getics of various phases of vertebrate development. For the il- 

 lustration of his ideas the author preferentially uses examples 

 from this work; he also extensively covers the Russian theoret- 

 ical work in this area. 



The emphasis in the treatment lies on the "growth" aspects of 

 development. Interactions between growth and differentiation 

 are only considered in the penultimate section of the last 

 chapter. The main tenet of the book is that development and 

 ageing can be equated to a continuous ("constitutive") decrease 

 of the energy dissipation function, and consequently of the 

 specific rate of entropy production. Conversely, oogenesis, re- 

 generation, and malignant growth would all represent "rejuvena- 

 tion", involving an increase of the dissipation function at the 

 expense of coupled processes in other parts of the system. 

 Proper attention is devoted to the definition of such concepts 

 as "steady state" and "stationary state", in connection with 

 homeostasis and homeorhesis. These ideas are adstructed with 

 numerous experimental data in chs.III through V. Ch.VI discusses 

 several old and modern types of growth equations from the view- _ 

 point of thermodynamics. 



The book is written in English that is perfectly readable 

 though not idiomatic. There are rather many printing errors. 

 The bibliography has about 500 titles. There are no indexes. 

 The book is rather expensive. 



Symposium reports 



8. 



J. D. COWAN, ed. 1972. SOME MATHEMATICAL QUESTIONS IN BIOLOGY. Ill 



Am, Mathemat. Soc, Providence. Lectures on Mathematics in the 



Life Sciences. Vol.4. VI, 151 pp., 28 figs., author and subject 



indexes 



These lectures were delivered at a Symposium held in Chicago 

 in December, 1970. We will only consider the three papers that 

 have a bearing on developmental biology. The two papers by L.A. 

 Segel and by A.Robertson deal with slime molds (the former also 

 partly with bacteria) and are partly simplified presentations 

 of published material, though the second paper contains prelim- 

 inary experimental data that were new at the time of writing. 



Segel and Robertson deal with their subject from quite dif- 

 ferent viewpoints. Segel formulates models for the initiation 

 of aggregation in homogeneously distributed populations of 

 amoebae, and his approach is based on random perturbations and 

 is related to the earlier work of Turing. Robertson essentially 

 deals with the whole slime mold life cycle and his starting 

 point is the periodic secretion of cyclic AMP. He presents no 

 new models but clearly favours the phase-shift model of Goodwin 

 and Cohen for the interpretation of his findings. Incidentally, 

 both papers contain interesting remarks on some conditions un- 

 der which mathematics can be useful for biology. 



B.C. Goodwin takes his starting point in experimental results 

 of R.M.Gaze on the retino-tectal projection in amphibians. He 

 subjects these to a qualitative analysis in terms of two dif- 

 ferent models, a double-gradient model and Goodwin and Cohen's 

 phase-shift model, and uses the results to tentatively discrim- 

 inate between the two types of model for this particular system. 



