THE VARIATIONS OF GLACIERS 253 



apparent irregularities of glacier variations. The increase in snow- 

 fall in the reservoir results in a thickening of the upper part of the 

 glacier, which thickening then progresses down the glacier, some- 

 what like a wave, more rapidly than the ice itself. The ice thus 

 advances faster than it melts, and the glacier is pushed farther down 

 its valley. When the supply in the reservoir diminishes, the pres- 

 sure from behind also diminishes, and the ice moves less rapidly 

 and melts back. 



Professor Finsterwalder then takes up the study of an ideal gla- 

 cier, subject to periodic variations of thickness at the neve line, 

 and subject to uniform melting along its whole length; and finds a 

 mathematical equation which represents the changes in thickness 

 and length w^hich the glacier undergoes. Although these condi- 

 tions are not exactly those which a glacier experiences, still they 

 are near enough to give results which correspond fairly well with 

 what is actually observed. The solution of the equation shows 

 that the glacier in advancing takes a steep slope in front and moves 

 with considerable velocity, and during the retreat takes a very gentle 

 slope in front and its velocity is much diminished. The variation 

 in thickness at the neve line produces a much greater relative varia- 

 tion in the length of the glacier, and the change at the end occurs 

 later than the change at the neve line. Under these conditions the 

 glacier advances slowly and retreats rapidly. This is in contradic- 

 tion to experience, as glaciers usually advance rapidly and retreat 

 slowly. This contradiction probably comes from the fact that wt 

 have assumed a uniform variation at the neve line, which, however, 

 is probably not at all regular, but makes a rapid increase and a slow 

 diminution. If now we introduce a variable rate of melting, and 

 assume that it has the opposite phase to the variation of thickness at 

 the neve line, we find the variation in length increased and the state 

 of minimum existing for a longer time, which Forel has described 

 as characteristic of glaciers. It thus appears that the Forel-Richter 

 theory is, in general, upheld by mathematical analysis; but there 

 are many peculiarities which are still unexplained. In the obser- 

 vations of the Vernagtferner glacier very great variations of velocity 

 were found without corresponding increases in thickness. 



Lately Hess has shown that ice yields more rapidly to a given 



