Ruler for Drawing Curves, (>()7 



It is evident that the slope of the tangent to the ruler at a 

 point can be given almost any value by altering the tension 

 on the core], while the curvature can be altered both by 

 varying the relative positions of the claws and pins on their 

 arms and by bringing the heads of the T's closer together or 

 further apart — in fact, the practical limit to the variation 

 in curvature lies in the physical properties and thickness of 

 the steel. 



In general, if the curvature change sign, the ruler, as the 

 apparatus is at present constructed, cannot be made to follow 

 the curve — an exception to this is afforded by a point of 

 inflexion near the end of the curve; here, as will readily be 

 seen, if the pin F 1 (fig. 1) be slid towards the ruler to such 

 a position that the line F 2 Ft, produced, cuts the T anywhere 

 between the two claws, a movement in a clockwise direction is 

 set up round d, thus giving a point of inflexion. 



If the curve begins as a straight line it may be necessary 

 to substitute a hook in place of the set screw E (fig. 2), and 

 pass the cord over this. 



Theoretically the ruler should be so adjusted that the curve 

 to be drawn comes between D] and C 2 , thus avoiding any 

 slight changes of curvature that there may be at these points, 

 but in practice I have found for curves of moderate curvature 

 that this effect is not noticeable. 



As a test, a curve of the natural sines plotted against the 

 corresponding angles was drawn on a scale such that 1° of 

 the abscissse = 7"5 cm., while O'l of the ordinates = 5 cm. 

 The following four points were taken as known — 0°, 18°, 

 72°, and 90°; and a curve was drawn through them, giving 

 for the values of the natural sines of 36° and 54° the number 

 *595 instead of '588, and '813 instead of '809, respectively. 

 An objection may be raised against this test in that a uniform 

 steel ruler, when its ends are pulled together by a small 

 force, must give a sine curve ; the validity of this objection 

 is greatly lessened when it is realized that the forces required 

 to get the steel to give the curve, on the scale mentioned, 

 were so great that the ruler was permanently and largely 

 deformed. 



Opportunity was taken to test this deformed ruler against 

 a logarithmic curve, by passing it through the logs (to the 

 base 10) of the numbers 1, 2, 4, 8, and 10, on a scale such 

 that 7*5 cm. = *075 in the logs and 1 in the numbers. The 

 interpolated value for the log of 6 was '7810, instead of *7782. 



The actual value of the apparatus lies not so much in 

 enabling one to draw curves such as these, but in getting 

 smooth graphs on an extended scale. For instance, suppose 

 we have obtained the densities (assumed correct to 1 in 50,000) 



