Fig. 62 shows the upper part of a masonry dam. The lines with arrows show the vertical force due to the weight of the masonry above A B, the horizontal force due to the water-pressure on it--acting at two-thirds of the depth,--and the resultant of these two. In order that there may be no tension on the masonry, the resultant must always fall within the middle third of the thickness of the dam. In order to prevent its falling outside the middle third, the downstream face must be splayed out, and the splay will go on increasing somewhat. Suppose, now, that the reservoir is laid dry. It will be found that in the case of a dam more than 100 feet high the pressure due to the weight of the wall alone will fall outside the middle third--to the upstream side of it, of course--of the thickness of the wall, and a slight splay must be given to the upstream side. The vertical pressure of the water on this splayed part must be taken into consideration. The limit of pressure, 15 tons per square foot, may eventually be reached owing to the height of the dam, and additional splay may have to be given for this. When the outside splay becomes considerable a further allowance is made for it, because the stress at the edge of a horizontal section is tangential to the face. In order that the tangential stress may not exceed 15 tons per square foot, the vertical stress at the outer edge of a horizontal section of the dam must not exceed about 12 tons. By following the above rules the section of the dam can be calculated, beginning from the top and working downwards. The resulting profile of the dam is somewhat as shown in fig. 63. If a masonry dam is designed on the principles given above--that is, so as to be safe as regards crushing and overturning--it will be safe as regards shearing or sliding horizontally, but a test calculation can easily be made for this. [Illustration: FIG. 62.] [Illustration: FIG. 63.] Calculations of the above kind do not, of course, enable all the stresses in a solid mass of masonry to be found. Great stresses are caused by expansion and contraction owing to changes in temperature. Others are caused by the connections of the dam with the rock on which it rests and with the sides of the gorge. The method of calculation described above indicates a suitable form for the profile of a dam. The large factor of safety adopted allows for other stresses. The sections of the oldest dams, made in Spain, were somewhat as shown in fig. 64, and contained about twice as much material as was necessary. The object of the calculations is to save this needless expenditure.