OF ARTS AND SCIENCES. 203 



directly as the versed siue of the curvature of the surface upon which 

 the scale is placed." 



(4.) " That this error very far exceeds that which would arise from 

 the difference of length between the arc and its chord, under similar 

 circumstances; so much so, that the sum of the errors from this cause 

 in a bar one inch thick, with a versed sine of not one-hundredth of an 

 inch, is nearly one-thousandth of an inch; whilst double the distance 

 between the chonl and the arc is not one fifty-thousandth." 



In the early observations of Kater, he used a wood surface for a 

 support, but later he seems to have preferred a marble slab, which, 

 however, was not planed. 



In 1844 Sir George Airy showed that, if n represents the number 

 of supports of a bar, the distance between the supports should be 



Length of bar 



\ - — 1 



in order to neutralize the effect of the flexure. Thus, in the case of 

 the yard, if the defining lines are near the ends of the bar, each 

 support should be placed 10.39 inches from the centre, and in the 

 case of the meter they should be placed 28.87 centimeters from the 

 centre. 



This general form of support was used by Mr. Sheepshanks in all 

 of his observations, and it is the form which is ordinarily employed at 

 the present time. In the construction of the National Standards it 

 was considered important that the bars should be supported at numer- 

 ous points in order that they should be exposed to as little strain as 

 possible. The particular form of support finally adopted will appear 

 from the following description by Sir George Airy, to whose sugges- 

 tion it is due. 



" Great facility is given to the arrangements for supporting a bar 

 with definite pressures applied at special points, by the use of levers. 

 Thus, if any portion of the bar rest upon two rollers which are placed 

 at the ends of a lever, and if the fulcrum of this lever (whether mov- 

 able or not) be in its centre, the pressure upwards produced by these 

 rollers will necessarily be equal. If there be another such lever, and 

 if the fulcrum of this and the former be upon the extremities of a 

 third lever, and if its fulcrum be at its centre, then the pressures up- 

 ward produced by the four rollers will be equal. By this arrange- 

 ment of the rollers and levers, one half of the bar may be supported. 

 If another similar system be applied to support the other half of the 

 bar, the pressures produced by its four rollers will also be equal among 



