1906] 



MICHELSON— FORM ANALYSIS. 113 



B. Spiral. 



C. Branching. 



D. Scattered. 



E. Irregular. 



It would far exceed the limits of time and space to develop these 

 in detail, but it may be mentioned that : 



Rhythmic forms may appropriately be divided into Line rhythms, 

 Nets or surface rhythms, and Space rhythms. 



Further the " element " of the rhythm may be constant or (regu- 

 larly) variable, and (in the case of linear rhythms) the line may 

 be straight or curved. 



Spirals may include flat, cylindrical or conoidal forms. 



Branching forms may include all the well-known systems of ar- 

 rangement of leaves and flowers, as well as the ordinary types of 

 branches, to which may be added a number of arrangements peculiar 

 to some of the lower organisms. 



Scattered forms are such as are typified by the arrangement of 

 the stars in space. 



Irregular forms may be subdivided into Definite, Indefinite, 

 Distorted. 



In many cases the essential character of both symmetrical and 

 unsymmetrical forms may be expressed in mathematical language; 

 and even in the cases where such formulae are only approximate 

 expressions of the reality, such expressions may be the best and 

 readiest means of ascertaining departures from the law. 



Doubtless the biologist will look askance at what appears a 

 grewsome array of mathematical symbols — at least until he finds 

 how much less vicious they are than they look — but for the student 

 of mathematics, there can scarcely be a more interesting and in- 

 structive practice for familiarizing himself with the properties of 

 analytical functions, than to exercise his ingenuity in fitting the 

 most appropriate expression to the forms he sees in Nature. 



A further possibility in the expression of natural forms in 

 mathematical language is the presentation of an ideal — so to speak — 

 which the object is trying to embody; and the attempt to determine 

 what this form would be under standard conditions would furnish an 

 interesting and fruitful subject for research. 



