70 Length arid Space. 



9. — But further, material objects are found to be longer 

 or shorter mot only in their distance from end to end, and 

 from side to side, but also from top to bottom, or from the 

 upper surface to the lower. This introduces the idea of 

 height, depth, or thickness. Our ideas of this quality 

 are obtained precisely in the same way as those of length 

 and breadth, are improved in the same manner, and 

 explained to others in the same way. The property itself 

 is measured in the same way, and admits of a similar 

 mathematical definition with breadth. 



10. — Such are the three dimensions, or measurable 

 properties of bodies, and they are not known to possess any 

 others. Of these three, the primary is /e«g'^/i. This is the 

 first which the infant, or rude mind contemplates; and it 

 is that which occurs most frequently in human life. What- 

 ever measure, therefore is adopted for it, is used also for 

 the other two. An accurate measure of it pre-supposes the 

 knowledge of the properties of a line, and of a straight 

 line, the exact meaning of both which terms, must be 

 communicated by example and explanation, as no logical 

 definition of them can be obtained. The measure of length 

 is the foundation of all other measures whatever, of time, 

 motion, weight, price, power, heat, electricity, moisture, 

 &c. No accurate measure is known to exist which has not 

 this for its foundation. Yet measures of length are adopted 

 by the individual only by arbitrary assumption, and used 

 by different individuals by convention or by imitation. 



11. — Some objects have a sensible breadth in every part 

 of them; others are so thin and narrow, that, to the 

 untutored mind, they appear to have no breadth at all, and 

 to possess only length. The former impression, when we 

 would speak of it, comes to be denoted by the various 



