Preface 



This book presents an introduction to many of the topics which 

 are presently considered part of biophysics. Biophysics deals with 

 biological problems; accordingly, the various chapters have been 

 grouped by the type of problem described rather than by the meth- 

 odology employed. The mathematical level required has been 

 limited, in most cases, to elementary calculus. 



As a separate discipline, biophysics is a recent addition to the 

 sub-divisions of natural science. Until the mid-nineteenth century, 

 it was quite common for investigators to be natural scientists con- 

 tributing to many diverse fields. A well-known scientist who exem- 

 plified this wide range of interest was Hermann von Helmholtz, 

 who was trained as a medical doctor and practiced medicine. He 

 not only conducted histological studies of the eye and ear, but also 

 worked on theories of vision and hearing. In addition to being an 

 excellent biologist, Helmholtz was an outstanding physicist. He 

 developed acoustic instrumentation which he used for frequency 

 analyses of speech and music. His contributions to thermodynamics 

 are emphasized by the term Helmholtz free energy. His name is asso- 

 ciated with a law in geometrical optics as well as with a differential 

 equation for sinusoidal waves. 



With the growth of factual knowledge, it became more difficult 

 for a person to do significant work in both the physical and biological 

 sciences. Within each division of natural science, large numbers 

 of subdivisions appeared; each small field had its own textbooks, 

 its own theories, and its own part of human knowledge. 



However, there is a group of problems for which extreme speciali- 

 zation is not desirable. Many of the problems of biophysics fall 



