1 88 American Quarterly Microscopical Journal. 



or hard wood, between the lathe centers, then on the face plate 

 (which of course should run quite true) chuck the cone on one 

 side either by cement or clamps, as shown in Fig. 5. With the 

 slide rest take off the section (a), remove the cone, and on the 

 parabolic face screw a well flattened piece of sheet brass, 

 slightly exceeding it in size; back this up by a block of the 

 same wood as the cone; fix both thereto by two counter- 

 sunk screws passing through holes drilled in the brass plate. 

 The cone is now returned to the lathe centers, and the surplus 

 piece of wood turned down, together with the edge of the brass 

 plate, by means of the slide rest, till the cone is again complete. 

 A dead smooth file may then be held against the revolving 

 cone; this trims the edge of the contained template, which 

 comes out as a true parabola. Unless this is made to match a 

 parabolic figure of known focus, it may be necessary to ascer- 

 tain the focal point of the blank parabola. This can be easily 

 found, as follows (Fig. 6): draw a line {ci) equal to the diameter 

 of the base of the parabola; take a perpendicular to this (<^), 

 equal to the height from the base to the vertex; from the ter- 

 mination of the perpindicular take a line (r) intersecting the 

 half diameter of the base-line at d\ another line is set off 

 from this point at right angles to c\ the distance at the inter- 



EXPLANATION OF FIGURES. 



Fig. 5. A wooden cone clamped down by screws on to the face plate of a 

 lathe. The axis from which the cone was turned inclined in the direction shown. 

 The dotted section {a) is turned off parallel with the opposite side ; on the para- 

 bolic face the template is formed. 



Fig. 6. Method of finding the focal distance of a blank parabolic figure : 



a. Diameter of base. 



b. Distance from base to vertex. 

 d. Half the semi-diameter. 



Connect d with end of b by line c; a perpendicular to this taken from d, at the point 

 where it intersects the axis below the base, will be equal to the focal distance 

 below the vertex. 



Fig. 7. Outline of rectangular brass plate to form a template for paraboloid. 



b. Focal distance. 



a. Equal to focal distance above vertex of parabola. 



Cross lines drawn at irregular, but increasing distances, as shown, measurements 

 on the axis, by compasses from a to each of these lines ; each line bisected by the 

 same measurements from the focus or point b describes the outline of a parabola. 



The dotted segment of a circle is struck from the focus b, representing a non-im- 

 mersion paraboloid. 



