The popular theory that a gentle undulating road is less fatiguing to horses than one which is perfectly level is erroneous. The asser tion that the alternations of ascent, descent, and levels call into play different muscles, allowing some to rest while others are exerted, and thus relieving each in turn, is demonstrably false, and con tradicted by the anatomical structure of the horse. Since this doc trine is a mere popular error, it should be utterly rejected, not only because false in itself, but still more because it encourages the building of undulating roads, and this increases the labor and cost of trans portation upon them.
Level Stretches. On long ascents' it is generally recom mended to introduce level or nearly level stretches at frequent inter vals in order to rest the animals. These are objectionable when they cause loss of height, and animals will be more rested by halting and unharnessing for half an hour than by travelling over a level portion. The only case which justifies the introduction of levels into an ascending road is where such levels will advance the road towards its objective point; where this is the case there will be no loss of either length or height, and it will simply be exchanging a level road below for a level road above.
Establishing the Grade. , When the profile of a proposed route has been made, a grade line is drawn upon it (usually in red) in such a manner as to follow its general slope, but to average its irregular elevation and depressions.
If the ratio between the whole distance and the height of the line is less than the maximum grade intended to be used, this line will be satisfactory; but if it be found steeper, the cuttings or the length of the line will have to be increased; the latter is generally preferable.
The apex or meeting point of all curves should be rounded off by a vertical curve, as shown in Fig. 8, thus slightly changing the grade at and near the point of intersection. A vertical curve rarely need extend more than 200 feet each way from that point.
Let A B, B C, be two grades in profile, intersecting at station B, and let A and C be the adjacent stations. It is required to join the grades by a vertical curve extending from A to C. Imagine a chord drawn from A to C. The elevation of the middle point of the chord will be a mean of the elevations of the grade at A and C, and one half of the difference between this and the elevation of the grade at B will be the middle ordinate of the curve. Hence we have in which M equals the correction in grade for the point B. The correction for any other point is proportional to the square of its distance from A or C. Thus the correction A + 25_ is M; at A -d- 50 it is i M; at A + 75 it 14I; and the same for corre sponding points on the other side of B. The corrections in this case shown are subtractive, since M is negative. They are additive when M is positive, and the curve concave upward.