52] THE REPRESENTATION OF THE CYLINDROID BY A CIRCLE. 47 



screw, and the line PT may be called the axis of pitch. We have, accord 

 ingly, the following theorem : 



The pitch of any screw on the cylindroid is equal to the perpendicular let 

 fall on the axis of pitch from the corresponding point on the circle. 



A parallel A A to the axis of pitch cuts the circle in two points, A and 

 A , which have equal pitch. The diameter perpendicular to the pitch axis 

 intersects the circle in the points U, V of maximum and minimum pitch. 

 These points, of course, correspond to the two principal screws on the cylin 

 droid. The two screws of zero pitch are defined by the two real or imaginary 

 points in which the axis of pitch cuts the circle. 



A fundamental law of the pitch distribution on the several screws of a 

 cylindroid is simply illustrated by this geometrical representation. The law 

 states that if all the pitches be augmented by a constant addition, the 

 pitches so modified will still be a possible distribution. So far as the 

 cylindroid is concerned, such a change would only mean a transference of 

 the axis of pitch to some other parallel position. The diameter 2m merely 

 expresses the size of the cylindroid, and is, of course, independent of the 

 constant part in the expression of the pitch. 



52. The Distance between two Screws. 



We shall often find it convenient to refer to a screw as simply equivalent 

 to its corresponding point on the circle. Thus, in fig. 6, the two points, A 



and B, may conveniently be called the screws A and B. The propriety of 

 this language will be admitted when it is found that everything about a 



