On Some Processes of Scientific Reasoning. 27 



elapses between impulse and repulse; yet this interval is 

 so short that it may practically be left out of account. 



An ideal conception which enters into nearly every 

 branch of Physics is that of an homogeneous body. A 

 body may be homogeneous in various ways ; if all the 

 parts of a body have the same density, it is homogeneous 

 as to density ; if they have all the same chemical composi- 

 tion, it is chemically homogeneous. A body would be said 

 to be absolutely homogeneous, or homogeneous in every 

 respect, if any two parts of it differed in no properties 

 except shape, size, and position, and such properties as are 

 dependent on these. There is, however, no such thing as an 

 homogeneous body, nor is there even any body which is 

 homogeneous in respect to any particular quality. It is 

 equally true that there is no body which is heterogeneous 

 according to any simple mathematical law; — an ideal con- 

 struction which is sometimes employed to give results more 

 in accordance with facts than those obtained from the con- 

 ception of simple homogeneity. 



In those higher branches of Dynamics which deal with 

 solids as not rigid, but susceptible of change of form 

 under the action of Force, that is as elastic bodies, the con- 

 ception of a particular sort of homogeneity, or of heteroge- 

 neity according to a definite law, is introduced. Such 

 conceptions enable us to obtain results more consistent 

 with facts than those derived from the conception of 

 an absolutely rigid body; yet, partly from the 

 mathematical difficulties of the subject, and partly 

 from the irregular heterogeneous constitution of real 

 objects, many practical problems of strain and stress 

 in solids remain unsolved. 



The Science of Heat assumes bodies to be homogeneous 

 as to the powers of conduction, radiation, &c. Such 

 assumptions afford examples of Ideal Construction. This 

 Science also gives a very excellent illustration of the In- 

 troduction of Metempirical Elements. 



Before the kinetic theory of Heat was accepted, what was 

 meant by saying that a body was hot ? The primary 

 meaning was that a particular sort of sensation, that of 

 heat, was produced in a person's mind when the body was 

 placed in contact with, or brought near to his skin. But 

 when it was discovered that all bodies which produced this 

 phenomenon produced other peculiar phenomena when 

 brought into proximity to other bodies, it was found 



