COMPUTATION OF THICKXESS OF STRATA AND DISTANCE TO A STRATUM. 



51 



the size desired for the finished product. 

 Angidar magnitudes are to be plotted, and as a 

 circle is measurable in degrees, the same 

 formula applies if x is considered to be the 

 angular extent of the scale. If several con- 

 centric circles or a spiral of several turns is 

 used to plot some one function, the circular 

 scale modulus is expressed thus: 



M = 



^360 



l0£ 



y- 



h 



where t is the number of concentric circles or 

 the numbers of turns in the spiral. 



The circular slide rule here considered was 

 computed with a circular scale modulus of 180 

 instead of 360. The logarithmic range from 1 

 to 10 is 1, but the logarithmic range from sin 

 90° to sin 0° 45' is almost 2, and it therefore 

 requires twice as long a scale 

 to plot the desired range of 

 sines as to plot the usual 

 numerical scale. If the nu- 

 merical scale is plotted to a 

 whole turn (3fi0°), the sine 

 range will require two turns, 

 and if an answer is to be read 

 off in sines, it will be am- 

 biguous, as the index will 

 give two possible values. 

 To avoid this result an 

 angular range of 180° was 

 used for the numerical scale, 

 which places the entire sine 

 scale in one turn. The 

 usual numerical calibration 

 therefore takes but half of 

 one turn, and to prevent 

 the index from yielding an 

 answer in the uncalibrated 

 half of the number scale, 

 the numerical range was 

 doubled — that is, to read 

 from 0.01 to 1, or from 0.1 

 to 10, as desired. Such a 

 . scale therefore takes a whole 

 turn. 



The tangent scale, if plotted with the same 

 angular range as the sine scale, rec[uires twice 

 as long a scale as the sine scale, and in order to 

 obtain this range the tangent scale is plotted 

 in a two-turn spiral, the same circular scale 

 modulus being used as before. As a result, 



any answer that is read off in tangents will 

 theoretically be ambiguous, as the index gives 

 two values, but practically the ambiguity is of 

 no consequence, for the two values given by the 

 index are so widely different that the operator, 

 if he knows roughly the magnitude of the 

 rer[uired answer, will be able to choose without 

 difficulty the proper one. 



The calibration of this computer is shown in 

 figure 9. The outer circle is the number scale; 

 the next circle inward is the sine scale; and the 

 tangent scale is placed inside the sine scale in 

 a two-turn spiral. This disk is mounted to 

 turn upon an underlying support which extends 

 outward a quarter of an inch or more and is 

 equipped with two overlying indexes, made 

 of transparent celluloid, which are attached to 

 the center of the disk. One of these indexes 



Trigonometric computer for the solution of such prol>lcms as arc readily solved with ths 

 I2-iuch straight slide rule. 



turns freely, but the other is attached at the 

 outside to the underlying support and is there- 

 fore immovable. It is intended that the 

 freely moving index may be attached tempo- 

 rarily to the underlying support by pressure 

 with the thumb ami one finger. 



