Byron Nelson Cooper Wilmot Hyde Bradley.

The American journal of science and arts online

. (page 5 of 42)
Online LibraryByron Nelson Cooper Wilmot Hyde BradleyThe American journal of science and arts → online text (page 5 of 42)
Font size
QR-code for this ebook


Cos (f — %') =cos (i+i') All the incident light is reflected.
(Cos (» — tO) ' =cos (i+i^) Half the incident light is reflected.
(Cos (t — t')) 3 =co§ (i+i') A third of the incident light is reflected.
(Cbs (t- i'))'*=cos (*+*0 ^^ ^^ V^^ ^^ ^^® incident light nearly

is reflected.

This law deviates from the truth by a regular progression as n
mcreases and always gives the value of the reflected light in de-
fect. Thus

Angles of Incidence. Values of n. Differences.

82^44' 2 .... .

78 34 ^. .... . 3 ..... 12

76 38 *. . .^ . . . 4 21

68 56 . . . \ . . 8 38

66 4 ...... 11 43

61 22 20 50

Vol. XXIIL— No. 1. 6



Digitized by VjOOQIC



34 On the Action of the Second Sutfaees, fye.

Let. us now apply the results of the preceding analysis to M.
Araoo's experiment shown in Fig. 1. Suppose tb^ angle of inci-
dence to be 78^ 7', and let the light polarized by reflexion at A (Fig.
3.) be^fiiy and that polarized by one refraction also^m.' Then
since the pencil bsis common light, the polarized light in the whole
reflected pencil AP, &« is=:i», whereas* the light polarized by the
two refractions is=2m ; so that M. Arago's experiment makes two
quantities appear equal when the one is double that of the other.
If the angle exceeds 78^ 7^ the oppositely polarized light in the pen-
cil 6 # will neutralize a portion of the. polarized light in the pencil
APy and the ratio of the oppositely polarized rays which seem to be
compensated in the experiment, may be that of 3 m or even 4 m to 1.

Having thus determined the changes which light undergoes by
reflexion from plates, it is easy to obtain formulae for computing the
exact quantities of polarized light at any angle of incidence, either
in the pencil C B S or 6 «•

The primitive ray RA being common light, AC will not be in that
state, but will have its planes of polarization turned round -a quantity
OP by the refraction at A; so that cota?= cos(» — f'). Hence we must,
adopt for the measure of the light reflected at C the formula of Fres-
nel for polarized light whose plane of incidence forms an angle x with
the plane of reflexion. The intensity of AC being known from the for-
mula for common light, we shall call it unity, then the intensity I of the
two pencils polarized —a?* and +a: to the plane of reflexion will be

, sin.»(»-'tO tan^ri— i') , .

*=:i;r]r?;~r77\Cos2a?+ - -~.-p^sin3a' and

/ cos{i+i') \ "

^-^V-^ l_oos(i+i)_Y)

■*''V(cos(t-t'))V
In like mianner if we call the iotensity of CB = 1 , we shall have
Ton , cos(*+tO

and the intensity I of the transmitted pencil b s

sin^fi— t'O tan^ft — lO .

1 = 1^ ' v\ CQS^a?+- — - \ , ..( sm'a?' and
sin'(»+t') ' tan'(i+t9



/ (cos(t — tO)n «
*"^\ cos(i+tO /



Digitized by VjOOQ IC



Hail Storms.



35



I shall now conclude this paper wiA the following table, computed
from the formulae on page 32, and showing the state of the planes of
polarization of the three rays AC, GS, and b #.





Angle of Refrac-
Uon at first sur-


IncliDation of


Inclination of


Inclination of


An^le of Inci^


plane of jx)-


plane of po-


plane of po«
lariutioa of


dence on the


face, sad angle


larization of


Urization of


fint surface.


of incidence on
second surface.


A C Fig. 3.


C S Fig. 3.


b $ Fig. 3.


o /


• O /


O /


O /


O /








45


45 .


45


32


20 33


45 34


32 20


32 51


40


25 10


45 58


24 12


24 56


45


27 55


46 17


17*49


18 38


56 30


33 30


47 22








67


. 37 34


48 57.


18 20


20 50


70


38 30


49 33


23 34


27 6


75


39 46


50 45


32 22


37 48


78 37


40 29


51 49


38 10


44 69


79


40 33


51 56


38 49


45 46


80


40 42


52 16


40 27


47 46


83


41 5


53 21


44 39


53 40


86 30


41 23


54 47


50 58


60 13


90


K 41 58


56 29


56 29


66 19



Alleriy, December 31, 1829.



Abt. VI. — On Hail^ Storms; by A. Jones, M. D. of Augusta,

Georgia.

These storms very often occur in the Southern States during the
spring, or the first months of summer. They are most frequent
when the thermometer ranges between 70^ and 80^. Lightning is
also more frequent and terrible in tbe south when the thermometer
occupies the above range.

in hail stormy I suppose it highly probable, that at first, large drops
of rain descend, till they come in contact in their passage, with a
much colder cuHrent of air, when they suddenly freeze, in the act
of doing which they expand, producing a hollow globular hailstone,
which enlarges as it falls, by the aggregation and freezing of other
drops of water, which seem to be drawn to it1)y some kind of at-
traction. They in this way enlarge, until before they reach the earth,
tbey often attain a most astonishing size. They have been seen to
fall in some places, of the size of hens' ^ggs, and of still larger



Digitized by VjOOQ IC



36



Hail Storms.



dimensions. It no doubt hai Appeared to manj a strange circum-
stance, that when falling of such large size, they have not been more
fatal to animals. For if a pebble, or any other solid .body of equal
bulk, was to fall from the same height, we must suppose that its
velocity, from its speci6c gravity, would be such as to render its
effects terrible and destructive. We can only imagine the large bail-
stones that often fall, to have in some way, their specific gravity so
much lessened as to render the largest of them, comparatively light and
inoffensive in their fall. This is done, by their expansion in the act
of freezing, by which means a hollow cavity is produced, filled with
air. This air cell, with others attached as they enlarge, greatly les-
sens their specific gravity. It acts like the air-bladder of a fish,
which enables him to rise to the surface in deep water, or the air
cells in the bones of birds which lessen their specific gravily, so
much as to assist their flying.

I first observed this peculiar structure of hail-stones, during a
short residence in Athens, Ga. in the spring and ^mmer of 1831.
In May of this year a cloud come over from S S E. It presented
the peculiar sea green appearance of hail clouds, and portions of it
seamed to move in irregular directions, as if acted on by contrary
currents of wind. It also was accompanied by a considerable wind
and vivid flashes of lightning. After the rain had commenced falling,
the wind was to a degree lulled, and large pieces of hail comnienced
falling, and continued to fall till the ground was covered. After the
storm had passed, I walked into the yard and examined many of the
stones of the largest size. I was surprised to find in the center of
each a circular air cell. The annexed figures in the plate represent
their most common appearance, The largest were a half, or three




Digitized by VjOOQIC ■



Jhipravement in Field Surveying, 37

fourtlis of an inch in diameter, and fj <i9«one and a half to two inch-
es in cireumference, and from this size down to that of a small bul*
let. Some were united by a narrow neck, as shown by Fig, 1.
Some were' irregular and ragged on their edges, and crossed by
irregular fractures, as is seen in Fig. 2. Others again, were dotted,
with several air cells around the center one, as exhibited in Fig. 3f
The center of each represents the ajr cells.

These hail storms are sometimes accompanied by violent winds.
They make their approach from every point of the compass save
directly from the east, and they come most frequently fro/n the south-
west or north west. A person who has once closely observed them,
can generally foretell their approach, from the appearance of the
riising cloud. It uniformly exhibits a sea green color, and often seems
much agitated, and small fragments of clouds often linger beneath
the main body, or seem to be suddenly formed and to fly in pursuit of
it. They occur when currents of air in the heavens, retain their winter
coldness, and intercept the drops of rain and convert them into hail-
stones. This operation is not a little aided also, by the sudden dis-
charges of the electric fluid of the clouds. In the south of France,
they are very frequent and often destroy extensive vineyards. The
people believe so fully in the idea that the discharges of electricity
influence their production, that they erect lightning rods by means
of poles in their fields to lessen their occurrence and effects. In
this ca$e, the discharge of the fluid is gradual, and unattended by
hail, at least in proportion to what would be the case, if let off in
heavy discharges.

Augusta, Geo. June 18th, 1832.



Art. VII. — Improvement in Field Surveying.

The general principle or method of computing the areas of irreg-
ular plane figures, as described in Art. Ill, No. 45 of the Journal of
Science, was introduced by E. F. Johnson, Esq. into the course of
instruction in the practical mathematics, in the institution of Capt.
Partridge, in the year 1824, and the method is no«v extensively prac-
ticed by many of the young men graduates of that institution, in
various parts of the country.



Digitized by VjOOQIC



38 Improvement in Field Surveying,

The same principles \#iHr« likewise applied by Mr. Johnson to
other branches of mensuration, and the whole, as I am informed, in-
corporated in a work, which is soon to be presented to the^ public.

The following are the general directions as given by Mr. J. for
calculating areas by the algebraic process.

1 St. Place in one column the courses and distances of the oudines
of the field whose area is to be calculated, in the order in which they
occur in traversing around it.

2d. Put the differences of latitude and the departures of each lioe
o{^site the course and distance of the same line, — ^tfae differences
of latitude in one column and the departures in another.

3d. Distinguish the. northings and the southings of the several dif-
ferences of latitude by the signs plus and minus, and do the same
with the eastings and westings of the departures ; or otherwise, call
the first difference of latitude, and all of the same name with it, af-
firmative, and all of a contrary name, negative, and do the same with
the- departures.

4th. Take the first departure and place it opposite, as the first
quantity in a column of multipliers. For the second multiplier, add
together the first multiplier, the first departure, and the second de-
parture ; and universally, to find any multiplier add together these
three quantities, viz; the last preceding multiplier, the departure be-
longing to it, and the next succeeding departure ; the number of mul-
tipliers to be the same with the outlines of the field, a multiplier to
each outline.

6th. Involve each multiplier into, the difference of latitude standing
against it, and the half sum of the several products thus obtstined, wiU
be the area of the field in square measures of the same denomination
in which its sides are measured.

The operations of adding^ and multiplying, are in every case to be
performed algebraically. If the additions for the multipliers are
. made correctly, the last multiplier will be equal to the last departure
with its sign changed.



Digitized by Vj'OOQ IC



Improvement in Field SUrtfeying.
Elusiration.



39







-






Factors or


Products or


No.
1.


Couraei.

S.EAB.E.


DUt

AB


Dlf. Ut


Dep.


multipliers.


areas.


AE


EB


EB


2AEB


2.


S.FCB.W.


BC


FC


-BF


eb+kC


2BEKC


3.


N.GCD.W.


CD


-CG


-GD


-HL*


2KHL


4.


N.HAD.E.


DA -HA


HD -HD


2DHA



2 |2ABCKLD

ABCKLD=ABCD

the triangles DLM and MKC being equal.*



The first meridian NS
passes through the first sta-
tion A. EB,DGandKC
are dra^n perpendicular
to, and FC parallel with
NS.




Calculation,







DUt.




.


Factors or


Products or


Np.
1.


Courses.


chs.


Dif. lat.


Dep.

7.79


mtiltipls.


areas.


S. 60° E.


9.00


4.50


7.79


35.0650


2.


s. 350 W.


8.00


6.55


- 4.59


10.99


71.9845


3.


N.70O W.


14.00


-4.79


-13.16


- 6.76


32:3804


4.


N.570 51' E.


11.76


-6.26


9.96


- 9.96


62.3496



2 1201.7695

10.088475 acrs.
It is stated in the article alluded to, that "in the common- method
of computing the area of a field, a meridian line is supposed to be
drawn at some assumed distance from the commencing comer."
This it is imagined is incorrect. The most "common mode,'^ is to
select for the point of commencement, the ejctreme East or West
station of the field. Through this station, the first meridian is inade
to pass, and the necessity of an " assumed distance" is thereby avoid- *

♦ DL is KC by construction.



Digitized by VjOOQ IC



40 Origin f Extensidn and Continuance of Prairies.

ed. The advctntage of the algebraic process, consists in its simpli-
city and in the universality of its application. This fesults from the
circumstance that the meridian line not being limited in its position,
may be made lo pass through any station of the field, wherever
it may be convenient to commence either the measurement or the
calculation. If its position is such as to divide the field into equal or
nearly equal parts, the multipliers or factors are lessened in quantity,
and considerable labor is saved in the calculation, and the liability to
error in the several computations in a corresponding degree dimin-
ished. B.



Art. VIIL — On the Origin, Extension and Continuance of Prairies;
extracted and abridged from unpublished MSS. on a theory of the
Earth; by Dr. Rush Ndtt, of Rodney, State of Mississippi.

We can conceive that a prairiie may proceed from the joint action of
two causes. First, from the influence of a cane-brake ; and secoadry,
from wind and fire. It has been shown that cane exerts a considerable
influence on a forest of timber; that it can completely obscure the rays
of the sun, as well as form by its roots an astonishing mat-work over
the face of the earth, so dense that it is Utterly impossible for any
seed to vegetate and for the- earth to bring forward a single tree.
Our knowledge of the natural history of the cane, does not enable
us to know the length of time it is in seeding; More than half of
the cane of Mississippi and Louisiana went to seed in the year 1830.
It had not seeded to such an extent, during the fifty preceding years.
A few stalks or a few square yards of the cane, seed and die every
year, but when stalks seed again from the same root, we do not know
whether so general a seeding as that just mentioned proceeded from
natural or from accidental causes ; such as long feeding up, with the
unusual vicissitudes of the weather of a few preceding years. The
stalk and root die with the ripening of the seed, which will vegetate
and come forward the following year,, unless prevented by such a
drowth as followed the period alluded to. However, our want of a
full knowledge of the natural history of the cane, Is not very important
in the case before us, as. we can readily conceive of a cane-brake
contending with, and finally overcoming, extensive regions of forest
'trees. If the cane keeps possession of the same land for five bun*
dred or a thousand years, (as we think it does,) it will of course wear



Digitized by VjOOQ IC



Origin, Exien$ion and Continuance of Prairiei. 41

out almost any family of trees. When the cane has driven out every
tree and has acquired exclusive possession, it then begins to experi*
ence the consequences of exposure, without the shelter from the
sun's rays which is afibrded by the trees. The influence of the sun
upon a cane-brake, unprotected by the trees, will in time produce
the destruction of both stalk and root, by which means the land will
fail to be occupied again by cane, until it has been covered anew
with trees. Under favorable circumstances, the seeds of grass are
always at hand, as well as those of trees; but the grass is quickest
to shoot, and grow, and will soon afford a dry carpet, which, if set on
fire at the proper time, will readily burn and destroy any young trees
that had sprung up ; the grass will now continue to increase in quan-
tity and to improve in quality as the cane-roots are decomposed and
the annual fire is continued. But, on the other hand, if the firing is
not carried on, the trees will, in a very few years, by their shade,
exclude the gras^ } and should the land be adapted to the kind of
trees that spontaneously appear, they may become so thickly set, as
to form such a complete barrier to the sun and light, that even the
cane will be kept from returning, and can regain its former residence
only by taking bold at the time the trees are exchanging places ; as,
for instance, when one family, composed of such trees as usually
accompany each other, are becoming thinned by death, -and thereby
making room for another to occupy the land.

There is no fact that can be better established than that prairies
are formed, and are now forming, by the operation of wip4 and fire.
Very abundant proof was exhibited to the writer, more than twenty
eight years ago, when making a pedestrian journey through the dis-
tant and extensive regions of the west. He has seen the prairie in
all its stages; he has seen the hurricane at work upon the forest.
He has seen places where the inroad had been made only the year
before ; where the grass stood but thinly on the ground, and where
it had become sufficiently luxuriant to huriL When the first burn-
ing took place, the timber was, in some places, partly consumed, and
in other places altogether burnt off, leaving holes in the ground, made
by the action of the fire upon the trees, which were burnt when stand-
ing, and thus the stump part was consumed beneath the surface of the
earth.

When a hurricane makes an inroad upon a forest, the rays of the
sun are then admitted to the earth, and this at once afibrds an oppor-
tunity for the grass to spring up ; and if the land is rich and the sun

VouXXni.— No. I. 6



Digitized by VjOOQ IC



42 Origin^ Extension and Continuance of Prairiei.

freely admitted, the carpet of grass will be from six to eight feet in
height. Should this grass be burnt during the fall season, or at anj
dry time through the winter or spring, and the practice annually con-
tinued, the ground would become more and more prepared for the
production of a still more luxuriant crop of grass, when not only the
dead timber would be consumed, but those trees that are alive would
Bufier by the fire and in a few years be killed, unless they stand on
the borders of ponds of water, or on some very unproductive spots^
in either case the grass is found to be short and puny, and insufficient
lo support a flame that would affect a tree. In extensive prairies, we
often observe little clusters of trees, which, by occupying peculiar
^tuations, are enabled to avoid the consuming flames of a burning
prairie.

In a few years, all the trees which come within the reach of the
fires will be killed, and thus the forest is annually dilapidated, until
no signs of it remain, except those which appear in the holes in the
land left by the standing trees, and in the little hillocks made by the
roots throwing up the ground when they are laid prostrate by the
wind. The hillock will be, in time, brought down by the action of
rain ; but on a very level piece of land the holes left by the burnt
stumps will remain, and perhaps would never be entirely obliterated.

The prairie, which is now in its infancy, continues to make annual
encroachments upon the surrounding forests. The grass of this prai-
rie becomes closely set, and may be from ten to twelve feet in height.
It pushes close up under the trees of the surrounding forest, and eve-
ry fire acts injuriously upon the nearest trees; and as ihey are killed,
the grass not only surrounds them, but passes on and crowds hard
upon other trees, so that the prairie is constantly increasing, and would
always exist and extend its borders while fire was applied.

FIRES IN THE PRAIRIES.

It is difficult to conceive of the horror excited at the sight of a
bnming prairie. It is an ocean of fire^ whose billows roll and heave,
and run together, when the mountain of pyramidal flames ascends
and drives detached bodies of fire seemingly into the very clouds.
The whole horizon appears to be on fire ; the earth and the sky are
hidden by the flames, and the eye can reach no point beyond their
boundary. When the wind is brisk, the burning grass ascends and
gives the appearance, as though the heavens were filled with fire-^
brands ; and such is the rapidity with which the flame moves over



Digitized by VjOOQ IC



Or^n^ Exteniian and Continuanee of Prairies. 48

«

the face of the earth, that an attempt at escape, by the swiftest ani-
mal, would prove abortive.

In these regions of natural beauty remote from civilization, the
exhausted spirits of the weary pedestrian are enlivened and fatigue
is allayed, as he beholds the unrivalled charms of these vast prairies
in their successive seasons of flowering. In May and June, they are
robed in flowers of white and pale yellow ; in July and August, in
those of sky blue and red ; and in September and October, in others
of deep blue and brown. Flora has here her paradise of innocence
andl)eauty, and vegetable and animal life know nothing of the tyran-
ny of man. He destroys vegetables and animals, to produce others
in their stead, and thus maintains a constant warfare with animated
nature.

Domestic animals travel less than the beast of the forest, and their
journeys, when performed, are not so extensive ; hence they collect
their food on a smaller and more contracted surface, by which means
they break down and tread under foot so much of the grass within
their usual bounds that the fire 13 either arrested on the borders of
their range, or runs lightly over it without injury to the shoots that
may have come forward the preceding spring. Such circumstances
favor the introduction of trees, which then immediately appear, and
as^ they obtain sufficient size to shade the land, the grass itself is driv-
en out; the cattle are thus driven to a greater distance from the plan-
tations in some new direction, where they soon crop the grass, and
place it beyond the reach of fire. As the cattle recede, they are
followed by the forest; and so soon as a farm can be enclosed by the
young trees, the farmer, for the convenience of his stock, moves nearer ,
to the prairie ; otherwise, from the receding of the prairie, the cattle
would seldom return to their home, and perhaps become wild by ab-
sence. In this way, the prairies of Kentucky have disappeared ; and
those to the west of the Ohio and Mississippi, retreat as the settle-
ments approach them. It should be remembered that some prairies
are so very level, and retain water so long at the surface, that the
seeds of trees will perish, and even the roots, if the seed had sprout-
ed, and the shoots had been burnt, or left standing.

Hence, you may observe such prairies to continue long after stock
are turned upon them. So soon as the fires are restrained, trees
come forth, upon all the prairies that are formed of rdling land.



Digitized by VjOOQ IC



44 Origitij Eoetensian and Continuance of Prairies,

M

A TORNADO.

We have stated that hurricanes and whirlwinds, by' their inroads
upon the forests, are chiefly instrumental in forming prairies.

It is believed that hurricanes are not so frequent and so violent as
formerly. For the last twenty-five years particularly, they have dimin-
ished in number and energy. The signs of hurricanes, previous to
the year 1805, would indicate in their case, a frequency and violence
unequalled in any subsequent period.

In the year 1805 it happened to the writer to be roving on ,that
most beautiful lawn, extending from Kaskasli^ia to Illinois, and which
is called the American bottom. There ^s the most charming alter-
nation of prairie, and woodland, and while he was musing on the
causes which gave rise to forests of grass, or cane, and of stu-
pendous oaks and cotton woods, he was roused, and his attention di-
rected to a scene of unequalled grandeur and horror. It was a whirl-
wind that had crossed the Mississippi, and was making its way through
the swamp, until it was near the charming prairie, which at that mo-
ment affi>rded rest and comfort to a solitary pedestrian. By the irre-
sistible force of the wind, whole forests were in a moment twisted
from the ground, and when thrown from the mouth of tlie vortex,
such was the violent collision of tree against tree, that they were



Online LibraryByron Nelson Cooper Wilmot Hyde BradleyThe American journal of science and arts → online text (page 5 of 42)