Enter a name, company, place or keywords to search across this item. Then click "Search" (or hit Enter).
Collection: Books and Periodicals > Mining & Scientific Press
Volume 12 (1866) (428 pages)

Copy the Page Text to the Clipboard

Show the Page Image

Show the Image Page Text


More Information About this Image

Get a Citation for Page or Image - Copy to the Clipboard

Go to the Previous Page (or Left Arrow key)

Go to the Next Page (or Right Arrow key)
Page: of 428

162 The Mining andl Scientific Press.
Gonmnniontions.
In rH18 DEPARTMENT we invite the FREE DISCUSSION
i dents alone being r
of all
Proper nT
for
he ideas and theories they advance.
{Wrltten for the MinIng and Scientific Press.j
THER TRACTORY CURVE, AND THE
PROPERTIES OF GRINDING PLATES,
BY W. A. GOODYEAR.
[conTInDED FROM PAGE 146.]
It is easy, however, to show analytically
that in the hranch of the secondary curve
which lies upon the concave side of the original tractory, there are always values of y/
that are greater than a, that is, that the
hook, above the line y = a, is always formed,
whatever be the value of 4, (provided 5 he
not ahsolutely 0, in which case there is no
secondary curve,) and, therefore, that this
curve is never a tractory, since in the latter
no value of y can he greater than a.
To show this, let us find the point where
the normal to the tractory, at the point 2, y,
erosses the line y= a. Represent the coordinates of this point hy 2”,y’. Now,
since the point x”, y’’, is in the normal to the
tractory at the point 2, y,its codrdinates must
satisfy equation (51). Therefore, we have
! a, dey
ea a, 2).
the point 2”, 7’, is also in the line y =a,
its codrdinates must satisfy this equation
also. Hence,
(57) o/’ =a. If, now, we substitute the
Since
kuown value of = in (56), and then ohtain
y
from (56) and (57) the value of 2’’ in terms
of x and y, we have
* (58) a =a aa (58) -y \i
in (58) 2 and ystill represent the codrdinates of points in the tractory,we know that
hy taking y as near @ as we please, we can
make x as near 0 as we please. Therefore,
(58) shows that hy taking yas near a as we
please, we can make x2’ as near 0 as we
please. In other words, that by taking
points in the tractory as near the point
y =a, % = 0, as we please, we can make
the normal at the poiut 2, y, eross the line
= a, as near the point y = a, x — 0, as
Now, since
we please. Therefore, however small 4 may
be (provided it he not ahsolutely 0), there
are still points in the tractory so near the
point y== a, «= 0, that their normals
cross the line 7 =a, at a less distance than
ba from the point y= a,2—0. There
are, therefore, always points in the secondary curve whose ahscissas are less than da,
and whose ordinates are greater than a, and
which, therefore, lie ahove the line y =a.
The hovt referred to is, therefore, always
formed, however small 6 may be. That
the hook is always formed when 6 is large,
is sufficiently evident.
The secondary curve, then, is never a
tractory; and this heing the case, the distances in a direction parallel with the axis
of x, from the original tractory to the secondary curve, are not constant.
The demonstration given upon page 108
of the Hand Book is faulty, inasmuch as in
the figure there used, the lines 0 ¢ and o! ¢’,
which are made to represent the wear
perpendicular to the tangent, and are proportional to tbe ordinate, are not drawn perpendicular to the tangent at the point of
contact, where this wear would actually take
place, if it could take place at all, hut at a
distance from it, so that the figure does not
answer to the conditions of the prohlem
there handled.
I may remark here, that although we
cannot conveniently ohtain the equation itself of the secondary curve ahove discussed,
we can yet, without difficulty, ohtain the
differential coefficient of y/ with respect to
zx in terms of y, and hy means of this, demonstrate one or two other points in relation
to the curve. The value of this differential
coefficient is the following:
(59) oa *
2b —abtaya—y
2b baYa—#/
From (59) we see that if we make y= a,
But from the conditions af =
under which the curve is formed, we know
that when y = a, y/ also = a, and a’ — ba.
Therefore, at the initial point 7’ = a, 7 =
ba, of the secondary curve, its tangent is
perpendicular to the axis of ahseissas, and
the curve itself is tangent to the tractory
which hegins at the same point.
then
di
Again, if we make ee 0, we shall ohtain the point or points where the tangent of
the secondary curve is parallel to the axis
ers)
daz!
can can he satisfied in two ways, viz., hy
making y = 0, or hy making
(60) 2by—a?b+ay/ae—y=?
Now, we know that when y = 0, then 7’
also == 0, and 2 and 2’ are hoth infinite.
Therefore the axis of ahscissas is also an
asymptote to the secondary curve.
Equation (60) gives
a I —
(61) yt avs (4480-14781).
Therefore, at the point in the secondary
curve, corresponding to the point in the
tractory, where
ey 4 Hl ee
Y—= 55 7 4F—-1+ 8+),
‘the tangent of the secondary curve is also
parallel to the axis of ahscissas. It is very
evident that this curve is not a tractory.
Let us now consider some of the conditions of grinding,
If two grinding plates, of tractory conoidal
or any other form, rest uniformly the
one upon the other without motion, the
pressure hetween the two, in direction as
well as in amount, is determined solely hy
the weight of the upper plate, and if the
latter he of uniform thickness in a vertical
direction, the pressure 7” a vertieal direetion is uniform, or constant.
If the plates he curved (whether they he
of tractory conoidal or any other curvilinear
form), the vertical pressure at any point
may he resolved into two components, one
of which is parallel and the other perpendicular to the tangent of the meridian curve
at the same point.
of ahscissas. But the equation
The component parallel to the tangent is
‘taken up hy the hody of the plates themselves, and hecomes null in effect. The
other component remains; and it is easy to
show that in tractory conoidal plates, if the
upper plate he of uniform vertical thickness,
this last component varies as y, and, in
fact, is equal at any point to R Z, if R denote the constant vertical pressure. These
conditions hold so long as the plates remain motionless. If the upper plate hegins
to revolve, the conditions of pressure are
then changed, and in a manner depending
upon the form and relative hardness of the
different portions of the plates.
[To be Continued.]
Ay old man anda little child stand upon
the threshold of time, the. two looking different ways.
{Written for the Mining and Scientific Press.)
From Our Regular Correspondent,
Enrrors Press: After a trip in the north:
eastern part of the county, I find myself enjoying the kindly hospitality of Mr. Bever of the
Rich Guleh Hotel, and having spent most of
this time ina highly interesting, but rather
unappreciated section of country, I am led to
believe that some account of my ‘‘ wanderings
and short comiugs” therein may be of interest
to the public.
Leaving Mokelumne Hill on the afternoon
of the 16th instant, I reached the residence of
Colonel Rust, three miles above which place,
about sunset, and accepted his kind invitation
to spend the night. ‘The Colonel is one of the
pioneer newspaper men of the coast, having
been at one time editor of the Marysville Eapress, and having heen at different times connected with many enterprises of the kind in our
mountain towns. He is fond of relating his
experiences in those early days of newspaper
work, and I was equally fond of listening ; so
between ns two, the evening passed quite
pleasantly away. The next morning I started
quite early for West Point, where I arrived
about one o’clock, having met on the way
many of those whose acquaintance [had made
last spring, in all of whom 1 found friends and
helpers. The most of my time was spent in
West Point and Sandy Gulch districts, which
lie hetween the north and sonth forks of the
Mokelumne river, and are separated by the
widdle fork.
WEST POINT DISTRICT
Lies on the north side of the middle fork of
the Mokelumue, and is at present the most
prosperous and enterprising quartz-mining district in the county. Itis well supplied with
wood and water, both being abundant and
cheap, thus offering every facility for working,
at small cost, the rich auriferous ores which
the numerous ledges so abundantly yield. The
veins of this district are situated in a granite
formation, and are quite irregular in width
above the water line; at which point they
were heretofore supposed to disappear, none
having been worked below thatline until withina yearortwo. They are also frequently
cut hy dykes or “elvans” of granite, trap or
slate, which gave rise to the helief that they
were generally of insignificant extent, longitudinally. The explorations on the Mina
Rica and Sacoterre, and the Cummings and
Hadley veins in this district. and the Belding
in Amador county, which is alsoon the same
range and in the same formation, have proved
almost heyond doubt that the veins in this
district are as permanent, though not so extensive, as any inthe State. The width of the
veins vary from two to three inches to as
many feet, and the yield of the ore is fram 20 to
$200 per ton ; quartz paying less than twenty
dollars not being considered rich enough for
profitable working. Owing to the belief that
the ledges, or “ bunches,” as they are here
called, were not extensive, but few mills have
been built for #he working of any particular
leads; but most of the quartz is crushed at
custom mills, whose charges vary from five to
seven dollars per ton; the latter price being
charged for working in an arastra; that process
being quite popular with some classes of the
population. The principal custom mills now
at work in this district are Henry’s of five
stamps, on the Middle Fork, one mile south of
town; Schmidts, of five woodeu stanips and two
arastras, on the same stream, some 400 yards
above Hendy’s; the Belcher mill, of eight
stamps and two arastras, abonta mile above
Schmidts, and the Skoll Flat mill, at Skull
Flat, two miles northeast of town, of eight
stamps, all of which were more fully described
iu my letter from this place in April last.
Besides these may he mentioned Carlton’s
mill, sitnated one and a half miles below West
Point on the Middle Fork, consisting of three
wooden-stem stamps and two arastras, driven
hy water power, with an overshot wheel. This
is one of the most substantially huilt mills of
the kind that I have ever seen. It is capable
of working two and a half tons of ordinary
quartz daily, the rock being first broken by the
stamps into pieces of the size of filberts, agai
which itis ground and amalgamated in the
arastras. ‘The old Nestor mill, now owned by
Mr. Lidstrom, of Masnn’s brewery, San Francisco, and ran by Mr. Fred Morris, formerly in
charge of the Mina Rica mine and mill, consists of three stamps and two arastras, driven
like the last hy water power; but is in a very
dilapidated condition, as is also Bryant’s mill
of two stamps and one arustra, situated near.
The owners of the latter, however, inform me
that they intend improving their mill soon.
Both these mills are located on a small stream
called Bear creek, about a mile east of town.
The principal mill of the district, is that of the
MINA RICA NE LAS FLORES MINING COMPANY,
Located at Camp Flores, one and a half miles
east of West Point. ‘This mill consists of ten
heavy stamps driven bya steam engine of
thirty hnrse power, and is well and substantially built. Amalgamation is performed in
small pans into which the pulp rans directly
from the hatteries. ‘The tailings are again
ground, aud amalgamated in one of Baux &
Guind’s amalgamators, by which means the
yield of the quartz is increased from twelve to
fifteen dollars per ton. ‘Lhe average yield of
the rock is from thirty to thirty five dollars; at
least this is the estimate of the superintendent.
This conipany own two veins, the Mina Rica
and the Lockwood. On the formera shaft has
heen sunk to a depth of 130 feet, showing a
well defined vein of quartz lroin fourteen inches
to two feet in width, and much of it heavily
charged with sulphurets. At a depth of 112
feet, drifts have heen run lengthwise of the
vein a distance of eighty feet, disclosing a large
vein of rich ore. ‘The course of this vein, like
that of all others in this range is nearly north
and south, with a very shght dip to the westward. As Ihave before stated, the surface
of this district is all of granite formation,
hut on reaching a depth of 100 feet, the hanging wall of this vein is of talcose slate. while
the foot-wall remains granite all the way down.
‘This is the only instance of the kind which has
come under my ohservation, and I should like
to see some explanation nf the case hy geologists. ‘The Lockwood has heen explored to a
depth of 100 feet, and by drilts along the vein
a distance of filty-nine feet. It is from eighteen inches to three feet thick and yields quartz
of a character very similar to the Mina’ Rica.
‘The rock is hoisted from both of these mines
by horse power, the mining being done by Corbishmen, on contract, at fixed prices per foot
for sinking or driftiug.
The richest lode yet discovered in the district, is believed to he
THE CUMMINOS & HADLEY,
Owned by the parties whose name it bears, and
who sre making a vigorous effort to tes‘ its
permanence and value, and with very fair proapects of success in developing a valuable mine,
‘This vein is crossed hy two dykes of hard slate
about ten fect apart, between which the shaft
has been sunk to 2 depth of ninety feet. No
attempt has been made to drift through that
onthe north side, and its thickness is not
known, but the ore on the south side of the
sha{t, has been found to be about three feet
wide at the top, and to narrow gradually as it
goes down, until atthe depth of ninety feet
it almost disappears, and the two portions of
the vein are almost united. The vein at the
hottom is about four feet in width, while its
average thickness is fully twenty inches. 1
visited the mine on Saturday afternoon, the
17th instant, in company with Mr. Robert
Briggs of West Point. We were informed
that the rock from this vein, worked at Carltou’s mill, which is ahout halfa mile distant,
had averaged from $140 to $150 perton. A
short distance south of this is the Aino lead,
owned by Messrs. Carlton and Fischer, which
has been opened to a depth of 100 feet. It
dips to the west,at an angle of thirty-three
degrees, and is about one foot inaverage width.
The quartz differs from most of that in the
district in containing no sulphurets. It has
yielded ahout $85 per ton in free gold.
On Monday morning I started to visit the
mines in the neighborhood of Skull Flat, and
nn the way, fell in with Mr. A.M. Harris, of
Sandy Gulch, who was visiting Skull Flat on
business.
The oldest and most productive mine in this
vicinity is
LA SACOTERRE,
Sitnated about half a mile sonthwest of the
Skull Flat mill, and owned hy the Cassner
Bros., who are also owners of that mill. ‘The
lead was first discovered in 1855, since which
time over $100,000 are said to have been ©
taken out. It has been opened bya shaft to a
depth of 120 feet, while on the level of the
bottom of this shaft a tunnel has been driven
into the hill a distance of 300 feet, eighty feet
of which is on the vein. Its usual width is
from fifteen inches to two feet, though I was
told that at the bottom of the deepest shaft,
its width wag three feet. The average yield
of the rock worked from this vein for the past .
eleven years is set down at $80 per ton. \
-.