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snapping nor pain was felt ; yet a very bright light appeared.

The rod, of 4 feet long, being placed on a stand, having a cross arm, with a
groove in it, to receive the rod ; and then the stand being placed on the glass
cylinder, they were set at such a distance, as that one of the points of the rod
might just touch the ball over against its centre ; then going to the other end
of the rod with the excited tube, he applied it as usual ; when he came to the
ball, the hand or cheek being near it, caused a loud snap, compared to those
made by the points of the rods, and the pain of pricking or burning was more
strongly felt ; the light was also brighter and more contracted. The rod being
then placed with its point at an inch distance from the ball, and applying the
rod as before, then touching the ball with his finger, there not only appeared a
light on the ball, but there also proceeded a pencil of light from the point of
the rod, after the same manner as when the experiments were made with the
rods only.

The following experiment was made with the 4-foot rod, and a brass plate 4
feet square. This was placed on a stand, so that the plate stood perpendicular,
the stand being set on the cylindric glass ; then the rod with its stand and glass
was set in such a manner, that one point of it was about an inch from the centre



VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 5

of the plate ; then the tube being applied to the other end of the rod, and after
going to the plate, on striking it gently with the finger on the backside, a light
appeared on the plate, and at the same time the pencil of light issued from the
point of the rod ; and when the hand or cheek was held near any of the angles
of the plate, a light issued from thence, with a small hissing noise, and the
pricking was felt, as when the experiments were made with the pointed rods.

A pewter plate being laid on the stand, which had been set on a glass cylin-
der, applying first the tube, and then the finger, a light appeared on the plate,
and the end of the finger was pushed ; and when the cheek was held near the
edge of the plate, a snapping was heard, but not so loud as when the iron rods
were used. On filling the plate with water, and applying the tube and finger as
before, there was the same light, with the pushing of the finger and snapping,
as when the experiment was made with the empty plate. When the experi-
ment is made with water by day-light ; by applying the end of the finger near
the surface of the water, it appears to rise in a little hill, but on the snapping
noise it falls down again, putting the water into a waving motion, near the place
where the water had risen.

He then took a wooden dish, and placed it on the stand, first empty ; then
applying the tube and the finger near the dish, a light appeared, but no pushing
of the finger, nor snapping. He then filled the dish with water, and the tube
being held over the surface of it, there appeared a greater light than when the
finger had been applied to the empty dish, but no snapping ; till by holding the
tube, after it had been well rubbed, within 2 or 3 inches of the finger that was
held near the surface of the water ; for then the finger was pushed, and a snap-
ping noise wafe heard, as when the experiment was made with the pewter
plate.

By these experiments we see, that an actual flame of fire, with an explosion,
and an ebullition of cold water, may be produced by communicative electricity;
and though these effects are at present but in minimis, it is probable that in
time there may be found out a way to collect a greater quantity of it ; and con-
sequently to increase the force of this electric fire ; which, by several of these
experiments, seems to be of the same nature with that of thunder and
lightning.

A General Method of describing Curves, by the Intersection of Right Lines,
moving round Points in a Given Plane. By the Rev. IVm. Braikenridge.
N° 436, p. 25. Translated from the Latin.

The following general method of describing lines of any order, by the inter-



6 PHILOSOPHICAL TRANSACTIONS. [anNO J 735,

section of right lines moved round poles, Mr. Braikenridge thinks is much more
simple than that of Sir I. Newton, and will give a solution of many difficult pro-
blems, which he doubts if they can be found by any other principles. The
author gave only one particular case of this in his Geometrical Exercitation,
printed at London in 1733, not thinking it convenient to explain the whole
method at that time, though he was then, he says, well acquainted with that
method. It is now, he says, 3 years since he fell upon the general theorem,
which he had many reasons for concealing ; being determined to let 2 years at
least pass, after the publication of that Exercitation, before disclosing this
general method : for he doubted not, that if any others were possessed of this
invention, they would, on the publication of a particular case, especially as they
were provoked to it, embrace the opportunity to publish their general method,
if they had really discovered one.

About 3 given points, as poles, a, b, c, fig. 1, pi. 1, in any plane, let there
be turned 3 right lines, ans, bos, cno, which may intersect each other in the
points s, n, o ; and let the two points of intersection s and n be drawn along
the right lines dks, knk, given by position ; then the remaining point o will
describe a conic section ; as is demonstrated in the Exercit. prop. 1. — If through
the points a, b, c, be drawn the right lines ab, ac, meeting each other in a,
and the right lines rk, dk, given by position, in r and m ; then the figure de-
scribed will pass through the 5 points b, c, k, m, r. And hence appears a new
method of describing a conic section through 5 given points, much easier than
any yet invented. See Exercit. prop. 3.

Let there be moved around 4 points a, b, c, d, fig. 2, as poles, in any plane,
as many right lines ans, bos, cno, dpo, three of which, ans, bos, cno, may
intersect each other in three points, s, n, o ; and let the two points of inter-
section s, N, be drawn along the right lines dK, rk, given in position ; and at
the same time let the right line dpo, drawn from the 4th pole d, pass through
the remaining point o, and cut the right line ans in p : then that point p
will describe a line of the 3d order : as is demonstrated prop. 1 1 of the exer-
citation.

Through the poles a, b, d, let there be drawn the right lines abr, bdh,
meeting each other in b, and the right lines kr, Kd, given by position, in r
and H : then the figure described by the motion of the point p, will pass
through the 3 points a, d, h, k, r, of which a will be double. Hence is de-
duced a method of describing a line of the 3d order through 7 given points,
one of which may be double. For let a, d, h, k, p, m, r be given, fig. 3, one
of which A is to be double. Through the two points h, r, and another k, let
the right lines hk, rk pass ; also join the points a, r, and h, d, and produce ar,



VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 7

HD, to meet each other in b. Then through a and the points p, M, draw the
right lines apms, amhs, cutting the right line kr in n and n, and the right line
HK in s, s ; tlirough these points s, s, to the point b, draw bs, bs ; and through
D, to the points p, m, draw the lines dpo, dmt, meeting bs, bs, in o and t.
Draw ON, xn, produced to meet in c. Then about the points a, b, c, d, as
poles, let there be revolved the lines as, bo, co, do, of which the three as, bo,
CO intersect in s, n, o ; and let the two s, n move along the lines hk, kr, while
the line do always passes through the remaining point o, and cuts ans in p ;
then this intersection p, of the right lines as, do, will describe a line of the 3d
order, passing through the ^ given points, a, d, h, k, m, p, r, and doubly
through the given point a.

Lines of the 3d order also are more generally, but less commodiously, de«
scribed after this manner, which also comprehends the former. About 5 given
points. A, b, c, d, e, fig. 4, as poles, let as many right lines ans, bos, cno,
dpo, EPS, revolve, of which the three ans, bos, cno intersect each other in
the points n, s, o; let the two s, n be moved along the lines dK, kr given in
position ; and through one s, of the two n, s, and the remaining point o, let
the lines eps, dpo pass, being drawn through the poles e, d, and meeting in p:
then this point p will describe a line of the 3d order, with a double point in the
pole E.

In like manner may lines of the 4th order be described. About the 5 given
joined points a, b, c, d, e, fig. 5, as poles, in any plane, let as many right lines,
ans, bqs, cno, dpo, EPa, be moved ; of which the three ans, bqs, cno meet '
in the three points s, n, o ; let the two points of intersection s, n be drawn
along the lines dK, rk, given in position, while the line dpo, moveable about
the 4th pole d, passes through the remaining point o, and cuts the line ans in
p ; then let the line epg, drawn from the 5th pole e, be drawn through p, and
be produced both ways to meet the lines sas, cno, in q and w : then will the
points a and w describe lines of the 4th order ; as is demonstrated by prop, ll
of the Exercitatio. Through the poles a, e, and b, d, let the lines aeh, bdf,
pass, meeting dK, given by position, in h and f ; join de ; and through the
poles d and a, the line ad being drawn, meeting dK in v; from which point v
let the line vb be drawn to the pole b, and cut the line de in g. Then the
figure described will pass through the 5 points b, e, g, f, h, and triply through
the pole B. Through the poles a, b, let there be produced the line abr, meet
ing the line kr, given by position, in r ; then the curve will also pass through
the points r, k.

Hence is derived a method of drawing a line of the 4th order through Q given
points, one of which is a triple point. For let b. e. f, g, h, l, m, t, a be given,



^



1



8 PHILOSOPHICAL TRANSACTIONS. [anNO J735.

one of which b is to be triple, fig. 6. Join the points bf, fh, he, and pro-
ducing these three lines ; and through the points eg, gb, let the lines egd,
BGV be drawn, of which let egd cut bf in d, and the other line bgv cut fh in
V. Then having joined v and d, and produced vd to meet he in a, draw the
line dABR through the points a, b. Then from the points b, e let the lines
Has, EPQ be inflected to the given point q, of which let the first Bas meet fh
produced in s ; and through the points a, s having drawn as, meeting eq in p,
let DPO be produced through p and d, and meet Bas in o : and note the point o.
In like manner, from the same b, e, to another given point t, let the lines
BTS, EpT (supply the figure) be inflected, of which let bts meet fh in s ; and
having drawn as cutting EpT in p, draw npz through p and d, meeting bts in
z, and mark the point z. And thus let lines be drawn from the same b, e, to
the other given points m, l, and drawing lines from a and d as before, let the
points so found be marked x, y. Then through the 4 points thus found,
o, z, X, Y, and the given point b, let a conic section be described (see prop. 3,
exercit.), cutting fh in the points i, k, and the line dAB in b, r. Through the
points A, I draw the line ax, cutting the conic section in i and c ; join the points
K, R, and let this line kr be produced. Now about the 5 points a, b, c, d, e,
as poles, let as many lines, as, bs, cn, do, Ea, revolve, of which three as, bs,
ON meet each other in n, s, o ; and let the intersections n and s, of the lines
as, on, and as, bs, be drawn along kr and fhk, while the line dpo passes
through the pole d, and the intersection o of the lines bs, cn, and cut the line
as in p ; and through p and the pole e, let EPa be produced to cut bs in a :
then this intersection a will describe a line of the 4th order, passing through
the 9 given points, b, e, f, g, h, l, m, t, a, one of which b will be triple.

By a method not much unlike this, a line of the 4th order may be described
through 8 given points, 3 of which are double; as also a line of the same order
through 1 1 given points, 2 of which are double ; with many other cases of that
kind.

As to the number of points which determine a line of any order, Mr. B. says,
that if n denote the number of the dimensions of a line ; then tr + 1 will be
the number of points through which the line may be described. For instance,
a line of the 2d order through 5 points, one of the 3d order through 10, of
the 4th order through 17, of the 5th order through 2d points. And hence is
deduced, that if a line of the 11th order have an « — 1 multiple point, it may
be described through 2n + 1 points. For instance, a line of the 3d order,
with a double point, (viz. n — 1 = 2) through 7 points, and a line of the 4th
order with a triple point, through Q, &c. And generally, if p, q, r, &c. denote
multiplex points, the number of which is m, a curve can be described through



VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. - Q

w'^ — p'^ — q- — r^ -\- m -\- \ points, of which there are m multiplex points.
Thus, a line of the 4th order, with 3 double points, may be described through
8 points : for n = 4, /) = 9 = r = 2, m = 3, and l() — 4 — 4 —44-
3+1=8.

There is another method also of describing lines of the 4th order, not much
different from the former, but a little more complex. About 7 poles. A, b, c, d,

E, F, G, (fig. 7), let there revolve as many lines, as, bs, cn, ds, en, fo, gt, one
of which ANS, by revolving, cuts the lines dK, kk, given by position, in the
points s, N ; let the lines cn, bn be drawn through one of them n, and the
lines BS, ds through the other s, and meet the lines cn, kn, in the points o, t,
describing conic sections as above; while the lines fo, gt, drawn from the poles

F, G, pass through the same o, t, and meet in p : then the intersection p will
describe a line of the 4th order, with a double point in both the poles f, g.

But not to dwell longer on these, Mr. B. now gives the following general
theorem. About the poles a, b, c, d, e, f, g, h, &c. (fig. 8), whose number is
n, let as many lines as, bs, cn, dp, eq, fw, gx, hy, &c. revolve, of which the
three as, bs, cn intersect each other in the points n, s, o ; let two, s, n, be
drawn along the lines dK, kr, given in position; while through the third o and
the pole D, passes the line dp, cutting as in p ; and through p and the pole e
draw the line Ea, cutting bs in a ; and from a through the pole f let Fa be
drawn, cutting as in w ; also through w and the pole g draw gw, cutting bs
in X ; and then through x and the pole h draw hy, meeting sa in y ; and so
on : then the concourse y, of the line hy, drawn from the last pole h, with
either of the lines as, bs, will describe a line of the n — 1 order, and have the
n — 2 multiplex point in the pole a or b, like as it was described by the inter-
section of the line as or bs. The points o, p, a, w, x, y, &c. will describe lines
of the 2d, 3d, 4th, 5lh, 6th, 7th, &c. order. But if all the poles a, b, c, d, e,
F, G, H, &c. be situated in the same right line, then those points o, p, a w x
Y, &c. will also describe as many right lines.

The Newtonian description of curves is also greatly promoted by this method.
It is well known, that if the given angles oan, obn. revolve about the given
points a, b (fig. 9) and the intersection n, of the legs an, bn, be drawn along
the line nr, given in position ; then the concourse o, of the legs ao, bo, will
describe a conic section. Now let another point c be taken, about which let
the line ocp be moved, which shall always pass through the intersection o of
the legs AO, bo, and meet the other leg an of the angle a in p : then the in-
tersection p will describe a line of the 3d order, passing doubly through the
pole a. In like manner, if by the intersection of the leg bn, of the angle b, a
curve be describedj it will be of the same order, and have a double point in the

VOL. VIII, C



10 PHILOSOPHICAL TRANSACTIONS. [anNO 1735.

pole B. And hence also it appears, how a line of the 3d order may be described
through 7 given points, one of which may be double.

Let the angles oan, obn, be moved as before, about the given points a, b,
(fig. 10) ; and through the intersection o, of the legs oa, ob, let the line ocp
pass, drawn from another given point c, meeting the side an, of the angle a,
in p ; then through p, and a 4th given point d, draw the line dpq, meeting
the leg Ao in Q ; then the point a will describe a line of the 4th order, having
a triple point in the pole a.

And thus, by increasing the number of the poles a, b, c, d, &c. so that their
number at length may be n, the line described will be of the same order n. But
it may be noted, that if for the angle obn, there be substituted a right line, re-
volved about the pole b, the description will become easier.

j4n Account of M. Seignettes* Sal Polychrestus Rupellensis, and some other
Chemical Salts. Bij M. Geoffrey. N" 436, p. 37.

M. Seignette's sal polychrestus rupellensis is a soluble tartar, composed of
cream or crystals of tartar, and the fixed salt of the kali of Alicant,-|- well de-
purated. This salt is very singular: for, though it be a fixed alcaline salt, it
has the peculiar property of crystallizing; nor does it easily dissolve in the open
air ; as other fixed salts do ; but on the contrary calcines in it like vitriols or
Glauber's salt. Another peculiar property M. GeofFroy observed of it is, that if
it be saturated with vitriolic acid, and the liquor be evaporated, there results a
salt that resembles Glauber's salt, and has all the properties requisite to make
M. Seignette's salt.

To produce this, take of the salt of kali [of Alicant] well depurated, 1 lb ;
dissolve it in water, add about 1 lb. ss. of crystals of tartar ; boil the whole, to
dissolve the crystals : but the exact proportion of crystals of tartar can be de-
termined no more in this operation, than in making the soluble tartar ; either
because the salt of kali has retained more or less humidity in its crystallization,
or because the tartar has more or less impurities in it. But if there be too much
tartar in the alkaline liquor, after the fermentation is over, filtrate the liquor,
and as it cools, the superfluous tartar will fall to the bottom. After the sepa-
ration of the tartar from the liquor, evaporate the lixivium by a gentle fire ; set
it in a cool place to crystallize, and you will have very fine crystals. If the

* M. Seignette was an apothecary at Rochelle, whence this salt has been called Rochelle salt.

t The kali of Alicant is a marine plant (Salsola sativa Linn.) from which, by incineration, is ob-
tained the fossil alkali or soda, which uniting with the superfluous acid of the crystals of tartar, forms
a triple salt, compounded of tartaric acid, potass and soda, and denominated in the modern chemical
nomenclature tartrite of potass and soda.



VOL. XX XIX. J PHILOSOPHICAL TKANSACTIONS. 11

liquor be evaporated a little too much, there will be no crystals of salt formed,
but the liquor will be converted into a hard transparent mass, not unlike glue.
But by dissolving this mass again, it is made to crystallize, as on dissolving
M. Seignette's salt.

This salt purges very well, from I to 2 oz. dissolved in a quart of water.

M. GeofFroy employed himself in perfecting this salt, and in examining the salt
of kali, and comparing it with borax. From the salt of kali he extracted Glauber's
salt, by mixing it with oil of vitriol. He next made experiments on borax. A
mixture of 4 oz. of borax with 1 oz. and I dr. of vitriol, on sublimation, gives
the sedative salt, described by M. Homberg ; and the residue exposed to a
strong fire, afforded Glauber's salt.* M. GeofFroy found out a method *o
shorten this operation : for, instead of subliming this salt, he procured it by
crystallization in light foliated laminae. This salt, whether sublimated, or
crystallized, has the property of dissolving in sp. of wine ; and when this sp. of
wine is set on fire, its flame is green. Sp. of wine has no effect on borax ; the
oil of vitriol, digested with sp. of wine, communicates no greenness to its flame;
it is therefore requisite that the borax be united with an acid, in order to pro
duce this green flame.

Sedative salt, made by crystallization, crystallizes in a peculiar manner : this
operation is performed with 4 oz. of borax, 1 oz. and 1 dr. of concentrated oil
of vitriol, the most fixed and weighty that can be had. The borax is put into a
glass retort ; the oil of vitriol is poured on it ; and then -J- oz. of common water.
This mixture being exposed to a fire, gradually increases, after the phlegm has
passed off, and even while it is passing there rise flowers, or a volatile salt, in
very beautiful foliated laminae, some of which melt by the heat of the fire.
After the operation, the finest of these flowers, which are round the neck of
the retort, are gathered ; and those that are grey are thrown on the remaining
mass ; which mass is dissolved in water, filtrated and evaporated slowly. Some-
times even without evaporation, the shining talcous laminse are to be seen in
the liquor. In 24 hours the liquor is poured from these laminae ; they are washed
in fair water, set to drain, and then to dry in a stove. -j~

If these crystals do not calcine in the stove, or in the sun, it is a sign there
is nothing crystallized but the sedative salt : if they do calcine, it is a sign that
there is some Glauber's salt mixed: and then this salt must be dissolved again in

• Borax being compounded of a peculiar acid termed boracic acid and soda, its own acid is ex-
pelled from the alkaline base by the vitriolic or sulphuric acid of the vitriol here employed ; which
unites with the said alkaline base, and forms with it Glauber's salt, i e. sulphate of soda.

t The product here termed sedative salt, is now known to be the acid of borax.

02



J2 HHtLOSUFHICAL TRAK8ACTIONS. [aNNO 1735.

hot water, and re-crystallized. No one before M. GeofFroy thought of extract-
ing this salt by crystallization, being always before sublimed.

An Account of a Machine for changing the Air of the Room of sick People iti a
little Time, by either draiving out the foul Air, or forcing in fresh Air ; or
doing both successively, without opening Doors or Windows. By Dr. J. T.
Desaguliers, F. R. S. N''487, p. 41.

Fig. ] , pi. 2, represents a case, secb, containing a wheel of 7 feet diameter,
and 1 foot thick ; being a cylindrical box, divided into 1 2 cavities, by partitions
directed from the circumference towards the centre, but wanting 9 inches of
reaching this, being open towards the centre, and also towards the circumfer-
ence, and only closed at the circumference by the case, in which the wheel
turns by means of a handle fixed to its axis a, turning in two iron forks, or
half concave cylinders, of bell-metal, such as a, fixed to the upright timber or
standard ae.

From the middle of the case on the other side behind a, comes out a trunk
or square pipe, called the sucking-pipe ; which is continued quite to the upper
part of the sick person's room, whether it be near or far from the place where
the machine stands, or in an upper or lower story, or above or below the ma-
chine. There is a round hole in one of the circular planes of the machine, of
18 inches diameter round the axis, just where the pipe is inserted into the case,
by which the pipe communicates with all the cavities ; and as the wheel is
turned swiftly round, the air which comes from the sick room, is taken in at
the •centre of the wheel, and driven to the circumference, so as to go out with
great swiftness at the blowing-pipe b, fixed to it

As the foul air is drawn away from the sick rooms, the air in the neighbour-
ing apartments gradually comes into the room through the smallest passages :
but there is a contrivance to apply the pipes which go to the sick room to the
blowing-pipe b, while the sucking-pipe receives its air only from the room where
the machine stands. By this means fresh air may be driven into the sick room,
after the foul has been drawn out.

This machine would be of great use in all hospitals, and in prisons : it would
also serve very well to convey warm or cold air into any distant room ; or even
to perfume it on occasion.

Fig. 2 represents the inside of the flat of the wheel, which is farthest from
the handle, and next to the sucking-pipe. 1,2,3, 4, represents the cavity or
hole which receives the air round the axis, having about it a circular plate of
iron, to hold all firm ; which plate is made fast to the wood and to the iron



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