Transtrom Extraction for CSN/ Ohio Teslathon

["harvey norris" <harvich-at-yahoo-dot-com> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

The following entry in completion did not post to my
messageboard in a late night entry so I am posting now
to tesla list. The Ohio Teslathon appears to be on
with 4 coilers interested in attending, notably the
Doc whose name I have  trouble spelling. But he puts
on a good show, so when he can arrange a day on his
busy schedule the event can be scheduled. I am
thinking now a Friday would be better for more stuff
the next day. Some readers of CSN have difficulty with
cm as a definition of both inductance and capacitance,
so H L Transtroms comments are welcome in this regard.
It is amusing that if we knew nothing of this a close
reading of CSN provides the clues, which incidentally
if someone could clue me in to the CSN commentary
published by the Richmond Virginia Groups Richard
Hull; I will immediately purchase this for perusal at
the Ohio Teslathon. So heres the rest of the story;

Concerning the use of the term "cm" as inductance and
capacitance as found in the turn of the century
terminology found in Tesla's CSN is explained as
follows;
Electricity at High Pressures and Frequencies by
H.L.Transtrom (1913) talks about the concept of
isolated capacities and gives some highly unusual
figures. 
I will quote from pg.157 which I happened to have
marked.{this was a deja vu as formerly recorded from
other  discussion list entries that has been amplified
in definition} The capacity of isolated spheres are
found to vary as their radii. A sphere having a radius
of 1 centimeter, hung up in space at an infinite
distance from any other conductor;has unit
electrostatic capacity;so the capacity of spheres in
electrostatic units can be given directly from their
radii in centimeters. Consequently, a sphere having a
radius of 9 times 10 to the 11th power cm has a
capacity of one farad, and a sphere of 900,000 cm.
radius equals one microfarad; hence some authors write
1 microfarad as 900,000 cm of capacity. This usage of
the term capacity is used in that terminology in
Tesla's day  is as evidenced in the Colorado Spring
Notes.  Of particular interest beyond the case
examples found in Transtroms book is the entry dated 
June 7, 1899. This is 8 days before actual
experimental work begins on June 15. Here Tesla is
estimating the inductance of a single loop by a
formula that gives only two parameters for input, and
those values given in centimeters correspond to an
ANSWER understood in those days readily by that
definition. Now the usual method of determining
inductance in the century beyond Tesla's time was
Wheelers formula, undoobably also known at that
time... But what we have here is a fairly long formula
that tesla used to calculate this from knowing only
the parameter of the radius A of the loop and the
radius a of the {orthogonal relationship}of that wire
in circumference relationship to pi. This is a fairly
long formula using a summation of natural logs in
typical mathematical reference to the smaller terms
becoming infinitesimal. The CSN refers to the natural
logarithm as log base(e){term}, I have shortened this
to the modern  calculus convention of ln{term} for the
formula. Amazingly when Tesla first begins his
experimentation, his secondary only consists of a
conical 14 turns with average width of 130 ft/turn.
>From there he rapidly deduces the extra coil effect:
also properly considered as an autotransformer
application. Tesla also refers to this inductance as
L(s), which brings some confusion as what he is
refering to in the single loop case must be L(p) or
primary. In any case the formula he supplies  for the
primary is assumed to be widely used at the time as
follows in CSN; with all {} as my comments also
designated as interior parentheses.

Also in Tesla's calculation he neglects the last term
as negligible. Having noticed this let us rerturn to
Transtrom's definitions: a man electrocuted in error
of judgement after noting Teslas  entry.
June 7,1899
Approximate estimate of a primary turn to be used in
experimental station.
L(s){?}= 3.14{pi}[ 4A{ln (8A/a)-2)} + 2a{ln
(8A/a)-5/4} - a^2/16A{2 ln(8A/a) + 19}]

TRANSTROM'S Definition of UNIT VALUES
Now concerning the use of inductance defined in terms
of cm , Transtrom also goes into this on pg 80-82.
The inductance of a circuit is sometimes expressed in
centimeters, one of the cgs units or absolute units.
By definition a circuit has a self induction of one
henry when it generates a counter emf of one volt when
the current is varied at a uniform rate of one ampere
per second-- that is the circuit cuts 10^8 lines per
second: so a circuit of one turn which has a flux of
one Weber (10^8) when one ampere is flowing through
it, has an inductance of one henry.
One volt then represents a movement of a single
conductor of 100,000 cm per second across a unit field
(1 line per square cm) In this way the emf in volts
can be given the dimension of length, namely 10^8 cm.
As a circuit of one henry inductance generates a
counter emf of 1,000,000,000 centimeters when a change
of one ampere, or one tenth unit of current per
second, it is plain that the counter emf would be ten
times as high, or ten volts (1,000,000,000 cm) when
the rate of current change per second is unity (or ten
amps per second) Therefore one Henry of inductance is
given the dimension of 1,000,000,000 cm.  In a circuit
of only one turn the inductance in centimeters can be
directly obtained from the number of lines enclosed
when a current of 10 amperes is flowing through the
conductor.
The Henry  was once called the secohm, because a
circuit having an inductance of one henry would only
permit a rate of change of one ampere per second when
the impressed current had an emf of one volt, and as
the counter emf acted as one ohm resistance, we see
from this that the inductance can be expresssed in
ohms.
The henry has also been called the quad, or quadrant
because in the metric system a quadrant of the earth
from the equator to the pole equals approximately 10^9
centimeters. Both terms mentioned above are now quite
obsolete.
Retracing these century old definitions further on
around  pg 10
(cgs measurement system)
In order to handle scientific subjects intelligently,
a system of units of measurements has been
constructed, in which the unit of time is one second,
the unit of length one centimeter, and the unit of
weight one gramme { A cubic cm of water is also one
gram, HDN}
If one gramme is moved one cm in one second the force
required to do this is one dyne. The work accomplished
is one erg. The force of gravity is 981.45 centimeters
per sec{note this may appear out of context as gravity
expressed as acceleration is expressed as m/sec^2 HDN}
Therefore the force required to oppose it in lifting
one gramme, one centimeter high is 981.45 dynes. Thus
the dyne can be expressed in weight or 1/981.45
gramme. { Aha! Henry is correct! In the English system
the force unit is often misinterpreted as the mass
unit. Because the acceleration of gravity is 32 ft
/sec^2  and the actual mass unit one slug, one lb unit
of force = mg= one slug*32 ft/sec^2= 1 lb. Thus in
earths gravity 32 slugs=1 lb.   Gramme is also the
spelling used in the book which I am leaving for
authenticicty HDN}
If a magnetic pole repels or attracts another magnetic
pole having the same number of lines of force issuing
from it, with a force of one dyne when they are
separated a distance of one centimeter, it is termed a
unit magnet pole. In other words the attraction or
pull is equal to 1/981.4 gram when they are 1 cm
apart. The strength of the magnetic field of a unit
magnet pole one cm away is one line of force per
square cm, and is called the unit magnetic field.
If we think of the lines of force of a unit magnet
pole as issuing in all directions with an equal
strength, or one line of  force=12.5664 lines of
force, which is called its magnetic flux. The magnetic
field or flux, is expressed by the Greek letter phi.
12.5664 =4 times Pi(3.14)
This figure 4*Pi times the radius squared= the surface
of a sphere, as the distance of one cm is the radius
of the unit magnet pole and the surface wold contain
4*pi*1^2 = 12.5664 sq cm, and as each of these squares
would contain one line of force, the sum of all the
squares would be 12.5664 lines of force. If the
strength of the magnet is doubled the DENSITY is
doubled the force in dynes is also doubled, for
4(pi)(rad)^2 X 2 lines =25.1328 lines = phi.
If the phi is divided by 4 (pi)(rad)^2 the result =
psi
The absolute unit of current is 10 amperes,since it
will produce a unit magnetic field of phi= 12.5664
lines around a conductor for every centimeter of its
length, provided it is straight and the return
conductor is very distant with the air as the medium
surrounding it. Therefore the practical unit of
current is .1 of the absolute unit which was found to
be to large for convenience.
{The unity employed with absolute units starts to make
sense on this pg 41 entry  concerning back emf effects
on generation of  electrical power  HDN}

The electromotive force depends on the RATE  of
cutting the lines of force. When a conductor is moved
ACROSS a unit magnetic field ( which is described as
containing in one line of force per square centimeter,
psi=1, being uniform throughout) in one second,
thereby cutting one line per second, there is
generated a UNIT emf. If the conductor is moved twice
as fast across the same field, the emf is doubled; but
if the field is weakened the conductor must move
faster to cut as many lines per second as before, and
slower if the field is strengthened.
{Note now this important entry}
 If unit emf is generated in the conductor and we find
the find that its motion is opposed with a force of
one dyne, the conductor would be carrying unit
current, and its resistance according to Ohms law
would also be unity, for E/I= R.  Or 1 unit emf/1unit
current=1, or one unit resistance.
As unit emf is so exceedingly small, a PRACTICAL unit
, the VOLT is used. It is equal to 100,000,000 times
the THEORETICAL unit, or it may be expressed as the
emf generated by cutting lines of force at a rate of
1,000,000 per second {The forms of} Ohms Law are all
in PRACTICAL units.

As the ampere is only .1 of unit current, and the volt
is 100,000,000  {10^9} times the unit emf, the ohm=
{10^9/.1 = 10^10, or 1 billion to one so unit
resistance can be expressed in decimals as .0000000001
ohms. {HDN Note: Scientific Notation is not used in
the book and I have done some paraphasing of contents
for simplicity enclosed by brackets when the
interjections are mine}

Unit work is done in unit time when unit force is
exerted against the motion of a conductor through a
unit field at unit speed: thus producing a unit
current at unit emf through unit resistance. The WORK
done in this case is one ERG per second, or one dyne
overcome through one centimeter.

As the force in dynes opposing the movements of the
conductor increases directly with every additional
unit of current,  and every additional unit of emf
represents an increase in movement of one centimeter
per second in a unit field, the work done must equal
their product,  As one volt represents a movement
through a unit field of 100,000,000 centimeters in one
second to cut 100,000,000 lines of force, and as one
ampere would exert only one tenth of a dyne of force
against the movement, the work done by one ampere
flowing through a circuit at one volt would by 1/10
dyne overcome through 100,000,000 cm, or 10,000,000
ERGS per second. This product is termed one WATT.
{HDN; We also know this as one joule per second
established in the m/kg/sec system which exact name
escapes me in this late entry.}
Sincerely getting the job done; HDN


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