194 Wisconsin Academy of Sciences, Arts, and Letters. 



latter, tmisf assume a spherical, or nearly spherical, form. The orbit of a comet being 

 nsually highly eccentric, the body moves the greater part of the distance from the 

 aphelion to the perihelion almost in a direct line towards the sun and must, therefore, 

 be subject to the law of acceleration and the varying force of gravitation according to 

 the square of the distance. By this latter law the impulse of solar attraction will be 

 strongest on the side nearest the sun, and less on the opposite side. This, with the 

 slight gravitating power in the comet to hold its particles in a spherical form, must cause 

 the body to hold its particles in a spherical form, must cause the body to elongate to a 

 spheroidal form more and more as the difl'erence in the square of the distance between 

 the two extremes of the comet increases and the sqaure of the distance of the whole 

 from the sun diminishes. This elongating process must be assisted, to some extent, by 

 the resisting ether in space (if any such exists) acting upon so light a body. 



As the comet approaches the sun from its intersection of the minor axis of the orbit, 

 the angle formed by the radius vector with the tangent of the orbit widens more and 

 more rapidly until they form a right angle at the perihelion. As this angle widens, the 

 centrifugal force comes into action in opposition to the centripetal and a new elongating 

 force is brought to bear upon the cometary mass. Thenceforward these two elongating 

 forces become subject to some curious modifications and transfers of power. "That 

 which results from simple solar Eravitation, or the accelerating force, goes on increasing 

 as the square of the distance diminishes, and diminishing as the angle of the radius 

 vector with the tangent of the orbit widens, till it reaches the perihelion where this force 

 is reduced to zero. At the same time that which results from the centripetal and centri- 

 fugal forces goes on increasing both as the square of the distance diminishes and as the 

 aforesaid angle widens, until, at the perihelion, this elongating lorce reaches its 7naxi- 

 mum power, 



The curve of the train is the necessary result of ditferent parts of the body being com- 

 pelled by the elongating forces to pursue orbits of difterent breadths with no increase of 

 orbital motion iu the outer portions which must needs fall behind the inner and form 

 a curve. When the train becomes largely curved, the centripetal and ceatrifugal forces 

 are brought to bear transversely upon the train and it is spread and llattem. d, least at the 

 front and more and more at the rear. The elongation, the curving, the spreading and the 

 flattening by the action of these forces, must, necessarily, all take place in the plane of 

 the orbit. 



When past the perihelion, the laws which brought the comet to its configuration at 

 that point being reversed in their action, their effects are reversed, of course, and the 

 body moves ofl", straightening, rounding and gathering up its train till it arrives at its 

 aphelion in the same form with which it left it. 



Ajourned to 7|^ o'clock P. M. 



Fourth Session. 



The Academy met at the hour appointed; the President in 

 the chair. 



The following persons were elected members of the Academy: 



Corresponding Membsrs.— Wm Stirapson, M. D., Secretary of the Chicacro Academy 

 of Sciences; J. C. Freer, M. D., President of Rush College, Chicago; Prof. T.^'W. Saflord, 

 Director of Dearborn Observatory, Chicago; Prof. Alex. Winchetl, Universitv of Michi- 

 gan; Prof. James Watson, Diriector of Observatory at University of Michigan. 



Annual Members.— II. W. Robv, Esq., Milwaukee; E. A. Charlton, President Platte- 

 ville State Normal School; Prof. Geo. Beck, State Normal School, Platteville. 



Reading of papers resumed. 



8. On the Kinetic Measures of Force. By Prof. John E, 

 Davies, Wisconsin State University. 



9. On the Duty of the State to its Idiotic Children. By Prof. 

 O. R. Smith, Milwaukee. 



This paper adduced evidence in favor of the capacity of the idiotic for receiving instruc 

 tion, and stronsly urged upon the State the importance of making provision for this 

 unfortunate class of persons, of whon statistics show the number to be much larger in 

 every community than is generally supposed 



10. On the Place which the Study of the Indian Languages 

 should hold in Ethnology. By Prof. John B. Feuling, of Wis- 

 consin State University. 



[Published in the Transactions p. 178.] 

 Adjourned to 9 A. M. of next day. 



