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, 

 i.e., 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 



