THE PROBLEMS OF GEOLOGY 537 



The consideration of the processes of geology by quantitative 

 methods is superlatively difficult, yet this task must be undertaken 

 if the science ever approximates certainty of conclusions. This leads 

 to the relations of mathematics to geology. The moment we pass 

 to the quantitative treatment of processes the assistance of mathe- 

 matics is needed. For simple quantitative calculations arithmetic 

 and algebra may suffice, but for the more difficult problems of geology 

 the assistance of higher mathematics is needed. This, then, raises 

 the question as to whether or not it is expected that the geologist, 

 in addition to knowing physics and chemistry, must also be a mathe- 

 matician. Undoubtedly this is the ideal equipment of a geologist, 

 which, unfortunately, few if any possess. There are many geologists 

 who apply simple mathematics to various problems. But the man 

 who is so familiar with forces, agents, processes, and phenomena of 

 geology that he is able to handle them, and at the same time is capable 

 of handling higher mathematical reasoning, is rare indeed. Those 

 geologists who have made the attempt to combine mathematical 

 with their geological reasoning usually have shown marked deficiency 

 in their mathematics. Upon the other hand, those mathematicians 

 who have attempted to handle the problems of geology mathematically 

 have usually been so deficient in a knowledge of geology that their 

 work has been of comparatively little value. In view of these unfor- 

 tunate results, it seems to me that the time has come for cooperation 

 between geologists and mathematicians in the advancement of the 

 science of geology to a quantitative basis. Two or more men should 

 work together, some of them geologists with a broad familiarity 

 with the phenomena and methods of their science, and the others 

 expert mathematicians. In continual consultation, the geologist 

 and mathematician will be able safely to handle the problems of geo- 

 logy quantitatively. This happy condition of cooperation, once 

 reached, will be sure rapidly to advance the science. 



The quantitative solution of geological problems is likely to empha- 

 size also another of the principles of geological method of the greatest 

 importance. The causes offered to explain the phenomena do not 

 necessarily exclude one another. It is believed that often each of them 

 is a real cause, and partly explains the phenomena, that the differ- 

 ent causes are complementary. While a majority of geologists have 

 been content with suggesting a single physical cause for a phenom- 

 enon, others have taken more than one possible cause into account. 

 Thus Chamberlin has formally adopted the method of multiple 

 hypotheses. But the great majority of those who have considered 

 more than one hypothesis in connection with a geological problem 



1 T. C. Chamberlin, The Method of Multiple Working Hypotheses, Journal of 

 Geology, vol. v. (1897), pp. 837-848. 



