C. E. WARRING. 107 



There will therefore be three rotations : 



1. That around the original axis. 



2. A lateral rotation or gyration. 



3. A tilting in the direction of the applied force. 

 Frisi's celebrated law differs from this. He says : 



" When a body revolves on an axis passing through its 

 centre of gravity, and a force is impressed upon it tend- 

 ing to make the body revolve about another axis also 

 passing through its centre of gravity, the body will re- 

 volve about neither, but a third axis, which lies in the 

 same plane with the other two," etc., etc. 1 

 This law includes in itself three distinct propositions : 



1. "The body will not continue to revolve around the 

 original axis." Bat we have seen that it does. 



2. "The body will not revolve around the second 

 axis." But we have seen that it describes at least a part 

 of a revolution around the second axis. 2 



3. " The body will revolve around a third axis, which 

 lies in the same plane of the first and second axis." As 

 it stands, this also is not true. If by the " third axis " 

 is meant the first axis in a new position, still it is not 

 true unless we also suppose the plane passing through 

 the first and second axis to revolve on the latter. 



The most important discrepancy is found in the asser- 

 tion that there will be no movement of rotation around 

 the second axis, i. e., no tilting under the operation, and 

 in the direction of the second force. 



I propose to apply these principles to our earth in its 

 actual astronomical conditions. 



In all laboratory experiments upon gyrating bodies — 



1 1 add the rest of this famous law : "And so situated as to divide the angle which they 

 contain into two part, such that the series of the parts are to each other in the inverse ratio 

 of the angular velocities with which the body would have revolved about the said axr- 

 respectively." 



2 "A part of a revolution." This " part " may be almost 180° ; but cannot be more rhan 

 that unless the direction of the applied force is changed. By judiciously changing that, the 

 body can be caused to make as many revolutions as you please around the second axis. 

 The force in the case spoken of above ceases to cause any tilting when the line of its direc- 

 tion passes through the fixed point of the gyrating body. 



151 



