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MATHEMATICS

The groupings of the topics under three headings as (1) related mathematics, (2) applied mathematics, (3) trade mathematics, is in process of completion. In the main, (3) deals with the use of tables and rules as found in handbooks, accessible to. machinists, and is "figuring"; (2) would give the reason for the rule by applying mathematical principles and methods to the topics under discussion; (1) would derive these principles. For example, to find the circular pitch when the diametral pitch is known, trade mathematics either would use. the tables in the handbook would divide 3.1416 by the diametral pitch; applied mathematics would work out the formula from the definition of the pitches and known facts as to circles, while relatable mathematics would teach the principles of the simple equation, how to find one quantity in terms of another, how to find the circumference of a circle, etc. The shop instructor will teach trade mathematics and as much applied mathematics as time will allow; the rest will be taken care of by the director. The entire list of topics; covered in the mathematics is here given.

Fractions. Reducing common and decimal to so-called binary or machinist's fractions. Reciprocals. Common operations.

Ratio and Proportion. Simple treatment as applied to speed ratio, gearing, tapers, circles. Essentials as used in finding. functions in trigonometry.

Square Root. Preparatory to work in threads, gears, lay-out, bolts and nuts.

Geometry. Basic facts and principles pertaining to angles, triangles, circles and hexagons, derived from measurement methods and constructive work. Application of these facts to practical uses. Areas of rectangular figures and circles.

Formulas. Simple treatment and solution for one value in tens of others. Handled by method of the equation. Working out formulas from rules; simplifying and applying to common shop-mathematics.

Trigonometry. Functions as derived from Geometry. Explanation and use of tables of Natural Logarithms. Finding functions of angles and angles corresponding to given functions. Application in solution of right triangles as found in topics following this and in laying out work with or without angle iron: Dove- tails.
Figuring Taper. Methods of expressing amount of taper in -shafts, pulley, etc. Finding off-set for cutting tapers.

Speed of Pulleys and Gears. Figuring. Use of ratios. Back gears.

Speeds and Feeds. Principally to find amount of stocks removed and time of operation.

Gearing Ratios. Compounding.

Indexing. Plain or Direct. Indexing for angles. Differential Indexing. Work 'with or without tables. Problems ,applied directly on Dividing Head.

Threads. Single, Double, Multiple Pitches. Angles. Lead. :Single and Double Depth. Approximate size of tap drills. Sharp V, U.S.S., Acme, and Square Threads. Clearance of cutting tool for square threads.

Worms. Finding Depth. Linear and Nominal Pitches. Lead, and Tool Clearance. Helix angle.

Spur Gear and Rack. Finding the tooth parts. Choral Pitch and Corrected Addendum.

Worm Gear. Circular, diametral and linear Pitches. Center .distance. Gashing angle.

Bevel Gears. Angles. Tooth parts. Diameters. Selecting cutters.

Spiral Gears. Calculating parts; angle, circumference, and lead. Use of milling machine tables. Finding normal Pitch. Depth. Figuring gears for the lead. Outside diameter. Selection of cutters.

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