In 1915, Lord Rayleigh commented that it was a shame that more physicists did not look at problems from the point of view of the underlying dimensions, rather than simply constructing sets of differential equations, and then attempting to solve those equations, or even undertaking a long series of complex experiments. This idea goes back to the very first use of dimensional analysis. One of the advantages of treating complex problems by dimensional analysis, rather than by a straightforward solution of a set of equations is that dimensional analysis allows one to incorporate physical insight into the resolution of the problem. Evidently, dimensional analysis was very much the Zeitgeist in physics at the beginning of the 20th Century. In addition, in 1911, Albert Einstein looked at the dimensionality of the heat capacity of solids. When presenting his model of the hydrogen atom in 1913, Niels Bohr used a dimensional argument in his article. Interestingly, Lord Rayleigh’s paper in Nature (1915), which demonstrated the power of the technique for handling complex problems without the need for long, difficult experiments, and the solution of coupled differential equations, appeared at about the same time as other applications of dimensional analysis. And how the foundations of dimensional analysis were laid in the first years of the last century particularly with the work of Lord Rayleigh (John William Strutt, 3rd Baron Rayleigh, 1842–1919). In this volume, we will look at the technique of dimensional analysis. And if that end can be reached by simpler means especially more physically transparent and intuitive means, all to the good. Such equations are often a means to an end, but not the end in themselves.
The purpose of physics is the understanding of the world around us, not the solving of differential equations.