28. Of 9 miles to 1.3 inches to show furlongs and chains.

29. Of one foot to show 1000th of a foot.

30. Of 4 miles 588 yards to 3.1 inches.

31. On a plan the distance between two points 4.27 inches apart represent 4587 yards: construct a scale of miles, furlongs and chains.

32. Draw a scale to measure feet on a plan on which the space between the two points 1.5 inches apart is of the real distance.

33. Construct a scale of metres comparative to one of 17 English yards to 1.2 inches 1 metre 39.34 inches.

34. The distance between London and Woolwich is 9 miles: construct the scale of a plan on which that distance is represented by .65 inches, and show furlongs and chains. 35. Construct a scale of 5000 for a regular enclosure, 1680 feet long and 1350 feet broad.

1

36. Construct a scale of yards 5 inches to 6 furlongs. 37. A regiment drawn up in order of battle occupies a front of 800 feet, and measures on the plan 29 inches: construct the scale of the plan to show poles and yards. N.B. 5.5 yards = 1 pole.

38. Construct a scale of fathoms 1

20,000.

39. On a plan of a mile occupies a space of 2.7 inches: construct a scale of yards to it.

40. On a map 183 miles occupy a space of 14.3 inches : construct a scale to show furlongs.

41. Construct a scale of paces for a plan, draw to a scale of, assume the pace to equal 2.67 feet.

42. Construct a scale of 1 to represent yards.

9050

43. Draw a scale of paces 11 inches to a mile: supposing 25 paces to equal 1 chain: 1 chain 66 feet.

44. Construct a scale of Milan miles : 5 to 1 inch. 1 Milan mile=1.0277 English miles.

45. Draw a scale of 4 inches to a mile, to show furlongs and spaces of 50 feet: give its representative fraction. to show English miles and

46. Draw a scale of 3

978900

Russian versts. 1 verst 1166.68 English yards.

=

47. Construct a scale of paces for a plan drawn to a

scale of the pace being assumed to equal 2.5 feet. 1 :

3298

48. On a plan 18000 paces measure 22.3 inches: show spaces of 10 paces diagonally.

49. Draw a scale of 14 yards to 1.1 inch, and a comparative scale of metres-1 metre 39.34 inches.

50. On a map of an inch represent 13.68 yards: show 100 yards and the representative fraction.

51. A table 14 feet 6 inches long is represented by a space of 5.2 inches: make a diagonal scale showing inches-to the drawing.

1 200

52. Construct a scale of to represent Belgian and Chinese feet.

1 Belgian foot = .90466 of an English foot.

1 Chinese foot = .8616 of an English foot.

800

53. Construct a scale of 2 to show English yards and Russian archines. 1 archine.7777 of an English yard. 54. Construct a scale of chains 1 inch to 1 mile.

55. On a plan, 4.65 inches, represent 13.5 miles: construct the scale and a comparative one of Russian versts. 1 verst 1167.68 yards.

=

56. Required, a scale of Belgian fuss, and one of Spanish palms corresponding to it.

1 Belgian fuss = .90466 of 1 English foot.

1 Spanish palm = .684

ditto.

57. The plan of a French fort is to be drawn to a scale of 50 English feet to 1 inch, and two other plans of the same fort are to be of the same size; but one reduced to a

scale of metres and decimetres, and the other to a scale of toises and feet

1 metre =

1.0936 English yards.

1 toise 76.731 English inches.

58. On a drawing 17.5 feet are represented by a space of 1.3 inches: construct a comparative scale of Spanish pies and pulgados.

1 pie = .9132 of an English foot, 1 pulgado of a = i pie or .0761 of an English foot.

59. Reduce 86.72 French metres to English yards.

1 metre = 1.0936 English yards.

60. On a scale 200 yards long, 24 yards = 1 inch, draw a scale of toises comparative to the above, and give its representative fraction. 1 toise 76.731 inches.

=

61. Draw a scale of 89.72 yards to of a foot, 100 yards long, and give its representative fraction.

62. Make a scale of Spanish varas and pies showing pulgados diagonally, comparative to another on which 5 yards are represented by 1.89 inches.

63. A Prussian fathom contains 6 Rhenish feet, each 1.0297 English feet long: construct a scale of fathoms showing feet diagonally.

4

700

64. A map, 40 inches long and 36 inches broad, contains an area of 25 acres : construct its scale to show poles, yards, and feet. 1 acre 4840 yards.

65. Construct a scale of 13 inches to a mile, showing furlongs and yards.

66. A front of fortification 287.38 yards long is represented by a length of 8.82 inches: show the value of 1 yard and complete the scale to 800.

67. Construct a scale of Bavarian rods and Belgian

ells corresponding to 14.5 English feet to 1.2 inches. The rod 3.1917 English yards (to show spaces of 10 feet) and the ell = .74845 of an English yard.

=

68. A range of buildings 2876 feet long is represented by a space of 7.25 inches long: construct to it a scale of 500 yards, showing single yards.

69. Construct a plain scale of yards, 346 yards to 1.7 inch, and also a corresponding scale of Russian sachines. The sachine 2.3332 yards.

=

70. On a military plan, 900 feet are represented by a length of 30 inches: construct a comparative scale of yards to it, and give its representative fraction.

71. Two plans on the same ground are drawn, the one to a scale of 2.95 inches to 1 mile, and the other 2.95 miles to one inch show the length of the line which for each plan will represent 5.57 miles: give also a representative fraction of each of the scales.

DEFINITIONS. (Euclid, Book XI.)

12. A pyramid is a solid figure contained by planes that are constituted betwixt one plane and one point above it in which they meet.

13. A prism is a solid figure contained by plane figures, of which two that are opposite are equal, similar, and parallel to one another; and the others parallelograms.

14. A sphere is a solid figure described by the revolution of a semicircle about its diameter, which remains unmoved.

15. The axis of a sphere is the fixed straight line about which the semicircle revolves.

16. The centre of a sphere is the same with that of the semicircle.

17. The diameter of a sphere is any straight line which passes through the centre and is terminated both ways by the superficies of the sphere.

18. A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.

If the fixed side be equal to the other side containing the right angle, the cone is called a right angled cone; if it be less than the other side, an obtuse angled; and if greater, an acute angled cone.

19. The axis of a cone is the fixed straight line about which the triangle revolves.

20. The base of a cone is the circle described by that side containing the right angle which revolves.

21. A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides, which remains fixed.

22. The axis of a cylinder is the fixed straight line about which the parallelogram revolves.

23. The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.

24. Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals. 25. A cube is a solid figure contained by six equal squares.

26. A tetrahedron is a solid figure contained by four equal and equilateral triangles.

27. An octahedron is a solid figure contained by eight equal and equilateral triangles.

28. A dodecahedron is a solid figure contained by twelve equal pentagons which are equilateral and equiangular.

29. An icosahedron is a solid figure contained by twenty equal and equilateral triangles.

30. A parallelopiped is a solid figure contained by six quadrilateral figures, whereof every opposite two are parallel.