An Essay on the Theory and Practice of Setting Out Railway Curves |
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Page 5
... radius of the curve , and half the subchord A 1. ( See diagram p . 8. ) . What is meant by the tabular sine of so ... logarithmic tables of sines , radius is taken to be 10. , which is the logarithm of 10,000,000,000 , and the other ...
... radius of the curve , and half the subchord A 1. ( See diagram p . 8. ) . What is meant by the tabular sine of so ... logarithmic tables of sines , radius is taken to be 10. , which is the logarithm of 10,000,000,000 , and the other ...
Page 9
... tabular radius ( or sine of 90 ° ) which in the table of natural sines is 1 , by twice the tabular sine of half the angle O. But if you work by logarithms , you have to subtract twice the logarithmic sine of half the angle O from the ...
... tabular radius ( or sine of 90 ° ) which in the table of natural sines is 1 , by twice the tabular sine of half the angle O. But if you work by logarithms , you have to subtract twice the logarithmic sine of half the angle O from the ...
Page 11
... sine of 90 ° by the diameter of the actual circle . Or by logarithms : subtract the logarithm of the diameter from the sum of the logarithm of the distance ( d ) and logarithmic tabular radius . The rationale of this formula is as follows , ...
... sine of 90 ° by the diameter of the actual circle . Or by logarithms : subtract the logarithm of the diameter from the sum of the logarithm of the distance ( d ) and logarithmic tabular radius . The rationale of this formula is as follows , ...
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Common terms and phrases
30 chains AC or BC actual sine adjusted alternate segment angle ACB angle AO1 angle CBA angle of deflection angle ß angles measured angular quantity apex arcs of equal bisect calculate offsets calculate the radius centre common tangent diagram direction distance double the sine equal circles equal the angle equi-distant Euclid 32 explain a plan Find the angle fixed Given radius ground half the angle hundred feet instrument internal angle junction length of radius line of collimation lines and angles logarithmic tabular radius mathematical means Natural Sines opposite angles plug point in line point of intersection proportional quantity ẞ radiating radius or sine RAILWAY CURVES side sine angle sine of 90 sine of half straight portions sub-tangents subchord subchord d supplement table of natural table of sines tabular sine tangent and chord tangent points tangent respectively thence the angle Theodolite triangle Trigonometry whole arc
Popular passages
Page 23 - ... double of that which measures the opposite angle ; that is, double the sine of that angle measured in the circle ; therefore the sides of the triangle are to each other as the sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in the circle whose radius is that of the tables.
Page 23 - ... as the sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in the circle whose radius is that of the tables. Hence the following proposition...