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case in the history of science.

The law of Titius was exclusively derived from observation.
It is empirical, as is the third law of Kepler. It is, moreover,
not exact, neither in its general form nor in its numerical results.
But neither is the famous law of Kepler exact, though, on ac-
count of the different circumstances connected herewith, this
latter law agrees better with the numerical data of observation
than Titius's law.

Newton discovered the true form of Kepler's law by deducing
it from a higher law, that of universal gravitation. Instead of
Keplers form, C being the same constant for all planets,

ll=C,. .... (70)

Newton fouad that the true law is

ii'=£5(M + «). . , . (71)

itt being the constant of gravitation, hence the same for all plan-
ets; hence,

Ca(M+m). . . . (72)

That is, Kepler's constant C is proportional to the sum of the
mass M of the sun and the mass m of the planet. By farther
analysis it is found that C even is dependent on aU the masses
and distances in the system.

So also in our case. We have given the true expression of
Titius's law by extending it to Mercury and have accounted for
the deviations of nature from the law, by demonstrating that it
is a necessary consequence of the higher law, viz : tlie intervals
between the abandonment of the different orbs of the same system are
equal (see § 13). Now tfiis is what we claim as our law. As Newton
deduced and corrected Kepler's law by his law of equal gravita-
tion^ so we have deduced and corrected the law of Titius by our
law of equal intervals.



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O. Hinricks an Planetology. 285

We referred to (38) as our " law" because it is a coTisequence of
our law, and certainly our formula ; we did not intend to oblit-
erate the merit of Titius, as will be seen wherever we have men-
tioned his name.

There is yet another circumstance which makes our demon-
stration of the law of planetary distances so important . It is
the touchstone of the nebular theory ; for as this ascribes the
formation of the planets to the slow descent of cosmical matter
to its center, it has to be proved that such descent will give
exactly the actual system. Already Plato held that' "the mo-
tion of the planets is such as if they had been all created by
God in some region very remote from our system, and let fall
from thence toward the sun, their falling motion being turned
aside into a transverse one whenever they arrived at their sev-
eral orbits." Galileo was the first who subjected this *' concetto
{)latonico" as he calls it to a numerical calculation based upon the
aws of falling bodies as discovered by him. He finds an admir-
able harmony between his calculations and the actual velocities
and distances as they were known at his time.' Next after him,
Newton took the matter in hand, and in his third letter to Dr.
Bentley he gives as his result, that it is impossible to account for
the configuration of the system in the manner of Plato and Gal-
ileo. This result is based upon his assumption of a vacuum.
By taking the influence of a resisting medium into account, we
have proved that the Platonic idea as embodied in the nebular
hypothesis does lead to the present configuration of the solar
world. We make these remarks to show that the idea we advo-
cate is old and venerable ; we hope, at some other time, to give
the highly interesting history of the law of planetary distances,
including the application of the Phyllotaxis, (Pierce, Agassiz,)
the radius of gyration, (Kirkwood,) the regular polyhedra,
(Kepler, Plato,) etc.

Mow grand and beautiful is the harmony of the planetary
world 1 What an admirable unity of plan is manifestea therein !
As now the planets are slowly sinking to the sun, so they have
cdways been sinking since the moment of their creation as a neb-
ulous mass ; the same motion that now brings them nearer to
their death has caused their formation, has brought them to life !
And how sublime is the plan of creation I To call forth the
harmonious system of the solar world with all its multiform as-
pects and dependencies fit to support life throughout almost end-
less ages — nothing but a collection of matter endowed with its

' Brewster, Life of NevBton^ Ch. 16.

' Dialogo intomo ai due mcuntni Sittetni del Mondo, ToUmeico e Copemicatuh
Gjornata I, (ed. Opere, Fireoze, 1842. Vol. i, p. 84-85.) He lincls: le graodezze
del cercbj, e le yelocitd del moti s'accostano tanto prossimamente a quel che ne dan-
no i oomputi, che h cosa mararigliosa.

▲m. Jous. Sci. - Sboond Sibixs, Vol. XXXIX, No. 117.— Mat, 1865.
37



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286 H. A. Newton on the height of Auroral Arches.

molecular forces was placed in a little spot of the house that con-
tains many mansions besides. This matter slowly collected to-
gether, in thus following the force of attraction planted in it
by eternal love, the whole great life of the solar world was
awaked ; and as the pulsation of the heart in man indicates the
fleeting moments of his life, so the pulsations of that great whole,
succeeding each other at equal intervals, gave each one birth tx>
a new world to mark the historic epochs of the Universe by its
position and to roll on for ages, a revelation of the Great Au-
thor, until, always following the same attractive force, it in death
finds rest at the bosom of the planet-mother, the sun. And
then — this grand system remains as a mere lump, a Cosmic Fossil,
suspended in space, where perchance some higher being may
meet with it, touch it, investigate it, and construct its whole past
history, as the geologist in our days studies the history of a
fossil shell I
Iowa City, Iowa, July— November, 1864.



Art. XXXV. — Tlie determination of the height of Auroral Arches
Jrom observations at one place ; by H. A. Newton.

In the dinplays of the Aurora Borealis the luminous cloud
often takes the form of an arch. Sometimes the lower boundary
of the auroral light is arch-shaped. Beneath is a dark segment,
while perhaps streamers run upward from the mass of light.
Again, there is sometimes a bank of light in the north, resting
apparently on the horizon. The upper boundary of this bank
forms a more or less regular arch. Again, there is sometimes a
narrow band or bow of light, spanning the heavens, coming
down to within two or three degrees of the horizon at each ex-
tremity, having one or both of its edges sharply defined, and
being often only two or three degrees in bread tn.

The arch in each of these three cases may be incomplete, or
broken, or otherwise irregular. But there is a manifest tendency
to form a regular curve. This curve, that is, the boundary
line of the arch, or the axis of the bow, is rarely, if ever, an
arc of a great circle. It cuts the horizon at points notably less
^than 180 from each other. It has apparently the same law of
formation in each of the three cases. Its peculiar shape is there-
fore probably due to a single cause.

There is no reason to believe that each observer sees a differ-
ent arch, just as each sees his own rainbow. There is no center
of light beneath the arch, and moreover a decided parallax is
very frequently found. The curve of the auroral arcn has then
a definite locus in the atmosphere.



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ft A, Newion on the height of Auroral Arches. 1^7

This curve is not caused by mists in the atmosphere obscuring
and revealing parts of an indefinite cloud. For the arch has
little or DO relation to the horizon, and cuts it at all angles.

It is not a straight line, for the arch does not cut the horizon
at points 180° from each other.

The arch resembles the projection of a portion of a circle, or
a sphero-conic. The venerable Hansteen nas in two instances
seen at Christiana nearly the whole ellipse. Prof. Twining has
observed, at Middlebury, Vt, in one instance at least, an arch in
which the extremities of the major axis of the ellipse were vis-
ible above the horizon.

It is reasonable to infer that, in general, the locus of the
light is parallel t^^the earth's surface. For the arch has the same
general form at all places, as will be seen in the diagrams of
Mairan and others.

This leads naturally to the hypothesis of Hansteen,* that the
auroral arch is a real ring, whicn in its normal form is parallel
to the earth's surface, and is symmetrically placed about the mag-
netic pole. The dark segment is seen when we look beneath the
ring into space beyond. The bank of auroral light is a similar
broader or more distant ring.

The results of Prof. Loomis's investigations respecting the
geographical distribution of the aurora' confirm and modify this
conclusion. He shows that there is a narrow belt of an ellipti-
cal form surrounding the magnetic and astronomical poles of the
earth, and at a considerable distance from them, which is the re-
gion of the greatest and most frequent displays of the aurora.
It is reasonable to infer that an aurora of considerable intensity
would naturally take a form symmetrical with this narrow belt
of the earth's surface. The portion of the curve which we see
at any instant should be regarded as part of a circle whose cen-
ter is the center of curvature of the nearest portion of this belt.

To obtain the parallax of the auroral cloud, observations at
two distant stations have been necessary. These have to be
made upon a moving object, the time of whose appearance can-
not be predicted. It is only by a happy chance that good ob-
servations can be secured. If the height can be computed from
measures made at a single station, a great advantage is gained.
A second observer is not essential, if the position and shape of
the auroral cloud is assumed to be as described above.

The distance on the earth's surface from the observer to the
center of curvature of the' nearest portion of the belt of frequent
auroral displays can be measured. Eepresent this by d. Let
the apparent altitude of the auroral arch be A, and its amplitude
on the horizon be 2a. Let x be the height of the auroral cloud

' Hdmoiret de TAcad^mie Royale de Bruxelles, tome xz, p. 118. See also
B. y. Marsh, this Journal [2], xxxi, 811.
* Thia Journal [2], zzz, 89.



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288 H, A. Newton on the height of Auroral Arches.

from the earth, E the earth's radius, b the distance from the ob-
server to the point on the earth directly under that part of the
cloud which forms the vertex of the arch, and c the distance in
like manner from the observer to the point underneath that part
of the arch seen in the horizon. We have then these equations,

R-|-^=H8ecc=Rco8A8ec(6+^); • • • • (^)
and since d, d— 6, and c, are the three sides of a spherical tri-
angle; and a the angle,

COs((f— 6)=ZC08dc08«-{-8iD(f SIDCCOSO. . . . • (2)

From these equations b and c may be eliminated, and x found
in terms of a, d^ A, and R.

From (1) co8(6+A)=cosA cose, and hence

COS ((^ - 6)=C09 ) d+h - {b+h) (

=cos (d+h) co8(6+A)+ sin (d+h) sin (b+h)

= C08 {d-{'h) cos h cos c-f- si n (c/-|-^) ( 1 — cos^ A cos* c)^. (8)

Equating (2) and (3) and dividing by cose,

cos <f-|-*in d tan e cos a=cos(i+^)^^ A+8in(<f-|-A)(8ec*c— cos^A)* (4)

But cos d=cos(d+A)co3 A+sin(c?+Ajsin h. Substituting, divid-
ing by sin(d+A) and placing sin 9 for sindcosacosec(S+A) we
have * 1

sin A-f-tan c sin ^=:(8ec*c— cos^A)*

Reducing, tan c=28in A sin q> sec* 9).

Hence, to compute the altitude of the auroral arch above the
earth's surface, we have the three equations,
sin 9)=:8in dcosa cosec (d-}-A),
tan c z= 28in A sin q> sec*9,
and a;=:R(8ecc — 1).

To apply these observations to particular cases I have selected
26 or SO auroral arches, observed by Pres. Stiles, Prof. Olmsted,
Mr. Bferrick, and Mr. Bradley. They were all observed at New-
Haven, except those in the year 1860, which were seen by Mr.
Bradley at Chicago. Most of these observations are from the
Auroral Registers of Mr. Herrick and Mr. Bradley. These Reg-
isters will form part of a volume of memoirs about to be pub-
lished by the Conn. Acad, of Arts and Sciences. The value of
d is assumed to be 32^, which is also very nearly the distance
from New Haven to the magnetic pole -of the earth. In the fol-
lowing table are given the dates of the auroras, the observed
appareot aUitudes and amplitudes of the arches, and the com-
puted values of x in miles, and in kilometers.

In selecting from the Registers the ^ux^hes for this table, I have
omitted those which were low in the north, as the horizontal ex-
tent is then concealed by the mists. I liave also omitted those
of which the obsarviitions were indefinite, or seemed imperfect



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H. A. Newton on the height of Auroral Arches. 2B9

IW4 of the oburwd altitudei and amplitudeM of auroral areheit wth the computed
height* above the earth i eur/ace.



Data.


Altitude.


Amplitude.


Height in
mile*.


Height in
kilometer*.


Obeerver.


Match 27, 1781



66i


16S


83


68


Stiles.


Sept 21,1840


10-12


120


62-68


84-109


Herrick.


March 6, 1843


6-8


100


42-88


67-188


a


April 18,1846


8


100


88


133


«


April 27. "


10


90±


166


260


«


Oct 9. "


8


100


83


138


Bradley.


Oct 19, 1846


8-10


80±


165-214


266-846


u


Dec 9, "


6


60


281


462


Herrick.


May 16, 1847


7-8


80


142-166


228-266


M


June 12. "


6


60


281


462


M


Aug. 4, "


4


60


164


248


Bradley.


U U €t


7


90


98


158


M


Sept 29, "


10


70-80


290-214


467-846


Herrick.


Not. 26. "


10-16


100


111-188


179-295


II


May 18, 1848


7-9


76±


168-222


270-868


u


Oct 28, "


6-6


70


184-166


216-266


Bradley.
Herrick.


March 18, 1849


10-16


100


111-183


179-296


April 6, 1860


10-13


90


165-198


260-810


Bradley.


Feb. 18.1861


23


120-180


164-104


248-168


M ^


March 18, **


12


120


68


109


Olmsted.


Sept 29, "


8


90


118


190


M


Sept 29, 1862


10-16


100


111-183


179-296


Herrick.


March 26, 1860





90±


80


129


Bradley.


March 27, '«


10


90-100


166-111


260-179


i<


July 4. '«


10-12


100-f-


111-140


179-226


M


Aug. 12, **


6


90±


62


100


It


M 4i ((


7


90±


98


168


«


Aug. 17, "


8


100±


83


188


U



The average height as indicated by the table is 134 miles, or
216 kilometers. The observations were not taken with refer-
ence to the use here made of them, and the results can there-
fore be regarded as only approximately correct. Mr. Bradley
informs me that his method of determining the amplitude of the
auroral arch was to place himself with his face directly towards
one end, and then compare the amplitude with the arc of 90*^,
which was easily estimated. He was accustomed to consider the
curve of the arch as continued down until it cut the horizon.

This method of determining the height of the auroral arch is
imperfect in that it supposes for it a given regular form. In fact
the auroral cloud is usually more or less irregular. Yet in view
of the very great difficulties in securing good observations for

Sarallax at two stations, the method is believed to possess very
ecided value, both independently, and as a check upon other
measurements. It furnishes moreover the means of determining
not only the magnitude of the auroral cloud, but also the
breadth and height of the streamers which often rise from the
arch-shaped mass of light.
Tale CoUege, March 18tb, 1866.



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290 /. P. Kimball on Iron Ores of Marquette, Michigan.



Art. XXXYL — On the Iron Ores of Marquette^ Michigan; by
J. P. Kimball, Ph.D.

It is proposed in the present article to record a few observa-
tions made, in the month of May last, in the Iron region of
Marquette county, Michigan, with the view of elucidating cer-
tain obscure points in the geology of the immense beds of earthy
red hematite, specular ana magnetic iron ores, with which this
district abounds to an unparalleled extent, constituting it beyond
any doubt the most opulent source of iron in the world yet dis-
covered. It was not my privilege carefully to explore this re-
gion beyond a limited district near the middle. I am therefore
unable to add any information as to the geographical extent of
the iron deposits to the published results of Foster & Whitney's
survey. Indeed, the following contribution to the knowledge of
this region is chiefly by way of observation of the instructive
rock-cuttings in the iron mines, or rather quarries, and in one
particular cutting of the Peninsula Railroad, all of which have
been presented to geological study since the close of the govern-
ment survey; and, inasmuch as neither population nor industry
has advanced beyond these quarries, no otner advantage to the
geologist at present exists over the means of exploration em-
ployed by the United States geologists at that time. It is ap-
propriate to remark in this connection that it must certainly be a
<5ause of great regret to all friends of natural science and mineral
industry in this country, that the federal government has omitted
to publish the special report upon the Marquette Iron Eegion by
Mr. J. D. Whitney, the results of a second geological exploration.

In their survey of that portion of the large area of tne North-
west exclusively occupied by schistose, metamorphic and crystal-
line rocks, which is included in the northern peninsula of Michi-
gan, Messrs. Foster & Whitney in 1851 marked out the out-
lines of two distinct systems of crystalline rocks, one of which
was defined as metamorphic, their Azoic proper ; while the
other, distinguished as a great development of granitic rocks
outstretching in separated expanses, was described under the
name of granite belts or ranges. The relation to each other of
these two systems was hardly traced to conclusiveness owing to
the concealment of their conditions of contact; but the latter
was assigned to an origin later than the Azoic series upon the
testimony of disturbances of the upper metamorphic strata by
intrusive masses of the granite, and earlier than the Silurian, as the
lower beds of the Potsdam sandstone are seen to rest undis-
turbed around them.^ The distribution of the Azoic and gran-

' Report OD the Qeol of the Lake Superior Land District, Pirt II, 1861, 44-48.



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/. p. Kimball an Iron Ores of MarqueUe, Michigan. 391

ite rocks, as laid down by the federal geologists, is presented in
their map of the district between Keweenaw Bay and Chocolate
Eiver, to which reference can readily be had without encum-
bering these pages with a verbal recital.

The metamorphic or Azoic rocks, consisting of gneiss, horn*
blendic, talcose and chloritic slates, and beds of argillite, no*
yaculite, quartzite, conglomerate, saccharoidal marble and crys-
talline limestone, were described as existing under conditions of
great displacement, and displaying evidences of metamorphism,
particularly in vicinity to the line of contact with the granite
or igneous outburst. The occurrence of granite within the area
of their distribution was recognized in the form of intrusive
masses, while the greenstones and some of the schists, both fol-
lowing the general stratification, were regarded as trappean
overflows, the former as an igneous product, the latter as pul-
verulent greenstone in the form of volcanic mud. The iron-
ores of this series of rocks were described as alternating with
the trappean ridges in the form of intrusive masses, and the re-
maining phenomena of their dissemination in many rocks of the
series, were ascribed to processes of elimination and mechanical
admixture prevalent during the accumulation of the oridnal
sediments. This explanation was believed to meet the mode of
occurrence of the larger masses, which, at the time it was pro-
posed, had not been extensively uncovered, and manifestly, as
appears in the concluding paragraph of the chapter on iron-ores,*
was not meant to be extended to oeds of specular and magnetic
oxyds of iron included within metamorphic strata, with a con-
formable range and dip, which indeed the federal geologists ex-
plicitly state their disposition to regard as the result of aqueous
deposition.

The granite belts were defined in general terms to occupy an
area of more than 2000 square miles, and, within the boundaries
of Michigan, to be developed in two distinct ranges or spurs, of
which the northern, including the Huron Mountains, forms the
coast between Presqu'isle and Granite Point, and expands west-
ward to a width of 25 miles. Along its southern intersection
with the metamorphic series — its longest direction — it is laid
down as continuous for sixty miles. It is separated by a zone
of metamorphic rocks of some fifteen miles in width, which em-
braces the present iron industry of the region, from the southern
belt, which is of very irregular outline, tnough nearly parallel
for a distance of 36 miles along its northern intersection with
the metamorphic belt. The large expanse of crystalline rocks
occupying the undeveloped tract of the northern part of Wis-
consm, stretching across the head waters of the Mississippi to

* Foster <& Whitney, ibid, 68.



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302 /. P. Kimball on Iron Ores of Marquette, Michigan.

the north and west of Lake Superior, was considered by the
federal geologists to be the continuation of these granite belts.
The granite was described as forming numerous parallel ridges
bearing east and west, and in both belts to indicate leading axes
of elevation. Gneiss was observed to flank the granite both on
the north and south with intercalated beds of quartzite, potash,
feldspar and homblendic schists, the whole dipping uniformly
from the axes of elevation. Hornblende sometimes was seen to
replace mica, forming a light grey syenite. The granite south
of the metamorphic belt is generally made up of feldspar and
quartz, mica being almost always wanting, or very sparingly

E resent. Feldspar is the most predominating mineral, large
odies of flesh-red orthoclase being of common occurrence. Two
systems of dykes, and extensive intrusive masses of greenstone
— the larger of a bearing uniform with the axes of elevation,
the smaller being N.E. and S.W. — were indicated as occurring
throughout the distribution of both belts. These are intersects
by veins of quartz.*

A most engaging, and, at the same time, a very wide field of
inquiry, is presented to geologists in addressing their attention
to the ancient crystalline rocks of the Northwest, with the ob-
ject of resolving the distinctive distribution of the Laurentian
and Huronian series.

Although no detailed description of the crystalline rocks of
the northern peninsula of Michigan has been given, so far as I
am aware, since the close ot the survey of the Lake Superior
Land District, a noticeable disposition prevails amone geologists
to assign to the metamorphic strata, distinguished oy Messrs.
Foster & Whitney as Azoic, an equivalency with the Huronian
series of Canada. Such a tendency appears to be due to the
investigations upon the south shore of Lake Superior of Mr.
Alexander Murray, of the Canada Geological Survey,* the
results of which have been employed by the provincial geolo-

gists in their comparative study of the crystalline rocks of
anada and its bordering districts.

The lines of demarcation between the Azoic strata and thi
granite, as laid down by the Land District Survey, appear to
have been determined by the succession of beds rather than
upon any evidence of unconformability. Orthoclasic gneiss,
succeeded by alternating beds of quartzite and hornblendic
slates, flanks the granite as it falls away from its axes of eleva-
tion, and the points at which these have been observed to be
succeeded by argillaceous, chlorite, and talcose schists, and beds
of conglomerate, afford the only clue to the boundaries of the

* Foster <& Whitney ; ibid, chap. iii.

* Oeol of Canada. 66, 696 ; Dana's Manual of Geology, 148.

* This Joaroal, [2], xzxi, 894.



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/. p. Kimball on Iron Ores of Marquette, Michigan. 208

two systems of rock, thus far presented. It has not been claimed
for the information upon the geological structure of the region
in question, that the relation of the Azoic series with the granite
ranges, has been established by sufficient or definite data. This



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