_Answer._ The lower plates should diminish regularly in their lengths. The reason for this will be apparent from the fact which has already been stated, that if a triangular plate of uniform thickness is clamped fast at its base, it will, if loaded at the end, be of uniform strength throughout its whole length. It is immaterial what the length of the base of such a triangle is, if the two sides are of equal length and the thickness of the plate is uniform, not only its strength but the amount of deflection or bending from any load will be equal all through its length. If, therefore, we make a spring by cutting a plate formed of two such triangular pieces united at their bases into strips, as has already been explained, evidently the spring made of them will have a uniform strength throughout its whole length. As the strips thus made diminish in length regularly, it is evident that if the spring plates are made of steel rolled of the requisite width, their length should be the same as that of those cut from the plate referred to above. When this is the case the lower outline, _a b b a_, fig. 183, of the spring will, when the spring is not bent, be straight lines. Sometimes the lower outline of springs is made curved, as shown in fig. 182. This gives too much strength near the strap _F_, and too little near the ends. In drawing springs, therefore, it is best to lay them out with the plates straight, as shown in figs. 182 and 183, and after determining the thickness, drawing a straight line from the strap to the end of the longest plate will give the best form of the spring and the length of each of the plates. It is necessary, however, to put a sufficient number of long plates in each spring to give it the required strength next to the attachment of the hanger. Sometimes one or more of these long plates are made heavier than the rest. The evil of this method of construction will be apparent if it is remembered that the greatest permissible deflection up to the breaking of the spring decreases with the _cube_ of the thickness of the plate and its strength increases with the _square_ of the thickness. Now if we have a spring with say ten plates ³⁄₈ in. thick and one on top ³⁄₄ in. thick, the thick plate will have a strength _four_ times that of the thin plates, but its elasticity will be only one-eighth that of the thin plates, and therefore it will require eight times as much load to bend it any given distance as is needed to bend the thinner plates the same distance. But its strength is only four times that of the thin plates, so that for any given amount of elasticity the thick plate must bear twice as much load as it has strength to carry. This shows what a great mistake is committed if some of the plates are made thicker than others, a conclusion which is supported by practical experience, as it is found that if the top plates are made thicker than others, the thick ones break most frequently, which is the necessary result of the