50 



SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1921. 



graphic solution of right triangles, but it is 

 here j)rcsented as an accessory chart, to be 

 used in connection with the charts shown in 

 Plates VI and VII. Three small index dia- 

 grams have been added as guides in the use 

 of the chart. For the convenience of geolo- 

 gists, for whom this chart has been primarily 

 constructed, the terms A^ertical distance, hori- 

 zontal distance, slope distance, and angle of 

 slope have been placed on the chart to prevent 

 ambiguity in its use. Also as in the preceding 

 charts, the calibrations are given as 100, 200, 

 300, etc., instead of 1, 2, 3, etc., for reasons 

 stated on page 45. 



USE OF CHART. 



A straight edge or, l)ettcr still, a i)i('ce of 

 transparent or semifrosted celluloid with a 

 black line ruled on the underside is recjuired 

 to solve (Hjuations (10) and (11). If, for ex- 

 ample, <j and /( are given, connect the a value 

 on AD (fig. 7) with the /; value on BC, and the 

 intersection on AC will give the value of s. 

 Or if <7 and .s are given, connect the a value on 

 AD with the s value on AC, and the continua- 

 tion of this line intersecting BC will give the 

 value of /( on BC. Similar solutions are used 

 when e. s, and a are involved. For equation 

 (12) a piece of transparent or semifrosted 

 celluloid will be required, on the underside of 

 which are drawn two black lines intersecting 

 at right angles. One of these lines is placed 

 to pass through the given values of e and //, 

 on CD and BC, respectively, and the other re- 

 quired to pass thi-ough the ])oint C. Then the 

 continuation of the line jjassing thi'ough C 

 will show on I)B the vahu^ of <r. 



TRIGONOMETRIC COMPUTER. 



OUTLINE. 



Two good reasons exist for the use of a trig- 

 onometric computer. First, the geologist or 

 surveyor will have numerous formulas to solve 

 which, though essential, are not frequently used. 

 It would be impracticable to have an aline- 

 ment chart for every such formula, and it 

 would be a laborious task to prepai'e so many 

 .such charts. Second, such charts, when re- 

 duced to a size which can be carried in the 

 field, might not give sufFiciently accurate results, 

 particularly when the formulas are complex. 



The alternative is some graphic computing 

 device, wiiich is accurate enough for general 



purposes and compact enough to be carried 

 without difficulty in the field. The straight 

 slide rul(! at once suggests itself as an instru- 

 ment for this purpose, but it is open to two 

 main objections — it is not of convenient shape 

 to be easily and safely carried, and it is not 

 easy to use for the solution of trigonometric 

 formulas. 



To fill this distinct want, the WTiter has 

 designed a cii'cular slitie rule, which will not 

 exceed five inches in diameter nor one 

 twenty-fifth of an inch in thickness, which will 

 be the equivalent in accuracy of a 12-inch 

 straight slide rule, and which can easily be car- 

 ried in a notebook, just as a protractor is car- 

 ried. The principal practical advantages of 

 this type of computer may be summarized thus: 



1. It- is compact and portable. 



2. It enables all computations, including 

 trigonometric computations, to be accomplished 

 with the same ease and by exactly the same 

 operations. 



3. It possesses a continuous scale, so that it 

 is never necessary to reset the instrument, as 

 it is with the straight slide rule, because the 

 answer may be off the scale. 



4. .Sufficient space is available tlirough the 

 use of concentric circles, or of a spiral, to plot 

 the entire tangent scale, only half of which is 

 plotted on the straight slide rule. This makes 

 possible a direct setting to the tangents of 

 angles between 45° and 90° and to the cotan- 

 gents of angles between 0° and 4.5°, doing 

 away with the necessity of computing these 

 values from reciprocals, as in the straight slide 

 rule. 



CONSTRUCTION OF COMPUTER. 



A circular slide rule is constructed in exactly 

 the same way as a straight slide rule, except 

 that the calibration is computed and laid off 

 m angular instead of linear magnitudes. In 

 constructing a straight slide rule x inches long, 

 for multiplication and division, which is to 

 range from a scalar value of y at one end to a 

 scalar value of z at the other end, the scale 

 modulus (M) is expressed as follows: 



M = 



og y-logz 



The calibration is computed bj' multiplying 

 the logarithms of each scalar value that will 

 appear on the scale by M. 



For a circular or spiral slide rule, consider a 

 circle of indeterminate diameter depending on 



