Lesson Two
DEFINITIONS page
Transformation formula
T |
Transformation |
c |
Concentration |
P |
Wand Power |
R |
Random Factor |
m |
Mass |
v |
Viciousness |
FOrmula units
Hz |
One hertz. Represents a cycle or count of action that occurs in one second. Used for concentration and viciousness. |
W |
One watt. Used to measure wand power. |
kg |
One kilogramme. Used to express the mass of the heavier object. |
m s |
One metre-second. Metre times second. Determines the random factor. |
G |
One gamp. The final product of the units of the main equation. |
Formula units converted
\[ \textrm{Hz}=\frac{1}{\textrm{s}} \]
\[ \textrm{W}=\frac{\textrm{N}\cdot\textrm{m}}{s} \]
\[ \textrm{N}=\frac{\textrm{kg}\cdot\textrm{m}}{\textrm{s}^2} \]
Let us substitute the newton per definition.
\[ \textrm{W}=\frac{\dfrac{\textrm{kg}\cdot\textrm{m}}{\textrm{s}^2}\cdot\textrm{m}}{s}=\frac{\textrm{kg}\cdot\textrm{m}^2}{\textrm{s}^3} \]
\[ \textrm{W}=\frac{\textrm{N}\cdot\textrm{m}}{s} \]
\[ \textrm{N}=\frac{\textrm{kg}\cdot\textrm{m}}{\textrm{s}^2} \]
Let us substitute the newton per definition.
\[ \textrm{W}=\frac{\dfrac{\textrm{kg}\cdot\textrm{m}}{\textrm{s}^2}\cdot\textrm{m}}{s}=\frac{\textrm{kg}\cdot\textrm{m}^2}{\textrm{s}^3} \]
How did we get to one gamp?
Let us go through it, step by step...
This is the main formula:
\[ T=\left(\frac{c}{v}\right)\left(\frac{p}{m}\right)R \]
If we wish to get the unit for T (transformation), we have to replace all the symbols with their respective units, like so:
\[ \left(\frac{\textrm{Hz}}{\textrm{Hz}}\right)\left(\frac{\textrm{W}}{\textrm{kg}}\right)\textrm{m}\ \textrm{s} \]
Hertz over hertz is voided, so we are left with:
\[ \left(\frac{\textrm{W}}{\textrm{kg}}\right)\textrm{m}\ \textrm{s} \]
To be able to parse our units further, we'll replace the watt with equivalent units (see above).
\[ \left(\frac{\dfrac{\textrm{kg}\cdot\textrm{m}^2}{\textrm{s}^3}}{\dfrac{\textrm{kg}}{1}}\right)\textrm{m}\ \textrm{s}=\left(\frac{\textrm{kg}\cdot\textrm{m}^2}{\textrm{kg}\cdot\textrm{s}^3}\right)\textrm{m}\ \textrm{s} \]
Kilogramme over kilogramme is voided as well and we are left with:
\[ \left(\frac{\textrm{m}^2}{\textrm{s}^3}\right)\textrm{m}\ \textrm{s}=\frac{\textrm{m}^3}{\textrm{s}^2}=\textrm{G} \]
Our entire expression equals metre cubed over second square, which is how we agreed to define one gamp.
This is the main formula:
\[ T=\left(\frac{c}{v}\right)\left(\frac{p}{m}\right)R \]
If we wish to get the unit for T (transformation), we have to replace all the symbols with their respective units, like so:
\[ \left(\frac{\textrm{Hz}}{\textrm{Hz}}\right)\left(\frac{\textrm{W}}{\textrm{kg}}\right)\textrm{m}\ \textrm{s} \]
Hertz over hertz is voided, so we are left with:
\[ \left(\frac{\textrm{W}}{\textrm{kg}}\right)\textrm{m}\ \textrm{s} \]
To be able to parse our units further, we'll replace the watt with equivalent units (see above).
\[ \left(\frac{\dfrac{\textrm{kg}\cdot\textrm{m}^2}{\textrm{s}^3}}{\dfrac{\textrm{kg}}{1}}\right)\textrm{m}\ \textrm{s}=\left(\frac{\textrm{kg}\cdot\textrm{m}^2}{\textrm{kg}\cdot\textrm{s}^3}\right)\textrm{m}\ \textrm{s} \]
Kilogramme over kilogramme is voided as well and we are left with:
\[ \left(\frac{\textrm{m}^2}{\textrm{s}^3}\right)\textrm{m}\ \textrm{s}=\frac{\textrm{m}^3}{\textrm{s}^2}=\textrm{G} \]
Our entire expression equals metre cubed over second square, which is how we agreed to define one gamp.