TEANSACTIONS OF SECTION A. 



543 



«rrors in the measurements -would have a greater influence on the eccentricity ; hut 

 in nearly every case the observations are now so numerous, and have been made by 

 so many observers, that the results given in the table must be nearly correct. 



It is my purpose to call attention to the relations between the distances of the 

 satellites and the eccentricities of their orbits, because such relations may thro-w 

 8ome light on the generation of these systems. Although we may gain but little, 

 yet the facts acquired will serve to test and control the: various hypotheses that are 

 brought forward on this obscure but interesting ques^tion. I will venture but one 

 suggestion. If we suppose the satellites with the smaller distances to have formerly 

 moved in a resisting medium, and denote by t the time, e the eccentricity, and k a 

 constant, there -will be a secular term in the motion of a satellite of the form — ket. 

 Such a term would tend to destroy the eccentricity of the orbit. 



12. Diagrammatic Bepresentation of Moments of Inertia in a Plane Area, 



By Alfred Lodge, M.A.^ 



The object of the paper is to give a simple construction for measuring the 

 moments and products of inertia about any pair of rectangular axes through a 

 point O of a plane section, and for finding the principal axes at the centre of area 

 of the section, having been given the moments and product of inertia about any 

 other pair of rectangular axes through the point O, 

 and the position of the centre of area. Two alterna- 

 tive methods are given, the first dealing with the 

 radii of gyration and with the product of inertia 

 divided by the area of the section, the second dealing 

 with the moments and products of inertia directly, 

 either containing the area of the section as a factor or 

 not, as most convenient. 



I. Let OX, OY be the given axes about a point O 

 in the section, PA the radius of gyration about OX, the area of the rectangle 

 OAPC = the product of inertia (after division by the area of the section), and 

 AQ the radius of gyration about OY. Bisect PQ in S, and with centre S and 



See Phil, Mag. for November 1886. 



