. •» . . . , SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE. 239 OBSERVATIONS Olf TERRESTRIAL MAGNETISM AND ON THE DEVIATIONS OF THE COMPASSES OF THE UNITED STATES IRON CLAD MONADNOCK DURING HER CRUISE FROM PHILADELPHIA TO SAN FRANCISCO, IN 1865 AND 1866. BY WM. BARENESS, M.D., PBOFE3SDB OF MATHEMATICS, UNITED STATED HAVY. [ACCEPTED FOR PUBLICATION, SEPTEMBER, 1871.] INTRODUCTORY NOTE. THIS paper was originally an official report presented to the Navy Department by Professor Harkness; but, as that department made no use of it, the National Academy of Sciences, in August, 18G7, passed a resolution asking for the manuscript. This request was complied with; and, an abstract of the paper having been read to the Academy in April, 1869, it was referred to a commission consisting of the President of the Academy, Professors J. II. C. Coffin, and F. Rogers, in accordance with whose recommendation it is now published by the Smithsonian Institution. JOSEPH HENET, Secretary S. I. CULMIS, PKIITKB, FUILAIIKLPUIA. TABLE OF CONTENTS. SECTION I. INTRODUCTION. PAGE Introductory remarks ..... .... 1 Plan of observation .......... 1 Instruments employed .......... 2 SECTION II. DESCRIPTIONS OF STATIONS. Philadelphia . . . . . . . . .' . .4 Gosport ............ 4 St. Thomas ........... 5 Isle Royal ........... 5 Ceara ............ 5 Pernambuco . . . . . . . . . 6 Bahia ............ 6 Rio Janeiro . . . . . . . . . . . ' C Monte Video . ......... 1 Sandy Point ........... 8 Valparaiso . . . . . . . . . . .9 Callao ............ 9 Payta ............ 10 Panama. . . . . . . .,„ . ,,10 Acapulco . . , . . . „ . . . .11 Magdalena Bay . . . . . . . . . . .11 San Francisco ........... 12 SECTION III. ASTRONOMICAL OBSERVATIONS. General remarks . . . . . • . . . .13 Observations of the sun for latitude ........ 13 Observations of the sun for time ........ 14 Mode of determining true bearings . . . • . . . .26 Observations of the sun for the determination of true bearings Triangulation at Ceara ........«• 32 Table of observed latitudes ....••.•• 34 Errors of pocket chronometer, Fletcher, No. 906 . . . . • .35 Chronometer comparisons .....•• True bearings of objects used as azimuth marks .... (iii) iv CONTENTS. SECTION IV. OBSERVATIONS ON TERRESTRIAL MAGNETISM. PACE Description of the portable declinometer, D. 22 Description of the transit theodolite General remarks on the methods of using the instruments Mode of determining absolute declinations Mode of making observations of vibrations Mode of making observations of deflections Mode of calculating horizontal force Determination of constants peculiar to the portable declinometer, D. 22 Temperature coefficients of magnets Value of magnet scales ....••• Moment of inertia of the magnet, C. 32 . The constant P. . Magnetic moment of the magnet C. 32. . Mode of making observations of inclination Mode of computing the vertical and total force . Abstract of observations for magnetic declination, inclination, and force . 60 Final values of the magnetic elements at each station . . . . . .61 Observations of magnetic declination ..... . . 62 Observations of magnetic inclination ..... . . . 75 Horizontal intensity. Observations of vibrations Horizontal intensity. Observations of deflections .... SECTION V. OBSERVATIONS ON THE MAGNETISM OF THE SHIP. Description of the Monadnock . . .119 Positions of the compasses . ... Mode of swinging the ship . Corrections peculiar to the After Binnacle and After Ritchie Compasses . . 121 Officers who observed the compasses ... . Mode of measuring magnetic force on board ship . ... Mathematical theory of the deviations of the compass .... . 123 Correction of observed deviations for constant errors . . . . 129 Observations for determining the deviations of the Admiralty Standard Compass . . 133 Observations for determining the deviations of the After Binnacle Compass . .140 Observations for determining the deviations of the After Ritchie Compass . . 147 Observations for determining the deviations of the After Azimuth Compass . . 154 Observations for determining the deviations of the Forward Alidade Compass . 160 Observations for determining the deviations of the Forward Binnacle Compass . 167 Observations for determining the deviations of the Forward Ritchie Compass . .174 Mode of computing the coefficients At, Bt, Clt D,, El . . . . .181 Values of these coefficients for each compass at each station ..... 182 Probable errors of the values of the coefficients A,, Bt, C,, D,, E, . . • .184 Computation of the constants A.,. -, —, *, -?, and A^, for each compass . .185 x x x x x x Values of the coefficients 9(, 33, S, £\ Q, for each compass at each station . . 1 1)1 Table showing the values of the constants A. = % c, ~, — , /, 9, *9, <£ and (?, x x x x x x for each compass . . . . . . . . . .193 CONTENTS. v . PAGE Computation of the coefficients $(, 33, @, £\ G, for each compass at each station, from the constants, J,, c, ?., ±*, /, # ^, £>, and @ . 193 X X X X X X Comparison of the coefficients thus computed with those found directly from the observations at each station . . . . . . . . . .196 Resulting probable errors ......... 198 Does the theory accurately represent the semi-circular deviation ? 199 Tables showing the most important features of the deviations of each compass during the cruise . . . . . . . . . . . .199 Hard and soft iron forces . . . . . . . . .201 Magnetic moment of magnets used for measuring horizontal force on board ship . . 202 Observations for absolute force at the Admiralty Standard Compass .... 205 Observations for absolute force at the After Azimuth Compass .... 206 Values of >. . . . . . . . . . . . 207 Values of g, h, k, R and A-Zf, for the Admiralty Standard and After Azimuth Compasses . 207 Values of a, b, e, and d, for the Admiralty Standard and After Azimuth' Compasses . . 209 General equations for the determination of the deviations of the Admiralty Standard Compass 210 General equations for the determination of the deviations of the After Azimuth Compass . 211 Variations of the hard iron force, during the cruise, at the Admiralty Standard and After Azimuth Compasses . . . . . . . . .211 Computation of the coefficients At, Bv Cv D,, Ev for each compass, at places where the deviations were observed on less than thirty-two points ..... 211 Recapitulation of results . . . . . . . . .219 Final conclusions .... . . . 220 REPORT ON MAGNETIC OBSERVATIONS. SECTION I. INTRODUCTION. the fifth of October, 1865, I was ordered to the U. S. Iron-clad Monad- nock1 for the purpose of making observations on the action of her compasses during the cruise which she was about to undertake from Philadelphia to San Francisco, by way of the Straits of Magellan. She was then fitting out at the Philadelphia Navy Yard, and the work on her was so far advanced that it was expected she would sail in about two weeks. As the department had not previ- ously intimated its intention of assigning me to this duty, and as everything relating to the number and kind of observations to be made, and the instru- ments required, was left entirely to my own discretion, it will be seen that the time available for making plans and collecting the necessary apparatus was very limited. The plan of observation ultimately adopted was that at every port in which we remained for more than twenty-four hours the following operations should be gone through with. 1st. The ship should be swung, and as her head pointed successively to each of the thirty-two true magnetic points, the reading of every compass on board should be recorded for each point. 2d. That at such of the compasses as were so situated as to render it possible, the horizontal force and inclination should be determined. 3d. The position of the dividing line be- tween the north and south polarity should be traced on each turret. 4th. The magnetic declination, inclination, and horizontal force should be determined on shore. While at sea it was intended to observe the declination — and consequently the deviation — and horizontal force daily, by means of the standard compass; but this turned out to be impracticable, because the only place in the ship where it was possible to mount that instrument was on top of the after pilot-house; a situation 1 The Monadnock is a double-tnrreted vessel of the monitor type. During the cruise in question, Lieutenant Commander Francis M. Bunce, U. S. N., was her captain, and she was attached to the squadron commanded by Commodore (now Rear-Admiral) John Rogers, U.S. N., at whose special request I was detailed by the Navy Department to make the observations which are the subject of this paper. 1 December, 1871. ( 1 ) 2 REPORT ON ^ where no binnacle could be put, and where the compass was nearly on a level with the top of the smoke-stack. Thus, while at sea, the position occupied by it was almost constantly enveloped in smoke and gas, rendering it absolutely necessary, whenever we left port, to dismount the instrument in order to preserve it from injury. Owing to the very short time at my disposal previous to sailing, there was great difficulty in providing proper instruments, but I succeeded in obtaining all that were absolutely necessary. The following is a list of them : Portable Declinometer and stand. Five-inch Altitude and Azimuth Instrument. Dip Circle, with two needles, each three and a half inches long. Pair of eight-inch Bar Magnets. Pair of eleven-inch Bar Magnets. ^ Admiralty Standard Compasses, with stands and deflectors. Burt's Solar Compass and stand. Prismatic Sextant of six inches radius. Mercurial Artificial Horizon. Pocket Chronometer, Fletcher, No. 906. Silver Comparing Watch. 2 Pocket Thermometers. 2 Pocket Compasses. 2 Magnetic Needles, not mounted, each 2.75 inches long, and 0.33 of an inch broad, i Fifty feet Chesterman's Patent Tape Line. i Case of Drawing Instruments. i Gunter's Scale, two feet long. The portable declinometer belonged to the U. S. Coast Survey, and was kindly lent by Prof. J. E. Hilgard. The small unmounted magnetic needles were intended to be used for measuring the relative horizontal force on shore and at each of the compasses on board ship. For this purpose it was proposed to vibrate one of them on shore, and then taking it on board ship to the compass at which it was desired to measure the relative horizontal force, to remove the compass card from the centre-point, and putting the small needle in its place, vibrate it again. Unfortunately the small needles were not finished till just before we left Philadelphia, and there was no opportunity of trying them till after we were at sea, when, to my great regret, it was found that the jewels were so small that they would not fit on the centre-point of any compass on board, thus rendering them entirely useless. Under the circumstances, for horizontal force on board ship it was necessary to rely entirely upon measures made with the deflectors belonging to the Admiralty standard compasses — a method certainly not so convenient, and, owing to the constant swinging of the ship when at anchor, probably not so accurate as counting the vibrations of a small needle. The observations on terrestrial magnetism, and for latitude, time, and true bear- ings, were all made by myself and recorded by Mr. Corrin F. Smith, who was cap- tain's clerk on the Monadnock, and acted as my assistant when I was observing. My best thanks are due to him for the efficient manner in which he performed his duties, sometimes under circumstances of very considerable physical discomfort. MAGNETIC OBSERVATIONS. 3 The reductions and discussions in this report have been made by me, so that I am personally responsible, not only for the general plan of the work, but for every figure contained in it. All the results have been very carefully checked, and it is hoped no material error will be found in them; still, absolute accuracy is scarcely to be expected in any work involving so many figures, the more especially as much of it has been done during moments snatched from other and more pressing professional duties. The observations naturally divide themselves into three classes: 1st. Those relating to astronomy. 2d. Those relating to terrestrial magnetism. 3d. Those relating to the magnetism of the ship. As that is the order in which they must necessarily be reduced, they will be so treated of in the subsequent sections of this report. SECTION II. DESCRIPTIONS OF STATIONS. UNLESS otherwise stated, the assumed positions of light-houses, forts, etc., have been taken from the English Admiralty Charts, or from the English Admiralty List of Lights, the latest editions obtainable in 1865 being employed. The longi- tudes are counted from the meridian of Greenwich. The method used in testing a station for local attraction by means of fore and back sights with a compass, was as follows : The compass was set up at the station, and the bearing of a point distant one hundred yards, or more, was observed. Then the compass was transferred to that point, and the bearing of the station was observed. These two bearings should evidently differ from each other by 180°; if they did not, it was certain that local attraction existed at one or both of the points, and a new station was sought for. This process is almost certain to detect any strictly local magnetic attraction, but it will not suffice to demonstrate the existence of an abnormal state of the magnetic elements extending over a large territory. PHILADELPHIA, Pa. The magnetic observations were made at a spot on the east bank of the Delaware river, about twenty feet from the water's edge. It is nearly southeast from the U. S. Navy Yard, from which it is distant about three-quarters of a mile. The soil is a dark — nearly black — earth, which appears to have been deposited by the river. The approximate position of the station was Lat. 39° 55' N. Long. 5h Ora 32" W. GOSPORT, Va. The magnetic observations were made on a white sandy beach, on the west bank of the Elizabeth river, about thirty feet from the water's edge. From the place where the instruments stood, the flagstaff in the U. S. Navy Yard bore due north by compass, and was distant about half a mile. Assuming the position of the flagstaff to be lat. 36° 49' 32" N., long. 5h 5m 9".8 W., as stated by the authorities at the Navy Yard, the position of the spot occupied by the instruments is approximately Lat. 36° 49' 0" N. Long. 5h 5m 9«.8 W. The ship was swung at the compass station in Hampton Roads, on November , in the usual manner. Her position at the time was lat. 36° 58' N long 76° 20' W. Joint XII on the after turret was 14.4 inches to port (4) MAGNETIC OBSERVATIONS. r, ST. THOMAS, West Indies. The ship was swung in this harbor, on November 18th, 1865, in the usual manner. Her position at the time was hit. 18° 19' N., long. 64° 56' W. Joint XII on the after turret was 14.4 inches to port. The observations on shore were made in Long Bay, at a spot about thirty feet from the water's edge, on a gravelly beach, to the eastward of the town. From the place where the instruments stood the true bearing of Fort Cowell, at the en- trance to the harbor, is S. 34° 50' W., and it is distant about one mile. Assuming the position of Fort Christian to be lat. 18° 20' 27" N., long. 4h 19™ 429.7 W., then, according to the English Admiralty Chart, the position of the spot where the instruments were set up is Lat. 18° 20' 22" N. Long. 4;i 19m 40 .6 W. ISLE ROYAL, Salute Islands. An attempt was made to swing the ship here, on November 30th, 1865, in the usual manner, but it failed on account of the continual rain which shut off the view of the distant azimuth mark. The position of the ship at the time was lat. 5° 17' N., long. 52° 33' W. Joint XII on the after turret was 0.6 of an inch to starboard. The magnetic and astronomical observations on shore were made on the south- west side of the island, at. a spot from which the corner made by the southeast and southwest faces of the government coal sheds bears N. 64° W. (true), and is distant one hundred and thirty-two feet. The place was examined carefully for local attraction by taking fore and back sights with a compass, but none could be detected. The position occupied by the instruments is in Lat. 5° 17' 29" N. Long. 3h 30m 118.4W. The latitude was determined from a single set of circummeridian altitudes of the sun observed by me, and the longitude was taken from the French chart. CEARA, Brazil. An attempt was made to swing the ship here, on December 19th, 1865, in the usual manner, but although a very favorable opportunity was chosen, she could only be made to turn through ten points. Her position at the time was lat. 3° 44' S., long. 38° 34' W. Joint XII on the after turret was 0.6 of an inch to starboard. The wind, current, and sea are so strong here that vessels at anchor in the roads always ride with their heads nearly in the same direction, never swinging more than about three points. At this place there is no harbor whatever, merely an open roadstead. A heavy surf is constantly running on the beach, and as there are almost no facilities for landing in small boats, getting the instruments on shore involved a good deal of trouble and some risk. However, I succeeded in landing them safely, and obtained a very good set of observations on the white sand beach at a spot about one hundred and fifty feet from the water's edge, and from which the true bear- ing of the southeast corner of the custom-house on the wharf is N. 53° 19' W., and its distance two hundred feet. From the same spot the true bearing of 6 REPORTON Point Macoripe Light-house is N. 75° 38' E. The position occupied by the instruments is in Lat. 3° 43' 59" 8. Long. 2h 34m 69 W.' The latitude was deduced from my own observations, and the longitude was taken from the list of geographical positions given in Raper's Navigation. PERNAMBUCO, Brazil. The ship was not swung in this port because there was not room to do it in the position where she took her coal, and as she only remained in the harbor twenty-four hours, there was not time to take up another position in order to swing. The magnetic and astronomical observations on shore were made on the white sand beach, at a spot from which the true bearing of the salient angle of the southeast bastion of Fort Brum is N. 15° 46' W., and its distance four hundred and thirty feet. Assuming the position of the light-house, near to Fort Picao, to be lat. 8° 3' 42" S., long. 2h 19m 268.8 W., as it is given in the English Admiralty List of Lights, edition of 1866, then, according to the English Admiralty Chart, the position occupied by the instruments is in Lat. 8° 3' 37" S. Long. 2h 19m 289.2 W. BAHIA, Brazil. The ship was swung in this harbor, on December 30th, 1865, in the usual manner. Her position at the time was lat. 12° 59' S., long. 38° 31' W. Joint XII on the after turret was 0.6 of an inch to starboard. The magnetic and astronomical observations of December 27th were made at a spot, one hundred and fifty feet from the water's edge, situated in a cocoanut grove on the beach about half-way between Monserat Point and Fort Victoria. The soil is a coarse white sand. It was not possible to get any bearings which would define the exact position, but the above directions are sufficient to enable any one to find the place very nearly. Assuming the position of Fort St. Antonio Light to be lat. 13° 0' 55" S., long. 2h 34m 6'.9 W., then, according to the English Admiralty Chart, the position occu- pied by the instruments is in Lat. 12° 56' 55" S. Long. 2h 34m 0'.5 W. Rio JANEIRO, Brazil The ship was swung in this harbor, on January 10th, 1866, in the usual manner; but, owing to a strong wind which was blowing at the time, it was not possible to get her through more than seventeen points. Her position was lat. 22° 54' S., long. 43° 9' W. Joint XII on the after turret was 0.8 of an inch to port. During the whole week we were at Rio there was not one clear day. Conse- quently it was extremely difficult to make astronomical observations, and it was only by patiently watching for the sun and seizing the opportunities when it was MAGNETIC OBSERVATIONS. 7 momentarily visible through breaks in the clouds, that the few sights necessary in order to complete the magnetic observations were obtained. With a single exception, all the magnetic and astronomical observations were made at a spot from which the true bearing of the entrance on the north face of Fort Caraguata (erroneously spelled Gravata on the English charts) is S. 70° W., and its distance fifty-five feet. There were no guns in the fort at the time. The surrounding country is very hilly, the bare, coarse, granite rocks cropping out every- where from the hill-sides, but in the more level places they are thinly covered with earth. Assuming the position of Fort . Villegagnon to be lat. 22° 54' 42" S., long. 2h 52m 36s.O W., then, according to the English Admiralty Chart, the position occupied by the instruments is in Lat. 22° 54' 5" S. Long. 2h 52ra 308.7 W. The exception referred to above is some observations of the sun for time, made on January 9th. They were got on Eat Island, the spot where naval officers usually go to rate their chronometers when lying in this harbor. Assuming the position of Fort Villegagnon as above, then, according to the English Admiralty Chart, the position of Rat Island is Lat. 22° 53' 45" S. Long. 2h 52m 37S.9 W. MONTE VIDEO, Uruguay. The ship was swung in this harbor, on January 24th, 1866, in the usual manner. We first attempted to get her around about 1 P. M., but owing to the force of the wind and tide we only obtained ten points, viz., those from E. by S. to S. S. W. Just at sunset we tried it again, and succeeded in getting the remainder of the circle. It was nearly dark when we finished, but as the dis- tant object used for an azimuth mark shone plainly against the sky, there was suf- ficient light to see pretty distinctly when it was in range with the sights of the compass. The readings of part of the circle on the After Ritchie compass were lost, owing to the failure of daylight and delay in procuring a lantern. The officer who usually read the After Azimuth compass was on shore at the time, and the duty of making the observations at that instrument was assigned to another, but it turned out that he did not understand how to read an azimuth compass, and his observations were worthless. While we were lying at Monte Video the tide was very irregular. Most of the time the ship only swung to it about 90°, but two or three times she swung 180°. At the time we swung her to obtain the deviation of the compasses her position was lat. 34° 55' S., long. 56° 13' W., and joint XII on the after turret was 4.5 inches to port. The greater part of the magnetic observations on shore were made on January 18th, at a station on the ground occupied by Tomkinson's slaughtering establishment. The instruments were set up at a spot where there are four large umbu trees stand- ing in a line. The exact position may be recovered by means of the following true bearings. The corner made by the south and west sides of the dwelling-house 8 REPORT ON bears N. 39° E., and is distant about one hundred feet. The light-house on the Mount, on the west side of the harbor, bears N. 59° 0' W. The water's edge is distant from the station about four hundred feet. The soil is a thin stratum of very poor earth, covering a greenish-colored slaty rock, which crops out in many places. Assuming the position of the light-house on the Mount to be lat. 34° 53' 15" S., long. 3h 44™ 599.0 W., then, according to the English Admiralty Charts, the position occupied by the instruments is in Lat. 34° 531 39" S. Long. 3h 44m 55".8 W. As a check, some magnetic observations were made, on January 19th, at a station from which the true bearing of the light-house on the Mount is N. 89° 41' W., and the true bearing of the light on the Cathedral is S. 17° 42' W. Assuming the ' position of the light-house to be as stated above, and the light on the cathedral to be in lat. 34° 54' 20" S., long. 3h 44m SO'.O W., as given in the English Admiralty List of Lights in South America, edition of 1865, the geographical position of this station was Lat. 34° 53' 16" S. Long. 3h 44m 488.3 W. It will be observed that the difference of longitude between the lights on the Mount and on the cathedral, as deduced from the Admiralty List cited above, cannot be made to agree with the positions given on the English Admiralty Chart. On January 24th some observations for time were made on Rat Island. Assum- ing the position of the light-house on the Mount to be as stated above, then, accord- ing to the English Admiralty Chart, the position of the station on Rat Island was Lat. 34° 53' 18" S. Long. 3" 44m 52'.9 W. SANDY POINT, Straits of Magellan. The ship was swung in this harbor, on February 10th, 1866, in the usual manner. Her position at the time was lat. 53° 11' S., long. 70° 55' W. Joint XII on the after turret was 4.5 inches to port. While we were lying here the ship was perfectly free to swing to the tide, but she generally turned through an arc of only about ninety degrees, namely, from W.N.W. to N.N.E. The observations on shore were made in the meadow, between the settlement and the beach, at a spot from which the true bearing of the flagstaff was N. 47° 8' W., and its distance about eight hundred feet. The soil is sandy, and there is no rock anywhere near. The place was examined for local attraction by taking fore and back sights with a compass, but nothing of the kind could be detected. Assuming the position of the flagstaff to be lat. 53° 10' 15" S., long. 4h 43m 36*. 0 \N .. as given on the English Admiralty Chart, edition of 1861, the position occupied by the instruments is in Lat. 53° 10' 20" S. Long. 4h 43m 35".3 W. MAGNETIC OBSERVATIONS. 9 VALPARAISO, Chile. The ship was swung in this harbor, on April 4th, 1866, in the usual manner. Her position at the time was lat. 33° 2' S., long. 71° 38' W. Joint XII on the after turret was 4.25 inches to port. While we were lying at Valparaiso the ship was perfectly free to swing to the tide, and she turned in all directions. The observations taken on shore March 2d were made on the south end of the white sand beach at the Estero de Quilpue, at a spot about two hundred and fifty feet from the rocks. Assuming the position of Fort San Antonio to be lat. 33° 1' 53" S., long. 4" 46m 46s.O W., then, according to the English Admiralty Chart, the position of this station was approximately Lat. 33° T.4 S. Long. 4h 46 m 3P W. The observations of March 19th, and all taken subsequently to that date, were made at a spot distant about six hundred and fifty feet, nearly true north, from the most northern of the custom-houses. The instruments were set up, near to the water's edge, on the public road which here runs along under a high bank of rock. The true bearing of the flagstaff at Fort San Antonio, on the top of the hill, was S. 31° 45' W., and its estimated distance was seven hundred feet. Assuming the posi- tion of the fort to be as stated above, the position occupied by the instruments is in Lat. 33° 1' 47" S. Long. 4" 46m 45s. 7 W. Both this station and that of March 2d were carefully tested for local attraction by taking fore and back sights with a compass, but none could be detected. In adopting 4h 46m 46s.O as the longitude of Fort San Antonio, I have followed Raper, but this value is doubtless too large. Capt. Jas. M. Gilliss, U. S. N., from a series of occultations and moon culminations, observed during the years 1850-51-52, determined the longitude of the Observatory on the hill of Santa Lucia, in Santiago, to be 4h 42m 33s. 8. Dr. Moesta, from subsequent observations up to the year 1862, corrected this value to 4h 42m 339.0. Capt. Gilliss, by means of the electric tele- graph, found the difference of longitude between the Observatory at Santiago and Mr. Mouatt's Observatory at Valparaiso to be 3m 568.5. Hence, adopting Dr. Moesta's value of the longitude of Santiago, we have 4h 46m 293.5 W. as the longitude of Mr. Mouatt's Observatory; but I have been unable to find any description of its position, and consequently cannot refer this longitude to Fort San Antonio. Findlay, in his "Directory to the South Pacific Ocean," edition of 1863, gives for the longitude of Fort San Antonio 4h 46m 288.8, and quotes Dr. Moesta as the authority. The Connaissance dcs Temps, for the year 1868, on the same authority- gives 4'1 46m 27S.5 for the same position. Which of the two values is nearest cor- rect I am unable to say. CALLAO, Peru. The ship was swung in this harbor, on April 29th, 1866, in the usual manner. Her position at the time was lat. 12° 3' S., long. 77° 14' W. Joint 2 December, 1871. 10 REPORTON XII on the after turret was 5.5 inches to port. While we were lying at Callao the ship was perfectly free to swing to the tide, but the wind and current were so strong that she did not do so, but always lay with her head pointing in a southerly direction. The observations taken on shore, April 26th, were made on the northeast side of San Lorenzo Island, about two and a half miles southeast of the light-house. The island is a mass of hills, rising to an elevation of more than a thousand feet, com- posed of loose friable rock which seems to be of volcanic origin, and which is con- stantly disintegrating into a fine yellow sand. The place selected for making the observations is at the foot of a gorge where there is a beach, about a quarter of a mile long, of the yellow sand mentioned above. On the beach stand a number of fishermen's huts, and a few steps back, at the foot of the gorge, stands a large, square, two-story house. The spot where the instruments stood is on the southeast end of the beach, a little beyond the fishermen's huts, and just above high-water mark. Assuming the position of the light-house to be lat. 12° 4V 0" S., long. 5h 9m IS'.O W., the position occupied by the instruments is in Lat. 12° 5' 14" S. Long. 5h 9m 9M W. The place was carefully tested for local attraction by taking fore and back sights with a compass, but none could be detected. PAYTA, Peru. We remained in this port only from 2h 30m P. M. of May 6th, 1866, till 6h P. M. of May 7th, and there was neither time nor opportunity to swing the ship. However, a complete set of magnetic observations were made on shore at a station on the beach four-tenths of a mile northwest of the large iron building which stands just back from the mole, and is used by the government as a custom- house, etc. As nearly as could be determined from angles carefully measured, and plotted on the English Admiralty Chart, this station is identical with the one occupied by the officers of H. B. M. surveying vessel "Beagle," in the year 1836, when making their observations for determining the position of Payta. According to their determinations it is in Lat. 5° 5' 36" S. Long. 5h 24m 22s.O W., the longitude depending upon the position of the northeast bastion at Panama, New Granada, which is taken to be 5h 18™ 4".6 W. The instruments were set up, just above high-water mark, on the gray sand beach, about fifty foot back from which the land rises into bluffs, two hundred feet high, composed of a h;ml yellow earth, alternating with sedimentary rocks. The station was carefully examined for local attraction, by taking fore and back sights with a compass, but none could be detected. PANAMA, New Granada. The ship was swung in this roadstead, on May 20th, 1866, in the usual manner. Her position at the time was lat. 8° 55' N., long. 79° 30' W. Joint XII on the after turret was 5.5 inches to port. While we were lying hero the ship was swinging freely in all directions to the wind and tide. MAGNETIC OBSERVATIONS. H The observations taken on shore, May 14th, were made on the northern side of Flamenco Island, to the westward of a small cocoanut grove, and northeast of the Naval Cemetery. The instruments were set up about ten feet north of the most western of the ruins which are to be found there. The island is rocky, but at this station the rocks are covered with earth. The spot was carefully tested for local attraction by taking fore and back sights with a compass, but none could be detected. If we assume the position of the northeast bastion at Panama to be lat. 8° 56' 56" N., long. 5" 18'" 49.6 W., as given by Capt. H. Kellet, E. N., then, according to the English Admiralty Chart, the position occupied by the instruments is in Lat. 8° 54' 31" N. Long. 5" 18m 18.8 W. AcAPULCO,.J/exj'co. The ship was swung in this harbor, on June 1st, 1866, in the usual manner. Her position at the time was lat. 16° 50' N., long. 99° 52' W. Joint XII on the after turret was 5.5 inches to port. During the three days we were lying at Acapulco the ship was swinging freely to the wind and tide. At the extreme south end of St. Lucia Bay, in this harbor, are two cocoanut groves, tlie most western of the two containing the graves of a number of our naval officers. The western end of the eastern grove is the place where the observations taken on shore, on May 30th, were made. The trees come almost close down to high-water mark, and the soil is a gray sand. The instruments were set up about forty feet from high-water mark, at a spot from which the true bearing of the gate of Fort St. Diego is N. 6° 22' E. If we assume the position of this gate to be lat. 16° 50' 56" N., long. 6" 39m 298.0 W., as given on the English Admiralty Chart, then, according to that chart, the position occupied by the instruments is in Lat. 16° 50' 3" N. Long. 6h 39m 293.4 W. MAGDALENA BAT, Lmoer California. An attempt was made to swing the ship in this bay, on June 9th, 1S66, in the usual manner, but owing to a very stiff breeze which was blowing at the time, she could only be turned through fourteen points. Her position was lat. 24° 38' N., long. 112° 6' W. Joint XII on the after turret was 5.5 inches to port. During the three days that we lay in this bay the wind was so strong that the ship did not swing to the tide, but rode with her head con- stantly to the west. As it is difficult to describe the land-marks here, the most convenient way of giving positions will be to refer them to the English Admiralty Chart, the position formerly occupied by Capt. Sir Edw. Belcher's observatory being taken to be lat. 24° 38' 18" N., long. 7" 28m 258.4 W., as given on the chart. On June 8th a landing was effected at a spot on the beach, about a mile south of the position of Capt. Belcher's observatory, for the purpose of making a set of magnetic observations; but, after getting a time sight, it was found that there was a great deal of local attraction, nearly all the stones on the beach being magnetic, and consequently it was useless to attempt anything there. The approximate position of this spot is 12 REPORT ON Lat. 24° 38' N. Long. 7h 28m 24s W. On June 9th, after going to the extreme northern end of the bay, and pulling a short distance up a creek, a place was found which, upon careful examination by taking fore and back sights with a compass, seemed to be entirely free frojn all local attraction. The land there is composed of fine white- sand hillocks, which. are constantly being shifted by the wind, and are- so loose that a man will sink half- way to his knees in walking over them. The only place where the surface was sufficiently solid to admit of the instruments being set up was below high-water mark, where the sand was wet. A complete set of magnetic observations, were made there, which, however, were not as satisfactory as could have been wished, owing to the magnets being disturbed by a stiff breeze which shook the instruments, and from which there was no shelter. The position of this station was Lat. 24° 39' 36" N. Long. 7" 28m 26S.2 W. It was on the east side of the creek (on its left-hand bank), at a place where there • i- a sharp bend in its course, and can easily be found by plotting the position, given above, on the chart. SAN DIEGO- BAY, California. We were only in this harbor from 11 A.M. of June 15th, 1866, till 11 A.M. of June 16th, and there was no time to swing the ship. However, during the afternoon of the 15th a complete and very satisfactory set of magnetic observations were made on shore at a spot on the beach near the extreme southern end of the slightly rising ground at La Playa. The instruments were set up just above high-water mark, and nearly due east of the U. S. Coast Survey Astronomical Station. The true bearing of the light-house on Point Loma was S. 3° 56' W., and its distance exactly two statute miles in a direct line. The spot was tested for local attraction by taking fore and back sights with a compass, but none could be detected. The position of the station, according to the U. S. Coast Survey Chart, was Lat. 32° 41' 58" N. Long. 7h 48m 529.6 W. SAN FBANCISCO, California. The ship was swung in this harbor, on June 23d, 1866, in the usual manner. Her position at the time was lat. 37° 48' N., long. 122° 22' W. Joint XII on the after turret was 5.3 inches to port. While we \\i re lying here the ship was swinging freely to the wind and tide. The observations taken on shore June 26th were made on the sand beach in a cove on the east side of Yerba Buena Island, the instruments being set up just at high-water mark, and about one hundred and fifty feet north of a long pier which runs out over a mud flat. The place was tested for local attraction by taking fore and back sights with a compass, but none could be detected. According to the U. S. Coast Survey Chart the position of this station was Lat. 37° 48' 46" N. Long. 8" 9m 22°,6 W. M A G iN E T I C OBSERVATIONS. SECTION III. ASTRONOMICAL OBSERVATIONS. THE observations contained in this section were all made on the sun, and are for the determination of latitude, local time, and true bearings. The instruments used were a prismatic sextant of six inches radius, by Pistor and Martins ; a mercurial artificial horizon ; and a pocket mean time chronometer, by Fletcher, marked number 906. The index correction of the sextant was usually obtained by measuring the diameter of the sun, both on and off the arc. For determining the density of the atmosphere thermometers with Fahrenheit scales, and a mercurial barometer graduated to English inches, were employed. The refractions have been computed by means of BESSEL'S tables, as given in LOOMIS' "Practical Astronomy;" from which book the tabular parts of the reduc- tions to the meridian have also been taken. The necessary fundamental data have been obtained from the American Nautical Almanac. Observations of circummeridian altitudes of the sun for latitude were made in sets of twelve, so arranged as to eliminate both the sun's semi-diameter, and all errors depending on the roof of the artificial horizon. Circummeridian Altitudes of the Sun for Latitude, observed at the south front of Fort Christian, St. Thomas, November 1865. 10" 55m o* 105 H' 20" - Index correction. 55 48 15 20 359° ii' 10" 0" 15' 5°" 56 M 16 5° — II IO 16 10 10 57 3 18 o ii 40 16 20 II o 31 21 40 i 5 22 20 35 ii 20.0 o 16 6.7 I T-J 104 18 IO OJ 2 9 18 2O Correction =-fi6' 1 6". 7 2 46 18 25 _ 3 28 18 5° Ex. ther. 83° 3 59 4 29 18 18 55 40 J At. ther. 86 Bar. 30. 1 6 inches. Mean of chronometer times . . . . . 1 1 om 2'.0 Chronometer slow of local mean time ° 40 47-3 Equation of time . . • + 14 47-i Local apparent time . ii 55 36-4 Mean of observed double altitudes i°4 48' 1 9". 2 Index correction . -i- 16 I6.7 Apparent altitude of sun's centre 52 32 18.0 Refraction . . . . . • • — o 42.1 14 REPORT ON Parallax Reduction to meridian Sun's declination Latitude •+ i i9-4 .—19 6 59.1 1 8° 20' o" N. Circummcridian Altitudes of the Sun for Latitude, observed at Isle Royal, Salute Islands, November 2&th, 1865. 10" 13- 57'- U 35-5 15 9-5 15 53 16 24.5 i? i-5 17 38 18 14-5 20 17 21 9 31 46.5 32 30 126 5° 3° 49 3° 49 3° 49 20 48 50 48 40 52 10 51 10 48 20 46 30 26 50 10 o Index correction. 359° n' ii to" 10 0° 1 6' 16 o" o 359 ii IO o 16 o Correction = + 16' 25". o Ex. then At. ther. Bar. 91 85 inches. Mean of chronometer times Chronometer slow o Equation of time Local apparent time Mean of observed d Index correction Apparent altitude of Refraction . Parallax . Reduction to meridian Sun's declination latitude Observations for time were usually made in such a manner as to eliminate both the sun's semi-diameter and all errors which might be produced by the roof of the artificial horizon. For full details of the method see page 33 of the " Reports on Observations of the Total Eclipse of the Sun, August 7, 1869," published by the U. S. Naval Observatory, Washington. The reduction of the observations for time has been effected by means of the following formula?: a=- — -_r-f_p : times . I0h i9m 37"-9 local mean time i 3° 19.4 . .+ 1 1 42.6 .... 12 i 39-9 ublc altitudes . 126° IS' 55"-° • . .+ 16 25.0 sun's centre . • • 63 16 IO.O . . 0 27.1 . .+ 0 3-9 n .+ 2 35-7 . . . 21 24 8-S . . . . - 5° vt 29" N. sn 1 == i/sin (S — a) cos S sec

= latitude of place Avhere observation is made. t = hour angle at the pole. t = equation of time. dt = correction of chronometer to reduce the reading of its face to local mean time. Double Altitudes of the Sun, for Time, observed at the flagstaff in the Navy-yard at Portsmouth, Va., October zgth, 1865. 8" STH, 7 S 49° 27' 50" ' 51 42 38 20 52 22 49 3° 53 23 5° 7 40 53 56 •5 17 5° 54 47 5° 32 20 55 5° 49 47 o 56 25 57 20 56 57 •5 5° 6 2O 57 59 •5 24 50 58 32 •5 34 3° 59 J3 •5 45 5° J r 20 Index correction, = + 15' 42" Ex. ther. 50°. Refraction = — 125" Parallax = + 8 At. ther. 92° Mean of observed double altitudes Local apparent time ..... Equation of time ..... Local mean time ..... Mean of chronometer times Chronometer fast of local mean time . Longitude west ...... Chronometer slow of Greenwich mean time Bar. 30.40 inches. Sun's declination — 13° 35' 16" Latitude +36 49 32 . - • • 5°° 7' 27" 9h 6m 4o".8 . — 16 10.6 8 50 30.2 . 8 55 11.3 o 4 41.1 •559-8 5 o 28.7 Double Altitudes of the Sun for Time, observed at the flagstaff in the Navy-yard at Portsmouth, Va., October 2<)th, 1865. Index correction, 42 nm 55' 40° 10' ff -\ 1 0 I 12 54 39 Si 20 !3 32- 5 38 30 } 14 9- 5 40 3° 3° 14 Si 17 o IS 36- 5 2 20 16 52. 5 39 37 3° 17 37 23 IO 18 24. 5 8 3° , '9 16. 5 37 46 ° 1 20 2 31 3° 20 55- 5 20 10 J 20 Ex. ther. 55° Refraction = — 1 70". i Parallax = + 8.0 At. ther. 79 Bar. 30.36 inches. Mean of observed double altitudes Local apparent time . Sun's declination — 13° 40' 42".o Latitude + 36 49 32. • 39° 1 6' 23". 3 16 REPORT ON Equation of time . . — o11 i6m n".6 Local mean t 3 ii 40-3 Mean of chr< »' Chronometer Longitude west . •559-8 Chronometer slow of Greenwich mean time . . . 5 o 29.7 Double Altitudes of the Sun for Time, observed at Fort Christian, St. Thomas, West Indies, November itf/i , 1865. 9" o™ 42'. 5 i 21.5 84° 32' 5°" 1 46 20 Index correction. 2 2 57 3° I 20 3 2-5 85 16 5° 359° 10' 50" o° 1 6' 20" 4 4 35 I0 ii o 16 10 4 54 • 85 Si «> . n 10 i 6 40 6 0.5 87 15 20 6 41 28 30 359 " °-° ° '6 23-3 7 10 7 54-5 37 ° I 2Q 50 20 U Correction = + 16' i8"-4 8 21.5 59 20 8 48-5 88 7 o J Ex. ther. 84° At. ther. 86° Bar. 30.12 inches. Refraction = — 57".; Sun's declination — 18° 5' 2". 5 Parallax i = -j- 6.2 Latitude + 18 20 27. Mean of observed double altitudes . 86° 26' 2s".8 I0h Im 20'.0 Mean of chronometer times 9 5 5-2 Chronometer slow of local mean time o 40 43.6 Chronometer slow of Greenwich mean time . ..50 26.3 Double Altitudes of the Sun for Time, observed at Isle Royal, Salute Islands, November zWi, i 8" 47- 58' 109° 58' 20" ' 48 35 no 9 50 Index correction. 49 20 ° I 20 49 58 35 3° 359° ii' o" o° 15' 50" 5° 31 45 5° n o 16 o 5» 56-5 52 5° . 10 50 16 10 51 44-5 5* 39-5 112 13 O 30 o 359 10 56.7 o 16 o.o 53 '3-5 40 ° I 2n 53 47 50 o [ u Correction = + 16' 31 ".6 54 19 113 o o 54 53-5 10 0 f Ex. ther. 93° Refraction = — 36". 3 Parallax = + 4.9 At. ther. 85° Bar. 30.13 inches. Sun's declination —21° 23' 3o"-3 Latitude +5 17 29. Mean" of observed double altitudes Local apparent time . Equation of time Local mean time Mean of chronometer times in0 35' 26".6 10 8 21 51 43-8 48.0 28.6 MAGNETIC OBSERVATIONS. 17 Chronometer slow of local mean time. Longitude west ...... Chronometer slow of Greenwich mean time i 3ora I9".4 3 3° IT-4 5 30.8 Double Altitudes of the Sun for Time, observed at Ceara, Brazil, December i$th, 1865. Index correction. IS™ 1 3'- 5 63° o' o' 15 58.5 62 40 o 16 41 20 o 17 3-5 IO 0 i-j 26 62 0 0 18 43 62 3° o 19 5 20 o 19 26.5 10 0 19 5° 62 0 0 20 "•5 61 5° 0 359° II? o" o° 1 6' o" 10 5° 10 10 40 o 359 10 50.0 o 16 3-3 Correction = + 16' 33". 3 Ex. ther. 84° At. ther. 82° Bar. 30.05 inches. Refraction = — 89". 5 Sun's declination — 23° 12' 4".o Parallax = + 7-4 Mean of observed double altitudes Mean of chronometer times Equation of time 62° 18' o".o 20-9 Reducing this observation with latitude = — 3° 43' 15", we find the chronometer 2h 26m 293.6 slow of local mean time. Reducing it with latitude = — 3° 44' 15", we find the chronometer 2h 2(?'n 32s.O slow of local mean time. Double Altitudes of the Sun for Time, observed at Ceara, Brazil, December \tfh, 1865. Index correction. 2m °'-5 99° 30' o" 2 24-5 40 0 2 49 5° o 3 12.5 IOO o o 3 36 IO o 6 9 IOO IO 0 6 32-5 20 o 6 57-5 30 o 7 21-5 40 o 7 45-5 IOO 5° o 359° 10' 30" o° 1 6' 10" 40 20 40 20 359 I0 36-7 o 16 16.7 Ex. ther. 81° Refraction = — 45"-9 Parallax = + 5-6 At. ther. 82° Sun's declination Correction = + 16' 33". 3 Bar. 30.12 inches. Mean of observed double altitudes Mean of chronometer times Equation of time 23° 14' \d".t IOO" 10 O .0 7" 4ra 5 2'- 8 - 4 59-5 Reducing this observation with latitude = — 3° 43' 15", we find the chronometer 2h 26m 339.7 slow of local mean time. Reducing it with latitude = — 3° 44' 15*, we find the chronometer 2" 26m 303.9 slow of local mean time. February, 1872. 18 REPORT ON Double Altitudes of the Sun for Time, observed at Ceara, Brazil, December itf/i, 1865. ii' SI- Si* 100° So' o" S'2 14-5 40 o 5* 37 3° 0 53 i-5 20 0 53 26 10 o 56 o 98 o 0 56 23 97 5° o 56 48 40 0 57 "•5 3° o 57 34 20 o Index correction. 2(3 359° I( )' So" o° 15' So" 40 16 20 20 16 0 359 * 3 36.7 o 16 3-3 Ex. ther. 86° Refraction = — 4s".6 Parallax = + 5.6 Correction = + 16' 4o".o At. ther. 83° Bar. 30.00 inches. Sun's declination — 23° 15' 27".4 Mean of observed double altitudes Mean of chronometer times . » Equation of time 99° nh 5' o".o S4m42'-6 4 53-7 Reducing this observation with latitude = — 3° 43' 15". we find the chronometer 2h 26" 30'. 7 slow of local mean time. Reducing it with latitude — — 3° 44' 15", we find the chronometer 2h 26m 33". 1 slow of local mean time. In order to determine both the latitude of Ceara and the error of the chronometer from the three observations which have just been given, we proceed as follows: Comparing the error obtained on the afternoon of December 13th, with that obtained on the afternoon of December 14th, we find that the chronometer was losing 1.17 seconds per day; and this rate is independent of any small change in the adopted value of the latitude. By means of this rate, reducing all the observed chronometer errors to 2h 26m P. M. December 14th, and then plotting them according to Sumner's method, we get for the place of observation Latitude 3° 43' 59" S. ••ind for the chronometer, Chronometer slow of local mean time 211 26™ 32'.s Longitude west . . . 2 34 6 Chronometer slow of Greenwich mean time . . . . 5 o 38.5 Double Altitudes of the Sun for Time, observed at Pcrnambuco, Brazil, December 2$d, 1865. 7" 30" '5' 3<> 39-5 3' 3 3* 52-5 33 '5 33 40 118° n.S Index correction. 359° 10' 50" o° 1 6' o" 5° 16 10 359 10 50.0 o 16 5.0 Correction = + 16' 32"-5 Ex. ther. 83° Refraction =• — 32". i Parallax = + 4.5 At. ther. Bar. Sun's declination — 23° 26' 31" Latitude — 8 3 37 Mean of observed double altitudes Local apparent time . Equation of time Local mean time 1 1 8° 20' ioh 9" — o 10 8 o".o 3'-5 31.2 32-3 MAGNETIC OBSERVATIONS. 19 Mean of chronometer times Chronometer slow of local mean time Longitude west Chronometer slow of Greenwich mean time 7 31 57-5 2 36 34.8 2 19 28.2 4 56 3-° Double Altitudes of the Sun for Time, observed at Bahia, Brazil, December z-]th, 1865. 6" 52" 52 S2 54 54 55 10s 3i- 54- 32 53- 16. 5 5 5 5 98° 98 3°' 40 5° 3° 40 5° °"1 - o lao o 3 359° Index coi 10' 40" 5° rection. 0° 1 6' 10" o 359 10 45.0 Correction = o 16 + 16' 35"-o 5-° Ex. ther. 88° Refraction = — 45". 9 Parallax = -f- 5.7 At. ther. Bar. Sun's declination — 23° 19' 33". 8 Latitude — 12 56 55. Mean of observed double altitudes Local apparent time ..... Equation of time ..... Local mean time ..... Mean of chronometer times Chronometer slow of local mean time Longitude west ...... Chronometer slow of Greenwich mean time •+ 98° 40' o".o 9h I4m22'.S i 27.3 9 15 49.8 6 53 43.0 2 22 6.8 2 34 0.5 4 56 7-3 Double Altitudes of the Sun for Time, observed at the Light-house in Fort St. Antonio, Bahia, Brazil, December 2<)th, 1865. 8" I4ra 46'. 5 134° 5°' o"' 15 IO 135 o o 15 31 IO 0 *S 56 20 o 16 19-5 3° o X7 17-5 r34 5° o 17 44 135 o o 18 7 IO 0 18 3^-5 20 o 18 54 3° o Index correction. 359° 10' 50" So 4o o° 1 6' o" IO 10 359 10 46.7 o 16 6-7 Correction = + 16' 31 "•3 Ex. ther. 84° Refraction = — 22".! Parallax = + 3.3 2Q 2Q At. ther. Bar. Sun's declination — 23° Latitude — 13 13 31". i 55- Mean of observed double altitudes Local apparent time Equation of time Local mean time Mean of chronometer times Chronometer slo> Longitude west . 10 . . . 1U .5" 2 27.6 ...... 10 38 53-3 - times .... . & 16 49-7 local mean time 2 22 3-6 . 2 34 6.9 Greenwich mean time . 4 56 10.5 20 REPORT ON Double Altitudes of the Sun for Time, observed at Rio Janeiro, Brazil, January <)th, 1 866. 5k 13" 17' 47° 40' o" 13 39 5° o »4 3-5 48 o o 14 26.5 10 o 15 43 47 40 0 16 8 5° o r? 16 29 48 0 o 16 53 10 o Ex. ther. 74° At. ther. Refraction =• — i23".2. Parallax = + ^ 9 Index correction. 359° i°' 40" 3° 0° 1 6' 15 o" 50 359 1° 35-° o 15 55-° Correction = + 16' 45". o 77° • Bar. 29.94 inches. Sun's declination — 22° 6' 24". 6 Latitude — 22 54 5. Local apparent time Equation of time Local mean time Mean of chronometer times Chronometer slo Longitude west juble altitudes • 47° 55' It . • . . - 7" j,m 1 9'- 5 % • . .+ 7 23.8 . . • 7 18 43-3 r times . • 5 IS 4-9 ' local mean time 2 3 38-4 . . 2 52 3°-7 Greenwich mean time 4 56 9.1 Doubt f Altitudes of the Sun for Time, absented at Rat Island, harbot of Rio Janeiro, January gth, 1866. 7k 27" o' 1 08° o' o" Index correction. 27 20 10 o 27 42-5 20 o 'O 359° 10' 30" °° 15' S°" 28 4-5 3° o 40 5° 28 26.5 40 o 40 5° 29 21 1 08 o o *9 45 10 o 359 10 36.7 o 15 50.0 3° 5 20 o 2Q 30 26.5 30 o Correction = + 16' 46". 6 30 48 40 o Ex. ther. 75° At. ther. 77° Bar. 29.94 inches. Refraction = — 39".8 Sun's declination — 22° 5' 37"-3 Parallax = + 5.1 Latitude — 22 53 45. Mean of observed double altitudes . 108° 20' o".o Local apparent time . •"..!• . . 9" 25™ oV7 Equation of time . ' . -f 7 26.0 Local mean time ...... 9 32 26.7 Mean of chronometer times .... 7 28 53-9 Chronometer slow of local mean time 2 3 32-8 Longitude west ........ 2 52 37-9 Chronometer slow of Greenwich mean time 4 56 10.7 Double Altitudes of the Sun for Time, observed at Monte Video, Uruguay, January i8//4, 1866. 0" 26'.5 45° So' o" • 0 5«-5 40 0 I 17 3° o 2 3-5 10 o 3 5-5 45 So 0 3 3«> 40 o 3 56.5 3° o 4 46 10 0 Index correction. 359° 10' 30" o° .5' So" 40 40 40 40 359 10 36.7 ° *5 43-3 Correction =-f 16' 50' '.o MAGNETIC OBSERVATIONS. 21 Ex. ther. 76° Refraction = — 130". 2 Parallax = + 8.0 At. ther. 79° Bar. 30.02 inches. Sun's declination — 20° 26' 55". 2 Latitude —34 53 39 Mean of observed double altitudes Local apparent time ..... Equation of time . ... Local mean time ..... Mean of chronometer times Chronometer slow of local mean time Longitude west ...... Chronometer slow of Greenwich mean time 45C 5 4 i 3 4 32' 3° -° 3m 5s- 2 10 51.4 13 56.6 29.6 27.0 55-8 56 22.8 2 II 44 Double Altitudes of the Sun for Time, observed on Rat Island, harbor of Monte Video, Uruguay, 29™ i'.5 . 82° 3°' 0 29 25-5 20 o 29 5°-5 10 o 3° '3-5 82 0 o 3° 38.5 81 5° o 31 38-5 82 3° 0 32 3 20 o 32 26 10 o 32 51 82 0 0 33 16 81 5° o Index correction. Ex. ther. 74° Refraction = — 62". 7 Parallax = -f 6.5 January z^th, 1866. 23 20 At. ther. Bar. Sun's declination — 19" 6' 33".8 Latitude — 34 53 18 359° 10' 10" 0° is' 40' i 10 10 40 10 10 20 359 10 10.0 0 15 33 3 Correction = + 17' 8" 3 Mean of observed double altitudes .... Local apparent time ...... Equation of time ....... Local mean time ....... Mean of chronometer times ..... Chronometer slow of local mean time Longitude west ........ Chronometer slow of Greenwich mean time Double Altitudes of the Sun, for Time, observed at Sandy Point, in the Straits of Magellan, February ith, 1866. . 82° • 3" .+ • 3 2 I • 3 4 10' 3ora 12 42 31 II 44 56 o".o 5s- 7 29.2 34-9 8.4 26.5 52-9 19.4 IO 9m 24'-5 90° 30' o' 0 ii 40 o I i 5° o i 49-5 91 o o 2 37-5 10 o 4 39-5 90 30 o 5 27-5 40 o 6 18.5 5° o 7 9 91 o o 7 58.5 IO 0 Index correction. 359° i°' 20" o° 15' 40" 3° 5° 35 35 359 I0 28.3 ° IS 41.7 Ex. ther. 52° Refraction = — 56". 9 Parallax = + 6. i Correction = + 16' 5s".o At. ther. 70° Bar. 30.04 inches. Sun's declination — 15° 14' is"-6 Latitude —53 I0 20 Mean of observed double altitudes Local apparent time . Equation of time 9° 5° ~h „! 10" O" 2B.2 25-5 22 REPORT ON Local mean time Mean of chronometer times Chronometer slow of local mean time Longitude west . Chronometer slow of Greenwich mean time ioh i6m 27". 7 10 3 39.6 O 12 48.1 4 43 35-3 4 56 23-4 Double Altitudes of the Sun for Time, observed near Valparaiso, Chile, March 2t/, 1866. 5°" l5'-5 62° 5° 39-5 61 51 3 Si 5i-5 52 52 62 53 J5-5 61 53 39-5 54 3° Ex. ther. 67° Refraction = — 92" Parallax = + 7. Index correction. 359° 10' 40" 45 40 0° 15' o" 5 10 359 10 41.7 0 15 5-° Correction = + 17' 6" 6 At. ther. Bar. Sun's declination — 53" Latitude •4 4 Mean of observed double altitudes Local apparent time Equation of time Local mean time . . . . Mean of chronometer times Chronometer slow of local mean time Longitude west Chronometer slow of Greenwich mean time Double Altitudes of the Sun for Time, observed in Valparaiso, Chile, March 2g/h, 1866. — 33 i. 4 61° 3" 42' 49m 3°". o 44"- 3 + 12 17.9 4 2 2.2 3 o 4 4 S2 9 46 56 I5.8 46.4 31 17.4 36" 55' 37 40 38 23 40 1.5 40 45-5 41 28.5 Ex. ther. 71° Refraction = Parallax = 73" 73 Index correction. 2O 359° 10' 20" 5° 45 o° 14' So" 45 55 359 10 38.3 Correction o 14 = + '?' T5 50.0 ".8 At. ther. -75-1 + 6-9 69° Bar. 30. 23 inches. Sun's declination + 3° 31' 38" Latitude — 33 47 Mean of observed double altitudes .... Local apparent time Equation of time ....... Local mean time Mean of chronometer times Chronometer slow of local mean time. Longitude west ..... Chronometer slow of Greenwich mean time Double Altitudes of the Sun for Time, absented in Valparaiso, Chile, April yth, 1866. 73° 15' o".o 2h 43m 52'. o 4 47.0 2 48 39-° 2 39 12.2 0 9 26.8 4 46 45-7 4 56 I2-5 36- 37 38 40 40 26'. 5 16.5 9 i-5 53 44-5 77° 78 77 78 30' 45 o 3° 45 o Index correction. 359° 10' So" So So o° 15' 10" 10 TO 359 10 50.0 Correction o 15 TO.O = + 17' o".o MAGNETIC OBSERVATIONS. 23 Ex. ther. 67° At. ther. 65° Bar. 30.17 inches. Refraction =_69".8 Sun's declination + 6° 53' 28".6 Parallax = + 6.7 Latitude —33 i 47 Mean of observed double altitudes Local apparent time Equation of time Local mean time Mean of chronometer times Chronometer s\o\ Longitude west . Chronometer slov Double Altitudes of the Sun for Time, observed in Valparaiso, Chile, April "jth, 1866. 2Q Index correction 2© qh 15 46" u .U 1 1 9'. 6 4. *rf 2 8 o . 9 48 o.y 28.5 r times . 9 39 5-2 local mean time o 9 23-3 . 4 46 45-7 Greenwich mean time 4 56 9.0 9" 43m I5*-5 79° 3°' 0 44 6-5 45 0 45 °-5 80 o o 46 57 79 3° o 47 49-5 45 0 48 44-5 80 o o = + 17' o".o Ex. ther. 67° Refraction = — 6 7". 3 Parallax = + 6.6 At. ther. 65° Sun's declination — Latitude Mean of observed double altitudes Local apparent time ..... Equation of time ..... Local mean time ..... Mean of chronometer times . • . Chronometer slow of local mean time Longitude west . ... Chronometer slow of Greenwich mean time Double Altitudes of the Sun for Time, observed in Valparaiso, Chile, April i^th, 1866. ir . 30. 17 inches. - 6° 53' 35"-4 -33 i 47 . 79° 45' o".o 9" 53m I4'.o . + 2 8.8 . 9 55 22.8 '. 9 45 58.9 0 9 23-9 . 4 46 45-7 . 4 56 9.6 3" 5<3m 20'. 5 51 i-5 51 39 53 7 53 46 54 24.5 36° 30' o") 15 o C2Q o o 3 36 30 o IS o Index correction. 359° 10' 40" 40 45 14- 50" 45 5° Ex. ther. 65° Refraction = — 1 70", 3 Parallax = + 8.1 At. ther. 359 10 41.6 o 14 48.3 Correction = -f 17' is".o 66° Bar. 30.13 inches. Sun's declination 4- 9° 33' 33". 6 Latitude — 33 i 47 Mean of observed double altitudes Local apparent time Equation of time Local mean time Mean of chronometer times Chronometer slow of local mean time Longitude west ...... Chronometer slow of Greenwich mean time 36° «s* o".o 4h 3ra ! 3'. 2 + o ii. 6 4 3 24.8 3 S2 23.1 o ii !-7 4 46 45-7 4 57 47-4 ^ 4 REPORTON Double Altitudes of the Sun for Time, observed on the Island of San Lorenzo, near Callao, Pent, April tbth, 1866. ii" i7m 45' 123" o' o" y index co rrection. o t '/ 18 52 15 o ft§ 359° "' i°" o° 15' o' 20 3 30 o 3 0 22 46 123 0 0 • 24 2 15 0 MO 359 ii 10-0 o 15 o.o 25 18 30 o 3 Correction = + 16' 55".o Ex. ther. 80° At. ther. Bar Refraction = — 29". 2. Sun's declination + 13° 35' 18" Parallax = + 4.0 Latitude -12 5 14 Mean of observed double altitudes 123° 15' o".o Local apparent time . , n" I2m33a.o 2 18.8 ii 10 14.2 Mean of chronometer times . . . . . II 21 27.7 Chronometer fast of local mean time .... 0 II 13-5 Longitude west . >...., 5 9 9-i Chronometer slow of Greenwich mean time 4 57 55-6 Double Altitudes of the Sun for Time, observed at Pay fa, Peru, May -]th, 1866. 8" 40" 44'. 5 62° o' o" Index correction. 41 17.5 15 o 2Q 359° «' 3°" o° 15' o" 41 51 30 o 25 0 43 i-5 62 o o 25 0 43 34-5 15 ° -O Z'Q/ 44 7-5 3° ° 359 ii 26.7 o 15 o.o . Correction = + 16' 46".6 Ex. ther. 78° At. ther. 80° Bar . 30.06 inches. Refraction = — 90". 7 Sun's declination -f- 16° 50' 46" . Parallax = + 7.3 Latitude -5 5 36 Mean of observed double altitudes .... 62° 15' o".o Local apparent time . • • . • « gh ^m 22l j Equation of time . . . , . . . . * 3 38-1 Local mean time . . , • . . * « 8 15 44-2 Mean of chronometer times . • . . « 8 42 26.1 Chronometer fast of local mean time .... o 26 41.9 Longitude west . . . . 5 24 22.0 Chronometer slow of Greenwich mean time 4 57 4°-i Doubli. Altitudes of the Sun for Time, observed on Flamenco Island, Panama Bay, May itfh, 1866. 9" 24" 59' 95° o' o'" Index correction. 25 3« 15 o '2© 359° "' 3°" o° 15' 10" 26 3-5 3° ° 20 M 55 27 12 95 o o " 20 14 40 27 43-5 15 o 28 15 30 o > 359 ii 23-3 o 14 55.0 Ex. ther. 85° Refraction = — 49"-5 Parallax = -\- 5.7 Correction = -f 16' so".8 At. tner. 85" Bar. 30.10 inches. Sun's declination + 18° 39' 49" Latitude + 8 54 31 MAGNETIC OBSERVATIONS. 25 Mean of observed double altitudes Local apparent time ..... Equation of time Local mean time Mean of chronometer times Chronometer fast of local mean time . Longitude west ...... Chronometer slow of Greenwich mean time 95° 15' o".o 9h iom i3".5 9 6 20.4 9 26 37.3 O 20 16.9 5 18 1.8 4 57 44-9 Double Altitudes of the Sun for Time, observed at Acapulco, Mexico, May $oth, 1866. ioh 25" 26 26 27 28 28 36' 5-5 38-5 49-5 22 54 89° 89 Index correction. 359° «' 10" 0° 15' o" 0 14 40 20 15 o 359 ii IO.O o 14 53-3 Ex. ther. 89° Refraction = — 5 4". 5 Parallax = -f 6.0 At. ther. Correction = + 16' 5 8". 3 ;° Bar. 30.10 inches. Sun's declination +21° 48' 7" Latitude + 16 50 3 Mean of observed double altitudes Local apparent time ..... Equation of time ..... Local mean time ..... Mean of chronometer times Chronometer fast of local mean time . Longitude west ...... Chronometer slow of Greenwich mean time 89° 8" 8 IS' 48m 2 45 o".o 46.4 52.0 10 27 14.2 i 4i 22.2 6 4 39 58 29.4 7.2 Double Altitudes of the Sun for Time, observed in Magdalena Bay, Lower California, June %th, 1866. Index correction. Sh 20- 49" 21 23 21 56 23 8-5 23 41-5 24 5 100" 45 3° 100 45 3° 15 o o o o o 2Q 359° 10' 50" o° 14' 40" ii 20 M 5° o/^S 10 3° 15 o 2Q 359 10 53-3 o 14 50.0 Correction = + 17' 8". 4 Ex. ther. 69° Refraction = — 46". 4 Parallax = + 5.4 At. ther. 70° Bar. 30.02 inches. Sun's declination + 22° 53' 42" Latitude + 24 38 Mean of observed double altitudes Local apparent time Equation of time Local mean time ..... Mean of chronometer times Chronometer fast of local mean time . Longitude west . . ... Chronometer slow of Greenwich mean time . too" 30' o".o . 2" 53m42".3 .— i 14.5 2 52 27.8 5 22 32.2 2 30 4.4 7 28 24.0 4 58 19.6 February, 1873. 26 REPORT ON Double Altitudes of the Sun for Time, observed at La Playa, San Diego Bay, California, June I5//4, 1866. Sb 1 6" 41'. 112° 3°' on 17 16 15 *2O i7 51.5 o 0 1 19 10 112 30 I 19 46 15 >2Q 20 21.5 0 0 1 Index correction. 359° 30" 35 20 14' 5°' 3° 5° Ex. ther. 71° Refraction = — 37". 4 Parallax = + 4-7 At. ther. 359 ii 28.3 o 14 43.3 Correction = + 16' 5 4". 2 72° Bar. 30.12 inches. Sun's declination +23° 20' 22" Latitude + 32 41 58 Mean of observed double altitudes Local apparent time . ... Equation of time Local mean time Mean of chronometer times Chronometer fast of local mean time . Longitude west Chronometer slow of Greenwich mean time 112° 15' 0".0 2h 27m 47'. 3 -f o 11.3 2 27 58.6 5 18 3I-1 2 50 32.5 7 48 52.6 4 58 20.1 Double Altitudes of the Sun for Time, observed on Yerba Buena Island, San Francisco Bay, California, June 2dth, 1866. Index correction. 4" i6m 40'. 5 75° '5' o" 17 18 3° 0 2Q >7 55-5 45 0 19 18.5 75 IS o »9 54-5 3° 0 2© 20 30 45 0 359° i t' 3°" o° 14' 30" 35 5° 25 5° 359 i i 30.0 o 14 43-3 Correction = + 16' 53". 4 Ex. ther. 67° Refraction = — 7 2". 5 Parallax = + 6.6 At. ther. Bar. Sun's declination Latitude •23C 1 22' 7" 37 48 46 f fi 75° 3° 0.0 8* 2ra 5»'-4 2 29.6 8 5 28.0 4 18 36-2 8 13 8.2 8 9 22.6 o 3 45-6 Mean of observed double altitudes .... Local apparent time Equation of time Local mean time Mean of chronometer times ..... Chronometer fast of local mean time .... Longitude west . Chronometer fast of Greenwich mean time . The chronometer used in making this observation was T. S. and J. D. Negus* No. 1287. True bearings were determined by measuring with a sextant the angle between the sun's limb and some well-defined terrestrial object, the time being noted at the instant the angle was observed. If the terrestrial object was much elevated above the horizon its angular altitude was also measured. Knowing the latitude of the place of observation, the local time, and the sun's declination, the sun's zenith distance and true bearing were calculated. Then, having the zenith dis- tance of the sun, the zenith distance of the terrestrial object, and the measured angle between the sun and the terrestrial object, the horizontal angle between them MAGNETIC OBSERVATIONS. 27 was computed, and applying it to the sun's true bearing the true bearing of the terrestrial object at once became known. The formulae employed were as follows. Let T = mean of observed chronometer times. dt = correction of chronometer to reduce the reading of its face to local mean time. r = equation of time. t = sun's hour angle, or the apparent time. £1 = mean of observed angular distances between the sun's limb and the ter- restrial object. o = index correction of sextant. s = sun's semi-diameter. a = apparent zenith distance of sun's centre. b = zenith distance of terrestrial object. c = true angular distance between the sun's centre and the terrestrial object. C = horizontal angle included between the sun's centre and the terrestrial object. <£> = latitude of the place of observation. A = azimuth, or true bearing, of sun's centre. £ = true zenith distance of sun's centre. <$ = sun's declination. r = refraction due to apparent altitude of sun's limb. B = true bearing of terrestrial object. Then we have t= T+dt + v tan 5 tan M — cos t tan t cos M tan A = -i — — — y/r sin (d> — M) tan = - - cos A where A is to be taken greater or less than 180°, according as t is greater or less than 180°. a = % — r c = n + co + s If b is exactly 90°, we have ~ cose cos C = -.— sin a But if b is either greater or less than 90°, we have CT + & + C AJ = - fi - sn am — Finally B = A± C 28 REPORT ON In a few instances true bearings were obtained by observing the sun when its apparent elevation above the horizon was equal to its diameter. In that case = 90° and then cos A = sin 8 COSlp i in which the azimuth will be north or south of the prime vertical according as the sun's declination is north or south. Observations of the Sun, made October $ist, 1865, to determine the true tearing of the object used as an azimuth mark in swinging the ship at Hampton Roads, Va. ioh iom 50* 127° 20' ii 45 38 12 15 45 14 o 128 4 14 39 8 T IO 12 42 a 127 47 Chronometer fast o 4 50 u + 16 * + 16 16 S + 16 Apparent time 10 24 8 c 128 19 t 23° 58' f 55 59 1 — 14 16 r — i t 36 58 a 55 58 M — *5 33 b nearly 90 * — M 52 31 C 138 26 True bearing of sun S. 28° 21' E. i. Seminary to sun ........ 138 26 i. Seminary to Rip Raps 62 44 / Rip Raps to tree . 114 37 True bearing of tree S. 10 34 W. Observations of the Sun, made November i%ih, 1865, to determine the true bearing of the object used as an azimuth mark in swinging the ship at St. Thomas, West Indies. 7h °m 5" 34° 13' 2 '5 15 4 45 10 8 15 12 9 45 12 T 7 5 i " n 34 12 Chronometer slow o 40 47 + 16 r + M 36 s + 16 Apparent time 8 o 24 c 34 44 / 59° 54' r 69 48 1 — 19 19 r 2 t 18 20 a 69 46 M — 34 57 b nearly 90 t M 53 '7 C 28 52 True bearing of sun S. 60° 27' E. L Sun to Peak 28 52 True bearing of Peak S. 3' 35 MAGNETIC OBSERVATIONS. 29 Observations of the Sun, made Novcm. er 28tA, 1865, to determine the true bearing of the object used as an azimuth mark in swinging the ship at Isle Royal, Salute Islands. 6" 27" 5" 74° 5°' 28 59 46 3i 8 40 T 6 29 4 n 74 45 Chronometer slow i 30 19 u + i? r + ii 45 S + 16 Apparent time 8 ii 8 c 75 18 t 57° 13' t 62 4 S 21 22 r 2 t 5 r7 a 62 2 M — 35 S2 b nearly 9° $ — M 41 9 C 73 '8 True bearing of sun . S. 62° 24' E. L Sun to Nob . . . . • • • 7* 18 . S. 10 54 W. Observations of the Sun, made December izth, 1865, to determine the true bearing of the object used as an azimuth mark in swinging the ship at Ceara, Brazil. 3" nm 8s 87° 30' 13 o 22 M 32 21 T 3 I2 53 n 8? 24 Chronometer slow 2 26 32 u +' 16 * + 5 47 S + 16 Apparent time 5 45 12 c 87 56 t 86° 18' c 85 4 S — 23 8 r — 18 t> — 3 43 a 84 46 M — 81 25 b nearly 9° 5 19 32 16 40 42 7 Chronometer slow 9 IS 19 0 12 48 Q u 119 + 3° 17 t — 14 30 S + 16 Apparent time 9 13 37 C 120 3 - 4i° 36' f 5° 32 — '4 37 r i V — 53 " a 5° 31 JfZ — 19 14 b 89 34 f M 33 57 C i to 54 True bearing of sun .... . N 56 0 20' E. L Mount St. Felipe to sun . . . . .' .' ',30 54 True bearing of Mount St. Felipe ... . S. 7 14 W. MAGNETIC OBSERVATIONS. 31 Observations of the Sun, made April zd, 1866, to determine the true bearing of the object used as an azimuth mark in swinging the ship at Valparaiso, Chile. T Chronometer slow •c Apparent time / S M 3" 18 15 n u S c f r a /> nearly C 86° 56' 58 6 17 39 o 20 17 + 3 53 86 57 + i7 6 i 15 87 14 90° 19' 18 31 8 55 89 3 — 80 8 86 54 — 14 86 40 90 86 14 32 REPORT ON True bearing of sun I, Peak to sun . True bearing of Peak . N. 71° 49' W. 8? M S. 20 57 W. Observations to determine the true bearing of the object used as an azimuth mark in swinging the ship in the harbor of Acapulco, Mexico. When determining the magnetic declination with the portable declinometer, on May 3oth, 1866, an observation of the sun with the theodolite gave N. 6° 22' E. as the true bearing of the gate of Fort St. Diego from the shore station. We then have True bearing from station to Fort . Monadnock to Fort . True bearing from station to Monadnock True bearing from Monadnock to station Clump to station True bearing of clump .... . N. 6° 22' E. . 26 54 . N. 20 32 W. S. 20° 32' E. 87 45 N. 71 43 E. Obsen>ations of the Sun, made June qtn, 1866, to determine the true bearing of the object used as an azimuth mark in swinging the ship in Magdalena Bay, Lower California. Owing to a combination of unfortunate circumstances, the only available method of determining a true bearing was by observing with the solar compass, set up on the quarterdeck of the ship. In that way I found True bearing of Peak S. 46° 30' E. which can only be considered as a near approximation to the truth. Observations of the Sun, made June 2$d, 1866, to determine the true bearing of the object used as an azimuth mark in swinging the ship at San Francisco, California. 7b 5« 1?. 92° 22' 6 52 39 7 55 43 T 7 6 41 Q 92 35 Chronometer fast o 3 12 • + i7 r — i 5i s — Apparent time 7 i 38 f 92 52 / — 74 35' f 64 8 8 23 26 r 2 » 37 48 a 64 6 M 58 3° b 89 5i * — M 20 42 C 93 i6 True bearing of sun N. 79° 26' E. L Red Rock to sun 93 16 True bearing of Red Rock N. 13 50 W. The following triangulation was made for the purpose of determining the geo- graphical position of some points in and about Ceara, Brazil. The angles were observed on December 14th, 15th, and 16th, 1865. Those between the Powhattan, MAGNETIC OBSERVATIONS. 33 Monadnock, and Custom-house were not measured simultaneously, and as the two ships were riding at anchor with a considerable amount of chain out, it is probable that they shifted their positions after the angle at the Powhattan was measured, and before the angles at the Monadnock and Custom-house were taken. This will account for the excess of the sum of the three angles over 180°. In the accompanying sketch the different points are designated as follows : A = Point Macoripie Light-house. B = Northeast corner of Custom-house on the wharf. C = U. S. Iron-clad Monadnock. D = U. S. Sloop of War Powhattan. E = most southern of the two steeples on the Church of the Conception. F = most southern of the two steeples on St. Joseph's Church. M = Magnetic and Astronomical Station of December 13th and 14th. Scale: 1 inch = 4000 feet. The observed angles were as follows: Angles at B. Angles at C. £> to A = 55° 12' Dlo A = 36° 19' D to C = 84 17 Z> to B = 71 14 F to C = 73 12 ^10^=42 28 E to C=I25 6 j? to .£ = 15 40 E to .F = 52 15 -<4 to .£ = 95 6 From these we obtain the following corrected Angles at B. Angles at C. A to E = 95° n' />to B = 70° 58 ^10^=52 9 Z> to A = 36 14 F\.o C = 73 14 A to /? = 34 44 f to D = 84 5 .Z? to ^ = 15 40 Z>tOv4 = 55 21 E to ^= 26 48 Angles at D. A to B = 101° 35' B to C = 25 13 vi to C = 1 26 49 Angles at D. A tC #=10!° 36' 24 57 Bio C = March, 1872. 34 REPORT ON The Powhattan fired a salute, and, from the mean of seven observations, the interval between the flash and report, noted at B, was 6.55 seconds. External thermometer 86°. Hence the distance from B to D was 7526 feet. Distance from B to M = 200 feet. Azimuth from M to A = N. 75° 38' E. Angle A MB = 128° 57'. From these data we find the 'distances between the several points as follows : BE = 1443 feet. CF = 3568 " AD= 1 581 4 feet. AC = 21491 " AB = 18826 " ^^=18702 " CE = 4355 feet. ^£• = 3358 ;; Angle BAM=o° 28' Azimuth from Mto A = " " B to A = Angle AMB=* 128° 57' Angle AB M=fso° 35' • N. 75° 38' E. N. 76 6 E. Azimuth from B to E = S. 8° 43' E. " B to ^ = 8.43 26 W. Assuming the position of M to be Lat. 3° Long. 2h we get finally 43' 59". o S. 34m 6'.oo W. Station. Latitude. Longitude. B E F A 3° 43' 5 7". 8 S. 3 44 12-0 3. 44 15-9 3 43 13-3 2b 34m 6'. 1 1 W. 2 34 5-97 2 34 7-25 2 33 54-10 For convenience of reference the results of the observations contained in this section, together with the chronometer comparisons made during the cruise, are here collected and appended. Observed Latitudes. Name of station. Latitude. Fort Christian, St. Thomas . 18° 20' o" N. Isle Royal, Salute Islands Magnetic Station, Ceara, Brazil Custom-house, " " . 5 3 •t 43 4-2 29 59 58 N. S. S Church of the Conception, Ceara, Brazil 3 44 12 S. St. Joseph's Church, " " . 44 16 S. Point Macoripie Light-house, " " . 3 43 S. MAGNETIC OBSERVATIONS. 35 Errors of Pocket Chronometer, Fletcher, No. 906. Station. Date. Error on Local Mean Time. Error on Greenwich Mean Time. Portsmouth, Va. October 29, 1865 Oh ^m 4I. j fasl 5h om 28'. 7 slow Portsmouth, Va. tt ft 4 40-1 " o 29.7 St. Thomas .... November 13, o 40 43.6 slow o 26.3 Isle Royal 28, I 30 19.4 o 30.8 Ceara . ... December 14, 2 26 32.5 5 o 38.5 Pernambuco .... 23. 2 36 34.8 4 56 3-° Bahia. . , . 27. 2 22 6.8 56 7-3 Bahia 29.- 2 22 3.6 S6 IO-5 Rio Janeiro . January 9, 18 6 2 3 38-4 56 9.1 Rio Janeiro . . tt 2 3 32.8 56 10.7 Monte Video .... 18, I II 27.0 56 22.8 Monte Video ... 24, I II 26.5 56 19.4 Sandy Point .... February 7, 0 12 48.1 56 23.4 Valparaiso ..... March 2, o 9 46.4 56 17-4 Valparaiso ..... 29, 9 26.8 56 12.5 Valparaiso ..... April 7, 9 23.3 56 9.0 Valparaiso ..... ( tt o 9 23.9 4 56 9.6 Valparaiso ..... i4, o ii 1.7 4 57 47-4 Callao 26, o ii 13.5 fa. t 57 55-6 Payta May 7, o 26 41.9 57 4o.i Panama ..... i4, o 20 16.9 4 57 44-9 ' Acapulco ..... 3°, I 41 22.2 4 58 7-2 Magdalena Bay .... June 8, 2 30 4.4 58 19.6 San Diego ..... 15, 2 5° 32-5 4 58 20.1 This chronometer (Fletcher, 906) was habitually carried in my pocket. It was accidentally allowed to run down on the night of December 17th and 18th, 1865, and after remaining stopped twelve hours was wound and compared. Some time between 5h P.M. of April 13th and 3h P.M. of April 14th, 1866, it stopped for about lm 37% but started again of itself. On June 20th, 1866, when its face showed gh ^gm p ]y[ if. stopped without any apparent cause, and, as it would not run again, it became useless. In observing at San Francisco the box chronometer T. S. and J. D. Negus, No. 1287 was used. The observations on June 26th, 1866, showed it to be gi, jgm gs 2 fast of local mean time; and Q, gm 45^(j fast of Greenwich mean time. 36 REPORT ON Chronometer Comparisons. D ite. Fletcher 906. T. S. and J. '3' D 7- Negus, T. S. and J. D. Negus, 1287. October 29> 1865 . . . 7" 39 - 56'.8 A. M. I2h 44m 0' 0 October 29> It 2 18 56.0 P. M. 7 33 0 o October 3*. tt 12 8 48.2 ft 5 13 0 o November 3> tt 4 17 33-° 1 1 9 22 o o November 13, t( 8 21 4-8 A. M. i 26 0 0 T^o vpm V)pr i * (t i 28 0 o ih 16™ 23'_5 J.'l U V CUI LJLI November 13> 17. tt 12 18 46.0 tt 5 24 0 o November 28, tf 6 55 10.8 tt 12 I 0 o November 28, tt 6 56 56.8 tt • • • • ii 50 o.o November 28, tf 2 39 9.8 P. M. 7 45 o o December I4» tt 6 29 23.0 A. M. ii 36 o o December M, ft 6 3<> 19.8 tt ii 25 o.o December 14. tt 12 43 22.5 P. M. 5 5° o. o December 1 6, ft 8 54 16.0 A. M. 2 i 0 o December 1 6, t( 8 56 15-2 tt . . I £1 0.0 December 1 8, (t 9 44 42.8 P. M. 2 47 0. o December 23. ft 8 7 28.0 A. M. I 10 0. o December 23> tt 8 8 32-5 ft . . . . 12 59 o.o December 29» tt 6 22 59-2 tt II 26 0. 0 December 29» ft 6 24 9.0 tt . . ir 15 o.o January 9. 1866 ! '. '. 6 46 21.8 tt II 5° 0 o January 9. tt 6 46 43-2 tt . . . . II 38 0.0 January 24, tt 12 41 4.0 P. M. 5 46 o. o January 24, tt 12 41 50.8 tt . . 5 34 o.o April 14, tt 4 1$ 24.4 1 1 9 29 0 o May 7, tt ii M 26.4 A. M. 4 49 0. o May 14, tt 12 s 49.6 P. M. S 18 0 0 May 3°. tt II 5.5 13.2 A. M. 5 12 o. 0 June 8, tt 6 28 24.8 P. M. ii 46 0 o June IS. tf 12 0 46.8 A. M. 5 19 0 o June 26, tt 6 Id o. o P.M. 6 17 0.2 WJ •5^ Table showing the True Bearings of the various objects used as azimuth marks in swinging the U. S. Iron-clad Monadnock during her cruise from Philadelphia to San Francisco in 1865 and 1866. Station. True bearing. Hampton Roads, Va. S. 10° 34' W. St. Thomas . . S. 31 35 E. Isle Royal, Salute Islands S. 10 54 W. Ceara N. 82 7 E. Bahia N. 81 57 W. Rio Janeiro ....... N. 53 28 W. Monte Video N. 77 52 W. Sandy Point S. 7 14 W. Valparaiso N. 31 7 E. Callao S. 83 21 W. Panama Bay S. 20 57 W. Acapulco N. 71 43 E. Magdalena Bay S. 46 3° E. San Francisco Bay N. 13 5° W. MAGNETIC OBSERVATIONS. 37 SECTION IV. OBSERVATIONS ON TERRESTRIAL MAGNETISM. THE observations of magnetic declination and force were made by means of the same instruments — a portable declinometer, and a transit theodolite. The Declinometer, kindly lent by the U. S. Coast Survey, and marked D. 22, was originally constructed by Jones, of London, but had been altered in many particulars so as to make it more convenient for field use. It was provided with two collir.iator magnets which were hollow cylinders of steel, each 0.70 of an inch in external diameter, and 0.58 of an inch in internal diameter. One of them, marked C. 32, was 3.92 inches long; while the other, marked S. 8, was 3.25 inches long. Each of these magnets carried in its south end a lens; and in its north end, at the solar focus of the lens just mentioned, a piece of plane glass on which was cut a scale of equal parts containing one hundred and seventy divisions, each division being equal to 0.00255 of an inch. Both magnets were provided with light sliding brass rings which were intended to be used for keeping them horizontal under great changes of magnetic declination, but the slight play which the magnets had in the stirrup was found quite sufficient for that purpose, and the rings were never employed. The same suspension was used during the whole of the observations. It consisted originally of six parallel fibres of unspun silk, each about nine inches long ; but at Callao one of the fibres was accidentally broken, and after that the remaining five were used. The torsion circle, which formed part of the suspension apparatus, was 0.88 of an inch in diameter, divided to every three degrees, and read by means of a vernier to single degrees. The Transit Theodolite, which perhaps might be more correctly called an altitude and azimuth instrument, was provided with a horizontal and a vertical circle, each five inches in diameter, and each reading by means of two opposite verniers to thirty seconds. The telescope had an object-glass with a clear aperture of one inch, and a focal length of about nine inches. It was provided with two eye-pieces ; a direct one magnifying about twenty times, which was employed in almost all the observations ; and a diagonal one of lower power, which was sometimes used for objects near the zenith. Both these eye-pieces had colored glasses for observing the sun. The system of wires in the focus of the object-glass was a simple rectangular cross, one wire being vertical, the other horizontal. For the sake of convenience in setting up the instruments, and also for the per- fect security which it affords against changes in the angular value of the divisions of the magnet scales depending upon changes in the distance between them and 38 REPORT ON the telescope, a special table was provided, which was mounted upon a tripod stand, and which carried both the declinometer and theodolite in a fixed and invariable position relatively to each other — the object-glass of the telescope being about three inches from the south end of the magnet. Pocket Chronometer, Fletcher, No. 906, was always used to note time. Its errors have been already given in detail in Section III. General remarlcs on tJie method of using the instruments. When observations were to be made the tripod stand was set up, and the table, having been placed upon it, was approximately levelled by the eye, and set, by means of a pocket com- pass, so that its longest side was nearly in the magnetic meridian, the end destined to carry the declinometer being to the north. In packing the declinometer for travelling, the glass suspension tube was never unscrewed from the magnet-box, but when the collimator magnet was lifted from the stirrup a cylinder of wood of the same size was at once substituted, and two pieces of wood, provided for the purpose, were slipped in, one from each side of the magnet-box. These pieces of wood completely filled up the box, and at the same time held the wooden cylinder securely between them in such a manner that it could neither break the suspension fibres, nor allow them to twist in the slightest. With this packing, after the suspension fibres were once thoroughly freed from torsion, they remained so, and it was not necessary to examine them whenever the instrument was used, but only at considerable intervals, thus saving much time in the field. The brass carriers for the deflecting magnet having been screwed, one on each end of the wooden bar, and the bar in its turn having been screwed to the bottom of the magnet-box, the declinometer was placed upon the table in such a position that its three levelling screws fitted into the cavities provided for their reception. Then the packing blocks were taken out of the magnet-box, and the wooden cylinder having been removed from the stirrup, the collimator magnet was put in its place, and left free to assume its proper direction. The magnet-box was next levelled. For that purpose the suspension fibres were used as a plumb line, and the box was assumed to be level when they were seen to hang in the axis of the suspension tube throughout its whole length. Finally, the magnet was made to hang nearly level by moving it a little endwise in its stirrup; its scale was placed horizontal, with the figures erect; it was shaded from the direct rays of the sun by covering the glass top of the box; the mirror was screwed to the back of the box and adjusted so as to illuminate the magnet scale properly; and a thermometer was placed inside the magnet-box. The theodolite was next placed in its proper position on the other end of the table and levelled; particular care briiig taken that the horizontal axis of the telescope was truly level — especially if the altitude of the sun was considerable. The telescope having been turned towards the magnet and adjusted so as to obtain distinct vision of its scale, the horizontal circle was firmly clamped in such a position that the vertical wire in the field of the telescope cut the magnet scale as nearly as possible at the magnetic axis. By means of the vertical circle the optical axis of the telescope was then placed truly level, and the final adjustment of the magnet for horizontally was MAGNETIC OBSERVATIONS. 39 made by shifting it endwise in its stirrup till the scale was seen in the field of the telescope parallel to, and just in contact with, the horizontal wire. When making my first observations considerable difficulty was experienced in getting a proper illumination of the magnet scale, but after some practice the fol- lowing perfectly satisfactory plan was adopted. In cloudy weather the light of a white cloud was reflected into the magnet by means of the concave mirror. In clear weather the light of the blue sky, reflected from the mirror, was not sufficient, and it would not do to throw in the direct rays of the sun because of their heating power, which would certainly have led to the use of a wrong value of the magnetic moment; because the magnet would have been at a higher temperature than that shown by the thermometer in the box. Under these circumstances, in place of the mirror a piece of perfectly white paper was substituted, and the direct rays of the sun being allowed to fall upon it, it afforded a beautiful illumination of the magnet scale. The copper damper, provided to slip into the magnet-box for the purpose of quieting the vibrations of the magnet, was never used. As the observations were all made in the open air, and as there was frequently wind enough to cause the instruments to vibrate perceptibly, the magnets seldom or never came to a state of absolute rest. Hence, the plan adopted to secure accurate readings of the scales was as follows. A screw-driver was slightly magnetized, and by approaching its south pole for an instant towards the south pole of the vibrating magnet, at a time when the magnet was moving towards the screw-driver, the arc of vibration was readily made quite small. Then, placing rriy eye to the telescope, I read off, and called out to my assistant, the scale reading at the instant the magnet attained the limit of its excursion in the eastern direction, and again when it attained the limit in a western direction — in other words, the greatest .and least readings of the scale were noted. Five complete vibrations were generally observed, thus giving three eastern and three western readings, and the mean of the six was assumed to be the reading which would have been obtained if the magnet had been in a state of perfect rest. In order to preserve the magnetism of the collimator magnets, they were always packed in a vertical position, with that pole downwards which would be lowest in a dipping needle. Absolute Declinations were observed as follows: The instruments having been set up and adjusted in the manner already explained, the long magnet, C. 32, was suspended in the magnet-box, the telescope pointed nearly to its magnetic axis, and the horizontal circle of the theodolite firmly clamped. Then, 1°. The horizontal limb of the theodolite was read. 2°. The magnet scale being erect — that is, the figures upon it being right side up— the point upon it cut by the vertical wire of the telescope was observed. 3°. The telescope remaining as before, the magnet scale was inverted — that is, the magnet was turned on its axis through 180°, so that the figures upon its scale were seen inverted — and the point upon it cut by the vertical wire was again noted. 4°. The horizontal circle was undamped, a colored glass placed upon the eye-piece, and the telescope pointed so that its verti- cal wire was just in advance of the first limb of the sun. Then the horizontal circle 40 REPORT ON was clamped, the time of transit of the sun's first limb over the vertical wire noted, and the horizontal circle read. 5°. If the observation was made at a time of day when the sun's azimuth was changing tolerably rapidly, the telescope was not moved in azimuth at all, but, the reading of the horizontal circle remaining pre- cisely as before, the sun was followed by moving the telescope in altitude, and the transit of its second limb was waited for and noted. If, however, the sun was changing its altitude much more rapidly than its azimuth then, in order to save time, the horizontal circle was undamped, the telescope moved till its vertical wire was just in advance of the sun's second limb, the horizontal circle clamped, the time of transit of the sun's second limb over the vertical wire noted, and the hori- zontal circle read. 6°. The telescope of the theodolite was reversed in its Y's. 7°. The transit of the sun's first limb over the vertical wire was observed, and the horizontal circle read. 8°. The transit of the sun's second limb over the vertical wire was observed, and the horizontal circle read. 9°. The colored glass was removed from the eye-piece of the telescope, and a reading of the magnet scale (which was still inverted) was taken. 10°. The magnet was revolved on its. axis through 180°, so as to place the scale erect, and another reading of the scale was taken. 11°. The horizontal circle was read. Immediately before, and immediately after, going through with the operations just described, the telescope should be pointed to some well-defined distant object, and the reading of the horizontal circle noted. By so doing a check is afforded against any accidental shift of the horizontal circle; and if the same station is occupied at another time, absolute declinations may be determined without again referring to the sun, thus rendering it possible to observe during cloudy weather. In the instruments under consideration the reading of the horizontal circle of the theodolite increases from left to right; and in both the magnets, C. 32 and S. 8, when the scale is erect an increase of scale reading indicates a motion of the north end of the magnet towards the east. Let p = reading of magnet, scale erect, p' = reading of magnet, scale inverted. R' '= reading of horizontal circle of theodolite at the time the readings p and p' were observed. d = value, in minutes of arc, of one division of the magnet scale. R"= reading of* horizontal circle of the theodolite at the time of transit of sun's first limb over the vertical wire. R"'= reading of horizontal circle of the theodolite at the time of transit of sun's second limb over the vertical wire. a = observed chronometer time of transit of sun's first limb over the vertical wire, a' = observed chronometer time of transit of sun's second limb over the vertical wire. dt = correction of chronometer to reduce the reading of its face to local mean time. f = equation of time. MAGNETIC OBSERVATIONS. 41 t = the sun's hour angle at the pole. <£ = latitude of the place of observation; positive when north of the equator. A = azimuth of sun's centre at the time of its transit over the vertical wire : the azimuth being counted from the south around by the west. S = sun's declination ; positive when north. Then we have tan M = tan tan A = cos t tan t cos M sin (

"• / 255 io-5 255 «-3 Magnetic declination . . . 8 20.2 E. 8 21.5 E. Observations of Vibrations were made as follows: The instrument having been set np and adjusted in the manner already explained, the long magnet, C. 32, was MAGNETIC OBSERVATIONS. 43 suspended in the magnet-box; and the telescope having been pointed so that its vertical wire cut the magnet scale approximately at the magnetic axis, the hori- zontal limb of the theodolite was firmly clamped. Then, 1°. By quickly approach- ing and withdrawing the magnetised screw-driver the magnet was caused to vibrate horizontally through an arc extending to about twenty scale divisions on each side of the magnetic axis — that is, through a total arc of about 1° 34'. The semi-arc of vibration being only 4?', no correction to the observed time of vibration was ever required on that account. 2°. My assistant having taken the chronometer, I placed my eye to the telescope, and at the instant the 80th division of the scale (which was very near the magnetic axis) crgssed the vertical wire I cried "time," and my assistant noted the minute, second, and fraction of a second indicated by the chronometer. Still keeping my eye at the telescope, I counted the transits of the 80th division over the wire, calling the one at which time was noted 0, the next 1, the next 2, and so on up to the 10th, when I again cried "time," and my assistant once more noted the minute, second, and fraction of a second indicated by the chronometer. The difference of these two chronometer times gave a value for the time of ten vibrations of the magnet which was correct within about half a second. However, to guard against mistakes, the process was always repeated a second or third time. 3°. The temperature indicated by the thermometer in the magnet-box was noted; and then putting my eye to the telescope, I read the scale at the instant the magnet attained the eastern extremity, and again when it attained the western extremity, of its arc of vibration. These were the "extreme scale readings." 4°. The chronometer employed was a pocket one, beating five times in two seconds. Taking it in my hand, I commenced counting its beats at some multiple of ten seconds. Then, holding it to my ear and still mentally count- ing the beats, I put my eye to the telescope and noted the beat, and fraction of a beat, at which the 80th scale division crossed the vertical wire. For example, suppose the beat was taken up at the instant the chronometer indicated 10h 2m 10s, and counting the first succeeding beat 1, the next 2, and so on, suppose that the 80th division crossed the wire exactly at the 14th beat. Then, as 14.0 beats are equal to 5.6 seconds, the time of transit of the 80th scale division was 10h 2m 153.6. The time of transit thus obtained was recorded as the 0 vibration. Adding to it the time of making ten vibrations — before determined — the approximate time when the 10th vibration would be completed became known. Taking up the beat of the chronometer at the nearest even ten seconds before that time, I put my eye to the telescope and observed the time of transit of the 80th division at the completion of the 10th vibration. In the same manner the time of completing the 20th, 30th, 40th, 50th, 100th, 150th, 160th, 170th, 180th, 190th, and 200th vibration was observed. Subtracting the time of completing the 0 vibration from the 150th, the 10th from the 160th, &c., there result six values of the time of making one hundred and fifty vibrations, from the mean of which a very accurate value of the time of making one vibration is obtained. It will not escape notice that when observing in the manner just described there is no risk of making a mistake of one vibration, because the magnet must, at all subsequent transits, be moving in the same direc- tion as at the first transit, while in order to make a mistake of one vibration it 44 REPORTON would be necessary that it should be moving in the opposite direction. 5°. The extreme scale readings attained by the magnet at the eastern and western extremities of its arc of vibration were again observed; and then the thermometer in the magnet-box was read. 6°. The necessary observations for determining the coefficient of torsion of the suspension fibres were made. When the instrument was properly adjusted for observation the torsion circle always read 300°. With it remaining at that reading the arc of vibration of the magnet was reduced to four or five scale divisions (by means of the magnetized screw-driver) and then the scale was read. Next the torsion circle was turned backward one-quarter of a revolution, so as to make it indicate 210°, and the scale was again read. After that.the torsion circle was turned forward half a revolution (passing through the point 300°), so as to make it indicate 30°, and the scale was read. Finally, the torsion circle was turned backward one-quarter of a revolution, so as to make it indicate 300°, and the scale was once more read. Subtracting the second scale reading from the first, the second from the third, and the fourth from the third, gave three differences, which were added together and divided by four. The result was the number of scale divisions through which the magnet was deflected by a twist of ninety degrees in the suspension fibres. Observations of Deflections were made as follows : The instruments having been set up and adjusted in the manner already explained, the short magnet, S. 8, was suspended in the magnet-box, and the telescope having been pointed so that its vertical wire cut the magnet scale approximately at its central division (not neces- sarily the magnetic axis) the horizontal limb of the theodolite was clamped firmly. Then, 1°. The time was noted. 2°. The thermometer inside the magnet-box was read. 3°. The long magnet C. 32 (which we will now call the deflecting magnet) was placed on the deflecting bar support, with its axis east and west, its centre on a level with and at a distance of two feet to the west of the suspended magnet, and its north end west; the vibrations of the suspended magnet were reduced to four or five scale divisions, by means of the magnetised screw-driver, and then its scale was read. 4°. The deflecting magnet (remaining in the same place on the deflecting bar support as before) was reversed end for end, so as to bring its north end east, and the scale of the suspended magnet was read. 5°. The reversals were repeated twice more, so as to give in all two scale readings with the north end of the deflecting magnet to the west, and two scale readings with it to the east. The mean of the two scale readings obtained with the north end of the deflecting magnet west, were subtracted from the mean of the two scale readings obtained with its north end east. The difference was twice the value of the angle of deflection, as resulting from observations made with the deflecting magnet west of the suspended magnet. 6°. The deflecting magnet was lifted from the deflecting bar support to the west, and placed on that to the east, of the suspended magnet; its distance from the suspended magnet being still two feet, and its north end being to the east, the scale of the suspended magnet, was read. 7°. The deflecting mag- net (remaining in the same place on the eastern deflecting bar support) was reversed end for end, so as to bring its north end west, and the scale of the suspended mag- net was read, 8°, The reversals were repeated twice more, so to give in all two MAGNETIC OBSERVATIONS. 45 scale readings with the north end of the deflecting magnet to the east, and two scale readings with it to the west. From the mean of the two scale readings obtained with the north end of the deflecting magnet east, the mean of the two scale read- ings obtained with its north end west were subtracted. The difference was twice the value of the angle of deflection, as resulting from observations made with the deflecting magnet east of the suspended magnet. The mean between this result and that obtained from the observations with the deflecting magnet west of the suspended magnet, was adopted as the true value of twice the angle of deflection, with the deflecting magnet at a distance of two feet from the suspended magnet. 9°. The thermometer inside the magnet-box was read. 10°. The time was noted. 11°. All the observations just described were repeated with the deflecting magnet at a distance of two and a half feet from the suspended magnet. 12°. The torsion of the suspension fibres was determined, precisely as described under the head of "observations of vibrations." Horizontal Force was calculated from the observations of vibrations and deflections by the following formula? : T0 = observed time of one vibration of the magnet. 7" = time of vibration, corrected for rate of chronometer and arc of vibration. T = time of vibration, corrected for rate of chronometer, arc of vibration, torsion force of the suspending thread, temperature, and induction. s = daily rate of chronometer, -f- when gaining, — when losing, a, a'= scmiarc of vibration, at the beginning and end of the observation, expressed in parts of radius. TT — ratio of the force of torsion of the suspending thread, to the magnetic directive force. q — coefficient of the decrease of the magnetic moment of the magnet produced by an increase of temperature of 1° Fah. (This is not constant for all temperatures, and the correction is more exactly expressed by a formula of the form — correction to t'=q(t' — t)-}-q'(t' — t)2, where I' is the observed temperature, and t an adopted standard temperature.) K = moment of inertia of the magnet, including its suspending stirrup and other appendages. (This is constant for the same magnet and suspension, but varies slightly with the temperature, owing to the expansion of the materials.) 71 = jatio of the circumference of a circle to its diameter = 3.14159. H = coefficient of increase in the magnetic moment of the magnet produced by the inducing action of a magnetic force equal to unity of the English system of absolute measurement. ra = apparent distance between the centres of the deflecting and suspended mag- nets in the observations of deflections. r = the same distance corrected for error of graduation and temperatxire. (r = r0 [ 1 + 0.00001(r — 62°)] -f- correction for scale error.) d = value, in minutes of arc, of one division of the magnet scale. u0 = observed angle of deflection, in scale divisions. 4g REPORTON u = angle of deflection, corrected for torsion force of the suspending thread. P= a constant depending upon the distribution of magnetism in the deflecting and suspended magnets. m = magnetic moment of the deflecting or vibrating magnet. X— horizontal component of the earth's magnetic force. (P \ 1 — -i ) / 5\__«>400+^ \l ' y) ~ 5400 where v = the angle, expressed in minutes of arc, through which the suspended magnet is deflected by a twist of 90° h- the suspension thread. m = r' tent* m __ m' / X~ X'\ m In order to facilitate the finding of log. tan M, in the reduction of observations of deflection, the following table has been prepared. With the argument log. u (u being expressed in minutes of arc) it gives the quantity (log. tan u — log. «), of, in other words, the quantity which it is necessary to add to log. u in order to obtain log. tan u. The arrangement of the table is such that the quantity (log. tan u — log. 7t) is to be added to the log. u on the same line with it, or to any other log. u less than the one on the line next below. For example, if it were required to find log. tan u corresponding to any log. u from 8.0000 to 1.4340, it would only be necessary to add 6.46373 to the given log. u. MAGNETIC OBSERVATIONS. 47 Log. a. Log. tan « — Log. «. Log. u. Log. tan « — Log. «. 8.0000 6.46373 2.1159 6.46394 I-434I 6.46374 2.1261 6-46395 1-5957 6.46375 2-I358 6.46396 1.6874 6.46376 2.1452 6.46397 i-75i7 6.46377 2.1541 6.46398 1.8014 6.46378 2.1626 6.46399 1.8414 6.46379 2.1708 6.46400 1.8756 6.46380 2.1787 6.46401 1.9047 6.46381 2.1864 6.46402 1.9310 6.46382 2.1937 6.46403 I-9S38 6.46383 2.2008 6.46404 1-975° 6.46384 2.2079 6.46405 1-9934 6.46385 2.2146 6.46406 2.OIII 6 46386 2.2209 6.46407 2.0274 6.46387 2.2271 6.46408 2.0426 6.46388 2.2332 6.46409 2.0565 6.46389 2.2393 6.46410 2.0700 6.46390 2-2453 6.46411 2.0824 6.46391 2.2509 6.46412 2.0941 6.46392 2.2565 6.46413 2-1055 6-46393 The following are specimens of the forms employed in recording and reducing the observations of vibrations and deflections. HORIZONTAL INTENSITY. Observations of Vibrations. Station, Acapulco, Mexico. Date, May 3oth, 1866. Magnet C. 32. Inertia ring No. Chron. Fletcher 906, rate, i8-38 losing on mean time. Number of dbrations. Time. Temp. t' Extreme scale readings. Time of 1 50 vibrations. o 8h 32™ 3s- 8 87° 57a-8 I02d.2 10 8 32 57.0 20 8 33 5°-6 3° 8 34 43-9 40 8 35 37-o 5° 8 36 30.6 100 8 40 57-2 150 8 45 23.4 i3m i9§.6 1 60 8 46 17.2 13 20.2 170 8 47 10.2 13 19.6 1 80 8 48 3-7 13 19.8 190 8 48 57-o 13 20. o 2OO 8 49 5°-5 91 65-2 95-° 13 19.9 Means, 89.0 13 19-85 Coefficient of torsion. Value of one scale div. = 2'. 349 Tor. cir. Scale. Diff's. Log's. 300° 3° 2IO 8od.i 83-5 76.7 3d-4 6.8 v= 8'.o 5400' + v' 3-733°4 5400 (ar. co.) 6.26761 300 80. i •4 , H [ + ~p~* 0.00065 Mean = v= 3-4° 48 REPORT ON HORIZONTAL INTENSITY. Calculation. (i-(t'-t)q) Observed time of 150 vibrations Time of one vibration Correction for rate 799'. 85 5-332 .000 = 5-332 q f — t (t'-t)q I— (f — t)q + 4-3 mX 'K T' •JVJ T1 «SK mX m 7-740 Log's. 0.72689 1-45378 65 9.99962 I-45405 2.17768 0.72363 9.83487 0.88876 * Ob's of defl'n. Date. May 3oth, 1866. 840-7 *m "X" 8-94854 mX m1 m 0.72363 9.67217 9.83608 The chronometer used in this observation was ih 41" 22'. 2 fast of local mean time. HORIZONTAL INTENSITY. Observations of Deflections. Station, Acapulco, Mexico. Date, May 3oth, 1866. Mag. C. 32 deflecting. Mag. S. 8 suspended. Observer, WM. HARKNESS. a I Time. A.M. h. m. i Temp, t Scale Readings. Alternate Means. Diff's. Dist. 1 W. E. W. E. 7 22 86° 53«.9 107.0 53-9 107.0 5 3d- 9 107.0 S34- 1 fO 0 IH o r<5 6 H f d o ti II IH jj W E. W. E. W. 7 3' 84 107-5 53-5 107.7 53-8 107.6 53-6 54-o Means, 85.0 2U« 53-53 MAGNETIC OBSERVATIONS. 49 Tors. cir. Scale. Diff's. 2Ud Log's. 300° 2IO 300 8od.4 7i:7 80.4 3d- 2 3-7 1.72876 0.15152 79 Sum Tan u Mean = v = 3.45 1.88107 6.46380 v = 9'.8 5400' + v' 5400 (ar.co.) •+T Lo.s u' Tanu r3 i m' "X7" m ~X~ 8.34487 0.90309 9.69897 3-733I8 6.26761 8.94693 8.94861 0.00079 HORIZONTAL INTENSITY. Observations of Deflections. Station, Acapulco, Mexico. Date, May 3oth, 1866. Mag. C. 32 deflecting. Mag. S. 8 suspended. Observer, WM. HARKNESS. Time. & "•a A. M. Temp. Scale Alternate Diff's. Dist. S is £ ° h. m. t Readings. Means. w. 7 32 84° 66". 9 jj E. 94.1 66d. 9 n»d - Tj- te ™ W. 66.9 94.2 27 -3 O\ E. 94.2 to o II ti> E. 94-4 i ' W. ' E. 66.8 94-4 94-4 66.8 27.6 d W W. 7 40 85 66.8 ci u Means, 84-5 2U* 27-45 Log's. 2U" I-43854 id ,r . j j~ O.I ^15 2 I + HL 79 F Sum * 1-59085 Tanu 6.46374 U' Tanu 8.05459 r" 1.19382 i 9.69897 m' X' 8.94738 m 8.94846 X 7 April, 1872. 50 REPORT ON The constants, peculiar to the portable declinometer D 22, were obtained as follows : Tlie Temi>erature Coefficients of the magnets were furnished by Mr. Chas. A. Schott, of the U. S. Coast Survey. They had been used with the instrument for some years, and I had no opportunity to redetermine them. They are as follows : For the magnet C 32 g = 0.00020 « « « S 8 5 = 0.00027 In reducing the observations a correction was always applied to the magnetic moment of the magnet C 32 to reduce it to what it would have been if C 32 had had the same temperature as S 8. Hence, the temperature coefficient of C 32 was the only one used, and in order to facilitate its application the following table was com- puted which furnishes the value of log. [1 — (<'— 0 q ] with the argument (t'—t). Correction of Magnet €.32 for Temperature (/'-/) Log- ['-(''-')?] (''-') Log. [i_(/'_/)?] 4- i° 9.99991 _ i° 0.00009 + 2 9-99983 2 0.00017 + 3 9-99974 — 3 O.OOO26 + 4 9.99965 — 4- 0.00035 + 5 9-99957 — 5 0.00043 + 6 9.99948 — 6 0.00052 + 7 9-99939 i 7 0.00061 + 8 9.99930 Q 0.00069 + 9 9.99922 — 9 0.00078 + 10 9-999'3 — 10 0.00087 P. p. O.I i O.2 2 °-3 3 0.4 4 °-5 4 0.6 5 0.7 6 0.8 7 0.9 8 The Value of One Division of {he Magnet Scale was determined for each magnet in the following manner: The instruments having been set up and adjusted as usual, the magnet was suspended in the magnet^box, and the packing blocks (before described as being used to prevent the suspension fibres from being twisted when the instrument was packed for travelling) were inserted in such a manner as to hold it perfectly ^ftdy. Then, the magnet scale being horizontal, the vertical wire of the theodolite telescope was made to coincide with any convenient scale division, and the horizontal circle of the theodolite was read. Next, the vertical wire was made to coincide with some other scale division, and the circle was again read. The difference of the two circle readings, divided by the difference of the two scale readings, gave the angular value of one scale division. The following are the observations in detail for each magnet : MAGNETIC OBSERVATIONS. Magnet C. 32. 51 Date. Circle Readings. Differences. Scale Diff's. Value of i Scale Readings. Division. Nov. 1 6, 1865 Nov. 16, 1865 4° 5' IS" o ii 45 3° 53' 3°" 50d.o 150.0 IOOd.O 2'-335 Nov. 1 6, 1865 4 6 45 50.0 Nov. 16, 1865 o ii 45 3 55 ° 150.0 IOO.O 2-35o Nov. 1 6, 1865 Nov. 16, 1865 3 7 45 i 10 15 i 57 30 75-0 125.0 50.0 2-350 Nov. 16, 1865 Nov. 1 6, 1865 3 7 45 i 10 15 i 57 30 75-o 125.0 50.0 2-350 Jan. 18, 1866 Jan. 18, 1866 5 36 15 i 40 30 3 55 45 50.0 150.0 IOO.O 2-357 Jan. 1 8, 1866 4 37 o _- o Jan. 1 8, 1866 2 39 30 1 57 3° 125.0 50.0 2-350 Hence for the magnet C 32, we have i scale division = 2'. 349 ± o'.oo2o. MagnetS. 8. Value of Date. Circle Readings. Differences. Scale Diff's. I Scale Readings. Division. Nov. 16, 1865 Nov. 16, 1865 4° 9' 45" 359 26 3° 4° 43' 15' 504.0 150.0 IOOd.O 2'- 833 Nov. 1 6, 1865 Nov. 1 6, 1865 4 9 45 359 26 30 4 43 15 50.0 150.0 IOO.O 2.832 Nov. 1 6, 1865 Nov. 1 6, 1865 2 58 45 o 37 o 2 21 45 75-o 125.0 50.0 2.835 Nov. 1 6, 1865 Nov. 1 6, 1865 2 59 o o 37 30 2 21 30 75-o 125.0 50.0 2.830 Jan. 18, 1866 Jan. 1 8, 1866 5 36 30 0 52 15 4 44 IS 50.0 150.0 IOO.O 2.842 Jan. 1 8, 1866 Jan. 1 8, 1866 4 25 30 2 3 30 2 22 0 75-o 125.0 50.0 2.840 Hence, for the magnet S 8, we have i scale division = 2'.835 ± o'.ooi3. TJie Moment of Inertia, and its Temperature Coefficient, of the Magnet C 32, was determined as follows : Let, JTT = moment of inertia of the magnet, including its suspending stirrup and other appendages, at the temperature r. AK= change in the value of K corresponding to a change of temperature of 1° Fah. in the magnet. K'^ = moment of inertia of the inertia ring, at the temperature r. dt = internal diameter of the inertia ring, expressed in feet, at the temperature ) s \f/t—t») Log. A''T Log. A'r Oct. 28, 1865 O .88210 .66424 .47811 0.18613 0.99849 .18462 Nov. 1 6, 1865 87.7 .72767 .50891 •32504 0.18385 0.99862 .18247 Nov. 28, 1865 90.O. •72835 .51108 •32345 0.18763 0.99864 .18627 Dec. 13, 1865 89-5 •74459 .52673 .34060 0.18613 0.99864 .18477 Dec. 27, 1865 98.0 .76681 .54810 .36412 0.18398 0.99872 .18270 Jan. 18, 1866 87.2 •77770 •55921 •37467 0.18458 0.99861 •18315 March 19, 1866 76.2 •75849 .54101 •35391 0.18710 0.99851 .18561 April ii, 1866 May 30, 1866 74.0 84.7 •75824 •67351 .54019 •45405 •35454 .27196 0.18565 0.18209 0.99850 0.99859 .18415 .18068 Nov. 2, 1866 70.O .90424 .68479 .50268 0.18211 0.99846 .18057 Nov. 2, 1866 70.O .90391 .68450 .50229 0.18221 0.99846 .18067 Nov. 2, 1866 53-5 .92843 . 70989 •5*548 0.18441 0.99830 .18271 79-5 1.18320 MAGNETIC OBSERVATIONS. 53 Let K0 represent the mean of all the logarithms of K in the above table ; then K0 = 1.18320 at a temperature of 79°. 5. Now, assuming Log. 7fT = K, + (T — 79°.5) AK we have 0 = K0 — log. Kv + (* — 79°.5) AK and each value of log. A'T , given in the table above, will furnish one equation of condition for the determination of AK, as follows : the absolute terms being in units of the fifth place of decimals. o = — 142 — 6.5 °=+ 73+ 8.2 ° = — 3°7 + IO-5 o = — 157 4- 10. o = + 50 4- 18.5 0=4- 5 + o = — 241— 3.3 o = — 95— 5-5 o= + 25 2+ 5.2 0=4-263 — 9 5 ° = + 253— 9.5 0=4- 49 — 26.0 From these equations of condition we obtain, by the method of least squares, the normal equation 0 = — 5856.2 + 1646.0 AK whence Log. AK= 0.55119 and finally or Hence we have or Log. /C = 1.18320 + (r — 79°.5) 0.0000356 ± 0.000368 KT = 15.248 + (t — 79°.5) 0.00125 _|- 0.0129 n-Kv = 150.49 -f (T — 79°.5) 0.01234 Log. 7t2/fT = 2.17750 + (T — 79°.5) 0.0000356 In Order to facilitate the reduction of the observations of vibrations, the follow- ing table has been computed from the formula last given. It furnishes the value of log. 7i2Kv to the argument T. * Log. irU"T P. P. 50° 2.17645 1° 4 2 7 60 2.17681 3 ii 4 M 70 2.17716 5 18 6 21 80 2.17752 7 25 8 28 90 2.17787 9 S2 IOO 2.17823 . The Constant P, depending upon the distribution of the magnetism in the mag- nets C 32 and S 8, was determined by means of the formula A- A ~'A_A r~z~r72 54 REPORT ON where A = value of m', determined from an observation of deflection with the deflecting -A magnet at the distance r from the suspended magnet. A' = value of ™-, determined from an observation of deflection with the deflecting JL magnet at the distance ?•' from the suspended magnet. The following table contains all the observed values of A and A', together with the computation of the corresponding values of P. The values of A were obtained from deflections at a distance of 2.0 feet: those of A' from deflections at a distance of 2.5 feet. Date. Log. A Log. A' Log. (A-A') «*t T A> Loe-pr, Log. (A A'\ V' ''I Log. P P October 30, 1865 9.1660 9.1669 6.4829/2 8.5640 8.3711 8.1187 8.3643* —0.0231 November 13, 1865 9.0084 9.0094 6. 3881* 8.4063 8-2135 7.9608 8.4274* 0.0268 November 16, 1865 9.0087 9.0088 5.1491* 8.4067 8.2129 7.9629 7.1863* 0.0015 November z8, 1865 9.0068 9.0078 6.3989?* 8.4047 8.2120 7-9591 8.4398* —0.0275 December 13, 1865 9.0234 9-0175 7-I527 8.4213 8.2216 7-9879 9.1649 +0.1462 December 23, 1865 9.0295 9-03I7 6-7332« 8.4274 8.2358 7.9798 8-7534« —0.0567 December 27, 1865 9.0421 9.0413 6-323° 8.4400 8.2454 7.9978 8.3252 + 0.02II January 6, 1866 9.0628 9-0633 6.0587* 8.4608 8.2674 8.0163 8.0424* O.OIIO January 18, 1866 9-°53i 9-0536 6.1399* 8.4511 8.2578 8.0064 8-1335* 0.0136 February 7, 1866 9.0486 9-0495 6-3751* 8.4465 8.2536 8.0012 8.3739* 0.0237 March 2, 1866 9.0328 9-0339 6.4250* 8.4308 8.2380 7-9852 8.4398* —0.0275 March 19, 1866 9-°3S° 9.0342 6.3106 8-433° 8.2383 7.9907 8.3199 + 0.0209 March 29, 1866 9-0347 90347 4.8740 8.4326 8.2388 7.9890 6.8850 + 0.0008 April 7, 1866 9.0367 9-0373 6.i5si« 8.4346 8.2414 7.9899 8.1652* 0.0146 April n, 1866 9-0356 9.0360 5-9295« 8.4336 8.2401 7-9893 7.9402* 0.0087 April 13, 1866 9-0343 9.0368 6.7852;? 8.4323 8.2409 7.9842 8.8oio« 0.0632 April 26, 1866 8.9902 8.9896 6.1515 8.3882 8.1937 7-9456 8.2059 + 0.0l6l May 7, 1866 8.9680 8.9704 6.7188* 8-3659 8.1745 7.9178 8. 8010* 0.0632 May 14, 1866 8.9468 8-9544 7. 1930* 8-3447 8.1585 7.8872 9.3058* O.2O22 May 30, 1866 8.9468 8.9472 5.8890* 8.3448 8.I5I3 7.9004 7.9886* O.OO97 June 9, 1866 8-9775 8.9817 6.9669* 8-3754 8.1858 7.9241 9.0427* —O.II03 June 15, 1866 9.0376 9.0346 6.8666 8-4355 8.2387 7.9970 8.8697 + 0.0741 June 26, 1866 9.0810 9.0826 6.6509* 8.4790 8.2868 8.0324 8.6185* 0.0415 November i, 1866 9.1991 9.1972 6.8414 8-5971 8.4014 8.1568 8.6847 + 0.0484 The indiscriminate mean of all the observations gives P= — 0.0166 ±0.0088 But Peirce's criterion for the rejection of doubtful observations throws out those of December 13 and May 14. Accordingly, excluding them, and taking the mean of all the others, there results P= — 0.0155 ±0.0057 and that value I have adopted. Hence, for r = 2.0 feet, we have and for r = 2.5 feet Log. (l - Jl) = 0.001 68 Log. (l - •-?) = 0.00108 MAGNETIC OBSERVATIONS. 55 The Magnetic Moment of the Magnet C 32 was computed as follows : Observations of deflection were always taken at two different distances, viz., at 2.0 feet and at 2.5 feet. In general, the two values of -™ thus obtained differed slightly from each other, and the mean of the two was assumed to be correct. This mean was com- bined with the value of mX, obtained from a set of vibrations observed on the same day, and thus m was determined. In no case was more than one set of observa- tions of deflections taken on any single day, but in a few instances several sets of observations of vibrations were made. Under such circumstances, the mean of all the observed values of mX was combined with the mean of the two values of "- , X and thus a single value of m was deduced. Let mr = observed value of the magnetic moment at the temperature t. m = value of mT after being multiplied by [ 1 -(- (r — 75°.8) q ], or, in other words, after being reduced to the temperature 75°.8 Fah. n>0 = mean of all the observed values of m. a = daily decrease in the value of log. m, expressed in units of the fifth decimal place. d = time in days at which m is taken; d being counted from March 7th, 1866. The following table contains all the observed values of log. mr , together with the computation from them of the final values of the same quantity. The column headed "days" gives the time in days counted from October 24th, 1865. Date. V Log. »zr Log. [i+(T-75°.%] Log. m Days. Concluded Log. m Concluded Log. mr October 24, 1865 o 57-5 9.84148 9.99841 9.83989 0 9.83990 9.84149 October 30, 1865 58-7 9.84139 9.99851 9.83990 6 9-83979 9.84128 November 13, 1865 85-5 9.83908 0.00082 9.83990 20 9-83951 9.83869 November 16, 1865 87.7 9-83951 0.00104 9-84055 23 9-83945 9.83841 November 28, 1865 90.0 9-83773 O.OOI2I 9.83894 35 9.83922 9.83801 December 13, 1865 89-5 9-83645 O.OOII7 9.83762 So 9-83893 9.83776 December 23, 1865 87.2 9.83768 O.OOIOO 9.83868 60 9-83873 9-83773 December 27, 1865 98.0 9-83655 0.00191 9.83846 64 9.83865 9.83674 January 6, 1866 74.2 9-839'5 9.99986 9.83901 74 9.83846 9.83860 January 18, 1866 87.2 9.83666 O.OOIOO 9.83766 86 9.83823 9-83723 February 7, 1866 69-5 9-83783 9-99945 9.83728 1 06 9.83784 9-83839 March 2, 1866 69.7 9.83831 9.99947 9.83778 129 9-83739 9.83792 March 19, 1866 76.2 9.83618 0.00004 9.83622 146 9.83706 9.83702 March 29, 1866 68.2 9.83780 9-99934 9.83714 156 9.83686 9-83752 April 7, 1866 67.0 9.83861 9.99923 9-83784 165 9.83669 9.83746 April ii, 1866 74.0 9.83716 9.99984 9.83700 169 9.83661 9-83677 April 13, 1866 65-7 9.83711 9.99912 9.83623 171 9-83657 9-83745 April 26, 1866 79.2 9.83626 0.00030 9.83656 184 9.83632 9.83602 May 7, 1866 77.0 9.83670 0.00009 9.83679 J9S 9.83610 9.83601 May 14, 1866 82.2 9.83448 0.00056 9-83504 202 9-83596 9-83540 May 30, 1866 84.7 9.83602 0.00078 9.83680 218 9-83565 9.83487 June 9, 1866 65.0 9.83662 9.99906 9.83568 228 9-83546 9.83640 June 15, 1866 71.0 9-83493 9.99958 9-8345I 234 9-83534 9-85576 June 26, 1866 63.0 9-83548 9.99889 9-83437 245 9-835H3 9.83624 November i, 1866 66.2 9.83326 9.99916 9.83242 373 9.83263 9-83347 Means 75-8 9.83729 >54 56 REPORTON The mean of the quantities in the column headed t is 75°.8. Accordingly, adding log. [ 1 + (t — 75°.8)2] to each log. mT , we obtain the values of log. m given" in the table. Taking the mean of these values, and also the mean of the numbers in the column "days," we find that at 134 days, which corresponds to March 7th, 1866, the value of log. m was 9.83729 = log. »i0. Then, assuming Log. m = log. w0 — ad we have 0 = 9.83729 — log. m — ad and each value of log. m furnishes an equation of condition for the determination of a, as follows. o = — 260 +1340 o = — 261 + 128 a o = — 261 + 1140 O = 326 +1110 o = — 165 + 99° o = — 33 + 840 o= — 139+ 74a o = — 117+ 7°<* o = — 172 + 60 a o = - 37+480 o = + 1+280 o = — 49 + 50 o = + 15 — 22 a o = — 55— 31" o = + 29 — 35 o o = + 106 — 37 a o = + 73 — 50 a, O = + 50 — 61 a o = + 225 — 68 o o = + 49— 840 o = + 161 — 940 o = + 278 — 100 a o = + 292 — ii i o o = + 487 — 239 o O = + 107 — 12 o By the method of least squares we obtain the normal equation 0 = — 397497 + 203965 a Solving, we get a = + 1.9488 Hence Log. m = 9.83729 — 0.0000195 d ± 0.000090 or m = 0.68753 — 0.0000310 d ± 0.000144 From the first of these expressions the quantities in the column " concluded log. »j" were computed. If, in the expression for log. m, given above, we introduce the correction for temperature, we obtain Log. mr = 9.83729 — 0.0000195 d — 0.000087 (t — 75°.8) by means of which the quantities in the column "concluded log. m" were com- puted. The probable error of a single observed value of log. m is i 0.000452, and of a single observed value of m it is -4- 0.000719. Observations of Inclination were all made with a dip circle by Henry Barrow & Co., of London. It was provided with two needles, marked A 1 and A 2, each 3.5 inches long, and having axles 0.016 of an inch in diameter. The distance between the agate planes on which they rested was 0.74 of an inch. By means of two microscopes, one opposite each end of the needle — each of which, assuming distinct vision to be obtained at a distance of ten inches, magnified 18 diameters — the inclination of the needle was referred to, and read off upon a vertical circle six inches in diameter, divided to half degrees, and reading by means of two verniers to single minutes. The pointing of the microscopes to the ends of the needle was MAGNETIC OBSERVATIONS. 57 effected by means of a clamp and tangent screw. The horizontal circle of the instrument was four inches in diameter, divided to half degrees, and reading by means of one vernier to single minutes. It was provided with a clamp, but no tangent screw. Readings of the position of the dipping needle were made as follows: In the field of view of each microscope was a plate of glass upon which was engraved three fine parallel lines, the middle one being intended to represent one of the two extremities of a diameter passing through a vertical circle described about the prolongation of the axle of the needle. The north microscope having been turned till the centre line in its field of view coincided with the north end of the needle, the vernier belonging to that microscope was read off", and recorded as the reading of the north end of the needle. Then the south microscope was turned till the centre line in its field of view coincided with the south end of the needle, and the vernier belonging to that microscope was read off, and recorded as the reading of the south end of the needle. In order to distinguish between the two microscopes the letter N was scratched upon one of them, and that one was always, in all positions of the instrument, used to read the north end of the needle. The instrument having been set up and levelled, before beginning to observe it was necessary to place the plane of the vertical circle in the magnetic meridian. At a few of the earlier stations this was accomplished as follows: The needle was placed on the agate planes, with the side on which the letters were marked facing the microscopes. Then 1°. The microscopes having been turned till they were nearly in a vertical line, the vernier of the lower one was set to 90° 0', and the vertical circle was moved in azimuth — so that its face (by which is meant the side on which the microscopes were) was south — till the lower end of the needle was bisected by the middle line- in the lower microscope; the Y's were raised and lowered gently, and if the bisection of the needle was altered, it was corrected by turning the circle in azimuth. Then the horizontal circle was clamped and read off; and this reading was called A. 2°. The vernier of the upper microscope was set to 90° 0', and the horizontal circle having been undamped, the vertical circle was moved in azimuth — its face still remaining south — till the upper end of the needle was bisected by the middle line in the upper microscope ; the Y's were raised and lowered gently, and if the bisection of the needle was altered, it was corrected by turning the circle in azimuth. Then the horizontal circle was clamped and read off, and this reading was called B. 3°. The horizontal circle was undamped, and turned in azimuth 180°, so as to bring the face of the instru- ment to the north, and then the 1° and 2° processes just described were repeated ; thus giving two more readings of the horizontal circle, which were called C and D. Then A+B+0+D_E 4 \ where E is the division of the horizontal circle at which it was necessary to set the vernier in order that the plane of the vertical circle might be at right angles to 8 April, 1872. 58 REPORTON the magnetic meridian. Therefore the vernier was set at 90° -f- E, and the plane of the vertical circle coincided with the magnetic meridian. However, it soon became evident that this process consumed too much time, and the following, which is quite as accurate and much more expeditious, was adopted : A fine line was marked permanently upon the top of the instrument parallel to the plane of the vertical circle; then, after the instrument had been levelled, but before the dipping needle had been placed upon the agate planes, a pocket compass, with a needle about one and a half inches long, was placed with its centre upon the fine line, and the verti- cal circle was tumed in azimuth till the compass needle and line were parallel to each other. That being the case, the plane of the vertical circle was known to be in the magnetic meridian, and the horizontal circle was clamped and read off. The following is the method which was adopted in making observations of dip: 1°. The agate planes, and those parts of the axle of the needle which would rest upon them, were carefully wiped with a piece of chamois leather (I have since, seen reason to believe that a piece of cork would liave answered the purpose better), and then the instrument was set up, levelled, and the plane of the vertical circle placed in the magnetic meridian by the process before described. 2°. The needle was secured upon a block, provided for the purpose, and magnetised by means of a ' pair of eight-inch bar magnets, in such a manner that its marked end acquired north polarity. It was considered to be saturated with magnetism when the bar magnets had been drawn from its centre to its extremities six times, the process being performed upon both of its sides, and then it was removed from the block and placed in position upon the agate planes, with its face (by which is meant that side upon which the letters were marked) towards the east. 3°. The plane of the vertical circle being in the magnetic meridian, with the face of the instrument towards the east, and the needle in position upon the agate planes, with its face also towards the east, the north and south ends of the needle were read. Let these readings be designated respectively as $' and ". 4°. The needle was reversed upon the agate planes, so as to bring its face towards the west, and its north and south ends were read. Let these readings be designated respectively $"' and $'". 5°. The horizontal circle was undamped, the vertical circle turned in azimuth 180°, so as to bring its face towards the west, and the horizontal circle again clamped. The face of the needle now being towards the cast, its north and south ends were read. Let these readings be designated respectively as T" and 3 +72 5 9.19956 0.46695 66.2 4.300 MAGNETIC OBSERVATIONS. fil Taking the means we obtain the final values of the magnetic elements at each station, as follows: Station. Latitude. Longitude West. Date. Declination. Jj 0 •s o Inclination. 4 *0 d X Horizontal Force. £ 'B o % Vertical Force. ll H Philadelphia, Pa. . . 39° S6' N. ^6 4Q N 75° 7' 76 17 Oct. 24, 1865 Oct. 29 1865 0 / 2 37 8 W l 0 / J_6q -?8 4.148 I 12 696 St. Thomas ..... 18 20 N f)A CC Nov 14 1865 i -4-4O 58 6 7 eg Salute Islands .... 5 17 N. 1 44 S. 52 33 •?8 -?i Nov. 28, 1865 Dec 13 1865 o 3.8 W. 8 28 8 W I i +34 35 -4-21 27 2 6.742 6 5O7 I 4.648 2 SJ.8 8.189 6 988 Pernambuco Bahia 848. 12 57 S 34 52 38 to Dec. 23, 1865 Dec 27 1865 10 59.6 W. 7 <;6 6 W I T -f 12 8 + A 2A. 2 6.392 I 1-374 6-538 22 54 S. 4"! 8 Jan. 8, 1866 2 41.8 W. T — 1 1 47 ? C QC2 0 I 24.2 6 080 Monte Video .... 34 53 S. C-I TO S S^ 13 7O <4. Jan. 18, 1866 Feb 7 1866 9 20.8 E. 21 52 o £ 2 | -31 6 — (M 1*7 3 7 6.040 3 3-644 8 725 7-054 10 658 n 28 71 4.1 March 29 1866 1C CI.I E. 6 . ..-?i; 21 T^* 6 126 R 4- 403 7 7CO Callao 12 q S. 77 17 April 26, 1866 10 29.6 E. • I — 6 28 ? 7.001 T O.7Q4 7.O46 Payta S 6 S 81 6 May 7, 1866 8 53.0 E. I 4- 4 e8 2 7.3SQ T O.64O 7. -187 8 S4 N. 70 "3O May 14, 1866 < ^.8 E. I +•11 ?6 7 7.614 1 4.741! 8.972 16 50 N. QQ C2 May 30, 1 866 8 22.2 E. ? 4-^Q ^4. 7 7.74.O I 6.472 10.089 Magdalena Bay . . . 24 40 N. 112 7 June 9, 1866 10 40.5 E. I +48 32 2 7.176 2 8.120 10.837 San Diego Bay . . . 32 42 N. "7 13 June 15, 1866 13 9.4 E. I +57 54 2 6.261 I 9.981 11.782 San Francisco .... Washington . 37 49 N. 18 u N. 122 21 77 T June 26, 1866 Nov. I 1866 16 25.5 E. 2 44.2 W. I I +62 22 + 72 2 2 2 5-643 4-300 I I 10.779 13.260 12.167 13.940 62 REPORT ON OBSERVATIONS OF MAGNETIC DECLINATION. MAGNETIC DECLINATION. Gosport, Va. October 30, 1865. Circle Readings. Reading of Magnet. Telescope Direct. 359° 59' IS" (i) Scale erect . (2) Scale inverted (i) — (a) -A . . . 8i".7 76.5 Vernier + 5-2 Transit of Sun's ist limb . . . 2d limb . . . ioh 4om 6'. 2 42 27.0 Vernier Mean 162 12 45 Mean .... 10 41 16.6 Telescope Reversed. Vernier ist limb . . . 2d limb . . . ioh 44™ 48*. o 47 8.8 Vernier Mean 163° 34' 45" Mean .... 10 45 58-4 Vernier Reading of Magnet. (i) Scale inverted (2) Scale erect . (2)-(l)=A . 64". 2 93-5 + 29-3 Telescope Direct. ' Telescope Reversed. Equation of time / ft l6-I3'.7 — 16° 47' 28" —13 5*5 3<5 Circle reading to magnet .... A X £ scale division Sun's azimuth 359° 59'- « + 6.1 339 29-6 Sum 180° + circle reading to sun 339 34-9 34* 12-7 Magnetic declination . 2 37.8 W. These observations were made before noon. Chronometer oh 4™ 40". 2 fast of local mean time. MAGNETIC OBSERVATIONS. 63 "o £2 IM o 1 o a_ J S ON ro s tj " co ON £K "[» ope Reversed. •* - 0 O M mod •* ^4- M 1 ; C C/3 "M N "M ^ | rt s <4-l u 4) S + 1 O ON ?s 0 i M '•a bo •n • vo 00 M 1 S 0) > S c i rt H • • . 1 4> 4* tj S s II | Q ° ~ 00 »n rt . g £ oo" /•^ u "^ d d w 0 4 0 rt CLINATIO ember 2 C/2U2 7 il rt 4) II c Cfi C/3 | Telescor •"* M N O CO N + 1 °o 'oo 00 OO 1- •* o C _O J-S 11 w 5 S -t- u 55 u 0 ST » 0 £ 01 QJ M te 0 S » " 5 " S % •* 1 ifl O C r*^ '*3 * y J3 ,5 ^ S "-1 | °0 GO 0 0 rt "* > M U D 4) — 3 rt u C 3 •§ 1 rt c4 », s S | 1 t/> H M cj " o C o >!a "+2 S c Vernier Vernier Vernier C rt 4> S Vernier Vernier i u Li 1 "S 1 • • "rt fil i- w rt . V | 'o •+ 'g 13 _O 4> P "VI 3doc »PI .p* ™, I ode osapx W*^-b D*J 6 o ^"2 rt S "S 00 ^ I 9 o u-l —" 1? 0 9 "^ O ON oo 4> Q lo « ^o ope Reversed. 0 i O in M S ^ m O •« o vO 00 ob t^-^o O 1 vo r» 5-° CO fO w o\ o 1 s "8 • • • E/2 **. %> » «, ON | :: : J 4> H 1 1 CO CO CO co | o . . . •5 u • -3 • tfi T3 • • ( ; M •*. 10 • iJ C .2 iJ • 4) »• ro <-• W i VO s O 41 "fl rt (5 "u ^ in O m ON ^- o c " Pi u C II c fc w *n"N M - -f ^ 9, ~ X -FH /-^ ' 1) M m CO B S CLINATIO mber 16 "rt "rt u y c/3 c/a •- c- ) T j j c j j I/! "CJ 1 "rt 'rt ^-* CJ 0 I Telescot o oo oo N 1-1 1 1 fe+a CO CO fO c^ O « ^ I -a -° > ^ ^ S ™ w x E * Q o u Z -0 o ?/-, m B$ ? a s S 3 "ON y 0 00 u-j « So I; < S 5 o « -C i o ON >n KJ 5. O ON u-i rn « ° S S u; 41 H 1 4) C! * 1 C/3 M in £ ° 4) O ^ ^3 U C H U 0 • • • • • . . . «fs • 6.9 •Jf 'S c o O •-« flj c Vernier Vernier Vernier c rt 4> f£t Vernier Vernier 41 1 g 4) •— 4> "3 !!1 " £ "u .'S + "u 6 T3 U 4> »na 3do DS3FX U9A3- £ sd< >3S3pX 3 c » n i5 ^ ^' . *0 . . o S « o II H pi .5 S " « O f^ W r^ ^ « $) vin H Sr, « « c | o INATION ber 23, u c 31 N 7 11 i-g 1 II i D ri rt o u u 1 S c/) t/) 1 4; C*^ w E-* ll & a" o o 1 i — ~ si 0 t a o i « u Q S s _ w.CO = S s - " 3 II A ' C s ^ o t 1 sl c •5 1 C rt *" e oo « V 1 £ - • ' C s S • as C o * 5> E . . . s .s • • -w S M U • • • • 1 *- > tt^r _c s c .S-ca «a « Vernier . II 1 Vernier Vernier cT £ S S Ifl 0 2 o u « O '& * S ado 353(31 •pa -I.IA '•H a iossopj. H^~ U 8 H c . c & ** H * (2 IS !l £ H e "6 « M '•# . v> — |J ' i J_ c o °™ z ? u * me 1 ~ \ -' « T /-* II i 11 2-8 4> V U 1 en to | C"c? *«" •/ *JD N + 1 SO vO t^ 00 I* B s •S I rt •> SM O U U J e E - •O %u 0 If o o E3 -, - yj ^i 7w«« 0 \rt S 13 .2 * V. . u a 2 S i 4 .„ 3 iri irj »r »/• - fcS £ = *3 B = 1 ? I * • • • V s> o hi s r es H • • • 1 § • 0 Vernier . . . Vernier . . . Vernier . | Vernier . . Vernier . . C e - ,> 0} .§ 1 * 8J S1^* 141 S « E 881 u-*.^ I * -. i - .'C 4 1 1 •3 U - '€ & •P9J doMSpJ L •P osaa A3H rfoOBpX g- ' H *. « a x = , 0 «J 3 or CO - rt 3 MAGNETIC OBSERVATIONS. 65 MAGNETIC DECLINATION. Rio Janeiro, January 9, 1866. Reading of Magnet. CO r) 0 •r. \ H O 00 £ q to ro Si Si 1 a 0 g Reading of Magnet. S ; Telescope Reversed. "* %. B -^ «.?! II ^. i-I vo CO « 00 rh w u-) ro oo « 00 ON N W 00 These observations were made before noon. Chronometer 2k 3° 38'.4 slow of local mean time. • T3 W > II U.S U U oi" •3*3 •-' U 0 | in en | 0* tj < IS ll (U U "^ *rt "rt "-- (J U i 0!^ | N- M N Telescope Direct. -t f^~b N (O TII o"+r° " £ P) «" ro 00^ 0\ S . . II ? MS e 4J 1> MM S Circle Readings. % o N O ""> 1-1 M S Cb oo o i? ° Magnetic declination . d H HI rt S 'u Vernier * . . Vernier J I • • "rt S 1 si - o .£ Ill •3'*'-" O > s -,33J!a ado3S3pX •I— H-loos^x MAGNETIC DECLINATION. Bahia, December 27, 1865. Reading of Magnet. 1:1 M ro 1 Transit of Sun's ChOO c do O ro GO r-*. *o r-. ft V0 c rt S IM O rt U 00 \0 ro SK - Telescope Reversed. 8 "* ON 0 n °. Ov 0\ ro "i O O rod fO — ON O q These observations were made before noon. Chronometer 2h 22™ 6'. 8 slow of local mean time. 6.3 U U *« r) I T 13 • " « II •~ " A . . . . Telescope Direct. 00 M CO O TI 5,"« °ro' Q ON N Vi ro (S to 1-1 n m . . . . "si c -« s 2^ S .0 .0 Circle Readings. 1O TO VI •* •* ~ "« 00 M3 ^ ftft S S HH 1-4 o o O M f 1 Magnetic declination ..... Q t« O CuO . C 'O E . 'o So 300 I/I « Vernier . . Vernier 1 • • I • • i W -s, > S V- Ui . a; u 11 i » s 9 W 'P3.I1Q 3doDS3[3J, [ay, 1872. -P3SJ3A3H 3doos3[31 6^1 66 REPORT OX Reading of Magnet. a M I is H ? to ^ £ 11 c* 9 s •s t-0 oo^- i -o u 1 S. D s *o s. „' OO QQ O\ vn M o + 1 oo 00 t^> N 0. These observations were made after noon. Chronometer ih Ilm 34'.o slow of local mean time. •o ' (l) Scale erect (2) Scale inverted .... I /-N r* 7 Telescope Direct. !.«- °00 (~- M + 1 ^?" 0^ 1 00 o *^ »A d oo r^ W iri O\ 1 (l) Scale inverte (2) Scale erect . i T N * 11 e *; I — « * 11 • ^ 8 w *^ ^ 1- N ^ Circle Readings. *n ft n "6 Oj to *** M Magnetic declination Sum . lgo° -(-circle reading to sun Vernier Vernier Equation of time . / » s§ . s'2 ^^3 rt "rt _§ — "*"."' 11 i » s .§.- « §s s » S •pajiQ adoasapx NATION a , y 18, 1 _ MAGNETIC DE Monte Video, Jan IT? "8 •'- .8.8 II adoosapi s 2 ' 6 fc 00 " N 0 00 " + 1 1) "i. ^ •6 - -' W W 1 ^* u . c •5 4- Sum 180° noon. local mean time. ere m 2J'.o MAGNETIC OBSERVATIONS. 67 MAGNETIC DECLINATION. Valparaiso, March 2, 1866. Reading of Magnet. ll c v: ^ i J 4 If. "c 3 C/3 *O o « w-, u-j s CO PI d > s fe.s CJ O C/^r/3 •• T ^/ •s : : s - ^ 4> CJ ^ 1 s II "rt 'ri — ' cfic« 1 /-N/-N ^-\ Telescope Direct. •-. •* M O II °>l? CO -0 II g " N S 1| : Circle Readings. iO : "o ""> 5b •* CO "^ *V N Magnetic declination Sum .... i8o°4- circle reading to sun Vernier Vernier J 1 ' • (3 K» ^' ||| « •*•« II I V &S> T : Reversed. C>- "w \A ro d 06 w o t; w ft ! S 1 O 1 c a •« 1 M • • 0 • • •2 JS S -£ j: M u c H U E 1 0 O O u o w *rt "3 E S'B E .S Vernier Vernier Vernier e rt u Vernier Vernier U .H lation of ti Sf3.s I-S.E | C ° . N vO vO u Z 00 4> t^ M f) CN r*> *^> N W"l vO R 5 « S* B •?• 8 S I/3C/J /^^^ — N ^^s T 1.1 s II 1 "B1 "T" tnc« 1 "v + 1 _|_ |2 » o ¥ u i: s W rt x 1 o s y «- t? ft rt 1 C T3 ^O ^ 3 • • • • • • 1 O S & U rn .- rt* i- a * r O £ o ' S £ ^ S o .S3 a o - Vernier Vernier Vernier s Vernier Vernier S | > .§ IH O I ' ' 111 si: | letic declir e observat nometer o> ixto 3»I'X •P= -J..A H»«i cosapx 3 . . Jxj O . LO O fO O Tf "O CO W These observations were made after noon, and prior to taking them the telescope was adjusted for collimation. Chronometer o11 9™ zv.fj slow of local mean time. i . . tj CJ ^ SI J!^ "73 rt N~' O U i « C/3 | S-'N-' \— ' •a • a; . U 0 D D 1 S C/2 t/3 | T rt H i 3 I D H 0 ^ B ^ O O ^ o C*00 CO °0 ' 0 N co 10 10 bH IO »O PO W O 00 •-" N i< II 9 — 4* Circle Readings. 1 1/1 { O 10 o o CO CO To T£ o •* O co Magnetic declination ..... c 1 •1 H . 0 1 •u So Q a .2 * * Circle reading to magnet A X i scale division Sun*s azimuth Vernier • . . • • 'e'e § II 3 .« .~ >> S •^O^w. T^^dcOSSpX MAGNETIC DECLINATION. Valparaiso, April 7, 1866. Reading of Magnet. i? o 1 in "c O M CO 8 o 00 00 &5> a ^_ M OO 04 00 Reading of Magnet. 00 ^ oo *"*• 10 1 Telescope Reversed. 00 10 1-1 !U« N 10 O u-> 1 + 2^ £r o q w co W O These observations were made before noon. Chronometer oh 9° 23". 6 slow of local mean time. ••a til < u.S 'I 4) 4) ^7* •a "a fi U U 1 c/: co | •C J 1 « flj 4) "rt 13 OJ C/3 i-t N | 7 N Telescope Direct. . ON "^ co Hs, O T+ ^o o "^ do M — N ^O H OS 0 i cd H 1? 1 ?! i Circle Readings. "6 CO M § O VO 8, Cb M CO •-" 0 10 O ^O N Magnetic declination C 3 w • .5 B • 'o II . . o a • • a ' Circle reading to magnet A X J scale division Sun's azimuth ti M . II i II § >> s •JDSJIQ odoasspx •pssi3A3^j adoasajaj. 70 REPORT ON MAGNETIC DECLINATION. San Lorenzo Island, April 26, 1866. Reading of Magnet. il to in I "o 1 1 I; 4 •* * n to Reading of Magnet. O ir> w '-8 9 Telescope Reversed. O N - o ^ i « 6 O »n 06 06 fo •§1 Cv o These observations were made after noon. Chronometer & Hm I3'-5 fast of local mean time. (I) Scale erect (2) Scale inverted .... j[ N 7 N.X •O u tS < 18 i 13 "rt ^ U U 1 cfi c/3 1 H4 N > S >> !S •pssjSAay adoasapx MAGNETIC DECLINATION. Valparaiso, April 13, 1866. Reading of Magnet. IS CJ H 00 00 foS 11 O 00 Reading of Magnet. Telescope Reversed.! These observations were made after noon, through clouds; collimation correct. Chronometer o" 9™ 2i'.4 slow of local mean time. i! ij U 4> Ij tnt/3 1 \-x 1 i- « 18 II w w O "3 "3 •-' U W 1 t^cn 1 /-sx^ x^ — N « Q 1 ™ N f * 9 OtN °o + o N to in *• Si to W ON in * * * ^ — -^ i 2*S s \\ I Circle Readings. » SS tn M Magnetic declination ..... Sum .... igo°4- circle reading to sun Vernier . 1 B | L; Circle reading to magnet A X i sca'e division Sun's azimuth " If 1 >> s 11 9 II 1 •piJ!a adooopi •p,*,^ adoanpx MAGNETIC OBSERVATIONS. 71 MAGNETIC DECLINATION. Flamenco Island, Panama Bay, May 14, 1866. I 'o U> I £l 1 *d 3 *O 00 00 NN 00 u->OO a o - 00 NO 00 "4J If 1 « 00 c< «'K 00 fr" vO 1 Telescope Reversed. a - co 2;oo o 1+ "r^OO* N >-> to N NO Wl W w> These observations were made before noon. Chronometer o11 20° i6".g fast of local mean time. S.2 c^ c/^ — rt 1 N T •3 ' " *j zz .5 S t/3 t/2 < ^ T Transit Telescope Direct. NO''2 1 + "to i-« oi o q \o o 10 \O vo w o NO . . In T3 ^ i-i N A J^ .3 .§.= c '— — ' rt Circle Readings. O ^o N O O O 00 N O O ON "b o o o ON o CO Magnetic declination ..... fi 3 .1° rt V . (U 'u £ ° . . | O e .2 • ' "5 3 o< W -fcj *0 Circle reading to magne A X i scale division Sun's azimuth u u II 1 4) 4> II 1 •poaiQ odoosojoj. •pasjaAay adoosapx MAGNETIC DECLINATION. Payta, May 7, 1866. 1 |M O M •q rt fi P? vO (^ Is O "e IM O to •-• s to r>. O CO NO ON O M 0 00 CO OS Reading of Magnet. •fc'od 00 ^ o 1 Telescope Reversed. ON a - rO « O 0 O *O T+ *« O l-l IO N rood "O to H 00 00 These observations were made before noon. Chronometer

S.S 4J 4J •a "a o o 1 T y-s V . OJ "o c S .3 u CJ 0) 0* 00 N 1 + M « M W M 8* 00 j — II g ~ ^ II g «•« ^ -1 PI f". 1 O > n 0 "^ 0 u^ O S "S Magnetic declination ..... C ' 2 M . '(j G ° 3 Equation of time . t . . . » . . . . B i g • s| .ffl ^•3 S B_51 j;-*1^ t fc ll 1 S 8 •p»j;(j adoDsaiajL •pMm.H'dooHpx MAGNETIC OBSERVATIONS. MAGNETIC DECLINATION. San Diego Bay, June 15, 1866. 1 IM O c 1 M K o tn "c CO VH O 1 8 N LO o CO 4^ "*• "fr o •* VO I "o bo C •3 s I Telescope Reversed. N 0) ro a r^ o o 0 I 00 N i w CN These observations were made after noon. Chronometer 2" 50°" 32'. 5 fast of local mean time. •*a . &+r, oo m cK o i-i 00 w fO ^2—5 . 4_l 4J M N S II c' ~ ~ rt J_l . w >2 N S Circle Readings. "b ro 0> &s> OO N O 0 00 7l CO o ooo 00 VO Magnetic declination ..... Sum ..... 180° -(- circle reading to sun M M " 01 0) N .- Vernier . . . . Vernier 1) I • • "rt we* sj . •*-• "> tx--- js £ w 'N £-*»» axg c3 O m H •^- W f) % | £ »o ^f 10 NX OO OO 0 These observations were made after noon. Coll Chronometer 2h 30" 4".4 fast of local mean tim .§ .S cl || e' MM S Circle Readings. 0 V o H O 0 OO I--. *^. r^-. Ct 0) o 00 « Magnetic declination . .1 b/> . o 1 w II Equation of time . t » 1.2 ' s| HI u X~£ -— 5 , U U . v a> II 1 I- Ul • " b jj » S •psjiQ adoasspx •pssWAsy adoosapx 10 June, 1872. REPORT ON MAGNETIC DECLINATION. U.S. Naval Observatory, Washington, November i, 1866. Reading of Magnet. 00 «- q Transit of Sun's ?' o NO 00 00 Reading of Magnet. 0 ON o\ B i I « 8. 8 u H so Sb w-> NO "ON M o +1 f3 N ON o "T" •>*• o NO These observations were made after noon, and the readings of the magnet scale were taken two hours before the transits of the sun. Chronometer sh 3™ 47s. 8 fast of local mean time. jj r^. «• - (i) Scale erect (2) Scale inverted .... 1 T ( I ) Scale inverted .... (2) Scale erect < T w Telescope Direct. Ha s "* « 0 ro « + 1 9 o N 'Co d (Ni N W N . . Vernier Equation of time . / >..... Circle reading to magnet A X i scale division Sun's azimuth IJ1 II 1 •p^.a^oos.px •P^H^RL • MAGNETIC DECLINATION. San Francisco Bay, June 26, 1866. Reading of Magnet a o Transit of Sun's NOO Sis A q » Wi IO r^. 1 s tJ) _o V « NO „ *f* 1 Telescope Reversed. t?£r°v "8*3 NO + "N Jf*0 o 1 N NO •+O o\;j 00 NO w NO NO These observations were made before noon. Chronometer 8h 13™ 8*. 2 fast of local mean time. (1) Scale erect (2) Scale inverted .... < ^ T (i) Scale inverted .... 1 T N . . Telescope Direct. !)>D o 1+ ONdg. 00 N d NO N « W NO NO • • iOJS .1.1 B "•2 S ** w ^ II 9 Circle Readings. i r N §8 00 00 &> 00 ° ft J? "8 00 O OO M Magnetic declination ..... Sum .... I So0 -\- circle reading to sun Vernier 1 • • I ' ' O1 ' ' w -*, e reading to magnet J scale division , azimuth s s 11 1 >> s *- V • •pMiaadaonpj. •pssjSASjj adoDsapj, .bx"§ O • V I vU c 5 - H oo O M Bn FH H Q S o & CO t^too o 2 Q W « 0) o (2 co s^^-i- o ON ON ON I Ov 1 f •o * ft S 00 N O vO U1 o i *ON« -« m "-" — *• Ov VO a 3 fe 1 ^ -° £ O OJ °OM7>Ov ON N o 1 °0 « ^ ^ 00 a 3 0 OJ "o O H fl CJ rt VvO* 00 g. H o o a ON r** ^" ?rj in in O 0 c5 •& tf 2 H fe CO O R2.R O VO 2 1 fa co 'o o o O " u a t/3 O O 2 s o • t^ in 2 S LI • * 1 c 1— 1 v^ VO 0 O ^ fO rj- in c ) Cv O B "3 " o ,_; U u! " o 0 O O 0 r^. *•>. t^. ** in ^ •-< ^ o a> )M rt ^ in i^ !>• rt fO rt fe co o fa CO o M £ O O O o t~- M H bri M T3 vO t^ O ^ vO fO O 0 C Tj- fO ^n ^" N >-• M « 4) jj ]7] o ,1 ^ O ^: 1 ? in 1 00 OO OO VO vO vO 00 vO 0 •s a s ^Ovto VO f >u u rt m O "-• S 00 VO "c • 0 \o 'ioO * to (1 Cl fl n M *n •'• 1 ^ "o^c^c^ g, 00 1 * o m in m K ff * M s V«vO- o 9, § SSg S? m in • " H l*< CO O i •z \n END SOUTH. CIRCLE WES °8,&& ft C^ END NORTH. CIRCLE EAS \T) iri ir> m rj- H ^ S 0 1 s £ Ua =8 g, g, a ace West. - - ri M o M in m in m - - - n *i- o\o 5: Q ' u J^ Q H b co %&& B> 8 Q h en 0 m in m Ov i CJ 11 S S ^ < S h o 1 - o o 9 H O i - 0 w ^O vn in in o i/i 10 in N N M m 2 in S S •a o Z H § JS^-S s 9, H V g ^> oo r*» fi in M 1 § 'N i 04 H b CO ^ o o in in in 2, O K 1 1 CO 0 W N N vn n * K o H 2 CIRCLE 1 £ tlftft 00 ft S, oo 2 s 3 Q 1 fc o U-.TJ- •<*• 0 a ^ N fO ro N co °s,s,s, a m to °S**2* I s \O m " s 00 i- * oo i * OO 00 00 N £"> 2 H m 2 ^ 3 « 25 o ^ CO 0 •« O CO i> - Q H M « N 2 ro Q is inmm m § "^ p.- if S 1 H 2* i 1 CO t?fOM O 1 - i - t ~ « R w Q u 1 en o \n m in 00 to in fO m V 1 MAGNEI jvember u. o 1 * "b jj-jn Us,s, N M in 10 S o 1 * ^-.00 N 222 NO M 2 N m a. Q | 0, S tf H 2 1 1 09 V in 0 M N 1 6 [2 CO \n\Q in o i ~ t ~ r , 00 m »n 3 (2 j 1 ^5 a m m m "* ^ P N N M n 2 § 00 in in 0 K 2 3 Q "b « to M g- c^ S J "* eS555 in S! K D I £ R-S-S- 9 8 •^^>« ? K B •i. MVO fO H CO O t CO i- r- r- t^. *nmm "i « ^ - MAGNETIC OBSERVATIONS. 77 V "^ M f*. rh "ft§°° ON i ^ OO OO OO 00 10 1 ^' O ^ o ^ NH 1- M l-l »o , ^ "^" ^*" "*• to M 8 "rt- m N ^ ^ o "boo •* m ^ rt C4 a -3 &. VO u o Co oo o w 00 W \-00 N- 00 ^ P "2 o ,3- H M Q W Q ft/ £ 05 OO OO 00 2 M Q U M ~J * 05 co« w 0 ^- <«• •<*• r-. in t ii PH < S ^ O *** ^"1 o 5 s> M s ^ ob ^ co N CO ^t o CO vd Q '•-r. «S £ h 1 N N N W m ^ 1 CO .£ " ^ o £ mxnm m m 0 ITI?^? CO CM 3 o £ H i O ON $•••• « N E i "« -O ^f ,- - : £• CO ro £ M *• -./ H fe 05 o M en ^ c/5 o PH ro co ro m fO j>. C3 ^ s *n in *n m CO ^ jg CO ro *O ro CO g o 2 3 0 XtOOO CO £ 2 H 3 u OOO Jj. ro t— 4 M J* £ , * n o *J ^ o u "K J5 0 55 H in m m in m ^ :?:?? &in & m V £ O O3 Q 17 CIRCLE 1 u - M M O O fc o K Q *-r CIRCLE 1 - "^ O 00 CO N o I OO V cu ^o P ^ A H Q M V u (2 w5 *b o o O ft £-\ Q a o c/5 o ON ON ON *S ON fO V H HI H ro M r/ "* m DH 5 n § ,2 P4 i a*s< 00 9 PH V co^ co ro ON a bo si o 1 °0>O 0 ^- in in o ON ts 0 1 °&°° ft ?r c O £ g LARITY i V ,w K 03 a^a o O H 2 ; WEST. a o £ 03 'boo <-. k- •— ft 0 ro H O 2 H 3 ^0*0 C4 CM C* 01 o 10 2 3 LJ as 8 0 & 06 • 55 U 1 w O ON ON ON ? Ti- ro U 1 o W CO CO ft 00 m S v o Ov *« t^. m m ON • co ^- m A c/5 PH o •"* ??§- ? ON ON ON N CS N 2 78 REPORT ON ^» toto m\n ' -s, 1 ^- ON ^n co co in ¥ 1 fc \ss M V i H * o O O O CO co co c^ ON in § ~b j^c^ CO a B in O ON I- CJ ff O co M ti fa CO o IB fa CO 0 jy •3 HI 1 fD NORTH CIRCLE WI 232 5 JD SOUTH. CIRCLE EA CO CO CO to «? V l fc PO mvO N "fr « H M •0- N N « - V o O^ ON ON to O CO N in fe ^ K w s WOt^ ro M • sl fa o 1 » Vj V, V"1 00 1*) Jj fa 0 i O O ON *tf° *T ^J" 3 8 cfl c 3 •1 E O *nvO o 00 fO B (J "o N OO o | U 3 3 H fa CO o Ov 00 3 1 a CO °ON O\ ON ? S s 2 d V m «, 2 S N O in i 5 1 * CO 00 OO •R M et o 1 £ m - « v r^ O oo 00 00 4) "u-i O m 0 pi, fa CO o 00 fa CO °0 O O O 10 in in ob -too ^ >« ON in 5p ^ n fl ^- N ct 1 * 0 w, 0 * I * CO CO fO * ON B P H M hM M H CO i ^2 ^ Jf m § ^h m o « ^ •* xo $ ^5 fc fa co o w H b co V S f m •* O td 5 CO *> I p I 3 g fO N "^ ^8 * m N m * to 2 a I 1 0 1* •* f 3 S 9 D « D * o in in in CO CO co m CO 00 M V cu oo w 0 t^uir. fO in w fa O 1 S N fa O 1 H ^^^ ^ ON to "a * H pj^g, ft S E u ^n ^- in n n n m C1 •g i H 1 (6 § CO CO PO fO S ft S I fa CO o ir^ m m m Q. 1 2 S . '"roi-i S S 2 S g ¥'??>>0 vo m m 1 D 1 * °SJ?^ S R D 14 o in m\o "1- *h *t m »n 1 00 OMn N »0 ^« 5 JO ob in O co vn fa CO 0 fa c/i W CO in in in -fr t -t m MAGNETIC OBSERVATIONS. 79 u - i w - o 8>° ° f u CJ 00° O H h s C/2 o H PH en 0 ^ K £ ^^^ •£ * X (-1 H «" cT pT «" * O O N "bOQvO oo ; K I fe en o *O r>. t^. m LO 10 * *, si i en 88S M CO 1! fc M MARKED 5 en °a-2-s •§ - MARKED fa en 0 « PI Pi 0 to o, Q be c . d £ N ^ ^ h w fc S ™ B O ^ o 0) o & € 8 POLARITY H to < U] CJ o [2 c/5 O N *n o N M POLARITY CLE WEST. U en 552; M M M Ov ff D rt a o\ u ^ H ^ 1 0 !G S "b r^ O VO t3 Tj" *^ O O h C/3 o 000 £ en °0»0000 00 N ^T^li1 M 80 REPORT ON 1 £ I - 8 t>,0 0 cx> 0 tnO O CO M (-• (2 en O y h en 0 ^ VO J X P ^0^00 Ml * K 5 CO 3 5 i I ~ jj I 1 a D ri S5 Q u Q 2> § -. o "boo ,^ o, r\ *" Q A en o D M M Q h en o \f) \f) If) un 00 + U M M •o \o ^o "£ •* t^ Qi U **> M t^ < VO Q SB " ° u S . £ s J ^ i S Q hi O •% o 1 H i o" u a o o o o H H 1 'tnO O 00 jrnambu POLARI RCLE EAST en o ">7 ~f VTi 00 8 POLAR] RCLE WES en o K 8 00 ™ s A U •g S5 0 •s w 9= 8 3,c^S * u rt "boo N M CO CO en 000000 00 en 0 HH M KH K | fc I M fc' O X/,0 m ^ U S, 10 O *n g « M I (4 en o t^ 1 ri a £ en o N N N VO ^ 1 a) o Q •y CIRCLE 1 - 3 g O eo s a u os C i - CO s MAGNETIC DIP. Dec. 23, 1865. OF MARKED El (2 c/i toO O •«•- •*• • s, OF MARKED El i en \f) O O *fr tO « O n CO c^ 0. g 1 1 - M i - M o u £ 2 § £ . boo r^ — — 222 ^J 8 t-H 2 1 1 (2 en Iss- s N H 1 2 M U •1 - M 2 CIRCLE 1 - 5 ^;ojo f? b *n o * * en 0 £ C/3 o M M M K ISs M MAUJSfETIC OBSERVATIONS. 81 | - 1 W - M g WEST. 0> f2 « O m in o Rvo'R to R CO X i I en "boo W »-l M O to O\ 10 m 00 •3 V CD * (^ 0 Q i- B I - ^ 1 Q CIRCLE 1 - 7 1* o "S H ~ W q 1 „ "in O O \n M M 0 \O vO vO Ov s Q 1 en *n O *n C4 « o 1-^00 CO ^ 0 U «-. ^ « 2 u h O 1 - o M S O 1 * 1 Q _c "3 u o u Q LARITY a (2 en %22 o t-4 00 bN h i— i 1 1 en "b m m 0 CO m to I Pi i m 2 o U 1 « N 2 CIRCLE 1 - 1 1 en &S>° ESS * e [2 ^ o CO CO CO oo CO "K u * O **"} O o vovo m r-. r>. t^. r*» M 1 * 0 mo o M m in ? K 1 u * *b m in 0 r-.t-.i-*. O vO w EAST. 1 en w to co o "8 m oo V 1 C O Q CIRCLE 1 - &0 ° o r— r-. *-. r-i vo t--. 00 CO I Q br CIRCLE 1 - o CO 9 P1 >o VO CJ °° C Q H M u 1 - O in in 0 r-^ r-. t-*. J vo Q M en 0>00 CO o * o\ to V ex W rC O IH ^ r- Pi a h 0 u - 0 r> O 0 8 - 'b >n O co"- o vO t^vO m CO m CO Q M c ul 1O •-• CO O N ro ro \O ^O \o in fO >o N < £ WEST. u u £ t/5 « K EAST. £ co ON CO V ! fe p< i Q •z CIRCLE 1 S5 •fe iy,O ui ro Vyim 00 u% IO g O 01 Q g I c Cfl 6 £ 5? "6 uMn « « ^> 0 N « >- VO ^O ^D to N •£> N * o £: as 3 h O 1 » ^^° JtSS M •* t-^ m 3 S h O 1 M ni ^) in »n 00 CX) OO O 00 t-> M s u c *3 I— > 2 1 g & 3 EAST. • u (2 U3 to in > 2 ,1 WEST. u — > o "A 2 § 5 j X5 iTS,^ o tr^iri to t^. r^ r*. 1%. f*) »O IN, •<*• t^. 2 CIRCLE 1 55 "u-i "MO l-l M 000000 u^ 00 M 00 1 CA S t2 w 1 55 th to O o *o CO M i ti Xrj in O ^J* M "r^oo oo ^0 VO ^O o « « X H i u £ w 0 to cd S 8 i co t^ CO £ I i 0 i 55 ^aa o « w « r*. N M I i G 1 55 t>> O m u% CO !$£ o $ i a« § o M 2 iO O CO *n ?« « « K M s s ! •— > 4 u B LARITY i 1 oj •R B 3 1 i 8 £ to to <4i & t2. s 8 9 c i 55 "fe «j>O I'I'S «, 1 •2 2 i 1 55* 10 »^> »^» M - CO fcss M "-1 1 •/: ;2 CO MAGNETIC OBSERVATIONS. 83 "bog * •ooo % i * o £> 1 - O . o 4) o ^ si 1 h cd 9 K £ 2 & en in 1 aa o Q "a i 1 ri ;:° o m o in O CIRCLE * - ooo ro- m o ON ON O\ o\ * 1 V 00 tn ol S W U 0) P "2 o - Q U £ en Q 1 en 1 H 'S M M to W S . "o o^o * R S ri "boo m m a 9, a "^ 3 fe O 1 ? 0 a a o ** o to to ro o to I i — > V id M 3 1 o en fc I 1 en N & ^ w n ^ •S S 2 1 "boo >H to N *T 1 2 ri p< "boo ^K ^ 3, to i 0 J A O 1 u IS * 0 S> 8 S 83 en S°i- S- OOO i-. N r^ o ,-J J7| ( • ^q s «5 jg ^« 1 M « « * 2" . u ^c i (2 t/3 H h en «J si w ri i 1 o a CIRCLE 1 - O O O TJ- - rj- 0 to IO to I vO N 1 a CIRCLE 1 - 8^OO N « "1*1 § 1 V M w u o O P <2 Q (2 en a (2 en to 1 o ., H M N | IN m w w C5 J^ M S ,. ft S1 3 s ^s j "boo M N CO « m s bo s « o * 10 0 1 1 ro to fO to O~ 1 g M H 1 en ! H WEST. U £ en S1 M U 2 3 o to O »n r^ S 2 a u OOO *• % S3 Q X O o tj ri o vf) ^ i irtr;0 10 1 CO fO fO to 8 ?{ b en £ en REPORT ON MAGNETIC DIP. Monte Video, January 18, 1866. Needle A. 2. POLARITY OF MARKED END NORTH. CIRCLE EAST. CIRCLE WEST. Face East. Face West. Face East. Face West. S. N. S. N. S. N. S. N. 148° 50' 149 o 149 3° 149° 20' 148 50 149 o 31° °' 31 10 31 20 31° o' 3' 4° 31 4° '49 7 '49 3 31 10 31 27 '49 S 3« «9 POLARITY OF MARKED END SOUTH. CIRCLE WEST. CIRCLE EAST. Face West Face East. Face West. Face East. S. N. S. N. S. N. S. N. 32° o' 32 o 3i 5° 31° o' 31 20 31 40 149° 10' 149 10 149 20 149° io/ 149 3° 149 50 3« 57 31 20 149 »3 149 3° 3< 39 149 22 8 Resulting Dip: — 31° 8' MAGNETIC OBSERVATIONS. 85 "boo O v ^^ ^p-. » co ^ ^ to 1 * o m ^ 1 - o in in *n 2 a . 0 i^O m Tt- S O "^ O W in M 1^- in rt M fe • en r^l en o H CO o o O X P m in m in X w N M N M O « in I o ° ^^ n t? ft ^o S5 H 0) O • "boo « m in ^ H V o m O 10 co "^ 10 5? rj- N o m PCX) l_( Q co o Q h CO o M 1 u H *" « in in in in in W H- rt- . x 2 S O *»n in m " « m 2 Id d "6 m in to in m *y M • H a ^ * 9 C/2 G $ 0 W M M 2 M in o 1 0 m m in VO m a § m in m *j- in « 00 10 j S in in O K, - ri M vO in f*< c/5 o ^^ h CO 0 "22 2 in in in in m O ""> ^ in O O 00 ^~ . m m -*J jgj o ^j ^ o 1 N M N m m m 10 00 1 N N > °z t-> If S 0 1 ^' V O in o So ^oo « N N a m in P^ S h 0 1 S? "inmo o m m m to in m 3 CJ) q 4-T _C 'o !* H jj i2 cri 0 OO t^-CO 00 ci « in ARITY j B i co O O *-o o m m m N m m it K PH J W h- •• I-H M ,4 13 2 M d p^ O ""> O •«• m m £• 2 S u £ g ^w« ro t->. m (3 0 S t/3 Q H OO t^CO N N W r- - CJ 1 r«* »-* t^ m m in m *• 0} y 0 O 0 1-* 00 8 ^nmm (4 M 5; i2 co 00 COCO N N N 00 N IS CO 0 r- r*. f^ in xn m in 86 REPORT ON 1O 1 ^oO O 00 , tf to . M M | 15 °to to.fr ro ro rO at 1 H * O Wi \O tr^ to S S H H Lii rn H PL, CO E i_ Z ^ d S CO to O I i 2 Q CIRCLE 1 w - o fO ro ro N CO 1 8 Q CIRCLE 0 - oog 0 * 3 fc • 8 s 0 Q" vo VO Q (2 CO Q h en ^_ CO 1 0 °= E „• U. U! < o M M < •"• 1 H, Q "bom 00 f» O O to to S5 o •*- • «•>•*••« CO S • to to s | O I i?zi? ¥ h O 1 o fO C ^ > U lx s S Q* £-, 1 H . • £4 I OS i A en M M 1 CO « g i 1 . V 00 $ O PL, 3 « •? o to I i ^ O in 0 •s * 0 •0 w 2" 2" ~ ^ fOroro fO u tt 1 9 en e en y) j; Irs s o 8 u £ IT) 10 to 0 s 1 rococo CO w 2" 2"^ 2" 8 o M jn a en H (*< CO ^ s H P N X 3 o ro u I a. g Q 2 u 1 « too« ^- ro to S1 ft O S S Q CIRCLE 1 * "»o O to ro N *O r^ •5- s, cC U 5 MAGNETIC D klarch a, 1866 OF MARKED (2 en fo OF MARKED en 9 T a. Q £ Z %M 00 00 ft 1 * 0 ro ro ro to 00 > 8 >, u .§ 2 H 5 H en M g' £ en i 3 a 1 i 00 w» 1 e S 3 - V vvS)S> 9 s, 1 2 a I 0 i - O to O ro*-!o o oo oo oo ro fO ro 00 00 8 S . • £ c/5 MAGNETIC OBSERVATIONS. 87 V^as fo ^o^. c? 55 0 ^J 55 0 1 coroco CO i H §•§•§ 1 (U 0 M ffi WEST. £ 83 OS 10 K EAST. h CO CO Needle 1 Q 55 CIRCLE 1 - "ioO O o 0^0 0^ $> O CO H Q 55 CIRCLE 1 - u~t o *n 1^1 M in O s P. H 0 W 0 O so Q [2 co Q fa c/i o tJ °° Ld m CO H ~ M VI W CO 1 W Cs 1 -* s j "boo in co N CO g, K < ^ ^S?8 CO S o. Q b«5 ^ rT 1L) 00 OO 00 00 f. s o o o o hrt S a o •£ 2" 2" 2" zt O 1 •* * 1- * C o 1 H 3 1 1 to 2- ^ARITY WEST. 1 CO CO $ Oc 2 d "bom m OS 2 3 u "boo « "ICO CO CO ON fO u | o ON O ON 1 o £ o CO co CO OS ro S ?! fa to $ CO .. f» . "ui O O y ^- \f\ \i~i 2 inirsu-i ^ mmm CO M S"*? 2 8 V U « B co (-' trt £ co i O O i-t co W « K M s . "inO O CO CO a. Q 41 " 5 I o >- 3 O III $ o > 1 a o CO CO co •<»• to M a 3 o" .2 H 3 fe fa co h 3 i £ CO V 2 1 2 i a ij 2 & M 2 u i m 2>° E K J °2S o CO t> o •5! *£< ^•«« * u ?! * o ,^ w J?? y 1 CO co co CO u (U fa^ co 1 CO REPORT ON 1 * «0 0 •:^r V) 1 W * III O M as 1 en •o- w H V Q en ? JJ 1 i m Q B j - 28S- « to Q c | * "boo o * £ fc ^ Q ^ O M Q w M O £ en O to Q H M 1 en 00 o It T I O* £ « 3 | S S S o 1 - III •<• * P4 s O 1 * "boo « N « 8 ft Q 2 ii H 3 i 1 en t 2 3 ^ 1 CO N 8 & 2 a u i •* o OsO O rj- >t it to 1 2 CIRCLE % - "° ITS I " 1 en B Q (2 en . 1 - o w-j w, u-t w 1 - 0 00 It ^ H p V en •8, M H 1 en '•? V I g g 0 1 * "it O O o * M i Q a g s 1 * III 5 * , - s M a H ei 1 en f. W Q W M 0) o en * O it CO 1 O J= s g 3 O 1 - o 8 If) i 0 1 * 0 l/~t IO \t » It S 1 B LARITY § 1 en fl B M 3 ,1 i s § en ^ & a. 1 i i - III M to 2 CIRCLE 1 - O O O Tf ^t M O r >o TO '5 en 1 en MAGNETIC OBSERVATIONS. 89 0^>0 00 "o o o • W M S coco C4 4_l ^ . ^ N N M £ CO CO CO CO W 2" 2"^" jj o 4) . 8 O i h CO H m CO a 5 N n a $ M o u u §m o « co « CO D H 3 (J *6 ^o 00 B •o Q o 1 ** °0 0- CO CO CO 0 co Q us D 1 S? °0 M M M 0 BJ W § W 0 o 1O O 00 H " w -. X *^ MARKED S CO 0 MARKED (2 CO S CO 1 o. S u> 8 "** N O co 10*^0 0 to s ^ 0 1 Os O O\ ? O 1 °o o o * J "3 ^ K^ u i i o H rt H I M 1 M H CO 5 K 1 H CO a t 2 1 "boo co t CO ? 2 S 1 *b o o m co rf ° CN CO u 1 * "boo \f\ if) 10 o o 1 'A 0 CO ?! U rt CO * CO 22* o "b tn 10 CO *J ^ 0 » ^ £ c^c^co co 1 »o ^ 10 ¥ | S . H a h co H £ co B p *CO " 5 N H _°8, * | V O to O 10 C) CO U "3 ^ %-!«•* ^ G ts ^ o VO vO vO VO W §2"? 5 1 CO CO CO co § u CO ^ CO 12 June, 1872. 90 RETORT ON •b^^o to *6 o o c^ .- *•* ir i » O M 1 ^i o O 0 0 * ** 0^ * (*i **i M S M " '~l 2 B H & . C/3 H cn M 13 to . 12 »o 5 X K H — p( i Q CIRCLE 1 ^ ^82 o " 1 Q CIRCLE 1 - "boo jo 'b i- o o o N . W M O 10 Q ** Q & c/i Q (2 ^ 1 o °° W U! N ^ M * ex W M" f£ •boo o a 0 «0 to m q 0 _ S i a "ooo* Ox 3 b 1 15 "-CJ.O o .s1 A A O £ 1^2" 2" 2" O i **! j,, ^ B f S H h c/i H S a £ cn I "rt 2 3 * 2 RCLE W ^°8 0 ? "boo ro **^ ^ s > 1 £ °?s>s, o in u 1 o to £ c/5 ui J * O m 1 * *b o o o t^ i? § s « s £ CO H b cn V I ri a 1 * 'O 0*r> « f^tO 00 - fc H v H o Q ^ Q [2 . Q (* to 1 2 "2 H Q a M * 1 Ci, 1 i 3 u. 0 1 55 o S a ^ S b O 1 * N "• O 8, V* CO Q UJ c 3 j £ (-1 jj (i i s i IK en 2, 1 c/5 0 2 2 2 . )US, r-* J 2 9 "b o^o^ s, vO fO •^ | '' *J. ^ J. . 0 to " *o 1 J ± ^ J ^ CO fO fO to § 0 £ CO * c/5 MAGNETIC OBSERVATIONS. 91 "6 1 >> VO m 1 14 0 I 14 0 CO 4J V H H & en 6: £ en •3 ID SOUTH. CIRCLE EA m , I - °0 CO " 1 - "4- °| - A W O H (U O Q M3 U 00 Q U ^ en 0 Q fa1 en N 1 1 S K 3 | S boo 10 in in 0 o CO » £ 'U o 1 ^ oo oo oo 00 0 I U! °0 • Q H M en VO M 1 g ro § " < ~ ^ ^ S a, M < S fa o 1 * o in 10 to 3 CO 3 S fa o a w fc' boo \o »mn o s, tO •a a cT rt "c3 POLARITY .CLE EAST. ^ en 0 POLARITY RCLE WEST. V en ^S (6 ¥¥¥ 3 S boo CO CO ^ •O M «j t> •o as | 1 tn in X EAST. 4) U [2 t/3 10 »o 1 !l p CIRCLE 1 ^ trj ro °0 I I Q b^ CIRCLE 1 55 0 PO •k »o t^. vO 00 fc ^ I* i § I c/i 00 H Q U M 8 A ui O ro ^> 1 o. w -"5 Z — i:- OH 3 fa O | 2; »A O M + 0 1 < S h O 1 H 55 * °2 N I Q u> c "3 i h- 1 O N E M i • £ U3 •^ ro >« 2 1 WEST. V tj £ t/5 w> •n V M „ ,3 a 2 CIRCLE j S5 •6 °o O + 2 CIRCLE 1 55 •& % HH N n 1 So t^ | a a o • 5 1 X •b o "i r*. •* 1^ H > >o da 1 gj 1 en MAGNETIC OBSERVATIONS. 93 *J 1 £ ^ 8 1 S "b O O LT) rt 10 H * M 0 1 sTD NORTH. CIRCLE WES 1 OO JD SOUTH. CIRCLE EAST co °0 M V o\ 1 - s 1 iz; O pj v H D O Xo H 4) •J, o Q H so W 00 ARKED & tri o OS vo CO A.RKED £ cn w Os cu 5 O 0 O n S . £ JjL S .jj 1 bJ) .s M ^ OJ h 2 ^ rt* O ^ O 1 n i rt OH POLARITY H i 1 cn CO °0 « POLARITY CLE WEST. 1 cn 'b °o * V O O H B 0 1 " o • Jj « w 1 J? a Q • 0 cn 0 A cri o ^ "b o ^ §- 0 f 1^. w a o V Q B i2 cn £ [2 cn M B W) K 3 8 «5 O 1 •^- 1C b 0 H 3 u H Xo *> jy •a D Q *7- D 1 * 1 cn Q »7 U 1 * s> t Q * flu M Q 1 A w Q 1 u5 °^ * y ^ H W In, W M S^O 00 2: « 5 < a. Q 8 * 10 «" o i .; ^ ^ bO o o ^3 p^ 1 Z 1 - ^. •o rt VO V V 53 j S £ to C4 K ^ Nl CO % S VO o s S | H j u 1 . 00 CH 00 <5 0 ^ ^ o ? ,£ Q Z (3 | VO O V Q* M H VO w 2. ^ Q $ u S Q U £ CO « Q (2 to o VO Oi o PQ a 9 s i *• to < a 1 * N Q | ^% S Q * O w s rt 1 i OS s to ?0 H S i 1 to -o i •o 3 2 a o to 2 £ ^ i ^ •* •R M 0 o 1 0 1 i u (8 a s J? £ a to %, to VO M •^ 0 n . .; »i ?H 00 'a * 0 | S i to o CO 5 u ^ •0 3 • to ^ fO ,1 3 •b A £ U | s- 00 8 0 1 A ft n U i •* 9 S "J "b M V 00 t £ w . £ to O - E ft 3 1 MAGXET1C OBSERVATIONS. 95 "b « o In ^ 0 *r ^ M « W to 10 S ^> (« § V t^ M S en o r-^ M fe fa en 0 to • H 1? to K w to ^ OJ O u 04 CO J? 3 U S £ % OJ u -^ *H t/1 4-1 ^ V gj Q H H U fO to Q s W 1 S vO ft ^- "b Tn Q vo 0 g ' Q W fa en o o Q £ e/3 o to J H « s w W CO to H £ O 1 ^ IT N i V m VO g. S bo s &• fa 0 1 fO 00 o 1 o ro H 0 % J M flj 1 en g o * 1) o (2 en m 0 9 M O £ 1 o O 1 H * %, 0 (1 S H . WEST. fa cri 0 § B 1 Q 1 en 0 00 to •3 a Bi g Q u u M 0 rt M - O ON o\ to M o en Q CIRCLE 1 - \ O c\ 00 PL, W u v 0V S O 0 o Q MS Q fa CO ' « Q (2 C/3 W * to O vo W ON in W Q _ — I— S. 00 1 J O & 3 s M S p, s tut) . 0 to * 0 CO § I? fa o 1 to o fa 0 3 W S- 00 a *s * >< (J 2 $ >• I ^ o s M 1 O POLARI y ^ s u fa OT °0 » POLARI CLE WES1 W °0 - to §. ~ir> a ^ M , • ^" tt * *• M U 1 o o O !/3 Ju ^ o CTv to ^ 8 •^ M fi 0 £ CO o fa en 0 96 REPORT ON "xo 0 . ^*" £• 8 * % ^ 1 vO <^- to 8 to 00 H | $ « • b en o 00 . « • I D NORTH CIRCLE WI 2 ID SOUTH CIRCLE E *t« I fc •b i N M S = ^ 0 0 . W •^ s* u 0 «J p oo o Q H i en N H Q M s en * c\ in i LH C^ 1 8 a 5? => 3 s ^ b CO 10 * Q c O 3 •< I— « 5s - h g i * O o o a Tf s> "3 a* « . i en O S> H H & s I en V n " I -o to 2 3- o 10 * 3 2 RCLE W IT V. O S, o r^ JJ 5 1 * o - G 1 "? 5 8 ^ M 8 0 (2 en o fi en o m -' . fc V „ * O OO > s? M H * ~ V •£, OO . u m fO a to T N t (2 en o " jj en o oo oo ^ £ 1 I? N SH M V I i o K Q CIRCLE i fc °° ro 1 Q G 1 - 0 o y M Q oo a 8 CO i O Q 1 en I 9 + •* M o. is 1 3 3 . ^ 9 — 5^ "b i •b M a 0 K 55 °0 0 4 2 o O 1 !? ^ H § ^ o § 0 A (2 en °S, £ en O MAGNETIC OBSERVATIONS. • 'b 4» ^ I 0 •g ^ s. o £ M u ft HH ~ 0 D O U "b •O H rt d . s S tn o H fe tn o •<5 W ^ o to ij < ^0 ^ V H HH r W • H ^ § ji^ fc 5 H ri u o (2 ^ J I o 2 « *^ S 1 C/3 *^. 00 60 u «j M v5 < J S 2 S u m 5 2 a V s d a. 8 j ^ o u •si fc o I oo v H ^ M * u •^ 0V "b ^. d w to • in cs en o en 0 M • o g o ^ 2 3. 1 K 10 U •Q N U o m ^ N O W WEST. 1 en O M 00 a ri (2 en o CO in u-l 00 13 V O W J U a* m m N H O CJ "b 00 10 S5 w d • •5 o en D •si ^< So PH ^^ Q Z W • w 2 >n Q g ! § in 8 00 1O 0 VO *b % O 00 M Q ' M & en °M " Q U en o CO _ o LH l-O « M m y cx 5 -1 M 3 tn 00 K vo Jo s o a < 3 kg 1 > a o £ * 0 m O S 6 1 * o 2 o .s t/1 M* h S m 00 H (4 u o •6 g1 u M 0 60 2 1 en & o 2 < H & en 0 CO M « Q § 2 CIRCLE I 2 CIRCLE ^ ^ o ON 00 u-i N 55 § O N M • M m ft " « u ^ a •s^ N s «? Si a CO 2 m en 0 fe en o N S N 13 July, 1878. 98 RE TOUT ON i si vo S 55 s a u 33 j« 1 X i vO *r> n a 1 £ CO 0 "1 1 •o V 1 i Q CIRCLE 1 X o M i a Q CIRCLE i - •b o vO vS a: 8 Q 1 a 15 W Q W (2 » o VO Q / i CO vO M °N vo a « * § 3* M S h o fe X £ " Bi 3 h O i - O vS .& 1 i | u E c* 3 i 1 t/i vS E 9 1 WEST. i co o o I M 1 2 CIRCLE 1 * ; 8 2 a o o i - I a I 1 CO I v? * CO "a M M 00 M MAGNETIC OBSERVATIONS. 99 ei ^ % • . * »0 o In U * o & »r» | 53 O T) J? t/% *^* IO 1 H V to s- U 0 « vd vo K I c/; 1 w K i co o 00 oo M M O I Q Z CIRCLI i - o o O o § Q *r CIRCLE 1 * S o £.' "TO MAGNETIC DIP. , Washington, N OF MARKED E 1 co 8 0 §• r*. 2 J OF MARKED El * w o N fO 0 S be d £ - 0 f? a * I 0 > Q £ g, H o I a j i 2 CO PH co 0 h- 1 n s CO > lH U 3 O 3 J O PH 1 • *- « V • H H 2 H & co o I « C ^ a *" "* ,_] ^ 2 1 0 O E 3 . ¥ N r^ 2 U 9 "b 1 c o o rt S w IN 9 D ? M 1 § to N u to Ov I n o CO £> N 2 100 KETUilT n i te - * ir> i w - O a 1 X » I hi en 0 u*> O 1 vO ffi EAST. u 1 en O o w t-» VO CO M K 1 Q CIRCLE 1 - V 1 I G 1 - 0 O *^ "V a A S o g a 8, 2; w s 1 „ i o {? s- M C D 1 en O ro o N ^ o N t^, a. MAGNEI Washinj g fe * o in 1 s o | - O ** Q c 1 X 1 S 3 i - * N in 1 (j § - I 2 ft O 2 CIRCLE 1 * i N 00 CO 2 « u i - 0 2 1 to V 1 - o fO ro 1 en o 2 2 M u 1 - s> O 1 U - 'J o T3 V i 1 1 CO o s- g M , EAST. 1 en . o r-. ! S i a CIRCLK 1. * O s- s- 9, 3 Q 3 g G £ - • "b 0 00 •^ o: S C c * & u Q U M I CO o 0* s- 00 U g U! 0) 1 en o 0 o HH t-S H- MAGNEI Wash in | S hi O i 55 0 w p£ 3 hi O s - o g. 00 5 .£ 1 ^ o E 3 i s A CO °^ 5 0 g C6 3 H 1 en 1 r* M 3 O 1 i ORCLE 1 - °N •0 u^ 2 CIRCLE i * 1 - CO I .i '°K ^ I CO °o 1 MAGNETIC OBSERVATIONS. 101 HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. Philadelphia, October 24, 1865. Gosport, October 30, 1865. No. Time P. M. No. Time P. M. Time of 156 vibrations. No. Time. No. Time. Time of 150 vibrations. o 10 20 30 40 5° 3h 27° 5". 6 3 28 17,2 3 29 29.6 3 3° 42.0 3 3' 54-4 3 33 6-4 Extreme sea At beginn At end . >56 1 66 176 1 86 196 206 le readin in? 3h 45» 50,.g 3 47 2.0 3 48 15-2 3 49 27.2 3 5° 39-2 3 5i 5i-6 18™ 45". 2 18 44.8 18 45.6 18 45.2 18 44.8 18 45.2 o 10 20 3° 40 5° I2h I7m 5". i 12 18 12.8 12 19 20.7 12 20 28.5 12 21 36.1 12 22 44.0 Extreme sea At beginn At end 150 160 170 180 190 200 le readi I2h 33m 58'. 8 12 35 7-8 12 36 16.4 12 37 24.0 12 38 29.6 12 39 39.2 1 6- 53-.7 16 55.0 '6 55-7 '6 55-5 «6 53-5 16 55.2 Mean . . . P. . c.o — 1 8 45.13 150.0 86.0 Mean . . . igs, Tr» 1 6 54.77 0 — 88.3 0 — 82.0 •7T O Coefficient of torsion v = 8. 12 div. Temperature .... 60°. 7 Time of one vibration . 7'.2I2 Temperature .... 60°. o Time of one vibration . 6". 765 Gosport, October 28, 1865. St. Thomas, November 13, 1865. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. 0 10 " 20 3° 40 5° 3h 43m 6'. 4 3 44 '4-4 3 45 22.0 3 46 29.6 3 47 37-2 3 48 45-6 Extreme sea At beginn At end 150 1 60 170 180 190 200 le readin inrr 4>> om 3". 6 4 I ii. 6 4 2 J9-5 4 3 27.2 4 4 34-9 4 5 42-8 i6m 57«.2 16 57.2 16 57-5 16 57.6 1° 57-7 16 57.2 o IO 20 30 40 5° 2h 23™ 6s. 2 2 24 3.2 2 24 59.8 2 25 56.9 2 26 2 27 49.0 Extreme sea At beginn At end '5° 1 60 170 1 80 190 200 .e readir incf 2h 37™ i8'.6 2 38 15-4 2 39 12.2 2 40 8.4 2 4i 5-7 2 42 2.8 14™ I2".4 14 12.2 14 12.4 14 11.5 H 14 13.8 Mean . . . gs, . - 60. 16 57.40 2 — 88.8 1 — 85.2 Mean . . . gs> fo 14 12.46 2 — 98.0 $ — 90.2 72. f 21 46.68 3 — 66.5 5 69.0 Mean . . . Pi co ! 14 11.42 5 — 98.8 !-89.s 88. 67.: Coefficient of torsion, v = 8.97 div. Temperature .... 70°. o Timr; of one vibration . 8s. 7 ' I Coefficient of torsion, v = 4.25 div. Temperature .... 87°. 5 Time of one vibration . 5". 676 102 REPORT ON HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. St. Thomas, November 16, 1865. Inertia ring on magnet. Ceara, December 13, 1865. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. o 10 20 3° 40 5° i» o- 6«.4 I 18.6 2 31.8 3 45-1 4 58.1 6 11.4 Extreme scale At beginnin. At end . '50 160 170 180 190 200 readin J •' i» 18" 20".5 '9 34-1 20 46. 6 21 59.8 23 12.9 24 26.2 18° 14'. I 18 15.5 18 14.8 18 14.7 18 14.8 18 14.8 o 10 20 3° 40 5° A ,,b 35m gi.3 ii 36 6.2 " 37 4-2 II 38 i.o II 38 59.1 ii 39 57.0 Extreme scale At beginnin] At end . . '5° 160 170 1 80 190 200 readin • t , i ih 49™ 36". o ii 50 34.2 ii 5" 33-4 ii 52 31.2 ii 53 28.2 II 54 25.6 ,4™ 27..7 14 28.0 14 29.2 14 30.2 14 29.1 14 28.6 Mean .... 5s. . . 61.8 — . 6!.C — 18 14.78 98.0 96.2 div. Mean .... Ss. . . 59-0 — 14 28.80 IOI.O 115.0 div. Coefficient of t Temperature Time of one vi orsion . .->•-= 5.22 .... 86°.o Coefficient of t Temperature Time of one v strong breeze bio somewhat unstea orsion . . v= 5.40 89° o bration . . 7'. 299 bration . . 5'. 792 wing, which made the vibrations Jy- Salute Islands, November 28, 1865. Ceara, December 13, 1865. Inertia ring on magnet. No. o 10 20 3° 40 5° Time A. M. No. Time A. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. 9" 43- 3'. 6 9 44 0.4 9 44 57-4 9 45 54-2 9 46 5' 3 9 47 48.3 Extreme scale At beginning At end . . '5° 160 170 1 80 190 200 •eadinj 9* 57° l7'-7 9 58 14-2 9 59 «>-4 10 o 8.6 10 I 5.6 10 2 2.5 14" 14-. I »4 '3-8 14 14.0 14 14.4 '4 14-3 14 14.2 o 10 20 3° 40 5° I2h 23° 14". I 12 24 28.8 12 25 43.8 12 26 59.0 12 28 13.6 12 29 28.2 Extreme scale At beginning 150 160 170 I So 190 2OO •eadin; I2h 4im 5 1'. 5 12 43 6.1 12 44 2O.O 12 45 33-5 12 46 49.2 12 48 3.8 18" 37".4 '8 37-3 18 36.2 18 34.6 «8 35-6 18 35.6 Mean .... P. • • 57-5 — < H J4-13 >9-8 6.0 liv. Mean .... js, . . 104.8 — 18 36.12 58.8 62.2 div. Coefficient of torsion . . # = 3.72 Coefficient of torsion . . v = 7.00 Time of one vibration . . 5*. 694 Time of one vibration . . 7". 441 Salute Islands, November 28, 1865. Inertia ring on magnet. Pernambuco, December 23, 1865. No. Time P. M. No. Time P. M. Time of 150 vibrations. >. No. Time A. M. No. Time A. M. Time of 150 vibrations. 0 10 20 3° 4° 5° n> 31- gf.S II 32 22.5 " 33 35-6 n 34 48.7 it 36 1-4 n 37 14.8 Extreme scale i At beginning At end . . 150 1 60 170 180 190 200 C.l'llll;, II* 49Di 25'.! II 50 38.6 II JI 51.6 " 53 4-7 ii 54 17.8 " 55 30-3 18" I5«.6 18 16.1 18 16.0 18 16.0 18 16.4 18 15.5 o 10 20 3<> 40 5° 6h 50" 1 6". 8 6 5' «5-7 6 52 14.0 6 53 12.6 6 54 10.9 6 55 9-6 Extreme scale i At beginning '59 160 170 180 190 200 cadin^. 7" 4'" S4-.4 7 5 52-6 7 6 51.1 7 7 49-6 7 8 48.0 7 9 46.4 '4° 37'-6 '4 3r'-9 '4 37- 1 '4 37-o '4 37-1 14 3(1.8 Mean .... •s, . . 54-8—1 . <•'-.. \ — a '8 15-93 °5-3 4-o liv. Mean .... t, . 46.0 — I H 37-08 15.0 9-0 iv. Coefficient of torsion . . v = 5.65 < Temperature 9i°.o Coefficient of torsion . . v = 4.27 c Time of one vibration . . 7*.3o6 Time of one vibration . . 5'.847 MAGNET I'C OBSERVATIONS. HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. 103 Bahia, December 27, 1865. Rio Janeiro, January 9, 1866. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time A. M. No. Time A. M. Time of 150 vibrations. o 10 20 3° 40 5° 7h 14"" 5".6 7 15 4-9 7 16 4-1 7 17 3.6 7 18 2.9 7 19 2.2 Extreme scale i At beginning At end 15° 1 60 170 1 80 190 200 •eadin 7h 28" 5 5'. 6 7 29 55.0 7 3° 54-4 7 3i 53-6 7 32 S3-o 7 33 52.2 14™ 5o".o 14 50.1 14 5°-3 14 50.0 14 50.1 14 50.0 0 10 20 3° 40 5° jh 30m ,,._g 5 3' 12.4 S 32 '3-o 5 33 '3-4 S 34 H-o 5 35 '4-6 Extreme scale At beginning At end . 15° 160 170 1 80 190 200 readin r jh 45111 20". 2 5 46 21. 0 5 47 21.5 5 48 22.1 5 49 22.6 5 5° 23.2 15°- 8'.4 15 8.6 15 8-5 15 8.7 15 8.6 15 8.6 Mean .... ;s> . . 92.8 — 1 Kf, X, t 14 50.08 53-1 ,8.3 iiv. Mean .... ?, , . 62.2 — t IS 8.57 |8.l 1.2 Coefficient of torsion . . # = 4.85 Temperature 92°-5 Time of one vibration . . 6".O57J Time of one vibration . . 5". 934 Bahia, December 27, 1865. Inertia ring on magnet. Monte Video, January 18, 1866. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. o 10 20 3° 40 5° 8* 3m 4».2 8 4 20.8 8 5 37-o 8 6 53.4 8 8 9.8 8 9 26.0 Extreme scale At beginnm] 15° 1 60 170 1 80 190 200 readin_ • gh 22" 9".4 8 23 25.8 8 24 42.2 8 25 58.6 8 27 14.8 8 28 30.8 1901 51.2 19 5-° 19 5.2 19 S-2 19 5.0 19 4.8 0 IO 20 3° 40 5° ,ll 27m g.-2 I 28 8.2 I 29 8.3 i 30 8.2 I 31 8.5 « 32 8-5 Extreme scale At beginnin] At end . 150 160 170 1 80 190 200 readin r | . h 42™ 9'. 4 43 9-5 44 9-7 45 9-7 46 9.7 47 9-9 ISm '.2 IS -3 IS -4 IS -5 IS .2 15 -4 Mean .... P. • • 57-9 — {.* « 19 5.07 100.4 39.2 div. Mean .... ^. . . 58.4- . 66.8 — < IS i-33 ?8.3 )0.2 iiv. Coefficient of t Temperature Time of one vi Drsion . . z/ =: 6. 70 Q7° C Coefficient of t Temperature Time of one v orsion . ,v= 5.10 .... 84°.o bration . . 7s. 634 bration . . 6'. 009 Rio Janeiro, January 6, 1866. Monte Video, January 18, 1866. Inertia ring on magnet. .No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. 0 10 20 3° 4 5° 3* 2i°> 6«.8 3 22 5.8 3 23 .6.6 3 24 7/0 3 25 7.7 3 26 8. i Extreme scale At beginnin 15° 160 170 180 190 200 readin T 3h 36°" 1 2*. 5 3 37 12.5 3 38 13-3 3 39 13-° 3 40 14-5 3 4> i5-° IS™ 5'. 7 IS 6.7 15 6.7 15 6.6 15 6.8 15 6.9 o IO 20 3° 40 5° 2h I0m 3". 2 2 II 20. 5 2 12 37.8 2 13 55-i 2 15 12.4 2 16 29.8 Extreme scale At beginnin: At end . 150 160 170 180 190 200 readin r . 2h 29»« 22". 9 2 30 40. 1 2 31 57-3 2 33 '4-6 2 34 31-8 2 35 49-3 igm 19'. 7 19 19.6 19 19-5 19 19-5 19 19-4 19 19.5 Mean .... gs, . . 62.1 — 15 6.57 96-3 89.2 div. Mean .... gs, . . 56.9 — . 6?. 9 — < 19 19-53 [01. 0 )i-4 div. Coefficient of torsion . .# = 5.10 Temperature 76°. o Time of one vibration . . 6».O44 Coefficient of 1 Temperature Time of one v orsion . . ^ = 6.25 .... 84°-5 bration •. . 7'.7JO 104 REPORT ON HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. Monte Video, January 18, 1866. Valparaiso, March 2, 1866. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time P. M. No. Time I>. M. Time of 150 vibrations. 0 10 20 3° 40 5° 2" 55" 9"-3 2 56 9.2 2 57 9-4 2 58 9-4 2 59 9-4 3 o 9-8 Extreme scale At beginninj At end 150 1 60 170 1 80 190 200 readin t f 3h io» ii'.4 3 « "-4 3 12 11.5 3 '3 »-9 3 '4 12-1 3 15 '2.1 I5m 2'. I 15 2.2 IS 21 IS 2-5 I5 2.7 15 2.3 o 10 20 3° 40 5° 5" o» 3«.4 5 i 2.2 5 2 0.6 5 2 59.4 5 3 57-4 5 4 55-7 Extreme scale At beginninj At end . 150 160 170 180 190 200 readin g 5h I4m 4i».o 5 '5 39-3 5 16 37-8 5 «7 36-6 5 18 35-1 5 19 33-7 I4"> 37».6 '4 37-1 '4 37-2 '4 37-2 "4 37-7 14 38.0 Mean .... P. . . 58.0 — fir 8 15 2.32 [00.2 >i.6 Mean .... S»i . . 99.8— 07.8 — «4 37-47 56.8 57-8 div. Temperature Time of one vi ... 86° o Coefficient of t Temperature Time of one v orsion . . i* = 6. r . . . . 72°. 5 brat ion . . 6".OI5 bration . . 5s. 850 Monte Video, January 19, 1866. Valparaiso, March 19, 1866. No. 0 10 20 3° 40 5° Time P. M. No. Time P. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. 3" 3" ».* 3 4 8.9 3 5 9-3 3 6 9-4 3 7 9-7 3 8 10.1 Extreme scale At beginning At end- . . ISO 160 170 i So 190 200 •eadin; 3* i8m IP.8 3 19 12.2 3 20 12.6 3 21 12.6 3 22 13.0 3 23 13.3 ,5m 3,.0 '5 3-3 IS 3-3 '5 3-2 '5 3-3 '5 3-2 0 10 20 3° 40 5° ih 42™ 6'. 6 i 43 5-6 i 44 4.2 i 45 3-° i -46 1.9 i 47 0.8 Extreme scale At beginning At end 150 160 170 180 190 200 readin jh j<3m rjQH 2 i 57 48.6 i 58 47-7 i 59 46-3 2 o 44.9 2 I 44.1 14™ 431-6 H 43-0 '4 43-5 H 43-3 H 43-Q '4 43-3 Mean .... P, . . 56.0 — fifi h i 15 3-22 02.0 M-5 Mean .... js. . . 65.0 — ( 14 43.28 >$.« ?6.8 ; div. Coefficient of torsion . . ^ = 4.7 Time of one vibration . . 6*.o2i Time of one vibration . . 5",889 Sandy Point, February 7, 1866. Valparaiso, March 19, 1866. Inertia ring on magnet. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. 0 1 20 30 40 50 u" 37" 4'- 5 » 38 4-5 tt 39 37 n 40 4.1 it 4t 33 u 42 2.5 Extreme scale At beginniiij, At end . . '5° 160 170 1 80 190 200 readin; n" 5«m58'.4 u 52 58.4 " 53 58.2 it 54 58-0 " 55 57-8 ii 56 57.8 14" 53'-9 "4 53-9 '4 54-5 H 53-9 '4 54-5 «4 55-3 o IO 20 30 40 5° 2" 32-" 5-. 4 2 33 21.2 2 34 36-8 2 35 52-5 2 37 8.2 2 38 23.9 Extreme scale At licginniiiK 150 1 60 170 1 80 190 200 •calling 2h 51"" o".4 2 52 15-8 2 53 3°-8 2 54 47-2 2 56 1.2 2 57 15-8 iS" 55«.o 18 54.6 18 54.0 '8 54-7 «8 53-o 18 51.9 Mean .... P. . . 61.0 — . 60. e < '4 54-33 oo.o >7-5 idiv. Mean .... h . . 61.6 — c -, „ i >8 53-8? 8.9 4.0 div. t Coefficient of torsion . . 2/=s6.8 Coefficient of torsion . . z/ = 6.8- Trni|H-rature 73°-o Time of one vibration . . 7". 559 Time of one vibration . . 5'. 962 Magnet rendered quite unsteady by the high wind. MAGNETIC OBSERVATIONS. HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. 105 Valparaiso, March 29, i860. Valparaiso, April n, 1866. No. Time P. M. No. Time P. M. Time of 150 vibrations. No Time P. M. No. Time P. M. Time of 150 vibrations. 0 10 20 3° 40 5° M caus 12" 37™ g8. o 12 38 7.4 12 39 5-7 12 40 4.3 12 41 3.4 12 42 2.0 Extreme scale At beginnini Temperature Time of one v ignet brought to ed by the wind. 150 1 60 170 1 80 190 200 readin ' . 12" 5i°"47"-4 12 52 45.8 12 53 46.2 12 54 44.2 12 55 40.4 12 56 — . 14" 3S".4 14 38-4 14 40.5 H 39-9 '4 37-o 14 — o IO 20 3° 40 So 12* 15™ I4».o 12 16 13.0 12 17 ii. 8 12 18 10.4 12 19 9.0 12 20 7.8 Extreme scale At beginnin At end 15° 1 60 170 i So 190 200 readin r f t 12* 29"" 56".6 12 30 55-4 12 31 54.2 12 32 53.2 12 33 52.0 12 34 51.0 14™ 42".6 14 42-4 H 42-4 14 42.8 14 43-o «4 43-2 Mean .... ?> . . 61.3 — . 76°.o 14 38.84 97-2 Mean .... js, . . 56.0 — f\i r H 42.73 103.0 01. 0 bration . . 5S.S59 rest by the vibrations of the instrument Temperature Time of one v . . . . 74° 5 bration . . 5'. 885 Valparaiso, March 29, 1866. Valparaiso, April n, 1866. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. o 10 20 3° 40 5° V one jh 28m 7«.2 I 29 5.2 I 30 6.8 I 31 2.4 i 32 0.6 l 32 58.6 Extreme scale At beginning At end . . ISO 1 60 170 1 80 190 200 read™ i" 42™ 49". o 43 48.0 44 46.9 45 45-2 46 43.8 47 43-0 14™ 4i'.8 14 42.8 14 40. 1 14 42.8 14 43-2 14 44.4 o IO 20 3° 40 5° I2" 3701 I2«.2 12 38 II. 0 12 39 9.8 12 40 8.6 12 41 7.4 12 42 6.4 Extreme scale At beginning At end . 150 160 170 1 80 190 200 readinj 12* 51°" 55".o 12 52 54.0 12 53 52.8 12 54 51.8 12 55 50.6 12 56 49.4 14™ 42'. 8 '4 43-o H 43-° H 43-2 14 43-2 H 43-0 Mean .... P. • • 63.0 — c 14 42.52 >S8 6.0 div. Mean .... P. • • 64-5 — S 14 43-°3 I.O 5.0 Coefficient of torsion . . z/ = 3.8c Temperature 8i°.o Time of one vibration . . 5s. 887 Time of one vibration . . 5s. 883 brations irregular on account of the wind, which, at ime, almost brought the magnet to rest. Valparaiso, April 7, 1866. Valparaiso, April n, 1866. Inertia ring on magnet. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. o 10 20 3° 40 5° I0h 2° I5'.6 10 3 14.2 10 4 13.2 10 5 ii. 8 IO 6 II. 2 10 7 9.6 Extreme scale i At beginning 150 160 170 180 190 200 eading 10" i6m 55".o 10 17 54.2 10 18 53.6 10 19 53.0 10 20 52.4 10 21 51.2 Hm 39'-4 14 40.0 14 40.4 14 41.2 14 41.2 14 41.6 o IO 20 3° 40 5° I" 8°> 6'. 6 I 9 22.2 i 10 37.8 i ii 53-7 i 13 9-4 i 14 25.0 Extreme scale i At beginning At end . ISO 160 170 1 80 190 200 eading I* 27m 2«.4 28 18.1 29 33-8 3° 49-4 32 S-2 33 21.0 18" 551.8 18 55-9 18 56.0 18 55-7 18 55.8 1 8 56.0 Mean .... •s, . . 59.8—1 cfi tr . i 14 40.63 02.8 06.5 div. Mean .... •s. . . 58.8—1 . 07.O Q 18 55.87 01.6 3-2 div. ttfoefficient of torsion . . ^ = 3.92 Coefficient of torsion . . #^5-5° Temperature 88°. o Time of one vibration . . 5".87I Time of one vibration . . 7s-572 14 July, 1872. 106 REPORT ON HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. Valparaiso, April 13, 1866. Flamenco Island, Panama Bay, May 14, 1866. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time A. M. No. Time A. M. Time of 150 vibrations. o 10 20 3° 40 5° 2h 4jm 23'. 6 2 46 21.8 2 47 21.2 2 48 19.6 2 49 19.0 2 5° 17.8 Extreme sea At beginn At end . 150 100 170 180 190 200 le readii ing . 3h o" 6".2 3 « 4-6 3 2 3.6 3 3 2-4 3 4 c.6 3 4 S8-6 14™ 42'.6 14 42.8 14 42.4 14 42.8 14 41.6 14 40.8 o 10 20 3° 40 5° gb j0m n..^ 8 51 5.! 8 5« 59-o 8 52 52.8 8 53 46-5 8 54 40.4 Extreme sea At beginn At end . 150 160 i?o 180 190 200 le reaelii infT 9h 3m 37'- 8 9 4 3i-4 9 5 25.2 9 6 19.0 9 7 13-0 9 8 6.9 13™ 26'.4 '3 26.3 13 26.2 13 26.2 13 26.5 '3 26.5 Mean . . . 'gs, . . 57-8- •7A f 14 42.17 101.5 85.2 Mean . . . igs, c.K. "3 26.35 2 — IOI.O 6 — 92.9 2.78 div. 0 76 66 Temperature .... 66°. 5 Time of one vibration . s'.88l Coefficient c Temperatur< Time of om f torsion . . . v = Q2° vibration . . . 5".; San Lorenzo Island, April 26, 1866. Acapulco, May 30, 1866. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time A. M. No. Time A. M. Time of 150 vibrations. 0 10 20 3° 40 5° 12* 40" 6".9 12 41 3.0 12 41 59.0 12 42 55.0 12 43 51.0 12 44 47.1 Extreme sea At beginn At end . 150 1 60 170 180 190 200 e rc.idin nrr 12" 54" 7'.4 12 55 3.0 12 55 59.2 12 56 54.9 12 57 S°-8 12 58 47.4 I4m o".s 14 o.o 14 0.2 "3 59-9 >3 59-8 H 0.3 o 10 20 3° 40 5° gh 32m 3 f torsion . . . v = 80° vibration . . . $'.t vibration . . . 5".; Payta, May 7, 1866. Acapulco, May 30, 1866. Inertia ring on magnet. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time A. M. No. Time A. M. Time of 150 vibrations. o 10 20 30 40 5° o> 21- 9«.8 9 22 4.4 9 22 59.2 9 23 53.6 9 24 48.2 9 a$ 42.8 Extreme sea At Iwuinn At end . 150 no 170 1 80 190 200 c readin 9b 34- 491.4 9 35 44-o 9 36 38.6 9 37 33-2 9 38 27.6 9 39 22.3 13- 39-.6 '3 39-6 "3 39-4 '3 39-6 >3 39-4 '3 39-5 o 10 20 3° 40 5° 9* 46" 9'. 2 9 47 «7-4 9 48 26.5 9 49 35-2 9 5° 43-8 9 5' 52-4 Extreme sea At beginn '5° 160 170 1 80 190 200 c readin nf lo* 3" I9--5 10 4 28.2 10 5 37.0 10 6 45.6 10 7 54.4 10 9 32 17-° IO-.3 •17 10.8 '7 'o-S 17 10.4 17 10.6 17 10.8 Mean . . . B* cQ '3 39-52 2 — IOI.8 5— 92.2 .20 div. 653 Mean . . . g*, c6. '7 10-57 : — 103.7 I— 94.8 t-55 div- -5 70 ft-! 6$. Coefficient o Temperature Time of one °7- : torsion . . . v = ' 87° Coefficient o Temperature Time of one " torsion . . . r = t . . : 90° vibration . . . 5'.^ vibration . . 6'.{ MAGNETIC OBSERVATIONS. HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. 107 Magdalena Bay, June 9, 1866. San Francisco Bay, June 26, 1866. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time A. M. No. Time A. M. Time of 150 vibrations. 0 10 20 3° 40 5° 100 In the i whic I1 8m 51.4 8 59.4 9 54-5 10 49.0 ii 44.4 12 39.8 17 16.4 Extreme scale At beginning At end . . 150 too 170 180 190 200 readin: • Ih 21™ 52S.8 I 22 49.0 I 23 44.4 I 24 40.2 I 25 36.0 I 26 30.8 ?» • • 55-0 — toi.o $5.0 0 IO 20 30 40 5° 3"> 21° 22».7 3 22 24.7 3 23 27.2 3 24 30.2 3 25 32.0 3 26 34.7 Extreme scale At beginnin 150 1 60 170 180 190 200 readin r 3" 36°57'-7 3 38 o.o 3 39 2.5 3 40 4-7 3 4i 7-2 3 42 10.0 15™ 35"-o '5 35-3 '5 35-3 '5 34-5 15 35-2 '5 35-3 Mean .... gs. • • 57-0 — AC rt '5 35-'° IO2.O ?'S div. Temperature Time of one vi this and the fol nagnet were ver; i shook the instn .... 79°.o oration . . 5s. 527 lowing observation the vibrations of irregular on account of a high wind iment. Coefficient of t Temperature Time of one v orsion . .2/5=4.35 . . . . 77°.o bration . . 6s. 234 Magdalena Bay, June 9, 1866. U. S. N. Observatory, Washington, Nov. i, 1866. No. Time A. M. No. Time A. M. Time of 150 vibrations. No. Time P. M. No. Time P. M. Time of 150 vibrations. o 10 20 3° 40 5° IOO Ih 4Im I28.2 42 7-8 43 3-o 43 59-o 44 54-o 45 48.4 5° 25.4 Extreme scale At beginning At end . . T 160 170 1 80 190 200 •eadinj ih 55™ 4S.8 56 0.4 56 56.0 57 5i-4 58 46.4 59 4i-6 P> • • 53-5 — ' >8.5 o IO 20 30 40 5° 5* 19°- S2-.7 5 21 5.0 5 22 16.0 5 23 27.5 5 24 39.0 5 25 50.7 Extreme scale At beginning At end . «5° 1 60 170 1 80 190 200 readin: 5" 37m46'.S 5 38 58.0 5 40 9-2 5 4i 20.7 5 42 3'-8 5 43 43-° I7m 53"-8 '7 53-o '7 53-2 '7 53-2 17 52.8 >7 52.3 Mean .... :s. • • 52.5 — 1 . fifi fi i 17 53-05 06.0 >5-2 iiv. Coefficient of torsion . . z/ = 4-37div. Temperature 86°. 5 Coefficient of torsion . . v = 5.80 Temperature 67°. 5 Time of one vibration . . 5s. 533 Time of one vibration . . 7'. 154 San Diego Bay, June 15, 1866. The following sets of observations of vibrations were made in the basement of the Observatory, where there is much iron, and are to be used only to determine the moment of inertia of the magnet. Set i. November 2, 1866. No. Time P. M. No. Time P. M. Time of 150 vibrations. No. Time. No. Time. Time of 150 vibrations. 0 10 20 30 40 50 gh nm gt.2 6 12 8.3 6 13 7-4 6 14 7.0 6 15 6.2 6 16 5.4 Extreme scale i At beginning At end 15° 160 170 180 190 200 eading 6h 25™ 58'. 2 6 26 56.6 6 27 55.8 6 28 55.4 6 29 53.8 6 30 53.0 14"" 49'.o H 48-3 14 48.4 14 48.4 H 47-6 14 47.6 0 IO 20 30 40 50 5b 37m3i'-7 5 38 4'-2 5 39 5°-7 5 41 0.2 5 42 9-7 5 43 '9-2 Extreme scale i At beginning At end 150 160 170 180 190 200 eading 5" 54m53'-8 5 56 3-2 5 57 12.7 5 58 21.5 5 59 3«-2 6 o 40. 7 17™ 22'. i 17 22.O 17 22.0 17 21.3 17 21.5 17 21.5 Mean .... s, . . 94.9—1 *rn n .._ S 14 48.22 08.9 8.0 liv. Mean .... A . . 59-1—5 66. o — c i? 2I-73 9.8 2.2 Coefficient of torsion . . v = 3.60 < Temperature 65° 5 Time of one vibration . . 6*. 945 Time of one vibration . . 5".92I 108 REPORT ON HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. Set No. 2. November 2, 1866. Inertia ring on magnet. Set No. 5. November 2, 1866. No. Time. No. Time. Time of 150 vibrations. No. Time. No. Time. Time of 150 vibrations. 0 10 20 3° 40 5° 6" 17- 25-. 3 6 is 55.2 6 20 24.2 6 21 54.0 6 23 23.7 6 24 53.0 Extreme scale At beginnin; At end . 150 160 170 1 80 190 200 readin r , ' . 6<> 39" 46'. 8 6 41 16.2 6 42 45.7 6 44 14.8 6 45 44.2 6 47 "3-7 22" 21". 5 22 21. 0 22 21.5 22 20.8 22 2O.5 22 20.7 o IO 20 3° 40 5° gh -jm 22'. 7 8 8 32.2 8 9 41.7 8 10 51.2 8 12 0.7 8 13 10.2 Extreme scale At beginnin: At end . 150 160 170 180 190 200 readin r t 8h 24°> 44'. 2 8 25 53.7 8 27 3.2 8 28 12.7 8 29 22.0 8 30 3'-7 I7m 2i!.5 17 21.5 17 21.5 17 21.5 17 21.3 17 21.5 Mean .... P. . . 58.9 — . 68.-! — 22 21. OO 100.8 )5-5 div. Mean .... js. • • 58.7 — fifi tr 17 21.47 39-3 JI.2 div. Coefficient of t Temperature Time of one v orsion . . v= 7.58 . 68°. ? Coefficient of t Temperature Time of one v orsion . . z/ = 6.c>5 60° t; bration . . 8". 940 bration . . 6s. 943 Set No. 3. November 2, 1866. Set No. 6. November 2, 1866. No. Time. No. Time. Time of 150 vibrations. No. Time. No. Time. Time of 150 vibrations. o to 20 3° 40 S° 6" 57m4i'-3 6 58 50.8 7 o 0.2 7 ' 9-8 7 2 19.0 7 3 28.8 Extreme scale At beginning At end . 150 160 170 180 190 200 readinj 7" I5m 3"-2 7 16 12.8 7 17 22-3 7 «8 3'-5 7 19 41.0 7 20 50.5 I7m 2i'.9 17 22.0 17 22.1 17 21.7 17 22.0 17 21.7 o IO 20 3° 40 5° I2h 31™ 58'.2 12 33 9-2 12 34 21.0 12 35 32-7 12 36 44.0 '2 37 55-7 Extreme scale At beginning At end 150 160 170 1 80 190 200 readin] 12" 49m 5i».2 12 51 2.5 12 52 14.2 •2 S3 25.7 12 54 37-2 12 55 48.7 I7m 53'-° «7 53-3 '7 53-2 '7 53-o '7 53-2 "7 53-o Mean .... P. . . 54.2 — 1 17 21.90 59-. 2 22 59.0 22 59.2 22 59.3 22 58.9 22 59-3 Mean .... •s, . . 56.5 — 1 . 6c.i c 22 20.63 03.6 6-3 Mean .... '. . 58.2—1 AB „ 22 59.15 OI.O 7.2 Temperature 7o°.o Time of one vibration . . 8".938 Time of one vibration . . 9'. 194 MAGNETIC OBSERVATIONS. HORIZONTAL INTENSITY. OBSERVATIONS OF VIBRATIONS. Set No. 8. November 2, 1866. 109 No. Time. No. Time. Time of 150 vibrations. 0 I" 40™ 1 9" 2 150 I» S8» i p. 5 17- S2M 10 I 41 3°- 7 1 60 I 59 23.0 17 52.3 20 I 42 42 2 170 2 0 34-5 17 52-3 3° I 43 53- 7 1 80 2 I 46.0 I? 52.3 40 I 45 5- 2 190 2 2 57-5 17 52-3 5° I 4° 10. 7 200 2 4 9.0 '7 52-3 Mean .... I? 52.30 Extreme scale readings, At beginning .... 60.0 — loi.o At end 68.0 — 92.8 Temperature 52°. 5 Time of one vibration . . 7s. 149 110 REPORT ON HORIZONTAL INTENSITY. OBSERVATIONS OF DEFLECTIONS. Philadelphia, October 24, 1865. & a 1 "c-o Time. Temp. aj 81 s s Diff's. Dist. s £u i ^^ <^ w. 4" 40- 59-° 1411.5 I E. W. 41-5 141.4 41-5 100^.0 E. 41.4 — 0 E. 40.5 J W. 141.8 40.5 || i E. 40.5 141.7 !>' • . W. 4 58 56- 141.6 Me ins 57-5 2Ud 100.60 Gosport, October 30, 1865. Gosport, October 30, 1865. . a, 3 ii s» v . 1 y. Time. Temp. H Ii •J V ~-z Diff's. Dist. ti 1 i |1 Time. Temp. t Ii « 2 E i II Diff's. Dist. W. ii» 6" 59° 39*. 2 W. II" 30" 59° 60^.5 1 E. VV. E. 127.7 39-4 127.4 39*- 3 127.5 88". 2 * E. W. E. 105.7 60.0 105-4 6o«.2 '°5-5 45d-3 i d o ii w ]j E. W. E. \V. ii 30 59 128.0 38-8 127-3 39- « 127.6 88.7 I E. \Y. E. W. ii 48 58 105.9 60.4 105.9 60.3 105.9 60.4 45-5 Meant 59-o 2U« 88.45 Means 58.5 2U< •45-40 Coefficient of torsion, v «= 7.82 dir. MAGNETIC OBSERVATIONS. Ill HORIZONTAL INTENSITY. OBSERVATIONS OF DEFLECTIONS. St. Thomas, November 13, 1865. St. Thomas, November 13, 1865. ,- 4) »; U d t» a o £ Time. Temp. 11 S « c 5 — C3 4) 4) Diff's. Dist. 4) I 11 Time. Temp. t -•I ii -_, 0) Diff's. Dist. & •A " M(* < S 2; " *i2 <" W. 2h jm 87°. 461.4 w. 2" 15"' 85." 611.7 | E. W. 108. 1 46.4 461.4 108.1 611.7 ti E. W. 93-2 61.6 6id.6 93-2 3I-.6 E. 1 08. 1 •" E. 93-3 d C E. 108.3 E. 93-2 |? . \V. 46.8 108.4 61 6 ii W. 61.6 93-2 ii « E. 108.5 46.8 y E. 93-3 . 6M * • k W \V. 2 '5 fs- 46.9 M W. 2 35 85. 61.5 Means 86.0 2Ud 61.65 Means 85.0 2Ud 3I-65 Coefficient of torsion, ^ = 4.80 div. St. Thomas, November 16, 1865. St. Thomas, November 16, 1865. a, 4J 1 CJ Pn •5 — " Time. Temp. oM 'rt "^ c ••• CJ ^ Diff's. Dist. | *— ^ Time. Temp. JU.S gs Diff's. Dist. a o c t o - S « " « 3 S ^ •" X ^ W. I21' IOnl Q0.° 43d- 6 W. I2h 20m 87.° 531.7 S E. W. 105.3 43-7 43d- 6 611.7 V E. W. 90.4 58.6 581.6 90.4 311.8 " E. ^ E. 90.4 o IM E. 105.6 N E. 90.4 M i W. E. W. 12 20 87. 43-9 105.5 43-8 105-5 43-8 61.7 II k 1 W. E. W. 12 30 87. . 59-i 90.5 58.9 90-4 59.0 3>-4 II k Means 88.5 2Ud 61.70 Means 87.0 2Ud 31.60 Coefficient of torsion, 17 = 4.55 div. Salute Islands, November 28, 1865. Salute Islands, November 28, 1865. & 0 a> V "rt y1' = 6-72 div. Pernambuco, December 23, 1865. Pernambuco, December 23, 1865. V 1 j JS . ^ Time. Temp. / 6 11 *J Alternate Means. Diff's. Dist. tJ 1 a .a . ti t3 0 C I8 Time. Temp. / Scale Readings. Alternate Means. Diff's. Dist. 1 W. E. W. E. 8" 35- 85° 48".4 H3-3 48.5 113-2 48'.4 113.2 64". 8 IM q ri II V i I W. E. W. E. 8h 50°' 88° 64". 6 98.0 64.8 98.! 64". 7 98.1 33d-4 V- \r\ M II W 1 E. W. E. W. 8 50 88 "3-9 49-5 114.4 497 114.2 49.6 64.6 E. W. E. \V. 9 o 88 98.2 64.9 98.2 65.0 98.2 65.0 33-2 64.70 Means 86.5 2Ud Means 88.0 2Ud 33-3° Coefficient of torsion, f = 5. 10 div. Bahia, December 27, 1865. Bahia, December 27, 1865. i *-. i — . P Time. Temp. / Scale Readings. Alternate Means. DifTs. Dist. 'o 1 7. |t Time. Temp. t Scale Readings. Alternute Means. Diff's, Dist. W. E. W. E. ii" 5- 98° 46^.5 112. 2 46.6 II2.7 46*. 5 112.4 65d-9 £. q ri II k 1 W. E. W. E. ll>> 12" 98° 62<>.9 96.6 62.8 96.6 62'1.8 96.6 33"-8 V- \f\ M II V. : M E. W. E. W. II 12 98 II3.6 46.4 "39 46.4 "3-7 46.4 »7.3 i M E. W. E. W. II 20 98 96.9 62.6 97-' 62.8 97.0 62.7 34-3 =T ,8.0 211* 66.60 Means 98.0 2Ud 34.05 Coefficient of torsion, .' = 5.27 div. MAGNETIC OBSERVATIONS. HORIZONTAL INTENSITY. OBSERVATIONS OF DEFLECTIONS. 113 Rio Janeiro, January 6, 1866. Rio Janeiro, January 6, 1866. o bd 3 s 0 P Time. Temp. t a, D.S T5 "^ e 1 1 Diff's. Dist. V rt O c Time. Temp. t E. 103.1 " E. 87.! H <*-. E. '03-3 q E. 87.2 i W. E. W. 6 3 70. 38-7 103.2 37-7 103.2 38.2 65.0 1 k 1 W. E. W. 6 14 68. 53-6 87.1 53-6 87.1 53-6 33-5 1 Me ans 70.5 2U* 65-I5 Means 69.0 2Ud 33-45 Coefficient of torsion, v = 6.87 div. • Valparaiso, March 19, 1866. Valparaiso, March 19, 1866. & B & a | M . Time. Temp. fl is S v Diff's. Dist. 1 * . Time. Temp. *rt *3 e i Diff's. Dist. «T O £ t ,y « 3 ° § t y S i a " *« •^ 5 Z M 2 w. I* 10" 75-° 37"-9 W. ,h 20m 76.° 54". 2 i E. W. 103.6 37-7 37d-8 103.6 65'. 8 i E. W. 87-7 54-0 54". i 87.7 33d- 6 '" E. 103.7 ~f- E. 87-7 0 d E. '03-7 E. 87.8 N i W. E. W. I 20 76. 38-4 103-7 38.5 '03-7 38-4 65-3 1 k i W. E. W. ' 35 78. 54-5 87.8 54-4 33-4 1 Means 75-5 2Ud 65.55 Means 77-o 2Ud 33-5° Coefficient of torsion, v = 4.80 div. Valparaiso, March 29, 1866. Valparaiso, March 29, 1866. i fl- Time. Temp. •il ^ g Diff's. Dist. | J3 Time. Temp. i jj .5 1 3 F, g Diff's. Dist. t t « ^ S 2 " 'X" ** " W. 12* 0" 69.0 36*- 9 W. 12" 13" 68.° 53d- 1 i E. W. E. IO2. 1 36-9 IO2.6 102.4 65'.5 1 E. W. E. 86.7 52.9 86.6 53d-o 86.6 33d-6 £ C E. 102.8 o d B 86.8 fi W. E. 37-2 102.8 102.8 37.3 65-5 1 1 W. E. 53-5 86.8 86.8 53-3 33-5 II W. 12 13 68. 37.3 i2 W. 12 28 68. 53-2 Means 68.5 2U< 65.50 Means 6S.O 2U« 33-55 Coefficient of torsion, ^ = 4.62 div. MAGNETIC OBSERVATIONS. 115 HORIZONTAL INTENSITY. O Valparaiso April 7, 1866. BSERVATIONS OF DEFLECTIONS. Valparaiso, April 7, 1866. V I 1 J3 . C "O o c I " Time. Temp. / a> uj 13 Alternate Means. Diff's. Dist. n 1 a x . ic a" Time. Temp. t i v .5 11 IJ Alternate Means. Diff's. Dist. W. E. W. E. 8" 55m 65° 38d.2 102.9 37-9 103.0 38*. o 102.9 64^.9 IM O ri II V. 1 W. E. W. E. gh Kjra 67° 53d- 8 87.2 54-o 87-3 53d- 9 87-3 33d-4 IM \n ej II V. 1 H E. W. E. W. 9 10 67 104.0 37-2 103.9 37-2 103.9 37-2 66.7 1 E. W. E. W. 9 25 69 87-7 53-6 87.6 53-4 87.6 53-5 34-1 Means 66.0 2Ud 65.80 Means 68.0 2Ud 33-75 Coefficient of torsion, 1/1=4.68 div. Valparaiso, April n, 1866. Valparaiso, April n, 1866. Id 1 a j= . 1"S 1 u Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. o 1 a %•* lg Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. 1 W. E. W. E. I>> om 74-° 39d-2 104-3 39-3 104.4 39d-2 104.3 65a.l C* O M II It 1 W. E. W. E. Ih Ilm 74° SS'-2 88.4 55d-2 88.5 33d- 3 e U"i « II k 1 W E. W. E. W. i ii 74- 105.2 38.9 105-3 39-2 105.2 39-o 66.2 i H E. W. E. W. I 23 74 88.9 54-9 88.9 54-8 88.9 54-9 34-o Means 74-o 2Ua 65.65 Means 74.0 2Ua 33-65 Valparaiso, April 13, 1866. Valparaiso, April 13, 1866. 1u 1 S a 1 " Time. Temp. t if •3 Alternate Means. Diff's. Dist. 1! s x • t: 13 o c I41 Time. Temp. * Scale Readings. Alternate Means. Diff's. Dist. 1 W. E. W. E. ,h SSm 7I°- 37d-2 IO2.0 36-9 101.6 37«.o 101.8 64*. 8 «£H O N II k 1/5 Q W. E. W. E. 2h ym 65°. 5'd-9 84.9 5«-5 84.9 5i"-7 84-9 33d- 2 *£ ir> N 1 i. 1 w E. W. E. W. 2 7 65. 102.2 36.0 IOI.7 35-6 101.9 35-8 66.1 1 E. W. E. W. 2 2O 62. 85.4 51.0 85.0 S°-9 85.2 51.0 34-2 Means 68.0 2Ud 6S-45 Means 63.5 2Ua 33-7° 116 REPORT ON HORIZONTAL INTENSITY. Sari Lorenzo Island, April 26, 1866. OBSERVATIONS OF DEFLECTIONS. San Lorenzo Island, April 26, 1866. S I J3 . P Time. Temp. / Scale Readings. Alternate Means. Diff's. Dist. D 1 a c-a Is Time. Temp. t s> ll 6 rt J^ Alternate Means. Diff's. Dist. W. E. W. E. nh 40" 79° 5ld.o 109.7 50.9 109.6 500.9 109.6 S8"-7 £ q ri II W £ w. E. W. E. ,,h j2» 82° % 65d-3 95-4 65.0 94-9 651.1 95- ' 30*. o £ \o N II >s E. W. E. W. II 52 82 110.4 50.9 110.4 5°-7 110.4 50.8 59.6 i m E. W. E. W. 12 7 74 95-4 64.8 95-4 65.0 95-4 64.9 30-5 Means 80.5 2U« 59- 1 5 Means 78.0 2Ud 30.25 Coefficient of torsion, f = 4.25 div. Payta, May 7, 1866. Payta, May 7, 1866. a •g-o o c X. - Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. "S 1 s Jl Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. 1 w. E. W. E. 7" 33" 77° 52d.2 107.7 52.0 107.8 52". i 107.7 55".6 IM O N II k 8 £ W. E. W. E. 7* 46°> 77° 6^.2 93-7 65.0 93-6 65". I 93-7 28d.6 IM U1 N II W 1 E. W. E. W. 7 46 77 108.4 51.6 108.3 51.6 108.4 5i.6 56.8 1 H E. W. E. W. 7 59 77 94.0 64.7 94.0 64.7 94.0 64.7 29-3 56.20 Means 77.0 2U* Means '.77-0 2Ud 28.95 Coefficient of torsion, » = 3.62 div. Flamenco Island, Panama Bay, May 14, 1866. Flamenco Island, Panama Bay, May 14, 1866. i s 1 Si Time. Temp. / Scale Readings. Alternate Means. Diff's. Dist. tj 1 S 1 IN zu Time. Temp. t Scale Readings. Alternute Means. Diff's. Dist. w. E. W. E. 7" 55" 83' 5*7 104.6 51.0 104.7 50*. 8 104.6 53".8 C-! O N II K w. E. W. E. 8" 5- 82° 64d.o 91.7 64.0 91.6 64^.0 91.6 270.6 £ *^» •i H k I E. W. E. W. 8 5 82 105.6 5°-4 i°5-5 50.1 'OS.5 52.2 S3- 3 1 E. W. E. W. 8 iS 82 92.0 63-8 92.0 63.8 92.0 63.8 28.2 Means 82.5 2Ud 53-55 Means 82.0 2Ud 27.90 Coefficient of torsion, !• = 3. 18 div. MAGNETIC OBSERVATIONS. 117 HORIZONTAL INTENSITY. OBSERVATIONS OF DEFLECTIONS. Acapulco, May 30, 1866. Acapulco, May 30, 1866. B a ED rt 1 i W J3 . o c 1 " Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. "w S, rt 2 43 . ~ ~ O £ 1 " Time. Temp t Readings. Alternate Means. Diff's. Dist. W. E. W. E. yh 22=1 86° 53d-9 107.0 53-9 107.0 53d-9 107.0 53", i IM 0 ri II k 1 W. E. W. E. 7h 32m 84° 66".9 94-1 66.9 94-2 66". 9 94-2 27d-3 d V> (S II W E. \V. E. W. 7 32 84 107-5 53-5 107.7 53-8 107.6 53-6 54.0 i H E. W. E. W. 7 40 85 94-4 66.8 94-4 66.8 94-4 66.8 27.6 27-45 Means 85.0 2Ud 53-55 Means 84.5 2Ud Coefficient of torsion, v = 3.45 div. Magdalena Bay, June 9, 1866. Magdalena Bay, June 9, 1866. "u 1 3 1 1 a x . o c 1 •" Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. 1 S3 ja • 1"S 1 « Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. W. E. W. E. ih 14™ 65° 49d-4 106.6 49-4 106.8 49d-4 106.7 57d-3 q N II V. 4) w. E. W. E. I* 40™ 65° 64d.o 93- 1 63-7 94.1 63d. 9 93-6 290.7 +s v« *r> « II k E. W. E. W. I 40 65 106.7 49.6 107.9 49-7 i°7-3 49-7 57-6 1 w E. W. E. W. 2 15 65 94-7 65.0 95-4 65.8 95- 1 65-4 29.7 Means 65.0 2Ud 57-45 Means 65.0 2Ud 29.70 Assumed coefficient of torsion, v = 3.87 div. Magnet very unsteady, and its readings uncertain on account of a stiff breeze which shook the instrument. San Diego Bay, June 15, 1866. San Diego Bay, June 15, 1866. •B s 6 J3 . SI 1 " Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. 6 1 3 IN a « Time. Temp. t Scale Readings. Alternate Means. Diff's. Dist. w. E. W. E. 2h 44™ 72° 45d-9 III.3 46-3 III. 2 46d.l in. 3 65d.2 IM q efl ii t. V £ w. E. W. E. 2" 53™ 71° 62d.2 95-4 62.2 95-4 62d.2 95-4 33"- 2 «ii w» ci II k 1 w E. W. E. W. 2 53 71 II2.6 45.8 II2-5 45.8 112.5 45.8 66.7 1 H E. W. E. W. 3 6 70 95-4 61.6 95-8 61.8 95-6 61.7 33-9 Means 7'-5 2Ud 65-95 Means 70.5 2Ud 33-55 Coefficient of torsion, z' = 4. 28 div. 118 REPORT ON HORIZONTAL INTENSITY. OBSERVATIONS OF DEFLECTIONS. San Francisco Bay, June 26, 1866. San Francisco Bay, June 26, 1866. 1" 11 Time. Temp. t A! 1 i C rt Diff's, Dist. •s rt •s^- Time. Temp. IT tie u.Z 1 s E a Diff's. Dist. ^ 1/3(4 <* * z u ">« ^ " W. 6* 40- ("=,." 42". 3 w. 6" 50"° 62.° 60". 8 B E. W. 114.8 42.6 42^.4 114.9 720.5 B E. W. 98.0 60.7 600.8 98.2 37'-4 E. 115.1 E. 98.4 0 £ E. II6.I E. 98.4 N 1 W. E. 43-° 116.3 116.2 43-° 73-2 1 i W. E. 61.0 98.4 98.4 60.9 37-5 II W u W. 6 50 62. . 43-0 w W. 6 59 63- 60.9 Means 63-5 2U* 72.85 Means 62.5 2ud 37-45 Coefficient of torsion, v = 5.30 div. U.S. N. Observatory, Washington, Nov. i, 1866. U. S. N. Observatory, Washington, Nov. i, 1866. | x . Time. Temp. || Alternate Means. Diff's. Dist. •£ 1 ji . Time. Temp. t 6 v .5 *— ; -^ Alternate Means. Diff's. Dist. W. E. W. E. Ik 4» 66." 280.5 123.6 28.5 122.8 280.5 123.2 944- 7 d 0 N II W | W. E. W. E. ,h 22m 66.° 100.9 52.6 100.5 52". 5 100.7 480.2 M II V. I E. W. E. W. I 22 66. 124.5 29-3 125.5 28.1 125.0 28.7 96-3 1 E. W. E. W. I 44 67. 102. 0 52.6 IOI.4 52-3 101.7 52.5 49-2 Means 66.0 2U« 95-5° Means 66.5 2U0 48.70 CoefTicient of torsion, v = 7.05 div. MAGNETIC OBSERVATIONS. SECTION V. OBSERVATIONS ON THE MAGNETISM OF THE SHIP. THE Monadnock is a second rate iron-clad vessel, of the Monitor type, of 1564 tons old or 1091 tons new measurement. On deck her length is 260.5 feet, and her breadth 52.0 feet. She has a wooden hull, but her deck is covered by three layers of iron plates, each one inch thick; and her sides, for a depth of five feet from the deck, are covered by six layers of iron plates, each one inch thick. Thus the deck is protected by three, and the sides by six inches of iron. She is provided with two iron turrets, cylindrical in form, each 22.8 feet in outside diameter, 9.0 feet high, and 11 inches thick. On top of each of them stands an iron pilot-house, 7.7 feet in outside diameter, 6.4 feet high, and 11 inches thick. Each of these pilot-houses is cylindrical in form, and so placed that its axis coincides with the axis of the turret upon which it stands. The sides of the turrets and pilot-houses are not solid, but are composed of iron plates, each one inch thick, placed one upon the other and bolted together till a total thickness of eleven inches is attained. To each of the iron pilot-houses are bolted wooden stanchions, which carry wooden pilot-houses whose floors are about nine and a half feet above the tops of the iron pilot-houses. The centres of the wooden pilot-houses are respectively in the same vertical lines with the centres of the turrets and iron pilot-houses over which they stand. The centres of the turrets coincide with the midships line. The distance from the stern of the vessel to the centre of the after turret is 84.5 feet; from the centre of the after turret to the centre of the forward turret, 99.1; and from the centre of the forward turret to the cut-water, 76.9 feet. Passing forward from the after turret, we come first to the ventilator, which is 6.5 feet in diameter, and 22.8 feet high above the deck; and then to the smoke-stack, which is 9.9 feet in dia- meter, and 31.0 feet high above the deck, both it and the ventilator being of iron. The distance from the centre of the after turret to the centre of the ventilator is 31.3 feet; from the centre of the ventilator to the centre of the smoke-stack, 16.5 feet ; and from the centre of the smoke-stack to the centre of the forward turret, 51.3 feet. At St. Thomas, before the magnetic observations on board ship were made at that place, a wooden mast 77.7 feet high was placed on the ship in order to enable her to carry some sail. Its centre is 22 feet forward of the centre of the forward turret, and what little iron was used in its construction is so placed that it is not at all probable that it affected the deviation of the compasses in its neighborhood in the slightest. 120 REPORT ON The following are the designations and positions of the compasses which were tised during the cruise : — The Forward Alidade was a Sands Alidade Compass, and was on top of the forward wooden pilot-house, 33.5 feet above the iron deck. The Forward Binnacle was a Ritchie Liquid Compass, and was in the binnacle of the forward wooden pilot-house, 27.2 feet above the iron deck. The Forward Ritchie was a Ritchie Monitor Compass, and was 6.7 feet above the top of the iron pilot-house on the forward turret. It was 22.1 feet above the iron deck. Of these three compasses, the Forward Alidade and Forward Ritche were placed exactly in the. vertical line passing through the centre of the forward turret, and the Forward Binnacle was placed about two feet further forward, but nearly in the same vertical plane. The Admiralty Standard Compass was on top of the after wooden pilot-house, 37.0 feet above the iron deck. The After Binnacle was a Ritchie Liquid Compass, and was in the binnacle of the after wooden pilot-house, 27.2 feet above the iron deck. The After Ritchie was a Ritchie Monitor Compass, and was 6.7 feet above the top of the iron pilot-house on the after turret. It was 2'2.1 feet above the iron deck. Of these three compasses, the Admiralty Standard and After Ritchie were placed exactly in the vertical line passing through the centre of the after turret, and the After Binnacle was placed about two feet futher forward, but nearly in the same vertical plane. The After Azimuth was a common Azimuth Compass which was set up temporarily on the quarter deck every time the ship was swung ; small cavities having been cut in the iron surface of the deck for the reception of the feet of the tripod, so as to make sure that the instrument always occupied precisely the same position. It stood 47.5 feet abaft the centre of the after turret, and there were two vertical iron stanchions, each two inches in diameter, 10.3 feet high above the deck, and 12.1 feet distant from the compass, one of them being directly forward and the other directly aft of it. This compass was elevated 4.6 feet above the iron deck ; but when observations of magnetic force were made, it was necessary to remove it and substitute an Admiralty Standard Compass, which occupied precisely the same position, except that it was 4.8 feet above the deck. When the dip circle was used it also stood 4.8 feet above the deck. It will be observed that all the compasses stood in the midships line, no matter what their elevation above the deck might be. All the observations for determining the deviations of the compasses were made by swinging the ship in the following manner : The true azimuth of a well defined distant, object was determined by a solar bearing, as explained in Section III, page 26, and the declination of the magnetic needle having been applied to it, its true magnetic azimuth became known ; then, supposing the sight vanes of the Admiralty Standard Compass to be kept pointed steadily to that object while the ship was swung, the reading which they would indicate on the azimuth circle attached to MAGNET 1C OBSERVATIONS. 121 the cover of the compass, as the ship's head pointed successively to each of the true magnetic points, was computed by means of the formula B = 180° + A — f where It = reading of sight vanes on the azimuth circle attached to the cover of the compass. A = true magnetic azimuth of the distant object; the azimuth being counted from the soutli around by the west. £ = azimuth of the ship's head, counted from the correct magnetic north around by the east. This having been done, on a tolerably calm day steam was got up in the boilers, and, the vessel riding at a single anchor, slack water was waited for. As soon as the tide ceased to run, the executive officer took the deck ; an officer was stationed at each of the compasses ; I'went to the Admiralty Standard ; and a quartermaster was stationed at the ship's bell. Then the helm was put hard-a-starboard, or hard- a-port, depending on the direction in which it was desired to have her head swing, and the engines having been started, one forward and the other backward (the Monadnock was provided Avith twin screws which were entirely independent of each other), the vessel at once began to turn, without bringing any considerable strain on her cable. Her motion was perfectly under control, and could be .made fast or slow at pleasure by merely varying the speed of the engines. I then set the sight vanes of the Admiralty Standard Compass to the reading (on the azimuth circle) of the point at which the ship's head would first arrive, and placing my eye to them I watched for the instant when they pointed to the distant object chosen as an azimuth mark. As the thread of the sight vane approached the object I cautioned the quartermaster to be ready, and at the instant it covered the object I made a signal, by dropping my outstretched arm, and the quartermaster struck a single stroke on the bell. Upon hearing this, every officer at once read off and recorded the heading of the ship, as indicated by the compass at which he was stationed. Then, the engines not having been stopped, I turned the sight vanes forward to the reading of the next point, and the same process was repeated ; and so on, till the readings of all the compasses had been observed at each of the thirty-two points, which was generally accomplished in about an hour, or an hour and a half. The difference between any observed reading and the true point to which the vessel's head was directed at the time that reading was made, was of course the deviation of the compass on that point. The forward iron and wooden pilot-houses were fixed and did not revolve with the turret, so that the lubber lines of the compasses in them always remained in the same position. But with the after iron and wooden pilot-houses the case was different. They were attached to the turret and revolved with it, and by so doing caused the lubber lines of the compasses in them also to revolve. As the turrets were frequently turned, it became necessary to establish marks by which the position of the after one could always be referred to some fixed position, so that a correction could be applied to the readings of the compasses in its pilot-houses to 16 August, 1872. 122 REPORT ON reduce them to what they would have been if their lubber lines had not moved For this purpose, whenever the ship was swung, a fixed line on the under side oi the hurricane deck was produced till it touched the after turret, and then the distance from its point of contact with the turret to a joint (marked number XII) on the outside of the turret was measured. This distance, having been converted into degrees and minutes by means of the known diameter of the turret, was the correction to be applied to the position of the lubber lines. The following table gives the measured distance, and its angular equivalent, at every station where the ship was swung ; but it must be noticed that these corrections apply only to the After Binnacle and After Ritchie Compasses. The lubber line of the Admiralty Standard Compass was always properly adjusted before beginning to observe. Station. Joint XII. Lubber Line. Hampton Roads i4in.4p 14.4 ' 0.6 sta 0.6 0.6 0.8 p 4-S 4-S 4-2 5-5 S-S S-S 5-5 n.t « ort t rboard rt < Assumed el 6° 1 8' ea 6 18 6 18 5 43 4 9 4 9 4 i7 3 44 3 44 3 44 3 44 •j An correct. 1 1 St. St. Thomas Salute Islands Ceara Bahia Rio Janeiro Monte Video Sandy Point .... Valparaiso Callao . . . Panama Acapulco Magdalena Bay San Francisco . When the ship was being swung, I always read the Admiralty Standard Compass myself. Each of the other compasses was usually read by the officer whose name is set opposite to it in the following table. Forward Alidade, Forward Binnacle, Forward Ritchie, After Binnacle, After Ritchie, After Azimuth, Lieutenant M. Miller. Lieut. Miller, assisted by a Quartermaster. Lieutenant Geo. Smith. Ensign F. Wildes. Master Wm. Barrymore. Mate Jno. Ponte. My instruments for the measurement of magnetic force restricted me to the method of deflections, and the only compasses on board at which that method could be applied were the Admiralty Standard and the After Azimuth. As the ship was always riding at anchor, and of course swinging a little, when such observations were made, in order to render them as accurate as possible the follow- ing plan was adopted. The deflecting bar was screwed to the movable circle which carried the sight vanes of the Admiralty Standard Compass in such a position as to be at right angles to them. That is, when the sight vanes pointed north and south the deflecting bar pointed east and west. Then, 1°. The sights being directed exactly MAGNETIC OBSERVATIONS. 123 north and south, as indicated by the compass card, the point, which we will designate by //, cut by them on the northern or southern horizon, as might be most convenient, was noted. 2°. The deflecting magnets were placed in the carriers, one to the east and the other to the west of the compass card, both being at the same distance from the centre of the card, and \vith their similar poles pointing in the same direction. Then, keeping the sight vanes pointed steadily to the object ff, as soon as the compass card ceased to vibrate it was read off by means of the prism attached to the sight vane. Let this reading be designated as A. 3°. Each deflecting magnet was reversed, end for end, in its own carrier, and, the sight vanes being still kept directed to the object //, the card was again read. Let this reading be designated as B. Then the observed angle of deflection is *0 The dip was obtained by removing the Admiralty Standard Compass with which the deflections had been observed, and putting in its place a dip circle ; the axle of the dipping needle occupying precisely the same position that had previously been occupied by the pivot of the compass card. The observations of the deviations of the compasses made during the cruise have been compared with the following theory, which is taken from the English Admiralty Manual of the Deviations of the Compass, edition of 1863. Let X, Y, Z, represent the force of the earth's magnetism drawing the north point of the compass needle to the ship's head, to the starboard side and vertically downwards. X\ Y', Z', represent the combined force of the magnetism of the earth and ship in the same directions, a, &, c, fZ, e, /, + Ccosf -\- D and 2 ( + E COS 2 { ' North »0 A + c + E N. by E. A + BS, + cs, + D Sa -f ES0 N. N. E. 8» A + BS, + cs. + DS, + E S4 N. E. by N. *i A + BS, + c s5 + DS, + E Sa N. E. A + BS4 + CS4 + D N. E. by E. J5 A + BS5 + CS3 -f D S6 -ES, E. N. E. J6 A + BS. + c s, + DS4 -ESt E. by N. «r A + BS, + c s, 4-DS, — ES0 East A + B -E E. by S. &» A + BS7 -cs, -D8, -ES6 E. S. E. *» A + BS. -CS2 -DS4 -ES4 S. E. by E. *,. A + BS6 — c s, — DS, -ES, S. E. *u A + BS4 -CS4 -D S. E. by S. A + BS, -css -DS8 + E Sa S. S. E. «u A + BS, -cs, -DS4 + E S4 S. by E. A + BS, — cs, -DSa + E S6 South | A — c + E S. by W. 817 A -BS, -cs, + D S, + ES6 S. S. W. «,„ A -BS, -cs, + DS, H-ES4 S. W. by S. »„ A -BS, — CS6 + DS, + E S, S. W. 1* A _BS4 -CS4 + D S. W. by W. A -BS5 -CS3 + DS8 -ES, W. S. W *H A -BS. -cs, + DS4 -ES4 W. by S. *0 A — BS7 — cs, + DS, -ES, West j A — B — E W. by N. *» A — BS7 + cs, — DS8 -ES, W. N. W. *M A — BS, + csa -DS4 -ES4 N. W. by W. *» A -BS6 + csa -DS8 -ESa N. W. BM A _BS4 + CS4 -D N. W. by N. ** A -BS, + c s6 -DS6 + E S2 N. N. W. «» A -BS, + cs, -DS4 + E S4 N. by W. 8,, A — BS, + cs, — D S., + E S, By the method of least squares we obtain, from these 32 equations of condition, the fivn normal equations S3 + &c =165. s6 + &c = 16 a - &s $o + &c =16 D. , St + &c = 16 E. For convenience of computation these equations have been put under the form 16 _j_ 8 + 2* \ ~2 / 'lO + '^20 2 MAGNETIC OBSERVATIONS. 127 19 _,_ 11 27 2 — \ I 1 /* + <2o! , 0\2 ~2 I _1_ 1 /^*~Ma _|^13 + 3 V~2~ ~2 I 1 /^6 + ^22 _|_ £u_~M»\ 2 \ 2 2 / I 1 /"\"l~^23 i 3 16 "I" ^ 31 N T 2 V 2~ ~2 / +~ 2 ^1+ ' 2 ^ .x x f I ° 2 0 18 „ . O 10 ( 26 2 1 0" 19 + 04 — 020 p i 012 — — ^ * ~T ~ , 0 5 — O 21 o | 0 13 O 29 ry T " o 6 "I o "s + "6 « 22 CY "1* ^--#eH o 06 0 0 14 « 3 + 7 - 02g „ . 016 - " 2 o , — «^ 1T + + 2 2 02 0\8 cr 05 + 03 Oig ,-, " — 2~~ s + ^4 ^20 o o °* 010 <^26 ~2 °2 o\i — _£sj 0 12 0 28 ~2~ w ia — *> M + 0 8"""*V 22 2^ + 07 — 023 2 ^15_— ««1 2 REPORT ON I I/ 1 /^0 + ^10 ^8 + ^24\ •A 2 ~2 / 1/^1 + ^17 ^•"f~'»Vfl 1/^5 + ^21 ^13 + ^29\« f I (,— 2 2~ / ° "" * V 2 2 / 2 l/«^2 + «5l8 ^10 + ^26\Q, 1/^6 + ^22 ^ 14 + ^ 30\ o "*\ — 2T" "2 / 4~ 2 2 / 4 1/^3 + ^19 ^ll + ^27\o 1/^7 + ^23 ^IS + ^Sl + * \ — 2~ ~2 / ' "" 2 \ 2~ ~2^ / But the deviations about to be discussed were all observed, not on the compass points, but on the correct magnetic points. Treating them in the manner which has just been described, we obtain the approximate coefficients A^ B^, C}, D^ E^ which belong to the correct magnetic points. Then, from equation (11) we get, going to terms of the third order inclusive, 5 = 21 (14) + (33 + 31 G) sin f + (G — 21 S3 cos £ - _S(V_ .^a_|_(23a-S2)Dj 8in4^+ - cos where 5 is expressed in terms of the arc which is equal to radius. If we suppose the complete expression for 5 to be 5 = ^11 + J51 sin^+C'! cos^ + D, sin 2^ + ^, cos 2£ (15) + F, sin 3£ + Gl cos 3f + H, sin 4£ + 7^ cos 4f sin 6 MAGNETIC OBSERVATIONS. log T her., comparing equation (14) with equation (15), we find, to terms of the third order inclusive, 81 =A, a + 5, ^ -L + iL IT 2f1 = lJ)1' "WThen the deviation of the compass is small, the several parts of which it is composed are simply added together; these parts are, 1. A, the constant deviation. 2. B sin £'-{- C cos £', the semicircular deviation. 3. D sin 2£' -f- £" cos 2£', the quadrantal deviation. "When the deviation is large, 21, 23, £, 35, (£, or the angles of which these quantities are the natural sines, may still be considered as the constant and as the several parts of the semicircular and the quadrantal deviation, each of these angles being in fact the maximum deviation which would exist if all the other coefficients were zero; but their effects are no longer combined by simple addition." Before submitting the observed deviations to comparison with the theory, it is necessary to free them from constant errors. These errors originated in two ways. 1°. When the ship was swung, the variation of the needle at the port where she was lying was seldom accurately known. Hence, in order to obtain the true magnetic azimuth of the object used as an azimuth mark, it was necessary to adopt, for the time being, the best value of the variation which happened to be accessible. In order to facilitate the setting of the sight vanes of the Admiralty Standard Compass while the ship was being swung, the value thus adopted was always so taken that, when the ship's head pointed successively to each of the true ^magnetic points, the reading of the sight vanes on the azimuth circle attached to the cover of that compass was always either some whole degree or some quarter of a degree. When the declinometer observations were reduced, the true value of the variation of the compass at each port became known, and then it was discovered 17 August, 1872. 130 REPORT ON that in some cases the adopted value was in error by more than three degrees. But an error in the adopted value of the variation produced an error of the same amount in the magnetic azimuth of the distant object used as an azimuth mark, and, there- fore, in the pointing of the ship's head to each of the true magnetic points. Bear- ing in mind that the observed deviations were obtained by simply taking the difference between the heading of the ship and the reading of the compass, it will be apparent that if we apply to each observed deviation the difference between the true and adopted variation of the compass, with its proper sign, we shall obtain the true deviations for the directions in which the ship's head actually pointed at the time the readings of the compasses were made. From these corrected deviations the deviations on the true magnetic points can be found by simple interpolation. Therefore, if we let ?n = the true, minus the adopted, magnetic azimuth of the distant object used as an azimuth mark : the azimuths being taken as increasing from the south around by the west. £' = the observed deviation of the compass when the ship headed in the direc- tion A. 5" = the observed deviation of the compass when the ship headed in the direc- tion A^\\° 15'; the upper sign being taken when m is positive, the lower when in is negative. i = the deviation of the compass when the ship heads to the true magnetic point which lies between A and A^ll° 15'; that point being of the same name as A was intended to be when the ship was swung. Then we shall have with sufficient accuracy the upper sign being taken when m is positive, the lower when m is negative. By this formula the deviations of the Forward Alidade, Forward Binnacle, Forward Ritchie, Admiralty Standard, and After Azimuth Compasses, on the true magnetic points, have been computed from the observed deviations. 2°. In addition to the correction which has just been explained, the observed deviations of the After Binnacle and After Ritchie Compasses require a further correction on account of the lubber lines of these instruments revolving with the after turret, and thus being frequently out of their true position. This correction, which we will represent by L, is constant, and is equal in amount to the displace- ment of the lubber line. Its sign is -|- if the lubber line is to starboard, -- if it is to port, of its true position. The deviations of the After Binnacle and After Ritchie Compasses, on the true magnetic points, were therefore computed from the observed deviations by the formula t __ t'_l /•„ I rN-i-"1^' — &") ~5~ • the upper sign being taken when m is positive, the lower when m is negative. To hiivc computed numerically all the values of f> for each compass by means of the expressions just given, would have involved a great amount of labor; it was therefore done graphically as follows: MAGNETIC OBSERVATIONS. 131 1 1 1* • 1 'I* '* - - 'i I 3 — i 4 i i 1 r 1 1 - i , li ,1, i 1 1 1 1 1 t 1 i ill i 1 i i 1 i il i 1 1 . i 1 , - _ 1 * i 1 i i - I - 1 - I — i ' 1 - *i 1 - *k - 1 *- 1 1 i I i 1 1 1 1 - 'i On a piece of cardboard of suitable size a horizontal line a b/ 5| inches long, was drawn, and divided into eighths of an inch ; each half inch representing one degree, and the whole line representing 11° 15', or one point of the compass. Touching the extremities of the line a b, and at right angles to it, were drawn the line cd and ef; and each of them was divided, upward and downward from the line a b. into points and eights of points;1 each point occupying the space of 2{| of an inch. Finally, a straight slip of drawing paper was divided on its edge into degrees and sixths of a degree, each degree occupying a space of one-quarter of an inch ; and the graduation was numbered from the middle towards each extremity. Then, to compute the values of <5 for any compass at any place, the paper scale was laid down parallel to, and to the right of, c d, and at a distance from it (measured on the line a 6) equal to TO; next, without moving the paper scale at all in the direction a b, it was slipped up or down, as might be necessary, in the direction parallel to c d, till the line a b cut the division on it which was equal to (m-\- L); the zero of the scale being above the line a b if (m -|- L) was negative, below it if 1 For computing the deviations of the Admiralty Standard and After Azimuth Compasses the lines cd and ef were divided into degrees and sixths of a degree, each degree occupying the space of one-quarter of an inch. 132 REPORT ON (m -J- L) was positive. Things being thus arranged, a weight was placed on the paper scale to prevent it from moving. Then a ruler being laid so that, while it crossed the line erf at a distance from a equal to b', it also crossed the line e/at a distance from b equal to 5" (the distances 6' and 5" being taken above the line ab if they were positive, beloio it if they were negative), the reading of the point on the paper scale where the ruler crossed its edge was the required value of $. In that way, without again moving the paper scale, the values of the deviations on each of the thirty-two true magnetic points were computed from the observed values. The following table contains the constants which were used in computing from the observed deviations the deviations on the true magnetic points. The first column gives the name of the station. The second column, the distance in miles from the ship to the object used as an azimuth mark. The third column, the assumed magnetic azimuth of the object used as an azimuth mark; the azimuth being counted from the south around by the west. The fourth column, the true magnetic azimuth of the same object, found by applying the magnetic declination given in the table on page 61, section IV, to the true azimuth given in the table on page 36, section III. The fifth column, the value of m. The sixth column, the value of L; and the seventh column, the value of (m -\- L). Station. Distance of Object in Miles. Assumed Magnetic Azimuth. True Magnetic Azimuth. m L . (m + L) Hampton Roads 6i 4i 9° 15' 127 1O I3° 12' 327 4X + 3° 57' + O 1C o° o' + 3° 57' Salute Islands .... 25 II 0 268 45 10 58 «• *3 0 2 + 1 CT + 6 18 + ft tK + 6 16 10 n Bahia 101 10 1 06 O 1 51 + 2 1O + 6 18 T ° 9 -4-8 AK Rio Janeiro Monte Video .... Sandy Point Valparaiso 5 5 26 ,1 126 30 93 o 345 IS IOC I C 129 14 92 47 345 22 + 2 44 — ° 13 + o 7 + 0 T + 5 43 + 4 9 + 4 9 + 8 27 + 3 56 + 4 16 + A T& Callao S *yo lo 72 JX 1yj JU U 1 + o 6 4 10 Panama 7 /* *o 1C O /" 0 l i r T -4- o i 3 5° Acapulco A 24t I< *0 A 2A'Z 2 1 + o 6 3 45 Magdalena Bay. . . . San Francisco .... 8 9 3°3 3° 15° 30 302 50 149 45 — o 40 -o 45 + 3 44 + 3 49 r 6 3° + 3 4 + 3 4 The following tables contain all the deviations of the compasses which were observed during the cruise. In each table the first column contains the assumed magnetic azimuth of the ship's head at the time the reading of the compass, given on the same line in the second column, was taken. The third column contains the observed deviation of the compass for each point, obtained by subtracting the readings in the second column from those in the first column. Hence, a deviation of the north point of the compass to the cast is designated by the sign -|- ; a deviation to the west by the sign — . The fourth column contains the deviation of the compass on each of the thirty-two true magnetic points, obtained from the observed deviations in the manner already explained. MAGNETIC OBSERVATIONS. 133 C/3 ^o CO 1 1 O cj » u CO '•3 ^ 5 °0 S + 8 J, ti .2 « u ~ d, fc.2 6 o > o o.c B co u .2 S a °.S £ o fe i! 8 8 8,8,8,8 8 §-2 £8,2 ° 8, 8, 8, 8, 8> ° ° ° 8 2 "O - PI -f ./I ^ I^KO vOQOvnuits CN N O O - fOwo-l-f-)^.Tf*^-Thrl-rr>fr,^oo M II I M II I I I II I || | H 2; tyj fK H H w W ^ -*,-H,^C^ w W oi OT w w trf o5 — u <» « "o, + = •I * I I i>^ 'D ^ ffi 50 5 'S _ *O o - > U o i +„- °o + fc « -2 ^ -4- ., .« S"S ' •5^ b. §5 „ g :i§«s £ i s.2 '£ ,2 .2 ^ 1) rt ™ M M en n O _ •2 ,3 o m * + g II II lf| CJ '£2 Pi Q"K 1 oooooooooopoooooooooooooooooooooo o •^ N *^"O ^ O ^ CN O ^^ O CNOO r^. ro fO fO O *•* N ^" ^O !•*• Is* t^» r^.\O *^ ^ r^ M ^^ Ip8 ^l& £.!« U fc fc w ri ^ u - pj W 'W W ^ ! ri w W W en ^- + 6 CO O 1 8 I I •s ^ u - rt rt o c W > on o ' Q ^ •-• . ii ^* W N = H O .. . fcJI-l 4j -° « rt 1:54 REPORT ON a i u in 6 o U Q I .S wj lil W '£ &• t.s s o > o ill :i|& •BJ il III E S.X- 8|« «sj-. pjl il 4.1 O •5 11 "booooooooo i^ifON «-»-i ri "booooooooo r^ r-*^o "t »n wi w^ t^ 1^00 ooooooooooooooooccoo :' aj ^-x . + ^ to •£ a "°'> u s u O Q u I ; -. I ft=3 111 lil ll>; "3.0 3- ri fcfcfcfcfcfcririMriricrfrfcrf •S e 2 '» S o (3 a 1 1 x tn c« ^ £ £ £ -S X Y. Y, Y. Y, S. MAGNETIC OBSERVATIONS. 135 - a j u O u q o H >- I a w Q H K 1 H Q i w w ra O o II . o ~ ^ II 0 O » 'Z Corrected Deviation of Compass. ooooooooooooooooo o ••>. u + * 6 -3 1 ! •k. U ^ ig « 1 8 vo f f 4 •oo .. •f « U> •5 ^ °° rt ,O a, *- o fl O »C 1 i,.|- K 1 o W w V- I _C 0 C « 0 <-• tc o I'* 1 4 •S ^, "xri^ll ^ *j O •> ^|11°N | '5 S I E ° -2 rt -a c ^ uj .2 rt u Q 'ooooooooooooooooo o "o .3 • |2U e .0 + 4.| II O t£ y 'C O Ji o ll* Bearing of Object by Compass. > > > > >' > > fe fe >' >' t-' > > > > > 'ooooooooooooooooo 0 fcfcfcfcfcfcfcfcfcfc******* Assumed Magnetic Direction of Ship's Head. £ w w OT w ^' .^ fc" WpqW.fr .frw'js .c/2 p4.fr j?p4 H E £g £• -fr £&>'95i>g|«9:>>'«>g ££^£££WWp3w'w'cflc/5c/2c/5c/2(/)c/2c/:!y2c/3c/3^:5^^^iz; ££;££;£; Bahia, December 30, 1865. Assumed Magnetic Bearing of Object = N. 76° 30' W. Correction for Object = -f- 2° 30'. Correction for Lubber Line = o. Corrected Deviation of Compass. "boooooooooooooooooooooooooooooooo 0 ++++++++++++++++++++ i T Ii M i i Ii ++ A deviation of the North Point of the Compass to the East is designated by the sign -f- ; • a deviation to the West by the sign — . From the observations given above, the following values of the coefficients of the deviation are obtained : A = +i° 4o'.2 B = + 3° 38'.$ C = + o° o'.4 D = 4-o° 47'. 8 E = o° o'.o Deviation of Compass in Degrees. "00000000000000000000000000000000 o Q HH i— M M M fO f~O N MM" Q O O O O1-"" MMrO<~O-^-^-^-^-^J-1^-<'OM'-« I+++++++++++++ 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 Deviation of Compass in Points. Bearing of Object by Compass. >>>>>>>"*>>>>>>>>>>> > > > > > > > >' >* fe > > > > "oooooooooooooooooooooooooooooooo^ o ^^^^^^g^g^a^^^^^^^^^^^^^x^^^^^z^; Assumed Magnetic Direction of Ship's Head. - •«! x • . .1 t - •> 4 l>«3 *** i'^' = iS^^-:lKS±-S:xf^K-K-SK-^-S 136 REPORT ON U 1 a. O U a I Q < Q u I a 8 I 2 £ o Sandy Point, February 10, 1866. Assumed Magnetic Bearing of Object = S. 14° 45' E. tion for Object = + °° 7'- Correction for Lubber Lin Co Corrected Deviation o Compass. viation of Compass in Degrees. De Deviation of Compass in Points. . o a Assumed Magne Direction of Shi Head. 2 &2 8 111 + MMOOOOOM**NNMMOO I I I II I I I I 1 + H W W W t4 W W W W W W W W W W W H W W W W W W W W W W W W H K H (4 "ooooooooooooooooooooooooooooooooo •fr * •*!- NO N N NiJ-MN "Ttrn-S- ~ "TS--* fl IO WV IOND ^O ^O I^«NO W1NO ^O NO NO *O NO IO 1ONO NO NO NO NO *t" Tf *tj- fO N N N f^ f^ ^- NO fc fc !? * * !« Wft5 W W en OT w w ui to «j«3 w ui + ) ' •s s I 1 u - 8" a « m , January 24, 1866. ing of Object = N. 87° o> W. 13'. Correction for Lubber Li o° Monte Video ed Magnetic for Object = — Ass ion Corrected Deviation o Compass. 'booooooooooooooooooooooooooooooo'o" M*t^~nro-«ulO'^fO"1«'*'t «0 to «MNT)-~~ TfMnLnn «tOf^^-Tl-io»ri'• >• <^ >^o c/5 aj «5 oi t/j en e/5 uj «5 cfl !5 Z, "f. \"f, Z> Z, i IS ',"£, v> x x '•£• ''Z- ^ ''f- ff ^ i !z 12 1^ ^i Assumed Magnetic Direction of Ship's Head. W g &Z W W U ij .£• . u 4J rt u II 1 1 .2 - » S •s c x a •1J fl 11 fl 1 •°'> MAGNETIC OBSERVATIONS. 137 D o 55 a j O 6 0! K B 0 O U n •A •t, i 9 X p fc. o w 5; O H S O as H O g - o •0*0 • v c % ooooooooooooooooooooooooooooooooo .A 4) + — o "tj O rt t£ £ o > o uou o +++++++++++++++ III 1 1 1 II 1 1 1 1 1 1 1 + & ^ v: (/) _e « *5 w >> | II "3 S a a> & to 10 ^ ^ ^ u-, m 10 wn 10 m ^ vn 10 ui tn u-> m m u-, u-j m ^ ^ ^ ^ ^^^ij^mmm 1 s ? O p 111 ~a ?• M •> i-s; 5°H Qu 0 1 * o O IM 1 •a o 1 .« ^ || ^. ill N O O Deviation of Compass in Points. S -2 U "" W g °o l»t o '5 - II x .2 v» W a 3 « .la o a « °N u « +^ W * II v" o^o U lu fi o S MClMM O OO O1-1 O ** « W W N r^ro^O'^r^Tj-Tl-Tt' iovO "^'O wj IAJ ir^ Tf r^ M •s ,- > i « ^i-s MC c.^e |> > + «S.» .£ *•§•& - II •o O OJ O • PQ io«ow »i wtocnOTOnooaw 1^3 ^Q SH ** 2 " O Ass Correction CJ f) |.|. e -a MC/2 ,2 — -d a°S5 "Soil «.4^,^W^^4.^ .S-s > S + •• S i 1 II BrSIJl |5ug< 304* ||a a AJ tJ S O 11 g ^ W W W ^ £\/2 ^-cn K (4 H- w- ^g ^aj ^' ^' ^ ^ -^ y ^ ^ ^ ^ ^ ^ -^g •°'> g 3 S S <3 »»»}>! S5»wriSrfri-oi«S«»oSidga5<«irf»i«5^>^^S5S5fc*'^lZ! rt "O •sl! - "boooooooooooooooooooooooooooooooo + 5 ill. « M « u^M « Ti-^- ^ * S) *° d ^ rt g 6'> O QU 1 +++++++++++++++++++++ Ml II 1 1 11 » CO •s 1 II (U «l 'S.S . fi t/J ei •SlS ^?»5?!g!?«8ja»5?SS5!J{»l?ff»SSSl??"?»5^ffS>52lw>«- 1 1 ^ to u rj 0 J ^J •2s"" SoQ Ou 8 C ' r. •0 0 || • •- s u 2 s^'^ Mjg *I1 •nO,° Deviation of Compass in Points. » ^ f3 1 ° ! -s1 e! i ^ o ^° ^ Mv- £-p « rt _ 'g«° rt u + •i-1 II t> "s CJ V "s e Pd W W H W W W W W W W W W W W W W W W W W W H W W W W W W W H W W -000000^^000000005.000^0005.005.5.0005.0 a, - - 1 | +N I -| i^ *K *9 o fi rt O C •— S -U- S^ -go g.R 1 ^^x^xz*x*^***z*x*x**x lll.f Assi Correction O tf) '-3 *a, „.£ txOl/J rt <— •— i 35! •g|s s " ^- H W ui ^ ^ . •'' V< • i i 1 1 **5!i!!*^JZi ^i1"! 18 August, 1872. 1:58 REPORT ON 6 Corrected Deviation of Compass. 'boooooooooooooooooooooooooooooooo NMJiCoN&Sj.ror'lN ~«*rorom"i*-'*«'** •a-Nio tin ° +++++++++++ ° f i TmT "m 777T771 " 1 1 + * .3° ° w -« _C ^" — .S tfONADNOCK. II . W *3 -j ^ Deviation of Compass in Degrees. ° +++++++++++ 1 1 1 1 1 1 1 III 1 1 M 1 Mil 1 1 i S 'ui &o o rC O •s *• r •S -s f .2 ui llo Q d i •^j Slg oo -.2 ".S.8 -"SS U^U Deviation of Compass in Points. I | <->-; | J ° -2 ^ v^ ii t5 'o ^"W t/j g ° 2. u . ^•S« O 3. J* N a_C i 73 -f" Id X S5 "« o §." + " 3 n 0 e 1 •5, O rt HWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW OOO^O^C^C^O^OOO^O^OC^^O^OO^OO^OOOOOOOOO 1(1 ^ o 85<3£'OvOOvO*>vO^O*000'OoS*0>OvOvO>0>0*OM3>0*0 (2 «.> ^-j. i 18 ii I KXKMKZKXMMKKKXKXXXXKKXKXXXXXKK Sfi.JS i AS! Correction ° -t* U .21— -3 S°S "2 oS aj • -1 1 • • ri * • • • x t>- •£* js- VB « 5 H .°l|| II '> '5 ^ o w IS g ^2 w w w 2 £& £+ + 1 & "8 1 1 •S u .- 0 :VIATIONS or V *J a -^ Deviation of Compass in Degrees. o +++++++++++++++++++ ° niT7T77TT'i!4- | f Object = S. Correction for "33 894 ifj •^ ^ rj°° jf J S Id If, if M 1 1 +o 1? fl : I » » » > > >' >'>'>'>•'>•'>>>>>>>>»'>>•'>>> > > > > W . V " *\fi Q a £ E U-L «-3 + II! ?! o S ^JOQOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO f>^-MNN M r*i MM«^J-^"N^»Oro "^ M 0 •£ i > P3 m - 'J f & rt o •I'3 2 + ATIONS !l K I W! t/5 1/3 C/5 tfj (/3 U3 VJ c/5 t/3 C/j t/3 C/5 !/3 «i C/3 «i C/j t/3 C/3 cn C/j C/j C/j t/j C/j C/3 C/j C/j C/j OJ C/j C/j <£ 14 ? ii |-s RO ^ « .2 •• °0 i 1 *j ;y = ww- ^d • ^ rf . ."* x>- . ^^> j>.-' w > rt w i a* c.= ~r 4) 1* cj II tM ^ r. — \ Sir '5 e j= « •e .2 - e II >5 ^ ^i If, ^ 5? W W w W W yj CA c/i c« c« in co c/i en en cc ? i^ i? J1 JS /'i X X 55 ^ ^ & n S.2 •°'> 2 « <^i£-> w *J rt -O MAGNETIC OBSERVATIONS. 139 6 || Corrected Deviation of Compass. ^ O O M N r*- .1 ^ *« & t | * V "p J> O ^ Deviation of Compass in Degrees. OOOOOOOOinOOOOOOOOOOOOOOOOOOOO^OOO 0 6QJ O • 9 * ^>>>->->>>>>>>->>>>>>>>>>t>>-"t> >>•">>>>> « oT II ^" rt 0 | g'i •si 2-3 *OOOOOOOO"'tOOOOOOOOOOOOOOOOOOOO«"iOOO 0 J I •+ d 1 ********2*x***s******ss*********;z; |*|.« CJ o o ^w &:^ |?1 •S oW a'rirf* jkj* • •! "" 'rf • 4 5U £** ^>-ri jijji 11 s w P^ JD 15 W W W ^; ^"j^ ,^c/5 K W W c/i ^^ ^c/3 ^^^y-1'£:^i'i:3'^^^^'^^^ 11 if -. U"^' rt s t* «!* - o< -2 o £ u fO a « +- lagdalena lagnetic Be ect = — • oc o i CL, W p4 W W W W W W H W W W W W W ~Q O OOOOOOOOOOOOO S *T II ^o •S , > x/1 - Us Mn 0 e « °o c .y a + •- W D "T^ (S^.a o || A^'S •go BJ m OTOT ^ M " " W " " " ^ ^ "5 M ^ N |Xg *fl ^ g - -a °° Ass Correction U U) if u55 Jjw-o s ° S •S §S .^ W' w' M 1 ^. • -fe't. >-> ' ' |^£.S + I!1!" I.H ll g ^ W W W jz; ^ ^u5 w- w a M- ^g ^-cn £ ^' ^' « ^ £ -^ ^ ^ ^ ^ ^ J= g u a £.2 •°'> g S jj ^ £' ^i ^ f5 ^' W W W W W c/5 en c/5 c« ui in c/> u5 1« oi c/j ^ ^ r* ? ? I2; 1? ^ I2; Z< ^ o tw O J g 1 •d v Sli. t.2 £ o > o o.S . o.S + 1 M +++ I I I + I I I I I I I I I I I I w g ^K W W w £ &+21&U H w- w- .g^^cri £ £ £ w ^«H.^ £ fc £ £ 2 fc W W W W W 03 03° 03' 03 03° 03 03' CO 03' 03 03 ^ j£ P£ I? .H ." ii w u « * „- W o c J g'= »-" I/I •» 5 c B o y, o _• ^ Ml J3 . £ 0)- 0 " .2 « u .&=• " "S S O I •8 ° - g •o.E M. ill oooo ooooooooooooooooooooooooooo * - - -- O « **> 'tO \O I^>00 00 t^\O u^^-ThPO^N«-O^«f^ 't'O *>. t>*00 tN. t^ *r> ^ M O 1+++++'+++++++++++++ I I I I I I I I I I I I M 111 .2|-1 :: i ~ J5- 2 35 Assu Dire + -3 w c « u & 6 '8 >- *& o •2 S -*c-H<(— fec-Hv.-'jto-tw-tMKKttr* Hoo «i-*«l-ev+^«(« O ~0 O I I +++++++++ I I I I I I I I I II I I I i I I I I 25 W H ° * o^> w I 3 o^ S V I 3 * {« •S i' > w fo - &s C -S C -L u, w in rt 07- ^S •§a«s' ij1! ijH « T3 MAGNET I'C OBSERVATIONS. 14] M 8 X O U o H £3 S o U M di u K H 6 Q bl « i s a w p £ H i M 2 s-3 U o as r? o C £ c % O O « CJ '^ Pt fc.a e .9 > .9 o.S . I |s° iifl i HI oooooooooo w W HOO ^H W w w I ^ B 1? •O O & o e « & •£ 8 >- T3 O > to ?'i - & »1|. 'i B 1 - + »o 00 J o S c 538 1 §•& s|<5 f 3 ^ bO ! I O w ai u ri u_i S t/j *J O *^ .^ . ^ ° ° U S •5 ex S •I .2 " c S '3 £ .2 142 REPORT ON X Q O S u H 2 I u •< x « g H H b. O 1 Q M g § 2 I .S ^O V II ri • » i ? u .a o F "SB . "boooooooooooooooo M in — — Tj-^-^N^minfOfON-**^ « -^ « O O O o S Sad SIB 5.^ 1 i l^l |.| I •z'!.i tB«|eoK4aoKNvci'^C)^ w WW + -s & -3 in „ s = •S .«; o* H"- •a § I 2 .« •£ *!^ -S -o M*B f.i~ •S.2 S.2 II 3 .1 i4^ - >o ^ S .2 S s =• ^£§0 2 S.S-8 ° 8,8,2 ° aaa^-S S-2 °,°,a° S 8 § 2 S ° g, o W ro »nvO \O vo 00 CO I»*.\O vO^-(*JPONfc-*-i« Q O O « Nf^fOw^u^w^u^ro^ O M ++++++++++++++4-+++++ I I I I I I I M I I + "35 o 3S 111 f I.S- |S^ W 01 I O 2 I 0 C rt fill 1^- Q - 2 - + MAGNETIC OBSERVATIONS. 143 O U I A Cfl O U H CA a E < a H o § w P w E o - O -f- 4 uary 10, 1866. ection for Lubber Li C Sa Corrected Deviation o Compass. Deviation o Compass in Degrees. Deviation o Compass in Points. ."• 0 .e«0 Assumed Magnetic Direction of Ship's Head. 8 & 5,8 §. 3.3. . ° ° °° oo o o o o o o o o o o o o o o o o og - « N ^-^^xoi^in^-n-r) M - o O 00 ~ « N « Tt-^ior^^t^^iOThN „ I I I I II i I I I I ! I M +++++ iiiiMiiiiii w W -f- the ffi ig th following values C C/. Co th A deviation of the North Point of t deviation to the West by the sign — From the observations given abo iations are obtained : A=— o° 24'.s a e + 4 deo, January 24, 1866. 13'. Correction for Lubbe Mon ct = . or O C Corre Deviati Comp Deviati Compas Degre Deviation o Compass in Points. Assumed Magneti Direction of Ship' Head. oooooooooooooooooooooooooooooooo « Ci^-Tfi-it-i ^-^-N ro MNW^-NTj-^-^-Mr^fOfiflco ^-^-N o O ++-r++++-f+ |l 1 1 II 1 1 1 1 1 1 1 1 1 1 1 1 1 II 144 REP OUT ON I I Q U 1 t— I cfl M ft - O U Y A u M i i R U Q O •>• 3 <£•§ 6 + f § 1 a •a"8* v c £ ^OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO •y o g El B °O-NrOm">MfO<") fcc- •!*• H 6 &< 1 1 1 ++ 1 1 1 1 1 1 1 ! 1 1 1 1 II 1 1 1 1 1 II 1 1 "2 s "a.'-) 3 en Assumed Magnetic Direction of Ship's Head. W'W . >•> w w 05 0i erf erf cri c/3 + -3 S Sl 9 ' 3 + J{,« • ° I \ Corrected Deviation o Compass. +++++++++++f "5= . ' Deviation o Compass in Points. *M**'o-*-to^oo te <» «i.'«xt»»jro OOO^*- — "-^ Tj-vO VO ^O Tf- f} HH o OOOOOOOOOOOO «Tj-Tr-)HOJ^^?i!xnloj^xH^M^-4»Htv«hctti^Ho^«Hac«i*^to-*w*» O O O O 11 -^. -•» . ^J"*1 •** ' ^^-w w w tf iw ^- is designated by th s of the coefficie East valu o° o th fol 3° A deviation of the North Point of the Co a deviation to the West by the sign — . From the observations given above, th deviation are obtained : A = — o° so'.o B = - 146 REPORT ON 55 Q O 2 u o en t) u •s 2 o a u 3 - u X b. O (A % O H Q u I i £ I : o o-S sn -^ « B u .2 C o 3 S! J5 II i J Sol «•£ a. Deviation of Compass in Degrees. eviation of Compass in Points. Assumed Magneti Direction of 'Ship' Head. &28 oooooooooooooooooooooooooooooo •^••^•'t^-^-'*^-1^-'*-^*-"- «-• N «ncs M IN r-i t/i rj- tN u-> f) iri u-i in L/-»\O ^O "i <"O tN MM 1 -.S- 55 W + - J **~ *u ^ S£ •a o a s 1 W •S 0 ^ it O 1 J " A deviation of the a deviation to the W From the observa deviation are ol-taine A = — < "3 o Corrected Deviation o g.o ^•* ooooooooooooo NNMN-^-w^NNNNMNmrO OO«NNui tnon \r> *ri in m M ++I 1 1 1 1 1 II 1 of in Devia Com De M S5 W + - g, "3 O || u-l 1 1 MAGNETIC OBSERVATIONS. 147 u; u O 55 O CJ O B! C3 H H O CO CU <§ a. H Lin 1865. for Lu Thomas, November t = + o° 16'. Correc St Obj Co Corrected Deviation o Compass. Deviation of Compass in Degrees. opooooooooooooooooooooooooooooooo o •«*• wico ^^^^.^^^^ O'NVO **"> -*fr <^ *« •* O O "•««-! fo^t^omto^t-fOO •-« ^t- 11111111111++ i Deviation o Compass -in Points. Assumed Magnetic Direction of Ship's ++++++ w "*"= -N- fcfcjaW W W ^-^H.5- -sz; w w a w H W !*«»«»•_„ • • . . < . . + 5 w> o ' t 1 8 U (4 &OJ O 6 ° •§ 'S + w . •5 ^ £ .S + « . JtS 8-1 •=• ui § g c w o 2 SS s w M £ H CO n O 865. Lubbe s, November i 57'. Correction ad Hampton Ro or Object = -f- 3 Corrected eviation o Compass. "boooooooooooooooooooooooooooooooo I I I I I I I I I I+++ of in + . •a a ° Deviati Compa Degr eviation of Compass in Points. 1 1 1.J ^ W W W W ^-^cwyj w W -° + Assumed Magnet Direction of Shi Head. £'5 si •e-5 B| 148 REPORT ON I I u .z 8 c/ o U a VO 00 u.H S| o > o S ' • a .2 |-5 js- v < 'booo ^f Tf ^- - oooooo - oo •- fO S3 •sf-s. Is I w -r .55 W + -3 1 *u C ; s « o Co 0 U o £* a «o Hill go°° o a u u 1§£ = illl s c - Q w E o 2 cfl § H 5 u „ ° o.S . "3 .3 § a a 111 I wu w c/5 + & £• £ •o § 1 I J - T3 O •f 8 o v to 1 1 ; • E Jll - MAGNETIC OBSERVATIONS. 149 W U o ft o < •7, O z J U o s U H •/•: O en C/) g O U H O , ^•s . i c S» o O rt 0 °«U +++++++++++++++++ o> J5 -= C *-• 1) >% 'o II e c b • a> Deviation of Compass in Degrees. V o 4J ® tuu ,n S s. T "° ° II •* .2 M J_J v' S ^ M I-H ^ *" -1 "c rt g Deviation of Compass in Points. o o o o o o o 1 ! C 1 * VO 1 ! 1 ^i 1* C o rt N X jo "a 8 " M° •"10 ™ Bt <— J3 O rt o c.&c (S II IS W W W rH _Q Hc*«ity3 tj tij p4 t/5 ,0* ^> ,Q*C/^ ? ^^i °-\\ it ^H^H^i^tWWWWc/!ic^C/2C/2C/3C/3C/]t/3C/3 j-t! » V« t; x i» «•> Q e* S t7 *J O O ^t Ifl 'Z2 " ^ orrection for U VI It tjoy} S'olj ^§S ^' W W en tn ^ _ . ^ ^- IIS-I + * 9 i 1 1 ~*^< C o w ^* I?J 5 1.8* a > '13 - S U 5 u 3 CD g ^ W W W £ £w ^cn w w W c/i ^-P ^cn ^' & & ^ -° w "^ ^' ^ ^' ^ ^ -^Q u rt 6.2 ffl! .i^Tj-Tl-Tj-N 1-1 •- ONOO OOOOOO^'O roPO« O O O O W *OvO 00 + 1 & -o & o >• o 5|a +++++++++++++++++++++++++++++++++ £ * B .§ « + II II c 3 Deviation of Compass in Degrees. V 0 1 •§ s 1 s 0 S « o & •« 1 ^ II- W y, U \. ^"3 <& H OO is "o.c B M oi •-• 1 1 °o M ,0 o- § *>l M u U o . a* .3 °« •3 -u rt i w || lip's Head by Compass. •z & * • ^t* H» W "** . "** ^ te • " ^ H'?*'^ y ..J "^H* t ^ ^> . f >-, ^. " • M fc^_j-._j_. ^"t-a- • >^ • hr* ^- ^ o -^j_n C/i * H^ ^ "N^w^ •£ ^* . •" Hc^•^c<^J ^ • . ^ n p^im^jO y HH & I? Cfi rt y ^ c/) f-^ • • • ^i j^! ^ j^ j* >^r"^ S u -4- o -3 U || r, «J flT cfi v' ^3 • > " ov "IS "" •— 1 — 0 _, « 0 c.&c 7. • ~ 1/3 1> ^^ — 1~ (S^.g. ^-T U G §" H ^ ^ ^ ^ ^ ^ ^ [T] ^q JT| ^ y^ c/3 C/3 C/3 C/3 C/j C/j C/3 t/3 C/3 ^ J^" !^ ^ ^-< ^H ^ ^i ^H XH •^ ^^ 1^3 0 Q "7 *j 2 ..00 orrection for U w IS- 1- . StS-S ^§K ^ W W w w ^ . /. ^ £* . . . «> s"S + j= ? £ c ' ^Ili i5 « g •ti C •£ rt l|*a u S-B 1 8 ^ -° ^ W W W ^ ^c/3 43 v5 y pj w c/5 ^^ _o*c/i p£^^^M*^^o •s|i-l H P H X H Q PS o § O 150 REPORT ON a o U o t/3 M • (- § I H b) i u en § H O g 1 I I ^ -|- 4 Lin 0, 1866 for Lubb Feb Co dy Po = + o San Corrected Deviation of Compass. "B.S . n of in Deviation pass ints. iat Poi gnetic Ship's "booooooooooooooooooooooooooooooo ^I^Cx^O^W ^ ON Ov O* N -^J-N "*• ^ W OO^W N C-> t^ TJ- •«*- tfr N r) H- ~ - rj ^- 4+++++++ +++++ ++++++++ 1 1 50W n • H m ~ , ^ ^ g j=- X W W U X £0 2s. H U W c/) ^-D ^u5 Ass Dir ^ 1 •^ S ^ lot; .2 ui I) W O II "~> 1 1 U°o ^ u + o 1 Jl « ^ v'W J « + in" 11^ w I £ B" 0 C rt o .2 - o S -a c j= « C « 1 vo 3 ^2 3 C 3 Corrected Deviation of Compass. ation of pass in ees. of in Devia Com Poi A-.unieil Magnetic Direction of Ship's Head. ++++++++++++ 1 1 ++++++++ ++++++++ III ++ . + y. «' X J5 XXX X W W W W W o o.S C r O « "' r* •2 s ,° > o « «^3 ^j if S-'-1 i ooooo '' oooooooooooooooooooo ' ~ O v£) vD O\ O Ov t> C^^O ^OvO^O f^fOfOfOf^fOf^f^^ I I I++I+++ + ++++++++++++ W a w w w & ^ ri.fr Assumed Direction He + -s 1 o 1 -3 +o e -2 o 1 • ' br u 5 •• < ^ S'^TJ II *£ P fl + »a|5 o o<; w u g 2 o •£ S o *i rt C .5 E s .a rt -o 'MAGNETIC OBSERVATIONS 153 U o t— ( c« P u H O o u H O u H W S Q 2 O I— ( (-1 I w C/3 « o s. " ON •o"3 . £ c if u o rt D 'z; cx b.2 S ° 9,2 9,8,8,8,8,2 §. ^^^° ° ° ° ° ° ^a§ o ° ° o o o^o o o o o .* o + -s & -3 ^ o > o 1/5 y. o ro up° ++++++++++++++++++++++ 1 II 1 1 11 + 1 ! >* ^ + II o .g . s * d * •g S v- H o»S S u fo • a 3 \o M If! a° 0 &u o ,a - 1 ^ 1 .2 „ II ^ ^o *3 00 =3 IH H *s.s 1 M ul La o w- J5 H«H*-«l'i'Hi>i*ti'»«l'f*:t-r«tr«i*-47tH^iH«H(N-»c-|^^r*-*^H^-HN-*~»H V W 5 ' . to *2 o O M - .£ c"o J3 til g 1 1 +++++++++++++++++++ MM II III •S N + 0 £ . • |, & 0 r- ^j Q ^ o i II i l-i ^ *W ^ 0 o. «2 „ o"u . • S V *0 o c/l x it if 1 '**• "^ ** a -s + 'o ^ " oj" II >n c •»• •S .' > • a o 5* rt u c/i II oJ S K| J5 ±,S ^fei J J^fv Siif ^ f S^-f ?rf^- i -:]i ^ 1*8 « «s| ^> + *-. v/2 ^,<^^^^^yp4wWc/ic/5c/5c/ivic/5c/ic/ic/5c/5c/5^^^^^^^^^ld •s " 5T V t; >^ w 1 ^ o 8* C "o ^s-S-i;^Q h Q U OT 6^bl + Iff '•£ "(^ a o CJ TJ &c/5 . v. «j S S u O .C J3 J3 •^ o o o Jv-'d ^W ri* c/3^ I^^H g o „ iX c _, 4) ti C -^ rt B 0 "S §K ^W^Xi -^W^jtyjpq^ ^pj pjK^^-^ ,O ^ CO • iC ^ 11* a U s — £ « S.2 3 g r^PK*' [jj P'K>P>^H^^ •°'> £ B a -o •0 ° - ii c y, o_o oooooooooooo .* 4, + " CJ O rt t» -r: ci. o e "s V t.S £ bfl w *3- 0 f> W ++ HNHhSTTTl."."? *J C -£ _o .^ "y O + *o.S •^ 1 °' . II *• "S 8 ^ V c '3 «l o ^ w 1 §•& £§Q «u o 1 | « 1 "8 II? w .„ " O >O p **- v O - oo ,3 0 .g 3 -5 " s 1 a| -to -*! -*i-tN'_. .^^ -s ,•£ «s, u .— o s « ^ • • >,^ ^ >> • - IJ rt O "O 1 K §• • a p«JB^ t/5 ^ ^i -0 -i*-*1-0 £:' j; ° a"8 - OX) 1 Oj II *^-t ."" 0 .S-L> ri ^ ^^--"^-*^^>»C» •I'3 s + Cu S > "Ml g " € *7 *7 ••^^I>-S?-^^H^^Hr^ "a & v- II 8 1) •o ^ ">r\ t: fe-oi «^w ^ o 0 S £ a -2 - % Q 0 tn D +J ^ J J^ S g + C5 '— "a | gs tJ3C/3 • •o|||J a^l T3 c h-< 5j O h" ^W Wt^ t/i^. -^.. ifil |i*j 11 g ^ W W W ^ ^ ^ K w W ^ J-D ^t« ^' 5= ^ ^ -°. u ^ ^ ^' ^' ^' ^ -^Q ilJI i.| f»fk*i(aBri« <:^^-> « T3 20 October, 1872. 154 REPORT ON O u o a. C/3 I I E a N be S Deviation of Compass in Degrees. Deviation of Compass in Points. s ? 0.( 1 med Magnetic ction of Ship's Head. 'Jj M ^.^.f^^^ _ ^.35 ON — W C^^O m« O r*1*tvr>f.f»Tfr* M fO **• *o m W « O 1 ++++++ 1 1 1 M M 1 1 1 +++++++ 1 1 1 1 1 1 1 1 +4++++ 1 1 1 1 1 M 1 1 1 ++++++++ 1 1 1 1 1 1 w" w'ww'wwu'w'w'w'w' www w' t^-^M O OO O t^vo ul -«t M N "* + * a, & •£ °- W + a. ' * W u u |- g '- \ ji .5 ".+ ^~ t£ v n b. O u Q u S i Q X O i g o ooooooooooooooooooooooooooooooooo - - ~ n — — iy-, -1- « ro n ro cl ro n M - - rf roro MNi^i^rou^ri^-^ O O O •- — O — r^i^C C» O O C^OO vO f^ O N "^vO t^t^t^.t^^-0 O •* rO^J-f^i-i O ++++++ I I I I I M I I I I +++++++++ I I I I I I + "booooooooooooooooooooooooooooooo fOfOfir^fOfOflfO o - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l-l 1 ++++++ 1 1 1 1 M 1 1 of in Devia Com Po * w w w w w w w w w w w w w w w w " )N O •- N N -H-vO — ft r^ \o 1^ . 0 » i u -(- th nts ci si t o t is ues o the Eas lu C o ,+ the A deviation of the North Point of the Com a deviation to the West by the sign — . From the observations given above, deviation are obtained : ° s'.o B N '"iA ro MAGNETIC OBSERVATIONS. 155 Q 3 U S o O X H J 10 v. vO O "J ON u :J u ^ o o.S B M £ -2 « £ •P« fl O lift sifi a" xs |J oooooooooo O\ O — CTs M •-( rj- u-)00 t** B +++++++ i u || ^o^o«o^o«o ll +++++++ ^3-Q i| u ii is fll « M _i_ ^ & *S S „ I 1 S ^ •o o f s - -S n ! I J " u o j: 0 " . '8 s fijl Q H P I* g en fc O H g in g .2 > S 1 •Si "-1 u U o 2 3 - 0 G ' •aas .2 g-g1 £ QQ 8.9 C Ul ,n O V) £ .•> o .0.0 W W RvS1 coco •5 .S .^ 'G ^ S 1 1 I ° 3 W] Q fi 4) § a o .- "' u (S^-S. ^ *-• ° " " 11 *^ *^ ^^£.5 1 B9 « II a 5 a s.s •- 156 REPORT ON o S ^ C X, s a. s u M O § > u Q u s H 2 1 H Q a: £ °0 II V H 14 .1 o1! ™ CJ 1 . .?.? 1 + ?» 0000000000 +++I i M i Ti TM++++ °.£ c * 1 6'^ * 71 3 V 4s I l-l I I I I M M I I I+H-+ fc' ^' ^ £ J5 W W W W W W W W £ £ & £ o W fci W W W° co in ui in en c/3 co cri to co tA ui w - "3 1 8 TJ O .— (fi SJ2 T2 w > ^ SbW ll ~ CO K " ^ 1 "21 fti •i i a | o i "o.a ^ a £• & ^.£ Hi O ^ « O fOOO O - 1^00 10 r^ H, O NO t^OO OO 1 1 I++++I Ml MM I++++4+++I 1 M M l 1 l II M 1 1 ++++++ M M M M 1 W to W W x t« - ^j. to _ N ro "I NcO"->^-CO*H n ^ -^ C i^ d tlsl "°'E sj rt ^ Deviation of Compass in Degrees. V o -N — HH O O O £) !->. -3- CO O M •<}• w» ^- r*} co Deviation of Compass in Points. •o „• |J S 'Si w w w w w w w w w w w w w w w w £ £ £ £ £ £ £ ^' ^' ^ ^ £ ^ ^' ^' ^" o « N ro ^ >-O t^iOO OO O LO *^ f) N «^ ^^ W N fO lOO t^»CO t^'O ^O "^ N « Assumed Magnetic Direction of Ship's Head. ^" W W w " ^ -^ ^ pnf^W^ .cfiJ^H -t/5w rQ -^W W ^ ^ rn[>c/3.(^-i'*1*'1-1 ^^cZ ^ -2 ^ W W W ^ ^Q C/3 -Q C/3 pj fsj pj rn ^^^i ^C/5 ^^^'^'"^fj?^'^'^^^ ^^^^^^^^^^^^^^^ 0 II O a . -js 0 "-I 00 u •* d o o I! I°° x| T3 u If Ui O o 1 o Corrected Deviation of Compass. *boooooooooooooooooooooooooooooooo A deviation of the North Point of the Compass to the East is designated by the sign -(- ; a deviation to the West by the sign — . From the observations given above, the following values of the coefficients of the deviation are obtained: A = — o° 5'.6 B = — 2° S7'.8 C = — o° 47^2 D = +7° i^'.z E= — o° 25'.5 o 1 ++++++ 1 I J 1 1 I ++++++++++ i 1 1 M Deviation of Compass in Degrees. 1 ++++++ 1 MM 1 ++++++++++ 1 MM Deviation of Compass in Points. 13 8 D cJ |J w a a a a w a w w' w w w w w a w w ^ ^ ^ ^ f %• £ $• f ^ 2 f ^ -- ^ («N-o\oO^'F',OC^'-«O r-»^O r»>O oo •* ^O r^"-o r— r^oo rt-o O o O ONCO >o o ^ i ^ Z 2; 2; '/f, [yi ',¥• \in tr. 1 c/5 -ji c/i c/i c/3 ui c/j c/i c/i t/j c/i t/i a: i aj t/; 2 2 x5 Z i5 £ 2; Assumed Magnetic Direction of Ship's Head. 55 w' W tn OT' ^ • •>'">, >> • 2^J^Jk-J^.'h-J J iririri 'S'>'''*''>''>^!7'^^^^ REPORT ON o Q a o CO p H E o in i u S N 3 ..» vo e SgJ - s o" fc « u X S v- flj O II (S t! f J § Corrected Deviation of Compass. eviation of Compass in Degrees. viation of ompass in Points. De o « II S.S 8 3> i O *+ '-O C*M "- N O ON t-» w> «* « 1 +++++ 1 1 I 1 M II 1 1 1 1 ++++++++ 1 1 1 1 *O w> O "^ 0 »•• c*j ^ *N« O »• N O w> O *^> O "•> O "^ O w> O "i O ro~ ^ m« ^J-rO*- *fr rO- *O O>»- — N O Ost^w>— ^ 1 O «i O w. O ""> O "•> O r^ •«$• «r^« Tj-ro u-iioM O « rou^Tfco 1 +-H-++ 1 1 1 M 1 M 1 1 1 f^OO «- ^- O*O iomfO"l^-»'>'vl»- O\O »-t N rooo OMO fO O ^ OvOO 5 00 \O 00. O.C W to + -5 & 'S C U ta ^ ' w I •£ t)3 .3 -s 9 f> 1" PQ N J.«|.2 S I o H g X Q I 1 866. ion for 29 I ected Deviation o Compass. Corre o.S . a eviation of Compass in Points. tS- & • S»l •Sis II boooooooooooooooooooooooooooooooo >«'l-'*-">«*M>"U1TCM-i^>'*Ni-imif'J-"T-">nThN~io o ^J- ro "- « f} M "- r^moooo wOOr^r^OOOdM-^J-NM fOvO "^ t^O t^ t^vo Ti- ll + IIIIIIIMl"lllll +++++ 1 1 1 1 1 1 III 1 1 + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +++++ 1 1 M M I H + .& ° "• I ^ & "£ O '8 >- | .2 »> II • °0 ,- f S," c •« c > •5^ £.5 4) flJ rt • i* • • MAGNETIC OBSERVATIONS. 159 u o S5 Q < O U 55 § 6 o u K H S Cd H fc. O w S5 O U P O a Q PJ o b. en 55 O I o Corrected Deviation of Compass. "bo ooooooooooooo o 1 1 ++++++++ 1 ++ 1 1 t i •s ^ s- ^ o c ^5 1 .- 5 Deviation of Compass in Degrees. o 1 1 -f+-f+++-f-f 1 ++ 1 •° £ •a * 1 « § -S ^ M % 2 •o -3 r (fl fune 9, i86( Correction for Deviation of Compass .in Points. r; ^ W "^ 1 1 s 1 i s •*» v' ^ 5 . cu 'G H 3°o - 1 C3 73 bo " •a ,,; Kf jn o o •1 f.a C l-o 0 e-c *J U) 0 fl'l c3 r! *l b .O i *&*& mmt/}{/}t/)^iA'£-i&'&'AA S.S** Wl «f!1 Correction 1 y w '•£ *Qj la «^ - S °T3 _. c OJ £ on; .^ ^ . H tn . . .^ ^ • . •!**« JWfc • ' i^§^ **!1 |{|1 .S 0 ° V >'S v A p-~ 1 S g ^2J W W H fc £•& £ri w H W aj ^g ^w £ & £ ^ ^ w ^ ^ ^ ^ ^ ^ "^Q iiJ2 ^ 53 r" i <3 ^^^^^^HWWHW^^^^^^^^^^^^^^&^^^^g^g <-SHg rt » 73 1 <"• "boooooooooooooooooooooooooooooooo + 1 O III ^a 1 1 1++I 1 II II 1 1 1 1 1 1 ++++++++ 1 1 1 1 1 1 1 1 c >- tJO " u " — .H .^ 'o V G 3 1 Deviation of Compass in Degrees. |||+ 1 1 1 1 M I M 1 1 1 ++++++++ 1 1 1 1 1 1 1 i* !£ oo 3 § * I s °° '8 C ,'. ^ •3 0 || -ro vd ^§ 0 E- oo o M "ZJ D *| U r S Deviation of Compass in Points. I 1 °° 1 .|P »| a ° 1—, v. ^ 0 fri % *- l'5 "3° §,+ n H u ^ "i 1 H W W W W W W W W W W H W W W W ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _rt . W ... w> - 1 g « "S SI'S "" < y V S1 O S 3jhG 55 ^' £ ^' ^i X ^' £ 2 tfl oi co en en ui co t« c/i wi ui tn in en en ui IS 2 & & £ fc ^ fc '1^1 v« H ^ sl^'o Correction 1 O ui '•" *Q- o> .« l™_j fcH **-" ^3 S° g •s §s £ '5 _^ ri _ _ M. - . . .1 t>-rf ^'J i>a PH ^"^ ^J m W ^ Jr*C/? ^ C/3 U LiJ U C/^ ^"H-* p*f/j [?{?[? £ '1 e ° "°'> 2 rt 3 U r. i- Z tZ Cl« CxJ W W W CO ^3 C/5 ^ t/5 V3 ^3 ^ C^ ^ t^ r** r** ? r^ t^ ^ " " " ^ " a -a 1GO REPORT ON o c a o u 1 M c a o u o 3 s i. E § u Q bl H O U u a i I H Lin St. Thomas, November 18, 1865. Object = 4- °° '<>'• Correction for Lu Corrected Deviation of Compass. o in s. Devi Com ip's Head by Compass. Assumed Magnetic Direction of Ship's Head. O — — — N.I- — oOOOOOOON««Mwr^WN'-"'-"'-'OOOOOOO I ++++++ 1 I I 1 I I I I +++++++++++ 1 I I I I I I ^-*c-*cHoe "^OOOOOOOO rn(QoH^-|fHx-43c-^oo oooooo SwW. W °o 15 is November I, 1865. '. Correction for Lubbe Hampton R ction for Object = -(- Corrected Deviation of Compass. OOOOOOOOOOOOO'-'NMfr>^f^O^1O»'>mvOTt-^fr^»-H* — MI-.O + I I ++ I I I I ++ I +++++++++++++++++++++ o in . lues C Deviation Compass Points. Assumed Magnetic Direction of Ship's Head. Compass to the East is designated by the sign -)- ; the following of the coefficients of th — i° S2'.o the North Point West by the sig rvations given ined : e e ai viation of tion to th the obs n are obt A = e at m io MAGNETIC OBSERVATIONS. 161 u o w § u H 1 •0*° »; a a ffi 0 O « o BO ++++++++++ *5 § O 0 £• 1 1 •s.s . CT3 |^^ •a 1 2 41 O ^" g e „ w o IS g 1 « o IH 1 §•& .& 4 - vt 1 8.M Qu a) ^.^ ~i~ M •a o II o 10 h ii -t- o u u n • Q °~ •a * ^5 . ^i ** - || «3 2 + g II " 0 ,; W ^ HvH«jW ^ . y^ ^* *1* 0 |fa : U u S So ^3 HO.^' W W W ^ JS'lq ^H •s^i ?t '€ En ^ ^ ^ ^ f, W W W W w li-a „« & t^ *j O .. « ol'Sil a O US ^^ > e + o i !•> MC/3 . . iiiii 3 s-3-s ffi • •'x ^. • W' " • . .^, V,>' • •£'£> ^•tefe'TH' .2 - u £ •S BJ3 S ^§K pWWj ^H^ujH^ ^"H W £ & ^ -° "^ ^f-I ^ . . . . . * H •s.2 a £ -g a o if " r^ " W H W ^ ,J~1 C/3 jXJ C^ pj flj plj y^ -Q ^ _O C/5 & I? I? frl ^ ^ *^ J~\ * f 1 1 ^ 0» r£ -^ la ^H J2, ^ ^( y^j ^ fij \~f\ ]T| ^TJ ^ ^ C/3 C/3 C/2 V3 C/3 C/2 C/3 CAJ C/J VJ ? ? ? ? ? 2 2 2 X ?H " ^•a* S o! -O •0*° n .* OJ + -s «j a S 2-3 s. - go o B.I a 's <» 0 '> 0 y u(j O 1 g 0^ (5 fc. 1 O . II o.S . rtJ tj" "S § \n i> a 3 O 'S cu & .& 1 o-l M-2 •s s^ SoP ftO 0 1 "8 II « •-1 « f 5 November rrection for Li Deviation of Compass in Points. M W v 1 1 1 ! » a w rt *o w o fu ^ 13 U - S ... J . o y u - n 1/5 N £*•• u . II t— 1 •S i > a £ o rt t/5 •o '-2 3 1 0 a la 73 , s w? 1-Vd w II TxU m ^JS-S II t— 4 C 2,'" 2 -« M 'Sfc'B Q >> JD as 3-° S ^S-S^' „ £ "3 a o « •1^ t| u 4> rt „ W 2 1 l> bcc/2 rt ._ . ^ ' «5 & £ ^ fepq WOT uj*'*'^ KJ ^ ^kj1 • • •ol^^ 8*11^ 0 a^-^ >, • • M •-»* * ^ ""^^ C/3 ^'^r^ J^^jjffi S e •£ •" 0 ^§x H ...... ^H >^ ... ^E"1 >, ^ >.* j?." c/5 ^c/^ ^»5 fe ^ ^ ^" ^(^ £'i s.2 11 ^III ^ 01 rT -r •y. k. ^•a* S w w' w ^ o > U2 t«u5 OT en c/3 + & ' U) W5 Cl •- u tj • if 00+ "o 41 (£ « | _•£ " e ' 865. n for Lubber Line 30 Bahia, Decembe ect •• -f- 2° 30'. Corrected Deviation of Compass. of in . D C I 6- .2." «.£• 4s « o o o x ** M °* H 000000000 ++++++ 1 1 1 1 55 « KuW^ g ia w u w ^ ^S 1- :'&>• I1 ^'c« .?;: "-'•'"•^S-. > > •> + v, I 1 ^ 1 8 T3 • Uoo •" & 2 « S.2 ~'J « MAGNETIC OBSERVATIONS. 163 u o p o p U I O U H R P < P « OS O PH H a u C u H M X 1 M P 0$ s o -~ 13 H o P^ .. T3 "S — .. — . cfi O 0 •3 ° • tj O rt £.2 S o ?• o § ffi g "3 S.& a •3 « C -^ Q-- — u o QJ ooooooooooooopooooo o^o oooooooooooo O ~ r^fOf^r^Tj-"tTj-f^cor^r^"H ro-^-rJ-^-Tt-uiTi-'.i-r^jnfOO O — "- — ~ « O I I I I 1 + _- r- o "S.S . "3 .3 § S 2 •a 3J J» 0 to ^00000000^00000000,0000000000000000 g^ ^Z^il? W WU W W en c/j en tfi c« en en en c« x c« en ^ !E •« § OJ y W t 0 u bo • . « O c rt o '5 = •.2 : o"o ' u a " a S.2 164 RETORT ON Q I O a O u o o U u o 2 g 1 8 c E Q u g O £ I I u Co Dev Deviation of Compass in Degrees. of in iation pass Points. Dev Assumed Magnetic Direction of Ship's Head. ooo oooo o o 1 ++++ + + +++++++++ 1 1 II 1 II W • H.* w W W «5 ^ c/J o5w-.fr -(- th th ie ted co desi East lu C to wi follo 4o'. E -f-o A deviation of the North Point of the Co deviation to the West by the sign — . rom the observations given above, th tion are obtained : A = + o° 2i'.o B a F devi Corrected Deviation of Compass. ^oooooooooooooooooooooooooooooooo ft ir> S> S> \n \n \n \n n f> m >n >^i ui >o ui >o >n ui ui >o u-> n m of in . eviati Comp Degr Deviation Compass Points. o Q Q o Q Q W > fc 0 •> '* Z U ign ents lowing values of 3o'.o C = E= — o° s'.2 A deviation of the North Point of the a deviation to the West by the sign — . From the observations given above, deviation are obtained: A==+l° S5'.2 B ° MAGNETIC OBSERVATIONS. 165 W U o X o i o u g § M H ^ O O U p j p a <: I H H O H O p I H b) P I to O I 3<. 0 " § - " .asfs1 £ IQ "o.S .5 g ' — 3.2 55 C 0 o „ o ++++++++ fOr^^-^rJ-Tj-f^fOM« O O O O O O O OOOOOO W c/j y^ Ha _<, ^ 2 Ed" W -toW r : . CO -to (/I w- «*» K;OJ "j?«5&:*Lf te'fe-«tfei >• .,• W co 64 'S &4J O N •3 i ^- '« I 9 U O C II w ° u" ' 1*1 -• •5 M »• *^ O M a* '-5 ^3 i >o a VO § CO '3 • a o O J c II i fc.2 S o > o ooooooooooooooooooooooooooooooooo -*+rr •« •-• « « u + o.S . i <• u .2 S3 « .a g-y £ 3 a °.S S »> »' O W) *- d b ip's Hea Compass |€ ^ 2 ,-N §3s u « 1. I I ed M ion o Hea ooooooooooooooooooooooooooooo «p*r*h**M -u->u-miN ir>r^uirOT}-»oi-ii-. I I I I I I I I I +++++++++++++ 1 + I I I -te-*x-*E -*c-*c-*n H»H^'^x<^ooc^ooHMHe«-^^-^*i^«M-»Hy-<^ I I OOOO OOO O O O O-W + I W + -3 ^ IE ." U »« O 4- a w d * 9 i. of Ijs*! s- "B jc ^ 5 II T) b. O tn Z O H Q u o •K I & I P "3.S t I O a a o •§ I •s.s |a( si K S. If 43 °00 1 + OOOOOOOOOOOOO "^vo r*iMNP^NNOOOOO ++++++++++ I I I w Q... — ^« — •"ll«HW^ffiB«n^^^ ^ »*»;*S?SBt4p4w»iJ|k5»5oioJoJo58u5«J«!^^3:?§ ''•'•' '" '" ' + -5 & o u r-» X 1« I £ o il'S . »» 4J O •• "• u S.2 "•> s « " ' MAGNETIC OBSERVATIONS. 167 o s o < J u •z, g c/5 I o U S H H O n O S-1 1. fc.2 E o^o 1 I I I I I I I I I I I I I I I U +++++++ 1 I I M I I I .0 c £ 4- S. II 4-1 21 en O | i £§Q o.S ||* - 1 J =r S .2 " O 0 O O O 0 I 1 I I I I I I I I +++++++ | | | | w e <— tjO O I | £• (6 t 1 S 2 rt .1 I o S u a * I :i * \£ ^5 l~ **- « ills •«-S«l-9 tf 00 3 I I S b QJ O £ ^ ro O K h i c S u O rt u '^ (X t.2 e o > o o .5 a » 8 ill > S /-x M In i M 1 1 1 ? j i !++++++++++++++ 1 1 o.S o a -2 Irl ll" HI S^53 isi I M M I I I I I I I I I I +++++++4- 1 I I I I I w ".a . + •s 5> "3 » a •f jo w .S-K g _»'& + £ *5 e o .15 •? --r « 168 REPOllT ON 1 I u S g a o u o 3 u H en | i Q td v o 3 Ell o.S . c «, S O g u Ift "B.S Assumed Ma Direction of Head. oooooooooo wj 10 *n •Min^-Tt-HP* «««fOM«OO«M +++++++ 1 I I o o o o o + III a *«s' W to + « " •s .1 P S - & -S 7 '3 W o I 111 6.2 1 g o.S .2 o o + fi 6 X * s •£ i S ^ ' -5 i jfi U II W S.2 MAGNETIC OBSERVATIONS. 169 O IE P «« O J U z O (d K g w 9 a, O U O a. I o" .2 S ,o 3 O a c! o O rt OJ '^ — - b.2 S o > o £§« Q^ _rt £-•; > S £ g S! ed ion, He A Di "boooooooooooooooo n-^-^-t^t-rJ-^-N -^ M w N w 4 w N 0000 0 I I fc H ^ ^K> W . . « J ^ W B W J5 O. ......... . .< • O + - '•» at •S .« s^ "3 J? ifi o + V i •s + ba . _c "" *r ^ 2 13 •£•§•§ Ijjfi •r I " o •sin H u h O g 5 S I Q c: g OT O < ei ^2 CO M o" CJ 1" rj cj 03 o "ooooooooooooooooooooooooooooooooo -' - ++++++++++ 1 1 1 1 +++++++++ ++I 1 1 1 + C t« ,,: -2 rt •§ oooooooo ooooooo I M M I II MM II <3 22 November, 1872. « § e; no REPORT ON y - < • 3 a u I CO D a H O a Q 0! I Id S •n O H E a • X o >: x s ul a / I - H _ - rt o 2 w t >> .1 "c .« rt ^* en o ation of pass in grees. Dev Co m De a C/3 ic 's agne Shi med ction o Hea 1-g22)008S8000?,82222°28i-5-0,08gSS8°r(5,$ : + ^ ~t*t*ir) t^.00 CO OO 00 00 t*- vn N K «. ii*uman>-+*-+r-1«-t*xt» H»4e*»"»P«l»'»««««»«'»««»»'*«-"l O O O O O O O 1 1 +++++++++++ » jWW^ »^^ w w w w £•; >> >*•- •8 S - rt rt H » •3 2 , I « a « 0 _ « •" So c .- c • -g .2 •• ° tSI"! 7 ? £ £ 1 ^Jll Video, January 24, 1866. — o° 13' Correction for Lubber Li Mon bject "boooooooooooooooooooooooooooooooo •^ >M r^ rn f*> ro ro •^•^•^I^I^"N«M"N>^IM»«^^ ^ f^ f^ HH O*-NN-^t-^-Tt-^J-«NN^i-iM«*.«O«^^OOO^fOf^<*<*fOf^f^fOO I +++++++++++++++ I +++ I I I I I I I I I || II Deviation of Compass in Degrees. Deviation of Compass in Points. + ; the t is designated by the s es of the coefficients +++++++++++++++ +++ III 1 1 val 5s'.4 C = — o° 4 E = — o° 2'. 2 ' f'- i >5 Z ^ ^ ^ 2 w W W W W uj uj x c« c« Lo t« tn c« cox Assumed Magnetic Direction of Ship's Head. S5 W o :~ <~ K%%!Q%%b)UHHH vS co' x •/ -s> deviation of the North Point of the Co viation to the West by the sign — . rom the observations given above, th iation are obtained : MAGNETIC OBSERVATIONS. 171 3 >j U O CJ w j u S H H H Q H en u t/i a O •o"3 • S S 8 ^000000000000000000000000000000000 .» 4J + « o' || ".2 a s « e- 5J<3 o & "5 '« 01 Ja = •5 u >, '« c 3 1 3 Deviation of Compass in Degrees. o * ifi "S S °° 1 1 : i •« u u Deviation of Compass in Points. II Ml +++++ I | | M 1 II 1 § r« a 5 u"0 •5^4- * 1 "II •> — v'r, a =5 ^>a $1 2 + ~* II u J! £ •Sa OJ rt w& .w O ^^. ^^ ^. ^4J" . d, « E „ „ a 5 7 6 ,' $ j " C I J »« 0 Cd Bo c-& N u "a1 .£^ ^1-a si ririss JB« ^ w a ri oi ^5tn«^-^ ^ £ ^ H«-I^-S ^ ^ ^; ^-^ (5^.§ t o ;*«* gi«5w5o5«5o5«5»5wo5o5»5^^^^!Z5S!»5S?»i>5 ^-M t! s-° s -A0 ^s-S^o Correctior o 6°| S§S ^•B." s-* s-.- -i s,ri-^i k- .,*•* «,-«• u >. rt oj Vi J= ? > C " " oj 0> 'd 1 ^•5^2 u c ^ ° ° H 2 " w S< l.s*2 isi g ^ w w w ^ ^w ^-to a a w ^ ^-D £ri ^-^^ ^ -^^ ^' £ ^' ^ ^g S « £ .2 ^'5 SS 1 ^^^^^^WWWHWco^^^tOcoco^co^cO^^^^^^^^^^^ <-Sn,-g rt T3 o' Corrected Deviation of Compass. ooopo^o^oooooooooooooooooooooooooo o 1 +++++++ ++ H 1 f 1 1. f H + -s ? *O en - ii o •o ° l»* :§j CO c i-i 0 *1 S c°, G rt B| * " -Z ^fe -te^2i a a a a £•-**&: w a a c/5 ^-*»«^ &' £' ^' ^ •^-"•^'^ ^' & ^ JS""* I. * « 1 ^ +r~ « J " R | -| «^ ^ d i J? 0 1 55 ^ ^' ^ ^' ^' fe ^' W W W W to oi w to 05 to to oi to tv5 to' ^ ^ ^ ^ ^ S5 S5 S5 S5 S Correction u t/j |r& f=« . a^l T3 S T1 > ^ . .^ . . • C fi J a 1 1*^5 H u gja^aaa^^co^c^wHfjj^ ^-g ^-^ ^^^^^a"". .'''''''z;-2o i-i 1'»u>vl**t'OO««WO>"O»«««i*««««>'>** | I | | | | 1 I I I I I I I M ++++++++ I 1 I I I I I I I 111 u d s s- « c "o-U 1 agne umed Ma Direction of Ship's Mead. c^coH* H«-+*-1N'-«N"-*» HOCHCO-HV*K-*N-*M-^K*O I I °°+++++° MINIM M . . . vi^S + - "S 8 K .3 H « u - <= C ^^ £ S C _£ 5? '« II l ' "boooooooooooooooooooooooooooooooo — Lr>*ou-ji^u-iu^i^u^w^—«"Nw»^"^N fOr^fOfOM"^"^^-^-^*'—^ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ++++ II 1 1 1 Deviation of Compass in Degrees. viation of ompass in Points. H»H»-to-fcO-teH*fllOOC"jQO-*N-*N-*Mri|'» 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 ++++ II 1 1 Assumed Magnetic Direction of Ship's Head. ign -f- of th nts ffi is designa th g — . bove Ii 6'. A deviation of the North Point o deviation to the West by the sign From the observations given viation are obtained: A = — 2° 3i'-9 MAGNETIC OBSERVATIONS. 173 M 8 a u a o Q o! a H 05 O w Q O a a vo O ian Francisc a = — o° 45 1 u o > ,o P n o. to .2 p SF £ §a •3 8 g .2 §-'3 ip's Head Compass. S U tn - '*'&• s°1 •sis 1 *H •-• rj- WWW o 1 1 miTTi m i iTi+++-++++++nci TTT11 1 I +++++++++ w. ^- . ^^-a waw ^ S W W en I ! U< o + I a JB-8 S * S g S » o rt o a o •o ° • i: a s 111 "o.S . 'B.S .a-U en I 1 ooooooooooooo +++++1 ITTTTTI +++++ M 2 £ ^' ^ 2 v W W w W W en t/j v5 en t/j en en in tn en en + -a ta ° '3 jj •S ,«; .^ 'G ^ IB £ 8 ^ flj .& 5 + jfllj 2 * i 3 1 174 REPORT ON J j : /. y. o 2 a U 5 c/5 S5 O B. O CJ 2* O a: I Id S H IK O in § Q u S 2 z I Q a: 2 in § 00 0 - '5 U W la V i + I i J | 8 1 ooooooooooooooooooooooooooooooooo ««^NNWNfOror>)"rOfnr*'>~NW«Tj-NNNTj-' « O O O « + 1 ++++++++ 1 +++ 1 1 1 ++++++ 1 1 1 1 1 1 1 1 1 + .2 S 2 s e-« I IS .2 §"'3 f: 5=* S.& + ++++++++ +++ ++++++ + -s 5 u o f) •£ o •B C O 'S s I a £ E u £S £.2 'I ,° .2 T * 5 rt -o o.S §2 "5.3 0 J» •— n s'g !.§ > C + D 5 H II u— X 0 4 I O •£ Jb J3 ' •Sill MAGNETIC OBSERVATIONS. 175 o S j u w a H d t/1 O u (5 a S o h O J-, O Ji o •;: a. fc " £ .55 o oooooooooo N Wl ^ cy^ t^GC O 00 *O 10 t^ MOO 'fixl-i * p1 S° |lq •gg^ Pu o in v.'o. § u s s <3 - w H^H WWW £ * W •- u • + 5 u & -5 I ! 3 '? 0 M + z « -I •• % Ji^llj^ Id a I B; u S a £ g o K M m O o .g I § •S ri CO BO! w '^: &. fc.2 £ o > o o.S . .2 fo S; S ^ *£ II K -*• W 2; ^' >? ^ ^ ^ W W W W W en ui en oi w w t/5 en ui en + I W o 'i o « « I I « 176 REPORT ON C/ - I o g V 3 I S-3 O.I ^ u ri .?* « M c + £.25 5 £6 •o.g M. ill "o.g (5 "6 O O O O O O £ O^ O^ O^ O^ O^ O O O^O 00 CO *O r^oo i^l^u->ioioioio*t*J-rof>Th umed ction o Hea< Ass Dire (4 w w w a £•„ to <» faHoo Hao-^wtoWrtHw-lTC-ft* o o o o o ++++++ I I I I I I I I t/5 w -"^W"-* H^' CO -h, w- . co 2 : ». I i • •a .s1 - s & v w "3 • * Z •o u c .li, aj _ET w o r- rt C 0 '> 0 •ill 1 if 2 <" II 0) .S" C J3 Ul*3 Assumed M Direction of Head. + * JS* i£ v 1 s 1 1 «2 U°o - +« ' W a* t >*.» & S~ O *£ 43 ,O ^ ~ o o I5U£. .«§-s« iiii •°'> S S <•££•>: 01 tf -O VO 3 vo i-l 00 u " v2 •* 3 ° o « ai ^ c^ fc.2 E o > o ooooooooooooooooooooooooooooooooo o M IOVO OO 00 00 00 ONOO w^ I I I I I I 1 + £§Q (50 o.c o S JS •s S = .2 ^'3 £ o ^ Q^ « Srfrf.fr a° •^3 c ' 5j o 23 November, 1872. tSa«r*HMHw*P.^«iMI O O O O O O ++++++++++++++++++++++++ I I W W W H W ** *&*&*?*?**** + -3 & "3 J, a "S 8 I I a w- •a o •2 S IQ «5 w S 5 '5 o I obU U " f l'l O _ M OJ ' S °. M " o + III s l 17S BE POUT ON z a z Q 3 U z o en Id H § — o U Id 3 9 o u< Id S i Q M S S a 8 M § :< 1 3 i 0° J3 + •3 n u • ecti C De C Deviation of Compass in . Degrees. Deviation of Compass in Points. w <3 i 3 -+ 'SI < •booooooooooooooooo oooooooo^oo oo oo °0 + 4 j i i I I I ++ J U 2 I rt 1 W 6 + II "~> u- II -0 ' s «& -a , rt o f§ + u S2 II J= J3 .0 " 0 J= «; . « B •§ Deviation of Compass in Degrees. •3.2 m i ooooooooooooooooooooooo M •* S> 5> N •*•*•* t Tj-NWU-lfOn D " + -5 V ~ S ifi o. §0 o^ W T3 O .2 8 J; bfl N I 2 I S|| I 3 °:w 0 . »5 S5»;2i2Z!<';wwauui(ntn(nc«(nScntfic«t«tn •5 I > O >- ' oca ^l^\\ •" u u S •< 'o'SJ^ e o ° S .2 " « S 3§5S £'5 s.l "° '> 2 .« W MAGNETIC OBSERVATIONS. 179 « 8 p U SB o P U c5 u: tn < ft S O U Q PS < I O H > a Q bl H pulco, June i, 1866. + o° 6'. Correction fo A t •o o . « e £ t> 0 « • o s in es. Deviatio Compas re om De Deviation o Compass "in Points. agnetic f Ship's d. Assume Directio w w w ^ X w + * c **- tJ3 O "5 in 4) -ti i 1 ^ 1£ S o I 8 a | , 1 v" E 8- 4. 866 Panama, May ct =+ o° i'. C 1.81 ^1 o > o •2 S S viation mpass Points. ev Co J" o CXCJ i OC'-'-'NNNW Ot--'ON««h-"^M'^'iri"^^"'^''-O'-NN'~IMH*0 +++++++ ++ ++++++++++++ 1 II 1 1 med Magnet Direction of Ship's Head. Ass + 6 ID "S ' — 0) I S ' -w , + 5 S * i ^e gi « 180 REPORT ON * c' £ < U 1 HH trt Id O O U I ! £ Q u g • .i Q ! I C Deviation o Compass in Points. ic 's 0000000^0000000000000000000,0 O'O 00 W w -{- by fEc is design es of the Eas lu C 2 s to follow i6'. E e . above, A deviation of the North Point of the Compas a deviation to the West by the sign From the observations given deviation are obtained : A = -f i° B ° 3'.8 Corrected Deviation of N | | OOOOOOOOOOOO TfS"1«>«r^ronN.tO o\ l^vO Th CO O m rrt ft ir>\O f^ +++++ 1 1 1 1 1 1 1 H^H-rH^sleB-**-** +++++ 1 1 1 1 1 1 55 sign -f- C i' of th MAGNETIC OBSERVATIONS. 181 The observations made at stations where the deviations had been determined on all of the thirty-two points were first discussed. For that purpose the values of the coefficients J.H JB,, C^ J5,, E^ for each compass, at each station, were computed from the deviations on the true magnetic points by means of the equations given on pages 126 to 128. A specimen of the form employed in making these com- putations is appended. It sufficiently explains itself. ADMIRALTY STANDARD COMPASS. COMPUTATION OF COEFFICIENTS B, AND C,, FROM DEVIATIONS , OBSERVED ON 32 POINTS, ON THE U. S. IRON CLAD MONADNOCK. Bahia, December 30, 1865. True Magnetic Direction of Ship's Head. I. Observed Deviation of Compass. True Magnetic Direction of Ship's Head. II. Observed Deviation of Compass. III. Half Sum of Quantities in Cols. I and II. IV. Half Sum of Cols. I and II, (changing Signs of Col. II.) Semi- circular Deviation. V. Computation of B,. VI. Computation ofC,. Multipliers. Products of Col. IV by Multipliers. Multipliers. Products of Col. IV by Multipliers. Unchanging Part of Deviation. NORTH. N. by E. N. N. E. N. E. by N. + 1° 40' + 3 20 + 3 40 + 43° SOUTH. S. by W. S. S. W. S. W. by S. 4- i° 40' + 1 20 -j- I OO + o 30 4- 1° 40' 4- 2 2O 4-2 20 + 2 3° 0° 0' + 1 0 4-1 20 + 2 0 0 | s, 0° 0' 4-0 12 + o 3' + i 7 I s, s, s, 0° 0 + o 59 + H + 4° N. E. N. E. by E. E. N. E. E. by N. + 4 40 + 5 o + 5 30 4-5 40 S. W. '•• S. W. by W. W. S. W. W. by S. 0 0 — o 40 I 10 — I 50 + 2 20 4-2 10 4-2 IO + i 55 4- 2 2O + 2 5° + 3 20 + 3 45 1 ^ + i 39 4-2 21 + 3 5 + 3 4i s' Is s; + 39 + 34 + '7 4- o 44 EAST. E. by S. E. S. E. S. E. by E. 4-5 20 + 5 10 + 4 40 + 4 20 WEST. W. by N. W. N. W. N. W. by W. — 2 0 2 10 — 2 O 2 0 + ' 40 + ' 30 + 1 20 + I 10 + 3 40 + 3 40 + 3 20 + 3 '0 I ST s, ss + 3 40 + 3 36 + 3 5 + 2 38 0 =1 -s, 0 0 — o 43 — >7 - 46 S. E. S. E. by S. S. S. E. S. by E. + 3 20 + 2 40 -j- 2 10 + 2 0 N. W. N. W. by N. N. N. W. N. by W. 2 0 I 10 O IO + o 30 4- o 40 + o 45 + 1 0 + i '5 + 2 40 + i 55 4- I 10 + o 45 | fe + i 53 + i 4 4-0 27 4-0 9 1 — 53 - 36 — 5 — 0 44 Sum of 4- terms = + 29 8 Sum of — terms = — + 9 7 — 94 Divisor 8 + 29 8 8+°3 B, = + 3 38.5 €, = + 0 0.4 N. B.— Easterly deviations are to be entered in this table with the sign +; Westerly deviations with the sign — . REPORT ON COMPUTATION OF COEFFICIENTS A,, D,, E,, FROM DEVIATIONS OBSERVED ON 32 POINTS. I. II. III. IV. V. VI. Half Sum Half Sum Computation Computation of of Cols. I of D,. of E,. Quantities and II, in Cols. I (changing Upper Half of Lower Half of and II. Signs of Col. II.) £ V Products of i 0 Products of Table A. Col. III. Table A, Col. III. Constant Part of Quaclrantal .£• 3 Col. IV by Multipliers. tic 3 Col. IV by Multipliers. Deviation. Deviation. *q z •f «° 4°' + 1° 40' 4- ° 4^ 0° 0' o 0° 0' I 0° 0' 4-2 2O 4- ' 3° 4- 55 4-0 25 s, 4-0 10 ^ 4- o 23 -j- 2 20 + 1 20 + 5° + ° 3° !>4 + 0 21 N 4- O 21 + 2 30 4- i 10 + 5° 4-0 40 s. + o 37 s» 4-015 + 2 20 4- o 40 4- 30 4-0 50 I + ° 50 0 0 0 J2 10 2 10 + ° 45 4- i o + 27 + 35 4-° 43 + ° 35 i 4- o 40 + o 25 — S, _S4 — o 16 — o 25 + 1 55 4-« '5 4- 35 4- 0 20 s, 4-o 8 -s* — o 18 Sum of 4- terms == -f- 13 22 Sum of 4- terms = 4- 3 I ' + 59 Sum of — terms = — Sum of — terms = — — 59 Divisor 8 + '3 22 Divisor 4 4~ 3 M 4 0 0 A, = 4- 1 4O.2 D, = 4-o 47.8 E, = o o.o NOTE.— S,=». 195. 3. S3=.5s6. .98i. The resulting values of the coefficients for each compass, at each station, are given in the following tobies : COEFFICIENTS OF THE DEVIATIONS OF THE ADMIRALTY STANDARD COMPASS. STATION. DATE. A, B, c, D, E, Hampton Roads . . . St. Thomas .... H.ihia November I, 1865 November 18, 1865 4- i°37'.4 4- o 14.6 + 1 AO 2 4-9° 4'-6 + 5 45-5 4-1 18 ? — o°33'.i + o 33-5 + O O.4. 4- O° 29'. 2 4- o 3.2 T ° 47-^ -o° 7'- 5 — o 48.2 o o.o Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 + « 32.8 t° 3Si 4- o ic. 6 + 3 4-8 -f- i 20.6 -f- I 2O 2 + o 5.8 — o 40. 6 — o 6.9 4- i 19.5 + o 53-5 4- o 54.2 4-o 14.5 4-0 1.5 — 0 IO.2 Callao April 29, 1866 + o o i -j- 2 21 I — o 1.8 4- O ?2.? 4- o s.s May 2O 1866 4-1 21 + O I .O + o ^s.o 4- o 8.0 + O C 1 4-o 56 8 4- o 8.0 San Francisco. . . . June 23, 1866 — o 39.6 + 4 53-2 — I 15-4 + o 51.2 + o 5.8 COEFFICIENTS OF THE DEVIATIONS OF THE AFTER BINNACLE COMPASS. STATION. DATE. A, B, c, D, E, Hampton Roads . November I, 1865 4-o° 27'. 5 4- 7° i6'.S — i° 14'. i 4- '° 39'-2 4-0° 6'. 2 Itahia . . + i 20 8 + e AT f, 4-o 78 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4 1866 + ' 3-1 — o 24.5 + O J. O 5 43'° + 5 30.6 -f- 5 44-4 4-1 58 8 + o 41-9 — o 14.6 4- i 57-5 4- i 58-5 + 2 1C — o 42.5 4-0 0.2 O O.2 Callao April 29 1866 J_ 2 7 C + O Q.O o 18.0 j ' 9- 5 O 17 2 San Francisco .... June 23, 1866 — o 35-2 T^ 3 4-4 4-3 28.2 — 2 13.9 4- ' 47-5 4-0 10.2 MAGNETIC OBSERVATIONS. 183 COEFFICIENTS OF THE DEVIATIONS OF THE AFTER RITCHIE COMPASS. STATION'. DATE. A, B, c, '. D' E, Hampton Roads . St. Thomas .... Bahia November I, 1865 November 18, 1865 4- 7° 40'. o + 3 14-4 -i- 8 47 I + 11° 26'. 5 + 8 .26.9 -1- ft CC fi -1° 44'. I + ° 40-4 + 0° i5'-5 + I 54-2 -o° 54'. 5 — o 37.2 Monte Video , Sandy Point .... January 24, 1866 February IO, 1866 + 8 "18.4 4- 4 3-2 ° 57'2 — 3 25.6 + ' 59-7 + i H.5 4- o 14.2 + ° 58.5 + ° 7-5 Panama . . . ... Acapulco May 20, 1866 + 5 20.6 + 4 3-1 4- o 14.1 0 10.2 + r it R + ' 3°-5 + i 17-0 + o 52.0 — ' 33-o San Francisco .... June 23, 1866 + 4 "-6 4- 6 46.2 — I 31.4 + 2 28.5 + o 47.0 +0 21.2 COEFFICIENTS OF THE DEVIATIONS OF THE AFTER AZIMUTH COMPASS. STATION. DATE. A, B, c, DI E, Hampton Roads . St. Thomas .... November i, 1865 November 18, 1865 December 30 1865 — i° S'.o — i i?-5 7 ^6 Q - 4° S3'-o — 3 °-9 — 4 28 6 — o° 9'. i + I 2O. O + 5° 35'- 2 + 6 49-2 + o° i?'.o -j- 0 12.2 5-5 Sandy Point .... February 10, 1866 April 4, 1866 — o 5.6 2 l6 2 —2 57.8 — 4. S4. I — o 47.2 4- 7 10.2 — ° 25.5 April 29, 1866 — 3 56 2 * ***i 2 0.6 O 4Q 6 I 5 3^'5 -4- s • 6 ; F u 37-5 May 20, 1866 — 2 60 — "? 4.7.2 + 1 4*1 6 -j- 6 21 2 June I, 1866 • •• 1 112 — 1 2; 8 — o 08 + O 21 8 COEFFICIENTS OF THE DEVIATIONS OF THE FORWVRD ALIDADE COMPASS. STATION. DATE. A, B, c, D, E, Hampton Roads . . St. Thomas .... November I, 1865 November 1 8, 1865 December 30, 1865 + 2° 8'. I + o 50.9 T 2 9-4 — 2° 28'.4 — o 35-1 — o 6.0 — 1° 52'.0 — o 46.2 — o 34.1 + ° 4'.2 4- iS-7 + 15-0 0° 0.0 + o 20.5 T ° '4-5 Monte Video .... Sandy Point .... January 24, 1866 February IO, 1866 April 4, 1 866 + 2 7-1 + 2 25.6 + ' SS-2 + ° 57-2 + o 58.5 4- ° 30.0 — I 5.0 — i 54-4 — o 53.9 + 23.0 + 47-° + 4-2 — o 9.8 — O 20. 2 — o 5.2 April 29, 1866 4- O 21. 0 4- o 40.9 — i 36.4 + 29.0 — o 6.8 May 20, 1866 4- 2 15.2 4- 0 I.I — I 22.1 + 21. 0 — o 6.8 Acapulco June i, 1866 + i 8.1 - I 28.4 — ° 33- ' + 52.8 -f 0 10.2 San Francisco .... June 23, 1866 4- o 40.6 — I 54-2 2 25.1 + o 58.0 + o 21.5 COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD BINNACLE COMPASS. STATION. DATE. A, B, c, Di E, Hampton Roads . St. Thomas .... Jiahia November I, 1865 November 18, 1865 December 30, 1865 + o° 49'.o — o 44.4 + o 57-9 - 5° 4o'.8 — i 56.2 + o 26.5 — 2° 33'.4 — o 12.4 -o 33-8 + 2° I7'.7 + ' 59-5 + 2 6.5 4- 0° 8'. 2 — o 7.2 0 II. 2 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 + o 17.8 — i 16.5 — o 14 6 + 2 55-4 + S l6-9 + i 47-9 — o 41.1 2 II. 0 — o 46. i + I 45-2 4-2 0.5 + i 33-7 — 0 2.2 — o 3.2 — o 9.0 CalHo .... \pril 29, 1866 — i 3-4 -f- I 10.2 — 2 6.8 + 2 8.2 4- ° 24-7 May 20, 1866 — 2 31.9 — i '-5 — i 33-0 + 2 6.5 — o 23.5 June I, 1866 — 2 31.2 — 2 2.4 — i 41.1 + 2 39-2 4- o 10.7 San Francisco .... June 23, 1866 — 3 9-° — 4 4'-" — 3 34-9 4- i 56.5 + o 30.2 184 REPORT ON COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD RITCHIE COMPASS. STATION. DATE. • A. B, c, D, E, Hampton Roads . St. Thomas .... Bihia November I, 1865 November 1 8, 1865 December 30, 1865 + 4° 22'. 5 + 1 3-7 -j- 2 6.2 + 1° I9'.2 + 2 4-0 + 3 29.1 - 3° 37'.2 — i 16.6 — i 33-9 + 2° I7'.2 + 3 «6-o + 2 35-7 + °° 27'. S — ° 25.5 — o 0.5 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 + 3 23-8 + I 46.2 -(- 3 33.4 + 3 48.o + 3 49-5 + 1 20.2 — o 0.4 — 2 44.2 — i 29.0 + 2 II. 0 -j- 2 II. 2 + 2 7-8 — o 28.5 — o 10.0 + ° 31.2 Callao April 29, 1866 + 2 37- ' + I 52.8 — i 58.0 + 2 3°-5 -j- O 12. 0 May 20, 1866 4- ' 34-° + 0 12.2 — i 53-8 4- 2 10.8 — o 14.0 June I 1866 + i 52-8 + o 38.2 — 2 II. 8 4- 2 24.2 -j- o 26.2 San Francisco .... June 23, 1866 + i 3-8 0 16.2 — 6 41.6 + I 48.5 — ° 33-5 In the case of the Admiralty Standard Compass, for some not very evident reason, the variations in the value of the coefficient. J., are greater than might have been expected. The After Binnacle, Forward Alidade, and Forward Binnacle Compasses were frequently removed from their places, and the fittings were not sufficiently exact to give any certainty of replacing them with their lubber lines always precisely in the same position. This source of error sufficiently accounts for the variations in the values of the .^s belonging to them. The Forward and After Ritchie Compasses were firmly fixed in their places, and were not removed during the cruise, except at Valparaiso; but the arrangements for reading off their cards were such that an improper position of the eye of the observer might easily intro- duce a large parallax, which accounts for the changes in the values of the Afi belonging to them. The After Azimuth Compass was always taken down after each swing, and as there was no fixed mark by which to adjust its lubber line, the changes in the value of its Al are not surprising. It now becomes necessary to determine the probable errors of the values of the coefficients which have just been given. To do this for any compass, at any parti- cular station, the value of 5 at each of the thirty-two points must be computed from the coefficients for that station. Comparing the values thus found with the corrected observed values, a scries of thirty-two residuals are obtained, from which the pro- bable error of b for that station is deduced by means of the formula r = 0.6745 I [w] \OT — H where r is the probable error of a single observed value of 8; [vv] the sum of the squares of the thirty-two residuals; m the number of the residuals, in this case thirty-two; and ft the number of the coefficients, in the present instance five. Then, letting pA, pB, pn PD-, Pr., represent respectively the weights, and rA, rn, rn rD, rE, the probable errors, of the values of At, 7?,, C^ D» E» when determined from a set of deviations observed on each of the thirty-two true magnetic points; we have rA = —r=z &c. MAGNETIC OBSERVATIONS. 185 From the normal equations on page 126, we also have, PA = 32 PD = 16 £^ = 16 pE— 16 Pa = 16 It is therefore evident that the probable errors of Bu (7,, Z>15 and E^ will all be equal to each other. The probable error of a single observed value of <•> has been computed in this way, for each compass, at three stations; namely, Bahia, Sandy Point, and Panama, and the results are given in the following table. The column headed " mean value of r" was obtained by adding together, for each compass, the sum of the squares of the residuals at Bahia, Sandy Point, and Panama; dividing the result by three; and then computing the value of r from the mean value of [CT] thus found. The « r " n r » column headed , — gives the probable error of A^; and the column headed —/= gives the probable error of Bv <7,, -D15 and E^ for each compass, when these coeffi- cients have been computed from a set of deviations observed on thirty-two points. Value of r. Mean r r Compass. value of r. i— »/~T Bahia. Sandy Point. Panama. Admiralty Standard ± 9'. 8 ± I 2'. 2 ± n'.3 ± n'.I ± z'.o ± 2'.8 After Binnacle . ± 25.8 ± 2O. I ± 26.2 ± 24.2 ± 4-3 ± 6.1 After Ritchie . ± 30- 6 ± 56.6 ± 38.8 ± 43-4 ± 7.7 rt 10.8 After Azimuth . ± 39-3 ± SI.I ± 32-6 ± 41.7 ± 7-4 ± 10.4 Forward Alidade ± 19.0 db 24.5 ± 23.6 ± 22.5 ± 4.0 ± 5-6 Forward Binnacle ± 40.2 ± 31-2 ± 25-3 •+• 72.8 ± 5-8 ± 8.2 Forward Ritchie ±59-7 ± 30-2 ± 37-8 ± 44.4 ± 7.8 ± ii. i As an incidental result, this table shows that for ordinary steering compasses (such as the Forward Alidade, Forward Binnacle, and After Binnacle) when read to the nearest eighth of a point, the probable accidental error of a single reading is about half a degree; for Kitchie Monitor Compasses (such as the Forward and After Ritchie) when read to the nearest eighth of a point, the probable accidental error of a single reading is about three-quarters of a degree ; and for Admiralty Standard Compasses, read to the nearest ten minutes, the probable accidental error of a single reading is about eleven minutes. From the mathematical theory of the deviations of the compass, given in a pre- ceding part of this section, we have and also Hence PI P 1 24 November, 1872. lyg REPORT ON But as P is liable to undergo a slow change", we introduce a term depending upon the time, and the equation becomes r P 1 AP t 0 = -Z?1 + A(71 + -tan0+TX H+ ^ X # where AP is the change of the value of P in one day, and I is the elapsed time in days, counted from November 1st, 1865. We have further 9 O = + O.O1O — 0.158 + 2.694 + 0.212 o = — o.oio O. IOO + 1.176 + 0.148 + 2.520 o = o.ooo — 0.064 + 0.077 + 0.161 + 9.516 0 = — 0.002 — 0.054 — 0.603 + 0.166 + '3-933 O = + O.OI2 — 0.023 — 1.426 + 0.164 + 16.522 O = + O.OO2 — 0.023 — 0.710 + 0158 4- 24-375 O = + O.OO1 — 0.041 — 0.113 + 0.143 + 25.608 o = — o.ooi — °-°53 + 0.623 + 0.132 + 26.316 0 = — O.OOi — 0.048 + 0.8-36 + 0.129 + 27.440 O = + O.O2.J — 0.085 + 1.910 + 0.177 i 4- 4i-5'9 o = o.ooo + 0.058 o -= — 0.699 — 0.037 + 16.294 o = — o. 109 — 0.006 + 0.826 + 0.258 o = — 9.869 — 1-057 + 70.177 + 28.825 o = + 0.037 — 0.699 o = + 0.006 — o. 109 o = + 1.057 — 9.869 Hence A,-. — = + 0.0240 Normal Equations. 4- 49S3-3 - = + 0.460 - = + O.OOIO2 + 16.294 + 0.826 + 0.258 4- 70-177 + 28.825 f- = — 0.0016 x ? = + 0.006 — -- = — 0.00023 + AFTER BINNACLE COMPASS. Equations of Condition. £ f &p / Q *c Absolute Terms. *t X X X X X X o = — 0.127 — O.O22 + 2.694 + 0.212 o = — o. loo 0.002 + 0.077 + 0.161 + 9.516 o = — 0.096 + 0.012 — o. 603 + 0.166 4- 13-933 o = — o. 100 — 0.004 — 1.426 + 0.164 + 16.522 o = — 0.070 + 0.002 — 0.710 + 0.158 + 24-375 o = — 0.073 O.OOI — 0.113 + o. 143 + 25.608 o = — 0.058 + 0.006 + 0.623 + 0.132 + 26.316 o = — 0.054 — 0.005 + 0.836 + 0.129 + 27.440 o = — 0.061 O = + O.O22 O = + O.OO2 O = — O.OI2 o = + 0.004 O = O.OO2 O = + O.OOI o = — 0.006 o = + 0.005 o = + 0.039 — 0.039 — 0.127 — O. IOO — 0.096 0. IOO — 0.070 — 0.073 — 0.058 — 0.054 — 0.061 + 1.910 • + 0.177 + 4i-5'9 1 I + 2.694 + 0.077 — 0.603 — 1.426 — 0.710 — 0.113 + 0.623 + 0.836 + 1.910 + 0.212 + o. 161 + 0.166 + 0.164 -l-o 158 -4- °- '43 + 0.132 + 0.129 + 0.177 + 9.516 + 13.933 + 16.522 4- 24-375 + 25 608 + 26.316 + 27.440 + 41.519 188 REPORT ON AFTER BINNACLE COMPASS. Normal Equations. p A/> / Q A X / X f Q 6.0 . X X X X X x~ o = — 0.023 — 0.063 4- 2.694 + 0.212 o = — 0.036 o = — o 061 o = — 0.066 o = — 0.067 o = — 0.023 ° = — 0.033 — O.O22 — 0.027 0.000 — 0.048 — 0.026 — 0.034 4- 1.176 4- 0.077 — 0.603 — 1.426 — 0.710 — 0.113 4- 0.148 4- o. 161 4- 0.166 4- 0.164 4- 0.158 4- o. 143 4- 2.520 + 9-516 + 13.933 4- 16.522 + 24-375 4- 25.608 o = — 0.004 0 = O.OII o = 4- °. 005 o = 4- 0.063 O = 4- O.O22 — °-°33 — 0.038 — o. 1 1 7 — 0.023 . — 0.036 4- 0.623 4- 0.836 4- 1.910 4- 0.132 4-0.129 4- 0.177 + 26.316 4- 27.440 + 41-519 4- 2.694 + 0.212 0 = 4- 0.027 o = o.ooo — 0.061 — 0.066 4- 0.077 4- 0.148 4- o. 161 + 2.520 + 9-5'6 o = 4- 0.048 o = 4- 0.026 0 = 4- 0.034 0=4- 0.033 0 = 4- 0.038 o = 4- 0.117 — 0.067 — 0.023 — °.°33 — 0.004 O.OII 4-0.005 — 0.603 — 1.426 — 0.710 — 0.113 4- 0.623 + 0.836 4- 1.910 + 0.166 4- 0.164 4-0.158 + 0.143 + 0.132 4- 0.129 4-0.177 + '3-933 + 16.522 + 24-375 + 25.608 + 26.316 + 27.440 + 41.519 + 4983.3 The value of the true A^ having thus become known for each compass, the values of the coefficients 53, @, £>, and (g, for each compass, at each station, wore next computed by means of the formulae (16). The results, expressed in parts of radius, are as follows: COEFFICIENTS OF THE DEVIATIONS OF THE ADMIRALTY STANDARD COMPASS. STATION. DATE. 3( 33 C £> (5 Hampton Roads . . . St. Thomas .... Bahia November i, 1865 November 18, 1865 o.ooo o ooo o ooo 4-0.158 4- o. 100 4~ o 064 — O.OIO 4- 0.010 o ooo "•""" 4- 0.021 4- 0.006 4- 0.016 — 0.004 — 0.013 o ooo Monte Video .... Sandy Point .... January 24, 1866 February IO, 1866 April 4 1866 0.000 0.000 o.ooo 4- 0.054 4- 0.023 4* o 023 4- 0.002 — 0.012 — O.OO2 4- 0.024 4- 0.016 4- 0.016 4- 0.004 0.000 — O.OO3 April 29 1866 o.ooo 4~ o 041 o.ooo 4- 0.016 4- O.OO2 May 20, 1866 o.ooo 4- 0.053 4- o.ooi 4- 0.017 4- 0.002 June I, 1866 o.ooo 4- 0.048 4- O.OO2 4- 0.018 4" O.OO2 San Francisco .... June 23, 1866 0.000 + 0.085 — O.O22 4- 0.018 o.ooo Means 4- 0.017 — O.OOI 192 HE TORT ON COEFFICIENTS OF THE DEVIATIONS OF THE AFTER BlNNACLE. STATION. DATE. 2( 33 a £> Ci Hampton Roads . . . St. Thomas .... Bahia November I, 1865 November 18, 1865 December 30, 1865 January 24, iS6l> February IO, iSoj O.OIO O.OIO O.OIO O.OIO — O.OIO O.OIO O.OIO — O.OIO O.OIO — O.OIO + 0.127 — 0.023 — 0.003 + O.OII — 0.005 + 0.002 O.OO2 + 0.006 — 0.006 — 0.040 4- °-°o7 + 0.034 + 0.039 + 0.040 + 0.038 + 0.040 + 0.046 + 0.041 + 0.032 O.OOI + O.OO2 — 0.012 O.OOI o.ooo + 0.002 — 0.005 — 0.006 o.ooo -f- 0. IOO -j- 0.096 -j- 0. IOO + 0.070 + 0-073 -j- 0.058 + 0.054 -j- 0.060 Monte Video .... Sandy Point .... Callao April. 29, KVJ May 20, liOu June 1, 1M>0 June 23, 1660 San Francisco. . . . Means + 0.038 0.002 COEFFICIENTS OF THE DEVIATIONS OF THE AFTER RITCHIE COMPASS. STATION. DATE. % 33 (5 © Q Hampton Roads . . . St. Thomas .... B.ihia November I, 1865 November 1 8, 1865 December 30, 1865 o.ooo o.ooo o.ooo + O. 2OO -j- 0.148 -j- 0. 121 — 0.030 + O.OI2 — 0.017 + 0.024 + 0.044 + 0.042 — 0.022 — 0.009 + O.OO2 Sandy Point .... February IO, 1866 April 4, 1866 o.ooo o.ooo + 0.071 + 0.067 — 0.060 + 0.004 + O.O22 + O.O43 + 0.013 + 0.002 Callao April 29, 1866 o.ooo -|- O. 102 + 0.004 + 0.032 + 0.016 May 20, 1866 o.ooo + 0.071 — 0.003 + O.025 — 0.027 June I, 1866 o.ooo + 0.078 + O.O2I + O.O24 + 0.015 San Francisco .... une 23, 1866 o.ooo + 0.118 — O.O27 + O.05O + 0.003 Means + 0.034 — O.OOI COEFFICIENTS OF THE DEVIATIONS OF THE AFTER AZIMUTH COMPASS. STATION. DATE. % 53 e £5 (£ Hampton Roads . . . St. Thomas .... November I, 1865 November 18, 1865 December 30 1865 O.OOO o.ooo — 0.085 — 0.053 — 0.003 + 0.023 -|- 0. IOI -j- 0. 1 20 + 0.005 + O.OO2 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 o.ooo — 0.052 o 086 — 0.014 + 0. 1 26 -j- o 1 06 — 0.007 Callao ....... April 29, 1866 May 20, 1866 o.ooo — 0.035 — 0.014 + 0.090 + O I 1 1 + O.OII O OI2 June i. 1866 + O 1OS + o 007 San Francisco .... June 23, 1866 Means -f- 0. I I 2 o.ooo COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD ALIDADE COMPASS. STATION. DATE. % 33 s £> e Hampton Roads . . . St. Thomas .... Bahia November I, 1865 November 18, 1865 — 0.025 — 0.025 — 0.044 — O.OIO — 0.032 — 0.013 + 0.019 + 0.022 + O.OOI • + 0.006 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 — 0.025 — 0.025 + 0.016 + 0.017 — 0.019 — 0.034 + 0.024 + 0.031 — 0.004 — 0.007 Callao April 29 1866 May 20 1866 June I, 1866 San Francisco. . . . June 23, 1866 — 0.025 — 0.034 — 0.041 + °-°33 + 0.017 + 0.007 Mean* + 0.024 0.000 MAGNETIC OBSERVATIONS. 193 COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD BINNACLE COMPASS. STATION. DATE. $( 33 e £> @ Hampton Roads . St. Thomas .... Bahia November I, 1865 November 18, 1865 December 30, 1865 0.000 o.ooo o ooo — 0.099 — 0.034 -f- o 008 — 0.045 — 0.004 + 0.044 + °-°35 + O O;7 -1- 0.007 — 0.002 — o.oo? Monte Video .... Sandy Point .... January 24, 1866 February IO, 1866 April 4 1866 o.ooo o.ooo o ooo -1- 0.051 4- 0.092 — 0.012 • — • 0.038 + 0.032 + 0.039 -j- o 028 O.OOl — 0.004 O.OOl April 29, 1866 o.ooo -\- O.O2O O O"17 4- 0.037 -f- 0.006 May 20, 1866 o.ooo — o 018 + O.O77 — 0.006 June I, 1866 o.ooo — 0.016 • — O O2Q 4- 0.046 4" 0.004 San Francisco .... June 23, 1866 0.000 — 0.082 — 0.062 + 0-035 4- 0.014 Means + 0.037 4- O.OOI COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD RITCHIE COMPASS. STATION. DATE. % 93 s £> <£ Hampton Roads . . . St. Thomas .... November i, 1865 November 18, 1865 December 30, 1865 o.ooo 0.000 + 0.023 4- 0.036 -f- o 061 — 0.063 — O.O22 — 0.027 + 0.038 + 0.057 4- 0.047 4- 0.006 — 0.008 — O.OO2 Monte Video .... Sandy Point .... January 24, 1866 February IO, 1866 April 4, 1866 o.ooo 0.000 o.ooo 4- 0.066 -j- 0.067 4- O.O27 0.000 — 0.048 — 0.026 4- 0.040 + 0.039 + °-°37 — 0.008 — 0.006 4- 0.008 Callao April 20, 1866 o.ooo + O.O3'! — 0.034 4- 0.044 -\- O.OO2 May 20, 1866 o ooo + o 004. O.OT? 4- 0.038 — 0.004 June I, 1866 O.OOO 4" O.OII — 0.038 4- 0.041 4- 0.007 San Francisco. . June 23, 1866 o.ooo — 0.005 — 0.117 4- 0.025 . — 0.009 Means 4- 0.041 O.OOI The values of the coefficients <£) and (£ for any compass should be constant. Therefore the mean of all the observed values has been assumed as the truth, and is given on the line marked " means" in the case of each compass. The constants thus far determined furnish the data with which to compute the values of the coefficients %, 33, @, £>, (£, in any part of the world, for any of the compasses under discussion. For convenience of reference these constants are collected in the following table: Compass. Al=3l c X p X p A X Q X X 0 g Admiralty Standard . After Binnacle . o.ooo O.OIO 4- 0.0240 — 0.0048 4- 0.460 4- 0.664 O.OOI02 — O.OOII2 — 0.0016 — 0.0084 4- 0.006 4- O.O02 — 0.00023 O.OOO22 4- 0.017 4- 0.038 O.OOI 0.002 After Ritchie . . . o.ooo 4- 0.0178 4- 0.766 — O.OOI 22 4- 0.0052 — o. 149 4- 0.00042 4- 0.034 O.OOI After Azimuth . o.ooo — 0.0026 — 0.373 — 0.00032 4- 0.0066 — 0.044 + 0.00039 4- O.I 12 o.ooo Forward Alidade . — 0.025 — 0.0162 4- 0.014 — o.oooio O.OOI2 — o. 106 — 0.00031 -j- 0.024 o.ooo Forward Binnacle . 0.000 — 0.0477 4- 0.140 — 0.00041 — 0.0059 — 0.075 0.00074 4- 0-037 4- 0.001 Forward Ritchie . . o.ooo — 0.0169 4- 0.367 O.OOIO2 — 0.0141 — 0.083 ' O..OOI2O 4- 0.041 O.OOI The values of the coefficients 2(, 33, S, £>, @, for each compass at each station, were next computed from the quantities given in this table, in the following man- ner. The coefficients 2t, £>, and G are constant for each compass, and were taken 25 December, 1872. 194 REPORT ON directly from the table; while the coefficients 53 and S were obtained by means of the formulae H 1 A£ H t H where 0 is the true magnetic dip; -Z^the earth's magnetic horizontal force, expressed in English units, namely, in feet, grains, and seconds; and t the time in days, counted from November 1st, 1865. The results, expressed in parts of radius, are as follows: COEFFICIENTS OF THE DEVIATIONS OF THE ADMIRALTY STANDARD COMPASS. STATION. DATE. 21 33 e s> i Hampton Roads . . . St. Thomas .... Bahia November I, 1865 November 18, 1865 December 30, 1865 o.ooo o.ooo o.ooo 4- o. 162 4- 0.004 -j- 0.066 — 0.003 — O.OO2 — O.OOI 4- 0.017 4-0.017 4- 0.017 O.OOI O.OOI — O.OOI Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 o.ooo o.ooo o.ooo 4- 0.048 + 0.024 + 0.031 — O.OOI o.ooo — 0.003 4- 0.017 4- 0.017 4- 0.017 O.OOI O.OOI — O.OOI Cnllao .... April 29, 1866 0.000 + °-°37 — 0.005 4- 0.017 O.OOI May 20, 1866 o.ooo + 0.049 — 0.006 4- 0.017 O.OOI June I, 1866 0.000 4- 0.052 — 0.007 4- 0.017 O.OOI San Francisco .... June 23, 1866 o.ooo + 0.085 O.OII 4-0.017 O.OOI COEFFICIENTS OF THE DEVIATIONS OF THE AFTER BINNACLE COMPASS. STATION. DATE. 3( 9 e £> e Hampton Roads . . . St. Thomas .... Bahia November I, 1865 November 1 8, 1865 December 30, 1865 O.OIO O.OIO 4- 0.128 4- 0.096 — O.O22 O.OO2 4- 0.038 4- 0.038 — O.002 O.OO2 Monte Video .... Sandy Point .... January 24, 1866 February to, 1866 April 4, 1866 — O.OIO — O.OIO — O.OIO 4- 0.098 4-0.097 4- 0.081 4" O.OO2 4- 0.009 4~ Q.OOI 4- 0-038 4- 0.038 T 0.038 — O.OO2 — O.OO2 — O OO2 Callao April 29, 1866 O.OIO 4- 0.067 — 0.004 4- 0.038 O.OO2 May 20, 1866 O.OIO + O.OS? — O.OII T 0.038 — O.OO2 June I, 1866 — O.OIO 4- 0.051 — O.OI I 4- 0.0^8 — O.OO2 San Francisco .... une 23, 1866 — O.OIO 4- 0.062 — 0.025 4- 0.038 — O.OO2 COEFFICIENTS OF THE DEVIATIONS OF THE AFTER RITCHIE COMPASS. STATION. DATE. 51 33 e £> <£ Hampton Roads . . St. Thomas .... Hahi.-v November I, 1865 November 18, 1865 December 30 1865 O.OOO o.ooo o ooo 4- 0.2II 4-0.131 + O I I 7 — 0.018 — 0.015 4- 0.034 4- 0.034 — O.OOI — O.OOI Monte Video .... Sandy Point .... January * 24, 1 866 February 10, 1866 April 4, 1866 o.ooo o ooo 4- 0.080 — 0.025 0017 ' 4- 0.034 — O.OOI Callao April 29, 1866 o.ooo + 0.076 O OI I + O Old. — O QOI May 20, 1866 o ooo 4- o 080 o ooi "«wj^ June I, 1866 o ooo 4. o 080 San Francisco. une 23, 1866 o.ooo 4-0.119 4- 0.001 + 0.034 — O.OOI MAGNETIC OBSERVATIONS. 195 COEFFICIENTS OF THE DEVIATIONS OF THE AFTER AZIMUTH COMPASS. STATION. DATE. % 33 <£ £> <£ Hampton Roads . St. Thomas .... November I, 1865 November 1 8, 1865 December 30, 1865 January 24, 1866 February 10, 1866 April 4, 1866 April 29, 1866 May 20, 1866 June I, 1866 June 23, 1866 0.000 o.ooo o.ooo o.ooo o.ooo o.ooo o.ooo o.ooo — 0.086 — 0.059 — 0.063 — 0.062 — 0.065 — 0.061 — 0.059 — 0.059 4- 0.008 4- O.OO2 — 0.003 O.OIO — 0.002 4- 0.003 4- 0.009 4- O.OII 4- 0. 112 -j- O.II2 4~ 0. 112 4- O.II2 + O.I 12 4" 0. 1 1 2 4- O.II2 4- O.II2 0.000 o.ooo o.ooo o.ooo 0.000 0.000 o.ooo o.ooo Monte Video .... Sandy Point .... Callao . . , San Francisco .... COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD ALIDADE COMPASS. STATION. DATE. % 8 6 £> @ Hampton Roads . . St. Thomas .... November I, 1865 November 18, 1865 — 0.025 — 0.025 — 0.041 — 0.017 — 0.026 — 0.018 4- 0.024 4- 0.024 o.ooo o.ooo Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 — 0.025 — 0.025 - — o 02 5 4- O.OII 4- 0.024 4- o 01 1 O.O2I — 0,02 1 — O O2 3 + 0.0-4 4- 0.024 o.ooo o.ooo Callao April 29, 1866 May 20 I S66 0.025 4- o.ooi — 0.023 -)- 0.024 0.000 June I, 1 866 — 0.02? o 014 o 023 San Francisco. June 23, 1866 — 0.025 — 0.032 — 0.034 -(- 0.024 o.ooo COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD BINNACLE COMPASS. STATION. DATE. % 23 g £> @ Hampton Roads . St. Thomas .... Bahia November I, 1865 November 1 8, 1865 o.ooo o.ooo — 0.099 — 0.036 + O OI ^ — 0.032 O.O2O — O.O2O 4- 0.037 + 0-037 + O O37 4- O.OOI 4- o.ooi 4- o.ooi Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 o.ooo 0.000 o.ooo -)- 0.046 4- 0.084 4- 0.046 — 0.019 — 0.016 — 0.026 + 0.037 + 0.037 -f- 0.037 4- O.OOI 4- o.ooi 4- o.ooi Callao April 29, 1866 o.ooo 4~ 0.015 — 0.029 4- 0.037 4" O.OOI May 20, 1 866 o.ooo O.O22 O.O31 4- 0.037 4" O.OOI June I, 1866 o.ooo — 0.033 — 0.035 4- 0.037 4- o.ooi San Francisco .... June 23, 1866 o.ooo — 0.083 — 0.056 + 0.037 + O.OOI COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD RITCHIE COMPASS. STATION. DATE. % 23 g £> @ Hampton Roads . St Thomas .... November I, 1865 November 18, 1865 0.000 o.ooo 4- 0.032 4- 0.032 — 0.056 — 0.032 -\- 0.041 4- 0.041 O.OOI — O.OOI Bahia December 30, 1 865 o.ooo 4- 0.048 — 0.026 4- 0.041 O.OOI Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 o.ooo o.ooo o.ooo + 0.057 + 0.067 4- 0.045 0.<522 — 0.013 — 0.032 4- 0.041 4- 0.041 4- 0.041 — O.OOI — O.OOI O.OOI April 29, 1866 o.ooo -f 0.028 — 0.041 4- 0.041 O.OOI May 20, 1866 o.ooo + O.OII — 0.051 4- 0.041 — o.ooi June I, 1866 o.ooo 4- 0.005 — 0.056 -\- 0.041 — O.OOI San Francisco .... June 23, 1866 o.ooo — O.OIO — 0.092 4- 0.041 — O.OOI 19G REPORT ON Comparing these computed values with the values before founu directly from the observations, the following residuals are obtained: VALUE OF THE COMPUTED MINUS THE OBSERVED COEFFICIENTS OF THE DEVIATIONS OF THF. ADMIRALTY STANDARD COMPASS. STATION. DATE. % 23 g 5) @ Hampton Roads . . . St. Thomas .... November I, 1865 November 18, 1865 December 30, 1865 4- 0.004 — 0.006 4" O.OO2 4- 0.007 — O.OI2 O.OOI — 0.004 4- O.OII -j- O.OOI 4- 0.003 -f- O.OI2 — O OOI Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 0.006 4- 0.001 4- 0.008 O.OO3 4- 0.012 O.OOI — 0.007 4- O.OOI -j- O.OOI — 0.005 O.OOI -}- O.OO2 Callao April 29, 1866 O.OO4 O.OO5 4~ O.OOI — O.OOI May 20, 1866 O.OO4 O.OO7 o ooo {une I, 1866 -f- O.OO4 0.009 O.OOI — o oo^ San Francisco. . . . une 23, 1866 0.000 4- o.ou O.OOI — O.OOI VALUE OF THE COMPUTED MINUS THE OBSERVED COEFFICIENTS .OF THE DEVIATIONS OF THE AFTER BINNACLE COMPASS. STATION. DATE. % 53 g £> ® Hampton Roads . . . Si. Thomas .... November I, 1865 November 18, 1865 4- O.OOI 4 O.OOI 4 O.OOI — O.OOI December 30 1865 Monte Video .... Sandy Point . . . . January 24, 1866 February 10, 1866 April 4, 1866 4- O.002 — 0.003 4~ o.oi I — 0.009 4- 0.014 — O OOI — O.OOI — 0 OO2 4- O.OIO O.OOI Callao April 29, 1866 May 20, 1866 o 008 June I 1866 O.OOJ San Francisco. . . June 23, 1866 4- O.O02 + 0-015 -j- 0.006 — 0.002 VALUE OF THE COMPUTED MINUS THE OBSERVED. COEFFICIENTS OF THE DEVIATIONS OF THE AFTER RITCHIE COMPASS. STATION. DATE. % 23 G £> g Hampton Roads . . . Si. Thomas .... lialiia November I, 1865 November 1 8, 1865 December 30, 1865 4- O.OII — 0.017 o 008 4- 0.012 — 0.027 4- o.oio — O.OIO o 008 4- O.02I 4- 0.008 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 4-0.009 4- o-°3S 4- O.OI2 — 0.014 Callao April 29 1866 May 20 1866 Acapulco June I 1866 -j- 0.009 4~ 0.009 San Francisco. . une 23, 1866 4- O.OOI 4- 0.028 — 0.016 — 0.004 MAGNETIC OBSERVATIONS. 197 VALUE OF THE COMPUTED MINUS THE OBSERVED COEFFICIENTS OF THE DEVIATIONS OF THE AFTER AZIMUTH COMPASS. STATION. DATE. 21 23 e £> e Hampton Roads . St. Thomas .... Bahia November I, 1865 November 18, 1865 December 30, 1865 — o.ooi — o.oc6 + O.OII — 0.021 + o.ou — 0.008 — 0.005 O.OO2 Monte Video .... Sandy Point .... January 24, 1 866 February 10, 1866 April 4 1866 — O.OIO + 0.004 — 0.014 4- 0.007 Callao ...... April 29, 1866 ' °'°22 Acapulco . June I 1866 San Francisco. June 23, 1866 ' °'°U -f- 0-007 VALUE OF THE COMPUTED MINUS THE OBSERVED COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD ALIDADE COMPASS. STATION. DATE. % 33 g £> e Hampton Roads . . St. Thomas . . ' . Bahia November I, 1865 November 1 8, 1865 December 30, 1865 + 0.003 — 0.027 + O OO2 + 0.006 — 0.005 + 0.005 + O.OO2 O.OOI . — 0.006 Monte Video '. Sandy Point .... Valparaiso Callao . . January 24, 1 866 February 10, 1866 April 4, 1866 April 29, 1866 — 0.005 + 0.007 + 0.003 O OI I — O.OO2 + 0.013 — O.OO? 0.000 — O.O07 + 0.005 + 0.004 + 0.007 + O.OO2 Panama May 20, 1866 O.OIO + O OOI June I, 1866 -|_ O.O12 San Francisco. June 23, 1866 + O.OO2 + 0.007 + 0.007 O.OO7 VALUE OF THE COMPUTED MINUS THE OBSERVED COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD BINNACLE COMPASS. STATION. DATE. % 23 g £> e Hampton Roads . . . St. Thomas .... Bahia November I, 1865 November 18, 1865 December 30, 1865 o.ooo O.OO2 + O OO7 + 0.013 O.OIO O OIO — 0.007 + O.OO2 O.OOO — 0.006 4- 0.003 + o 004. Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 — 0.005 — 0.008 + 0.015 — 0.007 + O.O22 — O.OI3 + 0.005 — O.OO2 + O.OO9 + 0.002 T °-O°S + 0.004 April 29, 1866 — 0.005 + O.OOS O.OOO — 0.005 May 20, 1866 — 0.004 — O.OO6 o.ooo + O.OO7 June I, 1866 + 0.003 O.OO6 — 0.009 — 0.003 San Francisco .... June 23, 1866 O.OOI + O.OO6 + O.OO 2 — O.OI3 VALUE OF THE COMPUTED MINUS THE OBSERVED COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD RITCHIE COMPASS. STATION. DATE. % 23 £ £> e Hampton Roads . St. Thomas .... Bahia November I, 1865 November 1 8, 1865 December 30, 1865 + 0.009 — 0.004 — 0.013 + o..oo7 O.OIO + O.OOI + 0.003 — 0.016 — 0.006 — 0.007 + 0.007 to. 001 Monte Video .... Sandy Point .... January 24, 1866 February 10, 1866 April 4, 1866 — . 0.009 0.000 + O.O22 O.O22 + 0.035 0.006 + O.OOI + O.002 + 0.004 0.007 + 0.005 — 0.009 Callao April 29, 1866 — O.OO5 — O.OO? — 0.003 — 0.003 May 20, 1866 + 0.007 — O.OlS + 0.003 + 0.003 June I, 1866 0.006 — O.OlS O.OOO — 0.008 San Francisco. June 23, 1866 0.005 + 0.025 + 0.016 + 0.008 198 REPORT ON In the following table the columns headed rs, r5, rB, re, contain respectively the probable errors of a single observed value of 53, (J, £), and (v, for each compass, computed from the residuals just given. But as these residuals were got by sub- tracting the computed from the observed values of the coefficients, and as each observed value was found from a set of deviations observed on all the thirty-two points, it follows that the probable errors here given belong to the coefficients when they have been computed from a set of deviations observed on all the thirty- two points. For convenience of reference we will designate these as the probable errors derived from all the observations of the cruise. r r r r r Compass. 8 ( D • V\b Admiralty Standard ± 0.0033 ± 0.0053 ± 0.0032 ± 0.0033 ± 0.0008 After Binnacle . ± 0.0036 ± 0.0069 ± 0.0026 ± 0.0028 ± 0.0018 After Ritchie . . ± 0.0090 ± 0.0153 ± 0.0072 ± 0.0106 ± 0.0031 After Azimuth db o.oioo ± O.OIOO ± 0.0094 ± 0.0074 =t 0.0030 Forward Alidade ± 0.0050 ± 0.0059 ± 0.0035 ± 0.0031 ± 0.0016 Forward Binnacle ± 0.0046 ± 0.0084 ± 0.0036 ± 0.0043 ± 0.0024 Forward Ritchie . ± 0.0070 ± 0.0127 ± 0.0056 ± o.oo47» ± 0.0032 Means . . . =fc 0.006 1 ± 0.0092 ± 0.0050 ± 0.0052 ± 0.0023 But we have before found the probable errors of B}, Oi, Z)j, and E^ when com- puted from observations made at a single station on each of the thirty-two points, by a totally different process, namely, from the thirty-two observed deviations the values of .A,, B» Ct, Z>,, and E^ were computed; next, with the values of A^ Blt (\, Z)j, and EI, thus found, the deviations were computed for each point; then, comparing these computed values of the deviation with the observed values, a series of residuals were obtained from which the probable errors in question (which are given in the table on page 185) were easily got. These we will designate as tlic probable errors obtained from observations at a single station; and it will be remembered that it was shown that, no matter what their numerical values might be, the probable errors of B» Ci, D» and Et must all be equal to each other. Although the difference between the probable errors of B,, C^ D^ En and those of 33, (J, S5, (£, can never be great, yet, in general, it would not be rigorously cor- rect to assume that they are equal to each other. However, in the case of the compasses under discussion we will make this assumption, for by so doing no error greater than the uncertainty of the probable errors themselves will be introduced. In order to facilitate the comparison of the two sets of probable errors, those of Bit Ct, Z),, EI are given in the table above, in the column headed I/ !<>' This column is identical with the column headed in the same manner in the table on page 185, except that the quantities are here expressed in parts of radius instead of minutes of arc. Now, comparing the probable errors derived from all the observations of the cruise with those derived from observations at any single station, we see that, taking the mean of the results for all the compasses, TV and rs are almost identical, as they should be, but they are each more than twice as great as ! . On the other hand, MAGNETIC OBSERVATIONS. 199 r«g and r^ are neither equal to each other, nor yet to r^ and r& but are, the one T nearly three, and the other four, times as great as —, — . Assuming the theory employed in this discussion to be correct, we should have expected to find r^, ra, ?* rt, rffi sensibly equal to each other, and all sensibly equal to — ; — . Such, however, y 16 is not the case; and, as the results for each compass all tend in precisely the same direction as ,the mean result, a doubt naturally arises whether or not the theory really represents the semi-circular deviation as accurately as it does the quadrantal. As this doubt is founded upon observations which may possibly have been affected by some unknown cause of constant error — as they were all made on a single vessel during a single cruise — perhaps it would not be well to insist upon it too strongly; but at all events, it shows the necessity for further investigation of the subject, and especially the great want of more observations. The probable errors of the coefficients 53, (£, ^ (£, for each compass, when com- puted from the values of A^ , — , -- , , — , — — , £), and (5, given in the table Ai fb f\i fd At /b on page 193, are as follows : r° r° r° r° Compass. a E y> • Admiralty Standard ± O.OOIO ± 0.0017 ± O.OOIO ± O.OOIO After Binnacle . ± O.OOI2 ± 0.0023 ± 0.0009 ± 0.0009 After Ritchie ± 0.0030 ± 0.0051 ± o 0024 ± 0.0035 After Azimuth . ± 0.0035 db 0.0035 ± 0.0033 ± 0.0026 Forward Alidade ± O'ooi6 ± 0.0019 ± O.OOII ± O-OOIO Forward Binnacle ± 0.0014 ± 0.0026 ± O.OOI2 ± 0.0014 Forward Ritchie. ± O.OO22 ± 0.0040 ± 0.0018 ± 0-0015 The following table shows, for each compass, the place at which the maximum value of its deviation, $, was the greatest, together with the point on which that maximum value occurred, and its amount. Also, the place at which the maximum value of its deviation was the least, together with the point on vvhicli that maximum occurred, and its amount. These deviations are given on the compass points, and in computing them the true A was used. Compass and Station. Point. J Admiralty Standard. Hampton Roads E. by N. + 9° 29' Sandy Point ...... N. E. by E. + 2 3 After Binnacle. Hampton Roads N. W. by W. — 9 IS Acapulco . . . . • • • N. W. by \V. — 5 « After Ritchie. Hampton Roads ..... W. N. W. -12 45 Panama ....... N. W. by W. — 5 4i After Azimuth. Hampton Roads ..... S. E. by E. — 10 5 St. Thomas S. E. — 8 45 200 RE POUT ON Compass and Station. Point. > Forward Alidade. N. W. by N. — 3° 39' N. W. — 4 34 Forward Binnacle. Bahia ....... N. W. S. W. • 3 3i + 7 43 Forward Ritchie. St. Thomas ...... San Francisco N. W. S. W. by S. — 4 55 + 6 53 The following table shows, for each compass, the maximum change, Ar\ in its deviation, which occurred on any single point, together with the azimuth at which, and the places between which that change occurred. Compass and Station. Azimuth. A» Admiralty Standard. Hampton Roads and Sandy Point g 88° 52' E. 7° 53' After Binnacle. Hampton Roads and Acapulco . S. 82 43 E. 4 23 After Ritchie. Hampton Roads and Panama . S. 84 27 E. 7 28 After Azimuth. Hampton Roads and Sandy Point S. 48 31 E. i 43 Forward Alidade. Hampton Roads and Sandy Point N • 85 20 E. 3 39 Forward Binnacle. Sandy Point and San Francisco N • 76 17 E. 9 42 Forward Ritchie. Sandy Point and San Francisco N • 43 16 E. 6 18 In order to show the difference between the values of the deviation computed from observations made at a single station, and those computed from all the obser- vations of the cruise, or, in other words, the difference between the theory and the observations, let ^ be the deviation of a compass on any point, £, at a given station, as computed from values of A» B^ Olt Dj, E^ derived from all the observations of that compass made during the cruise; and also let b' be the deviation of the same compass, on the same point, at the same station, as computed from values of A}, BI, (7,, Z>,, EI, derived from observations of that compass made on each of the thirty-two points at the station in question. Then the following table shows, for each compass, the maximum value attained by ^ — <$' during the cruise, together with the point on which, and the station at which, that maximum occurred. Compass. Station. Point. »— »' Admiralty Standard St. Thomas S. S. W. + i° 41' After Binnacle Panama S. S. E. + i id. After Ritchie After Azimuth Forward Alidade . Forward Binnacle Forward Ritchie . Sandy Point 1 'all. in Acapulco Valparaiso San Francisco S. by E. S. E. by S. S. E N. W. by W. N. N. E. — 2 5I -3 4 + i 36 - i 41 -|- 2 II MAGNETIC OBSERVATIONS. 201 As the After Azimuth Compass was a very poor instrument, the descrcpancy between theory and observation in the case of its deviations is not surprising. In the case of all the other compasses, except perhaps the Forward and After llitchic, the agreement of the observed and computed values of the deviations is much more satisfactory; and indeed the differences between them arc so small as to be of very little consequence for the ordinary purposes of navigation; still, viewed from a purely scientific stand-point, they are larger than might have been expected. The hard and soft iron forces involved in the production of the semi-circular deviation were next examined in order to ascertain whether or not their relations to each other were such as to render it possible, in the case of a vessel swung for the first time, to predict from the observed deviations of her standard compass what the deviations would be at any other place. The coefficients of the semi-circular deviation are 33 and (2, and the components of the hard iron force involved in their production are . and -¥-\ Avhile the components of the soft iron force are and f. A A A A As these components act at right angles to each other, the total hard iron force will be JaF+a?1 and if we let a represent the direction in which it acts, measured from the ship's liead toward the right hand, we have tan a. = In the same way the total soft iron force will be C* ~ "ji A and to determine its direction we have . 2 I 12 tan a ' = c T By means of these formufa; the following table was computed. It shows the amount and direction of the hard and soft iron forces acting on each compass on November 1, 1865, and June 23, 1866. Hard Ire n Force. Compass. Novembe r I, 1865. June 2; !, 1866. Amount. Direction. Amount. Direction. Amount. Direction. Admiralty Standard After Binnacle 0.460 0.664 000°. 8 OOO.2 0.226 0.639 348°.o 353-o 0.024 O.OIO 356°- 1 240.4 After Ritchie 0.780 349-0 0.4:51 354-o 0.018 16.3 After Azimuth 0-375 186.8 0.449 173-9 0.007 III. 2 Forward Alidade . Forward Binnacle 0.107 0.159 277.6 331-9 0.178 0.254 267.3 280.1 0.016 0.048 184.2 187.1 Forward Ritchie . 0-376 347-2 0.387 289.1 O.O22 219.9 26 December, 1872. '20-2 REPORT ON The following table shows the change, in amount and direction, of the hard iron force between November 1, 1865, and June 23, 1866; the ratio of the hard to the soft iron force on each of these dates; and also the mean ratio of the same forces. Change of Ha rd Iron Force. Ratio of Hard to Soft Iro n Force. Amount. Direction. Nov. I, 1865. June 23, 1866. Mean. Admiralty Standard — 0.234 — I2°.8 19.2 9-4 14 3 After Binnacle — 0.025 — 7.2 68.8 66.1 67.4 After Ritchie . — 0.299 + S-o 42.1 26.0 34-o Alter Azimuth. + 0.074 — 12.9 52-6 62.8 57-7 Forward Alidade + 0.071 — 10.3 6.6 I I.O 8.8 Forward Binnacle + 0.095 -Si-8 3-3 5-3 4-3 Forward Ritchie -f- O.OII -58-1 17.1 17.6 17-3 An examination of the last two tables shows that during the whole cruise the hard iron force was changing in a very remarkable manner, both in amount and direction. In the case of the three compasses mounted above the forward turret, the force was increasing: while in the case of those mounted above the after turret, it was decreasing. In other words, there seems to have been a transfer of hard iron force from aft forward. Now, looking at the change in direction of the force, we see that in every case, excepting only that of the After Ritchie, it took place in such a manner as to correspond to a rotation from right to left. Further, the ratio of the hard to the soft iron force was slowly varying at each compass; and for the different compasses it ranged between 4.3 and 67.4. Finally, there was not a single compass on board at which the direction of the hard and soft iron force coincided ; from which it follows that in no case was the ratio of the hard and soft iron forces the same in the coefficient 33 as it was in the coefficient @. Under these circumstances we arc forced to conclude that, so far as can be judged from the observations here given, in the case of a vessel swung for the first time it is impossible to make any reliable estimate of the ratio of the hard to the soft iron force in the coefficients 33 and (J; and, therefore, it is also impossible to make any reliable estimate as to what changes her deviations will undergo upon a change of magnetic latitude. As a further proof of this, we see that the After Azimuth Compass, with a maximum deviation of 10° 5', changed its deviation during the cruise by only 1° 43'. that is, by about one-sixth of its whole amount; while the Forward Binnacle Compass, with a maximum deviation of only 7° 43' changed its deviation during the cruise by 9° 42", that is, by about one and a quarter times its whole amount. In the beginning of this section it was stated that, at the positions occupied by the Admiralty Standard and After Azimuth Compasses, observations of deflection and dip were made in order to determine the absolute magnetic force; and the details of the method followed in taking these observations were explained. We will now proceed to reduce and discuss the observations themselves, and for that purpose the first thing necessary to be known is the magnetic moment of the di-Hccting magnets. For its determination we have the observations recorded in the following table, which were all made on shore. The first and second columns MAGNETIC OBSERVATIONS. 203 of the table give the place where, and the date when, each observation was made. The third and fourth columns give respectively the observed deflections when the north ends of the deflecting magnets were directed towards the west and towards the cast; the distance of their centres from the centre of the compass needle being in both cases eleven inches. The fifth column gives the mean of the four observed deflections recorded in the third and fourth columns. The sixth, seventh, and eighth columns contain, in precisely the same manner, the observed deflections, and their mean, when the centres of the deflecting magnets were at a distance of fifteen inches from the centre of the compass needle. Now, let r be the distance, expressed in feet, between the centres of the deflecting magnets and the centre of the compass needle ; u, the observed angle of deflection given for each value of r in the column headed "mean"; 777, the combined magnetic moment of the two deflecting magnets; and //, the earth's horizontal force at the place where the observation was made, taken from the table on page 61. Then we shall have 771 jr tan u = -=. and the ninth column contains the mean of the two values of log. — computed respectively from the angles of deflection observed with r= 11 inches =0.917 foot, and r = 15 inches = 1.250 feet. The tenth column contains the value of log. m, found by adding to log. the known value of log. H. Jl Deflections. LOP- m Log. m . Station. Date. r= II inches. r= 15 inches. Log.-. West. East. Mean. West. East. Mean. Oct. 30, 1865 19° 3°' 19 o 22° 40' 22 20 20° 52' 14° 30' 14 20 17° 30' 17 40 *l6° 0' 9.1617 9-8344 St. Thomas .... Nov. 13, 1865 15 20 14 50 4 20 6 40 15 3° 14 40 '5 5 4 3° 6 40 5 32 8.9961 9.8251 Salute Islands . Nov. 28, 1865 H 35 IS o 5 20 5 20 H 35 IS 5 14 49 4 55 5 20 5 '4 8.9799 9.8079 Bahia Dec. 27, 1865 15 4° 16 40 16 10 16 10 16 10 6 10 5 40 5 30 5 30 5 42 9.0184 9.8108 Rio Janeiro .... Jan. 6, 1866 17 o 17 o 17 o 17 10 17 2 6 40 6 o 6 o 6 o 6 10 9.0476 9.8216 Monte Video . Jan. 1 8, 1866 16 40 17 o 16 40 16 40 16 45 6 20 6 10 5 30 5 3° 5 52 9.0328 9.8130 Sandy Point Feb. 7, 1866 16 30 16 40 16 20 1 6 20 16 27 5 4° 6 o 6 40 6 30 6 12 9.0408 9.8270 Valparaiso .... March 2, 1866 17 o 16 40 IS o 14 40 15 5° 7 20 7 3° 5 o 5 o 6 12 9.0320 9.8326 Valparaiso .... April 7, 1866 14 4° H 3° 17 40 17 3° 16 5 4 3° 4 20 7 30 7 40 6 o 9.0284 9.8290 Callao April 26, 1866 14 3° H 30 H 3° 14 3° H 3° 5 20 5 1° 5 1° 5 3o 5 '8 8-9777 9.8222 May 14, 1866 12 50 13 10 '3 3° 13 3° 13 '5 4 30 4 40 5 20 5 o 4 52 8.9387 9.8195 Acapulco .... May 30, 1866 12 30 12 40 12 20 12 10 12 25 4 40 5 30 4 30 4 40 4 50 8.9227 9.8107 San Francisco . June 26, 1866 17 40 18 o 17 o 16 40 17 20 7 o 7 10 6 10 6 30 6 42 9.0698 9.8208 * In this observation n=i2 inches. 204 REPORT ON The observed values of log. m show no trace whatever of any change depending upon the time, and therefore the indiscriminate mean of them all has been taken as the truth, and we have Log. m — 9.8211 ± 0.0016. The probable error of a single observed value of log. m is i 0.0058. The following table contains all the observations which were made at the position occupied by the Admiralty Standard Compass on board the Monadnoek, for the determination of absolute force. The first nine columns contain quantities precisely similar to those in the columns headed in the same manner in the table last given. The column headed "Log. //'" gives the logarithm of the combined horizontal force of the earth and ship, obtained by subtracting log. - ' from the value of log. H m given above. The column "0"' contains the dip, Avhich was observed immedi- ately after the deflections. The column "Log. Z'" contains the logarithm of the combined vertical force of the earth and ship, computed from the quantities in the TTI tenth and eleventh columns by the formula Z' = H' tan 0' . The columns " Log. ," yi H and "Log. —"^ explain themselves when it is stated that // represents the hori- zontal force of the earth ; H' the combined horizontal force of the earth and ship ; Z the earth's vertical force; and Z' the combined vertical force of the earth and ship. The column "£'" contains the azimuth of the ship's head as read off from the compass card at the time the deflections were observed; and the column "£" contains the same azimuth, counted from the true magnetic north. MAGNETIC OBSERVATIONS. 205 - (4 °Cx OO W 0 in W oo fc O Pi oo W Ox c/i Ox 8 C/3 ft Tf in to O c/5 VO W W oo C/) /-N pq J W ~ W 0 r--. W >o CO * c/5 W o M c/i Ox to O c/i 1C o tfl f W ft U2 W 8 | vo OO n CO (S o1 1 o | 0 8 oo oo N O Cx c? ? 0 ON *O OO Ox xO vO CO o 00 vo 0 CO s O 00 00 Ox S M N CO l^. 0?" of ,3 O O O 0 o 0 o o o 0 0 0 O O O 8 ft 00 00 it CO N vO W vO ro N O O Cx m O oo 1 CO 3- 00 00 o r^ O f FO IN O O ON CO I ON CO s fO O . ON ON ON Ox 0 Ox Ox ON Cx Ox Ox Ox CO OO ON q 3 W 8» 2 vO vO VO vO 0 : M VO .* 0 vo VO N 10 N CO 1 - 5 1 ii O O O O *• ^ 0 t^. !•>. iovo 0 O VO vo °a O vO 0 0 vo O O 0 o o vO t- 8ft O 0^ *«, ft° °ft 10 ^- 0 O *J- 10 IO >O 0 O ON O i o ^ o vO O VO vO °ft O O txl to VO vO 88 0 0 o o. 88 vO vo ft8 1! 8ft 88 O O 1O iO *ft vo m 0 ro 00 o 00 CS vO o CO CO 1O O 8 M M M •g •5 i " w "6000 oo oo co rl- -«t 10 8° 0 0 vo vO 3-* 0 0 -3- ^h 00 X o o CO 00 8ft 0000 82 o o O O O O *t ^*- Tf -,*• o o 88 II — V "b o o o oo oo 0 0 O 0 ft£ o o •& CO 00 00 o o CO OO vovo o o 80 N o o co «J- vO >o o o 0 0 co co CO co O Ox vo iO IO VO vo VO in vo in vO i oo vO CO vo 00 VO vO oo VO vo OO vo vo CO 1 LI i "rt Q .-T 10 o" M CO 1 1 1 00 1 Ox y Q *t ^— > c • C ft Ox 1 March 20, 1 |- ft 0. rt CO g CO N | 1 • 1 * s § § i 3 t £ 3 .J 13 M I/) t« 2 U ^d M | S rt i — i O 2 o '5 G d o i2 o B rs a 1 s 'c 2 t 9 tAl Valparaiso . . . Valparaiso . . § a u Panama . . . 0 o 1 • s < San Francisco) £• o u O S5 5 o 206 REPORT ON The following table contains, in precisely the same manner, all the observations which were made for the determination of absolute force at the position occupied by the After Azimuth Compass on board the Monaduock. - w£w£££w££w "V >O CO t-. CO fON Bk »<% «S ft ^ M M || M^ ^> ^ (•; O - f? f" • • • • ^ w H; > v N N » CO 00 O CO PI I-. GO '0 GO irt 00 •- 5 ov dd\ddoNOChdddds ^to 0° 1 1 I I I 1 1 IIII1III 5 d.o>o\d>c>vij>o' o>ONcKdv»dvdvo> N O Ov O\ M. w * *^ 5^ CO O ^ fO CO NO OOt-*rOvoChvO>O«l^.COON > o + ^-iITT''!^^^ i I ! doddddddddddddd o u H J? *** 0 ^ ^ ^ OO f^ N CO N l/> O\ ^H vQ "-N-*w*-OO^*i«OO ^ O O ••* N d s ^NiO^-wjfO "^ lOU^^-M • o a E .5 - g ^2.22*2° °° °° oo oo oo oo oo oo oo oo oo f> ^ fl C*> 41 t*> M IA, rf M U ^ u-> •-}- -t- ^ 9* ^ <*) if fft 0 1 * ^8 8° 02/20,oh5.5.oioo/05.og)oo og oo gooo^ o **O ^ ^^ *** ^*QO 00 OO vO vO ift if) OO O^ t"* t^ r»» Is* vO t^ f>« *ft ^O O t^^O t** t^ c Q § tf * o ^ npoosoovoo^Ot^-*t-vnvooo .= - ^,°88 §-8 S-8 5-5-82 22 8° 2,2,S,3-08,80-°2,82)0f0 8,° v. ^ J085-20>ofoo>o go oo oogoog gg 05.00 go oooo i^'S IT H? °N°l0 OxO\ »^>r^ •-.*• O\ON FN.ts. O** *-« sO»n OsOv fOfO "i\O CO t^. O^ l>. MM • WM f| - , MM MM «CI NM MN- MM MM MM MM MM s ssssilillillll o a o o v v c e a -fi S 'C 'C §" ;? c S^ S5S5QQi2,tf>'a[iI>— S? c o i nn : : • : ; : : : 8 II: 1 I 1 I 1 1 i a «^(j|l2s 233 I MAGNETIC OBSERVATIONS. 207 From the data already given, the value of a, was next computed by means of the formulae sm 6 = , ^ TTO! 21 4- 2^ sin £' -f- G cos f ' -f £> sin 2f ' + (£ cos sin i 21 + 55 sin f + GO-OS £ -f £) sin 2£ -f <£ cos 2£ The individual results obtained from the observed values of H arc as follows: H Value of X Station. Admiralty Standard Compass. After Azimuth Compass. Salute Islands 0.918 Ceara . 0.896 Bahia . 0.922 Rio Janeiro. °-939 0.942 Rio Janeiro. 0.904 0.884 Monte Video 0.913 0.814 Sandy Point 0.914 0.821 Valparaiso 0.954 0.848 Valparaiso c-934 0.886 Callao 0.905 0.820 Panama 0.952 0.861 Acapulco 0.947 0.816 San Francisco 0.914 0.947 Taking the means, for the Admiralty Standard Compass, we have finally a = 0.924 ±0.0036 and the probable error of a single observed value of /I is ^ 0.013. For the After Azimuth compass we have finally a = 0.864 ±0.0107 and the probable error of a single observed value of % is ^ 0.034. Z' In order to determine these coefficients which depend upon the value of --, we cos sn have equation (6 a), which is Z' . But as R is liable to a slow change, a term depending upon the time is introduced, and then we get Z' cos sn /c , , (6b) where AR is the daily change in the value of R, and t is the time iri days, counted Z' from November 1, 1865. Each observed value of — furnishes an equation of con- JU dition of the same form as (6 b), and from all the equations of condition thus obtained the most probable values of g, h, 7t, R, and AR, can be found by the method of least squares. 208 REPORT ON The following are the equations of condition, formed in the manner just explained, for the Admiralty Standard Compass. Absolute Term. g h k A> A/v O <• — O.I 60 + 0.008 - 1.448 + .000 + 0-215 + 6.24 o ~ — 0.899 -1- 10-23 — 8.007 + .000 + 2-097 + 125-8 o _ + 0.320 — 4-779 — 0.376 + .000 — 0.806 - 51.61 o — . — 0.141 + 4-791 — 0.164 + .000 — 0.806 — ' 51-61 o _ — 0.108 + 1.561 + 0.558 + .000 — 0.275 23.10 o = — 0.129 + 0.545 — 0.442 •+• .000 — 0.115 11.48 o = — o. 1 49 + 1-322 — 0.485 + .000 — 0.223 - 30-76 o = — 0.016 — 1.401 — 0.140 + .000 — 0.223 — 34.32 o = — 0.068 + 8.822 — 0.033 + .000 — 1.263 — 227.3 o =- — 0.175 + i-i32 + 1-136 + .000 -f O.2I I + 41.59 0 = O.II8 — 1.046 — 0.580 -f .000 + 0-155 + 32.66 O =5 O.O58 — 0.497 — 0.165 + .000 + 0.093 + 21.74 From these equations of condition, the following normal equations have been obtained by the method of least squares. Absolute Term. f h k R loo AA' o = — 12.462 + 237-337 0=4- 7.286 79.068 + 68.794 o «=« — 1.701 •f 20.688 — 10.147 + 12.000 o = — 1-957 + 9-858 — 16.451 — 0.941 + 7-605 0 = I. 112 — 7-5'3 • 9-444 2.O22 + 6-735 + 7.892 Solving, we find g = -f 0.04070 h = -f 0.00504 R = 0.1006 0.16(55 = -f <).()(i!)4 Substituting these results in the equations of condition, we find that the probable Z' error of a single observed value of is ^ 0.024, and the probable error of a com- yi £ putcd value of r is -j- 0.007. 7' In a precisely similar manner, from the values of ~ observed at the position of /! the After Azimuth Compass, we obtain the following equations of condition. Absolute Term. f h i A- A A' O »• + O-50I - 4-79° + 0.173 + .000 — 0.806 — 51.61 0 «- — 0.625 + 4.663 — 1. 114 + .000 — 0.806 — 51.61 o ™ — 0.115 + 0.979 + '-338 + .000 — 0.275 — 23.10 o ™ -f 0.059 + 0.358 — 0.603 + .000 — 0.115 — 11.48 0 =• O.IOI + 1-370 — 0.324 + .000 — 0.223 — 30.76 o — + 0.154 — '-393 — o. 205 + .000 — 0.223 — 34.32 o = — 0.602 + 8.823 + 0.031 + .000 — 1.263 — 227.3 o — — 0.165 + 1-250 + i. 006 + .000 + O.2II + 41.59 o ™ — 0.049 + 0.314 + i-'54 + .000 -f o^ss -f- 32.66 o ™ -f- 0.094 — 0.257 — 0.456 -f .000 + 0.093 + 21.74 MAGNETIC OBSERVATIONS. 209 And the resulting normal equations are Absolute Term. g h i K 100 A/I? o = — 11.313 + 129.164 ° = + o-3JI — 3.078 + 6.125 o = — 0.851 + ii-S1? + I.OOO -f- IO.OOO o == + 0.840 — ii-°53 + 0.888 — 3-253 + 3-i6i o = + 1.367 — 19.634 + 1.042 — 3-342 + 4.084 + 6.305 Solving, we find g = + 0.11398 7i = + 0.00981 k = — 0.0509 = — 0.3918 = -(- 0.3634 Substituting these results in the equations of condition, the probable error of a 7' single observed value of - - comes out ± 0.030, and the probable error of a com- Z' puted value of -~- comes out + 0.010. For the Admiralty Standard Compass we found 31 = 0.000, £> = + 0.017, and (£ = — 0.001. We have also a = a, ( 1 + £>) — 1 e = a, ( 1 — £)) — 1 b = x (£ - Hence a = _ 0.0605 I = — 0.0008 e = — 0.0917 d = — 0.0008 (S For the After Azimuth Compass we found 31 = 0.000, £) = -f 0.112, and — 0.000. Hence, in the same manner, a = _ 0.0396 e = - 0.2324 6= 0.0000 d= 0.0000 Collecting our results, we have the following final values of the coefficients of the ADMIRALTY STANDARD COMPASS. = o.ooo = + 0.0240 tan 9 + 0.460 JL — 0.00102 — ± o.ooi — 0.0016 tan 9 + 0.006 -L _ 0.00023 — ± 0.002 - — '£1 z = + 0.017 ± o.ooi = - O.OOI ± O.OOI + 0 0407 ' tan 0 27 December, 1872. _ 0.0050 tan 9 .1006 + 0.1665 4- +0.000694 4 ±o-°°7 210 REPORT ON x = 4- 0.924 ± 0.004 = 4- 0.0240 p —— = 4. 0.460 C = 4" 0.0221 /"= 4-0-425 b = — 0.0008 d = — 0.0008 = 0.00102 X A/* = + 0.00094 e = — 0.0917 •J— «= — 0.0016 x -i- = 4. 0.006 / = — O.OOI5 Q = 4- 0.006 £•=4- 0.0407 h = 4 0.0050 — ^ «. — 0.00023 A(? = O.OOO2I « = 0.0605 /& = 4- o. 1006 7? = 4- 0.166 AT? = 4- 0.00069 Hence, the general equations for the determination of the deviations of this compass are X' •= X — 0.0605 X — 0.0008 F+ 0.0221 Z 4- 0.425 — 0.00094 / y = Y — 0.0008 X — 0.0917 Y — 0.0015 Z 4- 0.006 — 0.00021 / Z' = Z + 0.0407 X + 0.0050 Y+ o. 1006 Z + o. 166 4- 0.00069 t The following are the final values of the coefficients of the AFTER AZIMUTH COMPASS. 21 = o.ooo 33 = — 0.0026 tan 9 — 0.373 -L — 0.00032 -— ± 0.004 Ji H Q, = + 0.0066 tan 6 — 0.044 -J. 4- 0.00039 — ± 0.004 H H !^=> 4- o. 112 ± 0.003 Q = o.ooo ± 0.003 cosf — a I + O.II40 0.0098 ^5-i 0.0509 0.3918 — 4- 7 ti« A ' *«« yi j 7 oy ^ T^ tan 9 X -i + 0.864 ± O.OII tan 9 _ ±0.010 — — — 0.0026 ^ = O.OO22 £ = o.oooo -^- — 0.373 P = — 0.322 d = o.oooo ~ . _ 0.00032 1- + 0.0066 A/* = — O.OOO27 /= + 0.0058 , = —0.2324 g = + 0.1140 -^-«_ 0.044 ,, E^ we remark that each observed deviation furnishes an equation of condition of the form 0 = — 6 -f A, + B, sin f -f d cos £ -f- DL sin 2% + El cos 2£ and from all the equations thus obtained the values of the coefficients must be found by the method of least squares. As all the compasses were observed simul- taneously; the deviations at each place are given on the same points in the case of each compass. Hence, although the absolute terms in the equations of condition will be different, the numerical coefficients of the unknown quantities Av #„ C]t DH EL, will be identical for all the compasses at any one station. Advantage has been taken of this circumstance in forming the following table, which gives the equations of condition for all the compasses at Ceara. The absolute terms of the equations of condition belonging "to any compass will be found in the column headed with the name of that compass, while the coefficients of the remaining terms of the equations will be found in the columns headed A^ /?„ C}, D , E{. For example, the first equation of condition for the Admiralty Standard Compass is 0 = _ 170 + A, + 0.195 B, + 0.981 <\ + 0.383 D, + 0.924 E,. 212 REPORT ON Iu the same way, the first equation of condition for the After Binnacle Compass is 0 = — 220 + A, -r 0. 195 B, + 0.981 C, + 0.383 A + 0.924 E,. EQUATIONS OF CONDITION AT CEARA. Absolute Terms. frt5 d Coefficients of the Unknown Quantities. II fcl *• i! 1| 11 J C •a _ c, A *, — 2IO — 310 — 820' — 820 — 180' — 270 — no' — IIO -430' — 520 + .000 4- .000 + 0.195 + 0.383 + 0.981 + 0.924 + 0.383 + 0.707 + 0.924 + 0.707 — 260 — 390 — 820 — 280 IIO — 600 4- .000 + 0.556 + 0.831 + 0.924 + 0.383 — 35° — 340 — 470 — 420 — 97° — 99° — 280 — 211 — 180 — 130 — 480 -380 4- .000 4- .000 + 0.707 + 0.831 + 0.707 + 0.556 + 1. 000 + 0.924 o.ooo — 0.383 — 33° — 410 — 1140 — 2OO — no — 300 4- .000 + 0.924 + 0.383 + 0.707 — 0.707 — 310 — 410 — 1 020 — 130 — 40 — 420 4- .000 4- 0.981 + 0.195 + 0.383 — 0.924 — 230 — 260 — 850 — IIO + 40 — 170 4- .000 + 1. 000 o.ooo o.ooo — I. OOO — 210 — 240 - 690 IIO + '30 — 40 4- .000 + 0.981 — 0.195 — 0.383 — 0.924 — 170 — 170 — 660 — 40 + 140 — 30 4- .000 + 0.924 -0.383 - 0.707 — 0.707 From these equations of condition five normal equations were obtained for each compass by the method of least squares; but on attempting to solve them the numerical coefficients of Z>, and Er came out so small that no confidence could be placed in the resulting values of these quantities ; and moreover, the uncertainty of them vitiated the values of A^ B^ and (7,. It was therefore considered best to reject the normal equations in Z>j and J?j, and to employ in their stead the equations using for £) and Q the numerical values already found. The following are the normal equations thus formed, and the resulting values of A^ -B,, (7, Z>,, and Et, for each compass. For convenience of computation, the unit of the absolute terms of the normal equations has been changed from minutes of arc to radius. ADMIRALTY STANDARD COMPASS. Hence 0 = — o 7505 + 10 .000 A ,+ 7.482 *,+ 3-999 ci + 3-938 D, — 2.631 o = — o, 5789 + 7 .482 A , + 6-3'7 *t + 1.969 c, + z-334 A — 3-774 o =» — o 3'83 + 3 999 A , + 1.969 *> + 3-685 c, + 3.708 A + 1.665 o = — o, ,0169 + A + *( B\- - C?) o = + o .0009 + E\ + B\ ct Al — 0.0102 = — 0° 35'.' /?, = + 0.0833 = + 4 46.3 C, = + 0.0405 =- + 2 19.2 A = + 0.0142 = + 0 48.8 — 0.0043 = — o 14.8 MAGNETIC OBSERVATIONS. 213 Hence Hence AFTER BINNACLE COMPASS. o = — 0.9599 + 10-000 Al 4- 7.482 £t 4- 3.999 C, + 3.938 Z>, — 2.631 EI — o-7253 + 7-482 A, + 6.317 £l + 1.969 <7, + 2.334 Dl — 3.774 £, ° = — o-44i3 + 3-999 ^ + 1-969 A + 3-685 C, + 3.708 Dl 4- 1.665 ^, o = _ 0.0385 + A + i (As— c;1) o = + 0.0018 +.£•,+ ^ c; + 0.0047 W— c,') Al== -{- 0.0062 = -f o° 2i'-3 -5, = + 0.0801 = + 4 35.2 c; = 4- 0.0362 = 4-2 4.6 A = 4- 0.0360 = 4-2 3.6 EI = — 0.0048= — o 16.3 AFTER RITCHIE COMPASS. o = — 2.5540 4- 10.000 A, 4- 7.482 £, 4- 3.999 Cl 4- 3.938 Z>, — 2.631 £, o = — 1.9282 4- 7.482.4. 4-6.317.5, 4- 1.969 C, 4- 2.334 A — 3-774 -£, o =— 1.0844 4- 3-999 ^i + 1-969 A + 3-685 Ci 4- 3.708 ZJ, 4- 1.665 ^i o = — 0.0340 4- Dl 4- \ (B* — Cf) 0 = 4- 0.0008 4-^4-^, c, A! =-- 4- 0.1030 = 4-5° 54'. 2 A = 4- 0.1385 = 4- 7 56.0 C, = 4- 0.0859 = + 4 55-4 A = i: 0.0281 = 4- i 36.6 £t = — 0.0127= — o 43-7 Hence o o o o o FORWARD ALIDADE COMPASS. °-5265 + 10.000 A, 4- 7.482 £l 4- 3.999 C, 4- 3.938 Z>, — 2.631 °-3589 + 7-482^,4-6.317^ 4- 1.969 C, 4- 2.334Z>,_ 3.774 • 0.3022 4- 3.999 At 4- 1.969 £t 4- 3.685 Ct 4- 3.708 Z», 4- 1.665 • 0.0235 +A + i W-Q) . 0.0007 + A, 4- B, c, 4- 0.0125 (A2— QO ^i = + 0.0359 = + 2° 3'-5 A = 4" O.OOOI = 4~ O O.2 c, = 4- 0.0188 = 4-1 4.8 A = + 0.0237 = 4- i 21.4 £t = 4" 0.0007 = 4" ° 2-4 Hence FORWARD BINNACLE COMPASS. o = — 0.1396 4- 10.000 Al 4- 7.482 Sl 4- 3.999 C, 4- 3.938 Z>, — 2.631 EI o — — 0.0593 4- 7.482 A, 4- 6.317 B^ 4- 1.969 C, 4- 2.334 Z>, — 3.774 .£, o = — 0.1831 4- 3.999,4, 4- 1.969^, 4-3.685 C, 4-3.708,0, 4- 1.665^, o = — 0.0369 -f D, 4- \ (£* — C,1) o = — o.oon 4- E, 4- ^ C, ^, =—0.0159 = — o° 54'- 7 .Z?, = 4- 0.0072 = 4-0 24-6 C, = 4- 0.0253 = + ' 26-9 Z>, = 4- 0.0372 = 4-2 7.8 El>^= 4- 0.0009 = 4-o 3-2 214 RETORT ON Hence FORWARD RITCHIE COMPASS. o = — 0.9803 + 10.000 Al + 7.482 BI 4- 3.999 Ct 4 3.938 Dt — 2.631 E, o = — 0.6394 + 7-482 At 4 6.317 JBl 4 1.969 Ct 4 2.334 Z>t — 3.774 £l o=— 0.6193 + 3-999^1 + 1-969 A + 3-685 C, + 3.708.0, 4 1.665^, o = - 0.0407 4 A + i W — <7) 0 = 4 0.0013 4- .£, 4 BI Cl A, = + 0.0614 = + 3° 3i'-° Bl = — 0.0076 = — o 26. i C, = + 0.0631 — + 3 36.9 /), = -)- 0.0427 = + 2 26.6 £t = — o.oon = — o 3.9 The following are the equations of condition, together with the resulting normal equations, and the values of the coefficients J.,, S^ Ci, !)» E^ as determined for each compass from the observations made at Rio Janeiro. EQUATIONS OF CONDITION AT Rio JANEIRO. Absolute Terms. Coefficients of the Unknown Quantities. ^•"O d _fj flj (3 d fl •3.3 "S" "2 Ji C "0 I 12 B g S2 "59 fc S - — 4 ^H ^ c S H 5« S Si3 u.~ I* &* j_ .— f jl *, c, A e, 4 290' — 320' — 840' — 160' -250' — 160' - 500' 4 i.ooo 40.556 4 0.831 4 0.924 4 0.383 4-360 — 410 — 840 — I2O — 250 — 160 — 500 4- i.ooo 4 °-7°7 4 0.707 4 «.ooo o.ooo 4 390 — 430 — 840 — 20 — 250 — 160 — 370 -j- .000 4- 0.831 4 0.556 4- 0.924 — 0.383 + 35° — 430 — 970 4 '3° — 180 — 160 — 460 4 -ooo 4 0.924 4 0.383 4 0.707 — 0.707 4 330 — 360 — 1010 4 160 — 160 — 160 — 500 4- .000 4 0.981 4 0.195 4 0.383 — 0.924 4 320 — 340 .— 880 4- 280 — 160 — 160 — 440 4- -ooo 4 i.ooo o.ooo o.ooo I.OOO 4 300 — 340 — 720 4 390 — 160 — IOO — • 420 4- -ooo 4 0.981 — 0.195 — 0.383 — 0.924 4 280 — 280 — 610 4 4>o — 160 — 140 — 350 4- .000 4 0.924 - 0-383 — 0.707 — 0.707 4- 260 — 260 — 59° 4440 — 160 — IOO — 330 4- .000 4 0.831 — 0.556 — 0.924 — 0.383 4 240 — 190 — 59° 4400 — 160 — 20 — 33° 4- .000 4 0.707 — 0.707 I.OOO 0.000 4- 201 — 170 — 510 4 320 — 160 — 60 — 330 4- .000 40.556 — 0.831 — 0.924 4 0.383 4- 2IO — no — 510 4 200 — 230 — 80 — 330 4- .000 4 0.383 — 0.924 — 0.707 4 0.707 + 170 — 9° — 510 4 70 — 250 — 80 — 270 4 .000 40.195 — 0.981 — 0.383 4 0.924 4 150 — 9° — 510 — 20 — 250 — 140 — 250 4- .000 o.ooo — I.OOO 0.000 4 i.ooo 4 140 — 20 — 510 — 190 — 3>o — IOO — 180 4 .000 — 0.195 — 0.981 4 0.383 4 0.924 4 120 — 10 — 510 — 290 , — 330 — 80 — 230 4- .000 — 0.383 — 0.924 40.707 4 0.707 4-90—10 — 510 — 310 — 33° — 80 — 250 4- .000 — 0.556 — 0.831 4 0.924 4 0.383 Hence Normal Equations. ADMIRALTY STANDARD COMPASS. o = — 1.2217 4- 17.000 AI 4- 8.442 BI — 5.641 C1, 4- 0.924 Z», 4- 0.383 Et o == — 0.7991 4- 8.443 A, + 8.310 Bt 4- 0.462 C, — 1.205 Dl — 4.543 £t o == 4- 0.1662 — 5.641 AI -f 0.462 Bl 4- 8.691 £", -f 3.900 Z>, — 4.438 £t o = — 0.0169 4- Z>, 4- i (B? — C,1) 0=4- 0.0009 +-£, + .», C, A, =-. + 0.0453 = + 2° 35'- 7 B\ = + 0-05I9 = + 2 58.5 C, = 4- o.oooi =4-0 0.2 Dt =-- 4- 0.0156 = + o 53 5 £t = — 0.0009 " — o 3- ' MAGNETIC OBSERVATIONS. 215 AFTER BINNACLE COMPASS. ° = — 1-1228 + 17-000.4, + 8.442^ — 5.641 C, + 0.924 A + 0.383 A o== — 0.8724 + 8.442,4, + 8.310^, + 0.462 Cl— 1.205 A — 4-543^, o = — 0.0346 — 5.641 Al + 0.462 £l + 8.691 q + 3.900 Z»' — 4.438 Et °= — 0-0385 + A + £ W— C,') o = + 0.0018 + El + A C, + 0.0047 (A2 — ci2) Hence At = -if- 0.0148 = -f-o° 50'. 8 -ff, = + 0.0947 = + 5 25.4 C\ = — 0.0073= — ° 25-2 A= + 0-0340 = + i 57-1 •El = — 0.0012= — o 4.1 AFTER RITCHIE COMPASS. 0 = — 3-3336 + i7-ooo A, + 8.442 £, — 5.641 Cl + 0.924 A + 0.383 £± o — — 1.9499 + 8.442 At + 8.310 J3i + 0.462 Ct — 1.205 A — 4-543 EI o = + 0.6086 — 5.641 Al + 0.462 BI + 8.691 C, + 3.900 Z>, — 4.438 ^ o = _ 0.0340 + A + i W — C,*) o = + 0.0008 + .£, + Jf, Cl Hence ^, = + 0.1684 = + 9° 39'-° A = + 0.0659 = + 3 46.6 Cl = + 0.0203 = + ! 9-8 A = + 0.0320 = + i 50. i JEl = — 0.0021 = — o 7.4 AFTER AZIMUTH COMPASS. o = + 0.4916 + 17.000 Al + 8.442 BI — 5.641 Cl + 0.924 DI + 0.383 E± o = + 0.6880 + 8.442 AI + 8.310 Bl + 0.462 C, — 1.205 A — 4-543 -^i o = — 0.2024 — 5-641 Al + 0.462 BI + 8.691 C, + 3.900 Z>, — 4.438 £t o = — 0.1116 + Z>, + i (£? — C^) o = + 0.0002 + £1 + BI C^ Hence ^, = — 0.0434 = — 2° 29'-3 ^, = — 0.0199 = — i 8.5 C, = — 0.0552 = — 3 9.7 Dl = + 0.1129 = + ^ 28.2 E^ = — 0.0013 = — ° 4-5 FORWARD ALIDADE COMPASS. o = — 1.0908 + 17.000 Al + 8.442 BI — 5.641 C, + 0.924 Z>, + 0.383 EI o = — 0.4111 + 8.442 At + 8.310 B^ + 0.462 (7, — 1.205 Z>, — 4-543 -^i o = + 0.4058 — 5.641 Al + 0.462 BI + 8.691 Ct + 3.900 Z>, — 4-438 EI o = - - 0.0235 + A + i (A1 — c-!) o = — 0.0007 + A + A c, + 0.0125 W — ci') Hence ^, = + 0.0615 = + 3° 3i'-5 BI = — 0.0084 = — o 28.8 C", = — 0.0166= — o 57.2 Dl = + 0.0236 = + i 21. i .£, = + 0.0006 = + o 1.9 216 REPORT ON FORWARD BINNACLE COMPASS. 0 _ _ 0.5643 + 17.000 At 4- 8.442 A — 5-64i Cl 4- 0.924 Dt 4- 0.383 Et o = — 0.3228 + 8.442 A, 4- 8.310 Bt + 0.462 Ct — 1.205 Dt — 4-543 ^, o = 4- 0.0861 — 5.641 A, + 0.462 Bt + 8.691 ^ + 3.900 Z>, — 4-438 ^i o = — 0.0369 + A + * W — C.') o = — o.oon •+• .£, + BI Ct Hence y4, = — 0.0050 = — 0° I7'.I Bt = 4- 0.0523 = 4- 2 59.8 C, = — 0.0307 = — i 45-5 A = + 0.0360 = + 2 3-7 2?,= -|- 0.0027 = + o 9.3 FORWARD RITCHIE COMPASS. o = — 1.7570 + 17.000 Al 4- 8.442 Bt — 5-64i ^ 4- 0.924 Dt + 0.383 -£", o = — 1.0582 + 8.44? At 4- 8.310 Bt 4- 0.462 C\ — 1.205 A — 4-543 -#1 0=4- 0.3128 — 5.641 At + 0.462 A 4- 8.691 C, 4- 3.900 £>, — 4-438 •#, o = — 0.0407 + A + i W -C,1) o = + 0.0013 + £t -f A C, Hence A, = + 0.0564 = -f 3° 14.0 ^, = + 0.0766 = -f 4 23.5 C, = — 0.0205 = — i 10.4 Z>, = + 0.0380 = -|- 2 10.5 .£, = o.oooo = o o.o The following are the equations of condition for the determination of the coeffi- cients of the After Ritchie Compass at Monte Video. o = — 240'+ i.ooo At o.ooo J5t -\- i. ooo C1, o.ooo Z), + i.ooo E^ o = — 570 + i.ooo At + 0.195 A + 0-98i C, + 0.383 Z>, + 0.924 EI o = — 570 + i.ooo ^, + 0.383 ^ 4- 0.924 C, + 0.707 Z>, 4- 0.707 Et o = — 740 4- i.ooo ^, 4- 0.556 Bt 4- 0.831 C, 4- 0.924 Z>, 4- 0.383 £t o = — 740 -(- i.ooo y4t 4" 0.707 £t 4- 0.707 C, 4- i.ooo Z>, o.ooo jff, o = — 740 4- i.ooo ^4, 4- 0.831 .5, 4- 0.556 C, 4- 0.924 Z>, — 0.383 EI o = — 910 4- i.ooo At + 0.924 2?, 4- 0-383 C, + 0.707 Z>, — 0.707 2?, o = — 900 -|- i.ooo At -\- 0.981 Bt 4- °-I95 C\ + 0-383 A — 0.924 Et o = — 560 4- i.ooo ^, 4- i.ooo /?, o.ooo C, o.ooo £>t — i.ooo EI o = — 240 + i.ooo At 4- 0.981 Bt — 0.195 £"i — 0-383 A — °-924 EI o = — 230 4- i.ooo ^, 4- 0.924 Bt — 0.383 C, — 0.707 Z>, — 0.707 EI o = — 60 4- i.ooo At 4- 0.831 Bt — 0.556 C, — 0.924 Dt — 0.383 EI o = 4- 27° + i.ooo At -\- 0.707 Bt — 0.707 C, — i.ooo Z>, o.ooo EI 0 = 4- I0° 4- i-ooo At + 0.556 Bt — 0.831 C, — 0.924 Z>, 4- 0.383 Et o = — 240 + i.ooo At + 0.383 Bt — 0.924 C, — 0.707 Z>, + 0.707 Et o = — 240 4- i.ooo yf, 4- 0.195 B\ — 0-98i C, — 0.383 Dt + 0.924 2?, o = — 240 4" i-ooo At o.ooo /?, — i.ooo C, o.ooo /?, 4- i.ooo Et o = - 410 4- i.ooo At — 0.195 A — 0.981 C, 4- 0.383 Dt 4- 0.924 .fi", o = — 410 + i.ooo At — 0.383 Bt — 0.924 C, + 0.707 Z>, 4- 0.707 EI o = — 240 + i.ooo .4, — 0.556 Bt — 0.831 C, 4- 0.924 Z>, + 0.383 Et o = — 240 + i.ooo ^, — 0.707 Bt — 0.707 C, + i.ooo Dt o.ooo /?, o = — 570 4- i.ooo At — 0.831 2f, — 0.556 C, + 0.924 Dt — 0.383 2?, MAGNETIC OBSERVATIONS. 217 The resulting normal equations are Hence o = — 2.5365 + 22.000 Al + 7.482 £, — 3.999 C, + 3.938 A + 2-631 &i o=— 1.0294+ 7.482^+9.685^,+ 1.969 C,— 2.334 A — 3-774 -E, o = — 0.3901 — 3.999 Al + 1.969 ^ + 12.316 Cl + 3.708 A — I-665 A ° — — 0.0340 + A -{- ^ (-^i* — ^V) o = + 0.0008 + £l + B^ C i 32'.8 50.3 10.9 1.8 5.5 .5,= + 0.0146 = + o C", == + 0.0555 = + 3 A = + 0-0354 = + 2 £l = — 0.0016 = — o The following are the equations of condition, together with the resulting normal equations, and the values of the coefficients A^ B,, C,, Z>15 Eu as determined for eacli compass from the observations made in Magdalena Bay. EQUATIONS OF CONDITION AT MAGDALENA BAY. Absolute Terms. Coefficients of the Unknown Quantities. 3s % "5 d •g-i fj "3 *o •"3 V 11 rt || jj fj « e li |3 <] M 1* |« 4 *, c\ *>l *, _i_ 20 — 10' — 100' — 300' — 300' — 540' + .000 — 0.707 — 0.707 + 1. 000 o.ooo + 60 10 — 180 — 370 — 290 — 460 + .000 — 0.831 — 0.556 + 0.924 - 0.383 + I 10 + 80 — 180 2IO 2IO —380 + -000 — 0.924 - 0.383 + 0.707 — 0.707 + 140 + 160 — 180 — 130 210 — 290 + .000 — 0.981 — 0.195 + 0.383 — 0.924 ti8o + 170 — 80 — 130 — 120 — 200 + .000 I. OOO 0.000 o.ooo — I. OOO 230 + 320 + 170 2IO + 50 + 50 + .000 — 0.981 + 0.195 — 0.383 — 0.924 + 230 + 320 + 330 — 13° + 130 + 2IO + .000 — 0.924 + 0.383 — 0.707 — 0.707 + 250 + 320 + 320 120 + 2IO + 2IO + .000 — 0.831 + 0.556 — 0.924 - 0.383 + 220 + 320 + 160 — 40 + 3°0 + 210 + .000 — 0.707 + 0.707 — I. OOO o.ooo + 22O + 320 + 160 — 40 + 380 + 300 + .000 — 0.556 + 0.831 — 0.924 + 0.383 + 160 + 320 + 15° + 40 + 380 + 370 + .000 — 0.383 + 0.924 — 0.707 + 0.707 tioo + 230 + 60 + 40 + 380 + 210 + .000 — 0.195 + 0.981 -0.383 + 0.924 40 + 150 100 + 40 + 370 4- 210 + .000 o.ooo + 1. 000 o.ooo + I. OOO + 30 + 70 — 190 — 50 + 290 + I 2O + .000 + 0.195 + 0.981 + 0.383 + 0.924 Hence o = + 0.5789 + 14.000 o= — 0.4310-- o = + 0.2352 + o = - 0.0169 + o = + 0.0009 + 8.825 4.717 A + Normal Equations. ADMIRALTY STANDARD COMPASS. t — 8.825 A + 4-7r7 ci — I-631 D\ — 1.090 £, i + 7-545 A — °-Sl6 ci + 0-934 A + 4-272 -Ei — 0.816 Bl + 6.456 C, — 4-554 A + 3-7§4 £t Al = + 0.0026 = + o° ^,= + 0.0559 = + 3 Cl = — 0.0204 = — i A= + °.°i56 = + ° £t = + 0.0002 = + o 9.! I2-T 10.3 53-5 0.8 28 January, 1873. 218 REPORT ON Hence AFTER BINNACLE COMPASS. o = + 0.8029 + 14-000 A, — 8.825 £l + 4-717 Ci — 1.631 A — 1. o = _ 0.5291 - 8.825 A, + 7-545 A - 0.816 C, + 0.934 A + 4. o = + 0.4497 + 4-7'7 A — °-Sl6 B* + 6>4s6 C' ~~ 4'554 DI + 3' o = — 0.0385 4 A + i W — C'') o = + 0.0018 + £t + B, C, 4 0.0047 (A1 — C,') AI = — 0.0208 = — i° n'-4 ^,= + 0.0393 = + 2 i5-° C, = - 0.0222= - I l6.2 A = 4- 0.0380 = 4 2 10-5 Et = — 0.0010:= — o 3.3 AFTER RITCHIE COMPASS. 090 El 272 E, Hence Hence o = + 0.0989 + 14.000 A, — 8.825 o = — 0.1171 — 8.825 At 4- 7.545 o = + 0.2238 + 4-717 A, — 0.816 o = — 0.0340 + A + i W — C,1 o = + 0.0008 + .£, + .ff, C, , + 4.717 C, — 1.631 /?„ — 1.090 », — 0.816 C, + 0.934 Z>, + 4.272 I + 6.456 C, — 4-554 A + 3-784 + 3° 3S'-5 B^ = + 0.0778 = + 4 27-3 C, = — 0.0497= — 2 51.0 A= + 0.0322 = 4 i 50.7 £t = 4 0.0031 = + 0 10.6 FORWARD ALIDADE COMPASS. o = — 0.4683 + 14.000 Al — 8.825 j9, + 4.717 C, — 1.631 A — I-°9° -^i o = 4-0.4115 — 8.825.4, 4- 7.545 .#, — 0.816 Cl 4-0.934 A 4-4.272^, 0 = 40.1082 4 4.717^, — 0.816^?, + 6.456 C, — 4-554 A + 3-784^, o = — 0.0235 + A + o = — 0.0007 + -^i At = 4 0.0200 = + i° 8'.8 ^, =: - 0.0361 = - 2 4. 1 C, =: - O.OI97 = - I 7-6 A= + 0.0230 = -\- 1 19.2 .£ = O.OOOO = O O.O FORWARD BINNACLE COMPASS. 0=4 0.3956 4 14.000 Al — 8.825 0=4 0.0125 — 8.825 A, 4 7.545 o = + 0.7497 4 4.717 /*, — 0.816 o = - 0.0369 + A + i W — C," o = — o.oon + EI 4 #, C, I + 4.717 C, — 1.631 A — I-°9° I — 0.816 C, 4 0.934 A + 4-272 ^ 4- 6.456 C, — 4-554 A + 3- 784 Hence ^, = — 0.0298 = — i 5, = 0.0478 = 2 C, = — 0.0719 = — 4 A = + 0.0384 =42 El = — 0.0023 — — ° 0 42'.6 44-3 7-3 ii. 8 7-9 MAGNETIC OBSERVATIONS. 219 Hence FORWARD RITCHIE COMPASS. 0 = + °-°o5S + 14.000 A, — 8.825 £l + 4.717 C, — 1.631 Dl — 1.090 El -. + 0.2058 — 8.825 A, + 7.545 B, — 0.816 C, + 0.934 Z>, + 4.272 .£, o = + 0.6749 + 4.717 A, — 0.816 A + 6.456 C, — 4.554 D, + 3.784 £l o = _ 0.0407 + A + i (A2 — c*) o = + 0.0013 + A + A Ci ^, = + 0.0477 = + 2° 43'-8 A = -f- 0.0116 = -|- o 39.9 Cl = — 0.1051= — 6 1.3 •A=+ 0.0462 = + 2 38.7 £1 = — 0.0004 = — o 1.3 For convenience of reference the values of the coefficients Alt Blt Ci, Dlt Eu obtained at stations where the compasses were not read on all the thirty-two points, have been collected in the following table. No use has been made of them. Stations and Compasses. A^ *i c, ^1 *, Ceara, December 19, 1865. Admiralty Standard Compass .... — o°3S'.i + O 21 ^ + 4° 46'-3 + 2° I9'.2 4-2 46 4- o° 48'. 8 + 2 1 A — o° I4'.8 After Ritchie Compass . + e C4. 2 4-i 36 fi Forward Alidade Compass + 2 3.C. + o 02 4-i 48 ° 43-7 Forward Binnacle Compass .... Forward Ritchie Compass .... — o 54-7 + •? -?T o -(- o 24.6 4- i 26.9 4-2 7-8 4-2 26 6 4-o 32 Rio Janeiro, January 10, 1866. Admiralty Standard Compass .... 4-2 35-7 4-0 S.Q 8 + 2 58-S J- c 2^ 4. -|- O O.2 4- o 53.5 -• o 3.9 — o 3.1 After Ritchie Compass 4- ^ 46 6 4-i 08 — 2 2Q. 3 — i 85 , i o 7 -f- 6 28 2 + 1 11 "\ — o 28 8 O S7 2 Forward Binnacle Compass .... — o 17.1 + -) 14. O + 2 59.8 4- 4. 21. <; — i 45-5 — I IO 4. + 2 3.7 + 2 IO 5 + ° 9-3 Monte Video, January 24, 1866. 4-6 -12 8 + O SO 3 + •? IO Q + 2 I 8 O C C Magdalena Bay, June 9, 1866. Admiralty Standard Compass . — . . . + o 9.1 — I 11.4 + 3 12.1 + 2 I5.O — i 10.3 I 1 6. 2 + o 53-S 4-2 10.5 + o 0.8 O 7.^ + 7 -it e + 4. 27 7 — 2 ei.o 4- ' 5°-7 -f- o 10.6 + i 88 — 2 4. I — i 7.6 4- i 19.2 o o.o Forward Binnacle Compass .... Forward Ritchie Compass . — i 42.6 4- 2 4^.8 — 2 44-3 4- 0 3Q.Q. -4 7-3 — 6 l.i 4-2 II. 8 4-2 18.7 — o 7.9 — 0 I.T At a number of the ports visited during the cruise, the line dividing the north from the south polarity, on the exterior of the turrets, was traced out; but as the boundary between the two kinds of magnetism was frequently very badly denned, and the observations were otherwise unsatisfactory; and further, as they throw no light whatever on the theory of the deviations of the compasses, and can only be shown by means of drawings on a rather large scale, it has not been deemed worth while to insert them here. In conclusion, the results of the observations made during the cruise may be briefly recapitulated as follows: 1°. The latitudes of seven points have been determined. 2°. The magnetic declination, inclination, and horizontal force, have been deter- mined at eighteen places. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. DEC 1 2 1967 RECEIVED DEC 5 '67- I_O/\N JDtHT \ 99? THE UNIVERSITY OF CALIFORNIA LIBRARY