120 THE SEVEN FOLLIES OF SCIENCE 



"If it be conceded that lines have breadth, then all we 

 have to do is to assign some definite breadth to each line 

 say the one-thousandth of an inch and allow for it. 

 But the lines of the geometer have no breadth. All the 

 micrometers of which Mr. Buckle speaks depend, either 

 directly or indirectly, upon lines for their graduations, and 

 the positions of these lines are indicated by rulings or 

 scratches. Now, in even the finest of these rulings, as, 

 for example, those of Nobert or Fasoldt, where the ruling 

 or scratching, together with its accompanying space, 

 amounts to no more than the one hundred and fifty thou- 

 sandth part of an inch, the scratch has a perceptible breadth. 

 But this broad scratch is not the line recognized by the 

 microscopist, to say nothing of the geometer. The true 

 line is a line which lies in the very center of this scratch 

 and it is certain that this central line has absolutely no 

 breadth at all." 1 



It must be very evident that if Mr. Buckle's contention 

 that geometrical lines have breadth were true, then some 

 of the fundamental axioms of geometry must be false. It 

 could no longer hold true that " the whole is equal to all its 

 parts taken together," for if we divide a square or a circle 

 into two parts by means of a line which has breadth, the 

 two parts cannot be equal to the whole as it formerly was. 

 As a matter of fact, Mr. Buckle's lines are saw-cuts, not 

 geometrical lines. Geometrical points, lines, and surfaces, 

 have no material existence and can have none. An ideal 

 conception and a material existence are two very different 

 things. 



A very interesting book 2 has been written on the move- 

 ments and feelings of the inhabitants of a world of two di- 

 mensions. Nevertheless, if we know anything at all, we 

 know that such a world could not have any actual existence 



1 "The Natural History of Hell," by John Phlllipson, page 37. 

 8 Flatland," by E. A. Abbott. London, 1884. 



