Record. lxiii 



paper gave the analytical conditions which define the brilliant 

 point of a surface, the brilliant point of a space curve, the 

 brilliant point of a plane curve and the brilliant point in space 

 of two dimensions, when the source of light is such that the 

 incident rays are normal to a given surface and the recipient is 

 such that the reflected rays are normal to another given sur- 

 face. Formulae were also given for the important special case 

 in which the source and recipient are points. The paper also 

 contained a general method for finding the equations of the 

 locus of the brilliant points of a moving or variable surface and 

 curve, together with a number of applications. Such loci 

 may often be perceived when an illuminated polished surface 

 is rapidly moved, as when a wheel with a polished spoke is 

 rapidly rotated. Another interesting example in loci of brill- 

 iant points is that of a circular saw which has been polished 

 with emery in a lathe and thus received a great number of 

 concentric circular scratches. The locus of the brilliant points 

 of this family of scratches was shown in this paper to be a 

 curve of the fourth degree. In the special case when the 

 point, source of light, and the eye of the observer (the point 

 recipient) are in a plane through the axis of the saw, the 

 curve degenerates into a circle and two coincident straight 

 lines. Accompanying the abstract is a photogram of the saw 

 curve. In this case the optical center of the camera lens is 

 the point recipient. Other interesting facts and a number of 

 geometrical constructions were also given in this paper. 



Messrs. Green, Baumgarten and Nipher, were elected a 

 committee for the nomination of officers for the year 1901. 



Mr. Joseph T. Monell, of Flat Kiver, Missouri, Mr. Elza 

 Edward Tyler, of Columbia, Missouri, and Mr. J. M. West- 

 gate, of Manhattan, Kansas, were elected to active member- 

 ship. 



One person was proposed for active membership. 



December 17, 1900. 



President Engler in the chair, forty-six persons present. 

 The nominating committee reported the following list of 

 candidates for 1901 : — 



