Their 



466 SCIENTIFIC THOUGHT. 



the mathematical methods to the data furnished by 

 observation and experiment ; the biological or concrete 

 sciences began with a study of living things, and have 

 progressed immensely in our times by viewing these not 

 in isolation, but in their relations to each other and to 

 the surrounding lifeless world — the so-called environ- 

 ment. An exact treatment, that to which the term 

 " scientific " has been pre-eminently applied, seems here 

 also to depend largely, if not exclusively, on the degree 

 to which the mathematical processes of numbering and 

 measuring can be applied, and on the utilisation of the 

 general results arrived at in the abstract sciences. 

 2. The method of the abstract sciences is that of building 



different up from Small beginnings, by the process of summation 



methods. 



or integration, intricate complexes which not infrequently 

 are found to correspond to phenomena of actual experi- 

 ence. It has at its command the unlimited resolving 

 powers of the calculus, and the well-established assump- 

 tion that things natural are made up of numberless 

 particles entering into innumerable combinations. The 

 wdiole is thus for the mathematical view the sum of its 

 parts. The concrete or natural sciences, on the other 

 hand, start with the ready-made things or creatures of 

 nature, or on a larger scale with the great order and 

 economy of our world or the universe, and only descend 

 into the minutiiK of the observatory, the dissecting-room, 

 or the laboratory, with the hope of better understanding 

 the great and complicated objects of their study. The 

 greatest progress in the abstract sciences has been made 

 by those minds that could concentrate their atten- 

 tion on special points, not infrequently expressed in 



