'V 

 409 



face of the bar which becomes convex, and the compression of tfct 

 surface which is concave ; Thirdly, that the error to which the same 

 scale is liable from this cause, is directly as the versed sine of the 

 curvature of the surface upon which the scale is placed ; Fourthly, that 

 the 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 difference be- 

 tween the chord and the arc is not one fifty thousandth. 



The author devised the following method of trying a surface sup- 

 posed to be plane ; namely, by applying to it in different directions 

 a piano-forte wire, one hundredth of an inch in diameter, which bears 

 a considerable degree of tension without breaking, strung on a bow 

 6 feet long ; a contrivance which, he states, may be applied to a 

 great variety of useful purposes, when a straight edge is required. 

 He could detect the nature, and in some degree the extent, of the 

 irregularities of a surface, by tapping with the fingers upon the wire 

 whilst it was pressed by the weight of the bow upon the board. 

 When it yielded no sound, the wire was of course in contact with 

 the surface, which was, in that case, either convex or plane. When 

 the wire yielded a sound the surface was concave, and some idea 

 might be formed of the extent by the acuteness or gravity of the 

 sound produced, the edges of the concavity serving as bridges which 

 limited the length of the string. So delicate is this test, that a 

 cavity can be detected by this method when the interval between 

 the wire and the surface under examination is imperceptible to the 

 eye. 



The error in question, resulting from the extension and compres- 

 sion of the surfaces of the bar dependent upon its curvature, is ob- 

 viated in the following manner. The neutral surface, which suffers 

 neither extension nor compression, is shown by the author to be at 

 about one third of the thickness of the bar from that surface, which 

 becomes convex. When the object is to have two points only on the 

 bar, marking for example the yard, by cutting away one half of the 

 thickness of the bar at its ends, and placing the points upon the new 

 surface, the error arising from flexure is reduced to the least possible 

 quantity ; but when a scale of inches is required, the nearest approxi- 

 mation to correct measurement is obtained by diminishing as much 

 as possible the thickness of the bar, and by providing another bar on 

 which it is to be supported, and on which it is allowed to slide 

 freely in a dovetailed groove, formed by two side plates of similar 

 thickness, screwed to the surface of the bar, and to which it is to be 

 fixed at its middle point by a single screw passing through it. 



