374 ELEMENTS OF SCIENCE 



that " things which are equal to the same thing 

 are equal to each other." This is an abstract, uni- 

 versal, and necessary principle, which our reason can 

 apprehend to be such, although it may never before 

 have been adverted to, save as implied in ordinary 

 facts of experience. If, for example, a man has 

 found that two pieces of wood are each of them 

 equal in length to a third piece of wood which is 

 a yard measure, he will at once be certain that the 

 first two pieces are of equal length namely, each 

 a yard long. From a variety of instances of equali- 

 ties of very different kinds, he will be led to appre- 

 ciate the force of the principle just quoted, when his 

 attention has once been directed to it. It will then 

 be evident to his mind that this equality between 

 the equals of a third thing must positively always and 

 everywhere exist. In our perception of the truth of 

 this principle this law some other very fundamental 

 principles are necessarily involved, as will become 

 obvious if we turn the mind inwards upon itself. Thus 

 it is obvious that this law, as it concerns equality 

 generally, must concern every kind of equality equality 

 not only between " quantities," but between " qualities " 

 and " relations " also. Two daughters and a son of the 

 same mother -are all equally her children, and if she 

 feels the same amount of love for each girl as she does 

 for her boy, then the love felt for one girl will be equal 

 to that entertained for the other. 



Things which agree in quantity, quality, and relation 

 are in so far alike. Yet they cannot be thought of as 

 being " alike," unless they are at the same time recog- 

 nised by the mind as being existing things which are 

 distinct. Thus in the above axiom we have involved 

 the ideas " distinctness," "similarity," and "existence," 



