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Volume 12 (1866) (428 pages)

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Page: of 428

146 The Wining and Scientific Press.
Gonmunications.
In Ta1s DErartwent we lnylte the FREE Discussion of
proper H Y alone being r
he ideas and theories they advance.
all
for
[Written for the MinIng and Sclentific Press.j
THE TRAQTORY QOURVE, AND THE
PROPERTIES OF GRINDING PLATES,
BY W. A. GOODYEAR.
[conzINvED FRoM PAGE 130.]
‘Let us now look at some of the points
relating to the wear and grinding effect of
certain plates as investigated in the Hand
Book.
Tadopt the two defintttons given under
“Laws of Grinding,’ 1 and 2, page 102.
Instead, however, of taking, without modification, the law given under 3, as it is there
expressed, I will modify its statement as
follows:
The wear (that is, the thickness of the
layer of material worn from the surface)
in any direction, at any point of grinding
surfaces of uniform hardness, is proportional
to the product of the pressure at that point
in the given direction, into the distance
passed over, provided that the surfaces he
of such a form that, this law holding true,
the plates can follow each other and remain
an contact as they wear away ; otherwise the
law does not hold. :
Iwill now discuss, to some extent, the
proposition attempted to he proved upon
page 103 of the Hand Book.
If I understand the author correctly, it is
there assumed that in tractory conoidal
plates, of uniform hardness, the pressure in
the direction of the normal to the surface is
constant (which is true when the upper
plate revolves ), and that, therefore, the grinding surface will wear into one, whose meridian curve is so related in form and position
to the meridian curve of the original surface (that is, the tractory), that the distance
intercepted hetween the two curves, on the
normal to the tractory at the point 2, y,
shall he proportional to the ordinate y
(which is zot true), and it is then attempted
to prove that the distance intercepted hetween these two curves, on a straight line
parallel to the axis of 2, is constant, and,
therefore, that the secondary curve is a
tractory equal to the first.
(I still use 2 and y in the same sense as
heretofore, viz. as representing the codérdinates of points in the tractory when the
origin is at I’, in the figure on page 103 of
the Hand Book.)
I will now show that if the distance intercepted hetween a tractory and a secondary
curve, on the normal to the tractory at the
point 2, y, he proportional to the ordinate y
of the tractory, then the secondary curve is
not a tractory, and therefore that the distance intercepted hetween the two curves,
on a line parallel to the axis of x, is not constant; for if it were the curve would hea
tractory.
Consider a point 2, y, of the tractory,
If X and Y he the running codrdinates of
the normal at this point, then the equation
of the normal is
(51) Yoy=—Z >». This
normal will cut the secondary curve in a
point x, y’, whose codrdinates must, therefore, satisfy (51). Hence,
(52) 7 —y=— Pi (z’ — 2). The distance hetween the points x, y, and 2’, y’, is
VY (x — 2)?+ (y—y)?. This distance
is, hy supposition, proportional to the ordinate y ; therefore,
(58) Y (#' — a) + (y¥ —y)? = by, where
bis constant. Substitute in (52) the known
value of 6 in terms of y, thus,
y
6)y—-y=s Vere (2).
If, now, hetween (53), (54), and (18),
we eliminate x and y, we shall ohtain an
equation expressing the relation hetween :c’
and y' , which is the equation to the secondary curve in question.
The elimination of # and y in this case,
however, involves the resolution of an equation of the fourth degree. If, for example,
we ohtain the value of (#’—zx) from (54),
and suhstitute this in (53), we are led to
the equation
(55) By! — at (B—1) ff — 2 ayy +
ey? = 0, an equation of the fourth degree
in y, which, if resolved, would give us four
complex expressions for as many different
values of y.
If, then, from (53) or (54) the values of
x corresponding to these values of y were
obtained, and these values of x and y substituted in (18), we should obtain the equation of the secondary curve.
I have not resolved equation (55), and
have, therefore, not ohtained the equation of
the secondary curve, as the operations involved would he tedious, and the resulting
expressions would he very complex.
The final equation, however, would represent a curve having eight hranches—that
is, two hranches for each hranch of the tractory—one lying upon the concave side, and
the other upon the convex side of the latter. This is as it should he, since there are
two points in the normal at x, y—one on
each side of the tractory—which will satisfy
the conditions of equations (52) and (53).
Let us now consider a single hranch of
the tractory and the corresponding pair of
branches of the secondary curve, and let
us suppose two other tractories described
equal and parallel with the first, hut heginning at the points y == 4, © = + 6a, instead of the point y = a, = 0.
It may easily he shown, geometrically, hy
constructing the curves under the ahove
conditions (as I have done for the particular
case 6 = 1): first, that the ranch of the
secondary curve lying upon the convex
side of the original tractory hegins at the
point y =a, = — éa, where it is tangent to the tractory which begins at the
same point, hut that the halance of this
branch of the secondary curve, though lying
helow the line y == a, does not coincide
with the tractory to which it is tangent, hut
lies upon the convex side of it; second,
that the hranch of the secondary curve,
lying upon the concave side of the original
tractory, hegins at the point y= @, «=a,
hut that heginning here, it immediately rises
above the line y = a, forms an unclosed
loop or hook, and then descending, crosses
the line y = a, and continues on, lying
then between the original tractory and the
one which hegins at the point y= e, z =2e,
instead of coinciding with the latter.
The construction which I have made
then (and which any one else can make at
pleasure), shows that at least in the case
where 6 = 1, the secondary curve is not
is not a tractory. ‘The question now arises,
whether for other values of 6 the case may
not he different.
Erratom.—Instead of x in equation (35)
read +.
[fo be Continued.]
Tue two kings that rule America—Jo-king
and Smo-king.
[Written for the Mining and Scientifie Press. ]
From Our Regular Correspondent.
Enirors Press: This place, which has been
my center of operations for the pasttwd weeks,
isa respectably decayed mining town of the
olden time, still retaining its name and organization ; hut whose glory has long since passed
away, with the richness of the gulches and
river placers, which once made it famous
throngbout the State and the whole coast.
Bat though I speak of it as decayed, I do not
wish to say that business has entirely deserted
the place, or that its streets are lined with
empty houses like some of the ex-mining towns
of the present day. The glory of tbe ancient
placers is still perpetuated, though feebly, by
numerous deep shaft claims, and a few hydraulic
diggings, which together with its being the
county seut of Calaveras county, keep up quite
a respectable show of business. It is only
respeciably decayed.
The principal] mining now being carried on in
tbis vicinity is deep placer mining; the gold
being obtained from deposits of gravel supposed to be the beds of an ancient system
of rivers, now covered by deposits of lava and
other voleanic debris. The most important
entarprise of this kind is the “ American Shaft,”
owned by Messrs. Paul, Larnard & Holbrook,
located on Chili Gulch, two miles below this
place. ‘The channel was strnck at a depth of
100 feet, at which depth a large stream of water
was tapped which compelled the owners to suspend operations for some time. and was only
removed at an epxense of over $30,000. When
the water was once checked, there was no
turther trouble, and the mine is now in successful operation, employing upwards of thirty
men, and ten stamps for crushing the cement.
The hoisting, pumping, and stamping machiuery, are all driven by tbe steam engine. The
daily prodnet of the ming is from $150 to $200
per day, yielding a very handsome profit to the
owners. ‘The deepest shaft in this section is
that on the claim of
SQUIRES & COMPANY,
Which is about 165 feet in depth. Tbe hed
of cement gravel in which the gold is found
varies from a few inches to four or five feet in
depth, averaging about two feet, and pays
about ten dollars per ton, by washing in sluices,
The width of the channel is uncertain, but is
known to bs upwards of fifty feet , tbe rock on
which it rests being ordinary slate. Some of
these claiins are opened by tunnels driven into
the sides of the hills, often at great expense.
Among thoss now in progress may be mentioned
THE INDIAN RAVINE TUNNEL,
Which is being driven into Stockton Ridge,
about three miles below Mokelumne Hill, by
Messrs. Pau] & Haerschner, and other
citizens of thistown. Itis estimated that to
reach the channel a rim of slate 1,100 feet in
thickness will have to be penetrated. The
work has been going on nearly two years, and
the tunnel is now in 430 feet, the rock having
been very hard thus far. It is estimated that
it can be finished in two years more,as the
slate is expected to be softer, as the work
progresses. ‘There area few hydraulic claims
also at work and many of them are doing quite
well, one of these, tbat of Messrs. Shaw & Co.,
is immensely rich. It is situated on the west
side of Chili Gulch, about a mile anda half
below Mokelumne Hill.
THE “OPAL CLAIMS” OF STOCKTON HILL.
Considerable excitement has been awakened
at different times by the discovery on Stockton
Hill, near this place, of soms beautiful concretions, believed at the time, to be opals, but
which subsequent observations have proved to
be agates, some of which are of marvelous
beauty, and doubtless of considerable value,
though there is no market for them in this
country. A company was finally organized
amonz the French residents of Mokelumne
Hill and vicinity, and the search commenced
inan earnest and systemitic manner. The
work is done by a Mr. Neven, who shuwed me
the excavations, and explained the different
processes employed. The claim of the company is known as the Occulis Mundi, (light of
the world), and is 5,000 feet in extent along
the northern slope of Stockton Hill, and extends to the top of the same. Several tunnels
bave been driven at different points along the
hill-side, the longest of which is in 150 feet.
The stones are found in a ledge of grayish
colored gravel orclay, from three to six inches
in thickness, having a slight inclination to the
northwest, of about two degrees from a_horizontal plane. Hach stone.is eocased in a brittle
white substance, supposed by Mr. Neven and
others to be produced by the decomposition of
the stone itself by the action of chemical
agents contained in the water in the hill.
Throughont the whole extent of the claim the
same regulnr formation exists, the line of the
Strata being easily traced, and perfectly straight
and parallel, Above the ledge is a belt of
“ trachyte” which is traversed at a hight of five
feet above the ledge, hy two strata of white
fieldspathic clay, each: about one inch in thickness. giving to the sides of the tunnel a regnlarity of appearance, as if they had been
purposely striped by the hand of man. '
Some very beautiful stones have also been
found in another hill east of town, and about
a mile from the Occulis Mundi. These are
principally “ moss-agates,” many of which are
exceedingly heautiful. They are found in veins
traversing a stratum of hard ferruginous, volcanic rock, in which they are so firmly imbediled .
aa often to break before they will be separated 1
from it. Many of the stones from hoth these .
claims have been cut and polished by Dr. H.
M. Stuart, of Mokelumne Hill, to whom the
company are indebted for the beuutiful dis) lay
of cut stones made by them last fall, at the
Mechanics’ lair at San Francisco. One of
these, a fine “imoss-agate” of about two carats
in weight, is now worn in a ring by Mr. Geo. \,
Leger, one of the owners ofthe Occulis Mundi
who takes great pleasure in exhibiting it to the i
curious. J am indebtedto the Superintendent, .
Mr. Neven. for some very fine specimens of {
the stones from these claims, some of which J
expect to preserve during life, as pleasing
reminders of a day very agreeably spent.
On the third day of my stay at Mokelumne
Hill started in company with a young friend,
a son of Mr. Thomas Loutlett of this place, to 4
visit the mine of the “Campo Seco Copper :
Mining Company,” situated near Campo Seco
and fourteen miles from here. A walk of eight Wy)
miles brought us to the residence of the Messrs. .
Young, near the Calaveras linie-kilns, who
very kindly volunteered to furnish us with saddle-horses for the remainder of our journey,
which offer, after such a walk, we were not at
all loth to accept, and after visiting the mine,
and the smelting works near, we came back a
little after dark, to ths residence of the Messrs.
‘Yonng. where we were very hospitably entertained for the night. and returned to town on
ths following day, well pleased with our trip,
and with what we had seen.
THE CAMPO SECO COPPER MINE i
Ts owned by a joint stock company of the same
name, and is superintended by Mr. D. L. Morril, onder whose able manngement, the mine .
is now more than paying its expenses, nnd
will probably soon be in a dividend-paying condition. It is opened at present to a depth of .
200 feet, at which depth the vein of ore, a :
solid mass of sulphides of iron and copper,
unmixed with slate, is twenty-three feet in
width, ahout one-sixth of which is estimated
by Mr. M. to be shipping ors, assaying from
twelve to twenty-three per cent. copper. ‘Ihe
lower grades of ore are sold to the proprietors
of the smelting works located near. The
shaft is not sunk on the vein, but west of it,
and drifts are run from it to the vein at points
where it is desired to open levels. The~body
of ore in the 150-foot level, is forty feet east 9)
of the shaft, and is twenty-three feet in width, )
and is divided nt the end of a drift extending 9)
eighty-five feet northward from the shaft by a .
“horse” of slate. This horse is not fonnd in
the lower level, but the vein is of uniform
width and character throughout tbe extent of
its drift. Besides the twenty-three feet: of ore,
the vein contains a massof slate somewhat
cupriferous, of unknown width, the we-tern or f
“hanging wall.” having never been reached.
It is believed that another hody of ore will be
found onder this wall, and acting under this
belief, a drift has been started on the 200-foot
level for the purpose of reaching it. This drift
has been continued 120 feet, and is still in the
vein It has cut a few narrow strata of rich 7
copper ore, but hag not as yet developed any f
very important deposits. One thousand tons
of ore were shipped from this mine during the
past year, averaging 16 to 17 per cent., and if
is confidently believed that the amount will be
much increased during the present one. The
hoisting works are driven by water power and
are capable of raising thirty tons of ore daily.
It is intended to erect steam works in a short
time, as the present machinery is entirely insufficient for the wants of the mine.
After passing through the mine we went in
company with Mr. Morril to visit the works of
THE TAUNTON SMELTINO COMPANY,
Located on the Mokelumne river, three-fourths
of amile beluw the Campo Seco mine, with
which they are connected by a railroad, on
which the cars are drawn by a horse. The .
® .