USEFUL TO THE MICEOSCOPIST 1135 



Geometrical Progression 

 m, multiplier or divisor. 



A = B B=Vm 



w'"- 1 '* m-l ' 



Properties of Circles and Spheres <c. 

 77 = 3-141592653589793 + log 77 = 0-4971498727 



77- = 9-8696 A/77~= 1-77245 = -31831 



A ='10132 --=-56419 



77 2 A/77 4 



^ = -5236 . A/2-1-41421 v/2 = 8-02496 



6 



Circumference, C. Area, A. Radius, r. Diameter, d. Volume, V. 

 Surface, S. 



" 6 * "77" 



Area of sector of circle - de * rees in wo_x_area _ofdrde 



360 



Length of arc = number of degrees x -017453 r. 

 Unit of circular measure = 57'29578. 

 Side of square of equal area to a circle = r \/TT. 

 Side of inscribed square = r A/2. 

 Area of ellipse = i major axis x i minor axis x 77. 



Volume of spheroid = polar axis x (equatorial axis) 2 x !T. 



6 



Number of Threads per inch in Whitworth's Standard Screws 



Sixes -fa . . No. of threads 150 Sixes . . No. of threads 20 



A 80 



,f & 00 



., 5, 40 j7 ff . 14 



& . 32 i . . 12 



A - 5, 24 I . 11 



Convenient Approximations for rapid Calculations 



6 knots = 7 miles, more correctly 13 knots = 15 miles. 



8 kilometres =5 50 kilometres = 31 



1 metre = 3 ft. 3 in. 32 metres = 35 yards. 



5 centimetres = 2 inches 33 centimetres = 13 inches. 



3 millimetres = ^ inch ,, ., 5 millimetres = inch. 



1 pole = 5 metres ; 1 furlong = 2 hectometres. 



; V = oth) <r inch ; T ^u inch = 5- mm. ; T^joWtf inch = ^ /i. 



2 are - 239 sq. yds ; 1 rood = 10 are ; 2 acres = 81 are ; 100 hectare 

 - 247 acres ; 3 cubic yards = 23 decisteres ; 1 decastere = 13 cubic yards ; 

 2 decilitres = 7 / (ounces); 4 litres = 7 pints; 2 grammes = 31 grains; 



