QC
UC-NBLF
ROE AND LABOR
UEODETIU SURVEY
O. H. TITTMANN.
DIRECTIONS
FOR
MAGNETIC MEASUREMENTS
BY
DANIEL L. HAZARD
COMPUTER, DIVISION OF TERRESTRIAL MAGNETISM
WASHINGTON
GOVERNMENT PRINTING OFFICE
, 1911
GIFT OF
DEPARTMENT OF COMMERCE AND LABOR
M ^ COAST AND GEODETIC SURVEY
O. H. TITTMANN, SUPERINTENDENT
DIRECTIONS
FOR
MAGNETIC MEASUREMENTS
BY
DANIEL L. HAZARD
COMPUTER, DIVISION OF TERRESTRIAL MAGNETISM
WASHINGTON
GOVERNMENT PRINTING OFFICE
1911
OF THE
UNIVERSITY
.-
or,
CONTENTS.
Page.
Preface 5
THEORY or MAGNETIC MEASUREMENTS.
The earth's magnetism 7
Introduction 7
Magnetic elements 7
Units of measure of intensity 8
Distribution of the earth's magnetism 8
Variations of the earth's magnetism 9
Derivation of formulas 10
Determination of the true meridian by observations of the sun 10
Dip '. 12
Horizontal intensity 14
Oscillations 15
Deflections 17
Total intensity 21
Determination of the constants of a magnetometer 23
Moment of inertia 23
Temperature coefficient 26
Induction coefficient 28
Distribution coefficients 30
Deflection distances 34
DIRECTIONS FOR MAGNETIC OBSERVATIONS ON LAND.
General directions 35
Equipment 39
Latitude from observations of the sun 40
Latitude from observations of Polaris 44
Determination of the true meridian and local mean time by observations of
the sun 45
Adjustment of the theodolite 45
Observations 47
Computation 50
Determination of the true meridian by observations of Polaris 52
Determination of the magnetic declination * 53
A . With a 'magnetometer 53
Coast and Geodetic Survey pattern 53
India Magnetic Survey pattern 59
Declination from horizontal intensity observations 61
B. With a compass declinometer or compass attachment of a dip circle. 62
Determination of the dip 66
A. With a dip circle 66
B. With an earth inductor 72
Determination of the horizontal intensity 74
Torsion observations '. 74
Oscillations 74
Deflections 75
Computation 78
Determination of the total intensity. 81
3
345597
4 \/ ; lC\ ; v CONTENTS.
DlREC?} OJJS .fSpa ;Q^\AT10N& AT' SEA .
.:. . /.*. : : ?.- !'." ....................................... 87
Decimation ............. : ............................................. 88
Dip and total intensity ................................................. 97
Special directions ...................................................... 102
DIRECTIONS FOR OPERATING A MAGNETIC OBSERVATORY.
Buildings .............................................................. 103
Variation instruments. . ................................................ 103
Conversion to absolute values ........................................... 106
Base-line values ................................................... 107
Scale values ...................................................... 109
Temperature coefficients ........................................... 113
Temperature ........................................................... 114
Time scale ........... .......................... ........................ 115
Reading of ordinates .................................................... 115
Programme of work .................................................... 115
General directions ...................................................... 116
TABLES.
I. Correction to the observed altitude of the sun for refraction and parallax. . 119
II. Correction in azimuth and altitude of the sun for semi-diameter ........ 120
III. Latitude from circum-meridian altitudes of the sun; values of m ........ 120
IV. Latitude from circum-meridian altitudes of the sun; values of A ........ 121
V. Correction for rate of chronometer. (Oscillations) ..................... 126
VI. Torsion factor. (Oscillations) ......................................... 126
VII. Reduction of log C from 20 C. to other temperatures. (Deflections) ____ 127
VIII. Correction for lack of balance of dip needle ........................... 127
IX. Diurnal variation of declination ...................................... 128
X. Diurnal variation of dip .............................................. 129
XI. Diurnal variation of horizontal intensity ............................... 130
XII. Multiples of the sines of the angles 22. 5, 45, and 67. 5 ................ 131
ILLUSTRATIONS.
FIG. 1 . Fundamental spherical triangle ..................................... 11
2. Position of magnets during deflections ........ ........................ 18
3. Coast and Geodetic Survey pattern magnetometer ..................... 54
4. India Magnetic Survey pattern magnetometer ........................ 59
5. Kew pattern dip circle ............................................. 67
.6. Remagnetization of dip needle ....................................... 68
7. Wild pattern earth inductor ......................................... 72
8. Four and six oscillations ............................................ 75
9. Lloyd-Creak pattern dip circle ...................................... 98
10. Relative position of variometers ..................................... 104
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
PREFACE.
Although the principles involved in the measurements of the earth's
magnetism have not changed since the publication of the third
edition of "Directions for Magnetic Observations with Portable
Instruments," * the methods of observing and the instruments
used have received so many modifications as the result of accumu-
lated experience that a new presentation of the subject has been
needed for some time to facilitate the field work and to secure
uniformity. In addition it is important that the principles involved
should be explained in more detail than was done in the above-
mentioned publication, so that the observer may have a better under-
standing of what he is doing and why he is doing it without being
obliged to refer to other publications. Moreover, with the estab-
lishment of five magnetic observatories and the inauguration of
magnetic observations on board the vessels of the Survey, the need
has arisen for printed directions for making the observations required
in those two branches of the magnetic work of the Survey. The
endeavor will be made to present the subject-matter in such form
that an observer familiar with the use of instruments of precision
but without experience in magnetic work may be able to make in a
satisfactory manner the various observations incident to the deter-
mination of the magnetic elements without other assistance than that
to be obtained from these directions.
In the preparation of this paper the following publications have
been consulted:
Principal Facts of the Earth's Magnetism, by L. A. Bauer. Wash-
ington, Government Printing Office, 1909. (Reprinted from U. S.
Magnetic Declination Tables, 1902.)
Theory of Magnetic Measurements, by F. E. Nipher. New York,
1886.
Spherical and Practical Astronomy, by Wm. Chauvenet. Phila-
delphia, 1887.
Traite de Magnetisme Terrestre, by E. Mascart. Paris, 1900.
Erdmagrietismus, Erdstrom und Polarlicht, by Dr. A. Nippoldt, jr.
Leipzig, 1903.
*Appendix No. 8, C. & G. S. Report for 1881. Gov't Printing Office, 1882.
6 DIRECTIONS FOB MAGNETIC MEASUREMENTS.
Handbuch des Erdmagnetismus, by J. Lament. Berlin, 1849.
Ableitung des Ausdrucks fur die Ablenkung eines Magnetnadel
durch einen Magnet, by Dr. Borgen. Hamburg, 1891.
Collimator Magnets and the Determination of the Earth's Hori-
zontal Force, by Charles Chree. Proceedings Roy. Soc. London,
No. 419, 1899.
The Law of Action between Magnets, by Charles Chree. London,
Edinburgh, and Dublin, Phil. Magazine, August, 1904.
La Section MagnStique de Tobservatoire de 1' fibre, by E. Merveille,
S. J. Barcelone, 1908.
Elementary Practical Physics, by Stewart and Gee. London,
1887.
Elements of the Mathematical Theory of Electricity and Mag-
netism, by J. J. Thomson, Cambridge, England, 1897.
A Treatise on Magnetism and Electricity, by Andrew Gray.
London, 1898.
A Physical Treatise on Electricity and Magnetism, by J. E. H.
Gordon. New York, 1880.
Practical Problems and the Compensation of the Compass, by
Diehl and Southerland. Washington, Government Printing Office,
1898.
Admiralty Manual for the Deviation of the Compass, by Evans
and Smith. London, 1901.
The subject will be treated under the following general headings:
I. Theory of magnetic measurements, including some of the more
important facts about the earth's magnetism and the methods
employed for determining instrumental constants.
II. Directions for absolute observations on land.
III. Directions for observations at sea.
IV. Directions for operating a magnetic observatory.
THEORY OF MAGNETIC MEASUREMENTS.
THE EARTH'S MAGNETISM.
INTRODUCTION.
Whether the earth is a great magnet or simply acts as a magnet
as the result of electric currents flowing about it, it is surrounded by
a magnetic field, and the measurements of the earth's magnetism at
any place consist in determining the direction and intensity of that
field.
A magnet suspended in such a way as to be free to turn about its
center of gravity would take a position with its magnetic axis tangent
to the lines of force of the earth's magnetic field. As it is practically
impossible to suspend a magnet in that way, it is usual to determine
the direction of the earth's magnetic field by means of two magnets,
one constrained to rotate in a horizontal plane and the other in a
vertical plane.
MAGNETIC ELEMENTS.
The magnetic meridian at any place is the vertical plane defined
by the direction of the lines of force at that place.
The magnetic declination, D t is the angle between the astronomic
meridian and the magnetic meridian and is considered East or West
according as the magnetic meridian is east or west of true North.
Declination is often called variation of the compass or simply variation.
The dip or inclination, I, is the angle which the lines of force make
with the horizontal plane.
Instead of measuring the total intensity, F, of the earth's magnetic
field, it is usually more convenient to measure its horizontal com-
ponent, H. These three quantities, declination, dip, and horizontal
intensity, are usually spoken of as the magnetic elements and from
them the total intensity and its components in the three coordinate
planes may be computed by means of the simple formulas:
F=H sec I Y = H sin D
X = H cos D Z = H tan 7
X and Y being the components in the horizontal plane, X directed
north ( + ) or south ( ) and Y directed east ( + ) or west ( ), and
Z being the component directed vertical!}' downward.
8 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
UNITS OF MEASURE OF INTENSITY.
The intensity of a magnetic field is the force which a unit pole
would experience when placed in it. A unit pole is one which repels
an equal pole at unit distance with unit force.
At the present time almost all measurements of the intensity of
the earth's magnetic field are made in terms of the C. G. S. system,
in which the fundamental units are the centimeter, the gram, and the
second. Before the metric system came into general use, it was
customary in English-speaking countries to use the British system of
units, based on the foot, the grain, and the second. To convert
measures of intensity expressed in British units into their equivalents
in the C. G. S. system, they must be multiplied by the factor 0.046108
(logarithm = 8.66378).
DISTRIBUTION OF THE EARTH 's MAGNETISM.
The magnetic poles of the earth are those points on its surface at
which the dip needle stands vertical and toward which the compass
needle points, throughout the adjacent region. The north magnetic
pole is approximately in latitude 70 N. and longitude 97 W.,
and the south magnetic pole in latitude 73 S. and longitude 156 E.
It must be borne in mind that these magnetic poles have not the
characteristics of the poles of a bar magnet. If they had, there
should be an enormous increase in the total intensity when approach-
ing the poles, which is not the case. They are not even the points
of maximum intensity, there being four areas, two in each hemis-
phere, in which the total intensity is greater. The earth acts like a
great spherical magnet; that is, a bar magnet at its center which
would produce the effects observed at the surface would have its
poles practically coincident.
If the earth were uniformly magnetized, its magnetic poles would
be at the opposite extremities of a diameter, the magnetic meridians
would be arcs of great circles, and a comparatively small number of
observations would suffice to determine the distribution of mag-
netism over its surface. As a matter of fact, according to Bauer,
only about two-thirds of the earth's magnetism can be represented
by a uniform magnetization and the distribution of the remainder is
very irregular, representing the resultant effect of irregularities which
are continental, regional, or purely local in extent. These local
irregularities or " local disturbances" are sometimes of sufficient
intensity to produce local magnetic poles, such as have been found by
observation near Juneau, Alaska, and between Kursk and Odessa,
in Russia.
It is usual to represent the distribution of the earth's magnetism
graphically by means of isogonic, isoclinic, and iso-dynamic charts,
THE EARTH'S MAGNETISM. 9
on which are shown lines of equal declination, equal inclination, or
equal intensity. For the construction of such charts many observa-
tions are required in order that the irregular distribution may be
represented properly, "and it is the usual experience that the addition
of new observations brings out new irregularities. Inasmuch as the
earth's magnetism is undergoing constant change, its distribution is
different for different epochs, and a knowledge of the amount of
change from one year to another is necessary before the results of
observations made at different times can be reduced to the year for
which it is desired to construct an iso-magnetic chart.
VARIATIONS OF THE EARTH'S MAGNETISM.
The continual change to which the earth's magnetism is subject
has been analyzed in various ways and shown to be the resultant
effect of several more or less systematic variations combined with
irregular disturbances, which from time to time attain considerable
magnitude^ constituting what are known as magnetic storms. These
" storms" occur at irregular intervals and may last only a few hours
or several days and sometimes attain an intensity sufficient to pro-
duce a range of 1 or 2 in declination and of 2 or 3 per cent in the
horizontal intensity. They usually occur almost simultaneously over
the entire surface of the globe, and often accompany auroral displays
and the appearance of large spots on the sun. The occurrence of a
storm during observations can usually be detected by the erratic
behavior of the magnet or needle, and calls for a repetition of the
observations after the storm has subsided.
Of the systematic variations the largest and most important is the
secular variation, so called because it requires centuries for its full
development. While magnetic observations do not as yet cover a
sufficiently long term of years to warrant a definite conclusion, yet
the evidence is strong that at least for the direction of the earth's
field the secular variation is of a periodic character, i. e., that the
change with lapse of time does not go on indefinitely in one direction.
Eventually a turning point is reached. In the case of the declina-
tion, numerous series of observations are available which are of
sufficient extent to include one and in some cases probably two such
turning points. Tables showing the secular change of the magnetic
elements in the United States will be found on pages 114-119 of
"United States Magnetic Tables and Magnetic Charts for 1905."
Of the periodic variations having for periods a year, a solar day
and a lunar day, the only one of sufficient magnitude to be of prac-
tical importance is the solar-diurnal variation, or as it is usually
designated, diurnal variation. Tables IX, X, and XI show the
diurnal variation of declination, dip, and horizontal intensity at four
of the magnetic observatories of the Coast and Geodetic Survey,
based upon several years' observations. They were condensed from
10 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
tables giving the average diurnal variation for 10 selected days for
each month of the years specified.
The diurnal variation appears to be closely associated with the
position of the sun above the horizon. During* the night hours there
is normally little change in any of the three elements. The daily
range is greater in years of maximum sun spot frequency than in
years of minimum, and varies somewhat with the season.
From an inspection of Table IX it will be seen that for all of the
observatories the diurnal variation of declination shows the same
general characteristics; a well-marked maximum (easterly extreme)
between 8 and 10 in the morning, and a well-marked minimum (west-
erly extreme) between 1 and 3 in the afternoon.
For dip and horizontal intensity, on the other hand, there is only
one well-marked extreme, except in the case of the summer months
at Cheltenham, and even there one extreme is much more pronounced
than the other. In all cases this extreme occurs not far from noon,
but at Sitka and Cheltenham it is a maximum for dip and a minimum
for horizontal intensity, while for Honolulu and Porto Rico it is a
minimum for dip and a maximum for horizontal intensity.
DERIVATION OF FORMULAS.
DETERMINATION OF THE TRUE MERIDIAN BY OBSERVATIONS OF THE
SUN.
As the magnetic declination is the angle between the true meridian
and the magnetic meridian, its measurement requires the determina-
tion of the direction of both of these planes. The direction of the
magnetic meridian is obtained by means of a magnet free to rotate
in a horizontal plane about a vertical axis. The direction of the true
meridian may be determined by observations either of the sun or of
a star, especially Polaris. In connection with magnetic work it is
usually more convenient to make the observations in the daytime
and the method in general use consists of a series of observations of
the sun both morning and afternoon, each observation comprising a
measure of the altitude of the sun and the angle between it and a
reference (azimuth) mark, and a record of the time. The computa-
tion of the azimuth of the sun and the local mean time from observa-
tions of this character involves the solution of the spherical triangle
defined by the pole, the zenith, and the sun, the three sides being
known. The fundamental formulas of spherical trigonometry have
been transformed to fit this special case as follows :
When the sides of a spherical triangle are known the angles may be
computed by formulas of the form:
sin s 1 sin (s l a)
in which 2s l = a + b + c.
DERIVATION OF FORMULAS.
11
In Figure 1 let Z P S represent the triangle defined by the zenith,
the pole, and the sun.
SP = a = 90- = 2? given in
the Ephemeris of the sun.
SZ = 6 = 90 - h determined
by observation.
PZ = c = 90 - < determined
by observation.
The angle SZP = A n is the angle
between the true meridian and the
vertical plane through the sun and
is therefore the azimuth of the sun
counted from the North. The
angle SPZ = B is the hour angle of
the sun, t. Substituting the values
. ; . - .
or a, o, and c in the tormina and
letting 2s = p-\-Ji + (j) ) the following transformations may be made :
-7i- < = 180
FIG. 1. Fundamental spherical triangle.
COS S COS (Sp)
As it is usual to reckon azimuths from the south, substitute
180 -A, = A n
and the equation may be written in the form:
ctn 2 -Jk4 8 = sec s sec (s p) sin (s(f>) sin (s Ji)
A similar transformation of the equation for the angle B = t gives
tan 2 4- 2 = cos s sin (s h) esc (s (j)) sec (s p)
and by combination with the equation for ctn 2 JJL s :
tan 2 i* = F1
and
tan 4- 1 =
sin (s Ji) sec (s p)
ctn iA,
a very convenient form when the azimuth and hour angle are to be
computed from the same set of observations.
12 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
The computed angle between the sun and the true south meridian
combined with the measured angle between the sun and a selected
terrestrial object (azimuth mark) gives the angle between the true
south meridian and the mark, or the true azimuth of the mark.
The computed hour angle of the sun combined with the equation of
time gives the local mean time of observation, and this compared
with the chronometer time of observation gives the chronometer
correction on local mean time. If the chronometer correction on
standard time has been determined by means of telegraphic time
signals, an approximate value of the longitude of the place can
readily be computed.
DIP.
The dip is usually measured by means of a dip circle in which a
magnetized needle is supported so as to be free to rotate in a vertical
plane. A steel axle through the center of gravity of the needle ter-
minates in finely ground pivots which rest on agate knife edges. The
angle of dip is measured on a graduated circle concentric with the
axle of the needle. In order to measure the angle of dip directly, the
needle must swing in the magnetic meridian. The observed angle
of inclination in any other plane will be too large, as will be seen from
the following considerations. In the magnetic meridian the hori-
zontal and vertical components of the total intensity are H and Z,
and Z = 77 tan 7. In a plane making an angle a with the magnetic
meridian, the components are H cos a and Z, and Z = H cos a tan I a .
Hence tan 7= cos a tan 7 a . As the cosine of an angle is always los
than unity, 7 a is always greater than 7. This formula may be used to
compute the true dip from observations out of the meridian, provided
the angle a is known. The equation may be written in the form
ctn7 a = ctn7 cos^. Let <r = 90; then ctn7 a = and 7 a = 90. That
is, when the instrument is in the magnetic prime vertical the dip
needle stands vertical, a fact w r hich furnishes a simple method for
setting the instrument in the magnetic meridian when a compass
attachment is not available for the purpose. Extreme accuracy in
the determination of the magnetic meridian is not required, as will
be seen if a be computed from the above formula assuming 7=45
and I a = 45 OOM, the resulting value of a being 37'. That is, unless
the instrument is more than 30 ' out of the magnetic meridian, the
effect on the dip is not as much as O'.l.
The true dip may be obtained by combining observations in two
planes at right angles to each other.
For Ctn T a = ctn 7 cos a
and ctn 7(9o- a ) = ctn 7 cos (90 a) = ctn 7 sin a
Hence ctn 2 7 a + ctn 2 7 ( 9o_ a ) = ctn 2 7
DERIVATION OF FORMULAS. 13
The ideal dip-needle would be perfectly symmetrical in size and
mass with respect to the axis of its pivots, but this condition can not
be exactly attained by the maker, and subsequent use of the needle
is liable to increase the divergence from this ideal condition. Most
of the errors due to lack of symmetry and adjustment are eliminated
by reversal of instrument and needle and reversal of the polarity of
the needle. Yet it will usually be found that different values of dip
are obtained before and after reversing polarity, indicating that the
needle would not exactly balance if demagnetized. This lack of bal-
ance may be ascribed without material error * to a small weight p
in the longitudinal axis of the needle at a distance d from the axis of
the pivots. The equations of equilibrium before and after reversal
of polarities will be:
pd cos I n = FM sin (/ I n )
and pd cos I s = FM sin (/, - /)
assuming that the magnetic "moment M of the needle is the same
before and after reversal.
Hence cos 7 TO _ sin (/ /)_ sin I cos I n cos / sin I n
cos I s sin(7 s I) sin I s cos 7 cos I s sin I
Clearing of fractions and dividing by cos I s cos I n cos 7,
tan Ig tan 1= tan / tan I n
tan 1= to*J*^d*
That is, where the observations give different values of dip before
and after reversal of polarities, the mean of the two quantities does
not give the true dip. Instead, the angle must be found whose
tangent is the mean of the tangents of the observed angles. To
avoid the necessity of making this computation for each observation,
Table VIII has been prepared, giving the correction required by the
dip obtained by using the formula
T 4 + A
2
For example, if the observed dip was 72 15'.0 before reversal
of polarities and 72 45 '.0 afterwards, the true dip would be
7230 / .0 + 0'.2 = 72 3Q'.2.
At a magnetic observatory an earth inductor is usually provided for
determining the dip. With this instrument more accurate results
may be obtained in less time than with a dip circle. The operation
of the earth inductor is based on the principle that when a closed
circuit is revolved in a magnetic field, electric currents are induced
unless the axis of rotation is tangent to the lines of force of the field.
* The needle is so long compared with its width that the lack of symmetry with respect to the longitudinal
axis is not apt to be appreciable.
14 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
After the instrument has been leveled and placed with the axis of
rotation in the magnetic meridian, the coil is rotated and its inclina-
tion is changed until the induced current becomes zero as shown by
a galvanometer placed in the circuit. The angle of inclination of the
coil, or dip, is then read off on the vertical circle.
Numerous comparisons of dip circles with each other and with earth
inductors have established the fact that, in spite of every refinement
of adjustment and care in observing, different dip circles give differ-
ent results and nearly all require corrections to reduce to the more
accurate earth inductor results. This is probably due in many cases
to irregularity of pivots of the needles and sometimes to slight
impurities in the metal entering into the make-up of the instrument.
While the effect of either of these causes would be different for differ-
ent angles of dip, it is the practice in the Coast and Geodetic Survey
to assume a uniform correction for the limited range of dip involved
in a season's work.
In the case of two dip circles which were used over a wide range of
dip and showed large and variable corrections, analytical expressions
of the form
sin I , cos /
-p-+*
were derived, from which to compute the required corrections, based
on the assumption that the varying corrections were to be ascribed
to the effect of the metal composing the instrument.
HORIZONTAL INTENSITY.
Up to the time of Gauss all measures of horizontal intensity were
relative, and consisted in comparing the times of oscillation at differ-
ent places of a magnet rotating in the horizontal plane about a ver-
tical axis. Assuming the magnetic moment of the magnet to be con-
stant, the horizontal intensity is inversely proportional to the square
of the time of oscillation. As a matter of fact, all magnets tend to
lose their magnetism gradually, but this decrease of magnetic moment
was determined and allowed for approximately by observing at a
base station both at the beginning and end of a voyage or a season's
work.
Gauss conceived the idea of combining with the oscillations a set of
observations in which the intensity magnet is used to deflect an
auxiliary magnet, and thus determine the horizontal intensity abso-
lutely, and this is the method in general use at the present day. Two
distinct operations are involved: Oscillations, which serve to deter-
mine the product of the magnetic moment of the magnet and the
horizontal intensity; deflections, from which the ratio of the same
two quantities is obtained.
DERIVATION OF FORMULAS. 15
OSCILLATIONS.
If a magnet be free to rotate about a vertical axis through its center
of gravity, it will come to rest with its magnetic axis in the magnetic
meridian. If it be turned out of that plane and then released it will
oscillate as a horizontal pendulum under the influence of the earth's
magnetism, the amplitude of its swing gradually diminishing until it
finally comes to rest again in the magnetic meridian. If T be the
time of one oscillation; i. e., the time between two successive transits
(in opposite directions) across the meridian, K the combined moment
of inertia of the magnet and stirrup about the axis of rotation, and
M the magnetic moment of the magnet, the equation of motion for a
pendulum becomes:
0.00000
02
3 04
4
5
12
subject, however, to certain corrections as explained below.
Reduction to infinitesimal arc. The above formula is based on the
assumption that the arc of vibration is infinitesimal. For a finite
arc the observed time of one oscillation must be diminished by a
small amount, the corrective factor being (1 ^- V in which
a' and a," are the initial and terminal arcs of vibration, expressed in
(a 2 \
1 ^j \ a being the average arc of vibration.
From the adjoining table it will be seen that for an
average arc of 3 this correction amounts to only 1
part in 25000, and as the arc of vibration need never
exceed this amount, and in the majority of magnet-
ometers is still more restricted by the limits of the
scale of the magnet, this correction is in general
negligible.
Correction for rate of chronometer. The observed time of one oscil-
lation must be corrected for the rate of the chronometer used. If r
be the daily rate of the chronometer in seconds, plus when losing and
minus when gaining, the observed value of T must be multiplied by
the factor ( 1 + r ") or T must be increased by 0.00001 16 Tr.
\ 8o400/
Values of this expression for different values of T and r are given in
Table V.
Correction for torsion. The earth's magnetism is not the only force
acting to cause the oscillations. It is usual to suspend the magnet
by one or more silk fibers or by a very fine wire or metallic ribbon,
the torsion of which must be taken into account. The ratio between
the force of torsion and the horizontal intensity may be determined
in the following manner : When the magnet is at rest in the magnetic
16 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
meridian, if the upper end of the suspension fiber be turned through
any angle, say 90, the magnet will be turned out of the meridian
through a small angle h (expressed in minutes) on account of the tor-
sion of the fiber. The equation of equilibrium between the two
forces for a twist of 90 is:
C (5400 -h)=MHsmh or C= ^^ y
in which C is the force of torsion per minute of arc. Experiments
have shown that the force of torsion is approximately proportional to
the amount of twist. In the case in point the upper end of the fiber
is turned through 5400', but the lower end is turned in the same
direction through the angle h, so that the amount of twist is (5400 Ji).
When during oscillations the magnet makes any angle, as 6, with
the meridian the force exerted by the earth's magnetism to pull it
back into the meridian is M H sin 0, and the force of torsion acting
,. ,. . OM H sin h , ,.
in the same direction is , , and the resultant of the two:
, , . . dMHsmh ,, . .fi 6 sin h ~]
MHsm 6+ 5400-ft = MH 8m l 1+ sin 6 (5400 -fc)j
since both h and 6 are small. Hence, in the oscillation formula,
540
must be substituted for M H in order to take into account the effect
of torsion. Values of the logarithm of [5400 -r- (5400 - h)] for different
values of h are given in Table VI, but for small values such as are
usually experienced in magnetometers the logarithm of this factor
may be assumed proportional to h, i. e. :
log 5400 -log (5400 -h)=7i [log 5400 -log (5400- l)] = /t [0.00008].
Induction. When a magnet is placed hi a magnetic field its mag-
netism is temporarily increased by induction by an amount propor-
tional to the strength of that component of the field which is parallel
to the axis of the magnet. In the case of the oscillating magnet, its
/ 77\
magnetic moment is increased from M to (M+/i H) or M(\+ p. 1,
/JL being the induction factor.
Temperature correction. As the magnetic moment of a magnet
changes with change of temperature, increasing as the temperature
decreases and vice versa, and as in general the temperature of the
magnet is different for the two sets of observations, deflections and
oscillations, it is necessary to allow for this difference in temperature
before combining the two equations to compute H and M. If M
DERIVATION OF FORMULAS. 17
and M' be the magnetic moments at temperatures t and t' respec-
tively, then the temperature coefficient, q, is represented by the
formula
M f - M 2
- t _ t >
As (M' M) is usually very small as compared with M and M r it
will not introduce a material error to substitute either M or M' for
. The change in M with change in temperature may then
A
be computed by the formula
M'=M[l+ (t-t'}q\
If t' be the temperature of the magnet during oscillations and t the
temperature during deflections, then the formula gives the magnetic
moment at the temperature of the oscillations expressed in terms of
the moment at the temperature of deflections.
The corrections for rate of chronometer and reduction to infini-
tesimal arc may be readily applied to the observed value of T. It
is more convenient to correct for torsion, induction, and change of
temperature by the addition of three factors to the oscillation formula
so that it becomes :
5400
or
DEFLECTIONS.
A magnet free to turn about a vertical axis will come to rest with
its magnetic axis in the magnetic meridian if acted on by the earth's
magnetism alone. If a second magnet be brought near to the sus-
pended magnet, the latter will be deflected out of the magnetic
meridian by an amount depending upon the relative strength of the
two forces acting upon it. The law of the action between two mag-
nets under these conditions was developed by Gauss for the special
cases where the two magnets lie in the same horizontal plane, (1) with
the axis of the deflecting magnet in the magnetic prime vertical
through the center of the suspended magnet and (2) with the center
of the deflecting magnet in the magnetic meridian through the center
of the suspended magnet and with its axis in the magnetic prime
vertical. Lament later extended the discussion to the cases where
the axes of the deflecting and suspended magnets are at right angles
to each other, (1) the deflector being to the east or west and (2) the
deflector being to the north or south. In 1890 Borgen developed
the formula for the most general case, placing no restrictions upon
7721311- 2
18 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
the relative positions of the two magnets, and derived therefrom the
forms applicable to the special cases already treated by Gauss and
Lamont. Nearly all magnetometers of recent make are arranged
with deflection bars attached at right angles to the telescope by which
pointings are made on the suspended magnet, and hence the deflec-
tions are made in Lament's first posi-
tion. It will be sufficient for our
purposes, therefore, to outline the
method of deriving the deflection
formula for that special case. Sup-
pose that the suspended magnet
Nj S t is deflected out of the magnetic
meridian through the angle u by the
magnet N S, placed so that the pro-
longation of its magnetic axis passes
through the center pf N t S r Let m
^ and m 1 and 2 Z and 2 l l be the pole
strength and distance between poles
of the two magnets and r the distance
between their centers. Then the
^ magnets during deflec- magnetic mome nts are H=2ml and
M l = 2m l l l . For an approximate so-
lution of the problem, assume that Z x is so small compared with
r that the distances from the pole N to .Nj and S t may be taken as
(r + Z) and from S to N t and S t as (r l). Then the force of attrac-
, i , XT . 771 771. . , . 771 771. Z,
tion between S and Nj is - ( jL and the turning moment is -, I,*
(T I) (T I)
771 771
The force of repulsion between N and Nj is , jL and the correspond-
T
ing turning moment is , _i_ yy- The total turning moment resulting
the action between the two magnets is therefore:
2 m TTij \ 2m m^ Z t _ 8 m m l ll 1 r _ 2 MM^ r
-IY~~ (r 2 -/ 3 ) 2 = (r^-Z 2 ) 2
3 Z 4 4 Z 6
The rigorous solution, taking into account the pole distance of N 1 S 1
yields an expression of the same form, namely : - |-
in which P, Q, and succeeding coefficients are functions of the dimen-
sions of the two magnets and the distribution of their magnetism.
The series converges so rapidly that the coefficients beyond Q need
not be considered for properly chosen deflection distances.
The turning moment of the force tending to pull the suspended
magnet back into the meridian is HM 1 smu, u being the angle of
DERIVATION OF FORMULAS. 19
deflection. When the magnet is at rest the two opposing forces are
equal and opposite,
P and Q are called the first and second distribution coefficients,
and their values could be computed from the dimensions of the mag-
nets by means of Borgen's formula, provided the ratio of distance
between poles to length of magnet was known. This ratio is difficult
to determine with accuracy and appears to be different for different
magnets, so that only approximate results can be obtained by this
method. Borgen concludes that on the average the pole distance is
a little more than 0.8 the length of the magnet and, assuming that it
is the same for both deflecting and suspended magnets, deduces the
formulas:
P = 2Z 2 -3Z 1 2
It is better, in view of the uncertainty of the above ratio, to depend
on observations for the determination of P and Q. It is evident that
if deflection observations are made at three distances there will
TJ
result three equations from which the three unknowns ^., P, and Q
can be computed, as explained later.
The above equations for P and Q are useful, however, to determine
approximately the relative length of the two magnets which will
make P or Q zero.
When P = 2Z 2 = 3Z t 2 and Z = 1.225^.
When Q = aft-lSP^+-O and Z = 2.15Z r
o
In deriving the deflection formula given above no account has been
taken of the effect of induction upon the magnetic moment M of the
deflecting magnet. It will readily be seen that the south end of the
deflecting magnet will always be inclined to the north of the mag-
netic prime vertical whether it is placed to the east or west of the
suspended magnet or with its north end east or west, and the effect
of induction will therefore always correspond to a decrease in its
magnetic moment. As already stated, the induction is proportional
to the strength of that component of the earth's field which is par-
allel to the axis of the magnet, in this case H sin u. Hence the
moment of the deflecting magnet when the suspended magnet is de-
flected through the angle u is really (Mp H sin it) instead of M,
fji being the induction factor of the magnet. As ^ H sin u is always
20 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
very small in comparison with M, we may substitute for H sin u
its approximate value 3-
and (M-f, H sin u) = M-
Making this correction to the deflection formula, it becomes:
H 2
H
or H-
It is probable that the distribution of the magnetism of a magnet
changes somewhat in the course of time, and consequently P, Q, and
fi. are subject to change, but results show that for a season's work, or
even longer, they may be considered constant without materially
increasing the uncertainty of the results, especially when the magnets
have become so well seasoned that the loss of magnetism is very slow.
The deflection formula may then be written:
H^ C
M sin u
in which = 4j 1 T^)(l+75 + ^) and is constant for a particular
deflection distance and a particular temperature. Its variation with
temperature may be readily computed from the coefficient of expan-
sion of the material, usually brass, of which the deflection bars are
made, since r is the only quantity in the second member which varies
with temperature.
The oscillations give the product of H and M
and the deflections give their ratio:
H_ 2 A2A/ P
M~r* sin u\ L iVV f*
from which the values of H and M can be readily computed, if we
assume that the values are the same for the two sets of observations.
So far as M is concerned this is a safe assumption, provided allowance
is made for the change in temperature between the two classes of
observations, as has been done in the formula for H M. Experience
shows that a magnet loses its magnetism quite rapidly for a short time
after magnetization, but soon settles down to a condition of very slow
change, inappreciable for the period covered by a set of intensity
observations. Exception should be made of the sudden loss of mag-
DERIVATION OF FORMULAS. 21
netism resulting from a shock such as would be caused by dropping
the magnet or from bringing it into contact with another magnet.
In the case of H there is constant change, usually small in extent
during the time covered by a set of observations, but at times exceed-
ing in amount the error of observation. To minimize the effect of
this variation, the observations are usually arranged in the order:
Oscillations, deflections, deflections, oscillations. The following con-
siderations show that small changes in H such as are exceeded only at
times of severe magnetic storms have no appreciable effect on the
result. For suppose H and H d are the values of H at the time of
oscillations and deflections, respectively, and let H d =H + 4H.
The combination of the observations on the assumption that H = H d
would give the value H=^H H d =^/H 2 +H AH. The quantity
under the radical differs from (H + ^JHj by - , a quantity so
small as to be negligible except in the case of a severe magnetic
storm. But H + H = -. Hence it is evident that the
assumption of no change in H between the deflection and oscillation
observations gives a value of H which is the mean for the period cov-
ered by the observations. To show the effe'ct in an extreme case,
suppose 4H = Q.Q5H, a range seldom reached in the course of a
magnetic storm, then
2 H.
H d +H
2
Under such conditions the magnet would be so disturbed as to render
accurate observations impossible.
TOTAL INTENSITY.
Under certain conditions it is inconvenient or impossible to use the
above method for determining the horizontal intensity. As the
magnetic pole is approached the horizontal intensity becomes so
small that the method fails for lack of accuracy. On shipboard the
motion of the vessel precludes the use of a fiber suspension, which is
essential to accurate oscillation observations. At times it is neces-
sary to reduce the instrumental equipment of a party as much as
possible. In such cases use may be made of the method devised by
Dr. E. Lloyd to determine the total intensity by means of a dip circle.
While inferior in accuracy under ordinary conditions to the method of
determining the horizontal intensity with a magnetometer, yet with
a good dip circle carefully handled it will usually yield very satisfac-
tory results. (See App. 3, C. & G. S. Report for 1905, p. 114.)
The method involves two operations, during both of which the dip
circle is so placed that the suspended needle swings in the magnetic
22 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
meridian: First, the measure of the angle of inclination with a needle
having a weight in the south end (in north magnetic latitudes) ; sec-
ond, the measure of the angle through which a second needle is
deflected by the loaded needle, when the latter is placed at right
angles to it in the place provided for the purpose between the reading
microscopes, with the axes of rotation of the two needles lying in the
same straight line. In the first case the earth's magnetism acting on
the loaded (intensity) needle is opposed to the force of gravity acting
on the weight. In the second case the force exerted by the intensity
needle on the suspended needle is opposed to the earth's magnetism.
Let 7' = the dip with loaded needle, considered positive when the
south end is above the horizon. Then the angle through which the
needle is turned by the weight is u f = 1 1'
u = Deflection angle.
M= Magnetic moment of the intensity needle.
M 1 = Magnetic moment of the second needle.
fc = Mass of the weight.
R = Distance of weight from the axis of rotation.
The equation of equilibrium for the dip with loaded needle is:
TcR cos /' = F M sin u'
For the deflection observations, the equation is:
in which Jc t is a factor depending upon the distance between the needles
and the distribution of their magnetism. Combining the two equations :
Wc l RMM l cos /' = F 2 MM l sin u sin u'
Let Iclc.R^C 2
s
Then C 2 cos /' = F 2 sin u sin u'
F= (7Vcos /' esc u esc u'
G= F^/sec 1' sin u sin u' '.
When the above observations are made at a place where the dip
and horizontal intensity (and hence also the total intensity) are
known, the value of C can be computed. Knowing C the value of
F at any other place can be determined by observation. As the
factor C involves the mass of the weight and its distance from the
axis of rotation and also the distribution of magnetism in the needles,
it is necessary to guard against change, in the interval between the
standardization observations and those at other places. The weight
should be left in position and care should be taken not to change the
magnetic condition of the needles. Hence they must not be remag-
netized in the course of a season's work. /
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER. 23
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER.
The two formulas used in the determinatidn of H and M from
observations of oscillations and deflections involve a number of factors
which must be determined by special observations or otherwise before
they can be used, namely, moment of inertia, temperature coefficient,
induction coefficient, and distribution coefficients, as well as the
deflection distances.
MOMENT OF INERTIA. i
The magnets of most magnetometers are of the collimator type, a
hollow steel cylinder closed at one end by a glass on which a scale is
etched and at the other by a lens. There is thus introduced a lack
of homogeneity which makes it impracticable to compute J, 7 the
moment of inertia of the magnet, from the dimensions of its com-
ponent parts. Moreover the magnet is usually supported by means
of a stirrup of more or less complex form, and it is the moment of the
magnet and stirrup combined which is involved in the formula. It
is usual, therefore, to determine the moment of inertia by means of
an auxiliary weight of nonmagnetic material and of regular form of
which the moment of inertia can be readily computed from its dimen-
sions and mass. A truly turned bronze ring or a circular cylinder of
about the same mass as the magnet are the forms commonly
employed. For a ring the moment of inertia is given by the formula:
in which d and d are the' inner and outer diameters and W is the mass.
For a cylinder the formula is :
#i=~(4Z 2 + 3<2 2 )
in which Z is the length and d the diameter. To find the value of K^
for any other temperature than the one at which the dimensions were
measured, the average coefficient of expansion of bronze, 0.000018
for 1 C., may be used, unless a special determination has been made
for the weight in question. It will be seen that 2 log (1.000018) =
0.000016 is the corresponding change in log K v for 1 change in the
temperature of the inertia weight.
If in addition to oscillations with the magnet alone, observations
are made with the weight added, two equations will result:
Hence K K+
5400
24 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
supposing H to remain constant and allowing for change of M with
change of temperature, t' being the temperature of the magnet dur-
ing oscillations without the weight and t the temperature during
oscillations with the weight.
Let ^rgx and
Then E _KK, _ (T?K {
That is, this simple formula may be used if the observed values of T 2
and Jj 2 are corrected for torsion and the former is reduced to the
temperature of the, latter. The following arrangement of the obser-
vations will practically eliminate small changes in H:
Begin with a set of oscillations without the inertia weight, deter-
mining the torsion factor with a torsion weight of the same mass as
the magnet. Then make a set of oscillations with the inertia weight
added, determining the torsion factor again, but with a torsion weight
of the same mass as the magnet and inertia weight combined. Con-
tinue making sets of oscillations alternately with and without the
weight, ending the series with a set without the weight. Determine
the torsion factor again with the last set of each class of oscillations.
Each set of oscillations will consist of 8 independent determinations
of the time of a selected number of oscillations. The first set of
oscillations without the weight and the first half of the second set,
combined with the intervening set with the weight, give one value
of K. The second half of the second set without the weight and
the first half of the third set combined with the second set with the
weight give another value of K, and so on. Five of these independ-
ent determinations will usually give a satisfactory mean value of K.
The change in K with temperature is a function of the temperature
coefficient of steel, which may be taken as 0.000011 for 1 C. For
a change of 1 in temperature the corresponding change in log K is
2 log (1.000011) =0.00001.
The method of separating the intermediate sets of oscillations with-
out the weight into two parts is shown in the following example. A
convenient form of computation is also given.
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER. 25
MOMENT OP INERTIA. OSCILLATIONS, without weight.
Station, Cheltenham, Md. Date, April 28, 1909.
Magnetometer No. 26. Magnet 26 L.
Chronometer No. 1107, daily rate gaining 8 8 .1 on mean time. ,
Number of
oscillations.
Chronometer
time.
Temp.
Extreme scale
readings.
Time of 70
oscillations.
h. m. s.
15 25 15.7
18.2
-22.8
+22.8
7
25 52.6
14
26 29.5
21
27 06.4
28
27 43.2
35
28 20.1
42
28 57.1
49
29 34.0
18.1
m. s.
70
15 31 24.8
6 09.1
77
32 01.6
09.0
84
32 38.5
09.0
91
33 15.3
08.9
98
33 52.2
09.0
105
34 29.0
08,9
112
35 06.0
08.9
119
35 42.9
18.1
-17.9
+ 17.9
08.9
Means
18.13
J 6 09.00 .
i 6 08.925
First
Second
half.
half.
s.
s.
t (preceding set)= 17. 97
Time of 1 5. 27143
5. 27036
t 1'= O.16
oscil.
* (following set) = 18.27
Corr'n for -49
-49
t-f=+0.U
rate ,
T 5.27094
5. 26987
Log T2
1.44378
1.44360
"(
' 5400 \
60
60
,5400-A/
[!+(*-*')<?]
- 5
+ 4
"(D*
1. 44433
1. 44424
(T?
27.818
27.812
26
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
Cheltenham, Md.
Magnetometer No. 26.
COMPUTATION OF MOMENT OF INERTIA.
April 28, 1909.
Inertia ring A.
Chron.
time.
Temp.
T 2
Ti*
and
2V T*
Log T*
and
log Ki
Log T*Ki
and
log(7V-r*)
log IT
lo g A' 2 o
ft. 771.
14 32
27.824
1. 44437
15 05
17.97
[27.821] 43.409 2.47036
3. 91473
15 29
27.818
15.588
1. 19279
2. 72194
2.-72196
15 32
27.812
1.44429
15 52
18.27
[27.816]
43. 419 2. 47036
3.91465
16 11
27.820 15.603
1. 19321
2. 72144
2. 72146
16 14
27.841 1.44433
16 36
18.53 [27.818]
43. 416
2. 47037
3. 91470
16 52
27.794
15.598
1. 19307
2. 72163 2. 72164
16 55
27.820
1.44439
17 12
18.95 [27.822]
43.409
2.' 47037
3. 91476
17 27
27.824
15.587
1. 19276
2.72200
2.72201
17 30
27.835
1.44458
- ,
17 48
19.33 | [27.834]
43. 433
2.47038
3. 91496
18 19
27.834
15.599
1. 19310
2.72186
2. 72187
18 22
27.846
1.44476
18 40
20.15 ! [27.846]
43.445
2. 47039
3. 91515
19 06
27.845
15.599
1. 19310
2. 72205 2. 72205
ftCean
2. 72183
JT=527.02 at 20 C.
When the weight is a cylindrical bar, there is usually a place pro-
vided in the stirrup for suspending it above or below the magnet.
When a ring is used, it must be balanced on top of the magnet, so as
to be horizontal and with its center in the line of suspension. To
facilitate placing it in this position, a wooden block is provided having
a socket in which the magnet will fit with its upper surface even with
the surface of the block. Suitable marks on the block indicate the
position in which the ring must be placed in order to be symmetrical
with respect to the center of the magnet. It will, in general, be neces-
sary to increase the number of suspension fibers in order to support
the increased weight.
The moment of inertia of a magnet will be affected by any change
in its dimensions or mass. A screwing up or unscrewing of one of the
end cells would produce a slight change of length. The removal of a
large amount of accumulated rust would produce an appreciable
change of mass. The magnet must be carefully protected therefore
from these or similar changes, and in case such a change should take
place its moment of inertia must be redetermined.
TEMPERATURE COEFFICIENT.
When the temperature of a magnet increases, its magnetic moment
decreases, and vice versa. Experiments have shown that the rate of
change is not uniform, but increases with increase of temperature. In
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER. 27
view of the small change of temperature usually experienced during
a set of horizontal intensity observations and the partial elimination
of its effect by a symmetrical arrangement of oscillations and deflec-
tions, no material error will be introduced by the assumption that
the rate of change is uniform for ordinary temperatures.
If M and M r be the values of the magnetic moment of a magnet at
temperatures t and t' and q be the temperature coefficient:
M(t'-t)
From an inspection of the oscillation and deflection formulas, it
will be seen that if two sets of observations of either class be made at
different temperatures, the value of q may be computed, provided
means are taken to allow for change of H. At an observatory this
may readily be done with the aid of the continuous record of the
magnetograph. In any case, the effect may be nearly eliminated by
observing alternately at high and low temperatures and combining
two sets of observations at about the same temperature with an inter-
vening set at a different temperature. Care must be taken to main-
tain a given temperature for a sufficient time to make sure that the
magnet and thermometer are at the same temperature, and rapid
changes should be avoided. If both oscillations and deflections are
made at high and low temperatures, the change in H is obtained from
the observations themselves. If the observations are made in a room
which can be heated and cooled artificially, no special apparatus is
required. Otherwise the value of q is most conveniently determined
by deflection observations, the deflecting magnet being surrounded
by a water jacket, which may be filled alternately with hot and cold
water. In this case allowance must be made for the effect of change
of temperature upon the length of the bar.
The computation of q may be conveniently made by logarithms,
bearing in mind that for our purposes log (l + (t t')g) may be
replaced by (t t f ) [log (1 +g)] without materially affecting the results.
log M f = log M+ (t-f) log (1 +g)
log Jf'-log M
log
If special deflection observations have been made, they give directly
TT TT
log M - log jj-, - log M' - log M
H H
It will be sufficient to use the approximate values of --,, and -%,
2 2
namely, -5 ^ and - -- . when the induction and distribution
j i r s sin u r $ sin u
28 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
coefficients are not known, r and r t being the values of the deflection
distance at temperatures t and t' .
A check on the correctness of an adopted value of q may be obtained
from the values of log M determined in the course of a season's work.
When all the values have been reduced to a common temperature,
they should show a fairly uniform decrease with lapse of time. An
error in the adopted temperature coefficient would be indicated by
deviations from a uniform change which conform in general with the
changes in temperature .
INDUCTION COEFFICIENT.
When a magnet is placed in a magnetic field its magnetic moment
is temporarily changed by induction by an amount which is propor-
tional to the component of the field directed parallel to the axis of the
magnet. The rate of change, i. e., the ratio of the moment of the
magnet to the change produced by a unit field, is called the induction
coefficient, 7i. The change in the magnetic moment M of a magnet
placed parallel to a field of intensity H would be hMH, or fiH,
// = Mh, called the induction factor, being the change in the magnetic
moment produced by a field of unit intensity. The induction coeffi-
cient is not constant, but varies with the strength of magnetization of
the magnet. It is different also according as the induction tends to
increase or decrease the magnetic moment; the more strongly a
magnet is magnetized, the less susceptible it becomes to increase of
magnetization by induction, but the more susceptible to decrease.
In the oscillation observations induction increases the magnetic
moment of the magnet, and the induction factor may be taken as con-
stant. In the deflection observations the effect of induction is to
reduce the magnetic moment of the magnet, but the magnet is in
general so nearly in the prime vertical that the effect is very small,
and hence the assumption that the induction factor is the same as for
the oscillations does not introduce an appreciable error.
Of the various methods for determining the induction coefficient,
the one devised by Lamont has been used exclusively by the Coast
and Geodetic Survey. The magnet of which the induction coeffi-
cient is desired is used as a deflector with its axis vertical, in the ver-
tical plane at right angles to the suspended magnet, but with its
center some distance above or below the horizontal plane through that
magnet. Observations are made first with north end up, magnet up,
and then with north end down, magnet down. In the former position
the magnetic moment of the magnet is decreased by induction, and in
the latter is increased. If care is taken to maintain constant conditions ,
except for the inversion of the deflecting magnet, the change in the
deflection angle will be a measure of the change in the magnetic
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER. 29
moment due to the inductive effect of the vertical intensity, Z. In
the first case
H C
M(lhZ)
and in the second case
H _C_
M(l + hZ) sin u 2
\-\-JiZ sin u 2
+ ^i )
This method involves the assumption that the induction coefficient
is the same whether it tends to increase or decrease the moment of the
magnet. As the corrections for induction are very small, this is a
safe assumption for all except the most refined observations.
As the induction coefficient is a very small quantity, the change in the
deflection angle (u 2 u^) is small also and a small error in observa-
tion or a small change in the relative position of the two magnets will
materially affect the result. It is usual to extend the observations by
varying the position of the deflecting magnet, as indicated in the fol-
lowing sample set, and also by making several sets using different
horizontal and vertical distances. For making the observations a
special L-shaped deflection bar is provided, to which is pivoted a
vertical arm so arranged that it may be rotated in a vertical plane
parallel to the suspended magnet, about a center in the horizontal
plane through the suspended magnet.
30
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
Cheltenham, Md.
Magnetometer No. 29.
Horizontal distance, 21 cm.
June 16, 1905.
Vertical distance, 2 cm.
No.
Position of deflecting
magnet.
North end.
Horizontal circle readings.
A.
B.
Mean.
1
East
up
up
53 32 40
53 32 40
32 40
2
East
down
down
53 56 10
56 10
53 56 10
3
East
down
up
43 05 10
05 50
43 05 30
4
East
up
down
43 23 40
23 50
43 23 45
5
West
up
down
54 08 10
08 10
54 08 10
6
West
down
up
54 28 00
28 10
54 28 06
7
West
down
down
42 37 30
37 30
42 37 30
8
West
up
up
13 03 00
03 20
43 03 10
ft. m.
Time of beginning 9 55 Temp. 27. 2
2 ui East (1-3) 10 27 10
Time of ending 10 25 Temp. 27. 6
2 tt, West (6-8) 11 24 55
Mean
i*
2u 2 East (2-4)
10 5G 02
2 4400
co log (#=0.20085) 0.6971
co log tan (7= 70 25') 9. 5511
10 32 25
log tan J(-Mi)
co log tan j(uj+tti)
log (ft= 0.0074)
0. 6047
1. 0172
2t/ 2 West (5-7)
Mean
i
11 30 40
11 01 32
2 45 23
7.8701
" (JfiM-697) 2.8432
i(uj-tti) 1 23
" (^-5. 17) 0.7133
i(ttj+ui) 5 29 23
DISTRIBUTION COEFFICIENTS.
n the deflection formula
2
H
~M l
r 3 sin
r 2 r
the distribution coefficients P and Q may be obtained by making
deflections at three distances and solving the three resulting equations
TJ
for the three unknowns , ., P, and Q.
, .,
.\L
Let
Then
sn H
r sn u
3 _ .
^ (r 3 2 -
- r
* - r 2 2 )
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER. 31
In case the relative lengths of the two magnets are such that Q is
nearly zero, the term 4 becomes so small that it may be neglected and
the value of P may be computed from deflections at two distances.
Using the same notation as above :
S 4 X 4
Al 1+ ^
When P is small it may be computed with sufficient accuracy by the
formula
9..- 9.
A,-\ogA 2 )
For deflection distances of 30 cm. and 40 cm. this becomes
P = 4737 (log A,- log 4,)
It is evident that a small error of observation in the deflections will
have a large effect on the accuracy of P, and little dependence can be
placed on the result from a single set of observations. It is only
from an extended series that a reliable value of the distribution
coefficients can be obtained. It is also evident from the form of the
r 2 r 2
factor r 2_y 2 that it is important to have the two deflection distances
differ by a considerable amount. Too short a deflection distance is
undesirable, however, since any uncertainty in the value of P has
too great an effect on the resulting horizontal intensity, and too long
a distance reduces the size of the deflection angle so much that a
small error of observation has a large effect on the result. For the
size of magnets generally used, the distances 30 cm. and 40 cm. are found
to be the most satisfactory.
The above formula for P may be used also to find the correction to
an adopted value of P required to harmonize subsequent observa-
tions. If it is found after a series of observations that the two values
TT
of log j^ computed from deflections at two distances differ system-
atically, one being greater than the other on the average, the cor-
rection to the adopted value of P is given by the formula
JP =
the quantity in brackets being the mean value for the series.
As already pointed out, approximate values of the distribution
coefficients may be computed from the dimensions of the magnets.
32 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
If 21 and 2\ be the pole distances of the long and short magnets,
respectively, then
P = 2l 2 - 3Z X 2 Q = 3Z 4 -
disregarding the small terms depending on the relative diameters of
the magnets. Borgen concluded from his experiments that the pole
distance is on the average about 0.805 the length of the magnet, and
this conclusion was confirmed in part by the standardization obser-
vations at Kew prior to 1904 (Dr. C.Chree, "Law of Action between
Magnets." L., E., and D. Phil. Mag., Aug. 1, 1904). From the
above formula it will be seen that P should be zero when ll\ = 1.225,
and this ratio has been adopted for the lengths of the two magnets
in nearly all of the magnetometers which have been made or remod-
eled by the Coast and Geodetic Survey. At the same time it has
been the practice to regard Q as negligible and to determine the value
of P from deflections at two distances in the manner explained above.
For seven of the eight magnetometers to which the above ratio
applies, the value of P derived in this way is in every case between
and 1.0, the average value being 0.54.
To show that this assumption is justifiable, let us examine the
results for five magnetometers of the design shown in Figure 3,
having magnets 7.375 cm. and 6.025 cm. in length, i. e., in the ratio of
1.224 to 1, and arranged for deflections at distances of 30 cm. and 40
cm. Using Borgen' s ratio of pole distance to length of magnet, his
formulas give:
Now suppose a series of deflections at the two distances gives on the
average
log A M - log A 4Q = - 0.00020
Assuming Q = Q P = 4737 (log A 30 - log ^4 40 ) -- 0.95
which is about the upper limit of the values found for this type of
magnetometer. On the other hand, if we assume P = 0, Q may be
computed by the formula:
Q = loge 10 -^L. Oog A, - log A 2 ) = - 546
'2 ~~'l
Finally, we may adopt the value of Q = - 350 computed from Bor-
gen' s formula, and find the value of P which will satisfy the equation:
log l+ + ao-logl+ + 40 = -0.00020
P Q
As - a and 4 are both very small quantities, we may put
DETERMINATION OF THE CONSTANTS OF A MAGNETOMETER. 33
Hence
= log
l +
log (l + ^ 30 - log (
^4o-log (1+^)30 -0.00020 =-0.00007
and P = 4737(- 0.00007) =-0.33
The effect of the different values of P and Q on the resulting value
of H may be determined by computing the value of log (
for the three cases.
I + +
P=-0.95 Q=0.
P=0 Q=-546.
P=-0.33 Q=-350.
r=30cm.
r=40cm.
r=30cm.
r=40cm.
r=30cm.
r=40cm.
p
r2
Q
7-4
-.001056
-.000594
-.000674
-.000213
-.000367
-.000432
-.000206
-.000137
3
.998944
.999406
.999326
. 999787
.999201
.999657
mi
9. 99954
9. 99974
9. 99971
9. 99991
9.99965
9.99985
Mean
-.00036
-.00019
-.00025
It will be seen that the difference between the logarithms of the
factor for the two distances is in each case the assumed difference
between log A 30 and log A M , but the mean of the two is greatest for the
assumption that P = and least for the case in which Q = Q. To
determine the effect on a resulting value of H we must take the square
root offl+^ + ^jor divide its logarithm by two. The effect of the
above three combinations of distribution coefficients would therefore
be to diminish the value of log H by .00018, .000095 and .000125
respectively. The ratio of the first two values is the number of
which the logarithm is .000085 or 1.0002; that is, they differ by only
1 part in 5000. Consequently the error involved in the case of the
Coast and Geodetic Survey magnetometers in assuming that Q is
negligible does not amount to more than 1 part in 5000 in H and is
probably less than that, and is therefore well within the probable
error of observation and reduction in field work under favorable
conditions.
7721311 3
34 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
DEFLECTION DISTANCES.
In a magnetometer with fiber suspension it is impossible to avoid
a slight variation in the relative positions of the suspended magnet
and the deflection bars and a corresponding variation in the deflection
distances. To eliminate the error to which this might give rise, the
instruments are made either with two deflection bars, one on either
side, or with a single bar having its middle point over the center of the
magnetometer. The deflection observations can then be made one-
half with magnet east and one-half with magnet west and a small
increase of the deflection distances on one side will be balanced by a
decrease on the other side.
The distance between corresponding marks on the two bars or on the
two halves of the single bar is twice the deflection distance. With the
single straight bar, such as is used in the Kew and India Survey pat-
tern magnetometers, this is readily obtained by direct comparison with
a standard meter. Experiments at Kew have shown that bars of this
type require a slight correction for bending, amounting to an increase
of about one part in 10000 in the case of the instruments of the latter
type in use by the Coast and Geodetic Survey (Fig. 4).
In the Coast and Geodetic Survey pattern magnetometer (Fig. 3), the
two bars are so constructed that their inner ends overlap and are held
together by two screws. It is thus possible to fasten them together
when not in position on the magnetometer and measure the deflection
distances as readily as for a single bar. These bars are very light,
since the outer ends are hollow, and it has therefore been considered
unnecessary to investigate the question of bending.
DIRECTIONS FOR MAGNETIC OBSERVATIONS ON LAND.
GENERAL DIRECTIONS.
Selection of stations. The conditions to be satisfied in selecting
a magnetic station are freedom from present and probable future local
disturbance, whether natural or artificial, combined with convenience
of access. A station on suitably situated public property, or property
belonging to an educational institution, is to be preferred, as it is less
likely to be disturbed or affected by change of the immediate sur-
roundings. Proximity of electric railways, masses of iron or steel,
gas or water pipes, buildings of stone or brick should be avoided.
A quarter of a mile from the first, 500 feet from the second, 200
feet from the third and fourth may be considered safe distances.
The station should be at least 50 feet from a building of any kind.
If any doubt arises in the selection of a station as to the existence of
local disturbance, two intervisible points 100 yards or more apart
should be selected and the magnetic bearing of the line joining them
determined at each end. A lack of agreement between the two
results would be evidence of local disturbance. Similar tests should
then be made in other directions until a satisfactory location is found.
Description of station. Each point occupied should be described
with sufficient detail to render possible its recovery. The description
should begin with the general location of the park or field in which the
station is situated. This should include the approximate distance
and direction from the center of the town or from some point which
can be definitely located on a map, so that a check on the latitude and
longitude may be available. In case a new station is selected in a
town where observations had been made before, the relative positions
of the new and old stations should be given, if possible.
There should follow measured distances to the fences or other fixed
objects in the immediate vicinity of the station and a description of
the manner in which the station is marked. If a meridian line is
established, the distance to, and location of, the second stone should
be given, the magnetic station being selected so as to form one end
of the line. It is desirable also to give. a rough sketch showing the
relation of the station to surrounding objects, indicating on it the
direction of north (which should always be toward the top of the
sketch), and the direction of the marks of which the true bearings are
determined.
Marks. These marks should be well-defined objects as nearly in
the horizon as practicable and likely to be available for future use.
35
36 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
It is desirable to have the one selected for reference fnark in azimuth
and declination observations in a souther!}" direction, so that it may
be sighted upon through the opening in the south side of the observing
tent. It should be a quarter of a mile or more from the station if
possible, so that an error of two or three inches in reoccupying the
station or a change of that amount in the position of the marking
stone would not materially affect the azimuth of the mark. As an
angle of 1' subtends approximately 1 inch at a distance of 300 feet,
the uncertainty at any given distance may be readily computed.
Marking of station. Every station' sn'ould be marked in as per-
manent a manner as conditions will warrant, to assist in its subse-
quent recovery. Either a natural or artificial stone, a glazed drain
pipe, or a post of hard wood can usually be obtained. To avoid being
disturbed, the station mark should project little, if any, above the
surface of the ground, and it should extend two feet or more into
the ground.
Meridian line. When a meridian line is to be established the
azimuth observations must be made with especial care and the com-
putations revised before the stones are set. The line should be not
less than 300 feet long (if possible not less than 500 feet), and extra
precautions should be taken to secure the marking stones against
future disturbance.
Repeat stations. Where observations are to be made at an old
station for the purpose of determining the secular variation, especial
effort should be made to reoccupy the precise point at which the
earlier observations were made. Any changes in the immediate sur-
roundings should be noted in the description of station. If local
conditions have changed to such an extent that a reoccupation is
clearly undesirable, then a new station must be established. There
may be cases, however, in which it will be best to reoccupy the old
station and also establish a new one; e. g., the old station, while not
satisfying the requirements of future availability, may still suffice to
determine the secular variation since the former observations. When,
owing to change in the immediate surroundings or defect of the
original description, it is impossible to locate the exact point from
the measured distances, the desired result may sometimes be accom-
plished with the aid of the bearings of prominent objects. Having
three well-defined objects which were connected by angular measures
at the time of the former occupation, successive trials with the the-
odolite will serve to locate the spot at which those angular measures
are reproduced.
Care of instruments. Care should be taken to keep the instruments
in good adjustment and free from dust. The magnets should be
touched with the hands as little as possible and should always be
wiped dr} r with clean chamois or soft tissue paper at the close of
GENEBAL DIRECTIONS. 37
observations to prevent them from rusting. They must not be
dropped or allowed to touch each other or other iron or steel objects.
They should be kept in the instrument box with north end down,
packed snugly to avoid jars in transportation. The dip needles
should be wiped with tissue paper both before and after observations
and the pivots cleaned with pith. In reversing polarities, the bar
magnets should be drawn smoothly from center to ends of the needle,
as nearly parallel to the axis of the needle as possible. In case the
needle projects above the surface of the reversing block the magnets
must not bear heavily upon it.
Chronometer. The utmost care must be exercised in carrying the
chronometer. A pocket chronometer requires more careful handling
than a watch to secure a constant rate. It must be kept at as uniform
a temperature as possible and wound at the same hour each day. It
must be protected from jarring or shaking. Past experience indi-
cates that the best results are obtained when it is carried in the
trousers watch pocket. Where unusual rough travel is anticipated
it is well to compare the chronometer with a well-regulated watch
both before and after the journey. At least once a week, and at
every station if possible without serious delay, the chronometer
correction on standard time should be obtained by means of Western
Union or other telegraphic time signals. The chronometer correction
and rate are given the sign with which they must be applied. For a
chronometer which is fast and gaining they are both negative.
Order of observations. When a complete instrumental outfit is
supplied the observations at a station comprise: Morning and after-
noon azimuth, latitude at noon; one set of dip with each of two
needles; two sets each of declination, oscillations, and deflections;
angular measures between prominent objects. It is desirable that
the azimuth observations should be made at nearly equal times
(preferably not less than two hours) before and after apparent noon,
giving nearly the same altitude of the sun for the morning and after-
noon sets. The effect on the azimuth of a small error in latitude
is in that way eliminated. Latitude observations should extend not
more than 15 minutes before or after apparent noon (maximum
altitude of the sun).
As the declination and horizontal intensity are usually changing
more rapidly in the morning than in the afternoon, it is preferable
to make the magnetometer observations in the afternoon. They
should be made in the order: Declination, oscillations, deflections,
deflections, oscillations, declination. The second set of deflections
and oscillations should be made with magnets inverted, and the
horizontal circle should be shifted in azimuth before the second set
of declination, in order to bring the readings upon a different part
of the circle.
38 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
Thermometer. The same thermometer should be used throughout
a set of horizontal intensity observations. It should be placed in
the hole in the magnet house during oscillations and near to the
deflecting magnet during deflections, either in the end of the deflec-
tion bar or (in magnetometers of the India Survey pattern) in the
box in which the magnet is inclosed. It should be changed from
one bar to the other with the magnet. Care must be taken to stop
up the hole in the magnet house when the thermometer is not in it.
Before beginning observations the thermometer should be examined
to see that the mercury column is not broken and that none of the
mercury is in the upper recess. A broken column can usually be
joined by holding the thermometer in the hand and striking the
wrist sharply against the knee, or by attaching it securely to a string
and swinging it rapidly in a circle.
Agreement of results. Before leaving a station the computation
should be carried far enough to show r that there is nothing essentially
wrong with the observations. In good work two consecutive sets of
azimuth should agree within one minute and the morning and after-
noon sets within two minutes. A greater difference is usually due
to lack of adjustment or level of the theodolite, or to a mistake in
pointing on the wrong limb of the sun, or in using the wrong line of
, the diaphragm. In case the morning and afternoon azimuth obser-
vations give results differing by more than five minutes, the observa-
tions should be repeated. The two sets of declination should agree
within two or three minutes when corrected approximately for
diurnal variation (see Table IX). The values of log Mil for the
two sets of oscillations should not differ by more than 0.00100, and
TT
the values of log ,, should agree equally well. The corresponding
agreement to be expected in the values of T and u can easily be com-
puted for a particular magnetometer and a particular locality.
When the dip results for the two needles differ by more than five
minutes in excess of the normal difference of the needles, the observa-
tions should be repeated. Thus,, if the observations show that on
the average needle No. 1 gives a value of dip three minutes greater
than No. 2, the observations should be repeated when No. 1 gives a
result more than eight minutes greater or two minutes less than
No. 2.
The record should be kept with hard pencil (or fountain pen) and
entered at once on the proper form (not kept on blank paper and
afterwards copied onto the form.) All computations should be made
in ink or inked over before the record is sent to the Office. The
different sheets will be punched and fastened together in the covers
provided (Form 367), arranged in the following order: (1) Descrip-
tion of station, angles connecting the azimuth mark with other
EQUIPMENT. 39
prominent objects, and chronometer correction on Standard time
(Form 441), (2) latitude observations (Form 267), (3) azimuth
observations (Form 266), (4) azimuth computation (Form 269),
(5) declination (Form 37), (6) dip (Form 42), (7) oscillations (Form
41), (8) deflections (Form 39).
Abstract. Before the record is sent to the Office the computation
should be completed and a copy made of the results and also of such
quantities as would be required to replace the computation in case
the record is lost (Form 442). This includes brief description of
station, chronometer corrections on Standard time, sun's maximum
altitude from latitude observations; mean of chronometer, horizontal
and vertical circle readings for each set of azimuth; mean reading of
mark and magnet, mean scale reading erect and inverted for each
declination set; time of whole number of oscillations and effect of
90 torsion, mean value of 2u for each deflection distance, tempera-
ture and time of each set of observations; the mean dip with each
needle for each half set (before and after reversal of polarities).
Computations. Five-place logarithms will be used. In the azi-
muth observations the means of circle readings will be carried to
whole seconds, means of times to tenths of a second; similarly in
computations. For declination observations, carry mean scale read-
ings to hundredths of a division, balance of computation to tenths of
a minute. For oscillations, compute time of one oscillation to four
decimal places, mean temperature to tenths of a degree. Compute
deflection angles to whole seconds. Dip computations will be carried
to tenths of a minute.
To secure the best results, particular attention should be paid to
the following points :
Be sure that all articles of iron and steel are removed to a safe distance
before beginning magnetic observations.
Be sure that the instrument is level and the levels in adjustment before
beginning observations, especially in latitude and azimuth observations.
Be careful to keep the magnets and dip needles dry and clean, espe-
cially the pivots of the dip needles.
Handle the chronometer with care at all times.
EQUIPMENT.
Observers engaged exclusively on magnetic work are usually pro-
vided with a theodolite magnetometer, a dip circle, a half-second
pocket chronometer, a tent, and minor accessories. When magnetic
observations are to be made only as opportunity offers in connection
with other branches of the field work of the Survey, the equipment
is often less complete, either a dip circle with special needles for total
intensity observations and a compass attachment for determination
of the magnetic declination or simply a compass declinometer for
40 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
declination alone. In such cases the true meridian is usually known
from triangulation or else the instrumental equipment includes a
theodolite and timepiece with which the necessary astronomical
observations can be made.
In the descriptions of instruments and methods which follow, the
erm alidade will be used to designate the upper part of the instru-
ment to which are attached the verniers for reading the horizontal
circle and of which the motion is controlled by the upper clamp and
tangent screw.
LATITUDE FROM OBSERVATIONS OF THE SUN.
For the greater part of the United States only approximate values
of the latitude and longitude can be obtained from existing maps.
It is usual, therefore, to include latitude observations in the program
of work at a magnetic station, in order that the azimuth may be
determined from sun observations with the required accuracy.
The most convenient method involves the measurement of the sun's
altitude at or near apparent noon, using the small theodolite pro-
vided for the azimuth observations.
At apparent noon, when the sun is on the meridian
being the latitude of the place, the sun's zenith distance, and
d its declination, south zenith distance and north declination being
considered positive for the northern hemisphere. As the sun's decli-
nation changes so slowly (the hourly rate of change never amounts
to 1'), no appreciable error is introduced by assuming it constant for
a series of observations beginning a few minutes before noon and
ending a few minutes after noon. The maximum altitude may also
be taken as the meridian altitude. The observations are made in the
manner shown in the example given below.
The observations should begin about ten minutes before apparent
noon and end about ten minutes after noon. Before making the
observations, therefore, it is necessary to find the chronometer time
of apparent noon, at least approximately, by the method given below.
After setting up, leveling, and adjusting the theodolite, as explained
later in connection with azimuth observations, the method of observ-
ing is as follows :
LATITUDE FROM OBSEKVATIONS OF THE SUN.
Form 267.
OBSERVATIONS or SUN FOR LATITUDE.
41
Station, Smyrna Mills, Me.
Theodolite of mag'r No. 20.
Chronometer No. 245.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
Temperature, 24 C.
Sun's
limb.
V.C.
Chronometer
time.
Vertical circle.
A.
B.
Mean.
h. m. s.
,
/ //
/ it
U
R
11 30 04
61 14 00
13 30
61 13 45
L
L
11 31 16
119 23 00
20 00
60 38 30
L
L
11 33 14
119 22 30
19 30
60 39 00
U
R
11 34 38
61 16 30
15 30
61 16 00
U
R
11 36 36
61 17 00
15 30
61 16 15
L
L
11 37 34
119 21 30
19 00
60 39 45
L
L
11 39 32
119 21 30
19 00
60 39 45
U
R
11 40 33
61 17 30
16 00
61 16 45
U
R
11 42 46
61 16 30
15 00
61 15 45
L
L
11 43 30
119 22 30
2000
60 38 45
Obs'd max. alt.
6058 15
R. &P.
27
h
60 57 48
r
29 02 12
8
17 06 18
4
46 08 30
With the vertical circle to the right of the telescope, point on the
sun with its disc bisected by the vertical line of the diaphragm and its
upper limb tangent to the horizontal line. Record the time of con-
tact as indicated by the chronometer and read and record both
verniers, A and B, of the vertical circle. Turn the alidade 180 in
azimuth and make another pointing on the sun, but with its lower
limb tangent to the horizontal line of the diaphragm, again recording
the time and vertical circle reading. As the vertical circle is usually
graduated from to 360, the reading in the first case will be the alti-
tude of the sun's upper limb, but the second reading must be subtracted
from 180 to get the altitude of the sun's lower limb. Combining the
two gives the altitude of the sun's center and eliminates the vertical
collimation error of the theodolite and the index error of the graduation.
The observations are continued for 15 or 20 minutes, reversing the
circle after the odd pointings, as shown in the above example. The
level of the instrument should be examined after the even pointings
and corrected if necessary. If the beginning is properly timed, the
maximum altitude will occur near the middle of the series. For the
field computation the pair of readings is selected which gives the
maximum altitude, and their mean, after being corrected for refraction
and parallax (Table I), is combined with the sun's declination to get
the latitude. The quantities for vertical circle left in the column
42
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
headed "Mean" are really 180 minus the means of the two vernier
readings.
A more accurate value of latitude is obtained by utilizing all the
observations by the "method of circum-meridian altitudes/' ex-
plained in detail in most textbooks on spherical astronomy (see, for
example, Chauvenet, Vol. I, page 235). In view of the degree of
accuracy required in a magnetic survey, or possible with the small
theodolite ordinarily used, many approximations in the method of
reduction to the meridian may be made. If Ji be the sun's meridian
altitude, 7i its altitude (observed) at a time t before (or after) appar-
ent noon, then approximately:
, , 2 sin 2 M
h = h + cos (f> cos d esc = ,",
SllJ. J.
2 sin 2 bt
Let A = cos (/> cos d esc and m = ^rr
Then Ji = h -\- Am and <f> = d -\- r
%
Table III gives the values of m for different values of t and Table IV
gives the values of A for different values of </> and d. It will be seen
that A increases as the sun's zenith distance decreases, and the method
is therefore not well adapted for observations where the sun crosses
the meridian near the zenith. The following computation of the set
of observations given above will best illustrate the method.
Form 268.
COMPUTATION OF LATITUDE FROM CIRCUM-MERIDIAN ALTITUDES OF SUN.
Station, Smyrna Mills, Me.
Date, August 5, 1910.
h. m. a.
Chron. correction on L. M. T. + 27 20
Local mean time of app. noon 12 05 53
Chron. time of apparent noon 11 38 33
t
m
A
A m
Reduced h of
sun's limb.
/ //
61 16 57
60 40 51
Reduced h
of0
m. 8.
-8 29
-7 17
141
104
1.36
192
141
1 II
60 58 54
-5 19
56
76
60 40 16
-3 55
30
41
61 16 41
-1 57
8
11
61 16 26
-0 59
2
3
60 39 48
+0 59
+200
2
8
3
11
60 39 48
61 16 56
60 58 22
+4 13
+4 57
35
48
48
65
61 16 33
60 39 50
60 58 12
Mean
60 58 25
R. &P.
- 27
h
60 57 58
C
290202
9
17 06 19
*
46 08 21
LATITUDE FROM OBSERVATIONS OF THE SUN. 43
In order to obtain the values of t, the time of observation before or
after apparent noon, it is necessary to find the chronometer time of
apparent noon. The chronometer correction on local mean time is
usually obtained from the observations of the sun for azimuth and
time, as will be seen later, but it may be obtained also from an approx-
imate value of the longitude and the chronometer correction on
standard time, as follows: For Smyrna Mills, Me., suppose the ap-
proximate longitude, 68 08'. 5, or 4 h 32 m 34 s , to be obtained from a
map. By comparison with Western Union telegraphic time signals on
August 4, 1910, chronometer No. 245 was 6 s . fast on 75th meridian
mean time. On August 5 it was 5 s . 8 fast, showing a loss of s . 2 per
day.
m. s.
At noon August 5 chronometer No. 245 correction on 75th mer. m. t 6
Smyrna Mills east of 75th meridian 27 26
Therefore chronometer No. 245 correction on local mean time +27 20
To find the local mean time of apparent noon, we must know the
difference between mean time and apparent time; that is, the equa-
tion of time, E. This may be found in any ephemeris. On page 128
of the American Ephemeris for 1910, the value of E at Greenwich
apparent noon on August 5 is found to be 5 m 53 s . 7 and decreasing at
the rate of s . 23 per hour. Hence, for Smyrna Mills apparent noon,
which occurs 4 h 32 m later, the value of E would be 5 m 53 8 .7- l s .0 =
5 m 52 s . 7. This is the amount which must be added to apparent time
in order to obtain mean time. As the equation of time for apparent
noon never differs from the equation of time for mean noon by as
much as s . 2, the latter may be used when the sun's ephemeris for
apparent noon is not available. The apparent time of apparent
noon is always 12 h 00 m 00 s , hence the mean time of apparent noon at
Smyrna Mills on August 5, 1910, was 12 h 05 m 53 s . The chronometer
was found to be 27 m 20 s slow of local mean time. Hence the chro-
nometer time of apparent noon was 1 1 h 38 m 33 s . Expressed analytically :
Chronometer time of apparent noon = mean time of apparent noon
chronometer correction, bearing in mind that the correction is con-
sidered positive when the chronometer is slow and negative when it
is fast. By subtracting the chronometer time of apparent noon
from the chronometer time of each observation, the corresponding
value of t is found. This is the argument required for obtaining m
from Table III.
For obtaining the values of A from Table IV only approximate
values of cf> and d are required, but as the value of d is needed later it
is just as well to compute it at this point.
h. m. s.
Chronometer time of apparent noon 11 38 33
Chronometer correction on 75th meridian mean time - 06
75th meridian time slow on Greenwich mean time. . . +5 00 00
Greenwich mean time of local apparent noon 4 38 27
44 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
This is the Greenwich mean time for which the sun's declination is
required. By referring to page 129 of the American Ephemeris for
1910 it will be found that the sun's declination at Greenwich mean
noon on August 5 was 17 09' 25". 8 N., and decreasing at the rate of
40 / M9 per hour. This rate is not uniform, however, the value for
noon of the 6th being 40 ".88. As the declination at 4 h 38 m 27 8 , or
4 h .64 after noon is required, we must find the average hourly change
for that interval, or, what is approximately the same thing, the change
for the middle of the interval, or 2 h .32 after noon. As the hourly
change increased 0".69 in 24 hours, it increased about T V of of that
amount, or 0".07 in 2.3 hours, and the desired average value for the
interval is therefore 40".19 + 0".07 = 40".26.
Sun's declination at Greenwich mean noon Aug. 5 ................... 17 09 25.8 N .
Change for 4 h .64=4.64X40".26=186".8 ....... ...................... -3 06.8
Sun's declination at 4 h 38 m 27 after noon ................. '-/. ? v ....... 17 06 19. I* .
In practice it is sufficient to carry the hourly change to tenths of
seconds only, and the allowance for second differences may then be
made by inspection. In fact, in most cases second differences might
be neglected entirely, as the maximum error would be only 3 ".5 in
assuming that the tabular value of hourly change is uniform for 12
hours before and 12 hours after the noon to which it refers.
The product Am is the difference between the altitude of the sun
at noon and at the time t before or after noon, and must therefore be
added to the observed altitude in order to get the corresponding
meridian altitude. The altitude of the sun's center is found by com-
bining an altitude ol the upper limb with one of the lower limb. The
mean of the different results is treated as the maximum altitude was
in the approximate field computation.
LATITUDE FROM OBSERVATIONS OF POLARIS.
If desired the latitude may be readily determined by observing the
altitude of the pole star, when the longitude and local mean time are
known approximately, using the formula:
(j) = h p cos t + ^P 2 sin 2 t sin 1" tan Ji
i
t being the hour-angle of the star, p its polar distance, and Ji the ob-
served altitude corrected for refraction. The refraction may be
obtained from Table I if the tabular quantities are increased by
8". 8 cos h, the amount of the solar parallax. When observations are
made at upper or lower culmination, the formula becomes
The right ascension and declination of Polaris for each day of the year
are given in the American Ephemeris. There also will be found on the
DETERMINATION OF THE TRUE MERIDIAN. 45
last page of the book a table giving the altitude of the star above or
below the pole at any hour-angle, computed for latitude 45 and the
mean declination of the star for the year.
DETERMINATION OF THE TRUE MERIDIAN AND LOCAL MEAN TIME BY
MEANS OF OBSERVATIONS OF THE SUN.
The following method is the one usually employed to determine
the true meridian in connection with the magnetic observations of
the Coast and Geodetic Survey. It is more convenient than others
in that it may be employed during daylight when the magnetic
observations are in progress. In connection with the time signals sent
out by telegraph from astronomical observatories it furnishes the
means also of determining approximately the longitude of the place of
observation. It requires a theodolite with a vertical circle and pris-
matic eyepiece for observing the sun, and a well-regulated time-
piece. The observations at a place usually consist of four independent
sets of observations, two in the morning and two in the afternoon,
each set comprising four pointings on the sun and two pointings on a
reference mark, symmetrically arranged as in the example given
below. For each pointing on the sun the time is noted, and the
horizontal and vertical circles are both read. For the best results
the observations sliould be made not less than two hours from
apparent noon.
ADJUSTMENT OF THE THEODOLITE.
Before beginning observations it is necessary to see that the theod-
olite is in good adjustment, especially as regards the levels.
To adjust the levels. After mounting the theodolite on the tripod,
set up the instrument over the station mark with the tripod head
approximately level and the legs planted firmly in the ground or
resting on suitable stubs. Most small theodolites are provided with
a quick centering device, by means of which the accurate setting
over the station mark is made after the tripod has been fixed in
position. Turn the alidade until one of the levels is parallel to the
line joining two of the leveling screws. Bring the level bubble to the
center of the vial by means of the leveling screws. Bring the bubble
of the second level to the center of its vial by means of the third
leveling screw (by the other pair of leveling screws, if there are four).
If necessary, repeat the operation until both bubbles are in the
center. Then turn the alidade 180 in azimuth. If the levels are
out of adjustment, the bubbles will no longer be in the center of the
vials. Correct one half of the defect by means of the adjusting
screws of the levels and the other half by means of the leveling screws.
Return the alidade to its original position and repeat the operation
if necessary. When the adjustment has been completed the instru-
ment will be level and the level bubbles will be in the center of the
vials no matter in what direction the telescope is pointing.
46 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
To insert new cross wires. The cross wires of a telescope are at-
tached to a metal ring which is held in position near the eyepiece
by four capstan screws. They may be spider threads (obtained from
a cocoon, not from a web), or fine platinum wire, or, more commonly,
lines etched on a thin piece of glass, called a diaphragm, which is
fastened to the ring by shellac. An extra diaphragm and a small
bottle of shellac should be kept with the instrument so that the
observer may insert a new diaphragm should he be so unfortunate as
to break the old one. To do this the eyepiece is removed, the ring
taken out, and the remains of the old diaphragm and shellac cleaned
off. The ring is then laid on a piece of white paper and the new
diaphragm placed in the position indicated by lines on the ring and
fastened by shellac around the edges. The ring is then put back in
the telescope tube, and adjusted in position by means of the capstan
screws as explained later.
To adjust the eyepiece. Point the telescope to the sky and move
the eyepiece in or out until the cross wires appear sharp and distinct.
Then turn the telescope to a distant object and move the object glass
in or out until the object appears sharply defined. If the adjust-
ment has been properly made there will be no apparent motion of
the object when the eye is moved from one side of the eyepiece to
the other. If the vertical cross wire is perpendicular to the hori-
zontal axis of the theodolite, an object which has been bisected by
one part of the wire will continue to be bisected throughout the
length of the wire when the telescope is revolved about its horizontal
axis. If this is not the case the capstan screws should be loosened
and the ring carrying the cross wires rotated slightly about the
optical axis. In the field the verticality of this cross wire may be
tested by pointing on the vertical edge of a house. At the same time
the horizontality of the transverse axis of the telescope may be tested
by turning the telescope in altitude and seeing whether the edge of
the house remains bisected for a considerable change in altitude.
To adjust the vertical cross wire for collimation. Point at a well-
defined distant object. Turn the alidade 180 in azimuth and reverse
the telescope and point on the object again. The amount by which
the difference of the two circle readings differs from 180 is twice the
error of collimation and may be corrected by moving laterally the
ring carrying the cross wires, by means of the capstan screws on the
sides of the telescope tube. When the telescope is mounted eccen-
trically, as it is in some magnetometers, allowance must be made for
that fact in adjusting for collimation. Two marks must be provided
which are twice as far from each other as the optical axis of the tele-
scope is from the vertical axis of the instrument.
This adjustment is usually attended to by the mechanician before
the instrument is sent from the office and rarely needs to be repeated
in the field unless it becomes necessary to insert new cross wires, since
DETERMINATION OF THE TRUE MERIDIAN. 47
the observations are so arranged as to eliminate small errors of col-
limation.
To adjust the vertical circle to redd zero when the telescope is level.
While the observations are usually so arranged as to eliminate the
effect of index error of the vertical circle and vertical collimation
error of the telescope, it is desirable to keep that error small so that
a setting on the wrong limb of the sun or an error in reading the
circle may be more readily discovered. This adjustment is made by
means of a slow-motion screw which operates on an arm of the frame
carrying the verniers by which the vertical circle is read. Bisect a
distant object with the horizontal cross wire and read the vertical
circle. Turn the alidade 180 in azimuth, invert the telescope, and
again point on the object and read the vertical circle. If the sum of
the two readings differs from 180, correct for half the difference by
means of the slow-motion screw which moves the verniers. When
this adjustment has been made, the level attached to the vernier
frame may be adjusted also. In some theodolites the vertical circle
is not attached rigidly to the telescope, but is held by friction or by
a clamp. In making the above adjustment for an instrument of
that class, a first approximation is obtained by shifting the position
of the graduated circle, and then the process is completed by moving
the verniers.
OBSERVATIONS.
Having leveled and adjusted the theodolite and selected a suitable
azimuth mark, a well-defined object nearly in the horizon and more
than 100 yards distant, the azimuth observations, are made in the
following order, as shown in the sample set given below.
Point on the mark with vertical circle to the right of the telescope
(V. C. R.) and read the horizontal circle, verniers A and B. Reverse
the circle, invert the telescope and point on the mark again, this
time with vertical circle left (V. C. L.). Place the colored glass in
position on the eyepiece and point on the sun with vertical circle
left, bringing the horizontal and vertical cross wires tangent to the
sun's disc. At the moment when both cross wires are tangent note
the time by the chronometer. If an appreciable interval is required
to look from the eyepiece to the face of the chronometer, the observer
should count the half-seconds which elapse and deduct the amount
from the actual chronometer reading. The horizontal and vertical
circles are then read and recorded. A second pointing on the sun
follows, using the same limbs as before. The alidade is then turned
180 and the telescope inverted and two more pointings are made,
but with the cross wires tangent to the limbs of the sun opposite to
those used before reversal. This completes a set of observations.
A second set usually follows immediately, but with the order of the
pointings reversed, ending up with two pointings on the mark.
Between the two sets the instrument should be releveled if necessary.
48
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
To avoid the necessity of moving both tangent screws hi making a
setting on the sun, it is convenient to clamp the circles with one
cross wire slightly in advance of the limb and then wait until the
limb moves up to it, at the same time keeping the other cross wire
tangent by means of the tangent screw. As the wires are seen more
distinctly when brightly illuminated, the limbs to be observed should
be so selected that one wire may cross the sun's disc until the moment
of tangency is reached. The observer must be sure to point on
opposite limbs in the two halves of a set, so that the mean of the
four readings will refer to the sun's center. If he should make the
mistake of pointing on the wrong limb, the reading must be corrected
for the sun's diameter. For a vertical circle reading the correction
is the diameter, which may be obtained from an ephemeris of the
sun or with sufficient accuracy from the second column of Table II.
For a horizontal circle reading, the sun's diameter must be divided
by the cosine of the sun's altitude in order to get the desired cor-
rection. The values for altitudes from 10 to 70 are given in
Table II.
Form 266.
OBSERVATIONS OP SUN FOR AZIMUTH AND TIME.
Station, Smyrna, Mills, Me.
Theodolite of mag'r No. 20.
Mark, Flagpole on school bulldinp.
Chronometer, 245.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
Temperature, 20 C.
Sun's
limb.
V. C.
Chronome-
ter time.
Horizontal circle. Vertical circle.
A.
B. Mean. A.
8. Mean.
L
Mark
124 43 40
43 50 124 43 45
R
'
304 43 40
43 40 304 43 40
124 43 42
h. m. s.
El
R
8 25 54
155 12 30
12 50 155 12 40 41 10 30
11 30 41 11 00
El
R
27 56 155 40 40
41 00 155 40 50 41 31 00
31 30 41 31 15
Q
L 30 03 337 00 10
00 20 337 00 15 138 47 00
45 30 41 13 45
D
L
32 06
337 28 20
28 30
337 28 25 138 27 00
2.5 30 41 33 45
8 28 59.8
336 20 32
41 22 20
57
JQ L 8 33 45 337 51 00
51 20
337 51 10 138 10 30 09 00 41 50 15
IQ
L 35 59 338 24 30
24 50
338 24 40 137 48 30 47 00 42 12 15
(
R 38 20 158 10 00 10 20
158 10 10 43 10 30 11 30 43 11 00
El
R 40 37 158 41 50 42 10
158 42 00 43 31 30 32 30 43 32 00
8 37 10.2
338 17 00 42 41 23
54
R Mark 304 43 40 43 50
304 43 45
L 124 43 20 43 40 124 43 30
124 43 38
DETERMINATION OF THE TRUE MERIDIAN.
49
Form 266.
OBSERVATIONS OP SUN FOR AZIMUTH AND TIME.
Station, Smyrna Mills, Me.
Theodolite of mag'r No. 20.
Mark, Flagpole on school building.
Chronometer, 245.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
Temperature, 21 C.
Sun's
limb.
v. c
Chronome-
ter time.
Horizontal circle.
Vertical circle.
A.
B.
Mean.
A.
B.
Mean.
/ //
/ //
Off/
/ //
/ //
in
R
Mark
28045 00
45 20
280 45 10
L
100 45 20
45 40
100 4530
280 45 20
ft. m. s.
d
L
3 12 38
96 35 50
36 20
96 36 05
143 03 00
00 00
36 58 30
El
L
14 38 97 01 20
01 50
97 01 35
143 23 00
2000
36 38 30
R
16 44 278 04 10
04 30
278 04 20
36 53 30
53 00
3653 15
R
18 46
278 29 00
2920
278 29 10
36 33 00
32 00
36 32 30
3 15 41. 5
277 32 48
3645 41
.
1 08
.0
R
3 20 12
278 47 20
47 40
278 47 30 ! 36 18 00
1730
36 1745
B
R
22 12
279 12 00
12 20
279 12 10 i 35 58 00
57 30
35 5746
^
L
23 50
98 57 40
58 10
98 57 55
144 56 30
53 30
35 05 00
L
25 50
99 22 40
23 10
99 2255
145 17 00
1400
34 4430
3 23 01.0
279 05 08
35 31 15
1 11
L
Mark
100 45 20
45 40
100 45 30
R
280 45 20
45 30
280 45 25
28045 28
The chronometer and circle readings for the four pointings of a set
are combined to get mean values for the subsequent computation.
When the vertical circle is graduated from zero to 360 , the readings
with vertical circle right give the apparent altitude of one limb of the
sun, while those with vertical circle left must be subtracted from 180
to get the apparent altitude of the other limb. The mean of the four
pointings gives the apparent altitude of the sun's center. This must
be corrected for refraction and parallax to get the true altitude.
The value of this correction is given in Table I for different tem-
peratures and altitudes for average conditions. The change in refrac-
tion with change in barometric pressure need not be taken into con-
sideration. The correction for refraction is so large and uncertain
near the horizon that observations of the sun should be avoided when
its altitude is less than 10.
It is important to test the accuracy of the observations as soon as
they have been completed, so that additional sets may be made if
7721311 4
50 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
necessary. This may be done by comparing the mean of the first and
fourth pointings of a set with the mean of the second and third, or by
comparing the rate of change in the altitude and azimuth of the sun
between the first and second pointings, the third and fourth, fourth
and fifth, fifth and sixth, and seventh and eighth. For the period
of 15 or 20 minutes required for two sets of observations the rate of
motion of the sun does not change much.
COMPUTATION.
For the computation of the azimuth of the sun and the local mean
time from observations made in the above manner, use is made of the
following formulas, the derivation of which has been explained in
the first part of this publication.
ctn 2 %A = sec s sec ( p) sin (s h) sin (s <j>)
tan %t = sin (a h) sec (s p) tan
A = azimuth of sun, east of south in the morning, west of south in
the afternoon.
<j> = latitude of the place.
h = altitude of the sun corrected for refraction and parallax.
p = polar distance of the sun at the tune of observation.
= the hour angle of the sun, or apparent time of observation,
expressed in arc.
The form of computation is shown in the following example, for the
sets of observations at Smyrna Mills, Me., given above.
DETERMINATION OF THE TRUE MERIDIAN.
51
Form 269.
COMPUTATION OF AZIMUTH AND LONGITUDE.
Station, Smyrna Mills, Me.
Date.
Aug. 5.
Aug. 5.
Aug. 5.
Aug. 5.
h
41 21 29
42 40 29
36 44 33
35 30 04
*
46 08 21
46 08 21
46 08 21
46 08 21
P
72 51 34
72 51 39
72 56 08
72 56 12
2s
160 21 24
161 40 29
155 49 02
154 34 37
s
80 10 42
80 50 14
77 54 31
77 17 18
s-p
7 19 08
7 58 35
4 58 23
4 21 06
s-h
38 49 13
38 09 45
41 09 58
41 47 14
s-t
34 02 21
34 41 53
31 46 10
31 08 57
log sec *
0. 76807
0. 79795
0. 67887
0. 65749
" sec (sp)
0.00355
0.00422
0.00164
0.00125
11 sin (s-h)
9. 79718
9. 79091
9.81839
9.82371
" sin (-tf)
9.74800
9.75530
9. 72140
9.71372
" ctnM
0.31680
0.34838
0.22030
0. 19617
" ctnM
0.15840
0. 17419
0. 11015
0.09808
A from South
69 33 04
67 36 43
75 37 17
77 10 09
Circle reads
336 20 32
338 17 00
277 32 48
279 05 08
S. Mer. "
45 53 36
45 53 43
201 55 31
201 54 59
Mark "
124 43 42
124 43 38
280 45 20
280 45 28
Azimuth of Mark
78 50 06
78 49 55
78 49 49
78 50 29
Mean
78 50 05
log sec (sp) sin (s h)
9.80073
9. 79513
9.82003
9.82496
" tan \ t
9. 64233
9. 62094
9.70988
9.72688
t in arc
47 23 24
45 20 52
54 17 25
56 07 55
h. m. s.
h. m. s.
ft. TO. S.
ft. TO. *.
t
-3 09 33.6
-3 01 23.5
3 37 09.7
3 44 31.7
E
+ 5 53.4
+ 5 53.3
+ 5 51.8
+ 5 51.8
Local M. T.
8 56 19.8
9 04 29.8
3 43 01.5
3 50 23.5
Chron. time
8 28 59.8
8 37 10. 2
3 15 41.5
3 23 01.0
A t on L. M. T.
+ 27 20.0
+ 27 19.6
+ 27 20.0
+ 27 22.5
J t on 75 M. T.
5.8
5.8
5.8
5.8
41
-27 25.8
-27 25.4
-27 25.8
27 28.3
Mean
-27 26.3=
- 6 51'.6
A=68
08'.4
The different steps of the computation are most conveniently made
in the following order:
Enter the corrected altitude, mean readings of the horizontal circle
for the pointings on the sun and on the mark, and the chronometer
time for each set of observations in their proper places. Enter the
value of latitude obtained from the latitude observations or other
source. Compute the chronometer correction on standard time for
the time of each set of observations from the comparisons with
52 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
telegraphic time signals. Unless the chronometer has a large rate
its correction may be taken the same for two contiguous sets of
observations. Compute the Greenwich mean time of observation for
each set, and find from the American Ephemeris, or H. O. Publication
No. 118, the sun's polar distance and the equation of time for that
time in the manner explained in connection with the computation of
latitude from circum-meridian altitudes. The succeeding steps
require little explanation. As the horizontal circles of theodolites
are with few exceptions graduated clockwise, and as the sun is east
of south in the morning and west of south in the afternoon, it follows
that in order to find the horizontal circle reading of the south point,
the azimuth of the sun must be added to the circle reading of the sun
for the morning observations and subtracted from it for the after-
noon observations. The horizontal circle reading of the south point
subtracted from the mark reading gives the azimuth of the mark,
counted from south around by west from to 360.
For the computation of t, the logarithms of sec (s p) and sin (s h)
are found in the azimuth computation and their sum can be written
down in its proper place. From that must be subtracted log ctn A
to find log tan %t. The corresponding value of t is the time before or
after apparent noon. If in the case of the morning observations
ctn i^ be substituted for tan ty, ^ will be counted from midnight.
The difference between the chronometer correction on local mean
time and the correction on standard time is the difference in longi-
tude between the standard meridian and the place of observation.
The angular measures connecting selected prominent objects are
conveniently made in connection with the mark readings at the
close of the azimuth observations. The various marks should be
pointed on successively with vertical circle left and then in the
reverse order with vertical circle right. They should be well-defined
objects not liable to be confused with similar ones near by. The edge
of a chimney, for example, is not a desirable mark, as there is always
danger of confusing the edges as they appear to the naked eye with
their reversed position as seen through the telescope.
DETERMINATION OF THE TRUE MERIDIAN FROM OBSERVATIONS OF
POLARIS.
The true meridian may also be determined by measuring the angle
between Polaris and a reference mark, when the local mean time is
known. The most convenient time for observing is just after sunset,
when the mark does not require illumination. The azimuth of the
star from the north is computed by means of the formula
sin t
tan A =
cos $ tan d sin cf> cos t
DETERMINATION OF THE MAGNETIC DECLINATION. 53
in which t is the hour angle of the star before or after upper culmina-
tion and d is its declination. For the purposes of magnetic work it is
sufficient to know the local mean time within one or two minutes.
At elongation the change in the azimuth of Polaris is inappreciable
for a considerable interval and even a less accurate knowledge of the
time will suffice. When the local time is not known the time of
culmination of Polaris may be determined with sufficient accuracy
from a knowledge of its position with relation to Ursse Majoris or
8 Cassiopeia.
A detailed explanation of these methods of determining the true
meridian, together with tables to facilitate their use, will be found in
" Principal Facts of the Earth's Magnetism," pages 79-91.
DETERMINATION OF THE MAGNETIC DECLINATION.
A. WITH A MAGNETOMETER.
The determination of the magnetic declination consists of two
operations ; first, the determination of the true meridian as explained
in the preceding section, and second the determination of the mag-
netic meridian, using either a magnetometer, a compass declinometer,
or the compass attachment of a dip circle.
Coast and Geodetic Survey pattern magnetometer. Most of the mag-
netometers in use in the field work of the Coast and Geodetic Survey
are similar in design to the one shown in Figure 3. It is usually re-
ferred to as a theodolite magnetometer since it comprises a theodolite
and a magnetometer arranged for mounting on the same base. It is
light, compact, of simple construction, and easily handled and is
therefore especially suited to the field work of a magnetic survey.
The horizontal circle is 5 inches in diameter graduated to 20' and
read by two verniers to 20". The magnets are hollow, octagonal,
1.1 cm. between opposite faces. The lengths of the two magnets
(7.4 and 6.0 cm.) are such as to make the first distribution coefficient
(P) nearly zero. The observer faces south when making observa-
tions of the suspended magnet. In the south end of each magnet is
a graduated scale and in the north end a collimating lens so arranged
that when the reading telescope is focused on a distant object the
graduated scale will be in focus also. The magnet is supported in a
brass stirrup consisting of three parallel connected rings joined to a
shank about 2.5 cm. long. This long shank presents any appreciable
change of level of the magnet for a considerable change of vertical
force. A short pin in the center of the stirrup engages a groove about
the center of the magnet. With the octagonal form of magnet the
scale is easily placed horizontal in either the erect or inverted posi-
tions. When not in use the stirrup is attached to a hook under the
roof of the magnet house to prevent breaking or twisting of the fiber.
54
DIRECTIONS FOB MAGNETIC MEASUREMENTS.
Silk fiber suspension is used, two strands usually being sufficient to
support the magnets without danger of breaking. The upper ends
of the fibers are held by a clamp, with a suitable arrangement of screw
and nut or rack and pinion for regulating the height of the suspended
magnet.
FIG. 3. Coast and Geodetic Survey pattern magnetometer.
The end of the reading telescope is connected with one end of the
wooden magnet house by a hood of dark cloth, so that no glass comes
between the objective and the magnet. Light to illuminate the scale
of the magnet is admitted through a hole in the other end of the
magnet house. This hole is closed by a glass window, which is
DETERMINATION OF THE MAGNETIC DECLINATION. 55
opened when pointings are to be made on the mark in declination
observations, in order to avoid the distortion likely to be caused by
irregular refraction of the glass.
The deflection bars used in the horizontal intensity observations
are of such shape that the deflecting magnet when in position on the
bar is on a level with the optical axis of the reading telescope and at
right angles with it and consequently with the suspended magnet
also. The bars are not graduated, but on each there are two troughs
for supporting the deflecting magnet. In the middle of each trough
is a short pin which fits into the groove around the magnet and thus
insures its proper setting. The pins are approximately 30 and 40 cm.
from the center of the magnet house. In Figure 3 the long magnet
is in position on the deflection bar, and the wooden sides of the magnet
house have been removed to show the suspended short magnet.
The theodolite shown at the right of the picture is easily mounted in
place of the magnetometer when azimuth or latitude observations
are to be made.
In order to minimize the change in torsion with change in atmos-
pheric conditions, the silk fibers should be well soaked in glycerin
before they are used. Extra fibers should be kept in soak in a bottle
of glycerin, to be ready for use in case of breakage. A convenient
way to insert new fibers is as follows: Draw the fibers through the
fingers several times to remove superfluous glycerin and undesirable
twists. Fasten one end to the eye of the stirrup with a small loop.
Draw the fibers even and fasten a small piece of wax or other weight
to the loose ends. Eemove the torsion head from the suspension
tube, turn the magnet house upside down, and drop the weighted ends
through the tube. The wax may then be removed and the ends
fastened to the torsion head at the proper distance from the stirrup,
care being taken to have the two fibers of the same length. When
the torsion head is at its lowest position the stirrup should be about
half an inch above the floor of the magnet house. Especial care must
be taken to leave no loose ends which might touch the magnet house
or the inside of the suspension tube.
The determination of the magnetic meridian with this type of
magnetometer is made as follows: Mount the magnetometer and
level carefully by means of the striding level provided for the reading
telescope (shown in position in the picture). Turn the alidade until
the telescope points approximately magnetic south. Place the
thermometer in the hole in the roof of the magnet house, suspend the
torsion weight (a solid brass cylinder of about the same mass as the
long magnet), and replace the wooden sides of the magnet house by
those of glass. Bring the torsion weight to rest and then watch its
vibration under the influence of the twist of the suspension fibers.
By successive trials turn the torsion head at the top of the suspension
56 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
tube until the weight comes to rest in a -position parallel to the optical
axis of the telescope, or until its arc of vibration, reduced to a small
amount, is bisected by that line. The suspension is then free from
twist that is, there is no tendency to turn a suspended weight out of
the vertical plane through the optical axis of the telescope and the
reading of the torsion head indicates the line of detorsion. With a
silk fiber suspension just strong enough to support the magnet, the
effect of 90 of torsion seldom amounts to as much as 5' and an error
of 10 in the determination of the line of detorsion would therefore
affect the resulting decimation by not more than 0'.5.
Open the glass window in the end of the magnet house and point
upon the object used as a reference mark in the azimuth observa-
tions, lowering the torsion weight below the line of sight. Read both
verniers and enter the readings in the proper place in the record.
Close the window, turn the alidade until the telescope again points
approximately magnetic south, remove the torsion weight and sus-
pend in its place the long magnet with its scale erect, being careful
to slacken the fibers as little as possible. Raise the magnet to the
level of the reading telescope, quiet its vibration as much as possible,
and replace the wooden sides of the magnet house. Adjust the
mirror so that it reflects the light onto the scale of the magnet.
Check the vibration of the magnet until the arc is reduced to one
or two divisions of the scale. This may be done by means of a screw-
driver, adjusting pin, or other small piece of steel, holding it a short
distance from the end of the magnet, first on one side and then on
the other as the magnet swings back and forth. It will often be
found that an adjusting pin has become slightly magnetized. In
such cases the alternate attraction and repulsion may be produced
by turning the pin end for end.
Turn the alidade until the division of the scale corresponding to the
magnetic axis swings by about equal amounts to the right and left
of the vertical wire of the reading telescope, and clamp the hori-
zontal circle. If the scale reading of the axis is not known approxi-
mately from previous observation, the middle division of the scale
will be used. This setting of the horizontal circle is not to be changed
until the time comes to point on the mark again.
Read the scale when the magnet comes to rest momentarily at the
extremes of its swing. When the scale is not numbered it is assumed
to be erect when the longer divisions project upward and the readings
are then considered as increasing from left to right. The "left"
reading is the one when the left end of the scale approaches nearest
to the vertical wire of the reading telescope, and is therefore less
than the "right" reading for magnet erect. After an interval of a
minute read the scale again.
DETERMINATION OF THE MAGNETIC DECLINATION.
57
Turn the magnet upside down in the stirrup, so that the scale ap-
pears inverted, reduce the arc of vibration, and make four readings
of the scale at intervals of one minute. The zero of the scale is now
to the right, and the "left" reading will be greater than the " right. "
Return the magnet to the erect position and make two more
scale readings.
Read the horizontal circle to be sure that it has not been disturbed
accidently; remove the magnet and complete the set by pointing on
the reference mark. When horizontal intensity observations are
to follow immediately, as is usually the case, it is more convenient
to make the first set of oscillations before removing the magnet and
repeating the pointing on the mark.
The mean of the erect and inverted readings gives the division of
the scale which corresponds to the position of the magnetic axis.
When the telescope is pointed on that division, it is in the plane of the
magnetic meridian. For any other scale reading the reading of the
horizontal circle must be corrected by the angular value of the
portion of the scale included between the observed scale reading and
the scale reading of the axis. With magnet erect the zero of the
graduation is at the apparent left and increasing scale readings
correspond to decreasing circle readings. Under ordinary conditions
the scale reading of the axis of a magnet will remain very nearly
constant for a long time. If it shows much variation from station
to station, the magnet should be examined carefully to make sure
that the scale glass and its mounting are not loose.
The angular value of one division of the scale is readily determined
by pointing successively on every fifth or every tenth division and
reading the horizontal circle in eac*h case, then repeating the opera-
tions in the reverse order, so as to eliminate gradual change of
declination during the observations, as shown in the following
example, the order of observations being indicated by the figures in
the second and fourth column:
SCALE VALUE OF MAGNET 11L OP MAGNETOMETER No. 11.
Scale
reading.
First set.
1
Second set.
Mean.
Value of 30
divisions.
1
146 46 45
12
146 46 15
146 46 30
(0-30)
10
2
146 11 15
11
146 10 30
146 10 52
(10-40)
20
3
145 33 30
10
145 32 30
145 33 00
(20-50)
30
4
144 57 45
9
144 57 15
144 57 30
1 49 00
40
5
144 20 45
8
144 20 00
144 20 22
1 50 30
50
6
143 42 30
7
143 42 30
143 42 30
1 50 30
30 divisions
1 5000
1 division
3'.67
58
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
The accompanying example showing the form of record and com-
putation needs little explanation.
Form 37.
MAGNETIC DECLINATION.
Station, Smyrna Mills, Me.
Magnetometer No. 20.
Mark, Flagpole on school building.
Magnet, 20L.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
Line of detorsion, 80.
Chron.
time.
Scale.
Scale readings.
Horizontal circle readings.
Left.
Right. Mean.
Mark.
Magnet.
A.m.
923
9 24
926
9 27
9 28
9 29
9 31
9 32
E
E
I
I
I
I
E
E
d.
28.8
28.9
28.7
28.7
28.7
28.8
28.5
28.5
d. d.
30.2 29.50
30.3 29.60
25. 6 27. 15
25.7 27.20
25.8 27.25
25.8 27.30
30. 9 29. 70
30. 9 29. 70
i
Before A
B
After j A
B
1 II
32538 40
145 3900
325 38 40
145 39 00
/ It
226 46 20
46 46 40
226 4620
46 46 40
Mean
325 38 50
226 4630
Mean scale readings. d.
Erect 29.62
Inverted 27.22
Axis 28.42
Mean scale reading, erect
Axis
Scale Axis
Reduction to axis
Circle reading
d.
29.62
28.42
Remarks:
Temp.: 27.OC.
Weather: Fair.
Torsion weight suspended 25
minutes.
1 division of scale=2'.0.
h. m.
Mean chron. time 9 27. 5
Chron. corr'n on L. M. T. +27. 3
+1.20
226 46.5
Mag'c S. M. reading
Mark reading
226 48.9
325 38.8
Magnetic azimuth of mark
True azimuth of mark *
98 49.9
78 50.1
Magnetic declination, W
Diurnal variation
19 59.8
+5.5
Mean declination, W
20 05.3
Local mean time
9 55
* Counted from south around by west from to 360.
The azimuth of the mark and the chronometer correction on local
mean time were obtained from the computation of the observations
of the sun, reproduced on page 51. The magnetic south meridian
reading subtracted from the mark reading gives the magnetic azimuth
of the mark, and that subtracted from the true azimuth of the mark
gives the magnetic declination, east when plus and west when minus.
The correction for diurnal variation is supplied in the Office from the
records of the nearest magnetic observatory, but its approximate
value may be obtained (except for periods of magnetic storms) from
DETERMINATION OF THE MAGNETIC DECLINATION.
59
Table IX, which gives the average diurnal variation for different sea-
sons of the year for the different observatories.
India Magnetic Survey pattern magnetometer. Magnetometers of
the type shown in Figure 4 are in use at three of the magnetic observa-
tories of the Coast and Geodetic Survey. They are very well adapted
FIG. 4. India Magnetic Survey pattern magnetometer.
for that purpose, but are rather too heavy for field work, although one
of them has been so used for several years. This type of instrument
was designed by Capt. H. A. Denholm Fraser, R. E., for use in the
magnetic survey of India, and is a modification of the well-known
Kew pattern. The long ma^giietJs^hollow cylinder about 9 cm. long
or THE
UNIVERSITY
60 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
and 1 cm. in diameter, with an aluminum cell mounted externally at
each end. The cell at the south end carries a piece of optical glass on
which are engraved two lines at right angles to each other. The cell
at the north end contains a collimating lens. On the glass diaphragm
of the reading telescope there are two scales, one vertical and the other
horizontal. Around the middle of the magnet is a shallow groove,
which is engaged by a screw pin on the under side of the stirrup. The
stirrup has another sheath above the one holding the magnet, in which
is placed an inertia bar of the same dimensions as the magnet when
observations are made to determine the moment of inertia of the
magnet and suspension. The magnet is not removed from the stirrup
except when repairs are necessary. Four longitudinal lines on the
magnet and a mark on the stirrup insure the horizontality of one of
the cross lines on the glass in the s,outh cell.
The short magnet is similar to w the long magnet, reduced in all
dimensions, but without the end cells. It is mounted in a stirrup
above and parallel to an aluminum collimator similar to the long
magnet. The magnets are suspended by phosphor-bronze ribbons
having about the same coefficient of torsion as a silk-fiber suspension.
The torsion weight is a xylonite disk mounted on a metal spindle. It
is divided on the periphery to degrees and is figured at every fifth
division. By the insertion of a small lens in front of the objective of
the reading telescope, the suspended weight may be read without
change of focus. The plane of detorsion is indicated by the zero of
the graduation.
The straight brass deflection bar is not graduated, but has a series
of holes bored in its upper surface at distances 22.5, 26.25, 30, 35, and
40 cm. on either side of the center. During deflection observations
the long magnet is placed in a small wooden box, on the under side
of which is a metal plug fitting snugly the holes in the deflection bar.
The box is so constructed that the center of the magnet is exactly over
the center of this plug and on a level with the suspended short magnet.
This arrangement eliminates all direct handling of the long magnet
during deflection observations.
Declination observations with this type of magnetometer differ only
in detail from those given in the example. The scale is on the glass
diaphragm of the reading telescope and the reduction to axis is
obtained by subtracting the mean of the scale readings (magnet erect
and magnet inverted) from 50, the middle division. The difference
between the erect and inverted readings is twice the angle between the
geometric and magnetic axes of the magnet and should remain very
nearly constant.
The angular value of one division of the scale may be obtained by
pointings on a distant object instead of on the magnet.
DETERMINATION OF THE MAGNETIC DECLINATION. 61
Magnetometers of other design are so seldom used in the field work
of the Survey that it is unnecessary to describe them in detail. Men-
tion may be made of No. 21, a very small instrument weighing only
4 kg., similar to the one used in the magnetic survey of France and
described by Mascart on page 212 of his "Traite* de Magne'tisme Ter-
restre," and No. 25, a combination instrument of the Prussian field
magnetometer type, consisting of theodolite, magnetometer, decli-
nometer, and dip circle, all arranged for mounting v on the same base.
A description of this instrument will be found in " Results of Obser-
vations made at the Coast and Geodetic Survey Magnetic Observatory
at Sitka, Alaska, 1902-1904."
DECLINATION FROM HORIZONTAL INTENSITY OBSERVATIONS.
In the directions for determining horizontal intensity, given later
on, it will be seen that provision is made for reading the scale of the
magnet and the horizontal circle in connection with the observations
of oscillations. This furnishes a check on the regular declination
observations which immediately precede or foUow, since the change
in scale reading should correspond with the change in circle reading;
or a value of the declination may be computed by assuming that the
mark reading and the scale reading of the axis are the same as during
the regular declination set. In the example given it was not necessary
to shift the setting of the horizontal circle between declination and
oscillation observations, since the axis reading was very near the
middle division (30).
A value of declination may also be obtained from the two sets of
deflections, provided the short magnet is erect in one set and inverted
in the other, and provided also that the position of the instrument is
not disturbed between a set of deflections and one of the declination
sets, so that the mark reading may be assumed to be unchanged. The
observations are so arranged that the horizontal circle is read when
the magnet is deflected by approximately equal amounts in opposite
directions from the magnetic meridian, and the mean of the readings
therefore represents the reading of the magnetic south meridian,
which combined with the mark reading gives the magnetic azimuth of
the mark. In the sample set of deflections on page 78:
Mean of 1, 4, 5, 8 226 29 36
2, 3, 6, 7 226 29 15
Magnetic south meridian reading 226 29 26
Mark reading, from declination above 325 38 50
Magnetic azimuth of mark 99 09 24
62 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
From the second set which followed with magnet inverted :
O / /'
Mean of 1, 4, 5, 8 295 32 26
2, 3, 6, 7 . 295 32 25
Magnetic south meridian reading 295 32 26
Mark reading, from second declination set 34 08 20
Magnetic azimuth of mark 98 35 54
Mean of two sets 98 52 39
True azimuth of mark ' 78 50 05
Magnetic declination, W 20 02 34
Diurnal variation -f- 2 00
Mean decimation, W 20 04 34
In this case the horizontal circle was shifted by means of the lower
clamp between the two sets of deflections. The difference between
the two values of the magnetic azimuth of the mark represents
approximately twice the angular distance between the magnetic axis
of the short magnet and the middle division of its scale.
B. WITH A COMPASS DECLINOMETER.
Two types of compass declinometer are in use in the Coast and
Geodetic Survey. The older form is essentially an improved pris-
matic compass with slit and thread arrangement for pointing on the
object selected as a mark. It consists of a cylindrical brass bowl
resting on three foot screws, in the center of which is the pivot on
which the needle rests. The needle is a flat (in the vertical plane)
rectangular bar 9 cm. long, terminating in steel points. It is ex-
panded at the center to inclose an agate cup which may be inserted
from either side, thus making it possible to invert the needle. The
change in balance of the needle with change in vertical intensity is
corrected by means of a small weight which may be slid along the
needle. The portion of the instrument which carries the alidade
forms the cover of the bowl and may be taken off and reversed. The
horizontal circle has a limb 12 cm. in diameter divided to 10' and
read by estimation to whole minutes. The instrument is provided
with a circular level.
The compass declinometer is intended especially for use by tri-
angulation parties, where the azimuth is known and time is not
available for more extended magnetic observations. As the slit and
thread arrangement can not be used for sighting on a very distant
object, it is usual either to place a temporary reference mark on line
from the triangulation station to a distant object by means of a
theodolite or else to set up the compass declinometer accurately in
line and use the triangulation station itself as the reference mark.
In a perfect instrument the point of support of the needle should
be in the vertical of the center of graduation, and the three objects
the slit at the prism, the point of support, and the sight wire should
DETERMINATION OF THE MAGNETIC DECLINATION.
63
be in the same vertical plane. When this is not the case, the instru-
ment will have an index correction, constant so long as the adjust-
ment of the instrument remains unchanged, which must be deter-
mined at the beginning and end of a season's work at some place
where the declination is known. Changing the position of the prism,
i. e., moving it up or down on its support, if the latter be not truly
vertical, will change the index correction. When making the ob-
servations to determine the index correction, therefore, the observer
should mark the position of the prism and in subsequent observa-
tions should be sure that it is in the same position.
Form 38.
MAGNETIC DECLINATION.
Station, Cheltenham, Md.
Compass Declinometer No. 741.
Mark, Hill's barn cupola.
Date, Monday, February 28, 19 10.
Observer, J. E. Burbank.
Chron.
time,
a. m.
Mark.
Circle direct.
Needle direct.
Circle reversed.
Needle inverted.
Mark.
North end.
South end.
South end.
North end.
A. TO.
/
/
,
f
/
,
11 24
257 08
183 05
2 54
182 54
2 57
257 09
77 06
3 04
182 54
2 53
182 57
7706
257 10
182 54
2 57
183 02
2 59
257 06
11 40
7708
2 53
18256
3 00
18257
77 04
Means
257 08.
182 59.0
182 55. 2
182 57. 2
182 57. 5
257 06.2
p. m.
h. TO.
16 13
17 06
302 50
122 49
122 40
302 38
17 03
197 04
122 50
302 48
30238
12237
197 02
17 04
302 48
122 49
122 48
302 35
17 04
16 28
197 02
122 49
302 48
302 44
122 34
197 02
Means
17 04.0
302 49. 2
302 48.5
302 42.5
302 36.0
17 02.8
Chron. correction on star
Difference of longitude, ;
Chron. correction on loca
idard 75th m
50'
h. m.
er. time* .. 2 25
7
1 mean time
n
2 32
Local mean time.
h. m.
9 00
ft. TO.
13 48
Remarks.
1
Mark reading
257 07. 1
1703.4
-.-, ,-.-;.
Needle reading
182 57. 2
302 44. 1
Magnetic azimuth of mark
74 09.9
74 19.3
True azimuth of mark f
68 51.3
68 51.3
.. .
Magnetic declination, W
5 18.6
5 28.0
Index correction
+14.4
+14.4 i
Diurnal var. correction
+ 2.0
- 5.0
Resulting declination, W
5 35.0
5 37.4
* Plus when slow, minus when fast.
t Counted from south around by west.
64 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
After leveling the instrument and adjusting the position of the
prism, the vertically of the sight wire should be tested by means of
a plumb line or the vertical edge of a building. The mark selected
should be nearly in the horizon, so that the error due to lack of ver-
ticality of the wire may be as small as possible.
Place the needle on the lifter, close the box, and lower the needle
gently onto the pivot. Adjust the balance if necessary by means of
the sliding weight. The order of observations will then be as follows,
both indices being read in each case: (1) Two pointings on the mark;
(2) one pointing on the north end of the needle; (3) one pointing on
the south end of the needle; (4) one pointing on the south end of the
needle; (5) one pointing on the north end of the needle; (6) invert
the needle and reverse the upper part of the instrument; (7) one
pointing on the south end of the needle; (8) one pointing on the
north end of the needle; (9) one pointing on the north end of the
needle; (10) one pointing on the south end of the needle; (11) two
pointings on the mark. The needle should be disturbed slightly
between readings (3) and (4) and (8) and (9) by means of a piece of
steel (screw driver or knife).
Record the times of beginning and ending of the pointings on the
needle and give the correction of the timepiece on standard tune.
It is preferable to make observations both morning and afternoon at
about the tunes when the easterly and westerly extremes of declina-
tion ordinarily occur or late in the afternoon when the reduction to
mean of day is usually small. (See Table IX.) If time permits,
three sets of observations should be made, shifting the position of
the foot screws on the tripod between sets.
While in theory the above type of compass declinometer has many
points to commend it, in practice it has not proved entirely satis-
factory. In two cases the index correction has been found to be
different for different positions of the needle with respect to the bowl,
indicating the presence of magnetic impurities in the metal of which
the bowls are constructed, although special tests have failed to detect
the seat of the trouble.
In supplying the demand for additional compass declinometers, the
satisfactory results which have been obtained in determining the
declination with compass attachments fitted to dip circles have led
to the construction of a new type of instrument from designs prepared
by Mr. E. G. Fischer, Chief of the Instrument Division. It is nothing
more than a compass needle with peep sights mounted on a graduated
horizontal circle, but some of the details are novel and all have been
worked out with great care. The base rests on three leveling screws,
has double centers, and the horizontal circle is read by two verniers.
This base supports a rectangular box, in which is mounted a compass
DETERMINATION OF THE MAGNETIC DECLINATION.
65
needle about 6 inches long. At each end of the needle is a graduated
arc, about 20 in extent, with the zero in the middle. Vertical peep
sights are attached to the ends of the box, so that the zeros of the
graduations and the point of support of the needle are in the vertical
plane through the peep sights. The lifter of the needle is of special
design, so arranged that the instrument can not be packed for ship-
ment without first lifting the needle off the pivot. Observations with
this type of instrument differ but little from those described in detail
for the older form of declinometer.
The instrument should be set low enough to permit the observer to
look directly down upon the needle when making the settings. After
the instrument has been leveled and the sliding weight adjusted in
position if necessary, the order of observations is as follows: (1) Two
pointings on the mark, one direct and one reversed; (2) one reading,
north end of needle set at zero; one reading, south end set at zero;
one reading, south end set at zero; one reading, north end set at zero.
In a similar manner (3) four readings with north end set 5 east of
zero or south end 5 west of zero; (4) four readings with north end 5
west of zero or south end 5 east of zero; (5) four readings with the
ends set at zero; (6) two pointings on the mark. Record must be
made of the time of beginning and ending. It will be sufficient to
read one vernier for settings on one end of the needle and the other
vernier for settings on the other end. The needle should be lifted
when pointing on the mark. The eye should be moved up and down
the slit to insure accuracy of pointing.
Observations with the compass attachment of a dip circle (shown
in Fig. 5) are made in the same manner and the method of computa-
tion is in each case the same as for the older form of declinometer. A
sample set of observations is given below.
Form 38a.
MAGNETIC DECLINATION.
Station, Sweetwater, Tex.
Compass of dip circle No. 30.
Mark, Cupola of schoolhouse.
Date, January 17, 1910.
Observer, W. H. Burger.
Chron. time.
Mark,
circle
direct.
Needle set at 0.
set at 0.
Needle set 5 right,
set 5 left.
Mark,
circle
reversed.
North end.
South end.
North end.
South end.
h. m.
1032
13 05
21 24
21 25
16 27
16 25
13 01
23
23
26
24
23
26
26 19
26 18
10 40
13 05
24
25
20
18
13 04
Means.
13 05.
21 23.5
21 24.8
21 23.0
21 21.2
13 02. 5
7721311-
66 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
DETERMINATION OF THE DIP.
A. WITH A DIP CIRCLE.
The dip or inclination is usually measured by means of a dip circle,
in which a magnetized needle is mounted in such a way as to swing
in a vertical plane about an axle through its center of gravity. The
form of dip circle in general use is the Kew pattern shown in Figure 5.
The pivots of the needle rest on agate knife edges, the supports of
which are horizontal or vertical according as the instrument is intended
for use in high or low magnetic latitudes. The needle is placed in
position by means of a lifter so arranged that when the needle is
lowered onto the agate knife edges, the prolongation of the axis of
the pivots passes through the center of the graduated vertical circle.
The vertical circle is read by two verniers, and in older instruments
is usually graduated from zero at either side to 90 at the top and
bottom. Some of the more modern dip circles are graduated con-
tinuously from zero to 360. To the frame carrying the verniers are
attached two microscopes for pointing on the ends of the needle, so
placed that when the circle reading is zero the line joining the micro-
scopes is horizontal. On the frame carrying the microscopes are
blocks for holding in position the needle used as a deflector in the
determination of total intensity by Lloyd's method, so arranged that
when the needle is in position its axis is at right angles to the line
joining the microscopes. Four needles are usually provided, two
for regular dip observations and two for the determination of total
intensity.
Some of the newer dip circles of this pattern are provided with a
compass needle mounted in a rectangular box, which may be placed
on top of the dip circle as shown in Figure 5. The angle between the
magnetic meridian as defined by the compass needle and the line to
some mark of which the true bearing is known may be measured with
the aid of peep sights.
In dip circles of the Lloyd-Creak pattern (Fig. 9), designed for
observations on shipboard, but suitable also for land observations,
the pivots of the needle rest in agate cups instead of on agate knife
edges and the ends of the needle are in close proximity to the gradu-
ated circle so that the end of the needle and the adjacent graduation
are seen through the reading microscope at the same time.
In dip circles of the Brunner pattern a movable graduated circle is
immediately behind the needle and carries at the opposite extremities
of a diameter two small concave mirrors, the centers of which are as
far apart as the points of the needle. A setting is made by revolving
the graduated circle until the point of the needle and its reflected
image coincide. The angle of dip is then read off on a fixed vernier.
The adjustment of a dip circle is usually made with care in the
instrument shop before the instrument is sent into the field and
DETERMINATION OF THE DIP.
67
seldom requires attention in the course of a season's work. As cases
may arise, however, where it is important to make adjustments in
the field, the following directions are given.
FIG. 5. Kew pattern dip circle.
The bearing surfaces of the agate knife edges should lie in a hori-
zontal plane which if produced would pass below the center of gradu-
ation of the vertical circle at a distance equal to the radius of the
pivots of the needles. A small level is provided to assist in making
68 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
this adjustment. The height of the agate surfaces with reference to
the center of graduation may be tested by placing the needle in posi-
tion and keeping it nearly horizontal by a strip of wood or piece of
stiff paper under the north end. If the two ends read the same (or
180 apart, if the vertical circle is graduated to 360) the needle is at
the proper height. Readings should be made in both positions of the
microscopes to be sure that they are placed exactly 180 apart and
in both positions of the needle, face east and face west, to correct for
lack of symmetry.
The lifter should be adjusted so that when the needle is lowered on
to the agate surfaces its pivots will both touch at the same time and
its axis of rotation if produced would pass through the center of
graduation of the vertical circle, so that the needle will rotate in a
plane parallel to the graduation. The vertical line through the center
of graduation may be determined by suspending a small plumb bob
at the end of a silk fiber, so that the fiber intersects the graduation at
two points exactly
's 180 apart. A small
movable hook is pro-
vided for this pur-
pose in the top of
most dip circles.
The microscopes
for pointing on the
FIG. 6.-Remagnetization of dip needle. en( j g Q f ^ neec Q e
should be exactly 180 apart and should be focused for clear vision
before beginning observations.
To avoid the necessity of carrying a separate tripod for the dip
circle, an extra head is usually provided, which can be fastened on top
of the magnetometer tripod when dip observations are to be made.
When the dip circle has been placed in position its level is adjusted
and the instrument leveled in the usual way.
The observer should have constantly in mind the necessity of
guarding the needles from falls or other accidents and keeping them,
especially the pivots, clean and free from rust. The pivots are best
cleaned by sticking them into a piece of pith. Before beginning
observations, the bearing surfaces of the agates should also be cleaned
with the edge of a piece of paper or with pith.
The polarity of the dip needles must be reversed before beginning
a set of observations as well as in the middle of the set. This opera-
tion is performed in the following manner: Place one needle on the
reversing block after having determined which end is attracted down-
ward (north end). Take one bar magnet north end down in one
hand, and the other magnet south end down in the other hand, each
inclined about 30 to the horizon. Draw the magnets lightly from
DETERMINATION OF THE DIP. 69
center to end of the needle, the magnet with north end down resting
on the end of the needle which was attracted downward. Make 5
strokes, then interchange the magnets and make 5 more. Then turn
the needle over and repeat the operation, making 20 strokes in all.
Care must be taken to stroke the same end of the needle with the
north end of the magnets throughout the operation.
The next step is to determine the plane of the magnetic meridian
and the corresponding reading of the horizontal circle. If the
instrument is provided with a compass attachment, the magnetic
meridian is readily determined by mounting the compass and turning
the instrument until the compass needle points to zero. The instru-
ment, that is, the plane of the vertical circle, is then in the magnetic
meridian, and the reading of the horizontal circle, as well as the one
differing by 180, is the one at which the circle is to be set when
making dip observations. Care must be taken to remove the com-
pass attachment before the dip observations are made, otherwise the
results will be vitiated.
In case no compass attachment is available, or in high magnetic
latitudes, where the compass needle is sluggish, the magnetic meridian
may be determined by taking advantage of the fact that when a dip
needle is mounted in a plane at right angles to the magnetic meridian
it will stand vertical. Raise the lifter, place one of the needles upon
it with its "face" toward the reading microscopes. (The face of the
needle is the side on which the letters A and B are engraved.) Set
the upper vernier at 90 and place the instrument at right angles to
the meridian, with the vertical circle toward the north. Lower the
needle onto the agates and bring it nearly to rest by means of succes-
sive liftings and lowerings. Turn the instrument in azimuth until
the swing of the upper end of the needle is bisected by the cross hair
of the upper microscope, gently lifting and lowering the needle several
times to make sure that it is swinging freely. Record the reading
of the horizontal circle. Set the lower vernier at zero and repeat the
operation, pointing on the lower end of the needle. Then turn the
instrument 180 in azimuth and repeat the operations, beginning with
the lower end of the needle. The mean of the four readings of the
horizontal circle is the reading of the magnetic prime vertical, and as
the circle is usually graduated by quadrants from to 90, the read-
ings of the magnetic meridian will be the same. The dip observations
proper may then be begun. It is usual to observe with two needles
at each station, and the work is so arranged that the middle time of
observation is the same for each needle. Observations should be
begun with the needle which was magnetized first.
Place the instrument in the magnetic meridian, (vertical) circle
east, needle face east, and reduce the swing of the needle to a small
arc by means of successive liftings, noting at the same time whether
70 DIRECTIONS FOB MAGNETIC MEASUREMENTS.
the swing of the needle appears to be free and regular. (If such is not
the case, the pivots and agates should be cleaned again.) Set on the
upper (south) end of the needle and read the upper vernier; then set
on the lower (north) end and read the lower vernier; then record the
two readings. Better results are obtained if the needle is observed
while swinging over a small arc, but it should not be disturbed between
the readings of the two ends, so that the swing at the time of the first
reading should be just sufficient to continue until the second has been
made. The needle is then lifted and lowered and the two ends read
in the reverse order. In general the two ends of the needle will not
read the same, but the difference between the two should be nearly
constant for a particular position of circle and needle. If such is not
the case, or if the readings before and after lifting differ by as much as
8', the readings should be repeated.
The circle is then turned 180 in azimuth and similar readings are
taken hi the position circle west, needle face west. Then the needle
is turned over and observations made with circle west, needle face
east, and finally the circle is reversed again and readings are taken in
the fourth position circle east, needle face west. The same operations
are then performed with needle No. 2.
Next the polarities of the two needles are reversed, so that the end
which was down before will now be up, and a second half set of obser-
vations is made, with No. 2, followed by a second half set with No. 1.
The tunes of beginning and ending should be noted for each needle.
The mean of all the readings gives the resulting dip, unless there
is much difference in the results before and after reversal of polarities,
in which case a small correction is required (Table VIII), as explained
on page 13. The computation is arranged for simplicity in such a
way that means of two quantities are taken successively, so that the
work may be performed mentally.
In case the vertical circle is graduated continuously from zero to
360, it will be necessary to subtract the circle readings from 180
or 360 for circle west in order to get the angle of dip.
DETERMINATION OF THE DIP.
71
Form 42.
MAGNETIC DIP.
Station, Smyrna Mills, Me.
Dip circle No. 5678. Needle No. 2.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
End of needle marked A down.
Circle east.
. Circle west. Circle west. Circle east.
Needle face east.
Needle face west. Needle face east. Needle face west.
S.
N.
1
S. N. S. N. S. N.
,
75 19
22
7520
22
75 39 ! 75 41 75 45 75 39 74 52 75 04
41 43 48 41 51 03
7520.5
75 21.0
7540.0! 7542.0 7546.5 7540.0 7451.5 7503.5
1 !
75 20.8
75 31
75 41. 75 43. 2 74 57. 5
3. 9 75 20. 4
Mean: 75 25 / .6
Polarities reversed. End of needle marked B down.
Circle east.
Circle west. Circle west. Circle east.
Needle face east.
Needle face west. Needle face east. Needle face west.
S. N.
S. N. S. N. S. N.
7504
02
7512
10
75 52 75 46 75 41 75 45 75 15 75 13
55 49 41 44 14 14
75 03.0
75 11.0
7553.5 7547.5 75 41.0 j 7544.5 7514.5 7513.5
75 07.0
752
75 50.5 75 42.S 75 14.0
;.8 7528.4
Mean: 75 28'. 6
Resulting dip: 75 27'. 1
Chron. time of begii
" " end
Mean chronometer
Chron. correction 01
Local mean time
Magnetic meridian
h.m. ' Instrument in mag. prime vertical,
ming 2 10
' ms 2a2 Vertical Vwidlp Hor. circle
circle. -Needle. readings.
bime 2 21 1
i L. M. T. + 27
North S. end at 90 55 48
2 * " N. end at 90 56 15
. South N. end at 90 55 14
S. end at 90 55 50
reads 55 47 Mean 55 47
72
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
B. WITH AN EARTH INDUCTOR.
A small earth inductor of the type designed by Wild is shown in
Figure 7. The coil is rotated by means of a gear and piece of flexible
shafting. A sudden starting or stopping of the rotation must be
avoided, as it is apt to break the flexible shaft. The galvanometer
should be mounted in a position where it can be observed conveniently
while rotating the coil. The axis of the vertical circle is leveled by
means of a stride level and the axis of the coil is placed in the mag-
netic meridian by means of a compass attachment. The observations
for determining the dip are made in the following manner :
Fio. 7. Wild pattern earth inductor.
(1) With vertical circle east, place the axis of the coil vertical by
means of the level inside the coil and read the vertical circle, first
with face of coil marked A east, then with face marked B east.
(2) Place the axis of coil approximately in the line of dip, rotate
the coil, and observe the galvanometer. If the instrument is set
accurately in the magnetic meridian, the galvanometer will be deflected
steadily in one direction. If it is not quite in the meridian, the gal-
vanometer will be deflected a small amount in one direction, and then
as the speed of rotation increases will go off in the opposite direction.
By successive trials find the setting at which no deflection of the
galvanometer is produced when the coil is rotated. Record the time
and the reading of the vertical circle. Rotate the coil in the opposite
direction, make another setting, and read the vertical circle. Make
DETERMINATION OF THE DIP.
73
two more settings, one for rotation in each direction. The circle
should be clamped when the coil is being rotated. After the first
reading the changes in setting can be made with the tangent screw.
The operation will be facilitated if the crank for rotating the coil is
supported so that one hand may be free to move the tangent screw
while the other rotates the coil.
(3) Place the axis of the coil vertical again, and read the vertical
circle in two positions of the coil.
(4), (5), and (6) Proceed in the same manner with vertical circle
west.
The difference between the circle readings for axis vertical and axis
inclined gives the co-dip. The form of observation and computation
is shown in the following example:
Form 407.
Station, Sitka, Alaska.
Earth inductor No. 2.
MAGNETIC DIP.
Date, February 5, 1908.
Observer, H. M. W. Edmonds.
Magnetic meridian reads: 10 40'.
Vertical circle east.
Vertical circle west.
AXIS VERTICAL.
Coil.
(Order). A. B.
Mean.
Coil. ! (Order). A.
B. l Mean.
! i
i
/ 1
-. t
/ / /
A-E
Begin 11. 10. 9
11.0
A-E Begin
9. 2 09. 2 09. 2
B-E (1) 10.8 10.8
10.8
B-E (4)
9. 9 09. 9 09. 9
A-E
End 11.0 10.9
11.0
A-E End 09.9 | 09.8 09.8
B-E (3) 10.9 10.8
10.8
B-E (6)
9.9' 09.7 ,09.8
Mean
10.9
Mean 09. 7
AXIS INCLINED.
Rot.
Chron. A. B.
Mean.
Rot. i Chron. A.
B. Mean.
h. m. '-:/ '
,
h. m.
/ / /
+
9 34 344 44. 5 44. 1
44.3
+ 9 46 15 3
2. 1 32. 1 32. 1
-
(2) 52. 52.
52.0
(5) 3
J. 33. 33.
+
45. 7 45. 3
45.5
+ 3
3.0 33.0 33.0
-
9 40 51.8 51.8
51.8
9 49 3
1. 9 32. 32.
Mean 9 37 344 48. 4
Mean 9 48
15 32. 5
Dip
74 37.5
Dip 7437.2
Mean dip 74 37'.35
h. m.
Mean chronometer time . . 9 42
Chronometer correction . . 5
Local mean tiir
e 9 37
74 DIBECTIONS FOR MAGNETIC MEASUREMENTS.
DETERMINATION OF THE HORIZONTAL INTENSITY.
As already explained, the determination of the horizontal inten-
sity involves two operations called li oscillations" and " deflections."
The observations at a station usually comprise two sets of each,
arranged in the order: Oscillations, deflections, deflections, oscilla-
tions. They are made with a magnetometer, two types of which
have been described, and as they usually follow a set of declination
observations it may be assumed that the instrument is in adjust-
ment, that the torsion has been removed from the fibers, and that
the long magnet is suspended.
TORSION OBSERVATIONS.
Point approximately on the middle division of the scale of the
magnet, reduce the arc of vibration to two divisions or less, and
read the horizontal circle. Read the torsion circle at the top of the
suspension tube and the scale of the magnet at the extremes of its
swing, as in declination observations, and record the readings in the
place provided on the form. Turn the torsion head 90 to the right
and read the scale of the magnet. Turn the torsion head 180 to
the left (i. e., 90 to the left of its original position) and again read
the scale. Turn the torsion head 90 to the right and read the scale.
The torsion circle now reads the same as at the beginning, and the
last scale reading should be very nearly the same as the first. The
differences between successive scale readings give the effect of 90,
180, and 90 of torsion, respectively, in scale divisions, and their
sum divided by four and multiplied by the arc value of one division
of the magnet scale is the average effect of 90 of torsion, the quan-
tity h required to correct the time of one oscillation for effect of
torsion.
OSCILLATIONS.
The oscillations are usually arranged in such a way as to give six
or eight independent determinations of the time of a selected number
of oscillations, which, for convenience in computing, should be some
multiple of 10. Increase the arc of vibration to about 20 divisions,
10 on either side of the middle, and determine the approximate
time of one oscillation by counting the number of seconds required
for four or six oscillations, and from that compute the time, approxi-
mating half a minute, which would be required for some odd num-
ber of oscillations. In the example six oscillations took about 34
seconds. Hence the time of five oscillations would be about 28 sec-
onds. The observer then arranged his program to observe every
fifth oscillation from to 35 and from 50 to 85, thus obtaining eight
independent determinations of the time of 50 oscillations. When
DETERMINATION OF THE HORIZONTAL INTENSITY. 75
the observing program has been outlined in the first column of the
form the succeeding operations are as follows: Read the ther-
mometer and the scale of the magnet. Note and record on the
first line of the second column of the form the time when the middle
division of the scale of the magnet crosses the vertical line of the
reading telescope, the magnet swinging from left to right. About
28 seconds later note and record the time when the middle division
of the scale crosses the vertical line, magnet swinging from right to
left, and so on at intervals of about 28 seconds until eight readings
have been taken. Then read the thermometer and scale again.
Compute approximately the time when the fiftieth oscillation may be
expected, and when that time arrives begin a second series of eight
readings at intervals of about 28 seconds. At the close read the
thermometer and the scale of the magnet again. This completes a
set of oscillations. By this
method it is necessary to
look in the reading telescope
for only a few seconds at
the time of each observation.
A few seconds before the
predicted time of transit the
observer picks up the beat
of the chronometer and be-
gins to count half seconds
. FIG. 8. Four and six oscillations.
and then looks into the read-
ing telescope and waits for the transit to occur. Thus, for the fifth
oscillation he might pick up the beat at 9 h 38 m 35 s and count: Half-
six half - seven half - eight half - nine half - ten half-one half -
two half-three, the transit occurring between half and three. The
fraction of the half seqond can best be estimated by noting mentally
the relative position of the middle division and the vertical line of
the telescope for the beats just before and after the transit and
dividing up the half second in the same proportion that the space
is divided by the position at transit. It will usually be possible
to hear the beat of the chronometer while observing, but in case
this is prevented by noise the observer can with a little practice
learn to count the half seconds accurately without hearing the tick
for the short interval involved. The chronometer should be kept
far enough from the magnet to guard against the disturbing effect
of the steel spring, etc.
DEFLECTIONS.
Place the deflection bars in position, remove the long magnet from
the stirrup and suspend the short magnet in its place with scale erect ;
taking care to keep the two at least 20 cm. apart. Remove the
76 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
thermometer from the magnet house and plug up the hole. Remove
the thermometer from its case (if it is in one) and place it inside the
east deflection bar. Place the long magnet with scale erect and north
end east at the shorter distance on the east bar and the torsion weight
as a counterpoise on the west bar. Be sure that the short magnet is
in the same horizontal plane with long magnet. Point on the middle
division of the scale of the suspended magnet, checking its swing to
about two divisions of the scale, and read the horizontal circle.
Move the long magnet out to the longer distance and again point on
the middle division of the scale of the suspended magnet and read the
horizontal circle. Turn the long magnet end for end and repeat the
pointing and reading; then move it up to the shorter distance and
make a fourth pointing and reading. Remove the thermometer from
the east bar, read it, and place it inside the west bar. Place the long
magnet with north end west at the shorter distance on the west bar
and the torsion weight on the east bar. The subsequent procedure
is the same as for long magnet east. Read the thermometer at the
close. The observer should bear in mind that it is the temperature
of the long magnet which is required both in oscillations and in deflec-
tions, and he should endeavor to place the thermometer so that it
will be of the same temperature as the magnet. If the temperature is
changing rapidly or if it is materially different on the two bars, more
readings should be taken than are specified above.
A second set of deflections should follow immediately after the first,
but with both magnets inverted and reversing the order of the posi-
tions of the long magnet. At its close, return the short magnet,
deflection bars, and torsion weight to the magnetometer case, suspend
the long magnet inverted, return the thermometer to its case and to
the hole in the magnet house, and make a second set of oscillations.
A second set of declination observations usually follows, but the
horizontal circle should first be shifted so as to bring the readings on
a different part of the graduation.
DETERMINATION OF THE HORIZONTAL INTENSITY.
77
Form 41.
HORIZONTAL INTENSITY.
Station, Smyrna Mills, Me.
Magnetometer No. 20. Magnet 20 L.
Chronometer, 245, daily rate losing 0.2 on mean time.
OSCILLATIONS.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
Number of
oscillations.
Chronometer
time.
Temp.
t/
Extreme scale
readings.
Circle reading.
ft. TO.
s.
o
d.
d.
,
9 38 14. 4
27.7
12.0
48.0
226 45 20
5
10
15
20
25
30
35
38 42. 9
39 11.6
39 40.1
40 08. 6
40 37.2
41 05.7
41 34.3
28.1
14.0
45.5
46 45 40
226 45 30
Time of
50 oscillations.
TO. S.
50
9 42 59. 9
4 45.5
55
43 28.5
45.6
60
43 56.9
45.3
65
4425.7
45.6
70
44 54.
45.4
75
45 22. 7
.
45.5
80
45 51.
45.3
85
46 19.7
28.7
15. 7 43. 5
45.4
Means.
28.17
13. 90 45. 67
4 45.45
Formula: MH=n 2 E
[/ ^400 \ /
T2 I ' 1 1 1 -i-f
-*')?) (H
H
)]
"IT
Torsion observations.
Time of loscil.
Corr'n for rate *
T
Log T*
5.70900
+ 1
Torsion
circle.
Scale.
Mean. Diff's.
5. 70901
d.
d.
d. d.
1. 51312
80
170
350
80
28.8
27.2
29.5
28.9
30.0
30.0
30.7
30.0
29.40 !
28.60 ! 0.80 (<-*') = - 0.87
30.10 1.50
29.45 0.65
(,5400^ft/
[l + (t-t')q]
0+4)
" Divisor
" 7T 2 K
" MH
12
- 18
123
1. 51429
Mean
ft= 0*74=1 '.48
3. 24733
One division of scale=2'.00.
1. 73304
Plus for losing rate and minus for gaining rate.'
78
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
Form 39.
HORIZONTAL INTENSITY.
Station, Smyrna Mills, Me.
Magnetometer, No. 20.
Long magnet deflecting.
DEFLECTIONS.
Date, Friday, August 5, 1910.
Observer, H. E. McComb.
Short magnet suspended.
Circle readings.
Mag- North
net. end. I. Distance r=30 cm.
II. Distance r-40 cm.
No. A. B. Mean.
No.
A. B. Mean.
2
3
|E. 1 236 57 10 57 20 57 15
W. 4 216 04 40 04 50 04 45
230 52 20 52 30 52 25
222 07 50 08 00 07 55
2tt 20 52 30
8 4430
1 W. 5 216 17 40 17 50 17 45
E. 8 236383038503840
6
7
222 11 10 11 20 11 15
230 45 20 45 30 45 25
2tt 20 20 55
834 10
Fondas: |- (. + fS) (.-) Jsi-.-als
I. II.
2 u (mean) 20 36 42 8 39 20
u 10 18 21 4 19 40
1
.
Value of log MH from oscillations:
h. m.
Began at 9 55 Temp. 26. 6
Ended at 10 13 " 28.0
Set.
I.
II.
log C
" Sin a
5.86935
9.25262
5. 49414
8.87773
a
M
8. 61673
8.61641
" MB
H
1.73304
9.17488
1.73304
9. 17472
H
.14958
.14953
log M
Red'n
20
log M t
to
i
2.55816
+ 152
2.55968
2.55832
+ 152
2.55984
Mean 10 04 /= 27. 3
Chron. corr'n +27
L. M. T. 10 31
Mean
2.55976
COMPUTATION.
The computation involves simply the substitution of the observed
quantities and the instrumental constants in the formulas and requires
little explanation. The observer is supplied with a table of constants
which gives, for the magnetometer he is to use, the results of the special
observations made for determining the scale value, moment of inertia,
DETERMINATION OF THE HORIZONTAL INTENSITY.
79
temperature coefficient, distribution coefficients, and induction coeffi-
cient of the long magnet and the deflection distances, and the com-
bination of the last four (log C) which enters into the deflection formula.
For the magnetometer used in the example, this table was as follows :
Constants of magnetometer No. 20.
One division of scale of long magnet = 2'. 00.
Deflection distances. log C at 20 C.
cm.
29.9874 log =1.47694 5.86953
40.0054 1.60212 5.49432
For an increase of 1 C. in temperature log C must be diminished
by 0.000025. (See Table VII.)
Temperature coefficient # = 0.00048 for 1 C.; log (1 + q) = 0.000208
Distribution coefficient P= 0.955
Induction factor JJL
TT
When log ^r>
6.81
6.50
6.55
6.60
6.65
6.70
6.75
6.80
log
log// = 0.833
0.00093
105
118
132
148
166
186
Moment of inertia K
Temp.
0C.
10
20
30
40
log
3. 24703
713
724
735
745
Computing the elapsed times between oscillations and 50, 5 and
55, 10 and 60, etc., gives 8 independent values of the time of 50
oscillations. The mean of these 8 quantities divided by 50 is the
time of 1 oscillation, T, which must, however, be corrected for
the rate of the chronometer. The loss in 24 hours being 8 .2, the
loss in 5 s . 7 would be 0.2x5.7-^86400, or, since the correction to the
fifth decimal place is desired, 0.2x5.7x1.16. Table V gives the
value of this correction for different rates and different times of
oscillation. The formula for MH is arranged for logarithmic com-
putation, so that log Jffl = log 7i*K-[\og T 2 + log( g ^i. ^
\ o4UU fl /
+ log ( 1 + (t t'} q) + log ( 1 + fj. ^rr 1 . As the second and third fac-
tors of the divisor never differ much from unity, their logarithms
80 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
are always nearly zero and it may be assumed without appreciable
error that the logarithm varies directly as the variable part of the
factor, i. e. : ,
log [5400 ^- (5400 -Ji)] = h log [5400 -s- (5400 - 1)]
log [1 + (*-*') q] = (t-t') log (l+q)
Now log (5400-^5399) = 0.00008. Hence the torsion correction, ex-
pressed in units of the fifth decimal place of the logarithm is found
by multiplying by 8 the effect of 90 of torsion. In the example,
7i=l'.48 and the corrective term is therefore .00012. The value of
this factor may also be obtained from Table VI. In the example
*-*' = 27. 30-28.17 = -0.87. From the table of constants for this
instrument it will be seen that
log (l + q) = 0.000208
hence log [l + (t-t') q] = . 000208 (-0.87)= -.00018
A table may readily be prepared for a particular instrument giving
the value of this factor for different values of (t t'). The value of
7T\
be found in the table of constants for different
(
H H
values of log ,,, and the value of log ,, is obtained from the com-
putation of deflections. The value of log T^K for the temperature
of the oscillations is found by interpolation from the table of constants.
When the computation has been completed, the value of log M H
is carried forward to the deflection form.
The differences between the pairs of circle readings at the two
distances give two values of 2 u, double the deflection angle, for each
distance, from which the values of u are obtained. The values of
log C for the two deflection distances are given in the table of con-
stants for the temperature 20 C. In the example the deflections
were made at a temperature 27.30 C. Hence the tabular values of
log<7 must be decreased by 0.000025 (27.30 -20) = 0.00018. The
TJ
values of log ^ are then obtained by subtracting log sin u from log C.
In good work the two values seldom differ by more than 0.00050.
Should they differ by as much as 0.00100 the computation should
be revised and if no mistake is found the observations should be
repeated.
TJ
The computation of H and log M from log H M and log ^ follows.
The resulting values of log M are for the temperature of deflections,
27.30. The magnetic moment of a magnet varies with temperature,
*,s we have seen, and in order to compare the values obtained at
DETERMINATION OF THE TOTAL INTENSITY. 81
different times it is necessary to reduce all results to the same tem-
perature. 20 centigrade has been adopted as a standard and all
values of log M are reduced to that temperature. For practical pur-
poses this may be done by means of the formula
log M 20 = log M+ (t - 20) log (1 + q)
In this case (-20) = 7.3 and log (1 +q) = 0.000208.
Hence the correction to be applied to log M is +0.00152.
Experience has shown that when a magnet is first magnetized its
magnetic moment decreases quite rapidly. The rate of loss of mag-
netism gradually diminishes . and after a few years becomes very
small. A comparison of the values of log M 2Q obtained at different
times in the course of a season's work is therefore valuable for several
reasons. (1) It furnishes a test of the accuracy of the horizontal
intensity determinations and sometimes leads to the detection of
errors of observation or computation. (2) It furnishes the means of
correcting the adopted value of temperature coefficient if there is
considerable variation in temperature involved in the series of
observations. (3) An accident to the magnet, such as a fall, or
improper packing for transportation, will usually be revealed by a
sudden decrease in log M 20 .
DETERMINATION OF THE TOTAL INTENSITY.
The determination of total intensity with a dip circle by Lloyd's
method involves two kinds of observations: Dip with loaded needle,
and deflections. As the accuracy of the method depends upon the
constancy of the condition of the needles between the time of stand-
ardization and the time of observation, every care must be taken to
secure that constancy. The needles must never be remagnetized
and must be kept from close proximity to disturbing influences.
The weight used in the standardization observations should be left
in place in the needle and any possibility of bending avoided. When
the standardization observations are made, that weight should be
selected which will be best suited to the region in which the instru-
ment is to be used. The weight should be in the south end for
places north of the magnetic equator and in the north end for places
south of the magnetic equator, so that its effect will be to diminish
the true dip. In the formula involved, F= C V cos /' esc u esc u' f
l f is the dip with loaded needle, u is the angle of deflection, and
u' = 11' . The effect on the result of an error in an observed value
of'/' will tend to diminish as I' approaches zero and u f approaches
90. The best approximation to these limits is usually secured by
using a weight sufficient to cause the loaded end of the needle to
7721311 6
82 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
dip by a small amount, so that /' differs from zero by about the
same amount that u' differs from 90.
If the season's work covers such a large range of dip that the weight
used during standardization can not be used throughout, or if for
some other reason a change in the weight becomes necessary, the
change should be made, if possible, at a place where observations can
be made before the change as well as after.
The remarks regarding care and cleaning of needles and agates and
adjustment of the dip circle made in connection with determination
of the dip apply with equal force here. The instrument having been
leveled and placed in the magnetic meridian, the observations of dip
with loaded needle follow in each of the four positions: Circle east,
needle face east; circle west, needle face west; circle west, needle face
east; circle east, needle face west, in the same manner as for regular
dip observations. If the south end is below the horizon the dip is
regarded as negative. The loaded needle is then fastened in the place
provided between the reading microscopes, "face" out, and covered
by the brass shield. The other (lighter) intensity needle is placed on
the lifter face east and lowered on to the agate supports. As the
microscopes are turned in order to make a pointing on the suspended
needle, carrying with them the deflecting needle, it will be found that
there are two positions in which the suspended needle may be pointed
upon by the microscopes, in one of which it is deflected toward the ver-
tical and in the other away from the vertical. The microscope which
in one case points on the north end of the needle will in the other case
point on the south end. The microscopes are considered direct (D)
when the south (upper) end of the suspended needle is deflected
toward the right and reversed (R) when it is deflected toward the
left. The angular difference between the two positions of the needle
is 2u, twice the angle of deflection. It may happen that the sus-
pended needle will be deflected out of one quadrant into the adjoin-
ing one. In a dip circle where the vertical circle is graduated in
quadrants from in the horizon to 90 at the top and bottom, this
fact must be noted in the record in order that the deflection angle
may be computed correctly. Thus, for a dip of 70 and a deflection
angle of 30 the circle readings would be 40 in the same quadrant
and 80 in the next.
Deflection observations are made with microscopes D and li in
each of the four positions: Circle east, needle face east; circle west,
needle face west; circle west, needle face east; circle east, needle face
west.
A second set of dip with loaded needle, similar to the first, is then
made. In the intensity observations, as in regular dip, two point-
ings on each end of the needle are to be made in each position, the
needle being lifted between.
DETERMINATION OF THE TOTAL INTENSITY. 83
In the Lloyd-Creak form of dip circle the needle is supported in
agate cups, and before a reading is taken the needle must be jarred
to a position of equilibrium by rubbing or tapping a metal point on
top of the instrument with an ivory scraper.
A value of dip may be obtained from the deflection observations,
since the suspended needle is deflected by approximately equal
amounts in opposite directions from its undeflected position.
A sample set of observations and computation is given below.
When the vertical circle is graduated from zero at the sides to 90 at
the top and bottom and the needle lies in the same quadrant for both
positions of the microscopes, direct and reversed, half the difference
of the two circle readings gives the deflection angle and half their
sum gives the dip. When the needle is in one quadrant for micro-
scopes direct and the adjacent one for microscopes reversed,
and /_90--
When the vertical circle is graduated continuously from to 360,
the readings with circle west are to be substracted from 180 in taking
the means.
Then D-R D + R
u = 2~~ and 1= 2
For obtaining u' =11' the best available value of 7 must be used.
This is generally the mean of the results with the two regular dip
needles, with the instrumental corrections applied. These corrections
and the value of log C are determined at some place where the dip
and horizontal intensity have been accurately determined by other
means, and are usually supplied to the observer from the office.
The formula arranged for computation by logarithms is:
i w\ n cos ~^ csc u "^ & csc
As it usually happens that the deflection angle is different for the
two halves of the deflection set, the form is arranged for computing
the two halves separately and two values of log C are determined
to correspond. The form is also arranged to compute the horizontal
intensity from the formula H^ F cos 7.
84
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
Form 389.
TOTAL INTENSITY.
Station, Fernandina, Fla.
Dip circle No. 35.
End of needle marked B north.
DIP WITH LOADED NEEDLE.
Date, April 14, 1910
Observer, S. S. Winslow.
Needle No. 4. Weight No. 6.
North end* up.
Circle east. Circle west.
Circle west.
Circle east.
Needle face east.
Needle face west.
Needle face east.
Needle face west.
S.
N.
S.
N.
S.
N.
8.
. N.
153 35
38
15408
08
/
334 02
05
333 38
42
'
26 24
25
206 27
30
25 40
40
205 32
35
36.5
40.0 24.5
28.5
40.0
33.5
08.0
03.5
-2621.8 -2626.5
-26 24. 2
Mean /', Set 1. -26
-25 36.8
-25
04'. 8
-25 54. 2
45.5
!*'-/-/' 88 29'. 3
Circle east.
Circle west.
Circle west.
Circle east.
Needle face east.
Needle face west.
Needle face east.
Needle face west.
S.
N.
S.
N.
S.
N.
S.
N.
153 28
25
333 30
27
26 31
28
206 25
25
25 46
45
205 40
38
154 10
08
334 00
333 58
26.5
28.5
29.5
25.0
45.5
39.0
oy.ii
59.0
-2632.5 -2627.2
-26 29.9
Mean /', Set 2. -26
-2542.2 -2556.0
-25 49. 1
09'. 5 u'-/-/'=88 34'.
Chron. time. Temp.
h. m.
Beginning 9 55 20.7
Ending 10 21 20.8
Mean 10 08 20.75
Corr'n on L. M. T. +23
Remarks:
L. M. T. 10 31
Magnetic meridian reads
84 17
Note whether north end is up or down. Do not reverse polarity.
DETERMINATION OF THE TOTAL INTENSITY.
85
Form 389.
TOTAL INTENSITY DEFLECTIONS.
Station, Fernandina, Fla. Date, April 14, 1910.
Dip circle No. 35. Needle No. 4 deflecting, No. 3 suspended.
Circle east, needle face east.
Circle west, needle face west.
D.*
R.*
R.*
D.*
S. N.
S. N.
S. N.
S.
N.
274 17 94 21
15 25
01 01
211 30 31 33
28 30
/ Of
266 58 87 00
55 86 58
1
329 22
23
149 23
23
16. 23.
29. 31. 5
56. 5 59.
22.5
23.0
94 19.5
125 49. 7
62 54. 9
7 = 62 22. 3
31 30.2
62 49. 3
31 24.6
93 02. 2
62 25.
31 12.5
u = 31 18. 6
30 37. 2
123 39. 4
61 49.7
Circle west, needle face east.
Circle east, needle face west.
D.
R.
R.
D.
S. N.
S. N.
S. N.
S.
N.
210 30 30 38
28 40
273 10
15
93 29
30
329 02 149 10
03 10
265 24 85 36
27 32
02. 5 10.
25. 5 34.
29. 39.
12.5
29.5
30 53. 8
125 24.0
62 42.
7 = 62 19. 8
94 30. 2
63 36. 4
31 48.2
30 34.
62 47.
31 23.5
u = 31 35. 9
93
123
61
21.0
55.0
57.5
Chron. time. Temp.
h. m.
Beginning 10 05 21.0
Ending 10 20 20.8
Computation of F and
77.
log cos 7' 9. 95336 !
" cscw 0.28427
" cscu' 0.00015
9. 95307
0.28070
0.00014
Mean
Corr'n on L. M. T.
L. M. T.
10 12 20.9
+23
10 35
Sum 0. 23778
Half sum 0.11889
log C 9.62333
0. 23391
0. 11696
9. 62497
" F 9. 74222 !
9. 74193
7 from deflections 62 21.
7 from regular dipJNo. 1 62 22. 3
needles (No. 2 62 26.7
Mean 9. 74208 F= . 55218
log cos 7 9. 66574
" 77 9.40782 77=. 25575
* If the vertical circle is graduated in quadrants, note whether the upper (south)
end of the suspended needle is north or south of the vertical.
DIRECTIONS FOR OBSERVATIONS AT SEA.
INTRODUCTION.
The instruments and methods employed for determining the
magnetic elements on land require a number of modifications for
observations on board ship. On account of the instability of the
ship as an observing platform, a magnetometer with fiber suspension
can not be used and in the dip circle agate cups take the place of
agate knife edges. The instruments must be mounted in gimbals
in order that they may remain approximately level in spite of the
motion of the ship. It is usual to determine the magnetic declination
by means of the standard compass and an azimuth circle, and the dip
and total intensity by means of a Lloyd-Creak dip circle.
On account of the disturbing effect of the iron and steel which
enter more and more into the construction of modern ships, the
direct results of magnetic observations on shipboard are different
for different headings of the ship, since they represent the combined
effect of the earth's magnetism and the ship's magnetism, and means
must be provided to separate the resultant into its component parts.
It is customary, therefore, to make observations on 8 or 16 equi-
distant headings while steaming in a circle, first in one direction and
then in the other. As a complete determination of dip and intensity
on each heading of the forward and back swings would consume too
much time, the practice has been adopted by the Coast and Geodetic
Survey of observing deflections alone while swinging ship in one direc-
tion and loaded dip alone while swinging in the opposite direction.
In addition to the total intensity derived from the combination of
these observations, a value of dip on each heading results from the
deflection observations.
The determination of declination, dip, and total intensity at sea
requires, first, that observations be made with the dip circle at a
base station on shore at the beginning and end of the cruise, to
determine the intensity constant for the particular weight used at
sea and the correction to the dip as derived from the deflection ob-
servations; and, second, that the ship be swung at the beginning and
end of the cruise (and, if possible, in the highest and lowest latitudes
reached) at a place near shore where the declination, dip, and in-
tensity are known with reasonable accuracy from shore observations,
in order to determine the deviations of the standard compass and of
dip and intensity at the dip circle position.
87
88 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
For the general theory of the analysis of a ship's magnetism the
reader is referred to the various publications of the hydrographic
offices of different nations, at least one of which is to be found on
almost every ship. (E. g. "Practical Problems and the Compensa-
tion of the Compass in the United States Navy;" (British) "Admiralty
Manual for the Deviations of the Compass;" "Der Kompass an Bord,"
issued by the Deutsche Seewarte, etc.)
DECLINATION.
The amount by which the compass needle points east or west of
true north is called the compass error.
The amount by which the compass needle points east or west of
magnetic north is called the deviation. In each case east is* considered
positive and west negative. As the angle between the true meridian
and the magnetic meridian is the magnetic declination, it follows
that:
Compass error Decimation = Deviation .
Hence for the determination of the declination on board ship
it is necessary to know the compass error and the deviation. The
deviation may be represented approximately by an equation of the
form
Deviation = A +B sin + C cos + D sin 2 + E cos 2
in which is the magnetic heading of the ship, counted from north
around by east. The second member of this equation may be divided
into three parts: A, which is constant for all headings; (B sin + C
cos ), called the semicircular deviation, the values on two headings
180 apart being equal but of opposite sign; (D sin 2 + E'cos 2),
called the quadrantal deviation, the values on two headings 90 apart
being equal but of opposite sign. In theory, the determination of
the deviations on any five headings will give five equations from which
to compute the five coefficients A, B, C } D, E. In practice, however,
it is found that satisfactory results can not be obtained unless ob-
servations are made on a greater number of headings properly dis-
tributed. It is apparent that when observations are made on 8 or 16
equidistant headings, the mean of the deviations will be A, the
constant part of the deviation, and the computation of the other
coefficients will be much simplified. For observations made in this
way near shore where the declination is known;
Mean compass error Declination = A
and for observations at sea when A has been determined:
Mean compass error A = Declination.
DECLINATION. 89
From this it will be seen that when observations are made on a mul-
tiple of four equidistant headings it is not necessary to compute the
coefficients B, C, D, E in order to determine the declination, but in-
asmuch as the deviations on all headings are required for purposes
of navigation, and as observations are sometimes made on only two
or three headings, it is important to determine B, C, D, E in order
that the deviation on any desired heading may be computed.
In the case of observations on 16 equidistant headings, there will
be 16 observation equations from which to compute the four co-
efficients by the method of least squares. In the formation of the
normal equations the observation equations may be combined in
such a way as to eliminate the constant term A and to leave only a
single unknown in each normal equation, as shown in the sample
computation given later on. As the declination is not known at sea
and the final value of A is not determined until the end of the season's
work, it is usually more convenient to make the analysis of that
part of the deviations which does not involve A.
Since
Compass error Declination = Deviation
and Mean compass error Declination = A
Compass error Mean compass error = Deviation A
For want of a better term this part of the deviation has been called
"star deviation" and designated by an asterisk after the word,
deviation*.
Deviation* = Deviation - A = B sin + C cos r +D sin 2 + E cos 2.
The compass error is usually determined in one of three ways:
(1) By observations of the sun; (2) by reciprocal bearings with a
shore station; (3) by observing on a range of which the true bearing
is known.
(1) The compass bearing of the sun is observed by means of an
azimuth circle, and the true bearing is computed from the latitude
of the place and the local mean time of observation. This requires,
in addition to the latitude, a knowledge of the longitude and the cor-
rection of the chronometer on standard time. The computation is
very much simplified by the use of United States Hydrographic
Publication No. 71, or similar azimuth tables.
(2) For observations near shore it is sometimes more convenient to
make use of the method of reciprocal bearings. An observer on shore
measures the angle between the ship's binnacle and a reference mark,
at the same moment that the observer on the ship measures the com-
pass bearing of the shore station. If the true bearing of the reference
90
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
mark from the shore station is known, the true bearing of the shore
station from the ship at the time of the compass observation may be
computed. An older form of this method, and one wliich may be
used when azimuth observations are impossible, is to mount a com-
pass on shore and observe the compass bearing of the ship, the dif-
ference of the reciprocal bearings being the deviation for that particu-
lar heading, provided the shore station is free of local disturbance and
the compass free of index error.
(3) In some harbors the true bearings of well defined range lines
have been computed for the convenience of navigators and the com-
pass error may be determined by observing the compass bearing of one
of these ranges.
The forms of record and computation are shown in the following
example. In this case the compass bearing of the sun was observed
on 16 equidistant headings while swinging first with starboard helm
and then with port helm, but only the starboard observations are
reproduced.
Form 364.
OBSERVATION OP COMPASS DEVIATIONS.
Steamer. Sache.
Date, July 10, 1909.
Weather, clear. Sea, choppy. Wind, SSW.
Ship swung with starboard helm.
Standard compass Xo. 30367.
Observer, W. C. Hodgkins.
Ship's head
by standard
compass.
Time by
hack watch
No. 141.
Sun's bearing
by standard
compass.
Remarks.
wsw.
ft. m. s.
5 49 40
,
N. 70 50 W.
1
Latitude 38 20
sw.
52 50 70 30
Longitude 76 22.3
SSW.
55 50 7000
s.
SSE.
SE.
58 10
59 50
6 0205
7000
70 05
69 10
Chronometer comparison:
ft. m. *.
ESE.
05 42
67 30
Hack reads
5 10 19
E.
07 30
66 05
Chron. 3012
100800
ENE.
10 10
65 00
Chron. corr'n
+ 54
NE.
12 30
6425
G. M. T.
10 08 54
NNE.
15 10
64 20
E.
- 5 05
N.
1700
6600
G. A. T.
10 03 49
NNW.
19 40
6700
Longitude
5 05 29
NW.
22 20
67 30
Local A. T.
4 58 20
WNW.
24 05
07 35
Hack reads
5 10 19
W.
26 10
67 05
Hack correction on local
- 11 59
apparent time
DECLINATION.
91
Form 355.
COMPUTATION OP COMPASS DEVIATIONS.
Steamer, Sache.
Lat. 38 20' N., long. 76 22'.3.
Ship swung with starboard helm.
Date, July 10, 1909.
Sun's declination, 22 14' N.
Ship's
head.
Local
apparent
time.
Sun's
bearing by
compass.
Sun's
azimuth
from tables.
Error of
standard
compass.
Deviation.*
h. m. s.
/
/
,
/
N.
6 05 02
N, 66 00 W.
N. 71 31 W.
5 31 W.
32 W.
NNE.
6 03 12
64 20
71 46
7 26
2 27 W.
NE.
6 00 32
64 25
72 09
7 44
2 45 W.
ENE.
5 58 12
65 00
72 28 7 28
2 29 W.
E.
55 32
66 05
72 51 6 46
1 47 W.
ESE. 53 44
6730
73 06 5 36
37 W.
SE. 50 07
69 10
73 36 4 26
33 E.
SSE. 47 52/
70 05
73 55
3 50
1 09 E.
S. 46 12
70 00
74 09 4 09
50 E.
SSW. 43 52 70 00
74 28
4 28
31 E.
SW. 40 52 70 30
74 54
4 24
35 E.
WSW. 37 42 70 50
75 20
4 30
29 E.
W. 6 14 12 67 05
70 13
3 08
- 51 E.
WNW. 12 07 67 35
70 31
2 56
203E.
NW. 10 22 67 30
70 46
3 16
1 43 E.
NNW.
07 42 67 00
71 08
4 08
51 E.
Means
5 56 42 67 42
72 41
4 59 W.
Magnetic declination from shore observations, 5 25' W.
92 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
Form 356.
Steamer, Bnche.
ANALYSIS OF COMPASS DEVIATIONS.*
Date, July 10, 1909.
Deviation.*
(D
Deviation.*
(2)
(3)
Ship's
Ship's
head.
head.
1
Port.
Starb.
Mean.
Port. Starb.
Mean.
(D+(2)
N.
- 53
- 32
- 42
S.
' i '
+ 39 +50
+ 44
a
+ 2
NNE.
- 142
- 147
- 144
ssw.
- 14 +31
+ 8
b
- 136
NE.
- 148
- 165
- 156
s\v.
- 17 +35
+ 9
c
- 147
ENE.
- 105
- 149
- 127
wsw.
+ 65 +29
+ 47
d
- 80
E.
- 79
- 107
- 93
w.
+106 + 111
+ 108
e
+ 5
ESE.
- 17
- 37
- 27
WNW.
+96 +123
+ 110
f
+ .83
SE.
+ 45
+ 33
+ 39
NW.
+ 114 + 103
+ 108
9
+ 147
SSE.
+ 58
+ 69
+ 64
NNW.
+ 55 +51
+ 53
h
+ 117
Computation of B and C.
Computation of D and E.
(4)
(5)
(6)
(7)
(8)
(9)
(D-(2)
(4)X(5)
(4)X(6)
From (3)
(7)X(8)
(7)X(9)
- 86
.000
mi
1.000
- 86
a e
- 152
.383
- 58
.924
- 140
- 13
.000
00
1.000
- 13
- 165
.707
- 117
.707
- 117
b-f
- 174
.924
- 161
.383
- 67
- 219
.707
-
155
.707
- 155
- 201
1.000
- 201
.000
00
c-g
- 137
.924
- 127
- .383
+ 52
- 294
1.000
-
294
.000
00
- 69
.707
- 49
- .707
+ 49
d-h
+ 11
.383
+ 4
- .924
- 10
- 197
.707
-
139
- .707
+ 139
8B
- 709
8C
- 319
8D
588
8E
- 29
B
- 89
C
- 40
D
-
74
E
4
N. B. When observations are made on only 8 points, the divisors must be changed from 8 to 4.
DECLINATION.
COMPARISON OF OBSERVED AND COMPUTED DEVIATIONS.*
Deviation*= Deviation A= B sin C+ Ccos Z.+D sin 2 Z+E'cos 2 C.
C is the compass azimuth of the ship's heading, counting from north around by east, south,
and west to 360.
93
Ship's
head.
- 89' ' - 40'
5 sinC CcosC
i
D sin 2 C E cos 2 C
Deviation.*
C-0
V
*
Comp'd.
Obs'd.
N.
00 - 40
00 - 4
- 44
- 42
- 2
4
NNE.
- 34 - 37
- 52 - 3
- 126
- 144 + 18
324
NE.
- 63 - 28
- 74
- 165
- 156 - 9
81
ENE.
- 82
- 15
- 52
+ 3
- 146
- 127
- 19
361
E.
- 89
00
00
+ 4
- 85
- 93
i + 8
64
ESE.
- 82
+ 15
+ 52
+ 3
- 12
- 27
+ 15
225
SE.
- 63
+ 28
+ 74
+ 39
+ 39
SSE.
- 34
+ 37
+ 52
- 3 i +52
+ 64
- 12
144
S.
00
+ 40
00
- 4
+ 36
+ 44
- 8
64
ssw.
+ 34
+ 37
- 52
- 3
+ 16
+ 8
+ 8
64
sw.
+ 63
+ 28
- 74
+17+9
+ 8
64
wsw.
+ 82
+ 15
- 52
+ 3 +48 +47
+ 1
1
w.
+ 89
00
00
+ 4 +93 +108
- 15
225
WNW.
+ 82
- 15
+ 52
'+ 3
+ 122 + 110
+ 12
144
NW.
+ 63
- 28
+ 74
+ 109 +108
+ 1
1
NNW.
+ 34
- 37
+ 52
-3+46 +53
- 7
49
1 J*
1815
Probable error of single observation, r= 8'.
For 16 points, r= 0.195 V^- For 8 points,
Before and after the sun observations the observing timepiece was
compared with the standard chronometer and its correction on local
apparent time computed as shown. The mean of the two compari-
sons gave the correction 1 1 m 58 s , and this was applied to the
recorded times of observation to get the local apparent times of
observation given in the second column of the form for " Computa-
tion of Compass Deviations."
Hydrographic Office Publication No. 71 gives the sun's azimuth
at 10-minute intervals between sunrise and sunset for each degree of
latitude from 61 N. to 61 S. and for each degree of declination of
the sun. As three interpolations are in general required to get a
desired azimuth, it expedites the computation of a series of observa-
tions to prepare from the azimuth tables an auxiliary table with
which only a single interpolation will be necessary. In the example
given the observations extended from 5 h 37 m to 6 h 47 m p. m., and
the following table was prepared to cover that period for latitude
38 20' X. and sun's decimation 22 14' X.
94
DIRECTIONS FOE MAGNETIC MEASUREMENTS.
Azimuth of the Sun on July 10, 1909.
Declination.
Latitude.
22 N.
38 N.
22 14' N.
38 N.
2214'N. ! 2214'N.
39 N. 38 20'
Change
permin.
h. m.
/
/
5 30
N. 76 30 W.
N. 76 18 W.
N. 76 38 W. N. 76 25 W.
40
75 07
74 55
75 13 75 01
8.4
50
73 44
73 32
73 48 73 37
8.4
600
72 20
7208
72 23 72 13
8.4
10
70 56
70 45
70 57 70 49
8.4
20
69 31
69 20
69 30 69 23 8. 6
30
68 06
6755
68 02 67 57
8.6
40
66 39
66 28
66 34 66 30
8.7
50
65 11
6500
65 04 65 01
8.9
A column has been added containing the values for latitude 28
N. and declination 22 N. taken directly from the azimuth tables.
A comparison of these values with the corresponding ones in column 5
shows differences changing gradually from 5' at the beginning to
10' at the end. From this it will be seen that the desired azimuths
may be obtained without the aid of an auxiliary table if the cor-
rections to the table for the nearest even degree of latitude and
declination be computed for the beginning and end of the series of
observations. As it is the usual practice to combine swings with port
and starboard helms, it will be sufficiently accurate for practical pur-
poses to determine the correction for the middle of each swing and
assume that it is constant throughout the swing.
The difference between the observed compass bearing of the sun
and its computed true bearing is the error of the compass for that
heading. By subtracting the mean compass error from the error
for each heading the corresponding deviations * (star deviations) are
found, provided observations have been made on each of 8 or 16
equidistant headings. It sometimes happens that the observation
on one heading is prevented by the mast or funnel coming in line
with the sun. In such case the missing compass error must be sup-
plied by interpolation before taking the mean. This can usually be
done with sufficient accuracy by comparison with the swing in the
opposite direction. If the observations on several headings have
been prevented by clouds, graphical interpolation should be resorted
to, plotting the observed compass errors and drawing a smooth curve
to represent them.
The analysis of the compass deviations * requires little explana-
tion, as the order of computation is indicated by the headings of the
form. For two headings and (180 -f) the observation equations
would be:
DECLINATION. 95
Deviation * () = B sin + C cos + D sin 2+E cos 2
and
Deviation * (180 +) = - 5 sin - C cos +Z> sin 2 + # cos 2
Hence
Deviation * () - Deviation* (180 +C) = ^i = 2 . sin + 2 (7 cos
and
Deviation* () + Deviation* (180 +) = ^ 2 = 2 D sin 2 + 2 #cos 2
It will be seen that the quantities on the same line in columns
headed (1) and (2) are in each case the deviations * for two headings
180 apart, and hence the quantities in column (3) involve only the
factors D and E (quadrantal deviation) and those in column (4)
involve only B and C (semicircular deviation).
From observation equations of the form:
J x = 2 B sin + 2 C cos
the values of B and C are obtained by the method of least squares
from the normal equations :
IA^ sin = 2 B I sin 2 + 2 C I sin cos
I A cos = 2 B I sin cos + 2 C I cos 2
The values of sin and cos for angles corresponding to the equi-
distant headings N, NNE, ____ SSE, are given in columns (5) and
(6) . It will be seen that I sin 2 = 4, 1 sin cos = and 2 1 cos 2 = 4.
Hence for the case of observations on 16 equidistant headings the
normal equations become:
2Ai sin = 8 B ZA^ cos = 8 C
and the computation is made in the simple manner indicated on the
form. For observations on 8 equidistant headings only the values
of sin and cos given on the first, third, fifth, and seventh lines will
be involved and the normal equations will be:
ZA^ sin = 4 E ZA^ cos = 4 C
In the publication of the various Hydrographic Offices treating of
the compass and its deviations, tables are given to facilitate the com-
putation of AI sin and A^ cos , where the deviations are expressed
in degrees and minutes. For the small deviations involved in obser-
vations on the ships of the Coast and Geodetic Survey it will be
found convenient to convert the deviations* to minutes and use
Table XIII given at the end of this publication.
It has been shown above that the sum of the observation equa-
tions for two headings 180 apart would be:
J = 2 D sin 2 + 2 E cos 2
96 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
For the two headings 90 from the first two the quantities in the
second member would be the same, but the signs would be changed.
The difference of the two equations would give:
J 3 = 4 D sin 2 + 4 E cos 2
The values of J 3 are given in the column headed (7), obtained from
column (3) in the manner indicated. The corresponding normal
equations are:
JJ 3 sin2 = 8# and JJ 3 cos 2 = 8 E
for observations on 16 headings,
and I J 3 sin 2 = 4 D and I J 3 cos 2 = 4 E
for observations on 8 headings. The quantities in columns (8) and
(9) are the shies and cosines of 0, 45, 90, and 135, respectively.
The analysis of the observations in the example gives:
Deviation *= -89' sin - 40' cos -.74' sin 2-4' cos 2r
from which the deviation * on any heading, , can be computed. As
a test of the accuracy of the observations a comparison should be
made between the deviations * derived from the observations and
those computed from the formula. For observations on 16 headings
the probable error of a single observation (mean of swings) is given
by the formula:
Vlv 2
1( ._ 4 = 0.195^V
Where observations are made on only 8 headings,
rw
= 0.6745^ 8 4 = 0.337 V- '"
In the example r= 8'. For observations under i'a vorable condi-
tions that represents about an average value.
For navigational purposes the complete deviations are required.
They may be obtained by adding the constant part of the deviation,
A, to the deviations.* As already pointed out, A is determined from
swings near shore where the declination is known at least approxi-
mately. As the declination where the ship is swung is in general
not exactly the same as at the point on shore where observations are
made, it is desirable to combine the results obtained at a number
of places to get a mean value of A. While this constant part of the
compass deviation is no doubt partly due to unsymmetrical distri-
bution of the ship magnetism with respect to the compass, the greater
part is to be ascribed to imperfections in the compass and the azimuth
circle, corresponding to an index error.
DIP AND TOTAL INTENSITY. 97
Since the deviation is the resultant effect of the forces exerted on
the compass needle by the ship's magnetism and the earth's mag-
netism, it follows that any change in the ratio of those two forces
will produce a change in the deviation. The quadrantal deviation
is due to the magnetism induced in horizontal soft iron and therefore
varies directly as H varies, and for a particular heading the ratio of
the two does not change when the ship goes from place to place.
Hence the coefficients D and E should be constant.
The semicircular deviation is due partly to the subpermanent mag-
netism of the ship and partly to induced magnetism in vertical soft
iron. The former is constant, or nearly so, and therefore produces an
effect on the compass needle which is inversely proportional to H.
The induced magnetism in vertical sof^ iron is proportional to the
vertical force or H tan 7, and its effect on the compass needle is there-
fore proportional to tan 7. As H decreases and 7 increases in going
from the magnetic equator to the magnetic poles, it follows that in the
northern hemisphere B and C should become greater as the ship goes
farther north and vice versa.
DIP AND TOTAL INTENSITY.
On several of the ships of the Coast and Geodetic Survey dip and
total intensity are determined by means of a Lloyd-Creak dip circle
mounted on a gimbal stand as shown in Figure 9. The balance of the
instrument is secured by a counter-poise at the back, and its stability
is regulated by a heavy ball threaded onto a rod extending below
the gimbal rings. The instrument is leveled in the same manner as
when mounted on a tripod on land.
Experience with the original form of Lloyd-Creak dip circle showed
that within 30 or 40 of the magnetic equator it was impossible to
observe deflections, as the earth's total intensity became too small to
offer sufficient resistance to the force exerted by the deflecting needle,
and the suspended needle would not come to rest at right angles to
the deflector. To remedy this defect several dip circles of this type
have been modified in the instrument shop of the Coast and Geodetic
Survey so as to increase the distance between the two needles when
making deflection observations. The loaded needle, when in use as a
deflector, is mounted in an aluminum case which fits in a frame
between the reading microscopes, as shown in Figure 9. The needle is
mounted to one side of the center of the case, so that the deflections
may be made at two deflection distances by reversing the position of
the case in its supporting frame. Originally the needles were 7.3 cm.
apart during deflections. With the new arrangement the distances
are 7.9 and 9.4 cm., respectively, and it is possible to observe, at least
at the longer distance, in any part of the globe. In the instrument
7721311 7
98
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
shown in the figure a small telescope was added, so that astronomical
observations on land can be made if desired.
Dip observations may be made with the regular dip needles in the
same manner and with nearly the same facility as on land. The only
difference is that the ivory scraper must be used continuously, and
when the needle swings through a large arc on account of the motion
of the ship, the extremes of the swing must be read and recorded
instead of attempting to estimate the middle. As it is usual to make
observations on 8 or 16 equidistant headings in order to eliminate
the varying effect of the ship's magnetism, a complete determination
of dip and intensity on each heading would require too much time,
FIG. 9. Lloyd-Creak pattern dip circle.
and the following scheme of observations has been adopted with
satisfactory results.
(1) Deflection observations are made while swinging ship in one
direction and dip with loaded needle while swinging in the opposite
direction. The combination of these observations will give a value of
total intensity for each heading, and from each observation of deflec-
tions a value of dip may be obtained, as explained on page 83.
(2) On each heading observations are made in only one position of
needle and circle, so as to require not much more time than the com-
pass observations, which are usually going on at the same time. As
the gimbal stand is set so that when the horizontal circle of the dip
circle reads zero the needle swings in the plane of the fore-and-aft line
DIP AND TOTAL INTENSITY.
99
of the ship, the instrument may be placed in the magnetic meridian
with sufficient accuracy by means of the heading of the ship as shown
by the standard compass. For observations on 16 headings the
arrangement would be as follows:
Heading.
Needle face.
Ver. circle.
HOT. circle
setting.
N.
E.
E.
36000
NNE.
E.
E.
337 30
NE.
E.
E.
315 00
ENE.
E.
E.
292 30
E.
W.
W.
90 00
ESE.
W.
W.
67 30
SE.
W.
W.
45 00
SSE.
w.
w.
2230
S.
E.
w.
36000
SSW.
E.
w.
337 30
sw.
E.
w.
315 00
wsw.
E.
w.
292 30
w.
W.
E.
90 00
WNW.
W.
E.
67 30
NW.
W.
E.
45 00
NNW.
w.
E.
2230
(3) Two readings of each end of the needle are made for each
position. In case the needle is so nearly horizontal that only one end
can be read, four readings are made of that end.
(4) The times of beginning and ending of observations for each
group of four headings and the corresponding temperatures are
recorded, also conditions of weather, sea, etc.
The variation in the values of 7, 7', and u for the four different
positions of circle and needle can be determined from the shore obser-
vations, and the values obtained on shipboard should be corrected
accordingly to reduce to the mean of the four positions, in case the
corrections amount to as much as 10 '; in any case the values of dip
must be corrected to reduce to the standard dip instrument. Sample
observations of the two classes and the corresponding computations,
and a summary of the results of a complete swing, are given below.
100
DIRECTIONS FOE MAGNETIC MEASUREMENTS.
Form 391.
MAGNETIC OBSERVATIONS ON BOARD C. AND G. S. S. BACHE.
LOADED DIP FOR TOTAL INTENSITY.
Date, July 10, 1909. Latitude, 38 20'. Longitude, 76 22'.
Dip circle No. 35. Needle No. 4.
Weight No. 6.
Ship's head N.
Hor. circle 360.
Ver. circle E.
Needle face E.
Ship's head NNE.
Hor. circle 337*-
Ver. circle E.
Needle face E.
Ship's head NE.
Hor. circle 315.
Ver. circle E.
Needle face E.
Ship's head ENE.
Hor. circle 292* .
Ver. circle E.
Needle face E.
S.
N.
S.
N.
S.
N.
8.
N.
345 00
344 10
164 40
164 30
346 20
34600
166 00
166 10
348 50
348 10
168 40
16830
350 50
351 00
170 30
170 50
34435
16435
346 10
16605
348 30
68 35
350 55
170 40
/' -15 25
-13 52
-11 28
-9 12
Form 390.
MAGNETIC OBSERVATIONS ON BOARD C. AND G. S. S. BACHE.
DEFLECTIONS FOR TOTAL INTENSITY AND DIP.
Date, July 10, 1909. Latitude, 38 20'. Longitude, 76 22'.
Dip circle No. 35. Needle No. 4 deflecting, No. 3 suspended.
Ship's head NE. Hor. circle 315.
Ver. circle E. Needle face E.
Ship's head NNE. Hor. circle 337*.
Ver. circle E. Needle face E.
D.
R.
R.
D.
N.
S.
N.
S.
N.
S.
N.
S.
228 40
30
48 20
30
285 10
20
105 20
20
287 10
20
107 30
40
J_".* 4U
40
4950
50
228 35
48 25
285 15
105 20
287 15
107 35
229 40
49 50
48 30
153 47.5
I 76 54
105 17.5
56 47.5
u 28 24
107 25
157 10
/ 78 35
49 45
57 40
u 28 50
DIP AND TOTAL INTENSITY/
Form 392.
COMPUTATION OF TOTAL INTENSITY*.
From observations on board C. and G. S. S. Bache.
Formulas: u'=II' and F= cVcos /'. cscTwTcsc u'
Date, July 10, 1909.
Computer, H. M. Armstrong
Ship's head.
N.
NNE.
NE.
ENE.
,
/
o /
/
r
-15 25
-13 52
-11 28
- 9 12
u
29 03
28 59
2833
27 49
u'
94 16
92 04
87 59
83 39
log cos /'
9. 98409
9. 98715
9. 99124
9. 99438
" cscw
0. 31375
0.31466
0.32064
0. 33101
" csc u'
0. 00121
0. 00028
0. 00027
0. 00267
Sum
0. 29905
0. 30209
0.31215
0. 32806
Half sum
0. 14952
0. 15104
0. 15608
0. 16403
log C
9. 62425
9.62425
9.62425
9.62425
p
9. 77377
9. 77529
9. 78033
9.78828
F
.5940
.5961
.6030
.6142
SUMMARY OF RESULTS.
Steamer Sache, July 10, 1909.
Head.
7 obs'd.
/corr'd.
/'
u obs'd.
u corr'd.
u'
F
/
/
/
/
o /
/
C, G. S.
N.
79 14
78 51
-15 25
28 54
29 03
94 16
0. 5940
NNE.
78 35
78 12
-13 52
28 50
28 59
92 04
.5961
NE.
76 54
76 31
-11 28
28 24
28 33
87 59
.6030
ENE.
74 50
74 27
- 9 12
27 40
27 49
83 39
.6142
E.
71 01
71 42
- 5 20
27 24
27 32
77 02
.6258
ESE.
68 11
68 52
- 2 42
26 19
26 27
71 32
.6473
SE.
65 52
66 33
- 58
25 28
25 36
67 31
.6662
SSE.
64 21
65 02
00
25 04
25 12
65 02
.6776
S.
64 48
64 29
+ 18
25 00
2450
64 11
.6846
SSW.
65 50
65 31
+ 02
25 20
25 10
65 29
.6768
sw.
68 18
67 59
- 48
26 02
25 52 ; 68 47
.6601
wsw.
71 28
71 09
- 2 40
26 42
26 32 i 73 49
.6424
w.
74 09
74 43
- 4 55
27 56
27 49
7938
.6202
WNW.
76 41
77 15
- 9 12
28 34
28 27
86 27
.6066
NW.
78 15
78 49
-13 02
28 55
28 48 I 91 51
.5988
NNW.
78 49
79 23
-15 05
2904
28 57 94 28
.5955
Mean.
72 20
72 28
- 6 31
27 14
27 14
7859
.6318
In the case of this dip circle, No. 35, it was found necessary to apply
the following corrections to 7 and u on the basis of the results of
observations at several shore stations :
/ ' u
Circle east, needle face east 23' + 9'
Circle west, needle face west +41 + 8
Circle west, needle face east 19 10
Circle east, needle face west , +34 - 7
102 OWRfjCJrfGSfcS FOB MAGNETIC MEASUREMENTS.
the values of dip and total intensity show
a large range in the course of the swing. It will be found also by com-
parison with shore observations in the vicinity that the mean values
of dip and intensity on board differ by considerable amounts from the
shore results. These differences do not remain constant, however,
when the ship goes from place to place. The deviations in dip and
total intensity may be derived and analyzed in a manner similar to
that given for the compass deviations. As it is seldom, however,
that dip-circle observations are made at sea except when swinging ship ,
it is usually sufficient to obtain by interpolation from the swings near
shore the corrections required by the mean values of dip and total
intensity for the swings at sea.
For the limited range of dip usually covered in a season's work and
with swings near shore in the highest and lowest latitudes reached, a
satisfactory approximation is obtained by assuming that the changes
in the corrections are proportional to the changes in dip.
SPECIAL DIRECTIONS.
In order to obtain the best results from observations on shipboard
especial attention should be paid to the following points:
(1) Avoid as far as possible any change in the condition of the intensity
needles. Keep them clean and free from rust and take especial care to
protect the pivots from injury. When removing a needle after observing
be sure that the point does not catch on the edge of the graduated circle.
(2) Have the ship as nearly as possible in the same condition as regards
location of boats, anchors, chains, etc., for the swings near shore as for
those at sea.
(3) Make the compass observations when the sun is not more than 30
high, if possible. Steady the ship on a heading for a minute or two before
reading the sun's bearing. In handling the azimuth circle, be careful to
have the compass bowl swinging free at the moment of observation.
(4) When there is much motion to the ship, select a moment for talcing
a reading when she is nearly on an even keel. In the case of the dip
circle, select a vibration of the needle which appears symmetrical.
DIRECTIONS FOR OPERATING A MAGNETIC OBSERVATORY.
BUILDINGS.
For the operation of a magnetic observatory there are required a
variation building in which the variation instruments are mounted,
and an absolute building in which the absolute observations are made.
In their construction scrupulous care is exercised to exclude all
material that might possibly affect the magnets, and in their subse-
quent use the same care must be exercised. No article of magnetic
material should be carried into the buildings unless absolutely
needed, and no person should be allowed to enter the variation build-
ing until he has divested himself of all such articles, as knife, watch,
keys, etc. The sole of a shoe or the brim of a hat often contains a
piece of stsel sufficient to disturb the sensitive variation instruments.
Such other buildings as may be needed are usually placed far enough
away to have no effect on the magnets. The variation building is
designed with a view to reduce to a small limit the range of temper-
ature inside. Those of the Coast and Geodetic Survey are all above
ground and built of wood, the amount of insulation varying with the
range of temperature to be overcome.
VARIATION INSTRUMENTS.
The variations in declination, horizontal intensity, and vertical
intensity are recorded photographically by means of a magneto-
graph, consisting of a recording apparatus and three variometers.
Light from a lamp is reflected from a mirror attached to the magnet
of a variometer and traces an irregular line (curve) on a sheet of
photographic paper (magnet ogram) wrapped around a revolving
drum of the recording apparatus. The reflection from a fixed
mirror traces a straight line (base line) on the magnetogram, and the
variation in the distance between the curve and the base line (ordi-
nate) is a measure of the variation in the direction of the suspended
magnet produced by the variation in the earth's magnetism.
The D variometer is mounted with its magnet in the magnetic
meridian and the direction of the magnet changes as the magnetic
declination changes. In the H variometer the magnet is suspended
in the magnetic prime vertical and a change in its direction corre-
sponds to a change in the horizontal intensity. In the Z variometer
the magnet rotatss about a horizontal axis, like a dip needle, but is
adjusted to lie approximately in the horizontal plane, so that a
103
104 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
variation in its inclination to the horizon corresponds to a variation
in the vertical intensity.
Each of the five observatories of the Coast and Geodetic Survey is
equipped with a magnet ograph of the Eschenhagen type, in which
very small magnets ar3 used, so that it is possible to have the vari-
ometers quite near to each other without appreciable interaction.
They are mounted in a row, magnetically east and west, as shown in
Figure 10, and all three record on the same magnetogram, the up and
down motion of the Z magnet being converted to horizontal motion
on the magnetogram by means of a prism. There is also a thermo-
graph attached to the vertical intensity variometer, which records
photographically the variations of temperature.
When the D variometer is east of the recording apparatus, a
motion of the north end of the magnet to the east (increasing decli-
nation) causes the registering spot of light to move to the north on
the recording drum. When it is west of the recording apparatus
the motion of the spot of light is toward the south. In the case of
the horizontal intensity variometer, when the north end of the
Magnetic Prime Vertical
FIG. 10. Relative position of variometers.
e
magnet points toward the recording apparatus, an increase of hori-
zontal intensity causes the spot of light to move toward the north on
the drum, no matter whether the magnet is east or west of the
recording apparatus. The vertical intensity variometer is mounted
with the north end of the magnet to the north, and an increase of
vertical intensity causes the spot of light to move toward the south
on the drum. In the D and H variometers the magnet is suspended
by means of a quartz fiber. To the lower end of the fiber is attached
a light frame supporting two mirrors, the vertical plane surfaces of
which make a slight angle with each other. They must be so
adjusted that the distance between the two reflected rays of light,
where they strike the recording cylinder, is slightly less than the
width of the magnetogram. The magnet hangs in a stirrup attached
to the lower part of the mirror frame and is inclosed by a cylindrical
copper damping box. As the diameter of the box is only slightly
greater than the length of the magnet and as the hole in the top is
not much larger than the shank of the stirrup, it is necessary in
adjusting the instrument to see that the shank is centered in the hole
in order to insure freedom of motion of the magnet, and the observer
VARIATION INSTRUMENTS. 105
should examine the variometers- from time to time to be sure that no
change of level has occurred. The moment of inertia of the magnet
system is so small that only a very small resistance is required to
appreciably affect the motion of the magnet. An accumulation of
mold or dust, or the web of a minute spider, such as occasionally
finds its way through the openings of the variometer, is often suffi-
cient. The appearance of the curve will usually indicate the pres-
ence of an obstruction, and it may be necessary to remove the damp-
ing boxes and clean them unless it is found that change of level
eliminates the trouble. It sometimes happens that a gradual slip-
ping of the joint between fiber and mirror frame causes a lowering of
the magnet in its damping box until it finally touches the bottom.
The magnet of the H variometer is held in its position at right
angles to the magnetic meridian principally by the torsion of the
supporting fiber, but partly also by control magnets placed below
the suspended magnet with their axes horizontal. Their primary
object, however, is to regulate the sensitiveness of the variometer.
In the Z variometer there are two magnets supported by a light
frame, like the beam of a balance, on the under side of which are
two conical steel points which rest in cup-shaped depressions in
agate surfaces. The steel points are so adjusted that the line joining
them is at right angles to the magnetic axis of the magnet system.
The horizontality of the magnet is secured partly by an adjustable
weight threaded onto a horizontal rod, and partly by a control
magnet directly under the center of the magnet, which partly coun-
teracts the effect of Z. The stability is regulated by a weight
threaded onto a vertical rod, so that the center of gravity of the
magnet system may be raised or lowered, as desired. Great care
must be exercised in working about this variometer, as a slight jar is
sometimes sufficient to change the balance of the magnet systsm or
even throw it out of balance altogether. This applies especially to
the deflection observations for the determination of scale value.
When the magnet system has become displaced by a jar or by an
unusually large deflection, as during a magnetic storm, it may gen-
erally be put back in adjustment by lifting and lowering two or
three times by means of the lifter. If further adjustment is required,
it can usually be done by raising or lowering the control magnet,
unless a change of sensitiveness is required.
Under unfavorable conditions the steel bearing points may become
rusted or otherwise blunted, in which case the magnet system will not
move freely and the curve will appear abnormally smooth. Extra
bearing points are provided for replacing those which may become
defective.
The distance between the D and Z variometers is so short that a
change in the position of the Z control magnet produces a slight
106 DIRECTIONS FOB MAGNETIC MEASUREMENTS.
change in the position of the D magnet, and the amount of this change
must be determined when the Z variometer is readjusted.
The thermograph consists of a Bourdon tube filled with mercury,
to the free end of which is attached a mirror.
The drum of the recording apparatus is usually made to revolve
once in 24 hours. At hourly intervals a system of shutters is raised
to a vertical position by means of a cam attached to a gear wheel and
after the lapse of a minute or two allowed to drop back into a hori-
zontal position. The shutters are so adjusted that when raised they
prevent the light from the fixed mirrors reaching the magnetogram
and thus produce a short break in each base line.
By a change of gearing the drum may be made to revolve once in
two hours and the time breaks then occur every five minutes. It is
then necessary to open wider the slit of the lamp, in order to secure
sharp lines on the photographic paper.
CONVERSION TO ABSOLUTE VALUES.
In order to determine the absolute value of D, H, or Z at any
moment from the continuous photographic record of the variometer
it is necessary to know: (1) The base-line value, that is, the absolute
value when the curve and base line coincide; (2) the scale value, or
value of 1 millimeter of ordinate expressed in absolute units (minutes
for D, gammas or units of the fifth decimal in the C. G. S. system
for H and Z) ; (3) in the case of H and Z, the temperature coefficient,
or the effect upon the ordinate of a change of 1 in temperature.
In the H variometer, the position of the magnet is the resultant
effect of the force of torsion, the force acting between the suspended
magnet and the control magnets, and the force exerted upon the
suspended magnet by the horizontal component of the earth's field.
A change in the magnetic moment of the suspended magnet due to
change of temperature will change the magnetic force acting and hence
change the position of equilibrium, irrespective of any change in H.
Similar conditions exist in the Z variometer and in addition the
moment of the balancing weight changes with temperature on account
of change in the length of the supporting rod.
Let d, 7i, 2 = the ordinates in millimeters at the temperature t, in-
creasing ordinate corresponding to increasing D, H, and Z,
d, h, z = scale values of D, H, and Z, respectively,
B d , B h , B z = base-line values for D, H, and Z (in the case of H and
Z, reduced to a standard temperature t ,
q h and q z = temperature coefficients of the H and Z variometers,
Then
D = B d +d.e d
H = B h +Ji.e h +q h (t-t )
CONVERSION TO ABSOLUTE VALUES. 107
BASE-LINE VALUES.
For the determination of the base-line values absolute observations
are made at least once a week. From an inspection of the above for-
mulas it will be seen that if the ordinates d, h, z be read for the times
at which absolute observations have been made, the base-line values
may be computed, provided the scale values and temperature coeffi-
cients are known. The absolute value of vertical intensity must be
computed, however, from the observed values of H and I. It is in
general not feasible to make simultaneous observations of H and 1,
but the value of H at the time of the dip observations may be deter-
mined from the record of the variometer after the H base-line value
has been computed.
The absolute observations are made in the manner already ex-
plained, but greater care must be exercised in the operations and a
greater degree of accuracy is to be expected than is the case in work
in the field. Absolute accuracy is impossible, however, and the base-
line values resulting from a series of observations will show more or
less variation, whereas they should be constant provided there has
been no change in the adjustment of the variometers. It has been
found in some cases that even when there has been no readjustment
of the variometer the base-line values show a progressive change.
This may be due partly to gradual change of the relative positions of
suspension fiber and stirrup, partly to the fact that the magnets suffer
gradual loss of magnetism with age and, in the case of H and Z where
the range of temperature has been large, partly to error in the adopted
value of temperature coefficient. It is possible also that the torsion
of the quartz fibers may change somewhat with age. Hence in deter-
mining what base-line values to adopt it is necessary to adjust the
observed values, having due regard to this progressive change. For
any particular set of instruments it must be found out by experience
how closely the adopted values should correspond to those resulting
from observation. In the case of D and H the mean of the values
determined in the course of a month is usually almost free of error of
observation and may be used as a basis for determining the gradual
change from month to month. In the case of Z the error of observa-
tion is somewhat greater. An abrupt and continued change in the
base-line values when there has been no readjustment of the vario-
meter would demand a careful examination of the absolute instru-
ment to make sure that there is no systematic error in the absolute
observations due to lack of adjustment. It is desirable to make
absolute observations at different times of the day, so that the com-
putation of base-line values will involve ordinates of different amounts.
The form of computation of H and Z base-line values is shown in the
following examples, in which the adopted standard temperature is
10 C.
m
108
Form 358.
DIRECTIONS FOB MAGNETIC MEASUREMENTS.
HORIZONTAL INTENSITY BASE LINE.
Sitka, Alaska. Magnetic Observatory.
Magnetograph No. 6.
Magnetometer No. 37.
Date.
Feb. 5. Feb. 11.
Feb. 17.
Feb. 20.
1908. L. M. T. Scaling. L. M. T.
Scaling. L. M. T.
Scaling.
L. M. T.
Scaling.
h. m.
mm. h. m.
mm. h. m.
mm.
h. m.
mm.
10 21 73. 4 14 40
71.7 917
73.6
1005
68.3
Oscillations.
24
26
79.4
74.4
43
46
69.3
66.7
20
22
73.7
73.6
08
10
68.1
67.7
29
76.6
48
67.5 25
73.4
13
67.4
i
10 41
73. 8 15 00
68.3 9 36
72.0
10 28
66.5
Deflections.
47
52
74.4
74.4
06
11
68.9 41
69.3 46
71.4
71.4
33
39
67.6
66.0
58
72.7
17
69.6
51
71.3
44
65.4
I
11 07
72.9
15 21
70.3
956
71.2
1048
65.3
Deflections.
71.8
71.6
26
32
70. 1 10 01
70.1 06
70.1
69.8
53
58
64.9
64.6
22
69.4
37
69.1
11
69.4
11 04
;-}. :,
11 29
65.3
15 45
69.5
10 19
68.3
11 12
63.5
Oscillations.
32
34
63.3
61.3
4X
50
69.3
70.0
21
24
68.5
68.7
15
18
63.5
63.4
37
59.3
53
69.5
27
68.6
20
63.4
Mean
70.9
69.3
70.9
65.6
r
r
r
r
c*
2.79
2.79
2.79
2.79
* and At
3. 7
196
5. 9
193
5. 7
198
6. 5
183
4
-46
-30
-31
-26
ft,
152
163
167
157
H
15536
15552
15555
15537
Base line
15384
15389
15388
15380
CONVERSION TO ABSOLUTE VALUES.
109
Form 359.
Sitka Magnetic Observatory.
Magnetograph No. 6.
VERTICAL INTENSITY BASE LINE.
Earth inductor No. 2.
Date.
Feb. 5.
Feb. 11.
1908.
Local
mean time.
Scalings.
Local
mean time.
Scalings.
H.
Z.
H.
Z.
h. m.
mm.
mm.
h. m.
mm.
mm.
9 29
77.2
-88.1
16 25
71.3
-80.6
31
77.6
88.1
27
70.7
80.9
34
77.4
87.7
30
72.1
81.2
36
77.4
87.5
32
71.3
81.3
39
79.4
87.4
34
72.8
80.7
41
79.4
87.3
36
73.3
80.5
44
78.2
86.7
39
73.3
80.6
Means
(i-T.ar)
78.1
-87.5
72.1
-80.8
Sh and Z
2.79
4.69
2.79
4.69
t and h t
3.8
r
218
5.9
r
201
At and Ah
6.2
-45
4.1
-30
h
173
171
H base line
at 10
15386
15386
H
15559
15557
I
74 36'. 4
74 37'.
logH
log tan 7
4. 19198
0. 56016
4. 19193
0. 56046
logZ
4. 75214
4. 75239
Z
(J l.Or) r
56512
o
r
56544
t and 2<
3.8 -410
5.9
-379
J and Az
6.2 +6
4.1
+ 4
2
-404
-375
Z base line
at 10 56916
56919
SCALE VALUES.
From the formulas on page 106 it would appear that the scale
value of a variometer might be determined by making absolute
observations at different times and comparing the change in the
observed values with the change in ordinate. In practice, however,
the uncertainty in the absolute observations is generally too great
to secure satisfactory results in this way.
The scale value of the D variometer depends directly upon the dis-
tance between the movable mirror of the magnet and the paper on
the drum, and is found by the formula
ctnl
110 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
in which d is the angular motion of the magnet corresponding to 1 mm
on the magnetogram, R is the distance from the magnetogram to
the face of the movable mirror increased by two-thirds the thickness
of the mirror, and li is the angle through which the magnet is turned
when the torsion head is turned through the angle/. The lens of
the Eschenhagen D variometer is usually focussed for a scale value
of 1 mm. = 1'. For this convenient scale value
mm
#=1718.c
There is so little variation in the torsion of a quartz fiber that after
its torsion factor has once been determined it is unnecessary to
repeat the operation, although it is usual to do so from time to time
as a check. When a new fiber is inserted, a determination of its
torsion factor is of course required.
In the case of the H variometer, the scale value depends upon the
rigidity with which the magnet is held in its position at right angles
to the magnetic meridian. In the older form of suspension (bi-lilar)
the desired sensitiveness is secured by varying the distance between
the upper ends of the two supporting fibers. Where quartz fiber
suspension is used, it is not practicable to regulate the sensitiveness
by the size of the fiber, but the desired result is obtained by means
of control magnets, which serve to increase or decrease the force to
be balanced by the torsion of the fiber.
The scale value is found by comparing the amounts by which an
auxiliary magnet deflects the magnets of the D and H variometers,;
when similarly placed with regard to them. The series of observa-
tions is begun by deflecting the D magnet by placing the deflector to
the east and west (in the magnetic prime vertical), north end east or
west. Then the H magnet is deflected by placing the deflector to the
north and south, north end north or south. This is followed by a
second set of D deflections. Unless the torsion of the D fiber is
known from previous observations, a set of observations to deter-
mine that factor is also require^. It is important to make deflec-
tions at two distances as a check on the accuracy of the work.
Such distances should be selected as will give deflections of consider-
able magnitude without throwing the spot of light beyond the limits
of the magnetogram. Care must be taken to use the same deflection
distances on both variometers and to have the deflector in the same
horizontal plane with the deflected magnet.
It is evident that the effect of the deflector on the // magnet
corresponds to an increase or decrease of the horizontal intensity by
an amount equal to the intensity of the field of the deflector at the
selected distance. The amount by which the D magnet is deflected
depends upon the relative intensity of the earth's field and that of
the deflector at the selected distance.
CONVERSION TO ABSOLUTE VALUES. Ill
Let ^ = the number of millimeters which the D spot is deflected.
7= the angle through which the D magnet is deflected.
u f = the number of millimeters which the H spot is deflected.
h = H scale value, i. e., the change in H, expressed in gammas,
corresponding to a change in ordinate of 1 mm.
W= field intensity of the deflector at the selected distance.
In the case of the H deflections :
e h .u'=W
In the case of the D deflections :
, = flu tan IV / \Bu(
Since the deflection angle is always small its tangent may be taken
as proportional to the angle and we have just seen that the D scale
value is
Hence
, Hu/ f \ 2u H / f
As the deflection observations give directly the values of 2u and 2u',
it is more convenient to introduce a 2 in both numerator and denomi-
nator of the formula and use it in the form given. It has already
been pointed out that there is very little variation in the torsion
coefficient of a quartz fiber. The distance between the D mirror and
the drum is constant so long as there is no readjustment and H may
be assumed as constant for a year without introducing a material
error in the scale value computation. Hence, for that period the
H /
factor H^> ' yriTT ma J be regarded as constant and the formula be-
comes simply
fc = ^(constant
The form of observation and computation is shown in the following
example. It will be noticed that the two results from deflections
at different distances do not agree exactly. A comparison of the H
ordinates for times when the deflector was not in use with the deflected
ordinates shows that the deflections were unsymmetrical, the amount
of deflection being greater when the ordinate was decreased than
when it was increased. It has been found that under certain condi-
tions of adjustment, as in this case, the scale value varies with
the position of the magnet and may be represented analytically as
a linear function of the ordinate.
112
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
A comparison of the different determinations at Cheltenham in 1909
gives the value J5 = .004. The mean of the scalings for the short
deflection distance is 13.0 mm. and for the long distance 18.3 mm.,
and the resulting scale values should differ by about 0.02^, as they
do. When adjusting the variometer, the control magnets should be
so placed that the deflections are symmetrical or nearly so.
It sometimes happens during deflections that the regular spot of
light is thrown off the magnetogram and a record is made by the
reserve spot. In such cases the two spots must be made to record at
the same time at the close of the observations, so that the distance
between them may be measured.
Form 373.
H SCALE VALUE.
ate, May 26, 1909. Magnetograph No. 5.
Observer, J. E. Durban
.J
I.
II.
o
Distance 26 cm.
Distance 31 cm.
a
Remarks.
I
a
J
No.
Scaling.
Diff.
No.
Scaling.
Diff.
i
mm.
mm.
mm.
mm.
D
E
E
1
38.0
4
46.1
E
W
2
78.0
3
70.0
23.9
W
W
8
77.9
I
69.8
W
E
7
38.1
39.8
46.4
B.
H
N
N
N
S
1
2
91.1
-66.9
158.0
4
3
64.6
-28.8
93.4
S
S
S
N
8
7
-65.6
93.2
158.8
5
6
-27.9
65.2
93.1
D
W
E
1
37.9
4
46.0
39.9
21
.7
W
W
2
77.8
3
69.7
'
E
E
W
E
8
7
78.0
37.8
40.2
6
69.9
45.8
24.1
*
D
2 u 39. 98
2tt
23.78
H
2 u' 158. 40
2tt'
93.25
Scalings with magnet away.
Torsion observations.
L.M.T.
Scaling.
Temp. Remarks.
"ch-cle" Scalin S- Diff -
h. m.
mm.
,
mm. mm.
D
11 02
57.7
Beginning of first set.
133 57.4
D
11 19
58.1
End of first set.
163 - 8 56.0
H
11 19
21.0
24. 6 : Beginning of set.
103 85.3
H
11 33
21.6
24.7 End of set.
133 57. 1
D
11 48
57.8
End of second set.
Sum 112.3
Mean for 30 28. 1
CONVERSION TO ABSOLUTE VALUES.
113
COMPUTATION.
.K= 1720.1 mm. H=19880r
I.
1
1
II.
Iog2w
1.6018
1. 3762
" H
4. 2984
/ f \
0.0068
t( (j^h)
0. 7686
colog 2R 6. 4634
" 2u'
7.8002
8. 0304
log, 0.1706
0. 1752
c I- 481
1.497
Mean 1. 49
The scale value of the vertical intensity variometer is determined
in a similar manner, but the deflector is placed differently. When
deflecting the D magnet the deflector is placed to the north or south
(magnetic) of the D variometer, with its axis directed magnetically
east and west. When deflecting the Z magnet it is placed to the
north or south, with its axis vertical. The formula for computing
the Z scale value is of the same form as that derived for J?, namely:
f
_2u
z ~2u' 2
u' in this case being the number of millimeters which the Z spot is
deflected.
Great care must be exercised when placing the deflector in the
various positions in order not to jar the variometer, and thus alter
the adjustment. The ordinate with deflector away should be read
at the beginning and end of the set, to show whether or not a change
has taken place during the observations.
At Cheltenham, where two magnetographs are in operation, the
scale value of the Adie Z variometer is determined by the method
explained above, but that of the Eschenhagen variometer is obtained
by comparing the daily range as given by the two variometers.
TEMPERATURE COEFFICIENTS.
When the variation building is well insulated, so that the diurnal
variation of temperature inside is limited to a few tenths of a degree
Centigrade and the seasonal variation is very gradual, only approxi-
mate values of the temperature coefficients of the H and Z vari-
ometers are required. They may sometimes be determined from the
regular observatory records by selecting periods free from large dis-
turbances during which there was both a rise and fall of temperature.
A comparison of the mean of the 24 hourly ordinates for the days of
7721311 8
114
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
high temperature with the corresponding mean for the days of low
temperature shows the effect of change of temperature. The follow-
ing example will illustrate the method :
Date.
Temper-
ature.
Mean ordinate.
1907.
Jan. 21, 22, 29, 30
-6.79
mm.
93.55
Jan. 23, 24, 25, 26
Differences
-2.96
95.15
3.83
1.60
1.60
'-sTS* 4 - 41 - 1 '*
being the scale value; that is, an increase of 1 in temperature
corresponds to an increase in the ordinate of 1.9f. In using this
method great care must be exercised in the selection of the periods in
order to eliminate as far as possible changes in ordinate due to other
causes than change in temperature, and an adopted value of temper-
ature coefficient should depend on a number of such determinations.
Where the insulation is so good that the temperature in the variation
building does not change sufficiently to use .the above method, the
instrument room may be heated and cooled artificially. For success-
ful results the changes of temperature should be so gradual that the
temperature of the magnet will be correctly represented by the ther-
mometer readings and a time should be selected when the changes in
H and Z are apt to be small, unless a second magnetograph is in oper-
ation and may be used to determine those changes.
In the case of the H variometer there is no reason to expect a
change of temperature coefficient. With the Z variometer, how-
ever, the factors making up the temperature coefficint are so hetero-
geneous that a radical change of adjustment may produce a change of
temperature coefficient.
TEMPERATURE.
In order to determine the temperature of the magnets from the
record of the thermograph, the thermometers attached to the H and
Z variometers are read morning and afternoon at times which corre-
spond approximately with the daily extremes of temperature.
Under ordinary conditions the variations in temperature may be
assumed to be the same for the two variometers. The change in
thermometer reading between morning and afternoon compared with
the change in ordinate of the thermograph curve will serve to deter-
mine the scale value of the thermograph.
PROGRAMME OF WORK. 115
TIME SCALE.
The recording apparatus is provided with suitable mechanism for
making a short break in the base lines at intervals of an hour. The
exact time of occurrence of the first and last time breaks on each
magnetogram, as well as of one occurring in the morning, is deter-
mined by the click made by the mechanism when the shutters are
raised and lowered. The times of stopping and starting the drum are
also recorded.
Time observations are made often enough to insure a knowledge of
the chronometer correction on local mean time to the nearest tenth of
a minute.
READING OF ORDINATES.
It is customary to tabulate the hourly ordinates of D, H, and Z
and also the maximum and minimum values for each day and from
them to compute the corresponding absolute values. Local mean
time is used and the hours are counted from midnight to midnight,
to 24. For the determination of the base-line values, ordinates
must be measured for the times when absolute observations were
made. In the case of the vertical intensity, H as well as Z ordinates
must be measured for the time covered by the dip observations,
in order that the value of H may be obtained for combining with 7 to
compute Z. The number of ordinates to be read for a base-line
determination depends upon the irregularity of the curve at that
time. At the Coast and Geodetic Survey observatories the ordinates
are measured from the bottom of the base line to the bottom of the
curve and at right angles to the base line. It is generally found that
the perpendicular at the end of the base line does not pass through
the end of the curve, and this fact must be allowed for when deter-
mining the time scale. For measuring the ordinates a reading board
has been found very useful. A picture and description of it will be
found in " Results of Observations at the Coast and Geodetic Survey
Magnetic Observatory at Cheltenham, Md., 1901-1904."
PROGRAMME OF WORK.
While the routine of an observatory is affected somewhat by local
conditions, the following programme of work to be done will be modi-
fied only in minor details :
(1) Enter the variation room in the morning in time to record the
8 o'clock time break. Read the thermometers, wind the driving
clock, see that the lamp is burning brightly and that the spots of
light are recording properly. Make psychrometric observations.
(2) Compare the timepiece used with the standard chronometer
and wind both of them.
116 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
(3) Put new sheets of paper on the seismograph, recording the
times of stopping and starting the drums. Wind the clocks when
necessary.
(4) Make meteorological observations in the open air.
(5) Enter the variation room in the afternoon in time to record
the time break at 16 hours. Read the thermometers. Remove the
magnetogram, prick holes for measuring shrinkage, date and put on
a new sheet of paper, wind the clock, trim the lamp wick and adjust
the light. The lamp requires filling every other day. Record the
times of stopping and starting the drum.
(6) Record the time break at 17 hours. Read the thermometers.
Examine the lamp and spots of light.
The clock will run for more than 24 hours, but a more uniform rate
can usually be secured by winding twice a day. When doing any
work in the instrument room requiring light, a ruby lamp should be
used or else the front of the recording box should be closed.
Absolute observations are made at least once a week, always on
the same day of the week. A week's observations comprise two or
three sets of declination, two sets of horizontal intensity, and two or
three sets of dip. About once a week the magnetograms are devel-
oped and the seismograms are fixed.
With a good chronometer time observations four or five times a
month will suffice.
Deflections for the determination of H and Z scale values are made
at least once a month. In case of a readjustment the scale value
should be determined just before the adjustment and again two or
three days afterwards.
GENERAL DIRECTIONS.
Magnetograph record. The magnetograph record should contain a
detailed account of whatever happens to any one of the component
parts of the magnetograph, so that the computer will have collected
in one place all the information needed to properly interpret the
results. If the H variometer is adjusted by turning the torsion head,
the amount and direction of change should be recorded. If the posi-
tion of the control magnets is changed, their position with respect to
the suspended magnet and each other, both before and after the
change, should be recorded. Similar record should be made of any
change in the weights or control magnet of the Z variometer. Any
change of adjustment which produces a change of base-line value
should be noted also on the base-line computation and on the monthly
tabulation of hourly values.
Adjustments. It is important to make a direct determination of
the effect of an adjustment, if possible. For that reason it is desir-
able to have a magnetogram on the drum at the time, so that a com-
GENEKAL DIRECTIONS. 117
parison may be made of the relative position of the spots of light
before and after the adjustment. Deflections for the determination
of scale value should be made just before a readjustment and again
two or three days later. When readjusting the H variometer, the
effort should be made to place the control magnets in such a position
as to give a constant scale value. If the deflections are symmetrical
about the undeflected position of the magnet, it is safe to assume
that the desired result has been obtained. The amount of deflection
on H or Z corresponding to a desired scale value can be readily com-
puted from the formula when the amount of deflection of D at the
same distance is known. (Compare formula on page 111.)
Arrangement of spots. The spots of light should be so arranged as
to secure as complete and distinct a record as possible. The relative
position of curve and base line should be such that increasing ordi-
nates correspond to increasing values of the element. Small ordinates
are preferable, but a mixture of positive and negative ordinates is
apt to give rise to mistakes. It is undesirable to have the curves
so near to each other that there will be many crossings. As the usual
effect of a magnetic storm is to diminish the horizontal intensity, the
H variometer should be so adjusted that the reserve spot will come
on at the top of the magnetogram when the regular spot goes off at
the bottom. To avoid confusion the D variometer should be adjusted
so that the reserve spot will come on at the bottom.
Amount of light. It should be borne in mind that during a mag-
netic disturbance the motion of the magnet is much more rapid than
on a quiet day, and consequently a greater volume of light is required
to record its motion on the photographic paper.
Reading of ordinates. All ordinates are to be read and checked at
the observatory. When making the second reading special atten-
tion should be directed to the elimination of gross errors, as, for
example, misreadings of 5 or 10 mm., reading from the wrong base
line, or reading base-line ordinates on the wrong day. Base-line ordi-
nates should be read at the same time as the hourly values. The
maximum and minimum ordinates should be compared with the
hourly values on the same day as a check against misreadings.
Correction for shrinkage will be made when necessary. Declina-
tion scalings will be converted at once to minutes (except in scale-
value deflections, where they are to be recorded in millimeters) with
the aid of a suitable table, giving the limiting ordinates between which
a certain correction is required to convert millimeters to minutes.
The torsion factor must always be included in computing the D scale
value.
Magnetograph temperatures will be obtained directly from the
photographic record of the Z thermograph, if possible, based on the
mean of the H and Z thermometer readings (corrected). If the varia-
118 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
tion in temperature is so small that the thermograph trace appears
as a straight line between two consecutive thermometer readings, the
magnetograph temperatures may be obtained by interpolation between
the thermometer readings.
The daily means will be computed on all the monthly tabulation
sheets, but the hourly means are required for declination only. A
day from which some hourly values are missing or on which a change
of base-line value occurred will be omitted in taking means. Missing
hourly values may be supplied by interpolation when they are only
few in number and occur in a period comparatively free from disturb-
ance.
Magnetic character of day. The magnetic character of the two
halves of each day, a. in. and p. m., will be indicated roughly by the
figures 0, 1, 2 on the monthly tabulation for each element, and the
character of each Greenwich day as a whole will be tabulated on the
same scale, and this tabulation (in duplicate) will be forwarded to
the Office as soon as possible after the end of the quarter. At the
same time there will be transmitted a table giving the times of occur-
rence and duration of the principal magnetic disturbances occurring
during the quarter.
Absolute observations will be made at least once a week. When
field instruments are to be compared with the observatory instru-
ments for purposes of standardization and two observers are available,
it is preferable to make simultaneous observations, exchanging the
positions of the instruments in the middle of the series in case the
relation of the two stations is not known. Where this plan can. not
be carried out, base-line ordinates will be read for the observations
with the field instruments, so that allowance may be made for the
variation of the earth's magnetism between the observations with the
two sets of instruments.
Transmission of records. The observatory records will be forwarded
to the office monthly, as soon as the necessary computations have
been completed. To guard against loss of records in transmission, a
summary of the results of absolute observations and a copy of the
monthly tabulations of variation observations, base-line determina-
tions, etc., must be retained at the observatory. Such a summary
is needed by the observer in order that he may exercise proper control
over the observatory work.
TABLES.
TABLE I.
Correction to observed altitude of the sun for refraction and parallax.
119
Apparent
altitude.
Temperature, centigrade.
Apparent
altitude.
-10
+10
+20
+30
+40
5
10 33
10 07 9 43
9 21
9 00
8 40
5
6
9 01
8 39 8 19
8 00
7 42
7 25
6
7
7 51
7 32
7 15 6 59
6 44
6 30
7
8
6 55
6 39
6 24
6 10
5 57
5 44
8
9
6 12
5 58
5 44
5 32
5 20
5 08
9
10
5 35
5 22
5 10 4 59
4 48
4 38
10
11
5 05
4 53
4 42 4 32
4 22
4 13
11
12
4 40
4 29
4 19 4 10
4 01
3 52
12
13
4 17
4 07
3 58 3 50
3 42
3 34
13
14
3 59
3 50
3 41 3 33
3 25
3 18
14
15
3 41
3 33
3 25 3 18
3 11
3 05
15
16
3 28
3 21
3 13 3 06
3 00
2 54
16
17
3 14
3 07
3 00 2 54
2 48
2 43
17
18
3 04
2 57
2 50 2 44
2 38
2 33
18
19
2 53
2 47
2 40
2 34
2 29
2 24
19
20
2 43
2 37
2 31 2 26
2 21
2 16
20
21
2 34
2 28
2 23 2 18
2 13
2 09
21
22
2 25
2 20
2 15 2 10
2 06
2 02
22
23
2 18
2 13 *
2 08 2 04
1 59
1 55
23
24
2 12
2 06
2 02 1 58
1 54
1 50
24
25
2 05
2 00
1 56 1 52
1 48
1 45
25
26
2 00
1 55
1 51 1 47
1 43
1 40
26
27
1 55
1 50
1 46 1 42
1 38
1 35
27
28
1 49
1 44
1 41 1 38
1 34
1 30
28
29
1 45
1 40
1 37 1 34
1 30
1 26
29
30
1 41
1 36
1 33 1 30
1 27
1 23
30
32
1 32
1 28
1 25 1 22
1 19
1 16
32
34
1 25
1 21
1 18 1 15
1 13
1 10
34
36
1 19
1 15
1 13 1 10
1 08
1 05
36
38
1 13
1 09
1 07 1 05
1 03
1 00
38
40
1 07
1 04
1 02
1 00
58
056
40
42
1 03
1 00
58
56
54
53
42
44
58
55
53
51
49
48
44
46
54
52
50
48
46
45
46
48
51
49
47
45
43
42
48
50
47
45
43
41
40
39
50
55
38
36
35
34
32
30
55
60
31
30
29
28
27
25
60
65
25
24-
23
22
21
20
65
70
19 j 19
18
17
17
16
70
75
14
14
13
12
12
11
75
80
09
008
08
08
07
07
80
85
04 04
04 ! 04
03
03
85
9fl
00
00
00 00
00
00
90
120 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
TABLE II.
Correction in azimuth and altitude of the sun for semidiameter.
Altitude correction= Semidiameter.
Azimuth correction Semidiameter-f- cos ft.
Date.
Altitude
correc-
tion. .
Azimuth correction.
ft- 10
A- 20
ft- 30
ft- 40
ft=50
ft- 60
ft- 70
Jan. 1
16 18 16 33
17 21
18 49
21 17
25 21
3236
47 40
Feb. 1
16 16
16 31
17 19
1847
21 14
25 18
32 32
47 34
Mar. 1
16 10
16 25
17 12
18 40 21 06
25 09
32 20
47 16
Apr. 1
1602
16 17
17 04
18 31
2056
24 57
3204
4653
May 1 ! 15 54 16 09
16 55
18 22
20 45
24 44
31 48
46 29
June 1
July 1
15 48
15 46
16 03
16 01
16 49
16 47
18 15
18 12
20 38
2035
24 35
24 32
31 36
31 32
46 12
4606
Aug. 1
15 47
16 02
16 48
18 13
2036
24 33
31 34
4609
Sept. 1
15 53
1608
1654
18 20
2044
24 43
31 46
46 26
Oct. 1
16 01
16 16
1703
18 30
2054
24 55
3202
46 50
Nov. 1
1609
16 24
17 11
18 39
21 05
25 07
32 18
47 13
Dec. 1
16 15
1630
17 18
1846
21 13
25 17
3230
47 31
TABLE III.
Latitude from circum-meridian altitudes of the sun.
2 sin*
t
0"
1m
2m
>
4m
5m
6m
7m
8.
2
8
18
31
49
71
96
10
3
9
20
34
52
75
101
20
3
11
22
37
56
79
106
30
4
12
24
40
59
83
110
40
1
5
14
26
43
63
87
115
50
1
7
16
29
46
67
92
120
60
2
8
18
31
49
71
96
126
t
8"
9m
10"
Urn
12*
13m
14m
15m
9.
n
a
n
//
126
159
196
238
283
332
385
442
10
131
165
203
245
291
340
394
452
20
136
171
210
252
299
349
403
461
30
142
177
216
260
307
358
413
472
40
147
183
223
267
315
367
422
482
50
153
190
230
275
323
376
432
492
60
159
196
238
289
332.
385
442
502
TABLES.
121
TABLE N IV.
Latitude from circum-meridian altitudes of the sun.
A = cos 3 cos <f> cosec C.
s
5
6
7
8
9
10
11
12
13
14
15
%
8.23
1.95
1.89
1.83
1.77
1.72
1.66
1.62
1.57
1.53
1.48
1.44
S.23
22
2.03
1.96
1.90
1.84
1. 78 j 1. 72
1.67
1.62
1.58
1.53
1.49
22
21
2.12
2.05
1.97
1.91
1.84
1.79
1.73
1.68
1.63
1. 58 1. 53
21
20
2.22
2.13
2.05
1.98
1.92
1.85
1.79
1.73
1.68
1. 63 1. 58
20
19
2.32
2.22
2.14
2.06
1.99
1.92
1.86
1.80
1.74
1.68 1.63
19
18
2.42
2.33
2.23
2.15
2.06
2.00
1.93
1.86
1.80
1.74 1.69
18
17
2.54
2.43
2.33
2.24
2.15
2.07
2.00
1.93
1.86
1.80 i 1.74
17
16
2.67
2.55
2.44
2.34
2.25
2.16
2.08
2.00
1.93
1.87
1.80
16
15
2.81
2.68
2.56
2.45
2.35
2.25
2.16
2.08
2.00
1.93
1.87
15
14
2.97
2.81
2.69
2.56
2.45
2.35
2.25
2.17
2.08
2.01 1.93
14
13
3.14
2.98
2.83
2.69
2.57
2.46
2.35
2.26
2.17
2.08
2.00
13
12
3.33
3.15
2.98
2.83
2.70
2.57
2.46
2.35
2.26
2.17
2.08
12
11
3.55
3.34
3.15
2.99
2.83
2.70
2.57
2.46
2.35
2.25
2.16
11
10
3.79
3.55
3.34
3.16
2.99
2.84
2.70
2.57
2.46
2.35
2.25
10
9
4.07
3.80
3.56
3.35
3.16
2.99
2.83
2.70
2.57
2.45
2.35
9
8
4.39
4.07
3.80
3.56
3.35
3.16
2.99
2.83
2.69
2.56
2.45
8
7
4.76
4.39
4.07
3.80
3.56
3.34
3.15
2.98
2.83
2.69
2.56
7
6
5.19
4.76
4.39
4.07
3.80
3.55
3.34
3.15
2.98
2.81
2.68
6
5
5.71
5.19
4.76
4.39
4.07
3.79
3.55
3.33
3.14
2.97
2.81
5
4
6.35
5.71
5.19
4.75
4.38
4.07
3.78
3.54
3.32
3.13
2.96
4
3
7.15
6.35
5.71
5.18
4.74
4.37
4.05
3.77
3.53
3.31
3.12
3
2
8.17
7.14
6.34
5.70
5.17
4.73
4.36
4.04
3.76
3.52
3.30
2
S. 1
9.53
8.16
7.13
6.33
5.69
5.16
4.72
4.35
4.04
3.75
3.50
S. 1
9.51
8.14
7.12
6.31
5.67
5.14
4.70
4.33
4.01
3.73
N. 1
9.49
8.12
7.10
6.29
5.65
5.13
4.69
4.31
3.99
N.I
2
9.47
8.10
7.07
6.27
5.63
5.10
4.66
4.29
2
3
9.44
8.07
7.04
6.24
5.60
5.08
4.64
3
4
9.41
8.04
7.01
6.21
5.57
5.05
4
5
9.36
8.00
6.97
6.18
5.54
5
6
9.31
7.95
6.93
6.14
6
7
9.25
7.90
6.89
7
8
9.19
7.85
8
9
9.13
9
10
10
11
9.36
1
11
12
8.00
9.31
12
13
6.97
7.95
9.25
13
14
6.18
6.93
7.90
9.19
14
15
5.54
6.14
6.89
7.85
9.13
15
16
5.02
5.51
6. 10 6. 84
7.79
9.06
16
17
4.58
4.98
5.47
6.05
6.79
7.73
8.98
17
18
4.21
4.55
4.95
5.42
6.00
6.73
7.66
8.90
18
19
3.89
4.18
4.51
4.91
5.38
5.95
6.67
7.59
8.81
19
20
3.62
3.86
4.15
4.48
4.86
5.33
5.90
6.60
7.51
8.72
20
21
3.37
3.59
3. 83 4. 11
4.43
4.82
5.28
5.84
6.54
7.43
8. 63 21
22
3.16
3.35
3. 56 3. 80
4.07
4.39
4.77
5.22
5.78
6.46
7.35 22
N.23
2.97
3.13
3.31
3.52
3.76
4.03
4.35
4.72
5.18
5.71
6.39 N.23
122
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
TABLE IV Continued.
Latitude from circum-meridian altitudes of the sun.
A cos d cos < cosec C-
y
1\
15
16
17
18
19
20
21
22
23
24
25
%
S.23
.44
.41
1.37
1.33
1.30
1.27
1.24
1.21
1.18
1.15
.12
S.23
22
.49
.45
1.41
1.37
1.33
1.30
1.27
1.24
1.21
1.18
.15
22
21
.53
.49
1.45
1.41^
1.37
1.33
1.30
1.27
1.24
1.21
.18
21
20
.58
.53
1.49
1.45
1.41
1.37
1.33
1.30
1.27
1.24
.20
20
19
.63
.58
1.53
1.49
1.45
1.41
1.37
1.33
1.30
1.27
.23
19
18
.69
1.63
1.59
1.53
1.49
1.45
1.41
1.37
1.33
1.30
.26
18
17
.74
1.69
1.64
1.59
1.53
1.49
1.45
1.41
1.37
1.33
.30
17
16
.80
1.74
1.69
1.63
1.58
1.53
1.49
1.45
1.41
1.37
.33
16
15
1.87
1.80
1.74
1.69
1.63
1.58
1.53
1.49
1.44
1.41
.36
15
14
1.93
1.87
1.80
1.74
1.68
1.63
1.58
1.53
1.48
1 44
.40
14
13
2.00
1.93
1.86
1.80
1.74
1.68
1.63
1.58
1.53
1.48
.43
13
12
2.08
2.00
1.93
1.86
1.80
1.73
1.68
1.62
1.57
1.53
.47
12
11
2.16
2.08
2.00
1.93
1.86
1.79
1.73
1.67
1.62
1.57
.51
11
10
2.25
2.16
2.07
2.00
1.92
1.85
1.79
1.72
1.66
1.62
.56
10
9
2.35
2.25
2.15
2.06
1.99
1.92
1.84
1.78
1.72
1.66
.60
9
8
2.45
2.34
2.24
2.15
2.06
1.98
1.91
1.84
1.77
1.71
.65
8
7
2.56
2.44
2.33
2.23
2.14
2.05
1.97
1.90
1.83
1.76
.70
7
6
2.68
2.55
2.43
2.33
2.22
2.13
2.05
1.96
1.89
1.82
.75
6
5
2.81
2.67
2.54
2.42
2.32
2.22
2.12
2.03
1.95
1.88
.81
5
4
2.96
2.80
2.66
2.53
2.41
2.30
2.20
2.11
2.02
1.94
.87
4
3
3.12
2.95
2.79
2.65
2.52
2.40
2.29
2.19
2.10
2.01
.93
3
2
3.30
3.10
2.94
2.78
2.6*
2.51
2.39
2.28
2.18
2.08
2.00
2
S. 1
3.50
3.29
3.09
2.92
2.76
2.62
2.49
2.37
2.26
2.16
2.07
S. 1
3.73
3.49
3.27
3.08
2.90
2.75
2.61
2.48
2.36
2.25
2.14
N.I
3.99
3.71
3.47
3.25
3.06
2.89
2.73
2.59
2.46
2.34
2.23
N. 1
2
4.29
3.97
3.69
3.45
3.23
3.04
2.87
2.71
2.57
2.44
2.32
2
3
4.64
4.27
3.95
3.67
3.43
3.22
3.02
2.84
2.69
2.55
2.42
3
4
5.05
4.61
4.24
3.92
3.64
3.40
3.19
2.99
2.82
2.66
2.52
4
5
5.54
5.02
4.58
4.21
3.89
3.62
3.37
3.16
2.97
2.80
2.64
5
6
6.14
5.51
4.98
4.55
4.18
3.86
3.59
3.35
3.13
2.94
2.77
6
7
6.89
6.10
5.47
4.95
4.51
4.15
3.83
3.56
3.31
3.10
2.91
7
8
7.85
6.84
6.05
5.42
4.91
4.48
4.11
3.80
3.52
3.28
3.07
8
9
9.13
7.79
6.79
6.00
5.38
4.86
4.43
4.07
3.76
3.49
3.25
9
10
9.06
7.73
6.73
5.95
5.33
4.82
4.39
4.03
3.72
3.45
10
11
8.98
7.66
6.67
5.90
5.28
4.77
4.35
3.99
3.68
11
12
8.90
7.59
6.60
5.84
5.22
4.72
4.30
3.94
12
13
8.81
7.51
6.54
5.78
5.16
4.66
4.25
13
14
8.72
7.43
6.46
5.71
5.10
4.61
14
15
8.63
7.35
6.39
5.64
5.04
15
16
8.53
7.26
6.31
5.57
16
17
8.42
7.17
6.23
17
18
8.31
7.07
18
19
9.91
8.20
19
20
9.77
20
21
8.63
21
22
7.35
8.53
22
N.23
6.39
7.26
8.42
X.23
TABLES.
123
TABLE IV Continued.
Latitude from circum-meridian altitudes of the sun.
A=cosd cos^cosec C
V
25
26
27
28
29
30
31
32
33
34
35
y,
S.23
1.12
1.10
1.07
1.05
1.02
1,00
0.98
0.95
0.93
0.91
0.89
S.23
22
1.15
1.12
1.10
1.07
1.04
1.02
1.00
0.97
0.95
0.93
0.91
22
21
1.18
1.15
1.12
1.09
1.07
1.04
1.02
0.99
0.97
0.94
0.92
21
20
1.20
1.17
1.14
1.12
1.09
1.06
1.04
1.01
0.99
0.96
0.94
20
19
1.23
1.20
1.17
1.14
1.11
1.08
1.06
1.03
1.01
0.98
0.96
19
18
1.26
1.23
1.20
1.17
1.14
1.11
1.08
1.05
1.03
1.00
0.98
18
17
1.30
1.26
1.23
1.19
1.16
1.13
1.10
1.07
1.05
1.02
0.99
17
16
1.33
1.29
1.26
1.22
1.19
1.16
1.13
1.10
1.07
1.04
1.01
16
15
1.36
1.32
1.29
1.25
1.22
1.18
1.15
1.12
1.09
1.06
1.03
15
14
1.40
1.36
1.32
1.28
1.24
1.21
1.18
1.14
1.11
1.08
1.05
14
13
1.43
1.39
1.35
1.32
1.27
1.24
1.20
1.17
1.14
1.10
1.07
13
12
1.47
1.43
1.38
1.34
1.30
1.27
1.23
1.19
1.16
1.13
1.10
12
11
1.51
1.47
1.42
1.38
1.34
1.30
1.26
1.22
1.18
1.15
1.12
11
10
1.56
1.51
1.46
1.41
1.37
1.33
1.29
1.25
1.21
1.18
1.14
10
9
1.60
1.55
1.50
1.45
1.40
1.36
1.32
1.28
1.24
1.20
1.16
9
8
1.65
1.59
1.54
1.49
1.44
1.39
1.35
1.31
1.27
1.23
1.19
8
7
1.70
1.64
1.58
1.53
1.48
1.43
1.38
1.34
1.30
1.25
1.21
7
6
1.75
1.69
1.C3
1.57
1.52
1.46
1.42
1.37
1.33
1.28
1.24
6
7
5
1.81
1.74
1.68
1.62
1.56
1.50
1.45
1.40
1.36
1.31
1.27
5
4
1.87
1.79
1.73
1.66
1.60
1.55
1.49
1.44
1.39
1.34
1.30
4
3
1.93
1.85
1.78
1.71
1.65
1.59
1.53
1.48
1.42
1.38
1.33
3
2
2.00
1.91
1.84
1.77
1.70
1.63
1.57
1.52
1.46
1.41
1.36
2
S. 1
2.07
1.98
1.90
1.82
1.75
1.68
1.62
1.56
1.50
1.45
1.39
S. 1
2.14
2.05
1.96
1.88
1.80
1.73
1.66
i.eo
1.54
1.48
1.43
N.I
2.23
2.13
2.03
1.95
1.86
1.79
1.71
1.65
1.58
1.52
1.47
N. 1
2
2.32
2.21
2.11
2.01
1.93
1.84
1.77
1.69
1.63
1.56
1.50
2
3
2.42
2.30
2.19
2.09
1.99
1.91
1.82
1.75
1.68
1.61
1.54
3
4
2.52
2.39
2.27
2.17
2.06
1.97
1.88
1.80
1.73
1.65
1.59
4
5
2.64
2.50
2.37
2.25
2.14
2.04
1.95
1.86
1.78
1.70
1.63
5
6
2.77
2.61
2.47
2.34
2.23
2.12
2.02
1.92
1.84
1.76
1.68
6
7
2.91
2.74
2.59
2.44
2.32
2.20
2.09
1.99
1.90
1.81
1.73
7
8
3.07
2.88
2.71
2.56
2.42
2.29
2.17
2.06
1.97
1.87
1.79
8
9
3.25
3.04
2.85
2.68
2.53
2.39
2.26
2.14
2.04
1.94
1.85
9
10
3.45
3.21
3.00
2.81
2.65
2.49
2.36
2.23
2.11
2.01
1.91
10
11
3.68
3.41
3.17
2.96
2.78
2.61
2.46
2.32
2.20
2.08
1.98
11
12
3.94
3.63
3.37
3.13
2.93
2.74
2.58
2.43
2.29
2.17
2.05
12
13
4 ?5
3.90
3.59
3.32
3.09
2.89
2.70
2.54
2.39
2.25
? 13
13
14
4.61
4.19
3.84
3.54
3.28
3.05
2.85
2.66
2.50
2.35
2.22
14
15
5.04
4.55
4.14
3.79
3.49
3.23
3.00
2.80
2.62
2.46
2.31
15
16
5.57
4.98
4.49
4.08
3.74
3.44
3.18
2.96
2.76
2.58
2.42
16
17
6.23
5.49
4.91
4.43
4.02
3.68
3.39
3.13
2.91
2.71
2.54
17
18
7.07
6.14
5.42
4.84
4.36
3.96
3.62
3.33
3.08
2.86
2.66
18
19
8.20
6.97
6.05
5.34
4.76
4.29
3.90
3.56
3.28
3.03
2.81
19
20
9.77
8.08
6.87
5.96
5.25
4.69
4.22
3.83
3.50
3.22
2.97
20
21
9.63
7.96
6.76
5.87
5.17
4.61
4.15
% 3.77
3.44
3.16
21
22
9.48
7.83
6.65
5.77
5.08
4.53
4.07
3.70
3.38
22
N.23
9.32
7.71
6.54
5.67
4.99
4.45
4.00
3.63
N.23
124
DIRECTIONS FOR MAGNETIC MEASUREMENTS.
TABLE IV Continued.
Latitude from circum-meridian altitudes of the sun.
A=cos d cos# cosec }
X
35
36
37
38
39
40
41
42
43
44
45
J7
/ *
8.23
0.89
0.87
0.85
0.83
0.81
0.79
0.77
0.75
0.74
0.72
0.70
8.23
22
0.91
0.88
0.86
0.84
0.82
0.80
0.78
0.77
0.75
0.73
0.71
22
21
0.92
0.90
0.88
0.86
0.84
0.82
0.80
0.78
0.76
0.74
0.72
21
20
0.94
0.92
0.90
0.87
0.85
0.83
0.81
0.79
0.77
0.75
0.73
20
19
0.96
0.93
0.91
0.89
0.87
0.84
0.82
0.80
0.78
0.76
0.74
19
18
0.98
0.95
0.93
0.90
0.88
0.86
0.84
0.82
0.80
0.78
0.76
18
17
0.99
0.97
0.94
0.92
0.90
0.87
0.85
0.83
0.81
0.79
0.77
1-
16
1.01
0.99
0.96
0.94
0.91
0.89
0.86
0.84
0.82
0.80'
0.78
16
15
1.03
1.01
0.98
0.95
0.93
0.90
0.88
0.86
0.83
0.81
0.79
15
14
1.05
1.03
1.00
0.97
0.94
0.92
0.89
0.87
0.85
0.82
0.80
14
13
1.07
1.05
1.02
0.99
0.96
0.93
0.91
0.88
0.86
0.84
0.81
13
12
1.10
1.07
1.04
1.01
0.98
0.95
0.92
0.90
0.87
0.85
0.82
12
11
1.12
1.09
1.06
1.02
1.00
0.97
0.94
0.91
0.89
0.86
0.84
11
10
1.14
1.11
1.08
1.04
1.01
0.98
0.96
0.93
0.90
0.88
0.85
10
9
1.16
1.13
1.10
1.06
1.03
1.00
0.97
0.94
0.92
0.89
0.86
9
8
1.19
1.15
1.12
1.08
1.05
1.02
0.99
0.96
0.93
0.90
0.88
8
7
1.21
1.18
1.14
1.11
1.07
1.04
1.01
0.98
0.95
0.92
0.89
7
6
1.24
1.20
1.17
1.13
1.09
1.06
1.03
0.99
0.96
0.93
0.91
6
5
1.27
1.23
1.19
1.15
1.11
1.08
1.04
1.01
0.98
0.95
IX 99
5
4
1.30
1.26
1.21
1.17
1.14
1.10
1.07
1.03
1.00
0.97
0.94
4
3
1.33
1.28
1.24
1.20
1.16
1.12
1.09
1.05
1.02
0.98
0.95
3
2
1.36
1.31
1.27
1.23
1.18
1.14
1.11
1.07
1.03
1.00
0.97
2
S. 1
1.39
1.34
1.30
1.25
1.21
1.17
1.13
1.09
1.05
1.02
0.98
S. 1
1.43
1.38
1.33
1.28
1.24
1.19
1.15
1.11
1.07
1.04
1.00'
N.I
1.47
1.41
1.36
1.31
1.26
1.22
1.17
1.13
1.09
1.05
1.02
N. 1
2
1.50
1.45
1.39
1.34
1.29
1.24
1.20
1.16
1.11
1.07
1.04
2
3
1.54
1.48
1.43
1.37
1.32
1.27
1.22
1.18
1.14
1.09
1.06
3
4
1.59
1.52
1.46
1.41
1.35
1.30
1.25
1.20
1.16
1.12
1.07
4
5
1.63
1.56
1.50
1.44
1.38
1.33
1.28
1.23
1.18
1.14
1.10
5
6
1.68
1.61
1.54
1.48
1.42
1.36
1.31
1.26
1.21
1.16
1.12
6
7
1.73
l!66
1.58
1.52
1.46
1.40
1.34
1.29
1.23
1.19
1.14
7
8
1.79
1.71
1.63
1.56
1.49
1.43
1.37
1.32
1.26
1.21
1.16
8
9
1.85
1.76
1.68
1.60
1.54
1.47
1.41
1.35
1.29
1.24
1.19
9
10
1.91
1.82
1.73
1.65
1.58
.51
1.44
1.38
1.32
1.27
1.21
10
11
1.98
1.88
1.79
1.70
1.63
.55
1.48
1.42
1.35
1.30
1.24
11
12
2.05
1.95
1.85
1.76
1.67
.60
1.52
1.45
1.39
1.33
1.27
12
13
2.13
2.02
1.91
1.82
1.73
.64
1.57
1.49
1.43
1.36
1.30
13
14
2.22
2.10
1.98
1.88
1.78
.70
1.61
1.54
1.46
1.40
1.33
14
15
2.31
2.18
2.06
1.95
1.85
.75
1.66
1.58
1.51
1.43
1.37
15
16
2.42
2.27
2.14
2.02
1.91
.81
1.72
1.63
1.55
1.47
1.40
16
17
2."54
2.38
2.23
2.10
1.98
.88
1.77
1.68
1.60
1.51
1.44
17
18
2.66
2.49
2.33
2.19
2.06
.94
1.84
1.74
1.65
1.56
1.48
18
19
2.81
2.62
2.44
2.29
2.15
2.02
1.90
1.80
1.70
1.61
1.52
19
20
2.97
2.76
2.57
2.40
2.24
2.10
1.98
1.86
1.76
1.66
1.57
20
21
3.16
2.92
2.70
2.52
2.35
2.20
2.06
1.94
1.82
1.72
1.62
21
22
3.38
3.10
2.86
2.65
2.46
2.30
2.15
2.01
1.89
1.78
1.68
22
N.23
3.63
3.31
3.04
2.80
2.60
2.41
2.25
2.10
1.97
1.85
1.74
N.23
TABLES.
125
TABLE IV Continued.
Latitude from circum-meridian altitudes of the sun.
.4= cos d cos 4> cosec C
V
\
45
46
47
48
49
50
55
60
65
70
*/
/*
.8.23
0.70
0.69
0.67
0.65
0.64
0.62
0.54
0.46
0.39
8.23
22
0.71
0.69
0.68
0.66
0.64
0.63
0.55
0.47
0.39
22
21
0.72
0.71
0.69
0.67
0.65
0.63
0.55
0.47
0.40
21
20
0.73
0.71
0.70
0.68
0.66
0.64
0.56
0.48
0.40
20
19
0.74
0.72
0.71
0.69
0.67
0.65
0.56
0.48
0.40
0.32
19
18
0.76
0.74
0.72
0.70
0.68
0.66
0.57
0.49
0.40
0.33
18
17
0.77
0.75
0.73
0.71
0.69
0.67
0.58
0.49
0.41
0.33
17
16
0.78
0.76
0^74
0.72
0.70
0.68
0.58
0.50
0.41
0.33
16
15
0.79
0.77
0.75
0.73
0.70
0.69
0.59
0.50
0.41
0.33
15
14
0.80
0.78
0.76
0.74
0.71
0.69
0.60
0.50
0.42
0.33
14
13
0.81
0.79
0.77
0.75
0.72
0.70
0.60
0.51
0.42
0.34
13
12
0.82
0.80
0.78
0.76
0.73
0.71
0.61
0.51
0.42
0.34
12
11
0.84
0.81
0.79
0.77
0.74
0.72
0.62
0.52
0.43
0.34
11
10
0.85
0.82
0.80
0.78
0.75
0.73
0.62
0.52
0.43
0.34
10
9
0.86
0.84
0.81
0.79
0.76
0.74
0.63
0.53
0.43
0.34
9
8
0.88
0.85
0.82
0.80
0.78
0.75
0.64
0.53
0.44
0.35
8
7
0-89
0.86
0.84
0.81
0.78
0.76
0.64
0.54
0.44
0.35
7
6
0.91
0.88
0.85
0.82
0.80
0.77
0.65
0.54
0.44
0.35
6
5
0.92
0.89
0.86
0.83
0.81
0.78
0.66
0.55
0.45
0.35
5
4
0.94
0.90
0.88
0.85
0.82
0.79
0.67
0.55
0.45
0.35
4
3
0.95
0.92
0.89
0.86
0.83
0.80
0.68
0.56
0.46
0.36
3
2
0.97
0.93
0.90
0.87
0.84
0.82
0.68
0.57
0.46
0.36
2
S.I
0.98
0.95
0.92
0.89
0.86
0.83
0.69
0.57
0.46
0.36
S. 1
1.00
0.97
0.93
0.90
0.87
0.84
0.70
0.58
0.47
0.36
N. 1
1.02
0.98
0.95
0.92
0.88
0.85
0.71
0.58
0.47
0.37
N. 1
2
1.04
1.00
0.96
0.93
0.90
0.86
0.72
0.59
0.47
0.37
2
3
1.06
1.02
0.98
0.94
0.91
0.88
0.73
0.60
0.48
0.37
3
4
1.07
1.04
0.99
0.96
0.93
0.89
0.74
0.60
0.48
0.37
4
5
1.10
1.05
1.02
0.98
0.94
0.91
0.75
0.61
0.48
0.38
5
6
1.12
1.07
1.03
0.99
0.96
0.92
0.76
0.61
0.49
0.38
6
7
1.14
1.10
1.05
1.01
0.97
0.94
0.77
0.62
0.49
0.38
7
8
1.16
1.12
1.07
1.03
0.99
0.95
0.78
0.63
0.50
0.38
8
9
1.19
1.14
1.09
1.05
1.01
0.97
0.79
0.64
0.50
0.39
9
10
1.21
1.16
1.12
1.07
1.03
0.98
0.80
0.64
0.51
0.39
10
11
1.24
1.19
1.14
1.09
1.05
1.00
0.81
0.65
0.51
0.39
11
12
1.27
1.22
1.16
1.11
.07
1.02
0.82
0.66
0.52
0.39
12
13
1.30
1.24
1.19
1.14
.09
1.04
0.84
0.67
0.52
0.40
13
14
1.33
1.27
1.22
1.16
.11
1.06
0.85
0.67
0.53
0.40
14
15
1.37
1.30
1.24
1.19
.13
1.08
0.86
0.68
0.53
0.40
15
16
1.40
1.34
1.27
1.21
.16
1.10
0.88
0.69
0.54
0.41
16
17
1.44
1.37
1.30
1.24
.18
1.13
0.89
0.70
0.54
0.41
17
18
1.48
1.41
1.34
1.27
.21
1.15
0.91
0.71
0.55
0.41
18
19
1.52
1.45
1.37
1.31
.24
1.18
0.92
0.72
0.56
0.42
19
20
1.57
1.49
1.41
1.34
1.27
1.21
0.94
0.73
0.56
0.42
20
21
1.62
1.53
1.45
1.38
1.30
1.24
0.96
0.74
0.57
0.46
21
22
1.68
1.58
1.50
1.41
1.34
1.27
0.98
0.75
0.57
0.50
22
N.23
1.74
1.64
1.54
1.46
1.38
1.30
1.00
0.76
0.58
0.54
N.23
126 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
TABLE V.
Correction for rate of chronometer (oscillations).
(The correction is to be added when chronometer was losing and subtracted when gaining.)
Daily
rate.
Time of one oscillation.
3.0
4.0
5.0
6.0
7.0
8.0
9.0
s.
*.
s.
*.
s.
0.
*.
*.
1.0
0.00003
0.00005
0.00006
0.00007
0.00008
0.00009
0.00010
2.0
07
09
12
14
16
19
21
3.0
10
14
17 , 21
24
28
31
4.0
14
19
23
28
32
37
42
5.0
17
23
29
35
41
46
52
6.0
21
28
35
42
49
56
63
7.0
24
32
40
49
57
65
73
8.0
28
37
46
56
65
74
83
9.0
31
42
52
62
73
83
94
10.0
35
46
58
69
81
93
104
20.0
69
93
116
139
162
185
' 208
30.0
0.00104
0.00139
0. 00174
0.00208
0. 00243
0. 00278
0. 00313
3 m 56'.6
0.00821
0. 01095
0. 01369
0.01643
0. 01917
0. 02190
0. 02464
The last line is added for the case in which a sidereal chronometer was used in observing.
TABLE VI.
Torsion factor (oscillations).
(Values of [log 5400-log (5400-ft)] are given in units of the fifth decimal
place; h is expressed in minutes of arc.)
A
0.0
0.1
0.2
0.3
0.4'
0.5
0.6
0.7
0.8
...
1
2
2
3
4
5
6
*6
7
1
8
9
10
10
11
12
13
14
14
15
2
16
17
18
18
19
20
21
22
23
23
3
24
25
26
27
27
28
29
30
31
31
4
32
33
34
35
35
36
37
38
39
39
5
40
41
42
43
43
44
45
46 47
47
6
48
49
50
51
51
52
53
54
55
55
7
56
57
58
59
59
60
61
62
63
63
8
64
65
66
67
68
68
69
70
71
72
9
72
73
74
75
76
76
77
78
79
80
TABLES.
127
TABLE VII.
Reduction of log C 'from 20 C. to other temperatures (deflections).
(The corrections are given in terms of the fifth decimal place in the logarithm.)
Temp.
Corr'n.
Temp.
Corr'n.
Temp.
Corr'n.
Temp.
Corr'n.
+50
10
+25
20
30
-25
1
47.5
11
22. 5
21
- 2.5
31
27.5
2
45 12
20
22
5
32
30.
3
42.5
13
17.5
23
7.5
33
32.5
4
40 14
15
24
10
34
35
5
37.5 15
12.5
25
12.5
35
37.5
6
35 16
10
26
15
36
40
7
32.5
17
7.5 !
27
17.5
37
42.5
8
30
18
5
28 20
38
45
9
27.5
19
+ 2.5
29
22.5
39
47.5
10
+25
20
30
-25
40
-60
TABLE VIII.
Correction for lack of balance of dip needle.
(dl is the difference of the two values of dip from observations before and after
reversal of polarities. The correction is always to be added.)
7
10
20
30
40
45
50
55
60
65
70
75
dl
10
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.02
0.03
0.03
20
0.00
0.02 0.03
0.03
0.03
0.04
0.04
0.05
0.06
0.08
0.11
30
0.00
0.03
0.04
0.05
0.06
0.08
0.09
0.11
0.14
0.18
0.24
40
0.01
0.05
0.06
0.09
0.11
0.14
0.16
0.20
0.25
0.32
0.43
50
0.02
0.08
0.10
0.15
0.18
0.22
0.26
0.31
0.40
0.50
0.67
1 00
0.03
0.10
0.15
0.22
0.27
0.32
0.38
0.45
0.56
0.72
0.97
10
0.05
0. 13 0. 20
0.30
0.36
0.43
0.51
0.62
0.76
0.98
1.33
20
0.07
0.17 0.26 0.39
0.47
0.56
0.67
0.81
0.99
1.28
1.74
30
0.09
0.22
0.33
0.49
0.59
0.70
0.85
1.03
1.26
1.62
2.20
40
0.12
0.27
0.41
0.60
0.73
0.86
1.05
1.27
1.56
2.00
2.71
50
0.15
0.33
0.50
0.73
0.88
1.04
1.26
1.54
1.89
2.42
3.28
2 00
0.17
0. 39 0. 60
0.87
1.05
1.24
1.50
1.82
2.25
2.88
3.91
128 DIRECTIONS FOE MAGNETIC MEASUREMENTS.
TABLE IX.
Diurnal variation of declination.
Month.
Jan., Feb., Nov., Dec.
Mar., Apr., Sept., Oct.
May, June, July, Aug.
Hour.
Sitka.
Ch.
Hon.
P. R.
Sitka.
Ch.
Hon.
P. R.
Sitka.
Ch.
Hon.
P. R.
1
-0.3
-0.2
-0.2
--0.2
-0.2
+0.2
-0.2
-0.2
-0.8
+0.1
-0.1
-0.2
2
-0.1
-0.2
-0.1
-0.3
-0.1
+0.3
-0.1
-0.2
-0.6
+0.2
0.0
-0.1
3
0.0
-0.1
-0.1
-0.3
+0.2
+0.6
0.0
-0.1
-0.2
+0.4
+0.2
0.0
4
+0.1
+0.1
0.0
-0.2
+0.4
+0.8
+0.2
+0.1
+0.9
+0.8
+0.4
+0.2
5
+0.3
+0.3
+0.1
-0.1
+1.1
+1.1
+0.4
+0.3
+2.6
+1.8
+0.7
+0.6
6
+0.5
+0.6
0.0
0.0
+2.1
+1.9
+0.9
+0.8
+4.5
+3.5
+1.9
+1.8
7
+1.0
+1.1
0.0
+0.1
+3.4
+3.3
+2.2
+2.0
+6.2
+5.0
+3.6
+3.4
8
+1.7
+2.1
+1.0
+1.1
+4.7
+4.2
+3.1
+2.6
+7.2
+5.3
+3.5
+3.G
9
+2.2
+2.9
+1.9
+2.3
+4.7
+3.6
+2.7
+2.5
+0.8
+3.9
+2.1
+2.5
10
+1.8
+2.3
+2.0
+2.8
+3.6
+1.7
+1.3
+1.8
+4.4
+0.9
+0.2
+1.0
11
+1.0
+0.5
+0.9
+2.1
+1.7
-1.0
-0.4
+0.6
+0.8
-2.2
-1.5
-0.4
12
+0.1
-1.6
-0.5
+0.5
-0.5
-3.2
-1.7
-0.6
-2.0
-4.3
-2.5
-1.3
13
-0.7
-2.8
-1.4
-0.8
-2.3
-4.2
-2.1
-1.5
-3.8
-5.0
-2.5
-1.9
14
-1.5
-2.8
-1.8
-1.5
-3.0
-4.0
-1.9
-2.0
-5.0
-4.6
-2.0
-2.1
15
-1.6
-2.1
-1.5
-1.7
-3.3
-3.0
-1.4
-1.9
-5.3
-3.4
-1.3
-1.9
16
-1.5
-1.4
-0.9
-1.4
-3.1
-1.7
-0.8
-1.4
-4.6
-2.0
-0.7
-1.4
17
-1.3
-0.6
0.0
-1.0
-2.6
-0.7
-0.5
-0.9
-3.5
-0.5
-0.4
-0.7
18
-0.8
-0.1
+0.1
-0.6
-2.0
-0.4
-0.4
-0.6
-2.2
+0.1
-0.4
-0.5
19
-0.4
+0. 2 +0. 1
-0.3
-1.4
-0.2
-0.3
-0.5
-1.1
+0.1
-0.3
-0.5
20
-0.2
+0.4
+0.2
-0.1
-0.9
0.0
-0.2
-0.4
-0.8
-0.1
-0.3
-0.5
21
-0.2
+0.6
+0.1
0.0
-0.8
+0.1
-0.2
-0.3
-0.7
0.0
-0.3
-0.5
22
-0.2
+0.4 0.0
0.0
-0.7
+0.2
-0.3
-0.2
-0.9
0.0
-0.2
-0.4
23
-0.2
+0.3 0.0
-0.1
-0.7
+0.2
-0.3
-0.2
-0.9
+0.1
-0.2
-0.3
24
-0.2
+0. 1 -0. 1
-0.2
-0.0
+0.2
-0.2
-0.2
-0.9
+0.1
-0.2
-0.2
Sitka, Alaska, 1902-1906. Mean declination, 29 56.6 E.
Cheltenham, Md., 1902-1906. 5 13.9 W.
Honolulu, Hawaii, 1902-190K. 9 20.9 E.
Vieques, Porto Rico, 1904-1906. 1 38. 4 W.
A plus sign indicates that e.ast declination is greater or west declination is less than the mean for the day.
TABLES.
TABLE X.
Diurnal variation of dip.
129
Month.
Jan., Feb., Nov., Dec.
Mar., Apr., Sept., Oct.
May, June, July, Aug.
Hour.
Sitka.
Ch.
Hon.
P. R.
Sitka.
Ch.
Hon.
P. R.
Sitka.
Ch.
Hon.
P. R.
1
-0.2
-0.1
+0.6
+0.2
-0.4
-0.3
+0.6
+0.3
-0.4
-0.1
+0.4
+0.2
2
-0.2
-0.2
+0.6
+0.2
-0.5
-0.3
+0.6
+0.4
-0.4
-0.1
+0.4
+0.2
3
-0.2
-0.2
+0.6
+0.2
-0.6
-0.3
+0.6
+0.2
-0.4
-0.1
+0.5
+0.2
4
-0.2
-0.2
+0.4
+0.2
-0.6
-0.3
+0.5
+0.2
-0.4
0.0
+0.5
+0.2
5
-0.2
-0.3
+0.4
0.0
-0.6
-0.4
+0.5
+0.2
-0.5
-0.1
+0.6
+0.2
6
-0.3
-0.3
+0.2
0.0
-0.5
-0.3
+0.6
+0.2
-0.6
-0.1
+0.8
+0.2
7
-0.2
-0.2
0.0
-0.2
-0.4
0.0
+1.0
-0.1
-0.4
+0.2
+0.9
-0.2
8
-0.2
-0.1
0.0
-0.5
-0.2
+0.5
+1.1
-0.4
-0.2
+0.8
+0.4
-0.3
9
-0.2
+0.2
0.0
-0.6
+0.2
+1.0
+0.6
-0.6
+0.2
+1.3
-0.3
-0.6
10
+0.1
+0.6
-0.4
-0.7
+0.6
+1.2
-0.4
-0.8
+0.8
+1.3
-1.0
-0.7
11
+0.4
+1.0
1.0
-0.7
+1.0
+1.1
-1.4
-0.9
+1.0
+0.8
-1.4
-0.8
12
+0.7
+1.0
-1.4
-0.6
+1.2
+0.7
-1.8
-0.8
+1.2
+0.2
-1.5
-0.8
13
+0.8
+0.7
-1.4
-0.2
+1.2
+0.3
-1.8
-0.6
+1.1
-0.4
-1.3
-0.5
14
+0.8
+0.4
-1.2
0.0
+1.0
0.0
-1.4
-0.4
+0.8
-0.7
-0.9
-0.1
15
+0.5
0.0
-0.7
+0.2
+0.6
-0.3
-0.9
0.0
+0.4
-0.7
-0.6
+0.2
16
+0.2
-0.2
-0.2
+0.4
+0.3
-0.3
-0.4
+0.2
+0.1
-0.6
-0.3
+0.4
17
-0.1
-0.3
+0.2
+0.4
0.0
-0.3
0.0
+0.4
-0.2
-0.3
+0.1
+0.5
18
-0.2
-0.3
+0.4
+0.3
-0.2
-0.3
+0.2
+0.4
-0.4
-0.2
+0.2
+0.4
19
-0.2
-0.2
+0.4
+0.3
-0.3
-0.3
+0.2
+0.4
-0.3
-0.2
+0.3
+0.4
20
-0.2
-0.2
+0.4
+0.2
-0.4
-0.3
+0.4
+0.4
-0.3
-0.2
+0.4
+0.3
21
-0.2
-0.2
+0.5
+0.2
-0.4
-0.3
+0.4
+0.4
-0.3
-0.2
+0.4
+0.2
22
-0.2
-0.2
+0.6
+0.2
-0.4
-0.3
+0.4
+0.3
-0.2
-0.2
+0.4
+0.2
23
-0.2
-0.2
+0.6
+0.2
-0.4
-0.3
+0.4
+0.2
-0.4
-0.2
+0.4
+0.2
24
-0.2
-0.2
+0.6
+0.2
-0.4
-0.3
+0.4
+0.2
-0.4
-0.2
+0.4
+0.2
Sitka, Alaska, 1905-6. Mean dip, 74 42.1
Cheltenham, Md., 1902-6. 70 24.2
Honolulu, Hawaii, 1905-6. 40 03.9
Vieques, Porto Rico, 1905-6. 49 19.6
A plus sign indicates a value greater than the mean for the day.
7721311 9
130 DIRECTIONS FOR MAGNETIC MEASUREMENTS.
TABLE XI.
Diurnal variation of horizontal intensity.
Month.
Jan., Feb., Nov., Dec.
Mar., Apr., Sept., Oct.
May, June, July, Aug.
Hour.
Sitka.
Ch.
Hon.
P.R.
Sitka.
Ch.
Hon.
P.R.
Sitka.
Ch.
Hon.
P.R.
1
+ 1
+ 3
- 5
-3
+ 6
+ 5
- 5
- 3
+ 7
+ 3
- 5
- 4
2
+ 2
+ 4
- 5
-2
+ 7
+ o
+ 5
+
- 4
A
- 2
+ 7
+ ff
+ 2
+
- 4
- 3
o
4
+ 3
+ 5
- 3
+ 8
+ 6
4
- 3
_
7
+ 8
<fi
+ 2
4
- 4
o
- 2
5
+ 3
+ 6
- 3
+1
+ 8
+ 6
- 2
+ 9
+ 3
- 4
- 2
6
+ 3
+ 6
- 1
+3
+ 7
+ 6
- 2
+ 1
+ 9
+ 4
- 3
7
+ 3
+ 5
+ 3
+7
+ 6
- 3
+ 2
+ 7
- 2
- 1
8
+ 3
+ 1
+ 5
+9
+ 2
- 9
- 4
+ 2
+ 1
-14
+ 3
+ 2
9
- 5
+ 6
+8
- 5
-19
- 2
+ 5
- 7
-24
+ 5
+ 7
10
- 4
-13
+ 8
+6
-11
-24
+ 3
+ 8
-17
-26
+ 8
+12
11
- 8
-21
+11
+5
-17
-23
+ 8
+10
-21
-19
+ 9
+14
12
-11
-20
+10
+2
-19
-16
+12
+10
-22
- 8
+10
+12
13
-12
-14
+ 8
-2
-18
- 8
+13
+ 8
-19
+ 4
+10
+ 8
14
- 9
- 6
+ 5
^3
-13
+11
+ 3
-13
+12
+ 9
+ 4
15
- 5
+ 1
+ 2
-4
- 8
+ 5
+ 7
- 1
- 5
+14
+ 5
- 1
16
- 1
+ 6
4
- 3
+ 8
+ 2
- 4
+ 1
+13
+ 2
- 6
17
10
+ 3
+ C
+ 6
- 3
-4
+ 1
+ 6
- 2
- 5
+ 5
+ 8
- 2
- 8
lo
19
O
+ 5
+ 5
- 5
-4
+ 6
+ 7
- 3
- 4
+ 6
+ 4
- 5
- 6
20
+ 4
+ 5
- 5
-3
+ 6
+
- 4
- 4
+ 5
+ 4
- 5
- 5
21
+ 4
+ 4
- 6
-3
+ 6
+
- 5
- 4
+ 5
+ 4
- 5
- 5
22
+ 3
+ 3
- 6
-2
+ 6
+
- 5
- 4
+ 6
+ 4
- 5
- 4
23
+ 2
+ 4
- 5
-2
+ 6
+
- 4
- 3
+ 6
+ 4
- 4
- 4
24
+ 3
+ 4
- 5
-1
+ 7
+
- 4
- 2
+ 7
+ 4
- 4
- 3
Sitka, Alaska, 1902-6. Mean horizontal intensity, 15491
Cheltenham, Md., 1902-6. 20121
Honolulu, Hawaii, 1902-6. 29245
Vieques, Porto Rico, 1903-6. 29278
A plus sign indicates a value greater than the mean for the day.
TABLES.
TABLE XII.
Multiples of the sines of the angles 22. 5, 45, and 67. 5.
131
22.5
45
67.5
22.5
45
67.5
1
0.38
0.71
0.92
51
19. 52
36.06
47.12
2
0.77
1.41
1.85
52
19.90
36.77
48.04
3
1.15
2.12
2.77
53
20.28
37.48
48.97
4
1.53
2.83
3.70
54
20.66
38.18
49.89
5
1.91
3.54
4.62
55
21. 05
38.89
50.81
6
2.30
4.24
5.54
56
21.43
39:60
51.74
7
2.68
4.95
6.47
57
21.81
40.31
52.66
8
3.06
5.66
7.39
58
22.20
41.01
53.59
9
3.44
6.36
8.31
59
22.58
41.72
54.51
10
3.83
7.07
9.24
60
22. 96
42.43
55.43
11
4.21
7.78
10.16
61
23.34
43.13
56.36
12
4.59
8.49
11.09
62
23.73
43.84
57.28
13
4.97
9.19
12.01
63
24.11
44.55
58.20
14
5.36
9.90
12.93
64
24.49
45.25
59.13
15
5.74
10.61
13.86
65
24.87
45.96
60.05
16
6.12
11.31
14.78
66
25.26
46.67
60.98
17
6.51
12.02
15.71
67
25.64
47.38
61.90
18
6.89
12.73
16.63
68
26.02
48.08
62.82
19
7.27
13.44
17.55
69
26.41
48.79
63.75
20
7.65
14.14
18.48
70
26.79
49.50
64.67
21
8.04
14.85
19.40
71
27.17
50.20
65.60
22
8.42
15.56
20.33
72
27.55
50.91
66.52
23
8.80
16.26
21.25
73
27.94
51.62
67.44
24
9.18
16.97
22.17
74
28.32
52.33
68.37
25
9.57
17.68
23.10
75
28.70
53.03
69.29
26
9.95
18.38
24.02
76
29.08
53.74
70.21
27
10.33
19.09
24.94
77
29.47
54.45
71.14
28
10.72
19.80
25.87
78
29.85
55.15
72.06
29
11.10
20.51
26.79
79
30.23
55.86
72.99
30
11.48
21.21
27.72
80
30.61
56.57
73.91
31
11.86
21.92
28.64
81
31.00
57.28
74.83
32
12.25
22.63
29.56
82
31.38
57.98
75.76
33
12.63
23.33
30.49
83
31.76
58.69
76.68
34
13.01
24.04
31.41
84
32.15
59.40
77.61
35
13.39
24.75
32.34
85
32.53
60.10
78.53
36
13.78
25.46
33.26
86
32.91
60.81
79.45
37
14.16
26.16
34.18
87
33.29
61.52
80.38
38
14.54
26.87
35.11
88
33.68
62.23
81.30
39
14.92
27.58
36.03
89
34.06
62.93
82.23
40
15.31
28.28
36.96
90
34.44
63.64
83.15
41
15.69
28.99
37.88
91
34.82
64.35
84.07
42
16.07
29.70
38.80
92
35.21
65.05
85.00
43
16.46
30.41
39.73
93
35.59
65.76
85.92
44
16.84
31.11
40.65
94
35.97
66.47
86.84
45
17.22
31.82
41.57
95
36.35
67.18
87.77
46
17.60
32.53
42.50
96
36.74
67.88
88.69
47
17.99
33.23
43.42 ,
97
37.12
68.59
89.62
48
18.37
33.94
44.35
98
37.50
69.30
90.54
49
18.75
34.65
45.27
99
37.89
70.00
91.46
50
19.13
35.36
46.19
100
38.27
70.71
92.39
Propor-
tional parts.
22.5
0.1
.04
.2
.08
.3
.11
.4
.15
.5
.19
00
.7
. / '
.27
.8
.31
.9
.34
45
0.1
.07
.2
.14
.3
.21
.4
.28
.5
.35
.6
.42
.7
.49
.8
.57
.9
.64
67.5
0.1
.2
.7
.18
.37
.46
.55
.65
.74
.83
NIVERSJTY OF CALIFC-NL1 LIBRARY
BERKELEY
THIS
expiration of loan peHod. apphcatlon is made before
.
20m-ll,'20
UNIVERSITY OF CALIFORNIA LIBRARY