IntroductionDuring the nineteenth-century, the Harvard College Observatory performed many photographic spectroscopic surveys of stars. This produced spectral classifications for roughly 225,000 stars, which created the Henry Draper Catalogue. Ejnar Hertzsprung realised that narrow lined stars had smaller proper motions compared to other stars of the same spectral classification. He was then able to estimate the stars’ absolute magnitudes\cite{1} by computing their secular parallaxes as a result of the difference of proper motions.DefinitionsBefore we start constructing and analysing a Hertzsprung-Russell Diagram, we should familiarise ourselves with some of the words used in this paper.Firstly, Absolute Magnitude (\(M\)) is a measure of the luminosity of a celestial object, on an inverse logarithmic astronomical magnitude scale. It is further defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs without extinction of its light.Apparent Magnitude (\(m\)) is a measure of the brightness of a celestial object observed from Earth. This value is dependent on factors such as the extinction of the body’s light, its intrinsic luminosity and its distance from Earth. We state a relationship, the brighter an object, the lower its magnitude value.Luminosity (\(L\)\(\circ\) or \(L\)*) refers to the absolute measure of radiated electromagnetic power emitted by a light-emitting object. We are interested in both the solar luminosity, denoted by \(L\)\(\circ\) and the stellar luminosity, denoted by \(L\)* of a particular star.Lastly, we define the Hertzsprung-Russell Diagram as a scatter plot of stars which shows the relationship between the stars’ absolute magnitudes or luminosities versus their stellar classifications or effective temperatures.Absolute MagnitudeWe know that absolute magnitude is measured by a body’s luminosity, which provides us with the relationship between Absolute Magnitude and Luminosity, which states that the more luminous an object is, the smaller the numerical value of its absolute magnitude. In terms of variables, we can express this relationship by the following:A difference of n magnitudes ( in absolute magnitude ) corresponds to a luminosity ratio of \(100^{\frac{n}{5}}\). In a general sense, subscripts are used alongside \(M\) to represent the filter band used for the specific measurement, e.g. \(M\)V for measurements in the V-Band. We generalise this over all wavelengths with an object’s bolometric magnitude. By applying a bolometric correction\cite{2a}, we can convert absolute magnitudes in specific filter bands to its absolute bolometric magnitude.\[M_{bol}=M_v+BC\]Where BC is the Bolometric Correction, needed to factor in specific types of radiation by celestial bodies.Apparent Magnitude A numerical scale by Hipparchus describes the brightness of stars that appear in the night sky, where \(m\) = 1 is assigned to the brightest stars and \(m\) = 6\cite{3} assigned to the dimmest stars.The equation,\[100^{\frac{mM}{5}}=\frac{F}{F_{10}}=\left(\frac{d}{10pc}\right)^2\]relates objects within the neighbourhood of the Sun, where their brightness differs by a factor of 100 for \(m\) and \(M\) from any distance \(d\). The following equation is derived, given that \(d\) is measured in parsecs,\[M=m-5\log_{10}\left(d_{pc}\right)+5\] Which when simplified produces,\[M=m-5\left(\log_{10}d_{pc}-1\right)\]This equation can also be written in two other forms,In terms of stellar parallax.(1) \[M=m+5\left(\log_{10}p+1\right)\]Where a distance modulus is known:(2) \[M=m-\mu\]For this paper, we will only be concerned with equation (1).Gathering DataThe following table was generated by using data available from VizieR. The Vmag column represents the H5 V Johnson magnitudes, Plx the Trigonometric Parallax, B-V the Johnson B-V Colours and finally SpType to represent all the Spectral Types.