every quantity ; yet, in any one application, the quan- 

 tity was considered as fixed and definite. But most of 

 the magnitudes of nature are in a state of continual 

 variation; indeed, since all motion is variation, thf 

 latter is a universal characteristic of all phenomena. 

 No serious advance could be made in the application of 

 algebraic language to the expression of physical phe- 

 nomena until it could be so extended as to express varia- 

 tion in quantities, as well as the quantities themselves. 

 This extension, worked out independently by Newton 

 and Leibnitz, may be classed as the most fruitful of 

 conceptions in exact science. With it the way was 

 opened for the unimpeded and continually accelerated 

 progress of the last two centuries. 



The feature of this period which has the closest 

 relation to the purpose of our coming together is the 

 seemingly unending subdivision of knowledge into 

 specialties, many of which are becoming so minute 

 and so isolated that they seem to have no interest for 

 any but their few pursuers. Happily science itself 

 has afforded a corrective for its own tendency in this 

 direction. The careful thinker will see that in these 

 seemingly diverging branches common elements and 

 common principles are corning more and more to light. 

 There is an increasing recognition of methods of 

 research, and of deduction, which are common to large 

 branches, or to the whole of science. We are more 

 and more recognizing the principle that progress in 

 knowledge implies its reduction to more exact forms, 

 and the expression of its ideas in language more or 

 less mathematical. The problem before the organizers 

 of this Congress was, therefore, to bring the sciences 



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