use these terms, I mean in full, because, in the second case, the stone lintel being cut in a curve, it is not as free as in the third, because to get any signs of thrust it is necessary to break the lintel; consequently, the effect of the thrust will begin when the resistance to the cohesion of the stone is finished, whereas in the third case this commences at once, because it is in several pieces and there is no cohesion.

Now, gentlemen, our barrel arches are working in the second case; I remark barrel arches because the domes are more advantageous.

Fig 4.

We are going to suppose the case of domes. The dome is the genuine form of cohesive system. Suppose Fig. 4, a big block of stone, say ten feet in diameter, and one foot, or one foot six inches, thick; if we support that on the four sides just as a lintel, we have practically no thrust, and if we make a cavity on the under side, Fig. 5, making a curve like a dome, we will have a dome arch, but will have no thrust. It is not the second case of the lintel, that is, taking off the material that is working as a rod the thrust commences to act. In this case of the dome it is not so, because the material that is working as a rod, that is, by

tension, is formed into rings which remain as in rings. This is our case, if we build the ceilings in the form of domes; and if it is well applied 'and properly built, practically we have no thrust; consequently, it is necessary to well understand the distinct cases, and not make confusion.

Fig 5.

Fig. 6.

+

The answer to the statement that it is so expensive that it cannot be used in competition with the slow-burning conIstruction is as follows:

First. As we have demonstrated before in this last case, that is, that the barrel arch has some thrust, and requires some material to counterbalance this, that is, rods, that is one of the causes which makes the barrel construction more expensive than the dome.

Second. The barrel arch requires two sides for the arch to rest on, such as girders or beams; these girders or beams must have the strength to support all the weight that the arch carries, besides the weight of the arch. The price of the girders or beams must be added to the price of the arch; consequently, we have the same inconvenience as in the regular fire-proofing, where the arches also rest against the beams, having only the advantage that our barrel arches are lighter, the span can be greater; consequently, these girders or beams can be lighter and cheaper. But, nevertheless, the fact remains that we must have the girders or beams, and the value of these must be added to the arch; the result is, that, if we have an economy over the ordinary fire-proofing, these barrel arches cannot compete with the slow-burning construction, in consequence of these heavy girders.

Third. But if, instead of using the barrel arches in the cohesive system, we use the domes in the same system, we have economy, if well applied, because we have not these two last inconveniences, - that is, the use of heavy rods. between heavy girders, and the use of the girders or beams themselves.

Now, suppose we receive a plan, as is generally the case with barrel arches and girders, and we give a price which is more expensive than the combination of dome without the heavy girders and heavy rods; the result is, that it is not as cheap as other combinations that we have already built and are now building. Is it the fault of the system, or whose is the fault? The fault is, that it is not well applied.

I must remark with great satisfaction that we have commenced to receive from every part of the country plans from architects, some of them showing that this system is commencing to be well understood and appreciated at its just value.

In regard to the question of height, I can say that, notwithstanding we give ten per cent. rise as a rule in all of the arches, it does not mean that it cannot be less 01 greater; just as, in the ordinary system of beams, we know that the higher section we give to beams the more economical is the result. For instance, if in a floor ceiling of beams twenty-five feet span we use beams eight per cent. of the span, the ceiling would be cheaper than if we give five per cent. for an equal load; for, in the first case, with less pounds of iron, we have the same resistance. The same is the fact in the arches and domes; the more rise we give, the more economical they are. This means that we use the same rules as in general bridging; we can reduce to eight per cent. in ordinary construction; and, as the arched form gives opportunity for greater height to the ceiling in the middle, the result is that practically the ceilings are higher in our system than in any other system, taking only in the crown six inches, but descending on the side occupying the place of small corners in all the regular ceilings; consequently, I cannot see in what way this system takes up more room than any other.

Another consideration has arisen in discussion, which I will ask permission of this audience to let me answer; that is, the question in regard to the patents; that is, if the system is patentable, in what does the patent consist, and by what is the patent warranted? In the first place, I must say that, allowing that in a small portion of Spain and Italy a similar system was applied empyrically, and on a smaller scale, it is a fact that it is not applied in any modern public building in either place, because, as I say, it has only an empyrical application; nor has any academy a regular system or scientific method for the right application of it.

This is due to the fact that the system was not perfected, as I have shown in my previous lecture, already referred to, of the 24th of October, 1889, showing how a system initiated by a patentee for Portland cement in the last century in England ended here in this country and in this city in a series of applications.

I may remark also, that here, notwithstanding to some architects the system is acceptable, the truth is that the day is very far distant when it can be given to the common use and free practices of all kinds of contractors, while they have not yet at their disposal the elements necessary, neither of material or expert hands; and for this reason the system would be dead if it was not restricted. Yes! For instance, suppose an architect, knowing and believing in the system and convinced of its utility, as to-day there are many, should project a building under this system, as insignificant as it is or appears to be; if he called for competitive estimates, in order to obtain the price, I am sure that neither the architect nor the owner would be certain that the contractor was practically able to erect the building with success in the construction. The architect, not having enough confidence in the contractor, because not knowing whether he was practical or not, and realizing that he personally is directly responsible, knows that he will be a slave of the building. On the other hand, the owner, knowing that the system was new and put in the hands of a contractor who cannot give references as to his knowledge of the matter, by his own record, will not have confidence, and would pay his money without guaranty. The contractor, too, would not be in any better position; he could not find the material nor the workmen, in the ordinary conditions. that other systems would allow, and consequently all would be against either success or economy.

This is the reason that it was necessary to accumulate here, year by year, elements of security for the architects and owners, and acquire elements for the supplying the market with material and expert hands, educating able fore