Rodolfo Amedeo Lanciani.

The American journal of science and arts online

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j)lace. This heat and light force has been in its natural opera-
tions opposed to the force of gravitation, and so essentially a
separating and decomposing force. It has been the great physi-
cal agent m all the processes of vegetable and animal life. It has
ever been passing through cycles of transformation into other
physical forces, but in all its transformations the entire amount
of energy, actual and potential, has remained invariably the same.
Chemical combination, the electric current, liquefaction, and so-
lidification, are instances of motion directly due to the general
gravitating force operating on the electric ether. All motions
of translation or rotation of bodies at the earth*s surface are
traceable directly to the same force, or to that of heat repulsion
and therefore indirectly to that of gravitation. We may accord-
ingly lay down the postulate, that the entire circle of what are
termed physical forces have originated in the living force of the
motions of condensation that have resulted from the natural
operation of the general gravitating force, initiated at the dawn
of creation and continued through all time. The very process
of formation, by gradual condensation, of the worlds that peo-
ple immensity, has developed the natural forces which have
presided and continue to preside over all the processes of chanffe
that diversify and beautify their surfaces, and fit them to be the •
abodes of hving beings. These diverse natural agents are
but the offspring of the one overshadowing force, which, in
the progress of countless ages has formed all worlds out of the
primordial material fashioned by the Hand of the Creator. We
may indeed, as we have seen^ rise to a still greater height of
conception, and refer this universal force to a primal force of
cosmical repulsion, associated by the Infinite Spirit, the Source
of all Power, with every atom of the one primeval matter that
fills immensity, and is the elementary substance of all worlda



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jET. M. Parkhurst on the Pkoto-Tnapper. 87



Art. IV. — The Photo-mapper; by Henry M. Parkhurst.

It is a remarkable fact that while vision is by far the laost
accurate of our senses, aiding us almost exclusively in obtain-
ing accurate measures, we have as yet discovered no method of
measuring the intensity of light The method of measuring
the brightness of a star by extinction, for example, is in fact
merely a method of assistmg the eye in estimation. If we were
to measure the diameter of a sphere by removing it to such a
distance that it should cease to be visible and multiplying that
distance by a certain constant ; or by subdividing it until we
could divide it no longer, or until the atoms should have no ap-
preciable weight, and multiplying by a constant ; it would be
analogous to determining the brightness of a star by ascertain-
ingwnat proportion of its light is too small to affect the retina.

The true mode of measurement is by substraction of certain
known quantities. To illustrate the advantage of this, were
the difference of brightness of Arcturus and Capella but .01™,
that difference would be visible to the naked eye ; and were it
but ,0001™, it would be easily visible with telescopic aid.
Could we construct a glass which would transmit, not a certain
proportion of the whole light of a star, but all its light exceed-
mg a certain absolute quantity, it would aflbrd us a perfect pho-
tometer. Or could we construct a glass which should transmit
polarized light, but which would not transmit common light,
that would accomplish the same result But in the mean time
we may be allowed to designate estimations assisted by mechan-
ical means as measures of the magnitude of a star.

My first experiments in determining by mechanical means
the magnitude of stars observed in zones, and recording that
magnitude at the time of observation on star-maps taken by
the instrument described in the Journal for September, were
made in 1865. I then constructed a hexagonal diaphragm so
arranged that a series of six plates over the object glass, moved
simultaneously by a lever extending the length of the telescope,
gradually diminished the aperture until the star ceased to oe
visible. I connected this lever with the system of levers ope-
rated by the star-key, and recorded upon the map, in the same
right-ascension with each star, a point whose position indicated
the aperture at the moment of extinction, and therefore gave
by a prepared scale the magnitude of the star.

My next step was to avoid the long and cumbrous lever by
adopting the principle of the apparatus invented by me in 1860,
and which I term a Bar Photometer, reducing the cone of light
fix>m a star at a point intermediate between the object-glass and
its focus, instead of directly reducing the aperture at the object-



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88 H, M. ParhhuTst on the Photo-mapper.

At a convenient point, say one-eighth of the distance fix)m
the focus to the object-glass, I place in the meridian a straight
bar one-eighth of the diameter of the object-glass in wicWi.
Clamping the telescope a little to the west of a star, the cone of
light IS OTadually intercepted by the bar, and gradually re-ap-
pears. The time during which the star is extinguished, or dur-
mg which it remains of less brightness than a standard artifi-
ci5 star in the field, indicates the brightness of the star by the
proportion of the light cut off by the bar at the moments of
occultation and reappearance.

A modification of this plan, is to make the bar wider, so that
it shall become a diaphragm, with a central aperture of the
width of the cone of rajrs, observing the duration of appari-
tion instead of the duration of occultation of the star.

By either of these methods the scale may be made one of
equal parts by a device similar to that which will presently be
explained. With or without such a device, this method is well
adapted for observations of small variable stars, requiring no
apparatus but the bar, whose distance fi'om the focus shsdl be
so determined that photometric accuracy shall not be sacrificed,
while there shall be no unnecessary consumption of time. In-
deed a plain Bar Photometer can at any time be extemporized
in a few minutes. Its adjustment in width or distance is not
essential, because its position and width can be determined and
the proper connections made without difficulty after the obser-
vations.

A further modification of this plan, is to revolve the dia-
phragm 90°, and make it movable in declination, occultating
the star on both sides of the center of the field, the magnitude
being indicated by the extent of the motion, which mav be con-
veniently and accurately measured, with a dim light, by a pair
of dividers.

By a still fiirther modification, the motion of the diaphragm
may be produced, by means of intermediate levers, by tne star-
key of my star-mapper ; and this constitutes the Photo-mapper,
which I will now more particularly describe.

The diaphragm is moved parallel to itself in an arc corres-
ponding to that described by the star-point and star-key, being
supported and guided by two parallel bars whose bearings are
screwed to the east side of the telescope tuba The diaphragm
being seven-eighths of the distance fi'om the object-glass to its
focus, the length of the supporting bars is seven-eiffhths of the
radius of the star-point As 1 use a camera-prism, which slightly
shortens the focus, I have, in mv instrument, made the proper
corrections, but need not here rerer to details of that descnption.

On the same center with the star-point, and star-point-bar,
shown in fig. 1 of my article on the Star-mapper, is another bar



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H. M. Parkkwrst en the Photo-mapper. 39

placed parallel to the axis of the telescope, pointing toward
the object-glass. The farther end of this magnitude-bar is con-
nected at right angles by a connecting-rod witn universal joints,
with the upright arm oi a lever, the lower arm of which is the
lower supportmg-bar. The length of this upright arm and of
the magmtude-bar must be equal In photo-mapping I place
the prism always in the meridian, to avoid the complicated ad-
justments which would be necessary if its position were to be
varied.

As the diaphragm will move seven-eighths as fast as the star-
point, it is evident that if it is so adjusted that it will not inter-
cept any of the light of a star in the center of the field when,
tiie star-point is brought to the declination of that star, then in
mapping a northern or southern star in the field its light will be
unobstructed. But moving the star-key to the north or south
of a star will intOTcept part of its rays. The light of the star
being thus equalized with that of a standard artificial star, or
extinguished, as the case may be, a magnitude mark is impressed
on the paper. The star is then mapped in its proper position,
and the distance upon the map, of the magnitude mark from
the corresponding star, will be the measure of the magnitude
of that star.

A perpendicular plate, with a circular hole through which the
connecting-rod passes, furnishes a convenient point from which
to measure with dividers when the instrument is used without
the mapper.

Thus fiir I have spoken of the " cone " of rays, as if the aper-
ture were circular. If it were so, the scale of magnitudes
would not be one of equal parts. It may be made one of equal
parts by placing over the ooject-glass an outer diaphragm with
an aperture of suitable form, and making the aperture of the
inner diaphragm of corresponding form.

Let x=2*5[y] be the equation of a logarithmic curve. Then,
the area between any two ordinates of that curve will be
2'5M Ay ; M being Modulua Constructing for the obiect-glass
of 6 inches aperture a diaphragm bounded by four such curves,
with values of x ranging from — 1*5 inches to +1'5 inches, lay-
ing oflF a; vertically, above and below the center, and y to the
right and left, and a similar inner diaphragm of one-eighth the
lineal dimensions, neglecting for the present the portion of the
curve which will pass outside of the circle, it will be seen that
the motion of each one-fourth of an inch of the inner dia-
phragm will leave an area corresponding to stars exactly one
magnitude smaller. The motion of the star-point will be one-
aeventh greater, and of the star-key still greater, according to
the scale of the map.
But while the object-glass is limited, the inner aperture may



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40 H, M, Parhhurat (m the Photo-mapper.

extend beyond the corresponding circle of one-eightli the diam-
eter. If therefore an area equal to twice the omitted portion of
the curves above and below is added to the inner diaphragm,
it wUl be almost immediately available, and the omission from
the outer aperture will cause an error of less than 1", and that
only at the commencement of the scale. The proper form of
this added portion is the inversion of the last l-™2 of the curve
within the circle, the final value of y being exactly three times
its value at the margin of the disk.

With the diaphragms thus constructed, the scale runs through
3*™0 as a scale of equal parts. Beyond that point the star may
still be extinguished, if not too near the center of the field ;
but the scale will be condensed..

The stars occurring in any zone may be divided into three
classes: those above the 6 -"5 being approximately measured
by the condensed scale, and being so few in number that they
may be conveniently, as well as more accurately, measured by
a different method, to be explained below ; those between the
6 '"5 and the 9*°5, which may be equalized in brightness with
an artificial star in the field previously brought to an equality
with a 9 '"5 star ; and those fainter than the 9 '"5, which may be
extinguished. The outer diaphragm will so diminish the aper-
ture mat 12 -"S stars will be tne smallest which can be seen.

The Disk Photometer. — For the brighter stars I employ an en-
tirely different apparatus, based upon a more accurate method.
I expand the stars into disks by drawing out the eye-piece be-
yona the focus, until a portion of the disk shining through an
aperture in the field of view shall either be exactly equal in
brightness with an adjacent luminous disk, or be imperceptible.
The extinction of a disk by expansion is only practicable with
a small aperture or with telescopic stars, and is not much, if
any, more accurate than extinction by reducing the aperture.
But comparison of disks, especially for the stars visible to the
naked eye, is the most accurate means of measurement known
to me, the error of the comparison being in my experience less
than the inequalities of the artificial disk, and the latter much
less than those of the sky.

The star and the disk can be compared, if desired, by the aid
of polarization, by the use of a double-refracting prism to com-
bine the two disks into one, and a selenite plate and another
double-refracting prism to form new colored disks ; but instead
of producing the final adjustment by further polarization, the
bundle of plates may be dispensed with, and the disks render-
ed colorless by the motion of the eye-piece.

For convenience I have made a slide with six equal open-
ings, to shade the disk with neutral shades, and a slide to shade
the star. I ascertained that one shade was equivalent to 1*°*08,



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H, M. Parhkurst on the Photo-mapper. 41

and that, although I admit the rule would not be accurate with
colored shades, five neutral shades were equivalent to 5*"15.
It is therefore convenient to compare directly stars differing as
much as « and A Ursae Minoris. In order to neutralize the yel-
low color of the artificial disk, and to make it appear indistin-
ffuishable fi:om the visible portion of the disk oi a star, I have
found it necessary to use a blue shade. I have extended the
telescope by various tubes, sometimes nearly two feet ; but with
the use of the slides I find that a tube five inches long to hold
the eye-piece, usually gives sufficient extension to the telescope
and sufficient range of brightness. The amount of the exten-
sion I measure with dividers, using a prepared scale which
gives directly, in magnitudes, the difference in brightness be-
tween the observed star and a standard depending on the bright-
ness of the disk.

The disk photometer is especially useful for observing the
brighter variable stars. It is inapplicable for determining the
brightness of stars so close together that the space between
them is not sufficient for a disk ; but in this case it may be used
to determine the aggregate brightness of the two stars. It may
be used for measuring the brightness of planets, small nebulfie
and comets, probably of the moon, and possibly of the sun.

The same apparatus may be used to determine the compara-
tive brightness of different portions of the sky, but requires a
different process.

The error of the determination of the magnitude of a star
by the method of equalizing disks, may be divided into four
parts:

L The error of the assumed magnitude of comparison stars.
In my series of observations, instituted to determine the rela-
tive amount of the several errors, this error hardly exceeds ""'Ol.

n. The error of observation, or inaccuracy of judgment as to
the e±act point where the disks are equalized. Not only accor-
ding to the statements of Arago, Silliman, and Crookes, redu-
ced by myself, but according to my own results, the error of
observation — ^I refer to the mean error — does not exceed "02,
in a series of stellar observations averaging forty to the hour.
For feinter stars than I observed in my series, the error of ob- '
servation is greater. There are three limitations :

1. One disk cannot be distinguished in brightness from an-
other, unless one-sixtieth brighter or fainter, according to Arago.

2. One disk cannot be distinguished as brighter than another,
if the subtraction of the light of the fainter disk from the other
would leave a disk too faint to be visible by itself. The same
principle is applicable to points of light U nless, therefore, the
aisk is at least sixty times as bright as is necessary for visibil-
ity, the error of observation will be greater.



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42 H, M. Parkhurat on the Photo-mapper.

8- If the disk is small, the accuracy of comparison is im-
paired Hence points of light cannot be as accurately compared
as disks. I have used a disk of an apparent magnitude of at
least I'', and have not investigated the amount of error with a
smaller disk.

UL The error fix)m the variation of the artificial disk during
observation. I have made many and careful experiments to
render this error as small as possible, and to avoid ascribing to
the irregularity of the sky discrepancies which might be owing
to variations of the artificial disk The brightness of the arti-
ficial disk may vary from four causes :

1. The illuminating quality of the gas may vary. Hence
observations on different evenings cannot be compared directly.
But the change of the gas will be so slow, excepting probably
from the heating of the apparatus when it is first lighted, as not
to appreciably affect the results.

2. From variation of the pressure the flame may be made
larger and brighter. I first partially corrected this by forming
upon the screen an image of a circle of the flame 05 in. in di-
ameter. I afterwards made a gas regulator, admitting the gas
into an inverted receiver suspended at one end of a lever, the
other end of which gradually shut off the gas as the receiver
rose ; so that whatever the pressure of gas in the mains there
should be no variation in the flame.

3. The flame varies in different parts. Hence, if on turning
the telescope upon a new star the lantern is not accurately ad-
justed to a horizontal position, a brighter or fainter portion of
the flame will come opposite the aperture. The flame as a
whole having been made uniform by tne regulator, I have intro-
duced a smoothly ground glass at the aperture nearest the flame,
and reduced the flame and mov^ it turther back, so as to use
the whole flame.

4. The light from the star is a sharp cone, wholly entering
the eye even if withdrawn several inches from the eye-piece.
The light from the illuminated screen is a hemisphere. Unless
therefore the eye-piece renders the rays parallel, which it will
not if the observer is either near-sighted or far-sighted, a differ-
ence in the distance of the eye will greatly affect the results.
I have therefore turned the plane glass in the eye-piece so as to
throw the light directly into the eye, reducing the aperture of
the lenses so that the cone of rays from the artificial disk near-
ly corresponds with that from the star. It is necessary that the
eye should be held so that both cones shall completely enter it
at once, which can be easily accomplished but requires care.

The error from the variation of the artificial disc, without the
gas regulator, I ascertained not to exceed ">"04. How much
this has been reduced by introducing the regulator and ground
glass screen, I have no means of estimating.



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W. D. Alexander en the Orater of ffaleaJcala. 43

IV. After allowing for the previous errors, amounting in the
aggr^ate to less than «n'05, the remaining discrepancies of ob-
servation of invariable stars must arise trom variations of the
apparent brightness of the stars from atmospheric obscuration.
I oivide this into two parts :

L The general and permanent obscuration depending on the
altitude of the star. I have ascertained that tnis follows the
law of refiraction; but the coefficient varies in amount on dif-
ferent evenings, sometimes eaualling ">*oO for an altitude of 20®,
and at other times not exceeoing one-third that amount I ap-
ply the correction for obscuration to each star, in reducing the
obBcrvations, so as to eliminate this ; and I therefore regard it
as no part of the error of observation. The correction may be
easily applied without directly determining the altitudes, by a
prepared scala

2. The temporary and local obscuration, from various atmos-
pheric causes. By more than 400 observations of 18 stars of the
2nd to the 4th magnitude, « Persei and y Arietis being the ex-
tremes, I found that the average mean error of an observation, from
all causes, amounted to "»'ll ; so that the mean error from the tem-
porary and local obscuration alone is on the average "» '10. There
IS a great difference between different days ; the average mean
error of all the stars being sometimes as low as '"O? for a whole
evening, and at other times for an evening apparently equally
dear, as high as «»*20. The difference between the stars is no
less conspicuous. The stars b and y Persei are near each other,
and nearly of the same brightness. Yet the mean error of an
observation of y Persei, assuming it to be an invariable star, is
nearly three times as great as of « Persei

It 13 evident therefore that if the results I have reached are
even approximately correct, the errors of observation and of
the instrument, if ordinary care is used, are of no material con-
sequence ; and accurate results can only be obtained by multi-
plying observations on different evenings, so as to eliminate as
ikr as possible the errors arising from the variations of the sky.



Abt. V. — On the Crater of ffaleakala, Island of Maui^ Hawaiian
Group; by Prof W. D. Ai^exander. (From a letter to one
of the Editors.)

I flAVE just been spending a summer vacation on Maui, and
in the course of it made a careful survey of the great crater of
Haleakala. During the vacation I went three times to the sum-
mit The first time I rode up from Makawao before sunrise, and
spent about seven hours in collecting mineral specimens and



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44 W, D. Alexander on the Orater of Haleakala,

plants, and forminff a plan for the survey of the crater. The
flora of this region nas been described befora I will only say
that the principal plants that survive on the bleak summit are
the Argyroxiphium^ Baillardia mo7itana^ ViUadinia^ and some
stunted ferns, viz : Pteris aquilina and Trichomanes, In the
belt between one and four miles from the summit, in addition
to the above, are found the beautiful Geranium cuneatum^
Sophora chrysophylla, Sandalwood, Coprosma, and a few ohelos
( Vacdmum reticulatum). Water boiled at 193° Fahrenheit when
the atmosphere was at 46° Fahrenheit At sunrise we enjoyed
the grand sight of the vast triangular shadow of the mountain
projected on the clouds in the western sky.

On the morning of August 4th, I ascended the mountain again
fix)m Makawao, with five natives, and furnished with a superior
theodolite, a dozen large bamboos for signal poles, a good tent,
and provisions for a week. We spent seven days on the moun-
tain, and enjoyed almost uninterrupted fine weather.

We commenced operations by setting signals on the prom-
inent points along the western side of the crater. The west-
em cliffs are very steep, though it is possible to descend in
many places, and are from 2,000 to 2,500 feet high. We
pitcned our tent on the lee side of a hill near the southwest
comer, called by the natives " Pakaoao " or the " fortress of
Kaoao." This nill is composed of a light gray solid clink-
stone, which splits into lammse like slate.

It has been much shattered, probably by the terrible convul-
sions that attended the opening of the Koolau gap, and for a
quarter of a mile toward the northwest the ground is strewed
with fragments of rock that have been hurled in that direction.
These rocks form a striking contrast with the darker and more
basaltic rock to the northward The same formation crops out
on the east side of the Koolau gap, at the southern foot of
Hanakauhi in the oasis surrounded by recent lava, at which
place it projects from the hill side in the form of huge perpen-
dicular slabs or lamellar masses, not more than ten feet thick,
and from thirty to fifty feet high, standing out of the grassy
slope like immense grave stones. The patches of gravel on the
summit contain numerous crystals of augite. The hill called
the fortress of " Kaoao " is partially terraced on the lee side,
and is covered with hundreds of little inclosures built of stone,
three or four feet high, and paved with thin flat pieces of clink-
stone. I noticed that a few had been covered over with a kind
of slate roof Here, according to tradition, encamped the army
of Kaao, a chieftain who had been driven out of Kaupo by his



Online LibraryRodolfo Amedeo LancianiThe American journal of science and arts → online text (page 6 of 109)