Elastic Solids to Metrology, 615 



sensitive to errors in the assumed values of the distances 

 between the deflecting and deflected magnets. To calculate 

 the direct effect on the calculated value X of the horizontal 

 magnetic component we may employ the formula 



X 2 = N 



-3 



where N is a function of certain observed quantities, including 

 time of vibration and sine of deflexion-angle, while r is the 

 distance between the centres of the two magnets. The cor- 

 rection SX to X, necessitated by a correction 6Y to the 

 received value of r, is given by 



28X/X=-3Sr/n 



For bar E, on the average of the results at 30 and 40 cms., 

 we have 



8r/r=+ '00013, 



whence 8X/X= - 000195. 



At London, where X = '184 c.G.s. approximately at present, 

 this would give 



SX= -'000036 c.G.s. 



Near the magnetic equator— e. g. in parts of India — X is 

 twice as large as in London, so that the error introduced by 

 the flexure of bar E under gravity might attain to +'00007 

 c.G.s. As it is usual to attempt to measure X — or at least 

 to record its value — to '00001 c.G.s., the source of error 

 now indicated possesses more than merely theoretical interest. 



Concluding Remarks. 



§ 38. A common remark applies to all our investigations 

 into the effects of flexure on length. So long as a bar is 

 always used at a fixed station, in one exactly specified way, 

 and its length is measured, or defined as holding, under the 

 exact conditions of use, it is immaterial whether flexure 

 affects its length or not. If a standard yard, for instance, is 

 supported in an absolutely uniform way on rollers, the mere 

 fact that the distance between the centres of the gold plugs 

 would be altered by shifting the rollers cannot be said to 

 constitute an unmistakable mark of its inferiority as com- 

 pared to the Bureau International's type B. There may, 

 however, be practical objections to particular forms of stan- 

 dards of lengths, and to particular positions of the supports. 

 It is undesirable, for instance, that a small accidental variation 



2S2 



