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stone or gravel, in consequence of the necessity of putting the gravel on in thin layers: this mixture of earth or clay, in dry warm seasons, expands by the heat, and makes the road loose and open; the consequence is, that the stones are thrown out, and many of them are crushed and ground into dust, producing considerable wear and diminution of the materials: in wet weather, also, the clay or earth, mixed with the stones, absorbs moisture, becomes soft, and allows the stones to move and rub against each other when acted upon by the feet of horses or wheels of carriages. This attrition of the stones against each other wears them out surprisingly fast, and produces large quantities of mud, which tend to keep the road damp, and by that means increase the injury."

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The above engraving represents the level employed by road-surveyors in laying out new works. On the horizontal bar A C are placed four sliding gauges, a, b, c, d, which move in dovetailed grooves cut in the horizontal bar, and when adjusted to their proper

depth below the bottom edge of the level, can be firmly fixed in their position by a thumb-screw. A section of this portion of the instrument, taken through the line at e, is given on the right, drawn to a larger scale; the remaining parts of the instrument require no explanation.

For laying out slopes, the clinometer, described at page 96, is the best instrument that can be used.

TABLE I.-Showing the reduction upon each chain necessary to reduce

hypothenusal to horizontal measure.

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APPENDIX.

IN the former edition of this work there was an error in the Rule which appears, in the present edition, at page 75, the word "tangent" having been written for "sine." A scientific friend, in noticing this mistake, has suggested a convenient method of arranging the figures of the calculation when the perpendicular and base of a right-angled triangle are both to be computed from the base-angle and hypothenuse. The directions are as follows:

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'1st. Write down the log. of the measured hypothenuse taken from the table of numbers.

"2nd. Over it place the log. sine of the measured angle from table of log. sines, &c., and draw a line above.

"3d. Under the log. of the hypothenuse write down. the cosine of the angle, and then draw a line under it. Add the hypothenuse to the sine upwards, and it will give the length of the perpendicular sought in the table of numbers. Add the hypothenuse and cosine together downwards, and it will give the length of the base in the table of numbers.

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