of long-styled flowers are depressed so far that they fall within the 

 average of the short-length parts considerably below their normal 

 positions. 



On motion of Mr. Wheeler, the paper was referred to the Com- 

 mittee on Publication, and the Academy passed a vote of thanks 

 to Mr. Eliot. 



A drawing of a mechanical device, designed by Mr. H. New- 

 ington for drawing the various conic sections, was exhibited, and 

 the mathematical problems involved were discussed. 



Prof. Nipher exhibited a second cast-iron cap, which had been 

 torn ofl' a six-inch pipe to which it was screwed, by shooting 

 into the pipe when filled with water with a Winchester rifle, as 

 described in the minutes of the meeting of the Academy, Nov. 

 3ist, 1887. In this case two shots had been required. He also 

 showed the efiect produced upon the iron of the cap by firing 

 upon it directly through the air only. 



Dece7nher igth, 1887. 



President Nipher in the chair ; eight members present. 



A paper by Dr. Liideking on the '^ Anomalous Densities of 

 Fused Bismuth" was read by the Secretary. From experiments 

 made with bismuth between 275° and 300° C. it was shown 

 that this metal exhibited the phenomenon of anomalous densities 

 in precisely the same manner, though in a less degree, as does 

 water. Referred to Committee on Publication. 



Prof. Nipher made some remarks on the graphical representa- 

 tion of certain mathematical functions, using as examples for 

 illustration the functions sin^a and cos^a, 



Mr. Engler exhibited a silk-thread model of a hyperboloid of 

 revolution of one nappe, showing the transformations of the sur- 

 face between the cylinder and cone, which are its limits, and the 

 rectilinear elements of both generations. 



January 2d, i' 

 President Nipher in the chair ; seven members present. 



