30 



Methods and Techniques 



the embryo has the disadvantage, from the 

 point of view of the investigator, of develop- 

 ing in time. The methods appropriated by 

 embryology from other disciplines, which 

 have a different concern for the time factor, 

 have been invented to describe material at 

 a given moment, not to analyze transition 

 from one moment to the next. Insight into 

 the problems of organization demands new 

 approaches to the physiology of development 

 as such, while as yet we confine our efforts 

 to the descriptive physiology of embryos, 

 which is something different. However, it 

 is possible that the clue to new methods for 

 analyzing organization may well come from 

 a deeper comprehension of structure than we 

 now enjoy; and in any case, any knowledge 

 of process we ever may hope to obtain is 

 certain to become more meaningful in the 

 light of as intimate an understanding as pos- 

 sible of ultimate structure. 



One evident superiority of the results of 

 the new morphology over those of the old is 

 that they allow quantitative expression. 

 There is no question but that embryological 

 descriptions must be as quantitatively exact 

 as is appropriate for the material and tech- 

 niques in question, and there is no greater 

 need to justify the benefits of this for em- 

 bryology than for any other science. There 

 are, however, certain sources of error in in- 

 terpretation which may be pointed out which 

 are inherent in some attempts to analyze 

 the significance of certain aspects of growth 

 and differentiation by presenting descrip- 

 tions of them in quantitative form. 



It is well to remember that mathematical 

 abstraction is a particular kind of abstrac- 

 tion which is in itself highly specialized. 

 Any progressive science deals in abstraction 

 as well as in measurement, but it requires 

 always to question the appropriateness of 

 whatever abstraction it utilizes to the partic- 

 ular material with which it deals. There is 

 no more fascinating collection of biological 

 facts than those by which Sir D'Arcy Thomp- 

 son referred growth and form to certain 

 mathematical relationships, but surely Sir 

 D'Arcy's analogies are provocative rather 

 than explanatory, and he himself hardly 

 claimed more for them. 



A curve, for instance, which describes the 

 "growth" of a colony of bacteria is useful 

 in that it designates periods of change at 

 particular moments, and these may be periods 

 with which the investigator may wish to 

 concern himself; but the "growth" of a 

 colony of micro-organisms is something dif- 

 ferent from that of a multicellular organ- 



ism, and the growth of one organism may be 

 controlled by different factors than that of 

 another. Weiss' warning of a few years ago 

 is still relevant and will continue to remain 



A purely formal treatment of growth, as is often 

 attempted through the interpretation of growth 

 curves, is only a valuable guide to and supplement 

 of, but never a substitute for, a precise analysis of 

 the different forms in which growth manifests it- 

 self. 



There can be no research on growth as such. We 

 can only study growing objects. And different grow- 

 ing objects follow different methods. ... To know 

 growth we must therefore break down each one of 

 its manifestations into its constituent elementary 

 processes and then study these and describe them 

 in objective terms. This is a long way to go, but 

 there is no short cut ('49, p. 182). 



Weiss' admonition holds equally true for 

 other aspects of development: differentiation, 

 determination, or whatever. Exact quantita- 

 tive description of embryological data is an- 

 other conditio sine qua nan for future em- 

 bryological progress, but only if the embryol- 

 ogist keeps in mind which of his problems 

 quantification cannot solve, as well as those 

 which it can elucidate. 



The success of quantitative methods in 

 creating the new morphology has tended to 

 encourage attempts to adapt quantitative 

 methods to the results of the older; and this 

 condition, together with the fact that the 

 journals ciirrently encourage the publication 

 of data in graphic and tabular form, leads to 

 a growing tendency to make material appear 

 quantitative which may not necessarily be so 

 in its own right. An example is the current 

 procedure of using morphological stage num- 

 bers from stage series to represent ordinates 

 or abscissae of graphs. This may be useful 

 provided the author works with a footnote, 

 in his thinking if not on his page, calling 

 for caution in interpretation, but it is a ques- 

 tion to what extent this reservation is kept in 

 mind. The presence, in the curve of such a 

 graph, of maxima or minima, and whether 

 a line rises or falls is surely significant; not 

 in the same way the slope of the line nor the 

 character of the curve in other respects. A 

 straight line in such a graph is not what it 

 purports to be; "morphological age," as Need- 

 ham ('42) calls it, is not equivalent to time, 

 which can be quantified. Stage 5 of an em- 

 bryo is not something that equals the sum 

 of stage 2 plus stage 3, which, unless spe- 

 cifically qualified, is what the conventional 

 graphic representation implies. 



There are innumerable cases, too, where 



