LETTERS
To the Editor: Recently1- three different methods were suggested to rrrover the solution of the differential equation
well known to neighbors of Brooklyn Polytech. would do well to read this most delightful bit of scientific journal prose.
from the solution of the differential equation
These methods involve series expansions, use of the L'Hospital Theorem and the limit of the series (1 x/n)". However, it is instructive to note that by a slight change of the form of the solution of eqn. (2), one can recover the solution of eqn. (1) without recourse to any mathematical theorem. To see that, we write the solution of (2) in the usual and rearranged forms
+
In b - In a b-a
+ ln(b - zb) --aIn(a - x)
(3)
Now the limit of the right hand side of (3), when b -c a is, by definition, the derivative of the logarithmic functions In b and ln(b - x), i.e.,
which is the solution of eqn. (1).
To the Editor: Your February 1966 issue mas of particular interest because of the article on Dipole Uxnents. Because of the considerable influence which attaches to an article in the JOURNAL of CHEMICAL EDUCATION, and the brief reference on page 67 to some of my work [J. Phys. Chem, 60, 1336 (1956); not J. Chem. Phys. as actually cited], I would like to make a few comments. My main thesis was not that accurate density measurements are unnecessary, but rather that no densities of solutions need be determined when v2 (the partial specific volume of the solute in solution) can be evaluated by other means, of which a number are available. The quantity v2 appears in the equation for the specific orientation polarization of the solute at infinite dilution according to the exact equation [cf. also: eqn. 7, J . Phys. Chem., 61, 376 (1957)J:
S. BAER HEBREW UNIVERSITY
JERUSALEM, ISR~EL
A. BEN-NAIM OF NEWYORKAT STOXY BROOK SWTEUNIVERSITY STONY BROOK, L. I., NEWYORK
A. S., J. CBEM.EDUC., 35,251 (1957). SAID, LOWELL, S., J. CHEX. EDUC., 42.552 (1965).
To the Editor: I wonder sometimes about the significance of some of the newer 'Lwords" that appear in textbooks. I recently found that the solution to which a titrant is added is 'alled the "titree"! I doubt it! This is hardly in the category of thesuggestion by Giauque, et al. [J. Chem. Phys., 42,8 (1965) ] that "pernt" he used to refer to approximate temperatures in connection with gradual transitions. Incidentally, readers who are not familiar with this West Coast advocacy of a word 680
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Journal o f Chemical Education
Although the idea that density measurements could be obviated occurred to me independently, a literature search showed that Treiber and Porod [Maatsh., 80,481 (1949)l suggested this much earlier. Therefore, my paper was in effectwritten to substant,iatethe validity of such obviation. Having been successfully applied to fifty cases, and failing in none, I feel the method is sufficiently substantiated. I am convinced that much time has been wasted (including my own) and is still being wasted in determining unnecessary densities.
To the Editor: Dr. Estok's proposal has great potential, and he has gathered very convincing evidence for it. Ap-
