Philosophical Transactions. 343 



that these conditions are not necessary to the stability of a system 

 of bodies subject to the law of attraction which governs one system ; 

 and lie gives expressions for the variations of the elliptic constants 

 which are rigorously true, whatever power of the disturbing force be 

 retained. 



7. On the Error in Standards of Linear Measure, arising from the 

 Thickness of the Bar on which they are traced. By Captain 

 Henry Kater, V.P., and Treasurer of the Royal Society. [Read 

 June 17, 1830.] 



WHILE engaged in the adjustment and verification of the copies of 

 the Imperial Standard Yard destined for the Exchequer, Guildhall, 

 Dublin, and Edinburgh, the author discovered a source of error 

 arising from the thickness of the bar, upon the surface of which 

 measures of linear dimensions are traced. A nctice to that effect 

 was published in the Philosophical Transactions for 1826; and the 

 object of the present paper is to give an account of the experiments 

 the author has since made on this subject, and to describe a scale 

 which he has had constructed so as almost entirely to obviate the 

 source of error thus introduced. 



From the experiments detailed in the first part of the paper, the 

 following conclusions are deduced. 1. That in a standard of linear 

 measure traced upon the surface of a bar, an error arises from the 

 thickness of the bar when it is placed upon a table, the surface of 

 which is plane. 2. That this error in bars of the same material 

 and of unequal thickness lies within certain limits us respects the 

 thickness of the bar, and depends upon the extension of the surface 

 of the bar which becomes convex and the compression of the bar which 

 is concave. 3. That the error to which the same scale is liable from 

 this cause is directly as the versed sine of the curvature of the sur- 

 face upon which the scale is placed. 4. 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 thousandth of an inch is nearly one thousandth 

 of an inch, whilst double the difference between the chord and the 

 arc is not one fifty thousandth. 



The author devised the following method of trying a surface 

 supposed to be plane ; namely, by applying to it in different direc- 

 tions a pianoforte wire, one 100th of an inch in diameter, which 

 bears a considerable degree of tension without breaking, strung on 

 a bow six feet long ; a contrivance which, he states, may be applied 

 to a great variety of useful purposes when a straight edge is re- 

 quired. 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 eon- 

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

 "When the wire yielded a sound the surface was concave ; and some 



