Improvements in Means or Apparatus for Facilitating Calculations relating to the Supply of Electrical Energy.
Year: 1890

page_text: Date of Application, 24th Jan., 1890
Complete Specification Left, 24th Oct., 1890-Accepted, 29th Nov., 1890
DDAYziara
ש-
LIUOTIAAL
STI
מחTA CET CIT
RUTTIVALIA.
Improvements in Means or Apparatus for Facilitating Calculations
relating to the Supply of Electrical Energy.
ALEXANDER PELHAM TROTTER of 28 Victoria Street, in the City of Westminster,
Civil Engineer do hereby declare the nature of this invention to be as follows:-
My invention has for its object the facilitation of calculations relating to the
selection and use of wire and cables to be used for the supply of electric energy.
To ascertain the proper size of a conductor which is to carry a current of electricity
to light a given number of lamps, each taking a potential difference of a given number
of volts, and taking power at the rate of a given number of watts, it is necessary to
consider the difference of potential due to the resistance of the conductor, and the
density of the current per unit of sectional area, since the heating effect depends upon
this density.
It has been the custom either to calculate the proper size of conductors from their
sectional area, from which their resistance may be found, or to use tables which have
been compiled to assist such calculations. In these tables a fixed fall of potential has
commonly been assumed, and a fixed voltage of lamps, and a fixed density of
current has been assumed as a maximum, generally one thousand amperes per square
inch.
By the use of my invention, it is not necessary to assume any fixed data. Lamps
of any size, taking power at rates varying over a considerable range, and requiring
any difference of potential within the limits used in practice; and any number of
such lamps, say up to one hundred, or two hundred; with any fall of potential due to
the resistance of the conductor within the usual limits of practice; or a given current
expressed in amperes; may be taken as the data of the calculation, together with any
length of conductor from say 40 to 1000 yards; and the required size of cable may
be found with ease, without any mathematical operation; the size being expressed in
the usual manner by the specification of the number of strands from which the cable
is formed, and the gauge of each strand expressed in terms of the Board of Trade
standard wire gauge, or in the Birmingham wire gauge, or other standard of
measurement.
Or if it is desired to ascertain the fall of potential when certain lamps are used
with a cable, of a given size and length, or with a given current; or if it be required
to know the number of lamps of a given kind which can be run on a given cable
with a given fall of potential due to the resistance of the cable; or briefly, if any six
of the data are given, the seventh may be found with ease, and in addition, the
density of the current in amperes per square inch may be found, and the maximum
current which the cable will carry, as defined by the Board of Trade regulation
that the temperature of the conductor shall not rise above 30 degrees of Fahrenheit's
thermometer.
In carrying out my invention, I provide four or more parallel scales, made of
cardboard, celluloid, ivory or wood, or other suitable material, of which two are fixed
relatively to each other, and the others are capable of sliding evenly between the outer
scales, in the direction of their length. I lay out on the parallel edges of the scales,
the differences of the logarithms of a series of numbers, in order, in such a manner
that a straight line drawn at right angles across any pair shall intersect them at
divisions denoting numbers in geometrical progression; then from the condition of the
arrangement, and the property of this logarithmic line, it follows, that every line so
drawn will, by its intersections, indicate a geometrical series of numbers; that such
series as are indicated by these straight lines will have the same common ratio; and
that the series thus indicated by two parallel straight lines at right angles to the edges
го .

page_text: where c is the current, and d is the diameter of the wire in inches. On the third scale,
between the two series of logarithmic divisions already described, 1 inscribe an inverse
logarithmic series, denoting the density of current in amperes per square inch for any
cable when a fall of potential of two volts is assumed. The scales may be arranged
in a manner similar to that already described, so that the density of current might be
read off for any fall of potential. On the first and second scales I draw a line
across the adjacent parallel edges, so that when the two scales are placed so that each
division of the one corresponds exactly to the similar division of the other, the
portions of this line on each scale form one continuous line, and against this line I
place the word amperes. If the problem be stated in amperes instead of in lamps of
a given uumber of watts and volts, these two lines are brought into adjustment, each
to each, and the numbers on the logarithmic scale on the other edge of the second
scale then denote the number of amperes.
In another form of my invention, I inscribe the logarithmic series of divisions on
circular discs of card or other material, and provide a common centre or pivot on
which they may be turned, so that any point on the circumference of one disc may
be brought in a radial line with any part of the circumference of any adjacent disc.
The dises are of different sizes, and are placed, the smallest at the top, allowing an
annulus of the next disc to appear, and on this annulus I inscribe the logarithmic
divisions and the numbers denoting their numerical value in terms of the datum which
each is arranged to express.

page_text: To use my invention for ascertaining the solution of any problem, for example, to
find the proper conductor to use under given circumstances; I find on the first scale,
the number of watts which each lamp takes, and by sliding the second scale I bring
opposite to the division denoting the watts, a division denoting the volts which the
lamps are to take. On the lower edge of the second scale I find the number of
lamps to be used on the conductor in question, and by sliding the third scale, I bring
opposite to this number, the number donoting the fall of potential allowed. Then, on
the fourth scale, I find the nearest size of cable, opposite to the number of yards
length of the cable. Below the size of the cable I find the maximum number of
amperes that can be permitted, and if the fall of potential allowed be two volts, I
find on the inverse series of divisions on the third scale, the density of the current in
amperes per square inch.
With the scales divided as described, the resistance of any cable may be determined
in the following manner. Bring the division numbered 100 on the lower edge of the
third scale, opposite to the size of the cable whose resistance is required to he found.
Leave the second scale and first scale set as for amperes. Find the length of the
cable on the lower edge of the second scale, and on the adjacent edge of the third
scale, the resistance may be read. If the units on the lower edge of the second
scale denote hundreds of yards, the numbers on the upper edge of the third scale
denote ohms.
ALEXANDER PELHAM TROTTER.
COMPLETE SPECIFICATION.
Improvements in Means or Apparatus for Facilitating Calculations
relating to the Supply of Electrical Energy.
I ALEXANDER PELHAM TROTTER of 28 Victoria Street, in the City of Westminster,
Civil Engineer do hereby declare the nature of this invention and in what manner the
same is to be performed, to be particularly described and ascertained in and by
the following statement :-
My invention has for its object, the facilitation of calculations relating to the
selection and use of wires and cables to be used for the supply of electric energy.
To ascertain the proper size of a conductor which is to carry a current of electricity
to light a given number of lamps, each taking a potential difference of a given number
of volts, and taking power at the rate of a given number of watts, it is necessary to
consider the difference of potential due to the resistance of the conductor, and the
density of the current per unit of sectional area, since the heating effect depends upon
this density.
It has been the custom either to calculate the proper size of conductors from
their sectional area, from which their resistance may be found, or to use tables
which have been compiled to assist such calculations. In these tables, a fixed
fall of potential has commonly been assumed and a fixed voltage of lamps, and a
fixed density of current has been assumed as a maximum, generally one thousand
amperes per square inch.
By the use of my invention, it is not necessary to assume any fixed data,
lamps of any size, taking power at rates varying over a considerable range, and
requiring any difference of potential within the limits used in practice; and any
number of such lamps say up to one hundred, or two hundred; with any fall of
potential due to the resistance of the conductor within the usual limits of practice;
or a given current expressed in amperes; may be taken as the data of the
calculation, together with any length of conductor from say 40 to 1000 yards;
and the required size of cable may be found with ease, without any mathematical
operation; the size being expressed in the usual manner by the specification of
the number of strands from which the cable is formed, and the gauge of each
strand expressed in terms of the Board of Trade standard wire gauge, or in the
Birmingham wire gauge, or other standard of measurement.
Or if it is desired to ascertain the fall of potential when certain lamps are used

page_text: with a cable, of a given size and length or with a given current or if it be
required to know the number of lamps of a given kind which can be run on a
given cable with a given fall of potential due to the resistance of the cable; or
briefly, if any six of the data are given, the seventh may be found with ease, and
in addition, the density of the current in amperes per square inch may be found,
and the maximum current which the cable will carry, as defined by the Board of
Trade regulation that the temperature of the conductor shall not rise above
30 degrees of Fahrenheit's thermometer.
In carrying out my invention, I provide four or more parallel scales, made of
cardboard, celluloid, ivory or wood, or other suitable material, of which, two are
fixed relatively to each other, and the others are capable of sliding evenly between
the outer scales, in the direction of their length. lay out on the parallel edges
of the scales, the differences of the logarithms of a series of numbers in order, in
such a manner that a straight line drawn at right angles across any pair shall inter-
sect them at divisions denoting numbers in geometrical progression; then from the
condition of the arrangement, and the property of this logarithmic line, it follows
that every line so drawn will, by its intersections, indicate a geometrical series of
numbers; that such series as are indicated by these straight lines will have the same
common ratio; and that the series thus indicated by two parallel straight lines at
right angles to the edges of the scales, supposed to move laterally, without either
changing their mutual distance or parallelism to themselves, will each have the same
ratio; and in all series indicated by two such lines, the ratio between the antecedent
and the consequent, the former taken on one line, and the latter upon another will
be the same, because the intervals on the logarithmic line, or the differences of the
logarithms of those numbers are equal, and the differences of the logarithms of
opposite numbers and therefore of their ratios will be always constant.
In one form of my invention, I arrange a logarithmic series denoting the power
taken in watts for each lamp, and I inscribe or engrave this series on one of the
pair of fixed scales.
On the adjacent and moveable scale, I inscribe a precisely similar logarithmic
series, denoting the difference of potential at which the lamps are to be run.
On the
other parallel edge of this second scale, I inscribe a logarithmic series, denoting the
number of lamps or the number of amperes, and on the adjacent edge of the third
scale which is independently moveable, I inscribe a logarithmic series denoting the
fall of potential due to the resistance of the cable the numerical value of any division
as indicated by numerals inscribed on the scale being, say, one fourth of the numerical
value of the corresponding logarithmic division on the adjacent edge of the other
scale denoting the number of lamps or amperes. On the other parallel edge of this
third scale, I inscribe a logarithmic series, denoting the length of the conductor in
yards or other convenient unit, and on the adjacent edge of the fourth scale which is
fixed relatively to the first. I inscribe a number of divisions corresponding to the
sizes of cables generally used in practice in Board of Trade standard wire gauge, and
in Birmingham wire gauge, or any other method of specification; the divisions being
placed on the scale at the point in each case corresponding to a logarithmic series
denoting the sectional area of the conductor in inches. On the same scale, I inscribe
a series of divisions corresponding denoting the maximum current which the conductors
can carry under certain arbitrary conditions, such as that of a conductor covered with
insulation and laid in a wooden casing, and taking such a current that the temperature
shall not be raised by the passage of that current, more than 30 degrees of Fahrenheits
thermometer, as determined by the arbitrary law :-
C. =
1000d2+156 d

page_text: arranged in a manner similar to that already described, so that the density of current
might be read off for any fal! of potential.
On the first and second scales, I draw a line across the adjacent parallel edges, so that
when the two scales are placed so that each division of the one corresponds exactly to
the similar division of the other, the portions of this line on each scale, form one con-
tinuous line, and against this line I place the word amperes. If the problem be stated
in amperes instead of in lamps of a given number of watts and volts, these two lines
are brought into adjustment, each to each, and the numbers on the logarithmic scale
on the other edge of the second scale then denoto the number of amperes.
In another form of my invention, I inscribe the logarithmic series of divisions on
circular discs of card or other material, and provide a common centre or pivot on
which they may be turned so that any point on the circumference of one disc may be
brought in a radial line with any part of the circumference of any adjacent disc. The
discs are of different sizes, and are placed, the smallest at the top, allowing an annulus
of the next disc to appear, and on this annulus I inscribe the logarithmic divisions and
the numbers denoting their numerical value in terms of the datum which each is
arranged to express.
To use my invention for ascertaining the solution of any problem, for example, to
find the proper conductor to use under given circumstances; I find on the first scale,
the number of watts which each lamp takes, and by sliding the second scale I bring
opposite to the division denoting the watts a division denoting the volts which the
lamps are to take. On the lower edge of the second scale I find the number of lamps
to be used on the conductor in question, and by sliding the third scale, I bring
opposite to this number, the number denoting the fall of potential allowed. Then, on
the fourth scale, I find the nearest size of cable, opposite to the number of yards
length of the cable. Below the size of the cable I find the maximum number of
amperes that can be permitted, and if the fall of potential allowed be two volts, I find
on the inverse series of divisions on the third scale, the density of the current in
amperes per square inch. With the scales divided as described, the resistance of any
cable may be determined in the following manner. Bring the division numbered 100
on the lower edge of the third scale, opposite to the size of the cable whose resistance
is required to be found. Leave the second scale and first scale set as for amperes.
Find the length of the cable on the lower edge of the second scale and on the adjacent
edge of the third scale, the resistance may be read. If the units on the lower edge of
the second scale denote hundreds of yards, the numbers on the upper edge of the third
scale denote ohins.
In order that my invention may he fully understood I proceed to describe the
manner in which the apparatus is used in practice. The slide rule consists of two
slides with graduated logarithmic scales on their edges, or it may consist of discs,
with graduations on the edges, such discs being capable of independent rotation on a
common axis. On the first scale is given the watts of the lamps on the circuit, and
above this is given candle power at 4 watts per candle. On the adjacent scale are the
volts of the circuit. For any particular case, the volts (say 100), are to be set under
the watts (say 64) or (being the same thing) under 16 candle power. The permissible
fall of volts, (say 2) is to be set under the number of lamps (say 15). Then under the
number of yards (say 160) the proper size of cable will be found, viz. With the
above data to find amperes per square inch, above 160 yards find 500. To find
naximum current allowed through see below it 40 amperes. Similarly, with the
above data to find the volts fall under given conditions set the volt of the circuit
against the watts or candle power of the lamps, and set the length in yards against the
size of the cable. Then under the number of the lamps find the fall of volts.
Conversely, given the fall of volts, above it the number of lamps may be found.
Again to find the maximum length of cable of a given size under given conditions;
set the slides to the conditions, and above the size of cable find the length. If amperes
are given instead of watts or candle power and volts, set the first two scales to coincide.
For any length of any cable, the amperes per square inch to give 2 volts fall are

page_text: given on the lower slide, and the maximum current which will raise a given cable in
wooden casing to 30 degrees Fah. is given below the sizes of cable.
Having now particularly described and ascertained the nature of my said inven-
tion, and in what manner the same is to be performed, I declare that what I
claim is.
1. The combination or arrangement and use of parts of scales for use in effecting
calculations relating to the selection and employment of wires and cables for the
supply of electric energy, substantially as set forth.
2. In scales for use in calculating sizes of wires and cables appropriate for the
supply of electric energy the combination or arrangement relatively of four or other
suitable number of scales in parallel or concentric order substantially as and for the
purpose herein before set forth.
Data sh 24h 1000
WM. BROOKES & SON,
55 & 56, Chancery Lane, London, Agents for the Applicant