REMAINING LAWS OF NATURE. 177 



about equality, it should afford a more copious supply 

 of marks of marks ; and that the sciences of number 

 and extension, which are conversant with little else 

 than equality, should be the most deductive of all 

 the sciences. 



There are, moreover, two or three of the principal 

 laws of space or extension which are unusually fitted 

 for rendering one position or magnitude a mark of 

 another, and thereby contributing to render the 

 science largely deductive. First ; the magnitudes of 

 inclosed spaces, whether superficial or solid, are com- 

 pletely determined by the magnitudes of the lines and 

 angles which bound them. Secondly, the length of 

 any line, whether straight or curve, is measured (cer- 

 tain other things being given,) by the angle which it 

 subtends, and vice versd. Lastly, the angle which 

 any two straight lines make with each other at an 

 inaccessible point, is measured by the angles they 

 severally make with any third line we choose to select. 

 By means of these general laws, the measurement of 

 all lines, angles, and spaces whatsoever might be 

 accomplished (to borrow an observation from M. 

 Comte), by measuring a single straight line and a suf- 

 ficient number of angles ; which is, indeed, the plan 

 actually pursued in the trigonometrical survey of a 

 country ; and fortunate it is that this is practicable, 

 the exact measurement of straight lines being difficult, 

 but that of angles very easy. Three such generaliza- 

 tions as the foregoing afford such facilities for the 

 indirect measurement of magnitudes, (by supplying us 

 with known lines or angles which are marks of the 

 magnitude of unknown ones, and thereby of the 

 spaces which they inclose) that it is easily conceivable 

 how from a few data we can go on to ascertain the 

 magnitude of an indefinite multitude of lines, angles, 



VOL. II. N 



