Elastic Solids to Metrology. 607 



In the publications of the Bureau International lengths 

 of standard metres seem usually recorded to O01/-6 and 

 occasionally to '001 ^. Benoit, however (I. c. p. 81), says: 

 " l'erreur probable de la determination d'une regie par 

 rapport au Prototype international .... a ete trouve de 

 + 0*04 n" As he is speaking of the highest class of metres,, 

 and admits an additional source of uncertainty in temperature 

 corrections, it would appear that quantities of the order 

 0*004 fx possess as yet hardly a practical significance. Thu* 

 the influence of the reaction of the supports in the above 

 types of bars possesses as yet only theoretical interest. 



The influence of barometric pressure stands on a somewhat 

 different footing. The departure of the barometric pressure 

 at a station from its mean value will seldom, it is true, 

 exceed 7/100 of an atmosphere ; but the effects of a change 

 of pressure of even this amount are shown by the table to be 

 comparable with 0'04/u,. Supposing a standard measure to 

 be in use at a high level Observatory, the decrease of the 

 pressure from that at sea-level would merit closer attention,. 

 and the same remark is true to a much greater degree in 

 the case of a standard subjected to artificial pressures of 

 many atmospheres. 



§ 30. We have seen in § 22 that the length of a supported 

 bar measured along the arc exceeds its horizontal projection 

 to an extent given by the formula 



2( Sj -Q/Z=0cP/E< B *y/(a/J), .... (98), 

 where 



f {a! l) =&-i(afl)*+M<W-M*n , + vhW' (»»> 



For values of a/l between and 1, Broch (/. c.) has shown 

 that /(«//) has no maximum and only one minimum. The 

 minimum answers to <7// = *5594 approx. (more exactly 

 (Broch I c. p. B. 67) -559380111)). The following are 

 approximate values lor f (a/l) x 10 5 : — 



a/l= 0-25 0-5 0*5594 0*5774 0*6 0*75 1*0. 

 10 5 x/(a/Z) = 1786 1105 71 8 15 260 868 5397 



The smallness of f (a/l) when a/l lies between 0*5 and 0*5774 

 is specially noteworthy. 



Table III. (p. 608) gives the difference between the entire 

 length 21 and its horizontal projection for specified positions 

 of the supports. 



