36 COSMIC PHILOSOPHY. [rT. i. 



N/liing can better illustrate the statement that scientific 

 and ordinary knowledge are alike in kind, while different in 

 degree. While the processes gene through by the child, the 

 savage, and the astronomer, are manifestly the same, the 

 immeasurable difference in the complication of the processes 

 is equally manifest. While the inference in the one case is 

 made instantaneously, so as almost to seem a part of the 

 original perception, and while it admits of verification by a 

 series of simple acts, — in the other case the inference is one 

 which depends ultimately upon a long chain of dependent 

 propositions, and the task of verifying it mathematically is 

 exceedingly complicated and difficult. Thus to our state- 

 ment, that science differs from ordinary knowledge in the 

 dejiniteness of its previsions, we have to add that it differs 

 also in the remoteness and complexity of its previsions. 



Thirdly, science differs from ordinary knowledge in the 

 greater generality of the relations which it classifies. And 

 this continuous increase in generality is one of the most 

 striking characteristics of advancing science. "From the 

 'particular case of the scales, the law of equilibrium of which 

 was familiar to the earliest nations known, Archimedes 

 advanced to the more general case of the unequal lever with 

 unequal weights ; the law of equilibrium of which includes 

 that of the scales. By the help of Galileo's discovery con- 

 cerning the composition of forces, DAlembert established for 

 the first time the equations of equilibrium of any system of 

 forces applied to the different points of a solid body — equa- 

 tions which include all cases of levers and an infinity of cases 

 besides." But, as Comte observes, "before hydrostatics 

 could be comprehended under statics, it was necessary that 

 the abstract theory of equilibrium should be made so general 

 as to apply directly to fluids as well as solids. This was 

 accomplished when Lagrange supplied, as the basis of the 

 whole of mechanics, the single principle of virtual velocities," 

 —or the principle that whenever weights balance each other, 



