The Saha equation

THE ``IONISATION EQUATION'' of Dr. Meghnad Saha (1893-1956) as a key factor in the launching of its space missiles by India to which Dr. A.P.J. Abdul Kalam, Principal Scientific Adviser to the Union Government, has paid a tribute should throw light on what was known to few outside a very small circle of the scientist fraternity. Dr. Abdul Kalam's recollection of the Saha equation reveals a great deal. He draws attention to how very far-reaching the equation was when, nearly half a century later, it came to the rescue of India's space scientists who had to do with a total lack of data relating to the re-entry phase of the Agni missile at a speed of fifteen times that of sound and when the experiment temperature was around 4000 degrees Celsius. If the equation was of such immense relevance when it was badly needed for the launching of missiles, it is a striking illustration of how rarefied higher mathematics wholly unintelligible to the non- mathematicians could be lifted out of textbooks for hurling missiles into space. A message from this could well be that ``pure mathematics'' to which the likes of the Saha equation perhaps belong is not as far away from applied science as one might imagine.

Dr. Saha's ionisation equation remains fundamental to the study of stellar spectrum and atmosphere and helps to determine stellar temperatures. He published his theory on the temperature ionisation of stars in 1922. The equation took shape way back in the letters exchanged between him and Albert Einstein on matters relating to Relativity in the Thirties. Dr. Saha's translation of Einstein's papers of the Theory of Relativity from German into English helped in getting for them a world-wide recognition. Of still greater importance is that the English translation by the two scientists was free from the error which the two British scientists C. B. Jeffrey and W. Perrett had committed in their translation. The error was attributed to a misreading of a German word resulting in the exclusion of a crucial possibility of alternative definitions visualised by Einstein. This itself should give an indication of the proficiency of Dr. Saha and the other distinguished scientist, Dr. Satyendranath Bose (1894- 1974), in both the languages. Dr. Saha also took on the still more difficult work of translating purely mathematical formulations of Relativity from the German original by H. Minkowski. His exploration of the interaction of radiation with free electrons which had earlier been studied by Wolfgang Pauli, a German scientist, took him to the still undiscovered areas of radiation and statistical physics.

Dr. Meha's ionisation equation paved the way for the first successful launch of the Agni, six decades later, in mid-1989, when his mathematical perceptions advanced from a dream to reality. The perfection of re-entry technology had to wait until the second launch of the Agni in 1992 and it was not wholly successful like the first one because of the central structural interaction problem associated with extreme flight loads. The extended application of Dr. Saha's ionisation equation to what would not possibly have been in his mind when he had formulated it to the development of India's nuclear detonators since it was primarily meant for the gaseous state mentioned by Dr. R. Chidambaram, Chairman of the Department of Atomic Energy. It is a revelation of how new realms would have remained undiscovered but for scientists like Dr. Saha. It is, therefore, a moot question whether this could be wholly attributed to the ``chance'' element in science since more discoveries and inventions like Newton's Laws of Gravitation and James Watt's steam engine did look at the time as though they were ``accidental''. Alexander Fleming also stumbled upon his discovery of penicillin from the remains on a glass saucer in his laboratory.

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