72 Mr. C. Chree on the Theory of 



terms will suffice to give its approximate value, assuming, of 

 course, the A's to be known. 



Thiesen then proceeds to correct the approximation 2 a to 

 the value of v/Y as follows : — 



(«) There is a correction to allow for the fact that v/Y is 

 really a periodic function of 0, the periodic part vanishing 

 when I is infinite. 



(/3) There is a correction to allow for the velocity due to 

 the rotation being really variable over the cup, and for the 

 centre of pressure being variable in position. 



(y) There is a correction to allow for the wind's action on 

 the arms. 



(8) It is stated that the hypotheses in (a) , that the resultant 

 pressure varies as the area of the cup and as the square of the 

 wind's velocity, are neither strictly true. It is apparently 

 concluded, however, that the deviation from these laws would 

 not affect the value found for v/Y to the degree of approxima- 

 tion attained. 



(e) There is a correction for the frictional forces of the two 

 classes specified above, one force proportional to the weight 

 of the apparatus, the other to the resultant horizontal force 

 exerted by the wind on the movable parts. 



There are, it must be confessed, a good many doubtful 

 points in the investigation. The whole system of applying 

 corrections is open to criticism, unless definite evidence can be 

 produced that the differences between the original theory and 

 the physical facts are small. In the present case one is not 

 in a position to affirm that all the divergences for which 

 corrections are applied are small in any given type of instru- 

 ment, and it may be doubted whether the forms the corrections 

 are supposed to take are necessarily correct. 



The degree of convergency of the series in (11) is very 

 uncertain. The correction (e) is supposed to introduce a 

 couple opposing the motion, of the form 



»(/3+yV 2 ), 



where /3 and 7 are constants, and this is manipulated so as 

 to appear as equivalent to a variation in the value of the 

 constant A! appearing in (11). I do not see how the 

 coefficient v is accounted for by the ordinary laws of friction, 

 and should have expected the coefficient of 7 to be U 2 instead 

 of V 2 . The method of treating the friction as a correction 

 would be of course wholly unjustifiable unless it were a com- 

 paratively unimportant item. 



As none of the constants A are really known, and the 

 various corrections introduce fresh quantities likewise un- 





