_Example:_ If an angle [alpha] of 20 degrees is required, and the disks are 1 and 3 inches in diameter, respectively, find the required center distance _C_.
20 ---- = 10 degrees; sin 10° = 0.17365; 2
3 - 1 ----------- = 5.759 inches = center distance _C_. 2 × 0.17365
=To Find Angle for Given Taper per Foot.=--When the taper in inches per foot is known, and the corresponding angle [alpha] is required. _Rule:_ Divide the taper in inches per foot by 24; find the angle corresponding to the quotient, in a table of tangents, and double this angle.
_Example:_ What angle [alpha] is equivalent to a taper of 1-1/2 inch per foot?
The angle whose tangent is 0.0625 equals 3 degrees 35 minutes, nearly; then, 3 deg. 35 min. × 2 = 7 deg. 10 min.
=To Find Angle for Given Disk Dimensions.=--When the diameters of the large and small disks and the center distance are given, to determine the angle [alpha]. _Rule:_ Divide the difference between the disk diameters by twice the center distance; find the angle corresponding to the quotient, in a table of sines, and double the angle.
_Example:_ If the disk diameters are 1 and 1.5 inch, respectively, and the center distance is 5 inches, find the included angle [alpha].
The angle whose sine is 0.05 equals 2 degrees 52 minutes; then, 2 deg. 52 min. × 2 = 5 deg. 44 min. = angle [alpha].
[Illustration: Fig. 17. Setting Center Mark in Line with Axis of Lathe Spindle by use of Test Indicator]
[Illustration: Fig. 18. Jig-plate with Buttons attached, ready for Boring]
=Use of the Center Indicator.--=The center test indicator is used for setting a center-punch mark, the position of which corresponds with the center or axis of the hole to be bored, in alignment with the axis of the lathe spindle. To illustrate, if two holes are to be bored, say 5 inches apart, small punch marks having that center-to-center distance would be laid out as accurately as possible. One of these marks would then be set central with the lathe spindle by using a center test indicator as shown in Fig. 17. This indicator has a pointer _A_ the end of which is conical and enters the punch mark. The pointer is held by shank _B_ which is fastened in the toolpost. The joint _C_ by means of which the pointer is held to the shank is universal; that is, it allows the pointer to move in any direction. Now when the part being tested is rotated by running the lathe, if the center-punch mark is not in line with the axes of the lathe spindle, obviously the outer end of pointer _A_ will vibrate, and as joint _C_ is quite close to the inner end, a very slight error in the location of the center-punch mark will cause a perceptible movement of the outer end, as indicated by the dotted lines. When the work has been adjusted until the pointer remains practically stationary, the punch mark is central, and the hole is bored. The other center-punch mark is then set in the same way for boring the second hole. The accuracy of this method depends, of course, upon the location of the center-punch marks. A still more accurate way of setting parts for boring holes to a given center-to-center distance is described in the following: