Example.- Suppose a screw is required to he cut containing 25 threads in an inch, and the leading screw, as before, having two threads in an inch, and that a wheel of 60 teeth is fixed upon for the end of the spindle, 20 for the pinion in contact with the screw-wheel, and 100 for that in contact with the wheel on the end of the spindle; required the Dumber of teeth in the wheel for the end of the leading screw.

25 ÷ 2 = 12.5, and 60 x 12.5 X 20 / 100 = 150 teeth.

Or suppose the spindle and screw wheels to be those fixed upon, also any one of the stud-wheels, to find the number of teeth in the Oilier.

60 x 12.5 / 150 X 100 = 20 teeth, or 60 x 12.5 X 20 / 150 = 100 teeth.

Table of Change Wheels for Screw-cutting; the leading Screw being ½ inch pitch, or containing 2 threads in an inch.

 Number of threads in inch of screw. Numb. of teeth in Lathe spindle-wheel. Leading screw-wheel. 1 80 40 1¼ 80 50 1½ 80 60 1¾ 80 70 2 80 90 2¼ 80 90 2½ 80 100 2¾ 80 ]10 3 80 120 3¼ 80 130 3½ 80 140 3¾ 80 150 4 40 80 4¼ 40 85 4½ 40 90 4¾ 40 95 5 40 100 5½ 40 110 6 40 120 6½ 40 130 7 40 140 7½ 40 150 8 30 120
 Number of threads in inch of screw. Number of teeth in Lathe spindle-wheel. Wheel in contact with spindle-wheel Pinion in contact with screw-wheel. Leading screw-wheel. 8¼ 40 55 20 60 8½ 90 85 20 90 8¾ 60 70 20 75 9½ 90 90 20 95 9¾ 40 60 20 65 10 60 75 20 80 10½ 50 70 20 75 11 60 55 20 120 12 90 90 20 120 12¾ 60 85 20 90 13 90 90 20 130 13½ 60 90 20 90 13¾ 80 100 20 110 14 90 90 20 140 14¼ 60 90 20 95 15 90 90 20 150 16 60 80 20 120 16¼ 80 100 20 130 16½ 80 110 20 120 17 45 85 20 90 17½ 80 100 20 140 18 40 60 20 120 18¾ 80 100 20 150
 Number of threads in inch of screw. Number of teeth in Lathe spindle-wheel Wheel in contact with spindle-wheel Pinion in contact with screw-wheel. Leading screw-wheel. 19 50 95 20 100 19½ 80 120 20 130 20 60 100 20 120 20¼ 40 90 20 90 21 80 120 20 140 22 60 110 20 120 22½ 80 120 20 150 22¾ 80 130 20 140 23¾ 40 95 20 100 24 65 120 20 130 25 60 100 20 150 25½ 30 85 20 90 26 70 130 20 140 27 40 90 20 120 27½ 40 100 20 110 28 75 140 20 150 28½ 30 90 20 95 30 70 140 20 150 32 30 80 20 120 33 40 110 20 120 34 30 85 20 120 35 60 140 20 150 36 30 90 20 120

Table by which to determine the Number of Teeth, or Pitch of Small Wheels, by what is commonly called the Manchester Principle.

 Diametral Pitch. Circular Pitch. 3 1.047 4 .785 5 .628 6 .524 7 .449 8 .393
 Diametral Pitch. Circular Pitch. 9 .349 10 .314 12 .262 14 .224 16 .196 20 .157

Example 1. - Required the number of teeth that a wheel of 16 inches diameter will contain of a 10 pitch.

16 X 10 = 160 teeth, and the circular pitch = .314 inch.

Example 2. - What must be the diameter of a wheel for a 9 pitch of 126 teeth ?

126 ÷ 9 = 14 inches diameter, circular pitch .349 inch.

Note. - The pitch is reckoned on the diameter of the wheel instead of the circumference, and designated wheels of 8 pitch, 12 pitch, etc.

Strength of the Teeth of Cast Iron Wheels at a given Velocity.

 Pitch of teeth in inches. Thickness of teeth in inches. Breadth of teeth in inches. Strength of teeth in horse-power at 3 feet per second. 4 feet per second. 6 feet per second. 8 feet per second. 3.99 1.9 7.6 20.57 27.43 41.14 54.S5 3.78 18 7.2 17.49 23.32 34.98 46.64 3.57 1.7 6.8 14.73 19.65 29.46 39.28 3.36 1.6 6.4 12.28 16.38 24.56 32 74 3.15 1.5 6. 10.12 13.50 20.24 26.98 2.94 1.4 5.6 8.22 10.97 16.44 21.92 2.73 1.3 5.2 6.58 8.78 13.16 17.54 2.52 1.2 4.8 5.18 6.91 10.36 13.81 2 31 1.1 4.4 3.99 5.32 7.98 10.64 2.1 1.0 4. 3.00 4.00 6.00 8.00 1.S9 .9 3.6 2.18 2.91 4 36 5.81 1.68 .8 3.2 1.53 2.04 3.06 3.08 1.47 .7 2.8 1027 1.37 2.04 2.72 1.26 .6 2.4 .64 .86 1.38 1.84 l.t)5 .5 2. .375 .50 .75 1.00