. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. 614 Now by [508] RICE ART. L da- dfXg da_ _ Olih Hence, if we neglect the cubes and higher powers, we can write (AmJ2 + ^-. (A/x,)2 ... + 2 777- ^^Ji,^^lH + ... < 0. W dfih^ dfigdnh Now at the outset of this section of the commentary, on page 606, we dealt with the conditions which render such a quadratic expression always positive or always negative in value. We see that in order to comply with the present condition of negativity a series of determinants beginning with
. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. 614 Now by [508] RICE ART. L da- dfXg da_ _ Olih Hence, if we neglect the cubes and higher powers, we can write (AmJ2 + ^-. (A/x,)2 ... + 2 777- ^^Ji,^^lH + ... < 0. W dfih^ dfigdnh Now at the outset of this section of the commentary, on page 606, we dealt with the conditions which render such a quadratic expression always positive or always negative in value. We see that in order to comply with the present condition of negativity a series of determinants beginning with }. , and so on, dfihdno duk will be alternately negative and positive for the values of the variables Hg, nh, ... which exist in the "single-accent" film, , ng^\ iJih^' ... Looking at the question from a purely mathe- matical point of view, if, in addition to these conditions, ba da —, —, ... djjLg dnh were all zero for the same values of Hg, Hh, ... then a regarded as a function of Hg, iJ^h, ... would have a maximum value for these same values of Hg, nh, ... This is the meaning of the cryptic remark at the end of the paragraph (p. 242). But of course the "necessary conditions relative to the first differential coefficients" are not fulfilled; in other words da/dug is not zero for the values HgS', fXh^', ... oi Hg, fjLh, ...; it is equal to — Tg\ and so on. To be sure, the conditions for the second differential coefficients are satisfied, but for a reader who is not familiar with the concrete forms of these conditions, the way in which the conclusion is. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Donnan, F. G. (Frederick George), 1870-1956; Haas, Arthur Erich, 1884-1941. New Haven, Yale University Press; London, H. Milford, Oxford University Press
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