146 OUTLINES OF NATURAL PHILOSOPHY. 



angles to one another, on any one of which, when 

 the body revolves, the opposite centrifugal forces 

 exactly balance one another. These are called the 

 Principal Axes of Rotation. 



This singular theorem was first proposed by SEGNER 

 in 1755, and first demonstrated by ALBERT EULER, 

 in a Mtmoire crowned at Paris in 1760. LEON. 

 EULER has also given a demonstration of it in his 

 treatise de Motu Corporum rigidorum, prob. 27. 

 See also FRISIUS, de Rotatione Corporum quorum- 

 cunque, theorema vn. ubi supra, p. 194*. 



These three axes have also this remarkable property, 

 that the momentum of inertia with respect to any 

 of them, is either a maximum or a minimum, that 

 is, is either greater or less than if the body revol- 

 ved about any other axis. LEON. EULER, ubi su- 

 pra. The momentum of inertia has already been 

 defined, to be the sum of the products made by mul- 

 tiplying every particle into the square of its distance 

 from the axis of rotation, 



APP- 



