170 REPORTS ON INVE;sTIGATIONS AND PROJECTS. 



of the small planets in the solar system. The previous theory is reviewed 

 with the substitution of Roche's formula for the internal variations of den- 

 sity, and, to serve as a basis of comparison, certain other formulas of the 

 distribution of density are deduced to satisfy special conditions. Criticism 

 in the line of general thermal dynamics leads to the suggestion that the 

 theory given is possibly an extreme view applicable to a substance in which 

 the work of compression is mainly frictional. 



In Part III a contrasting theory is outlined applicable to the case of a 

 substance whose nature is such that the work of compression is done mainly 

 against volume-elasticity under the assumption that the successive strata 

 deposited at the surface are reduced to uniform entropy by free radiation 

 while their material was exposed. The thermal phenomena arising in this 

 case are compared with those developed under the conditions outlined in 

 Part I. 



This paper thus treats mathematically a considerable range of funda- 

 mental propositions that enter basally into the problems discussed in the 

 preceding and following papers. 



Paper V. — On Certain Problems of the Lithosphere. By T. C. Chamberlin. 



This paper is concerned chiefly with the application of the deductions of 

 the preceding papers to the deformation of the lithosphere. It attempts to 

 differentiate deep bodily deformations from those affecting a limited super- 

 ficial shell. The nature and depth of this superficial shell, its relation to a 

 postulated zone of shearing below and to the more general deformations of 

 the deeper body of the earth on which it is dependent, are discussed. It is 

 assumed that tensional stages of the protuberant portions of the earth follow 

 compressive stages and give rise to a slow glacier-like creep of the unbalanced 

 protrusive portions and to relaxitative movements of the superficial shell. 

 Certain special applications of these deformations are outlined. 



Paper VI.— On the Former Rates of Rotation of the Earth. By T. C. Chamberwn. 



This theme is discussed here under the belief that it bears vitally on con- 

 ceptions of the constitution of the earth and on certain modes of deforma- 

 tion, as well as on superficial sea action. The paper opens with a review of 

 the grounds currently assigned for a high primitive rate of rotation based 

 upon cosmogonic hypotheses and on tidal deductions, and it endeavors to 

 show that these may be radically modified by alternative cosmogonic con- 

 siderations and by alternative interpretations of the nature and value of such 

 tides as affect rotation. The purpose of this introductory review is to free 

 the problem from preoccupying presumptions springing from extra-terrestrial 

 sources and cosmogonic hypotheses and to open the way for the untrammeled 

 application of the geological evidences that bear upon the problem. These 

 are then set forth. The paper is given this place in the series because of its 

 bearings upon problems of deformation. 



