ABSTRACTS OF TECHNICAL ARTICLES 1245 



characteristics which have led and are leading to greatly expanded fields of 

 application. Principal am;)ng these are the tolerances of one per cent or 

 better attainable in production, the stability in use, the relatively small 

 and predictable temperature coefficient of resistance, and the low noise level. 

 These properties result in large part from the ultimate crystalline structure 

 of the carbon films. 



Some Methods of Solving Hyperbolic and Parabolic Partial Differential 

 Equations. R. W. Hamming.^ International Business Machines Corp. Com- 

 putation seminar. Proceedings, Dec, 1949, Ed. by C. C. Hurd. N. Y ., I.B.M., 

 pp. 14-23, 1951. 



Abstract — The main purpose of this paper is to present a broad, non- 

 mathematical introduction to the general field of computing the solutions 

 of partial differential equations of the hyperbolic and parabolic types, as 

 well as some related classes of equations. I hope to show that there exist 

 methods for reducing such problems to a form suitable for formal computa- 

 tion, with a reasonable expectation of arriving at a usable answer. 



I have selected four particular problems to discuss. These have been 

 chosen and arranged to bring out certain points which I feel are important. 

 The first problem is almost trivial as there exist well-known analytical 

 methods for solving it, while the last is a rather complicated partial differ- 

 ential-integral equation for which there is practically no known mathemati- 

 cal theory. 



Electrography and Electro-Spot Testing.*!!. W. Hermance^ and H. V. 

 Wadlow.^ Physical Methods in Chemical Analysis; Ed. by W. G. Berl. 

 N. Y., Academic Press, v. 2, pp. 155-228, 1951. 



Correlation Energy and the Heat of Sublimation of Lithium. C. Herring.^ 

 Letter to the editor. References. Phys. Rev., v. 82, pp. 282-283, 

 Apr. 15, 1951. 



Some Theorems on the Free Energies of Crystal Surfaces.* C. Herring.^ 

 References. Phys. Rev., v. 82, pp. 87-93, Apr. 1, 1951. 



Abstract — Although the interpretation of experiments in such fields as 

 the shapes of small particles and the thermal etching of surfaces usually 

 involves problems of kinetics rather than mere equilibrium considerations, 

 it is suggested that a knowledge of the relative free energies of different 

 shapes or surface configurations may provide a useful perspective. This 

 paper presents some theorems on these relative free energies which follow 

 from the Wulff construction for the equilibrium shape of a small particle, 

 and some relations between atomic models of crystal surfaces and the sur- 

 face free energy function used in this construction. Equilibrium shapes of 



* A reprint of this article may be obtained on request. 

 1 BeU Tel. Labs. 



