1841 1842 1843 1844 703 683 691 816 811 697 672 692 804 806 687 664 692 805 802 671 659 686 798 793 667 657 679 784 783 664 650 672 782 780 Means' 722 717 712 703 698 692 Noon 13 14 15 16 17 18 19 20 21 22 23" Min. 665 643 662 780 776 676 643 658 773 781 680 647 659 783 791 698 663 666 799 805 708 677 677 808 809 706 682 685 811 816 +17 +17} +23i +23} 687 688 693 706 717 721 +20.4 1 Let reading for any even hour = n for the year 1844, for the odd hours preceding and following n p & nf, mean np-\-nf np+ny — 2 — ~; hence mean for the even hour J (n + -- 8 February —198 +033 —132 —165 +099 +231 +264 +396 + 198 —264 —330 —132 March —178 +086 —046 —112 +086 +119 +251 +317 +020 —178 —145 —211 April —353 —155 —122 —023 +175 +274 +274 +340 +241 —023 -•-320 —320 May —412 —346 —214 +049 +247 +280 +346 +445 +313 +016 —313 —412 June —528 —297 —198 —033 +198 +396 +594 +462 +363 —066 —429 —462 S3 July —571 —406 —241 +056 +221 +419 +584 +551 i +386 —043 — 406 —538 August — 485 —386 —287 —089 +109 +406 +736 +571 +340 —023 —386 —485 September —469 —304 —271 —205 +092 +323 +521 +521 +356 +026 —271 —337 October —099 +066 ! —000 —099 +231 +198 +198 +198 —033 —198 —264 —198 November —043 _043 —142 —109 +086 +122 +254 +221 —010 —076 —109 —109 December —059 +139 +040 —059 +040 +139 +205 +205 —092 —290 —191 —125 Year —287 —115 —131 — OG8 +129 j +257 +366 +377 +165 —121 —282 —290 Summer —469 —317 —221 —040 +175 +350 +508 +482 +333 —020 —353 —426 Winter —106 +086 —040 —096 +082 +162 +224 +274 —000 —221 —211 —155 Multiplying the above numbers by Y=12.83, we obtain the solar-diurnal varia- tion in absolute value. TABLE IV. — REGULAR SOLAR-DIURNAL VARIATION or THE VERTICAL FORCE IN ABSOLUTE MEASURE. A greater force than the mean is indicated by a plus sign, a less force by a minus sign. The first two places of decimals 0.00 are placed on the side. 1841-5. 0" 2 4 6 8 10 Noon. 14 16 18 20 22h +20™. 6 January —076 +305 +051 —034 —034 +220 +220 +389 —118 —415 —289 —203 February —254 +042 —170 —212 +127 +296 +338 + 508 +254 —338 —423 —169 March —229 +110 —059 —144 +110 + 152 +321 +406 +025 —228 —186 —271 April —452 —198 —157 —030 +224 +351 +351 +436 +309 —030 —410 —410 ^ May —529 —444 —275 +064 +317 +360 +444 +571 +402 +021 —402 —529 o June —677 —380 —254 —042 +254 +508 +761 +592 +465 —085 —550 —592 d July —732 —520 —308 +072 +283 +537 +749 +706 +495 —055 —520 —690 August —622 —495 —368 —114 + 140 +520 +943 +732 +436 —030 —495 —622 September —601 —389 —346 —263 +118 +415 +668 +668 +457 +034 —347 —431 October —127 +085 —000 —127 +296 +254 +254 +254 —042 —254 —338 —254 November —055 —055 —182 —140 +072 +157 +326 +'J83 —013 —098 —no —140 December —076 +178 +051 —076 +051 +178 +263 +263 —118 —372 —245 —161 Year —368 —148 —168 —087 +165 +329 +470 +483 +212 —156 —364 —372 Summer —601 —406 —284 —051 +224 +448 +651 +618 +426 —025 —453 —546 Winter —136 +110 —051 —123 +106 +207 +288 +351 —000 —283 1 —271 —199 Annual Inequality in the Diurnal Variation of the Vertical Force. — If we examine the average curve of the diurnal variation as observed throughout the year, and shown on diagram (A) by a full black line, we find the principal maximum value about 1 P. M., and the principal minimum value about 9| P. M. ; besides these characteristic values there is an indication of a secondary maximum about 2 A. M., and of a secondary minimum about 4 A. M. Dividing the year into a summer OF THE MAGNETIC FORCE. 45 and winter season, the diagram exhibits the diurnal variation in summer to be a curve of but one maximum and one minimum occurring about noon and midnight respectively, whereas in winter the double feature of the curve becomes very con- (A.) DIURNAL VARIATION OF THE VERTICAL FORCE IN SUMMER, WINTER, AND FOR THE WHOLE YEAR. + 500 x-v 400 g 300 •3 20° •| ICO * 0.000000 | 100 "o 200 1 30° fe 400 — 500 / "'•• v , ,•• \ • •-""/ ? _^.^- A \ • A '//,.' ^"' \ i *. \ \ *•'•' vv $' \ y\ •by "* -xf '/ \\ 4i*X / \ \ \^ ^ — •* 5 X'"'' •' ...... .-- **• 0" 2 4 6 8 10 a 14 16 18 20 22 24" (+20m.6) 1 Philadelphia mean time. spicuous, the secondary maximum and minimum occurring about 2 and 6 A. M. respectively. The phenomenon, in the two seasons, changes therefore from a single to a double crested curve. The semi-annual change of the diurnal variation is better shown in diagram (B) , which contains the difference from the annual curve in summer and winter, viz. : — 0" 2 4 6 8 10 Noon. 14 16 18 20 22" (+20-.6) Summer —182 —201 —90 +28 +46 +93 +142 +105 +168 +101 —71 —136 Winter +181 +202 +91 —28 —47 —95 —142 —103 —165 —100 +71 +135 (B.) SEMI-ANNUAL INEQUALITY IN THE DIURNAL VARIATION OF THE VERTICAL FORCE. + 200 160 120 080 040 | 0.000000 040 080 12° 160 — 200 -""""~ \ / \ f *-S ps / \ s \ \ fllft Vy ~ / N, / \ \/ v (-•^ v / •*— T__^ A / >s. / \ / ' § N -^ \ / \ / \, / \ \ ^^ / \ 0" 2 4 6 8 10 § 14 16 18 20 22 24 (+20».6) I Philadelphia mean time. 46 DISCUSSION OF THE VERTICAL COMPONENT At 5| A. M. and 7 P. M. there is no change in the diurnal variation throughout the year ; at the hours 2 A. M. and 4 P. M. the change is a maximum, viz : range equal 0.000403 parts and 0.000333 parts of the force, or equal 0.00517 and 0.00427 when expressed in absolute measure. The turning epochs of the annual inequality as found from the hours 2 A. M. and 4 P. M. are derived from the following table, in which the numbers are expressed in parts of the force ; the numbers in the last column were obtained by changing the sign of the afternoon difference before taking the mean. 2 A. M. 0.000. Differences. 0.000. 4 P. M. 0.000. Differences. 0.000. Mean difference. 0.000. January .... February .... +238 +033 +086 +353 +148 +201 —092 +198 + 020 —257 +033 145 + 305 +058 +173 — 155 — 040 +241 +076 058 May —346 297 —231 — 182 +313 +363 + 148 +198 —190 190 July August . . September .... —406 —386 —304 +066 —291 —271 —189 +181 +386 +340 +356 —033 +221 + 175 +191 — 198 —256 —223 —190 + 190 November .... December .... —043 + 139 +072 +254 —010 —092 —177 —257 +125 +256 Mean —115 +165 The figures in the last column are represented by the equation Aa = : + 0.000260 sin (0 + 86°) + 0.000031 sin (20 + 180°) the angle 0 counting from January 1st at the rate of 30° a month. According to this expression the transition of the inequality from a positive to a negative value, and vice versa, takes place in the first quarter of April and October, or about 17 days after the equinoxes. The retardation of the phenomenon in the declination, horizontal and vertical force is, therefore, 10, 22, and 17 days respectively, or 16 "days on the average. Analysis of the Solar-Diurnal Variation of the Vertical Force. — For greater facility of the investigation, and for purposes of comparison, the numbers of Table I. have been expressed analytically. The angle 0 counts from midnight at the rate of 15° an hour. For January, A. = 714d.2 + 4.8 sin ( e + 134° 09') + 5.5 sin (2 0 + 224° 22') + 0.8 sin (30 + 61°) For February, A, = 712d.O + 7.5 sin (9 + 91° 47') + 5.1 sin (20 + 226° 22') + 1.6 sin (SO + 273°) For March, A. = 703d.6 + 5.5 sin ( e + 98° 24') + 3.6 sin (29 + 220° 22') + 0.7 sin (36 + 95°) For April, A, = 701d.3 + 10.5 sin ( 0 + 89° 12') + 2.2 sin (20 + 175° 59') + 1.3 sin (30 + 232°) For May, A. = 693d.5 + 13.1 sin (0 + 85° 17') + 1.9 sin (20 + 144° 31') + 1.8 sin (30 + 278°) For June, A, = C89d.O + 15.8 sin (6 + 81° 22') + 3.1 sin (20 + 193° 56') + 0.4 sin (39 + 210°) OF THE MAGNETIC FORCE. 47 For July, A, = 704". 7 + 17.4 sin (9 + 86° 30') -f 2.6 sin (29 + 174° 16') + O.T sin (39 + 300°) For August, A, = 703d.3 + 17.1 sin (9 + 81° 10') + 3.7 sin (20 + 215° 50') + 0.5 sin (39 + 75°) For September, A, = 708d.8 + 14.3 sin (0 + 73° 57') + 2.9 sin (20 + 210° 24') + 0.3 sin (39 + 165°) For October, A, = 691d.O + 6.1 sin (9 + 119° 48') + 3.1 sin (20 + 236° 28') + 1.1 sin (30 + 210°) For November, A, = 689d.7 + 4.4 sin ( 0 + 83° 33') + 3.0 sin (20 + 254° 00') + 0.0 For December, A, = 701d.2 + 4.5 sin ( 0 + 133° 49') + 4.3 sin (20 + 231° 57') + LO sin (30 + 63°) 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 diurnal variation : — For summer, A, = 700d.l + 14.6 sin (0 + 83° 40') + 2.5 sin (20 + 191° 01') + 0.5 sin (30 + 255°) For winter, A, = 702d.O + 5.1 sin ( 0 + 108° 54') + 4.0 sin (20 + 229° 58') + 0.0 For year, A, = 701d.O + 9.7 sin (0 + 90° 17') + 3.0 sin (2 0 + 216° 22') + 0.2 sin (30 + 255°) The following comparison may serve to show the general representation of the observations by the analytical expressions : — COMPARISON FOR AUGUST. Observed. Computed. Difference. 0" 20°>.6 718 718.2 0 2 715 715.1 0 4 712 711.3 +1 6 706 707.0 —1 8 700 699.9 0 10 691 690.0 +1 12 ' 681 683.0 —2 14 ' 686 684.3 +2 16 ' 693 693.5 0 18 ' 704 705.0 —1 20 ' 715 713.9 +1 22 " 718 718.4 0 The summer months are better represented than the winter months ; in May the difference is below half a scale division ; in the winter season in several instances it rises to 3, and in one case to 4 scale divisions. Diagram C exhibits the diurnal variation, observed and computed, for the six summer months. Diagram D the same for the six winter months. 7 48 DISCUSSION OF THE VERTICAL COMPONENT (C). SoLAR-DltTKNAL VARIATION OF THE VERTICAL FORCE, APRIL TO SEPTEMBER, 1841 TO 1845. (Expressed in scale divisions.) 11 = 0.000033 parts of the force. April. May. June. July. August. 691 3 5 679 7 1 9 3 701 1 5 3 3 7 5 5 9 7 7 1 9 9 693 11 1 5 13 3 7 15 5 9 7 1 689 3 1 5 3 7 5 9 7 11 9 1 3 705 — September. I I 0" 2 6 8 10 g 14 16 18 20 22 24" Philadelphia mean time. OP THE MAGNETIC FORCE. 49 (D). SOLAR-DlURNAL VARIATION OP THE VERTICAL FORCE, OCTOBER TO MARCH, 1841 TO 1845. (Expressed in scale divisions.) 1" = 0.000033 parts of the force. -3 - • 3 .2 _ / • "\ S o - • / f \ - 7 9 October. 691 0 3 - • • / ' X^ '•> \ \ \ / ; 2 3 4 5 6 7 8 9 \ '—^ November. C90 1 - ""—-•, [ 7 •^v \ J ^ " 3 2 . '. — "" / . \» '•-' — • 5 4 • x '— N ./ / \ - 7 6 9 December. 701 <5 I . >- * .^ * \ / „ 3 8 - . / / - 5 0 . ( / / _ 7 2 0 4 2 - / :\ / /" >- - 9 January. 6 4 8 6 - >^ ? / \ \ / *- 0 8 y •. \ f 2 0 4 712 4 - f / \N x_ 2 - February. 4 6 6 8 ^ \ / / •^"^ \ \ /- 8 0 0 2 2 704 - • ./ • \ \ \ / - March 4 6 - / • "*** -^ •\ • i) 8 10 - . \ / •_ ,0 *•*•'•** * •c 12 _ - 5 "o to _ a a? *g 0" 2 10 § 14 16 18 20 22 24" I Philadelphia mean time. 50 DISCUSSION OF THE VERTICAL COMPONENT The numerical values of the coefficients Bl Bz B3 in the general equation A.= A 4- Bl sin ( 0 + CJ + B2 sin (20 + (72) + B3 sin (30 + (73) expressed in parts of the horizontal force, are given in Table V. The first three decimals (0.000) have been placed in front of the table. TABLE V. Month. B, B2 B, January 158 181 026 February 247 168 053 March 181 119 023 April 346 073 043 May 432 063 059 June 521 102 013 July . 574 086 023 August o 564 122 016 September 472 096 010 October 201 102 036 November 145 099 000 December 148 142 033 Summer . 482 082 016 Winter 170 132 001 Year . 320 099 007 The next table contains the numerical values of Bt B2 B3 expressed in absolute measure, and the angles Cl C% C3 obtained by the addition of 180° to their pre- ceding values, so as to make increasing values correspond to increasing force. The first two decimals for B are placed at the head of the columns. TABLE Y] [. Month. B, 0.00 c, B2 0.00 C2 B3 0.00 C3 January . 203 314009' 233 44022' 034 2410 February 317 271 47 216 46 22 068 93 March 233 278 24 152 40 22 030 275 April 444 269 12 093 355 69 055 62 May 554 265 17 080 324 31 076 98 June 668 267 22 131 13 56 017 30 July 736 266 30 no 354 16 030 120 August 723 261 10 157 35 50 021 255 September 606 253 57 123 30 24 013 345 October . 258 299 48 181 66 28 047 30 November 186 263 33 127 74 00 000 December 190 313 49 182 51 57 042 243 Summer 618 263 40 106 11 01 021 75 Winter . 218 288 54 169 49 58 002 Year 410 270 17 127 36 22 008 75 The next diagram (E) exhibits the general feature of the diurnal inequality for the year and its summer and winter season, as computed by means of the preceding formulae. The greatest difference between the observed and computed values at any one hour is but 2j scale divisions at 2 A. M. in the winter season, and 1 1 divisions at the same hour in the annual curve. The absence of the secondary wave in the early morning hours during summer is as conspicuous as its presence OF THE MAGNETIC FORCE. 51 in the winter season ; in the annual curve there is barely a trace of it left. We also recognize again the earlier occurrence of the maximum and minimum values in winter and their later appearance in summer. If we examine the resulting curves at Toronto1 we find there the secondary morning fluctuation equally well marked (E). REGULAR SOLAR-DIURNAL VARIATION OF THE VERTICAL FORCE FOR WINTER, SUMMER, AND THE WHOLE YEAR. ' (In parts of the force.) 0" 6 8 10 14 16 18 20 22 24" Philadelphia mean time. in summer and winter ; and if we inquire into this feature for each year separately, we find great irregularities between the hours 14 (Toronto astro'l time) and 22; in 1843 the secondary maximum and minimum is plainly developed, in 1844, and espe- cially in 1845, it cannot be traced. Diagram (F) exhibits the curves for Philadel- phia for each year. In 1841 and 1842 the curves are smooth, in 1843 the wave appears well marked, in 1844 it is just perceptible. These apparent irregularities are probably due to imperfections in our instruments ; on the other hand, if we take the Philadelphia series, there may be a cyclic appearance and disappearance of this wave. * VoL III of the Toronto Observations, Table LXVIII. 52 DISCUSSION OF THE VERTICAL COMPONENT DIAGRAM (F). 647 49 51 53 55 57 j 69 61 63 65 67 69 71 73 75 77 79 81 s 664 66 68 92 70 94 72 96 74 98 76 700 78 02 80 04 82 84 86 88 90 92 / ' » / x /, — 2 / X* I/ A ^ ; / 7 •^\ ^: •4 0" 2 4 6 8" A. M. Philadelphia mean time. Table VII exhibits the computed times of the principal maximum and minimum of the vertical force, together with the amount of difference from its average daily value at these epochs, expressed in scale divisions ; also the time and amount of the early morning secondary fluctuation traceable only in the winter months ; for these last values the diagrams have been made use of. TABLE VII. Maximum at Amount in scale divisions. Minimum at Amount in scale divisions. Time elapsed between max & mlii Secondary maximum at Amount Secondary Minimum at Am't. Secondary ranj;e. January Febrnary March April May June July August September October November December 13h07ra 13 41 12 46 13 52 14 34 13 09 13 33 13 02 13 23 11 16 12 35 12 31 — 8".5 —11.5 — 8.9 —10.2 —13.1 —17.2 —18.2 —20.8 —16.8 — 7.6 — 7.4 — 7.8 19h27™ 20 21 21 04 22 04 22 58 22 35 23 10 23 06 23 20 20 34 19 59 19 09 + 9d.4 +10.6 + 6.7 +11.8 +12.6 +16.2 +17.3 +15.5 +12.6 + 8.7 + 3.9 + 7.8 6h20"> 6 40 8 18 8 12 8 24 9 26 9 37 10 04 9 57 9 18 7 24 6 38 2J" 1* 3 —4 + 1 —1 71 41 6j +2 +4 +2 6 3 3 2 1 3 —1 +1 —3 5 ? +1 +3 fl 2 2 4 Summer Winter Year 13 29 12 43 13 02 —15.8 — 8.2 —11.9 22 55 20 08 21 25 +14.1 + 7.6 + 9.7 9 26 7 25 8 23 2 —1 6 +2 3 The extreme variation in the time of the maximum in the course of a year is 3h 18m, and of the minimum 4h 11'". At Toronto the occurrence of the maxima and minima is later than at Phila- OF THE MAGNETIC FORCE. 53 delphia ; from Table LXVIII, Vol. Ill of the Toronto Observations, we find the maximum at 5h, a secondary minimum at 14h, a secondary maximum at 18b, and the minimum at 22h ; the maximum is therefore apparently delayed at Toronto 4h, the minimum 4^h, the secondary wave is likewise retarded by about 4 hours. This epochal difference I take, most likely, to be a distinctive feature due to the localities ; there is also a remarkable difference in the amount of the diurnal range as will presently appear. The degree of sensibility in the adjustment of the centre of gravity of the instrument affects most the latter difference, whereas the epochal difference may be supposed to depend, in a measure, upon the sensibility of the magnet in regard to changes of temperature and consequent changes of magnetism. The change in the adopted value of the correction for 1° of change in the tem- perature (expressed in scale divisions) as used in present reduction (10.8), and as used in four volumes of record and reduction (13.5) gives us the means of a partial test of the effect on the epochs, we find from the plates in Vol. IV the time of the maximum 1| P. M. and of the minimum 11| P. M., which though somewhat nearer to the Toronto epochs, still leave a large discrepancy. TABLE VIII. — AMPLITUDE OF THE DIURNAL VARIATION OF THE VERTICAL FORCE. Maximum 0.00 Minimum 0.00 Range 0.00 Maximum 0.00 Minimum 0.00 Range 0.0 January ..... February ..... March ..... April ...... May .... 028 038 029 034 043 057 060 068 055 025 024 026 031 035 022 039 042 054 057 051 041 029 013 026 059 073 051 073 085 110 117 119 097 054 037 052 359 484 377 431 555 725 7ri9 878 712 323 313 330 398 447 288 500 535 686 733 654 532 369 166 332 0757 0931 0660 0931 1090 1411 1502 1532 1244 0692 0479 0662 July August ..... September ..... October ..... December ..... .Summer ..... Winter Year 052 027 039 046 025 032 098 052 071 667 349 503 597 322 410 1264 0671 0913 In parts of the force. In absolute measure. The diurnal range at Toronto is very much less than at Philadelphia; in 1841-42 the range was but one-half of that observed at Philadelphia, and for later years (see Table LXVIII of Vol. Ill of the Toronto Observations) the ranges compare as fol- lows: Toronto 0.00019, Philadelphia 0.00071. In diagram G the diurnal range for each month is exhibited (expressed in parts of the force). 54 DISCUSSION OF THE VERTICAL COMPONENT (Q). DIURNAL RANGE OF THE VERTICAL FOKCK (In parts of the force.) 0.001200 1100 1000 0900 0800 0700 0600 0500 0400 0.000300 ,/ '\ / \ / \ i / / 1 JL / A / \ J \ / \ / \ / JflltltttJljM Table IX contains the times when the mean value of the vertical force is reached each day— arranged for monthly averages. In some months the average daily value is attained four times, but generally only twice. The table contains the two prin- cipal epochs (one A. M. the other P. M.) ; those produced by the secondary wave can easily be made out by means of the preceding diagrams. TABLE IX. — PRINCIPAL EPOCHS OF MEAN VERTICAL FORCE. A.M. P.M. January ..... February March ...... 8" 58™ 7 42 8 27 6 15 5 55 6 36 6 08 7 30 7 51 6 34 8 11 8 27 3»47"> 5 16 4 53 6 13 6 21 6 04 6 10 6 04 6 28 4 19 4 49 3 39 May July September ..... October. ..... December . 6 43 7 52 7 06 6 13 4 29 5 33 Winter ...... Year The next table contains the computed diurnal variation of the vertical force, expressed in absolute measure ; compared with Table IV, it shows the differences between the observed and computed values. OF TIIE MAGNETIC FORCE. 55 TABLE X. — COMPUTED SOLAR-DIURNAL VARIATION OF THE VERTICAL FORCE, EXPRESSED IN ABSOLUTE MEASURE. The first two places of decimals 0.00 are placed on the side; + indicates more, — less than the monthly average. 1841-45. Oh 2i 4 6 8 10 Noon. 14 16 18 20 22" +20"».6 January +025 +165 +123 —030 —046 + 161 +355 +258 —080 —351 —376 —203 February —072 —085 —178 —123 +063 +258 +436 +465 +203 —241 —444 —283 March —135 —017 —008 —072 —013 +207 +372 +304 +059 —165 —275 —258 April —385 —266 —165 +008 +216 +338 +402 +436 +317 —025 —385 —491 May —516 —461 —262 +068 +309 +372 +448 +554 +423 —000 —402 —533 g Juiie —601 —419 —245 —042 +241 +533 +711 + 681 +398 —068 —503 —685 c July _706 1 —550 —279 +034 | +305 + 537 +723 +744 +457 —051 —499 —714 August —630 —499 —338 —157 +144 +563 +859 +804 +414 —072 —448 —639 September —512 —431 -351 —207 +076 +431 + 673 +677 +436 +047 —321 —516 October — 055 +030 —030 —008 +165 +309 +300 +182 —004 —237 —377 —275 November —059 —089 —148 —131 +017 +207 +313 +233 +046 —123 —161 —106 December —008 +110 +097 —008 —008 1+182 +330 +203 —114 —313 —304 —165 Year —309 —211 —152 —055 +123 +343 +495 +457 +211 —131 —368 —402 Summer —558 —440 —275 —050 +212 +465 +634 +651 +410 —025 — 423 —600 Winter —046 +017 —021 —051 +034 +216 +338 +271 +021 —228 —321 -216 A graphical representation of the above tabular numbers is given in diagram H, based upon the three variables : the hour of the day, the month, and the difference of vertical force from the normal monthly value. The contour lines of the mag- netic surface differ 0.001 of vertical force (in absolute measure). Full lines indi- cate greater value, lines of dashes less value than the normal, dotted lines represent the normal value. 56 DISCUSSION OF THE VERTICAL COMPONENT (H). DIFFERENCES FROM ITS NORMAL TALUE OF THE VERTICAL FORCE, FOR EACH HOUR AND MONTH. (Expressed in absolute measure.) 0.00. January November December January 14 16 18 20 22 24" Philadelphia mean time. Annual Inequality of the Vertical Force. — The minor and irregular disturbances in the adjustment of the magnetometer, as well as the effect of the progressive and secular changes, tend to make the determination of the annual inequality in the vertical force a task of some delicacy, and the results deduced from our series of observations should be considered as approximate. Taking the monthly normals of the years 1842, 1843, and 1844, the only years which could be made complete, and correcting the monthly means for 42 scale divisions of annual increase, the following table was formed : — OF THE MAGNETIC FORCE. 57 MONTHLY NORMALS. Year. January. Feb'u'ry. March. April. May. June. July. August. Sept'ber. October. Nov'ber. Dec'ber. 1842 . 658 707 658 659 656 655 662 677 682 706 716 710 1843 . 702 710 i 691 707 686 678 677 691 708 710 742 746 1844 . 731 728 760 756 756 758 796 773 1 801 778 770 749 Mi'nn . 697 715 703 707 699 697 . 712 714 730 731 743 735 Corr'd +19 +16 |+12 + 9 + 5 + 2 — 2 — 5 — 9 —12 —16 —19 Cdrr'd m. 716 731 715 716 704 699 710 709 721 719 727 716 Mean monthly val. _ l _16 0—1 +11 +16 + 5 + 6 — 6 -4 —12 — 1 The vertical force appears, therefore, to be greater in May, June, July, and August, and less in the remaining months; the range is about 32 scale divisions = 0.00105 parts of the force, or 0.0135 in absolute measure. PART IX. INVESTIGATION LUNAR INFLUENCE ON THE MAGNETIC VERTICAL FORCE, INCLINATION, AND TOTAL FORCE. (59) INVESTIGATION OP THE INFLUENCE OP THE MOON ON THE MAGNETIC VERTICAL FORCE. THE method of discussion of the lunar effect on the vertical component of the magnetic force in no way differs from that employed for the horizontal component, which latter has been explained in Part VI. The series of observations available for the lunar discussion extends from Febru- ary, 1841, to June, 1845, inclusive. From February, 1841, to October, 1843, the observations are bi-hourly ; from October, 1843, to the end of the series they are hourly. The record of May, 1841, is not quite complete, and in January, February, ami March, 1843, but one observation a day is recorded. As increasing numbers demote a decrease of force, a positive sign of the tabulated differences between monthly normals and each individual undisturbed reading (at the normal tempera- ture) indicates a greater force than the normal value, a negative sign indicates the reverse. 30 scale divisions being the limit beyond which difference an observation has been considered as belonging to the class of disturbances, all differences here recorded are below this limit. One scale division is 0.000033 parts of the force. The tabular numbers are expressed in scale divisions. In tracing out the lunar effect upon the vertical force we have to contend with greater irregularities than was experienced in the case of the horizontal force. The vertical force magnetometer is more subject to changes, and the correction for tem- perature far exceeds that of the horizontal force. The total number of observations and differences formed in the inquiry of the dependence of the force upon the moon's hour angle is 19513, which distribute themselves over the months and years as follows : — TABLE I. — XUMBER OF OBSERVATIONS FOR LUNAR DISCUSSION. Month. 1S41. 1842. 1843. 1844. 1845. Sam. January .... February .... March .... April .... May .... 239 257 256 207 219 258 283 267 280 275 239 '207 198 286 255 246 275 281 284 246 298 299 304 250 288 296 308 314 292 580 528 541 544 549 502 512 617 529 581 535 568 607 596 559 611 554 539 581 602 571 1362 1540 1584 1854 1960 1890 1428 1416 1373 1765 1698 1643 July September .... October ..... November .... December .... 2780 3179 3397 6699 3458 19513 62 DISCUSSION OF THE INFLUENCE OF THE MOON TABLE II. — DISTRIBUTION OF NUMBERS ACCORDING TO WEST- ERN AND EASTERN HOUR ANGLES OF THE MOON. Year. Western hour angles. Eastern hour angles. 1841 1842 1843 1844 1845 1388 1588 1694 3321 1728 1392 1591 1703 3378 1730 Sum 9719 9794 TABLE III. — DIFFERENCES FROM THE MONTHLY NORMALS, 1841. Western hour aiigles of the moon. U. cul. 1841. 0" 1 2 3 4 5 6 7 8 9 10 11" . February +3 +1 +3 —2 +8 —5 0 +1 —1 +4 —2 —3 March —6 +5 —3 + 6 +1 +9 —6 +2 —7 —3 0 April —1 +1 0 +2 —1 +3 —1 0 —1 +7 —7 +2 May +5 —1 +2 +1 +4 +7 +3 +4 +4 +1 +5 —5 June 0 —6 —5 + 2 —8 —2 +5 £ —4 +8 +7 0 July —4 +8 —6 +2 Y +5 —3 +1 —1 —7 +5 — 4 August —1 —5 +1 —6 —5 —6 0 —1 0 +1 —3 —1 September +3 +3 +1 +1 —6 +5 —2 +2 0 —4 —3 —3 October —8 —1 —2 0 —2 —1 —4 0 +1 0 +6 +4 November —3 +3 —1 +3 —3 —3 —6 —5 +1 —3 +4 —1 December —5 —4 0 —1 —2 —5 —3 —3 +5 +2 —3 ' —2 Year —1.5 +0.4 —0.9 +0.7 —2.0 +0.6 —1.5 —0.2 —0.3 +0.7 +0.5 —1.2 Eastern hour angles. L. cal. 1841. 0 1 2 3 4 5 6 7 8 9 10 11" . February —3 —2 +1 —3 +3 —2 +4 —3 +3 +2 + 2 —1 March 0 +2 +3 +7 —1 +8 —7 +1 —8 0 —6 +1 April 0 —4 0 0 —2 —1 —3 —1 —1 1 +1 May —2 —2 +1 —6 +1 —5 +1 —8 +3 —10 +3 —4 June +1 +5 —2 +1 +5 —7 +5 +3 —1 —6 —2 —8 July +1 —4 +6 0 —2 +5 —2 +5 —2 +2 —2 +7 August +1 —1 +2 0 0 +1 +4 +5 +2 +4 +1 +3 September —3 +2 —4 0 —1 +2 —1 —2 +1 0 +2 +8 October + 3 +4 +4 —1 +1 +1 +4 —1 +2 —2 —4 —4 November +2 —3 +1 0 —1 +5 —3 +5 0 +8 —2 +2 December +6 +6 +1 +6 +3 +2 +3 —10 0 —10 0 7 Year +0.5 +0.3 +1.2 +0.3 +0.7 +0.7 +0.6 —0.7 —0.1 —1.2 —0.8 —0.2 ON THE MAGNETIC VERTICAL FORCE. 63 TABLE IV. — DIFFERENCES FROM THE MONTHLY NORMALS, 1842. Western hour angles of the moon. U. cul. 1842. 0 1 2 3 4 5 6 7 8 9 10 11" January — 6 0 —1 —7 —6 —5 +4 +8 —3 + 9 +4 +7 February ' — 3 0 +5 —6 +4 —3 —9 —11 +6 +3 +7 +6 March +5 +2 +3 0 +2 —4 —6 —6 +4 —1 —5 +5 April +2 +2 0 0 —11 —2 —5 —3 —1 -1 ! —5 May —5 +3 —3 +2 —3 +4 0 0 +5 —2 -3 —7 June +3 +5 +3 +2 —2 +1 +3 —3 +8 —7 -6 —7 July —2 —4 —3 • +2 —6 —2 0 +2 +4 +3 -7 +1 August +2 —2 +1 -4 0 +1 —3 —2 +1 —1 -8 —3 September +3 —5 —2 1 —7 —5 —3 +3 —1 —3 +6 _ -4 +5 October 0 0 —3 +4 +1 —5 +4 —1 +1 +4 —3 0 November —3 +1 +1 —3 +2 +2 +3 0 +1 —4 +2 0 December —1 —3 +1 +4 ! —4 i +4 —1 +1 +4 —1 —3 +3 Year —0.4 —0.1 +0.2 —1.1 —2.3 —1.0 —0.6 —1.3 +1.8 +0.7 +2.0 +0.4 Eastern hour angles. L. cul. 1842. 0 1 2 3 4 5 6 7 8 9 10 11" January +5 +4 —3 —1 —5 -3 —2 +3 —4 +4 0 —4 February +6 +1 —2 +4 —3 +3 —1 —7 —1 +9 —5 +3 March —4 +3 —4 —3 —4 —6 +2 —4 +2 +2 1 0 +4 April —3 +4 —1 +6 +3 +10 +1 +4 +1 0 +6 +2 May +5 +2 +6 —4 0 —2 —2 —1 —12 +8 -8 +3 June 0 —6 0 —8 +3 —5 —3 —9 +3 —5 +3 —5 July +2 +1 +2 +1 —3 —1 +1 —2 —1 0 —3 —1 August +5 —3 —1 0 +1 0 +2 0 +2 0 +7 —3 September —6 —2 —1 +2 —1 —1 +2 +9 +2 +12 +4 —3 October —9 +1 —1 —3 0 —3 +2 +2 +2 +2 0 +2 November +3 —1 —6 —2 —2 0 +2 +2 +1 +3 —1 0 December +5 -1 —2 —1 —1 0 0 0 —5 +1 —3 —3 Year +0.8 | +0.2 —1.3 —0.8 —1.0 —0.7 +0.3 —0.3 —0.8 +3.0 0.0 —0.4 64 DISCUSSION OF THE INFLUENCE OF THE MOON TABLE V. — DIFFERENCES FKOM THE MONTHLY NORMALS, 1843. Western hour angles of the moon. 1843. U. cul. 0 1 2 3 4 5 6 7 8 9 10 11" January February March April May June July August September October November December +10 +6 +1 +7 0 —3 +2 +1 +1 —3 —3 —1 +5 —2 +8 +2 +2 +2 +14 +4 —4 +4 +2 0 +3 +2 +3 —5 +3 +2 +5 +5 +3 —3 —2 +8 +3 +2 +4 +4 —3 +2 +1 0 +1 —3 +2 +8 0 +4 +2 —2 +2 0 —3 +1 +3 +5 +4 —1 +2 +1 —5 +2 +3 —3 —7 —4 +1 +1 —5 —1 +1 +3 +3 +3 —2 0 —1 +3 —4 +3 + 1 —4 —3 3 +1 0 —2 + 1 +4 —1 +2 +1 —2 +4 +1 —3 —5 +4 —1 —2 —3 —3 0 —2 Year +2.4 +1.3 +3.0 +0.4 +2.0 +1.3 +0.8 —1.1 —0.2 — o.e +0.9 —1.7 Eastern hour angles. 1843. L. cnl. 0 1 2 3 4 5 6 7 8 9 10 IP January February March April May June July August September October November December —2 —2 +2 —5 +2 —2 —5 —1 —2 0 —6 0 —4 —2 0 —1 0 0 —1 —3 +1 —5 0 —3 +1 —3 —2 —6 0 +2 —5 —1 —1 +1 +1 —5 +2 —3 —1 —6 0 +3 —3. —6 —1 +2 —5 —1 —3 0 —1 —2 +5 +1 —2 —6 +5 —2 0 —1 —3 +1 +2 +1 —3 —2 +4 0 —3 —3 +4 +4 +2 +2 +3 0 —1 —3 0 +2 0 +1 —4 +1 +2 ±1 —2 +6 +2 +3 +4 —2 +3 —2 —3 +1 +2 —2 +4 +2 +4 0 +1 0 Year —1.9 —1.2 —1.6 —0.9 —1.2 —1.7 —0.6 —0.8 +0.5 0.0 +0.0 +1.1 In making up the annual means, the October, November, and December values have received double weight; they are derived from double the number of observations. OX THE MAGNETIC VERTICAL FORCE. 65 TABLE YI. — DIFFERENCES FROM THE MONTHLY NORMALS, 1844. Western hour angles of the moon. tJ. cul. 1844. 0 1 2 o 4 5 6 7 8 9 10 11" January +1 +5 0 0 —2 —1 —2 —1 —1 —1 —1 0 February —1 —1 +1 +1 0 —1 +3 +3 0 +1 —1 —3 Maivh —4 —5 + 2 —1 +3 —1 +1 —2 +1 —1 0 —3 April +1 —1 +5 +2 0 +1 +3 +3 0 —2 —3 May 0 +1 +1 +1 +1 +2 +3 +2 +2 +1 +2 0 Jnne +1 —2 —2 —2 —2 —1 —2 0 0 +3 0 +3 July +2 +2 +2 +1 +1 +3 0 0 —2 0 0 0 August +1 —2 2 —2 —1 —2 —2 —6 —2 —4 1 0 September +1 + 1 +1 —1 —1 —1 —2 0 —2 —2 —3 0 October 0 0 0 —2 —1 —3 —2 —3 —3 —2 0 +3 November +2 +5 +5 +3 +2 0 +1 +3 +1 0 —2 —3 December —1 0 +1 +3 0 —1 —1 —1 +2 +1 0 0 Year +0.3 +0.3 +1-2 +0.3 0.0 —0.4 —0.6 —0.2 —0.1 —0.3 —0.7 —0.5 Eastern hour angles. L. cul. 1844. 0 1 2 3 4 5 6 7 8 9 10 11" January —1 —4 —2 —3 —2 —2 —3 0 +1 —2 —1 +3 February —3 —1 +2 +1 0 —3 —4 —2 +1 —1 —1 0 March —6 +1 —4 —2 —1 +4 +2 +5 +2 —4 —4 —1 April —1 +1 +1 0 —1 —1 —3 —1 0 —1 —1 +2 May —1 2 0 —2 —2 —1 —3 —2 —2 —1 0 0 June +1 0 +1 +1 0 +1 +2 —2 —1 +2 0 —1 July +1 0 0 +1 0 —1 +1 +2 +1 0 +1 +1 August —2 —1 —1 0 +2 +6 +4 +4 +3 +2 +1 September —1 —2 —1 —1 0 0 +2 +3 +2 +1 +4 +4 October +4 +1 +1 +1 0 +2 +1 +1 0 +3 +1 +3 November —4 —\ —1 +1 +1 +1 +2 +1 0 +1 +3 +2 December +2 +2 +1 +2 0 +1 —3 —3 —1 —1 +2 —1 Year —1.0 —0.8 —0.2 —0.1 —0.3 +0.6 —0.2 +0.5 +0.5 —0.1 +0.4 -f-1.0 66 DISCUSSION OF THE INFLUENCE OF THE MOON TABLE VII. — DIFFERENCES FROM THE MONTHLY NORMALS, 1845. Western hour angles of the moon. 1845. U. cul. 0 1 2 3 4 5 6 7 8 9 10 11" January February- March April May June +1 —2 0 —2 —1 +1 +2 0 —1 —4 +1 +1 +2 —3 —2 —2 +2 +2 +2 —2 +1 0 +1 0 +2 —2 +1 —1 +2 —2 +4 —2 0 —1 +3 0 +1 0 +2 0 —2 —1 +1 0 +1 +2 —1 —2 +1 —2 +5 0 —3 0 0 0 +4 +1 —4 +3 —1 +4 +4 —1 —3 +2 +1 +2 0 —2 Mean —0.5 —0.2 —0.2 +0.3 0.0 +0.7 0.0 +0.3 —0.2 +0.2 +1.0 +0.3 Eastern hour angle. 1845. L. cul. 0 1 2 3 4 5 6 7 8 9 10 11" January February March April May June 0 +2 +4 —1 1 —1 —1 +3 +2 +1 +1 —5 +3 —1 —2 0' —3 +3 +2 —3 +1 0 +2 —2 —2 —2 +2 —1 0 +1 —2 —1 +1 0 0 1 —1 —1 +2 —2 —1 +1 —1 0 +2 —2 0 —2 0 +1 +1 —4 —1 —2 +1 +1 +3 —3 —2 —3 +1 0 +2 0 0 3 + 1 —1 +3 Mean +0.5 +0.9 —1.0 —0.2 —0.3 —0.3 —0.2 —0.2 —0.3 —0.3 —0.9 0.0 Before we combine the above results of years and parts of years, it is desirable to inquire into the variability of the lunar effect in summer and winter. Consider- ing the months from April to September (inclusive) as summer months, and those from October to March (inclusive) as winter months, and combining the differences from the monthly normals in each year according to the number of observations, we obtain the following results : — TABLE VIII. — LUNAR-DIURNAL VARIATION IN SUMMER AND WINTER, 1841 TO 1845. (Expressed in scale divisions.) Western hour angles. U. cul. 0 1 2 3 4 5 6 7 8 9 10 11" Summer Winter +1.0 —0.8 —0.1 +0.8 +0.6 +0.9 +0.2 +0.1 —1.0 +0.4 +0.8 —0.6 —0.4 —0.5 —0.4 —0.5 +0.1 0.0 —0.1 +0.1 +0.6 +0.4 —1.0 0.0 Eastern hour angles. L cnl. 0 1 2 3 4 5 6 7 8 9 10 111- Summer Winter —0.5 —0.2 —0.8 +0.3 —0.3 —0.9 —0.9 —0.4 +0.3 +0.4 —0.4 +0.2 +0.4 —0.5 +0.4 —0.7 +0.6 —0.5 +0.6 0.0 +1.1 —1.1 +0.8 0.0 These numbers are sufficiently irregular to indicate that we cannot hope to deduce any separate results for the seasons, the number of observations (about 9800) being altogether insufficient. We can therefore in our general combination ON THE MAGNETIC VERTICAL FORCE. 67 of the annual means give equal weight to the results from the six months of hourly observations in 1845, and to the results from the twelve months of bi-hourly obser- vations in 1842; compared with these results, those of 1844 have the weight two. TABLE IX. — RECAPITULATION OP THE ANNUAL MEANS EXHIBITING THE LUNAR-DIURNAL VARIA- TION FROM OVER 19,500 OBSERVATIONS BETWEEN FEBRUARY, 1841, AND JUNE, 1845, INCLUSIVE. Western hour angles. Weight. Tear. U. cul. 0" 1 2 3 4 5 6 7 8 9 10 11" 1 1 1 2 1 1841 1842 1843 1844 1845 —1.5 —0.4 +2.4 +0.3 —0.5 +0.4 —0.1 +1.3 +0.3 —0.2 —0.9 + 0.2 +3.0 +1.2 —0.2 +0.7 —1.1 +0.4 +0.3 +0.3 —2.0 —2.3 +2.0 0.0 0.0 +0.6 —1.0 +1.3 —0.4 +0.7 —1.5 —0.6 +0.8 —0.6 0.0 —0.2 —1.3 —1.1 —0.2 +0.3 —0.3 + 1.8 —0.2 —0.1 -0.2 +0.7 +0.7 —0.6 —0.3 +0.2 +0.5 +2.0 +0.9 —0.7 +1.0 —1.2 +0.4 —1.7 —0.5 +0.3 Mean +0.10 +0.33 +0.75 +0.15 —0.38 +0.20 —0.42 —0.45 +0.15 +0.07 +0.50 —0.53 Eastern hour angles. Weight. Tear. L. cul. 0" 1 2 3 4 5 6 7 8 9 10 11" 1 1 2 1 1841 1842 184H 1844 1845 +0.5 +0.8 —1.9 —1.0 +0.5 +0.3 +0.2 —1.2 —0.8 +0.9 +1.2 —1.3 —1.6 —0.2 —1.0 +0.3 —0.8 —0.9 —0.1 —0.2 +0.7 —1.0 —1.2 —0.3 —0.3 +0.7 —0.7 —1.7 +0.6 —0.3 +0.6 +0.3 —0.6 —0.2 —0.2 —0.7 —0.3 —0.8 +0.5 —0.2 —0.1 —0.8 +0.5 +0.5 —0.3 —1.2 +3.0 0.0 —0.1 —0.3 —0.8 0.0 +0.6 +0.4 —0.9 —0.2 —0.4 +1-1 + 1.0 0.0 Mean —0.35 —0.23 —0.52 —0.30 _0.40 —0.13 —0.05 —0.17 + 0.05 +0.22 —0.05 +0.42 If we represent these values graphically, we find the general shape of the curve to be similar to that of the horizontal component, it is double crested with a prin- cipal maximum a little before the upper culmination, and a principal minimum about 3| hours after the lower culmination of the moon; the average epoch of the vertical force tide is, therefore, about one and a half hours apparently in advance of the culminations. The secondary wave is very feeble, its greatest value (A.) LUNAR-DlURNAL VARIATION OP THE VERTICAL FORCE, 1841 TO 1845. I U. C. L. C. 0123456789 10 11 0123456789 10 11 12 68 DISCUSSION OF THE INFLUENCE OF THE MOON happens about 9h, western hour angle, and its least value about three hours before, giving a range of nearly one-tenth part of the principal range. The observed values for the hours 8, 9, 10 (west) however, seem to indicate that the secondary wave is really larger, but in the present case apparently reduced by the accidentally low values at the hours 11 and 12. The following expression has been deduced to express the lunar-diurnal variation of the vertical force : — Fc = —0.04 + 0.27 sin (0 + 72°) + 0.20 sin (20+ 134°) 6 counts from the upper culmination, westward ; F<£ is expressed in scale divisions. The smooth, full curve in the diagram is computed by the formula ; the differences between the observed and computed values are sufficiently well exhibited in the diagram. The probable error of any single hourly value is +0.20 scale divisions. In the following expression M signifies millionth parts of the force : — M M M Fc = _ 1.3 + 8.9 sin (6 + 72°) + 6.6 sin (20 + 134°). Maximum value of F<£, 28m before the upper culmination, = + .38 scale divisions; minimum value at 15h 30m, — 0.43 scale divisions, hence lunar-diurnal range 0.81 scale divisions = 0.000027 parts of the force — 0.00034 in absolute measure. This range is so small that the correction for temperature due to a change of but 0°.08 would surpass it. We have already seen that we cannot bring a sufficient number of observations to bear upon any part of the entire series, and are therefore not in a condition to pursue this subject of the lunar effect to any greater length. At Toronto the curve is also double-crested with maxima three and a half hours after the moon's transits, but compared with Philadelphia the principal and second- ary waves appear exchanged. The range at Toronto is 0.000012 parts of the force, nearly one-half of the Philadelphia range ; we have already noticed a similar differ- ence of range in the solar-diurnal variation, the Toronto range of which was also about one-half of that at Philadelphia. In connection with this it may be well to state that the dip at Toronto is 75° 15', and at Philadelphia 71° 59.' Lunar Effect upon Inclination and Total Force. — The combination of the hori- zontal and vertical components to inclination and total force, is effected by the formulae: — <£> X. Y in which expressions X— horizontal force, F= vertical force, <£>= total force, and 0 = inclination. The discussion of the observations for dip, in Part XII, gives the value 0 = 71° 59', answering to the year 1843. Column 2 of the following table is derived from the preceding Table IX, after changing the scale divisions into their equivalents of parts of the force, one division being equal to 0.000033 ; column 3 is formed similarly from Table VIII, of Part VI, one division being equal to 0.0000365. Columns 4 and 5 contain the corresponding values of the lunar-diurnal ON THE MAGNETIC VERTICAL FORCE. 69 variation of the inclination and total force, the former expressed in seconds, the latter in parts of the total force. The letter M, heading columns 2, 3, and 5, sig- nifies units of the sixth place of decimals or millionth parts of the force. TABLE X. — LUNAR-DIURNAL VARIATION OF THE INCLINATION AND TOTAL FORCE. O &Y *X A* hour angle. Y X A« * M. M. ft M. U. C. + 3.3 +11.0 —0.5 + 4.0 1 +10.9 +18.2 —0.4 +11.6 2 +24.7 +32.8 —0.5 + 25.4 3 + 5.0 +40.1 —2.1 + 8.3 4 —12.5 + 7.3 —1.2 —10.6 5 + 6.6 +25.5 —1.1 + 8.4 6 —13.9 0.0 —0.9 —12.6 7 —14.8 + 3.6 —1.1 —13.0 8 + 5.0 —21.9 +1.6 + 2.4 9 + 2.3 —14.6 +1.0 + 0.7 10 +1B.5 — 7.3 +1.4 +14.2 11 —17.5 + 3.6 —1.3 — 15.4 L.O. —11.6 +25.5 —2.2 — 8.1 i — 7.6 + 7.3 —0.9 — 6.2 2 —17.2 +14.6 —1.9 —14.1 3 — 9.9 —11.0 +0.1 — 9.9 4 —13.2 + 3.6 —1.0 —11.5 5 — 4.3 —25.5 +1.3 — 6.3 6 — 1.7 — 47.4 +2.8 — 6.1 7 — 5.6 —21.9 +1.0 — 7.2 8 + 1.6 —18.2 +1.2 — 0.3 9 + 7.3 —36.5 +2.7 + 3.1 10 — 1.7 — 3.6 +0.2 — 1.9 11 +13.9 + 7.3 +0.4 +13.3 The numbers in column 2 are deduced from observations between 1841 and 1845, those in column 3 from observations between 1840 and 1845, the difference, how- ever, is immaterial as far as it refers to the dip and total force, the lunar variations being nearly the same for a few adjacent years. The total number of observations employed in the combination is 41558. The lunar-diurnal variation in the dip is well represented by the formula, 0C =__ 0".06 + 0".86 sin (0 + 156°) + 1".30 sin (26 + 206°) the ^corresponding curve, as well as the observed values, are exhibited in the follow- ing diagram. The heavy smooth curve is the Philadelphia computed variation, the dotted curve the Toronto variation, inserted here for comparison. The correspond- ence between these curves is certainly remarkably close considering the minuteness of the lunar effect and the somewhat long process of deducing it. 70 DISCUSSION ON THE MAGNETIC VERTICAL FORCE. (B.) LUNAR-DIURNAL VARIATION OF THE INCLINATION. + 2". 8 2.4 2.0 1.6 1 2 .8 .4 .0 .4 .8 1.2 1.6 2.0 — 2.4 M f fc^i. I LA # I v a, '•3 •8 .£• -3 U. C. L. C. 0" 12345 6789 10 11 012345 6 7 89 10 11 12" Maxima at 8h and 20h (principal), minima at 3h (principal) and 13|h. Total range 3". 6. Probable error of any single hourly representation + 0".7. The lunar diurnal variation in the total force is represented by the equation : — MM M $£= — 1-3 + 8.9 sin (6 + 63°) + 6.3 sin (20 + 84°) an expression not differing much from V& owing to the large dip. The observed and computed values of — * are shown in the diagram, which nearly resembles that <2> of the vertical force. (C.) LUNAR-DlURNAL VARIATION OP THE TOTAL FORCE. -f-U.UUUUi/ 24 21 18 II1 1 1 1 ( I 1 I i /i M 15 e 12 / t —i \ jf| .2 09 | 06 / \\ /I K •' \ * /I /\ VII 'I / / \ •3 03 •e o.oooooo i ffl JE f °3 06 N / 1 .^ / / V 09 12 LJ I/ \ /W-_r/ 15 —0.000018 I/ v —"^ iii i t i i i i i i 0. C. L. C. 012345 6 7 89 10 11 01 2345 67 89 10 11 12 Maxima at |h (principal) and IP; minima at 7|h and 17h (principal). Total range 0.000026. Probable error of any single hourly representation ± 0.000006. SMITHSONIAN CONTEIBUTIONS TO KNOWLEDGE. 186 DISCUSSION OF THE MAGNETIC AND METEOROLOGICAL OBSERVATIONS MADE AT THE GIEABD COLLEGE OBSERVATORY, PHILADELPHIA, IN 1840, 1841, 1842, 1843, 1844, AND 1845. FOURTH SECTION, COMPRISING PARTS X, XI, AND XII. DIP AND TOTAL FORCE. ANALYSIS OF THE DISTURBANCES OF THE DIP AND TOTAL FORCE ; DISCUSSION OF THE SOLAR DIURNAL VARIATION AND ANNUAL INEQUALITY OF THE DIP AND TOTAL FORCE ; AND DISCUSSION OF THE ABSOLUTE DIP, WITH THE FINAL VALUES FOB DECLINATION, DIP AND FORCE BETWEEN 1841 AND 1845. BY A. D. BACHE, LL.D., F.R.S., MEM. CORR. ACAD. BC. PARIS ; PKEST. If AT. ACAD. SCIENCES; StTPEBlHTEHDENT IT. 8. COAST SCBVET. [ACCEPTED FOR PUBLICATION, MAT, 1864.] PART X. ANALYSIS OF THB DISTURBANCES OF THE DIP AND TOTAL FORCE. 1 December, 1864. ANALYSIS DISTURBANCES OF THE DIP AND TOTAL FORCE. IN the preceding discussion of the disturbances of the horizontal and vertical components of the magnetic force at the Girard College Observatory, the laws of their variations, as far as they have been recognizable from the series, were brought out and discussed, and this suffices, perhaps, in most cases, for any future applica- tion of theory, or for the purpose of testing hypotheses ; but as it is also desirable for other comparisons to deduce the corresponding results for dip and total force from previous researches, it is proposed here to present the results of this combina- tion numerically and in tabular form. This combination is effected by the formulae: — /AY AJTx A* AY AX Av = sin 0 cos 6 ( -^ v~ ) and — = sin 26 -^ + cos 2d—v~ \ i .A I

adjoining column. The corresponding values of A0 and — were then easily com- puted for each disturbance, whether it occurred in both components or in one only. Trustworthy contemporaneous readings of the two magnetometers commence with February, 1841, and continue to the close of the series in June, 1845 ; there is, however, an interval of time between the readings of the instruments which we are obliged to disregard ; it amounts to but 5 minutes, the bifilar magnetometer having been read so much later. As there is not generally a contemporaneous disturbance in the vertical and hori- zontal force, the total number of disturbed values obtained by the process explained above and employed, is necessarily much greater than it was for either of the com- ponents; it becomes therefore necessary to fix upon some limit of recognition for a disturbed value of the dip, and also of the total force. This is best done by the adoption of that value which will separate an equal proportion of disturbed values from the total number, as was done in the components ; for the vertical component one in every 10.5 observations, for the horizontal component one in every 19.3 observations was separated as a disturbed value between February 1, 1841, and June 30, 1845; on the average, therefore, one in every 15 observations should be separated in the dip and total force series. During the time mentioned the number of observations of vertical force was 22,092, and of horizontal force 22,150, from which we should accordingly derive nearly 1470 disturbances. Now the number of computed values of A0 and of — — is 2362, hence, marking in each set the 1470 highest values, the limit of + 1/1 is reached in the dip, and +0.00094 in the total force, which constitute the limiting values at and beyond which disturbances are recognized in each element. To render the series of disturbance results homo- geneous, the disturbances at the odd hours after October, 1843, have been omitted. At Toronto the limit for the recognition of disturbances in the dip(1) was I/O, and in the total force 0.0004 parts of the force. ANALYSIS OF THE DISTURBANCES OF THE INCLINATION. The number of values of inclination differing +1/1 or more from their normal amount, and which constitute the disturbance values is 1446, those arc variously combined in the following tables, and, when necessary, arc separated into two classes, those which increase and those which decrease the inclination ; to the former the sign + is prefixed, to the latter the sign — . The aggregate and mean amount of disturbances are expressed in minutes of arc. The columns containing the num- ber of disturbances are headed with the letter n. When ratios are given, they 1 Vol. Ill, p. xliii. DISTURBANCES OF THE INCLINATION. exhibit the proportion of the amount of disturbances during any given sub-period to the average amount of disturbances during the whole period. In the first and three subsequent tables the values for the first five months of 1841 are omitted, as there are no adequate means of extending the series beyond four full years. TABLE I. — AGGREGATE AMOUNT AND NUMBER OP DISTURBANCES OF THE INCLINATION IN EACH MONTH, DIVIDED INTO DISTURBANCES WHICH INCREASE AND WHICH DECREASE THE INCLINATION. The values in brackets for January, February, and March, are interpolated, and are the average values of the corresponding months of the year preceding and the year following. 1841 and 1S42. 1842 and 1S43. 1843 and 1844. 1844 and 1845. Sums 1S41 to 1845. Ratio. + . - D + n - n + n - • + Tl - n + u - u + - July . . 24. '5 16 15/710 31.'5 17 17.'2 9 16/9 in 4. '4 a l.'l 1 12/8 8 74/0 44 50/1 30 0.55 0.73 August . 34.5 1614.0 !) 13.6 8 33.5 22 20.8 13 0.0 0 42.4 2'.) 3.9 3 111.3 (jti 51.4 34 0.83 0.75 Sept'ber . 104.7 40 14.4 10 20.7 9 114.8 64 8.4 4 7.2 6 25.4 14 10.9 6 159.2 07 147.3 Be 1.19 2.15 October . 69.7 3213.6 9 19.5 11 40.2 27 7.2 4 10.1 l! 10.0 7 21.8 11 106.4 54 85.7 53 0.79 1.25 November 79.9 31 12.4 B 35.2 16 6.8 4 9.9 7 3.9 3 40.3 10 1.5 1 165.3 73 24.6 }:>, 1.24 0.35 December 75.5 36 27.2 18 12.4 8 9.5 6 29.6 20 4.9 4 31.7 17 37.3 2( 149.2 SI 78.9 48 1.12 1.15 January . 72.3 3340.5 •24 (50.7) (27) (23.2) (14) 29.1 21 5.9 4 23.7 10 7.7 5 175.8 91 77.3 47 1.31 1.12 February 101.6 45140.3 26 (57.6) (26) (22.2) (14) 13.7 8 4.2 3 5.8 3 0.0 0 178.7 82 66.7 41! 1.34 0.97 March 31.6 17 27.0 n; (37.5) (20) (18.6) (12) 43.4 24 10.3 8 19.1 13 5.5 4 131.6 74 61.4 -Ill 0.99 0.92 April . . 52.2 26 142 in 56.0 30 17.4 10 29.5 2o 12.0 6 29.4 17 6.6 4 167.1 03 50.2 30 1.25 0.73 May . . 41.1 26 30.5 15 39.7 18 34.5 18 7.9 4 1.6 1 22.0 10 4.7 3 110.7 57 71.3 37 0.83 1.04 June . 39.9 21 21.8 i:; 9.1 7 20.7 11 1.4 1 5.9 4 23.8 17 8.8 5 74.2 40 57.2 33 0.56 0.84 It would appear that during the colder season both sets of ratios present greater values ; between September and February (inclusive) this ratio is, on the average, 1.16, and in the other months it is 0.84. Of the ratios decreasing the inclination the September and November values are somewhat anomalous, the first too high, the second too low. The following table gives the annual inequality of the disturbances, irrespective of their sign. TABLE II. — AGGREGATE AMOUNT AND NUMBER OP DISTURBANCES OP THE •INCLINATION IN EACH MONTH. The series comprises the four years between July, 1841, and July, 1845. The ratio is that of the sums. Sum. • Ratio. July 124/1 74 0.62 162 7 100 0 SO September 306.5 153 1.51 192 1 107 0 95 189.9 86 0 94 December 228.1 129 1.13 253 1 138 1 25 245.4 125 1 22 March 193.0 114 0.96 217.3 123 1 07 May 182.0 94 0.90 June 131.4 79 0.65 The ratio near the autumnal equinox is the greatest of all, that abdut the vernal equinox is a little below the average value ; the least value occurs probably near the summer solstice. 6 A N A L Y S I S OF THE TABLE III. — AGGREGATE AMOUNT AND NUMBER OF DISTURBANCES OF THE INCLINATION IN THE DIFFERENT YEARS OF OBSERVATION. The ratios exhibit the variation due to the eleven year inequality. Year. Sum. n Ratio. 1841—1842 1842 1843 P99.'l 742.1 288.2 396.2 503 408 184 227 1.65 1.22 0.47 0.66 1843—1844 1844 1845 ...... The minimum amount of disturbances in the eleven year circle, therefore, occurred in the beginning of 1844. TABLE IV. — AGGREGATE AMOUNT AND NUMBER OF DISTURBANCES IN EACH YEAR ARRANGED FOR DISTURBANCES INCREASING THE INCLINATION AND FOR THOSE DECREASING IT; TOGETHER WITH THE RATIOS OF THE SUMS. Sum. . Sam. Ratio. Year. + n - n + - 1841—1842 1842—1843 1843—1844 1844—1845 727.'5 383.5 217.8 274.7 338 197 136 157 271.'6 358.6 70.4 121.5 165 211 48 70 1.81 0.96 0.55 0.68 1.32 1.74 0.35 0.59 The minimum of the eleven year period is equally well marked in the disturb- ances increasing and in those decreasing the inclination. The sum of the positive values (1603/5) is to the sum of the negative values (822/1) as 1.95 to 1. At Toronto, between 1844 and 1848, this ratio was 5.6 to 1 ; the ratio, however, increased from 2.7 to 8.5 to 1 during this time. In Tables V and VI, which exhibit the diurnal inequality of the disturbances, the whole series between February, 1841, and June, 1845, is employed. The sums, numbers, and ratios given do not in strictness apply to the even hours, but to an epoch 20 minutes later. TABLE V. — AGGREGATE AMOUNT AND NUMBER OF DISTURBANCES OF THE INCLINATION, DISTRIBUTED OVER THE EVEN HOURS OF THE DAY, AND RATIO SHOWING THE DlURNAL INEQUALITY OF THE SUM. Hour. Sam. n Ratio. 0 ... 244.8 183.2 .184.1 170.8 154.8 213.6 250.7 260.9 232.4 245.0 253.6 238.0 143 110 111 98 94 116 141 131 130 126 121 125 1.11 0.83 0.84 0.78 0.70 0.99 1.14 1.19 1.06 1.11 1.16 1.09 2 4 .... 6 8 10 Noon .... 14 .... 16 18 .... 20 22 DISTURBANCES OF THE INCLINATION. The hourly disturbances of the inclination exhibit a regular progression ; between 1 A. M. and 1 1 A. M. the numbers fall short of the mean hourly value, and during the remaining afternoon and night hours they exceed this average value. The minimum occurs near 8 A. M. and the maximum near 8 P. M. There is, however, an indication of a superimposed smaller progression which, owing to the short series of observations, is not distinctly brought out. At Toronto we have a double pro- gression, and the above ratios approximate to it. At Philadelphia a secondary maximum probably occurs about noon and a secondary minimum about 4 P. M. Table VI shows the ratios at the different hours for disturbances increasing and disturbances decreasing the inclination. TABLE VI. — AGGREGATE AMOUNT AND NUMBER OF HOURLY DISTURBANCES OF THE INCLINATION FOR INCREASING AND DECREASING VALUES ; AND MEAN EFFECT OF DISTURBANCES. Ratio of Minis. Excess or Average Hour. Snm. Sam. increasing dig- diurnal effect + a u + - turbances. of disturbances. 0 163. T) 94 80.'9 49 1.15 1.06 +83.'0 +0.'06 2 101.7 61 81.5 49 0.71 1.06 +20.2 +0.02 4 82.4 51 101.7 60 0.58 1.33 —19.3 —0.02 6 97.1 57 73.7 41 0.68 0.96 +23.4 +0.02 8 97.8 58 57.0 36 0.69 0.74 +40.8 +0.03 10 130.2 64 83.4 52 0.91 1.09 +46.8 +0.04 Noon 139.3 75 111.4 66 0.98 1.45 +27.9 +0.02 14 193.2 90 67.7 41 1.35 0.89 +125.5 +0.10 16 148.5 79 83.9 51 1.04 1.09 + 64.6 +0.05 18 178.7 86 66.3 40 1.25 0.87 +112.4 +0.09 20 198.3 87 55.3 34 1.39 0.72 +143.0 +0.11 22 181.5 91 56.5 34 1.27 0.74 +125.0 +0.10 The disturbances which increase the inclination show a very regular single pro- gression (the value at 2 P. M. only being slightly anomalous) ; their minimum occurs at 4 A. M., and their maximum at 8 P. M. The disturbances decreasing the inclination are small in number at all hours, and show a tendency at double pro- gression ; principal maximum about noon, principal minimum about 8 P. M., second- ary maximum about 4 A. M., and secondary minimum about 8 A. M. At Toronto the results appear different, but it is absolutely necessary for effective comparison to have results from contemporaneous series. As at Toronto, the disturbances increas- ing the inclination greatly preponderate over those decreasing it ; the accumulated effect of this difference is shown in the column headed " Excess" (Table VI). At the hour 4 A. M. alone, we find the increasing disturbances inferior, at the hour 8 P. M. the difference has reached its maximum ; at Toronto this maximum occurred an hour or two after midnight. The last column of Table VI exhibits the average diurnal effect of the disturbances (exceeding l.'l their normal value), the plus sign indicating a preponderance of increasing dip ; the number of days is 1297. The distribution of the disturbances according to their magnitude for an equal increase of 1' is as follows: — 11 8 ANALYSIS. OF TIIE Between Number of disturbances. l.'l and 2.'1 1 1096 2.1 " 3.1 247 3.1 " 4.1 65 4.1 " 5.1 27 5.1 " 6.1 5 6.1 " 7.1 3 7.1 " 8.1 3 beyond none. ANALYSIS OP THE DISTURBANCES OF THE TOTAL FORCE. The number of values of total force differing 0.00094 parts of the force from its normal amount, and which constitute the disturbance values, is 1470, which have been combined in a manner similar to that of the disturbances of the dip ; an increas- ing total force is indicated by a + sign, a decreasing one by a — sign. The aggre- gate amount and mean amount of disturbances are expressed in parts of the force, and the letter n indicates the number of disturbances. In the tables of the annual inequality the series commences with July, 1841, in those of the diurnal inequality it commences with February, 1841. The ratios given are those of the aggregate amount. TABLE VII. — AGGREGATE AMOUNT AND NUMBER OP DISTURBANCES OP THE TOTAL FORCE IN EACH MONTH, DIVIDED INTO DISTURBANCES WHICH INCREASE AND WHICH DECREASE THE FORCE. The values in brackets for January, February, and March are interpolated, and are the average values of the corresponding months of the year preceding and the year following. 1841 and 1842. 1842 and 1S43. 1843 and 1844. -f n - n + n - n + n - n July . .02944 25 .04552 32 .01115 8 .02518 15 .00000 0 .00377 3 August .01239 10 .00438 4 .00758 5 .02658 24 .00830 8 .00200 2 September .01759 15 .02807 19 .02395 16 .06228 42 .01355 10 .00734 7 October •02658 20 .00697 6 .01148 10. .00410 4 .00663 5 .00585 5 November .02357 17 .02413 20 .00781 6 .00960 9 .01563 13 .02485 21 December .07598 47 .05026 35 .00715 7 .00898 7 .03267 28 .00645 6 January .06321 38 .04939 36 (.04792) (32) (.03222) (24) .03264 27 .01506 13 February .07043 50 .03481 28- (.04151) (30) (.01984) (Hi) .01259 10 .00486 4 March .01895 15 .02730 19 (.02711) (22) (.02574) (19) .03527 2!) .02419 19 April . .04122 28 .02820 19 .03523 24 .02084 18 .02181 19 .01940 14 May . .04586 27 .02443 16 .02697 17 .01736 14 .00977 6 .00000 0 June . .02777 21 .01191 11 .00561 3 .01038 7 .00342 3 .02193 20 1844 and 1845. Sums 1841 to 1843. Ratios. + n - n + n - n - + July . .iiosn.-, 8 .01076 9 .04864 41 .08523 59 0.56 1.28 August .04661 35 .01348 10 .07488 58 .04644 40 0.87 0.70 September .00715 5 .00108 1 .06224 46 .09877 69 0.72 1.48 October .00331 3 .00809 5 .04800 38 .02501 90 0.56 0.38 November .00000 0 .00100 1 .04701 36 .05958 51 0.54 0.89 December .01365 12 .00416 4 .12945 94 .06985 52 1.50 1.05 January .00210 2 .00543 4 .14587 99 .10210 77 1,68 1.53 February .00000 0 .00216 2 .12403 90 .06167 50 1.44 0.92 March .02489 20 .01231 11 .10622 86 .08954 68 1.23 1.34 April . .00513 4 .00463 3 .10339 75 .07307 54 1.20 1.10 May . .02511 12 .00211 2 .10771 62 .04390 32 1.24 0.68 June . .00270 2 .00108 1 .03950 29 .04530 39 0.46 0.68 DISTURBANCES OF THE TOTAL FORCE. 9 The ratios of the increasing disturbances of the force have a double progression, as have also those of the decreasing disturbances, though not so well marked. In- creasing disturbances show a principal maximum in January, a principal minimum in June, and a secondary maximum and minimum in August and November, respectively ; decreasing disturbances show a principal maximum in January, a principal minimum in October, and a secondary maximum and minimum in Septem- ber and May, respectively. It appears, therefore, that upon the whole we observe the same laws as at Toronto, viz : the disturbances increasing the force and those decreasing the force follow the same progressive monthly change, and exhibit maximum values about the equinoxes, and minimum values about the solstices. This last remark also applies to the results of the following table in which the annual inequality of the disturbances is given irrespective of sign. TABLE VIII. — AGGREGATE AMOUNT AND NUMBER OF DISTURBANCES OF THE TOTAL FORCE IN EACH MONTH AND RATIO OF SUMS. Sum. n Ratio. July .013387 0.12132 0.16101 0.07301 0.10659 0.39930 0.24797 0.18620 0.19576 0.17646 0.15161 0.08480 100 98 115 58 87 146 176 140 154 129 94 68 0.87 0.79 1.05 0.47 0.70 1.30 1.62 1.22 1.28 1.15 0.99 0.56 June ........ TABLE IX. — AGGREGATE AMOUNT AND NUMBER OP DISTURBANCES OF THE TOTAL FORCE IN THE DIFFERENT YEARS OF OBSERVATION. The ratios of the sums exhibit part of the eleven year inequality. Tear. Sum. n Ratio. 1841— 1H42 1842—1843 1843—1844 1844—1845 .78836 .51657 .32798 .20499 558 379 272 156 1.72 1.13 0.71 0.44 The minimum of the eleven year period, according to the above ratio, occurred probably in 1845. 2 December, 1804. 10 ANALYSIS OF THE TABLE X. — AGGREGATE AMOUNT AND NUMBER OF DISTURBANCES IN EACH YEAH (JULY TO JULY) ARRANGED FOR DISTURBANCES INCREASING AND DISTURBANCES DECREASING THE FORCE, WITH RATIOS OF SUMS. Sum. Sam. Ratio. Year. + n - n + - 1841—1842 1842—1843 1843—1844 1844—1845 .45299 .25347 .19228 .13870 313 180 158 103 .33537 .26310 .13570 .06629 245 199 114 53 1.75 0.98 0.74 0.53 1.67 1.32 0.68 0.33 The inequality of the eleven year period is equally well marked for disturbances increasing and for disturbances decreasing the total force. The sum of the positive values is 1.03744, and of the negative values 0.80046 ; increasing disturbances are therefore preponderating in the ratio of 1.3 to 1. In the year 1842-1843, however, decreasing disturbances were in excess over increas- ing ones, and at Toronto between 1844 and 1848, the general effect of the larger disturbances of the force was to decrease the total magnetic force more than to increase it. The excess in the different years appears to be rather irregular. The following tables exhibit the diurnal inequality of the disturbances, the* whole series (beginning with February, 1841) is employed. The sums, numbers, and ratios given apply to an epoch 20 minutes later than indicated by the tables. TABLE XI. — AGGREGATE AMOUNT AND NUMBER OF DISTURBANCES OF THE TOTAL FORCE, DISTRIBUTED OVER THE EVEN HOURS OF THE DAY, AND RATIO SHOWING THE DIURNAL INEQUALITY OF THE SUM. Hoar. Sum. n Ratio. 0 2 .19733 .20046 .20018 .17163- .13858 .13691 .15058 .19949 .14958 .13974 .13176 .16077 150 148 148 121 106 105 115 144 116 103 97 117 1.19 1.22 1.21 1.04 0.84 0.83 0.92 1.21 0.91 0.85 0.80 0.98 4 6 . . ' . 8 10 Noon 14 16 18 20 22 The hourly disturbances exhibit a regular double progression with a principal maximum at 2 A. M., and a principal minimum at 8 P. M., also a secondary maxi- mum about 2 P. M., and a secondary minimum abut 10 A. M. At Toronto these hours were respectively 3 A. M., 11 A. M., and 5 P. M., 9 P. M., showing an ex- change of the hours of the principal and secondary minimum ; the disturbance at the hour of maximum is about eleven times greater than at the minimum hour, whereas this proportion is but one and a half to one at Philadelphia. DISTURBANCES OF THE TOTAL FORCE. 11 TABLE XII. — AGGREGATE AMOUNT AND NUMBER OP HOURLY DISTURBANCES OP THE TOTAL FORCE FOR INCREASING AND DECREASING VALUES, RATIOS, AND MEAN EFFECT OF DISTURBANCES. Hour. Sum. + n Sum. n Ratio of sum. Differences or Minis. Average diurnal effect. + — 0 ... 2 . .10570 .08589 83 68 66 57 48 46 51 86 66 64 60 71 .09163 .11457 .11754 .08714 .07597 .07327 .079J64 .06866 .06294 .05094 .04953 .06286 67 80 82 64 58 59 64 58 60 39 37 46 1.22 0.99 0.95 0.97 0.72 0.73 0.82 1.50 1.00 1.02 0.95 1.13 1.18 1.47 1.51 1.12 0.97 0.94 1.02 0.88 0.81 0.66 0.64 0.80 +.01407 — 02868 — 03490 —.00265 —.01336 — 00963 —.00870 +.06217 +.02370 +.03786 +.03270 +.03505 +.000011 —.000022 —.000027 —.000002 — 000010 —.000008 —.000007 +.000049 +.000018 +.000029 +.000025 +.000027 4 . . 6 .... 8 . .08264 .08449 .06261 10 . Noon 14 . .06364 .07094 .13083 16 . .08664 18 . 20 . .08880 .08223 22 . .09791 The ratios of the increasing and decreasing disturbances appear to follow the same law, that is, the values at any hour appear to be complementary to one another, a high plus value corresponding to a low minus value ; the phenomenon is, however, not so distinctly brought out as from the longer series at Toronto. The last two columns contain the difference of the sums at each hour, and the average effect of the larger disturbances of the total force. From 1 P. M. to 1 A. M. the larger dis- turbances augment the total force ; from 1 A. M. to 1 P. M. they diminish it ; greatest augmentation at 2 P. M., greatest diminution at 4 A. M. The greatest augmentation is nearly twice as great as the greatest diminution, whereas at Toronto the opposite effect was observed. The distribution of the disturbances of the total force, according to their magni- tude for an equal increase of .00090 parts of the force, is as follows : — Between Number of disturbances. .00094 and .00184 1324 .00184 " .00274 122 .00274 " .00364 17 .00364 " .00454 4 .00454 " .00544 2 .00544 " .00634 0 .00634 " .00724 1 beyond none PART XI. SOLAR DIURNAL VARIATION AND ANNUAL INEQUALITY OP THE INCLINATION AND TOTAL FORCE. ( 13) SOLAR-DIURNAL VARIATION OF THE DIP AND TOTAL FORCE. To make the combination of the horizontal and vertical force components com- plete, there remains the discussion of the regular solar-diurnal variation and its annual inequality, of the resulting dip and total force. Table III, of Part V, contains the solar-diurnal variation, expressed in parts of the force, of the horizontal component, freed from the larger disturbances ; Table III, of Part VIII, contains similar information with regard to the vertical component. The numbers of these tables, however, cannot be combined directly, owing to the eleven year inequality which requires that the two sets of components should cover precisely the same interval of time. In the present case the table of the horizontal force extends from July, 1840, to July, 1845, a five year series; whereas the table of the vertical force extends over four years only ; a new table of monthly normals of the horizontal component was therefore prepared, in which the first year's obser- vations were omitted. This was done by the same method as had been followed in the preparation of the former annual values of Part V. The following table differs from that of Table I, of Part V, only in the number of observations employed, and extends from July, 1841, to July, 1845. TABLE I. — RECAPITULATION OF THE HOURLY NORMALS OF THE HORIZONTAL FORCE (EXPRESSED IN SCALE DIVISIONS) FOR EACH MONTH OF THE YEAR, AND FOR SUMMER, WINTER, AND THE WHOLE YEAR, BETWEEN JULY, 1841, AND JULY, 1845. 1841-45 Ob 1 2 3 4 5 6 7 8 9 10 11" +21 J" July 791 790 789 788 787 786 785 788 796 803 806 804 August 813 813 813 8] 2 811 809 808 815 825 835 837 830 September 829 827 830 829 826 824 821 830 842 850 853 852 October . 850 846 847 845 844 844 844 848 854 860 865 864 November 853 852 850 849 848 846 845 849 853 859 862 865 December 883 879 878 877 874 873 871 872 874 878 885 892 January . 905 902 902 901 899 899 899 898 900 908 914 918 February . 915 914 913 912 910 908 906 908 : 910 914 920 922 March 919 917 915 915 915 913 91 :J 915 920 927 931 936 April 945 944 944 942 940 938 938 940 948 958 965 966 May 947 946 944 942 942 940 938 944 954 961 960 956 June 972 972 972 972 969 966 962 968 973 980 983 980 Year 885.2 883.5 883.1 882.0 880.4 ! 878.8 877.4 881.2 887.4 894.4 898.4 898.8 Summer . 882.8 882.0 882.0 880.8 879.2 i 877.2 875.3 880.8 889.7 897.8 900.7 898.0 Winter . 887.5 885.0 884.2 883.2 881.7 880.5 879.5 881.7 885.2 891.0 896.2 899.5 12 16 SOLAR DIURNAL VARIATION The summer months comprise April to September, inclusive The winter October to May, One scale division equals 0.0000365 parts of the force. Increasing numbers denote decrease of force. 1841-1845 12" 13 14 15 16 17 18 19 20 21 22 23" +2U,, (.V.I, Mil July 797 788 782 780 779 783 788 791 793 793 793 793 August . 820 811 803 802 804 809 815 816 817 816 816 815 September 844 834 829 828 828 832 834 834 832 834 832 832 October . 866 860 856 854 854 854 854 854 855 853 853 852 November 861 858 853 852 851 853 851 851 852 852 853 853 December 894 889 885 880 878 878 879 880 882 884 884 883 January . 916 909 905 900 899 902 905 905 904 905 905 904 February . 925 920 915 912 915 915 916 919 921 917 915 915 March 934 930 923 918 921 923 924 923 921 920 921 920 April 960 957 947 944 943 944 948 948 949 950 947 947 May 951 943 938 938 938 939 945 947 949 949 948 945 June 974 969 962 961 on 965 970 971 971 972 973 973 Year 81)5.2 889.0 883.2 880.7 880.9 883.1 885.7 886.5 887.2 887.1 886.7 886.0 Summer . 891.0 883.7 876.8 875.5 875.5 878.7 883.3 884.5 885.2 885.7 884.8 884.2 Winter . 899.3 894.0 889.5 886.0 886.3 887.5 888.2 888.7 889.2 888.5 888.5 887.8 Subtracting each value from its respective monthly mean value and converting these differences into parts of the force, we obtain the numbers of Table II ; a + sign indicates a greater force than the normal value, a — sign a smaller one. The first three decimals are placed at the head of the table. TABLE II. — REGULAR SOLAR-DIURNAL VARIATION OF THE HORIZONTAL FORCE BETWEEN JULY, 1841, AND JULY, 1845. VALUES OF — x • 0.000 0" 1 2 3 4 5 6 7 8 9 10 11" +21 A* January —025 +085 +085 +121 +194 + 194 +194 +231 +158 —134 —353 —499 February —005 +032 +068 +105 +178 +251 +324 +251 +178 +032 —186 —259 Marcb +087 +160 +233 +233 +233 +306 +342 +233 +050 —205 —351 —534 April +110 +146 +146 +219 +292 +365 +365 +292 000 —365 —620 —657 May —036 000 +073 +146 +146 +219 +292 +073 —292 —547 —511 —365 Jane —056 —056 —056 —056 +054 +163 +309 +090 —092 —348 —457 —348 July —017 +019 +056 +092 +129 +165 +202 +092 —200 — 455 —565 —492 August +080 +080 +080 +117 +153 +226 +263 +007 —358 —723 —796 —540 September + 168 +241 +131 +168 +277 +350 +460 +131 —307 —599 —708 —672 October . +116 +262 +225 +298 +335 +335 +335 +189 —030 —249 —435 —395 November 000 +035 +109 +145 +181 +254 +291 +145 000 —220 —329 —439 December —091 +055 +091 +128 +237 +274 +347 +310 +237 +091 —164 —420 Year +027 + 088 +103 +143 +201 +259 +310 +171 1 —055 —310 —456 —469 Summer . +043 +072 +072 +116 +174 +247 +317 +116—209 —505 —610 —512 Winter . +014 +105 +134 +171 +226 +269 +305 +225 ' +098 —114 —303 —424 i 1 OP THE DIP AND TOTAL FORCE. 17 C .000 (Noon) 12" 13 14 15 16 17 18 19 20 21 22 23" +21 J» January —427 —171 —025 +158 +194 +085 —025 —025 +011 —025 —025 +012 February —370 —186 —005 +105 —005 —d05 —042 —151 —224 —078 —005 —005 March —461 —315 —059 + 123 +014 —059 —096 —059 +014 +050 +014 +050 April —438 —328 +036 +146 +182 +146 000 000 —036 —073 +036 +036 May — 182 +109 +292 +292 +292 +256 +036 —036 —109 —109 —073 +036 June —129 +054 +309 + 346 +346 +200 +017 —019 —019 —056 —092 —092 July —236 +092 +311 +384 +421 +275 +092 —017 —090 —090 —090 —090 August —175 +153 +445 +482 +409 +226 +007 —029 —066 —029 —029 +007 September —380 —015 +168 +204 +204 +058 —015 —015 +058 —015 + 058 +058 October . —468 —249 —103 —030 —030 —030 —030 —030 —067 +006 +006 +043 November —293 —183 000 +035 +072 000 +072 +072 +035 +035 000 000 December —493 —310 —164 +018 +091 +091 +055 +018 —055 —128 —128 —091 Year —838 —112 +100 +189 +183 +103 +006 —023 —046 —043 —028 —003 Summer . —257 +011 +262 +309 +309 +192 +025 —019 —044 —063 —030 —008 Winter . —416 —236 —059 +068 +057 +014 —012 —030 —048 —023 —023 +004 To render the preceding table uniform with the similar one of the vertical com- ponent, the values at the odd hours will, hereafter, be dropped, their weight is less than one-half of that of the even hours ; the small difference in the times (0.9m) will be disregarded, and the values of the dip and total force, immediately deduced from the horizontal and vertical components, will refer to an epoch 21. lm after the full hour. For greater completeness, Table III, of Part VIII, is here inserted. TABLE III. — REGULAR SOLAR-DIURNAL VARIATION OP THE VERTICAL FORCE BETWEEN JULY, A V 1841, AND JULY, 1845. VALUES OF — y • 0.000 0" 2 4 6 8 10 Noon 14 16 18 20 22" +20. 6" January. —059 +238 +040 —026 —026 +172 +172 +304 —092 —323 —224 —158 February .—198 +033 —132 .—165 +099 +231 +264 +396 + 198 —264 —330 —132 March —178 +086 —046 —112 +086 +119 +251 +317 +020 —178 —145 —211 April —353 —155 —122 —023 +175 +274 + 274 +340 +241 —023 —320 —320 May —412 — 348 —214 +049 +247 +280 + 346 +445 +313 +016 —313 —412 June —528 —297 —198 —033 +198 +396 + 594 +462 +363 —066 —429 —462 July —571 —406 —241 +056 +221 +419 + 584 +551 +386 —043 —406 —538 August —485 —386 —287 —089 +109 +406 + 736 +571 +340 —023 —386 —485 Beptembn —469 —304 —271 —205 +092 +323 +521 +521 +356 +026 —271 : —337 October . —099 +066 000 —099 +231 +198 +198 +198 —033 —198 —264 —198 November —043 —043 —142 —109 +086 +122 +254 +221 —010 —076 —109 —109 December — 059 +139 +040 —059 +040 +139 +205 +205 —01)2 —290 —191 —125 Year —287 —115 —131 —068 +129 +257 +366 +377 +165 —121 —282 —290 Summer. —409 —317 —221 —040 +175 +350 +508 4-482 +333 —020 —353 —426 Winter . —106 +086 —040 —096 +082 +1C2 +224 + 274 000 —221 —211 —155 Solar-Diurnal Variation of the Inclination. — The combination of the component values of —- and — _ to form the corresponding values of the dip is effected by the _ Y formula A0 = sin 0 cos 0 — AO will be expressed in minutes. 6= 71° 59'. A 4- sign indicates an augmenta- tion of the north dip ; a — sign the converse. 3 December, 1864. 18 SOLAR DIURNAL VARIATION TABLE IV. — REGULAR SOLAU-DIUKNAL VARIATION OF TIIK DIP BETWEEN JULY, 1841, AND JULY, 1845. ArALUES OF A9. 0" 2 4 6 8 10 Noon 14 16 18 20 22" +21.1" Jan'y —0/03 +0/15 —0/16 — 0.'22 — 0.'19 +0.'53 +0.'61 1+0. 'S3 —0/30 — 0/31 —0/24 —0/13 Feb'y —0.20 —0.04 —0.32 —0.50 —0.08 +0.42 +0.63 +0.40 +0.20 —0.22 —0.11 —0.13 March —0.27 —0.15 —0.28 —0.46 +0.04 +0.48 +0.72 +0.38 +0.01 —0.08 —0.16 —0.23 April —0.47 —0.30 —0.41 —0.39 +0.18 +0.91 +0.73 +0.31 +0.06 —0.02 —0.28 —0.36 May —0.38 —0.43 —0.37 —0.25 +0.54 +0.80 +0.53 +0.15 +0.02 —0.02 —0.20 —0.34 June —0.47 —0.24 —0.25 —0.34 +0.30 +0.87 +0.75 +0.16 +0.02 —0.08 —0.40 —0.37 July —0.56 —0.46 —0.37 —0.15 +0.43 +1.00 +0.83 +0.24 —0.04 —0.14 —0.32 —0.45 August —0.57 —0.47 —0.44 —0.35 +0.47 +1.22 +0.92 +0.13 —0.07 —0.03 —0.32 —0.46 Sept. —0.63 —0.43 —0.54 —0.66 +0.41 +1.05 +0.92 +0.36 +0.15 +0.04 —0.33 —0.39 Oct. —0.23 —0.17 —0.35 —0.45 +0.25 +0.64 +0.67 +0.30 —0.02 —0.18 —0.21 —0.22 Nov. —0.04 —0.15 —0.32 —0.40 +0.09 +0.47 +0.56 +0.22 —0.08 —0.15 —0.14 —0.11 Deo. +0.03 +0.05 —0.20 —0.41 —0.20 +0.30 +0.71 +0.37 —0.18 —0.35 —0.14 —0.00 Year —0.32 —0.22 —0.33 —0.38 +0.19 +0.72 +0.71 +0.28 —0.02 —0.13 —0.24 —0.27 Sum'r —0.51 —0.39 —0.40 —0.36 +0.39 +0.98 +0.78 +0.22 +0.02 —0.04 —0.31 —0.40 Winter •—0.12 —0.05 —0.27 —0.41 —0.01 +0.47 + 0.65 +0.33 —0.06 —0.22 —0.17 —0.14 Annual Inequality in the Diurnal Variation of the Dip. — The comparison of the above diurnal variations for summer and winter, with that of the whole year, is given in the following Table. TABLE V. 0" ' 2 4 6 8 10 Noon 14 16 18 20 22h +21.1" Summer Winter —0/19 +0.20 —0/17 +0.17 —0/07 +0.06 +0/02 —0.03 +0/20 —0.20 +0/26 —0.25 +0/07 —0.06 —0/06 +0.05 +0/04 —0.04 +0/09 —0.09 —0/07 +0.07 —0/13 +0.13 The tabular quantities are exhibited in diagram A. (A). SEMI-ANNUAL INEQUALITY IN THE DIURNAL VARIATION OF THE INCLINATION. 0" 22 24" (+21.1°-) Philadelphia mean time. O F THE DIP. 19 The diagram shows the hours of no semi-annual change as follows: 5| A.M.; 1 P. M.; 3 P. M., and 7 P. M.; greatest change at 10 A. M., secondary at 6 P. M., with a range of 0/51 and 0/18, respectively. The turning epochs are found by the variation at the hour 10 A. M., when the monthly differences from the annual mean are as follows : — January .... — 0.'19 July . +0.'28 February .... —0.30 —0.24 August . +0.50 +0 33 -4-0.19 0 08 May 4-0 08 0 25 +0.15 0 42 These values are represented by the formula Aa = 0.'35 sin (6 + 253° 38') + 0/10 sin (20 + 328° 39') the angle 6 counting from January 1st. This formula gives a change of sign for the middle of April and the middle of October, or about 25 days after the equinoxes. ANALYSIS OP THE SOLAR-DIURNAL VARIATION OP THE DIP. In the following formula? expressing the solar-diurnal variation of the dip for each month, summer, winter, and year, the angle 0 counts from midnight at the rate of 15° an hour ; a positive sign indicates increase of north dip, a negative sign the reverse. The expressions are derived directly from Table IV. For January A. = 0.'24sin (9 + 284O 19') + 0/33 sin (28+ 78° 15') + 0.'14 sin (39+282O) For February A, = 0.'34 tin (9 + 246O 28') + 0.'30 sin (28 + 75° 40') + O.'OS sin (38 + 308O) For March A( = 0.'40 sin (8 + 251O 24') + 0.'24 tin (29 + 85O 27') + 0.'12 sin (38 + 303O) AJ = 0.155 sin (8 + 2630 10') + 0.'23 sin (28 + 109° 36') + O.'IS tin (38 + 330°) A, = 0/50 sin (9 + 2710 33') + O.'22'sin (28 + 146O 40') + 0.'14 sin (39 + OO) A( = 0/53 sin (9 + 2740 37') + 0/2] sin (28 + 109O 03') + 0.'19 sin (38+ 331O) Al = 0.'G4sin (8 + 2750 34') + 0. '24 sin (28 + 131O 08') + 0.'14 sin (38+322O) For April For May For June For July For August A, = 0.'68 sin (9 + 272O 55') + 0/32 sin (28 + 132O 56') + 0.'24 sin (38 + 331O) For September A, = 0/70 sin (8 + 260O 14') + 0/27 sin (28 + 116° 49') + 0.'23 sin (38 + 349O) For October AS = 0/41 sin (8 + 256O 31') + 0/27 sin (28 + 101O 19') + O.'ll »in (38 + 335O) For November A, = 0/28 sin (8 + 259O 21') + 0/27 sin (29 + 99O 30') + 0/08 stn (38 + 328O) For December A, = 0/20 sin (9 + 258O 09') + 0/37 sin (29 + 77O 45') + 0/12 sin (38 + 258O) We have also : — For Summer A, = 0/60 sin (8 + 269O 37') + 0/25 sin (29 + 125O 02') + 0/18 sin (39 + 335°) For Winter A, = 0.'30sin (8+ 260° 57') + 0/29 sin (28+ 85O 12') + 0/10 sin (38 + 300O) For Year A, = 0/45 sin (8 + 266O 47') + 0/25 sin (29 + 103O 19') + 0/13 sin (38 + 322O) Summer is comprised of the months from April to September; winter of the months from October to March. The following comparison of the observed 'and computed values for August shows about average differences ; in general the summer values are a little better repre- sented than the winter values. 20 SOLAR DIURNAL VARIATION COMPARISON FOR AUGUST. Time. Observed. Computed. 0-c. 0" 21.1" — '.57 — '.53 —'.04 2 " — .47 — .43 —.04 4 _44 — .52 +.08 6 — .35 — .33 —.02 8 + .47 + .50 —.03 10 +1.22 +1.18 +.04 12 + .92 + .92 .00 14 + .13 + .18 —.05 16 — .07 — .12 +.05 18 — .03 — .05 +.02 20 ' — .32 — .24 —.08 22 ' — .46 — .55 +.09 OF THE DIP. Diagram (B) exhibits the observed and computed diurnal variation for mer months, and diagram (C) for the winter months. 21 the sum- (B). SOLAR-DIURNAL VARIATION OF THE MAGNETIC DlP APRIL TO SEPTEMBER, 1841 — 1845. (Expressed in minutes.) if •a I •8 + -'8 .6 .4 .2 .0 .2 .4 — .6 +1.0 .8 .6 .4 .2 .0 .2 .4 — .6 +1.0 .8 .6 .4 .2 0 .2 .4 .6 — .8 i i I i i \ \ \ ! ( t 1 t \ N \ I 1 t t April May June .8 .6 .4 .2 0 .2 .4 .0 + -8 .6 .4 .2 0 .2 .4 — .6 July +1 August September £ % o 0" 6 8 10 g 14 16 18 20 22 2411 Philadelphia mean time. 22 SOLAR DIURNAL VARIATION (C). SOLAR-DIURNAL VARIATION OF THE MAGNETIC DlP OCTOBER TO MARCH, 1841 — 1845. (Expressed in minutes.) .B-T i • o r \ 1 1 i 1 1 +0/8 .6 1 \ .4 1 - . x.^ .2 October 0 .2 - :—-. / •"^••\-^H +0.'6 - >Xs--^_ / ^_ .4 .4 - /' "\ — .6 .2 0 .2 — .4 - / \ - November + .8 .6 m ~X_ / ; \. - / \ \ - .4 + .8 .6 " — — -»• / \ ~ .2 December 0 .2 .4 - N •^ / \ \ v ^/ - .4 - \ . — 6 .2 0 .2 - ^-•-^ / \ - January + .8 . X . / \ ^^-^ _ — .4 - / "^^ - .6 / \ _ .4 + .8 .6 / \ - .2 February 0 .2 .4 - X^ y / \ :-—:— ;^ •- .4 \ - — .6 .2 0 .2 .4 — .6 ./ . - o. =3 i £ 2 i i i i i i 1 1 1 1 1 1 1 1 1 11111 0" 2 4 6 8 10 a 14 IS 18 20 22 24" Philadelphia mean time. OF THE DIP. 23 Diagram (D) exhibits the diurnal variation of the dip for summer, winter, and the whole year. • , (D). SOLAR-DlURNAL VARIATION OF THE MAGNETIC DlP BETWEEN 1841 AND 1845. Winter Year Summer I 1 1 1 1 1 1 1 1 .8 .6 .4 .2 Winter ° Year Summer .2 .4 — 6 0" 6 8 10 14 16 18 20 22 24" Philadelphia mean time. The general character of the above three curves is the same ; the annual curve has its greatest value about 11 A.M., and its least value about 5 A.M., with a range of about 1/2; in summer the epochs occur a little earlier, with a range of about 1/5; in winter the epochs are a little later, and the range is contracted to about 1/0. There is also a secondary maximum between 1 and 2 A.M., with a less regular secondary minimum occurring at some hour in the afternoon or early in the night ; in summer, however, these minima appear interchanged. The Toronto curves are similar to those above, the shifting of the epochs is the same as at Philadelphia ; the morning minimum is less prominent, and the afternoon minimum constitutes the principal minimum during summer, and also, on the average, during the year. The total annual range is almost exactly the same at the two places, and the times of the principal maxima also nearly coincide. The following table contains the computed times of the principal maximum and of the morning minimum, also the elapsed time, together with the amount and range for each month and season ; also the times and amount and range of the afternoon or early night minimum, taken from the preceding diagrams. 13 24 SOLAR DIURNAL VARIATION TABLE ^ 1. ~~T Elapsed Range of Principal Amount A. M. Amount time A. M. Afternoon Early night afternoon maximum in minimum in between range. minimum minimum minim um 1841 to 184«. at minutes. at minutes. max. and about about & principal min. maximum. January 11" 59"> +0.'69 6" 39'° — 0.'32 5h 20" 1/01 6" h l.'O February 12 15 +0.67 6 04 —0.48 6 11 1.15 8 — 0.9 March 11 57 +0.72 5 54 —0.43 6 03 1.15 — 11 — April . 11 11 +0.92 5 11 —0.48 6 00 1.40 — 10 — May . 10 24 +0.81 4 07 —0.46 6 17 1.27 — 11 — Jane . 11 01 +0.91 5 16 —0.36 5 45 1.27 5 10 1.0 July . 10 57 +1.00 3' 15 —0.43 7 42 1.43 5 11 1.1 August 10 49 +1.21 4 45 —0.53 6 04 1.74 4 11 1.3 September 10 56 +1.10 4 57 —0.69 5 59 1.79 — 10 — October . 11 25 +0.73 5 17 —0.49 6 08 1.22 — 10 — November 11 29 +0.60 5 28 —0.40 6 01 1.00 6 — 0.7 December 12 24 +0.69 6 45 —0.41 5 39 1.10 6 — 1.0 Summer 10 55 +1.00 4 45 —0.48 6 10 1.48 Winter . 11 55 +0.67 6 00 —0.39 5 55 1.06 Year . . 11 22 +0.81 5 18 —0.40 6 04 1.21 The diurnal range is greater about the time of the equinoxes than at any other time, and in general less in winter and greater in summer. The afternoon minimum disappears about the time of the equinoxes, and is best marked about the solstices ; the early night minimum only disappears about the time of the winter solstice. TABLE VII. — PRINCIPAL EPOCHS OF NORMAL DIP. The morning epoch is computed to the nearest minute or two, the afternoon epoch is taken from the diagrams. 1841—1845. A. M. P. M. January ....... February 8"38-» 8 49 8 35 7 46 6 52 7 11 6 55 7 16 7 37 8 03 8 10 9 14 3^ 5 5 6i- 5, 3; 3- 3 6| 5 U 3* May July August September ...... November December Summer Winter ....... 7 22 8 33 7 50 4 84 31 Year Solar-Diurnal Variation of the Total Force. — The combination of the component values of and — - to form the corresponding values of the total force is effected by the formula

—065 —099 —102 December —059 +137 +062 —017 +062 +112 + 142 +173 —071 —254 —174 —122 Year . . —257 —094 —099 —031 +112 +187 +298 +351 +167 —108 —260 —265 Summer . —421 —279 —184 —007 +137 +257 +435 +460 +331 —016 —325 —389 Winter. . —094 +091 —014 —056 +088 +118 +161 +241 +004 —200 —195 —142 Annual Inequality in the Diurnal Variation of the Total Force. — The comparison of the above diurnal variations for summer and winter, with that of the whole year, is given in the following table : — TABLE IX. 0.000 0" 2 4 6 8 10 Noon 14 16 18 20 22" +21.1- Summer . Winter . . —164 +163 — 185 +185 —085 +085 +024 —025 + 025 —024 +070 —069 +137 —137 +109 —110 +164 —163 +092 —092 —065 +065 —124 +123 | Those tabular quantities are exhibited in diagram E, which closely resembles diagram B, Part VIII, of the Vertical Force. (E). SEMI-ANNUAL INEQUALITY IN THE DIURNAL VARIATION OP THE TOTAL FORCE. + 180 150 i i i i i i i i i i i i i •^ \ • . 120 090 060 :. \ /X \/ : 030 0 000000 v — / v 030 060 090 120 150 — 180 /~\ A : & / \ i \ -,Jf yy \; I 1 1 1 1 1 1 ! t 1 1 1 1 2 4 8 10 g 14 16 18 20 22 21" (+21.1") 4 December, 1864. Philadelphia mean time. 26 SOLAR DIURNAL VARIATION The hours of no semi-annual change are 6 A. M. and 7 P. M. ; the greatest changes take place about 2 A. M. and 4 P. M., with a range of .000370 and .000328 parts of the force respectively. The turning epochs are found from the variations at the hours 6 A. M. and 7 P. M. The following numbers are the differences from the respective annual means. For 20h the sign has been changed. 6 A. M. Mean 18 and 20. Mean 6 A. M. 7 P. M. January February . +027 —084 — 037 —122 —037 — 095 —048 — 060 066 April . May . +046 +104 +030 +060 +080 +090 +053 +092 +060 July . August September October November December + 100 —025 —111 —025 —043 +01*4 +097 +091 +055 —044 —059 —116 +098 +033 —028 —034 —051 —051 All expressed in units of the sixth place of decimals. The values in the last column are represented by the formula : — Aa= 0.000075 sin (6 + 280°) + 0.000025 sin (26 + 131°) 6 counting from January 1st. The change of sign occurs about April 4th and about September 12th, on the average, therefore, the change takes place about three days after the equinoxes. ANALYSIS OF THE SOLAR-DIURNAL VARIATION OF THE TOTAL FORCE. In the following expressions of the solar-diurnal variation of the total force, 0 is counted from midnight at the rate of 15° an hour ; a positive sign indicates increase of total force, a negative sign the reverse. The coefficients are expressed in parts of the force. The formulas are deduced directly from Table VIII. For January ,Af = 0.000139 sin (8 + 318O 14') + 0.000157 sin (28+ 37° 57') + 0.000020 sin (38 + 217°) For February A, = 0.000215 sin (8 + 276° 00') + 0.000143 sin (28 + 41° 01') + 0.000060 sin (38 + 96°) For March Ar= 0.000148 sin (8 + 284° 00') + 0.000106 sin (28 + 31° 27') + 0.000014 sin (38 + 242°) For April A, = 0.000283 sin (8 + 270° 27') + 0.000084 sin (28 + 342° 03') + 0.000042 sin (38 + 74°) For May A, = 0.000383 sin (8 + 264° 08') + 0.000084 sin (28 + 325° 13') + 0.000062 sin (38 + 108°) For June A( = 0.000470 sin (9 + 266° 26') + 0.000108 sin (28 + 2° 57') + 0.000016 tin (38 + 96°) For July Af = 0.000513 sin (8 + 265° 24') + 0.000103 sin (28 + 344° 53') +0.000036 sin (38 + 126°) For August Af = 0.000500 sin (8 + 259° 41') + 0.000109 sin (28 + 29° 29') + 0.000025 sin (38 + 193°) For September Ar= 0.000405 »in (8 + 252° 37') + 0.000097 sin (28 + 15° 05') + 0.000010 sin (39 + 163°) For October A, = 0.000170 sin (fl + 307° 00') + 0.000084 sin (29 + 45° 35') + 0.000033 sin (38 + 44°) For November Af = 0.000122 sin (8+266° 37') +.0.000074 sin (28+ 68° 28') + 0.000010 sin (39 + 119°) For December A, = 0.000136 sin (9 + 317° 52') + 0.000112 sin (28+ 46° 38') + 0.000017 sin (38 + 234°) The months from April to September are counted as summer months ; those from October to March as winter months. For Summer A, = 0.000426 sin (8 + 262° 51') + 0.000095 sin (28 + 358° 00') + 0.000026 sin (33 + 114°) For Winter Ar= 0.000146 sin (8 + 292° 00') + 0.000110 sin (28 + 43° 20') + 0.000007 sin (39 + 1 1 !i ) For Year A, = 0.000277 sin (8 + 270° 45') + 0.000095 sin (28 + 22° 29') + 0.000018 sin (38 + 115°) OF THE TOTAL FORCE. 27 The following comparison of the observed and computed values for September shows about average differences ; in general the summer values are better repre- sented or less irregular than the winter values. COMPARISON F( >R SEPTEMBER Time. Observed. Computed. 0— C. 0" 21.1" —.000408 —.000355 —.000053 2 — 000263 —.000298 +.000035 4 — 000218 —.000217 —.000001 6 —.000142 —.000127 —.000015 8 +.000054 +.000029 +.000025 10 +.000226 +.000236 — 000010 12 +.000436 +.000439 — 000003 14 +.000488 +.000492 —.000004 16 +.000343 +.000325 +.000018 18 ' +.000022 +.000033 — 000011 20 ' —.000240 —.000223 —.000017 22 ' —.000299 —.000344 +.000045 28 SOLAR DIURNAL VARIATION Diagram (F) exhibits the observed and computed diurnal variation for the sum- mer months, and diagram (G) for the winter mouths. (F). SOLAR-DlURNAL VARIATION OP THE MAGNETIC TOTAL FORCE APRIL TO SEPTEMBER, 1841 — 1845. (Expressed in parts of the force.) o • +.000400 300 200 100 0 100 200 300 —.000400 +.000400 300 200 100 0 100 200 300 —.000400 +.000400 300 200 100 0 100 200 300 —.000400 i i i i i April May June July + August Septemb. — 4 g a "a 3 ..000400 300 200 100 0 100 200 300 -.000400 .000400 300 200 100 0 100 200 300 ..000400 000500 400 300 200 100 0 100 200 300 400 000500 0" 2 6 8 10 a I 14 1C 18 20 22 24" Philadelphia mean time. OF THE TOTAL FORCE. (G). SoLAR-DlUENAL VARIATION OF THE MAGNETIC TOTAL FORCE OCTOBER TO MARCH, 1841 — 1845. (Expressed in parts of the force.) • l{ I i I I 1 i i i i i i ' i i i - 2 "o - +.000300 200 S . .^ • •~~\C _ 100 o a ^-"— — -: ,x"^ _\ October 0 100 •f • \ / '. \ i ir _ 200 +.000200 - —~x: Ns^t>X - —.000300 100 0 100 - /^ \^ - November - — -s-, ^ ^ ^.^r-" _ —.000200 - _ - ^* - +.000200 • - 100 December 0 100 7 t-v ••_ +.000300 200 . \ *^r _ 200 —.000300 100 0 100 /"~^-\ y ' \ - January +.000400 _ • ^~—'~^ \ ./ 200 - s^~\ • S - 300 —.000300 - ../ Y •\ X - 200 - g_ \ - 100 February 0 100 _ ^\_.^ •^ \ / _ +.000300 - • \ / • _ 200 200 - / * \ \^y - . 300 100 0 100 - - •s* \ - —.000400 March - /^ • \ / 200 - f^ '! - i —.000300 - - •3 i 1,111 i i i > i i i i > i i i i i i fo Is 0* 2 6 8 10 g 14 16 18 20 22 24" Philadelphia mean time. 30 SOLAR DIURNAL VARIATION. Diagram (H) exhibits the diurnal variation of the total force for summer, winter, and the whole year. (H). SOLAE-DIURNAL VARIATION OP THE TOTAL FORCE BETWEEN 1841 AND 1845. - ~T^ i FT- ~i — r— r—| — r~ ~I — 1 — 1 — 1 — 1 — - +.000500 - c\ - 400 . . - 300 . /S^ "~"x- \ \ _ 200 Winter - ^^L N\\\ - 100 .000000 Winter . r^ XN'-- ^/ Year - ' / ^....--- • - Year 200 300 Summer - *55.'2 71°55.'8 ] 11 18 10 10 0 0 71 58.6 72 00.9 71 53.6 71 55.0 56.1 57.9 [ 710 51.15 25 10 0 71 56.3 71 04.4 60.3 j February 1 10 0 72 01.9 71 57.1 59.5 1 8 15 10 10 0 0 72 03.6 71 58.0 71 55.1 71 53.2 59.4 55.6 [ 71 58.4 22 10 0 72 02.0 71 56.7 59.3 J 1 It is the same instrument with which I made the observations at stations in Europe (Amer. Phil. Trans. Vol. VII, Part I, 1840), and those in the magnetic survey of Pennsylvania, in 1840 and 1841, and at other stations farther northward and eastward, in 1843. ( 35 ) 36 RESULTS AND DISCUSSION OF THE Dip. Needle No. 1. Tear. Month. Day. Hour. Minute. Moan monthly A north. B north. Mean. dip. 1842 March 1 10 0 720 08/1 71049.'5 71°58/8 l 8 10 0 72 04.6 71 51.0 57.8 15 10 0 72 07.5 71 52.7 60.1 71059/5 22 10 0 72 08.2 71 55.7 62.0 23 10 0 72 02.6 71 54.9 58.7 April 5 10 0 71 46.4 71 55.5 51.0 : 12 10 30 72 06.2 71 57.0 61.6 19 9 35 72 08.5 71 55.3 61.9 71 59.0 26 9 58 72 10.5 71 52.4 61.4 May 3 10 19 72 11.4 71 56.1 63.7 : 17 9 29 72 09.4 71 59.4 f 64.4 17 10 43 71 54.2 72 02.6 '•] 58.4 1+ 1-7 71 61.3 24 10 0 72 11.6 71 51.3 61.4 31 10 1 72 06.7 71 48.9 57.8 June 7 10 15 72 11.8 71 53.4 62.6 : 14 21 9 9 46 56 72 09.1 71 57.1 71 52.9 71 59.1 61.0 58.1 . 71 60.7 28 9 24 72 07.8 71 54.3 61.0 July 13 9 11 72 10.2 71 58.3 64.3 ' 19 9 52 71 54.2 71 53.1 53.6 . 71 57.2 26 9 34 71 49.2 71 57.9 53.6 August 3 9 42 72 01.4 72 00.5 61.0 • 9 16 10 9 1 57 72 06.3 72 04.2 71 53.5 71 54.8 59.9 59.5 . 71 60.2 30 9 40 72 05.0 71 56.2 60.6 September 6 9 4 72 10.0 71 58.7 64.3 13 9 55 71 56.7 71 58.8 57.8 . 71 61.2 27 9 43 72 08.6 71 54.6 61.6 October 4 10 12 72 07.0 71 55.4 61.2 11 11 10 11 8 17 72 06.4 71 51.3 71 55.6 72 03.2 {61.0 57.2 71 60.6 + 1-7 November 1 10 6 72 11.9 72 01.5 66.7 15 9 48 72 08.3 71 52.3 60.3 71 64.1 22 10 13 72 13.3 71 57.1 65.2 December 27 9 16 72 08.2 71 55.3 61.7 71 61.7 1843 April 11 10 53 71 58.0 71 42.5 71 50.3 18 13 10 72 08.2 71 48.9 58.5 71 54.9 25 10 0 71 59.7 71 52.0 55.8 May 2 9 40 72 11.7 71 44.7 58.2 9 9 25 72 11.8 72 08.2 70.0 16 10 22 72 00.3 72 14.9 67.6 71 63.2 23 9 50 71 59.2 72 12.9 66.1 30 9 55 72 05.6 71 42.7 54.1 June 6 10 22 72 09.5 71 54.5 62.0 13 20 10 10 20 5 72 10.7 71 56.5 71 57.8 71 45.4 64.2 51.0 71 57.7 27 9 65 71 58.8 71 48.2 53.5 July 4 10 25. 72 01.4 71 56.3 58.8 11 10 35 72 07.9 71 44.3 56.1 18 10 5 72 04.9 71 51.5 f 58.2 18 11 20 71 58.8 71 55.5 >1 57.2 71 57.5 (+ 1.7 20 16 37 !71 56.2 '71 45.3 5fi.7 +1.9 +10.0 August 22 10 5 •71 53.4 "72 12.3 64.1 +4.3 — 1.8 24 11 17 72 02.0 71 50.7 ( 56.3 24 12 . 0 72 01.6 72 00.2 i 1 60.9 26 17 46 "71 54.0 '71 51.2 1+ 1-7 58.6 71 60.5 +1.9 +10.0 29 10 25 72 05.1 71 55.5 f 60.3 29 11 55 *71 56.3 »71 50.3 \ 59.3 +1.9 +10.0 ' Needle No. 2. « Lloyd needle No. 1, A end north. 4 Needle No. 1, B end north. 3 Lloyd needle No. 3, A end north. 6 Needle No. 2, B end north. OBSERVATIONS FOR MAGNETIC INCLINATION. Dip. Needle So. 1. Year. Month. Day. Hour. Minute. Mean monthly A north. B north. Mean. dip. 1843 September 5 9 42 720 07. '3 71052/0 710 1 59/6 1 5 11 12 *71 58.9 "71 49.3 t 60.0 + 1.9 +10.0 12 9 56 72 02.7 71 53.7 r~ 58.2 12 11 17 71 54.8 71 57.0 1 55.9 ' + 1.7 71060.'? 12 13 5 271 57.1 "71 48.4 58.7 + 1.9 +10.0 19 9 40 72 02.9 71 59.6 61.8 26 9 52 72 04.1 72 03.1 63.6 October 3 9 25 71 55.2 71 49.0 52.1 10 9 32 71 56.9 71 55.2 56.0 17 9 42 71 50.8 72 00.7 55.7 71 64.8 24 9 40 72 00.1 71 53.4 56.8 31 9 32 71 50.3 71 51.0 53.6 November 7 9 45 72 01.2 71 51.5 S6.4 • 14 21 10 10 17 10 72 00.7 72 02.1 71 57.5 71 47.7 59.1 54.9 71 56.4 28 10 25 72 02.5 71 48.1 55.3 December 5 10 20 72 01.9 71 51.7 56.8 I 12 19 10 10 42 12 72 05.7 71 59.0 71 58.3 71 51.8 62.0 55.4 (• 71 57.7 26 10 40 72 00.5 71 52.6 56.6 J 1844 January 2 10 20 71 57.6 71 53.8 71055/7 -, 9 9 52 72 04.0 71 54.0 59.0 . 16 10 40 72 01.2 71 52.8 57.0 71 56.2 23 10 12 71 57.8 71 50.5 54.1 30 10 17 71 58.9 71 51.7 55 3 February 6 10 25 71 59.3 71 57.9 58.6 ' 13 10 22 72 01.0 71 59.1 60.0 nro K 20 10 12 71 59.1 72 01.2 60.1 W*B 27 10 47 71 59.7 71 58.5 59.1 March 5 11 10 71 56.6 71 59.1 57.8 * 12 9 56 71 56.6 71 58.7 57.7 71 58.6 19 10 22 72 01.5 72 02.2 61.9 26 9 55 71 58.6 71 55.3 57.0 April 2 10 57 72 04.1 71 52.7 58.4 • 9 10 1 71 55.2 71 54.8 55.0 16 10 7 71 59.1 71 55.9 57.5 71 55.9 23 10 18 71 65.7 71 49.4 52.6 30 9 55 72 00.6 71 51.5 56.1 May 7 9 50 71 57.2 71 54.5 55.8 ' 14 9 49 71 59.0 71 54.4 56.7 nfi7 1 21 10 9 71 57.5 71 57.0 57.3 U 1 . 1 28 9 50 71 59.5 71 57.6 58.5 June 18 11 47 71 59.5 71 55.1 67.3 71 57.3 July 4 12 53 71 56.5 71 56.6 56.6 1 16 10 37 72 02.1 72 06.7 64.4 1 71 KQ Q 23 10 48 71 56.3 ' 71 57.7 57.0 > fl t)O,i7 30 10 40 72 00.4 71 54.8 57.6 ] Determination of corrections to results by needle No. 2, by Lloyd needles Nos. 1 and 3, and for want of reversal of polarity for needles Nos. 1 and 2 on August 22, 1843. Needle No. 1 being that ordinarily used, the exceptional readings with the other three needles have been referred to the indications of needle No. 1. 1 Needle No. 2. * Lloyd needle No. 1, A end north. ' Lloyd needle No. 3, A end north. 38 RESULTS AND DISCUSSION OF THE The index error to needle No. 2 we find by direct comparison with needle No. I on the following dates : — .... correction -)-6.'0 " +3.8 . . . " +1.0 " —4.6 . . . . " +2.3 . 17, 1842 11, 1842 18, 1843 24, 1843 Mean +1.'7 May October July August September 12, 1843 The correction to the Lloyd needles No. 1 and No. 3, A end north, we obtain also by direct comparison, viz : — August 29, 1843, correction to Lloyd No. 1, +4.'0 to Lloyd No. 3, +10.'0 September 5, 1843, " " " +0.7 " +10.3 September 12, 1853, " " " +1.1 " " +9.8 Mean correction, +1.9 " +10.00 The corrections for polarity to needles 1 and 2 in 1843, are determined as follows: — • For needle No. 1. Mean dip in 1843 from 34 results, A north, 71° 62/4 " " " " " B north, 71 53.8 Mean dip 71 58.1 Hence correction to needle 1, A north, — 4/3, and B north + 4/3 For needle No. 2 we have the following differences : — May 17, 1842, A north — B north . . . — 8/4 1 October 11, 1842, " " ... —11.9 July 18, 1843, " " . + 3.3 August 24, 1843, " " . + 1.4 September 12, 1843, " " ... — 2.2 Hence correction to needle 2, A north +1/8, B north, — 1/8 Mean —3/6 The above corrections have been applied. RECAPITULATION OF MONTHLY MEANS OP THE INCLINATION. Month. 1842 71"+ 1843 71°+ 1844 71°+ 57/5 58.4 59.5 59.0 61.3 60.7 57.2 60.2 61.2 60.6 64.1 61.7 54/9 63.2 57.7 57.5 60.5 60.7 54.8 56.4 57.7 56/2 59.5 58.6 55.9 57.1 57.3 58.9 February ....... April May July December ....... Mean ..... 60.1 58.2 57.6 The preceding results indicate an annual diminution of the dip of 1.'2. To com- plete the dip for the year 1843, the values for January, February, and March have been inteispolated by taking the means of 1842 and 1843 of these months respectively. The interpolated dips are 71° 56/9, 58.'9, and 59/0. We have the final values: — Dip for 1842.5 72° 01/1 « 1843.5 71 58.2 " 1844.4 ,71 57.6 OBSERVATIONS FOR MAGNETIC INCLINATION. 39 If we divide the monthly means (inclusive of the interpolated dips for January, February, and March, 1843) into two parts, we find the values: — From January, 1842, to April, 1843 (inclusive) . . .71° 59. '4 " April 1843, to July, 1844 " ... 71 57.9 The corresponding epochs are September 1, 1842, and December 1, 1843, which again give an annual decrease of 1.'2. It is desirable, however, to extend the investigation of the annual effect of the secular change of the dip beyond the years above stated. In the Coast Survey Report for 1856,1 Assistant Schott discussed the secular change of the dip at various places, and finds that the middle of the year 1842 (1842.7 +0.7 years) was an epoch of minimum dip for places between Cambridge, Mass., Toronto, Canada, and Wash- ington, D. C. The expression for the secular change for Philadelphia (page 241 of the 1856 report) is derived from 19 observations, contracted to 8 normals, between 1834 and 1855. The dips extracted from a manuscript paper on my magnetic surveys in various parts of the Northeastern States during the years 1834-5, 1840 1841, and 1843, are as follows : — Observed dip at Philadelphia, July " " October " " April " " July " " October " " Novembi A collection and combination of all the observed values for dip at Philadelphia (as far as they have come to my notice) are given in the following table : — 21, 1840 . . 710 52. '6 28, 1840 . . 71 53.0 26,1841 . . 72 00.6 20, 1841 . . 71 57.0 9, 1841 . . . 71 58.2 1, 1841 . . 71 59.1 Date. Observer. Dip. Mean dip. Mean epoch. July, 1834 1838 Prof. Bache and Prof Courtenay 71060.'2 n + y (t—Q + z (t—t,Y where 0 = resulting dip at any time between 1830 and 1860 01= assumed dip at epoch, x its correction, Ol = 72°.00 *0= epoch or 1840.0 t = any other time between the above limits. We obtain from the following combination of the observations by the method of least squares, the- values of », y, and z. Mean dip. Mean year. Group I .... " II .... " III .... 3 results 5 " 2. " 72.000 72.00 72.20 1838.3 1843.5 1859.2 whence 0 = + 72.°00— 0.00011 (t— 1840) + 0.00060 (t— 1840)2 The observed and computed dips compare as follows : — Epoch. Observed dip. Computed dip. Obs'd — comp'd. 1834.5 72.000 72.002 — 0.002 1839.7 72.12 72.00 4-0.12 1840.7 71,88 72.00 —0.12 1841.5 71.97 72.00 —0.03 1842.5 72.00 72.00 0.00 1843.6 71.97 72.01 — 0 04 1844.3 72.03 72.01 4-0.02 1846.4 72.02 72.03 — 0.01 1855.7 . 72 29 72 15 4-0.14 1862.6 72.10 72.31 — 0.21 The probable error of any one representation is +4.'8. The minimum dip, according to the above formula, occurred in January, 1840; at Toronto this minimum occurred in 1843. By means of the formula we find the dip for the middle of each year : — Tear. Computed dip. Observed dip. Adopted dip. 1840.5 . . . 72 O()0 71O59' 1841.5 72 00 71 59 1842.5 72 00 72 ooo 72 00 1843.5 72 01 71 97 71 58 1844.5 . . '. . . 72 01 71 97 71 58 1845.5 72 02 72 01 OBSERVATIONS FOR MAGNETIC INCLINATION. 41 We may now collect in one table the numerical values of the magnetic elements as found in the preceding discussion. The units for the force are feet and grains. -\- indicates west declination and north dip. Epoch. Oirard College, Philadelphia. 4 6 X Y t January. 1841 1842 " 1843 " 1844 .... +3° 23' 3 28 3 32 3 36 3 41 +71° 59' 71 59 71 59 71 58 72 00 4.178 4.175 4.173 4.170 4.168 12.05 12.84 12.83 12.81 12.83 13.51 13.50 13.49 13.47 13.49 " 1845 Mean : January, 1843 .... +3 32 +71 59 4.173 12.83 13.49 The latitude of the Observatory is 39° 58'.4 And its longitude west of Greenwich . . . .75 10.1 Or, in time 5" 00m 40.-3 6 January, 1866. :':,'y:J.;:: 5 i - -- :- • RETURN CIRCULATION DEPARTMENT 202 Main Library LOAN PERIOD 1 HOME USE 2 3 4 5 5 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS Renewals and Recharges may be made 4 days prior to the due date. Books may be Renewed by calling 642-3405. DUE AS STAMPED BELOW nn 2 Q 1989 AUiu. DISC JUL B O I38S otRr.uiATir M 7 -- • , fc „__.:-.•- j&jj 8^ • fig i 5 . - - 8 w •-, i-i -.. jj i jg '• ja FORM NO. DD6 UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CA 94720 |p • - . .;•.; - \ _ ., ... m • '•-' " " -T- ' ',. -'• '/:-"- ' -' -, ;. ,.-.^':;^ '- • - U.C. 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