Siemens Mercury Unit of Electrical Resistance. 307 



The greatest difference which occurred between values which 

 ought to agree with each other amounted to 0*018 second. 

 Hence the error assumed is 



At 1 



t - 2000 



5. Lastly, the arcs of vibration A and B may each include an 

 error in reading of +0*2 millim., which observations, to be 

 afterwards communicated, will probably show to be too high. 

 Now, measured in divisions of the scale, A = 370 millims., 



A 



B = 225 millims.; and therefore ^ = 1*64, \ = log nat 1*64 



=0-50. 



If we express the errors produced in w by the separate errors 

 AT, AS, ... by Aw T , Aw S) . . . , we have 



'*«**■ =2 ^ =±0-0020, 



w 



T 



^- s =2 ^ =±00010, 



Aw K AK 



w K 



Aw t _ At 



w ~~ t 



Aw A AA / 



w 



n 



= +0-0013, 



= +0-0005, 



\ = +00000, 



' 



1 



4 > 



X 



1 



, B 2 



1+ A^ 

 4 ' 



^5 = **ll-Z ^ = +0-0019. 



w B 



It will be observed that the ratio of A to B is just of such a 

 kind that a small error in A has no influence. 



If we were to add together the whole of the errors in the most 



unfavourable sense, the total error would be — = +0*0067, or 



' w ~ 



§ per cent. The mean error to be feared in the case of a single 

 determination, or the root of the sum of the squares, amounts 

 to +0*0033, or about ^ per cent. 



The error of observation in the comparison with Siemens's 

 standard need not be considered; for it does not exceed 0*0001. 

 In order to eliminate the alteration due to change of tempera- 

 ture, the influence of which cannot be directly determined in 

 large masses of wire, one comparison was made at the beginning 



X2 



