Manchester Memoirs Vol. xliv. { 1 899), No. 5. 1 3 



the delicacy obtained in this way is due to a partial annul- 

 ment of gravity during the downward acceleration and 

 consequent diminution of frictional effect at the bearings. 



Some of the observations presently to be discussed 

 were made in this way, but in most of them the arrange- 

 ment was rather different. The wheel was removed from 

 its bearings and suspended by a fine wire, whose torsion 

 was insufficient to check the rotation seriously. The wire 

 was pulled up verticall)^ by a cord running over a pulley 

 overhead. Although this arrangement offered some 

 advantages, they were largely neutralised by disturbances 

 due to draughts ; and it is probable that equally good 

 balances might be obtained by the simpler method. 



According to an old and long discredited law, the 

 normal pressure upon a vane moving through the air at 

 given speed would be proportional to the square of the 

 sine of the angle (a) between the plane of the vane 

 and the direction of motion. The resolved part of this in 

 the direction of rotation would be sin'o cos a, which 

 expression would represent the efficiency of the vanes of 

 our mill as dependent upon the angle of setting. When a 

 is small, the second factor is of little importance. A very 

 simple experiment v.'ill now decide whether the law of 

 sin'-'a is, or is not, an approximation to the truth. Wcfind, 

 in fact, that four vanes set at 6° markedly overpower two 

 vanes set at 9", whereas according to the law of sin-o the 

 reverse should happen. In order to balance the four 

 vanes at 6°, the two vanes need to be be at about 14^°. 



B}' observations of this kind materials are collected 

 for a complete plotting out of the curve of efificienc}-. 

 The efficiency necessarily vanishes when a = 0, and also on 

 account of the resolving factor, when a = 90°. In order to 

 balance four vanes set at 5^, we may set the remaining 

 two vanes either at \oY' or at about 58^'. The efficiency 



