the Robinson Cup- Anemometer. 83 



in terms of Vi by means of a continued fraction, and v x is got 

 from (40) by putting n = l. 



After a large number of intervals T x and T 2 have succeeded 

 each other, a species of steady state is reached in which the 

 phenomena in successive intervals T 2 are practically identical, 

 and the phenomena in successive intervals T x are practically 

 identical. When this stage is reached we may in (45) take 



and so find 



U 2n-2 ~ U 2n'> 



Similarly we should find 



, B'-c V(b / --c / ) 2 +4a 7 d / 



W 2n-1— V 2»-l~" V l ~ 2D' + 2D' ' ^ ' 



where A', B', C, D' are derived from A, B, C, D respectively 

 by interchanging v[ with v'{, v 2 ' with ^ T x with T 2 , and so 

 x' with #". 



The space actually travelled by the centres of the cups in a 

 single double interval T x + T 2 during this species of steady 

 state is 



^w, = »; wt 2 + iio g { i +^=j*(i- jo } 



+ M 1+ S' (i -*' J }' (50) 



where v 2n and v 2n _ 1 are given by (48) and (49) for all 

 possible circumstances of the kind under consideration. 



The space which would be travelled on the equilibrium 

 theory would be instead 



The mean velocity in the final state is in reality 



« = (*,. +1 +«J/(Ti+t.)>- • • • < 51 > 



whereas on the equilibrium theory it would be 



WTx+oJ'iy/eEi + T,). 



In any individual case, supposing we knew the values of 

 the constants appearing in (14), there would be no difficulty, 

 except in the length of the arithmetical operations, in deter- 

 mining the error of the equilibrium mean velocity . 



The most interesting case occurs when the alternations of 



G2 



