444 



SCIENCE. 



[N. S. Vol. IV. No. 91. 



by Meissel. The next thirty roots of the 

 equation J'o(a;) = o, and the values of Ji(a;) 

 corresponding to the first forty roots, have 

 just been computed by Prof. B. O. Peirce 

 and Mr. E. W. Willson by means of Vega's 

 ten place table of logarithms, except in the 

 few cases where a greater number of places 

 was necessary, and then recourse was had 

 to Thoman's tables. The computation has 

 been done twice. 



The total number of papers read was 

 greater by two than the number read at 

 last year's summer meeting. The attend- 

 ance was the same as last year. The Coun- 

 cil announced that the regular October 

 meeting of the Society would be replaced 

 by a special meeting to be held at Prince- 

 ton, on October 17th, in honor of Profs. 

 Felix Klein and J. J. Thomson, who would 

 be in Princeton at that time as delegates to 

 sesquicentennial celebration of Princeton 

 University. Thomas S. Fiske. 



Columbia University. 



copper wire; c is a thin conical brace to sus- 

 tain the brass tube (cZ), which holds the 

 peacil (e) normally to the web. The whole 



A CUBVE-TBACING TOP. 



Some time ago I constructed a top (since 

 called the gyrograph) for directly map- 

 ping out the curves corresponding to the 

 precessional and progressive motion of a 

 spinning body. I have since found the 

 instrument of service in teaching this rather 

 troublesome subject, and I will, therefore, 

 venture to give an account of some of its 

 performances. 



The instrument is exceedingly simple, 

 and consists merely of a form of stably 

 spinning top, not too heavy, having a 

 socket at the bottom of the stem for the 

 axial insertion of the pencil on which the 

 top is to spin. Particular care must be 

 taken, however, to have the top well bal- 

 anced and the pencil centered, and I have, 

 therefore, sketched in the annexed figure 

 the form with which I obtained my best re- 

 sults. Here a is a thin disc or web of tin 

 plate carrying a circular ring (6) of ^-inch 



Fig. 1. — Sectional elevation of the top in position 

 for curve tracing (reduced to one-fourth). 



is revolvable around the handle (/), the 

 round stem of which passes nicely through 

 central perforations in the web and a dia- 

 phragm fixed within the brass tube. The 

 string for spinning is wound around d. The 

 figure is drawn to scale the diameter of the 

 web, being about 6 inches. The weight 

 should not exceed about 5 ounces. It is 

 not desirable to hasten the precessional 

 motion as the curve tracing is best shown 

 with a leisurely swinging top. Further- 

 more, a tablet at least a foot square, prefer- 

 ably of plate glass, framed and provided 

 with leveling screws, is needed for the ac- 

 curate delineation of the curves. On this 

 is placed a smooth sheet of white paper. 

 The top, after being spun on the handle, is 

 placed down with its axis oblique to the tab- 

 let, so that precessional motion may be in- 

 itiated at the outset. 



If the tablet is quite level the curves ob- 

 tained are spiral with but very slight, if any^ 

 lateralness. Two cases are to be distin- 

 guished : If the pencil is hard and blunt 

 ( preferably cut square off at the lead with a 

 sharp circular edge) precession is markedly 

 accelerated; the top begins with a wide 

 sweep and gradually rising from the oblique 

 to the vertical position, describes a series of 

 spires which converge rapidly from a wide 

 circumference towards a center. If the point 

 is hard and sharp, the top does not rise so 



