148 THE CYCLIDE. 



Second Constntction by Points. 



Draw the two fixed lines, and find points S and T given by equations (11) 

 iuul (12), then draw ST, and cut it in R, so that the ratio of the segments is 

 that given by equation (13). R will be a point on the cyclide. 



This construction is very convenient for drawing any projection of the 

 cyclide, as the distances are measured along the projections of the fixed lines, 

 and the line ST can be divided in the required ratio by means of a ruler 

 and " sector," without making any marks on the paper, except the position of 

 the required point Jt. 



In this way I have drawn stereoscopic diagrams of four varieties of the 

 cyclide, viewed from a position nearly in the line 



x=y = z, 

 .shewing the circles corresponding to various values of a and B*. 



On the. Forms of the Cyclide. 



We shall suppose b and c to be given, and trace the effect of giving 

 different values to 7*. Since the cyclides corresponding to negative values of r 

 differ from those corresponding to equal positive values merely by having the 



* A r ote on a Real-Image Stereoscope. In ordinary stereoscopes the virtual images of two pictures are 

 Huper|>oed, and the observer, looking through two lenses, or prisms, or at two mirrors, sees the figure 

 ;t|ijrviitly behind the optical apparatus. In a stereoscope, which I have had made by Elliott Brothers, 

 the observer looks at a real image of the pictures, which appears in front of the instrument, and he is not 

 conscious of using any optical apparatus. 



This stereoscope consists of a frame to support the double picture, which may be a common stereoscopic 

 lide inverted. One foot from this a frame is placed, containing (tide by side two convex lenses of half a 

 foot focal length, and having their centres distant one and a quarter inches horizontally. One foot 1" 

 these U placed a convex lens of two-thirds of a foot focal length and three inches diameter. 



The observer stands about two feet from the large lens, so that with the right eye he sees an image of 

 the left-hand picture, and with the left eye an image of the right-hand picture. 



These images are formed by pencils which pass centrically through the two small lenses respectively, 

 so that they are free from distortion, and they appear to be nearly at the same distance as the large lens, 

 o that the observer fixing his eyes on the frame of the large lens sees the combined figures at once. 



The figures of the cyclide, though constructed for this stereoscope, may be used with an ordinary 

 stereoscope, or they may be united by squinting, which is a very effective method. 



