1884.] resistance between two neighbouring points on a conductor. 137 



In the present case da and db are known to be less than "0005, 

 and dO is less than "1. The errors of c are due to inaccuracy in 

 resistance box and to errorsin reading. the galvanometer deflections. 

 The first we may dismiss as less than •01, the second we proceed 

 to find. 



Let us call the differences given in last column of table, 

 h (= "67 app.) when c = 183, and k (= '9) when c = 184. By inter- 

 polation the true value of c is 



183+ ' 



dc = 



h + k' 

 kdh^-hdk 



(h + k) 2 ' 

 Since dh and dk are certainly not greater than *3 the greatest 



possible value of dc is -, ^ = - . This gives ^. < z-^7wT . 



We may then conclude that the accuracy of the determination 

 is 1 in 1000. 



This result has been verified by using Matthiessen and Hockin's 

 method, when more than six independent experiments have given 

 the same result as above to the 3rd significant figure. 



The experiment just described was not made in the best way 

 possible. Having once found the limits 183 and 184 between 

 which c lay, it would have been best to have restricted the observa- 

 tions entirely to those limits, and by carefully adjusting the galvano- 

 meter and scale, the errors dh and dk might no doubt be reduced. 

 It would not be too much to say that the necessary accuracy 

 could have been carried to the 4th significant figure, though this 

 would involve some careful attention to changes of temperature. 



(3) On dimensional equations and change of units. By W. N. 

 Shaw, M.A. 



Since the introduction of methods of measuring electrical and 

 magnetic quantities in absolute measure considerable attention has 

 necessarily been turned to the question of the dimensions of units 

 and dimensional equations. Maxwell, as is well known, has in 

 various places discussed such questions, and they naturally form 

 an important part of Everett's ' Units and Physical Constants.' 

 But I do not recollect having anywhere seen any precise statemeut 

 of the manner in which dimensional equations arise and what their 

 actual significance is. I therefore venture to suggest the following 

 exposition of the method of deducing dimensional equations, and I 

 do so with more confidence as there seems a general tendency to 

 attribute to the well-known symbol in square brackets more of the 



