"5th. It remains only to determine the constants which depend on the initial state; which is done by elimination of the unknowns from an infinite number of equations of the first degree. We multiply the equation which relates to the initial state by a differential factor, and integrate it between defined limits, which are most commonly those of the solid in which the movement is effected. There are problems in which we have determined the coefficients by successive integrations, as may be seen in... the temperature of dwellings. In this case we consider the exponential integrals, which belong to the initial state of the infinite solid... The most remarkable of the problems... and the most suitable for shewing... our analysis, is... the movement of heat in a cylindrical body. In other researches, the determination of the coefficients would require processes of investigation... we do not... know. But... without determining the values of the coefficients, we can always acquire an exact knowledge of the problem, and of the natural course of the phenomenon... the chief consideration is that of simple movements."