carbonic acid is from that time constant; we obtain it simply by assuming that the acid disengaged is distributed through the volume of air introduced by the ventilation. This proportion-limit is, then, independent of the disposable cubic space. A ration of forty cubic metres of air, for example, with a production of twenty litres of carbonic acid, to which are added the sixteen litres of acid contained in the forty cubic metres of fresh air, gives the proportion of 0·0009, whatever may be otherwise the disposable space. The capacity of the inclosure plays no other part than that of delaying the moment when the constant régime is established; the space acts as a reservoir which is gradually filled till it contains the same proportion of acid as the current of air that traverses it; but, once saturated, it intervenes no more in the course of the phenomenon. The advantage of a considerable cubic space consists, then, chiefly in the fact that it retards the approach of the moment when the alteration of the air attains the limit which it will not pass. This consideration becomes of some importance in fixing the size of rooms that are to be occupied only for a definite number of hours at a time; for it will be always possible to arrange matters so that the proportion-limit shall not be reached before the end of the contemplated time.
Let us suppose, for example, that the ventilation can supply six cubic metres of fresh air per person per hour. This is the ration of air which, according to Péclet, might be sufficient in case of extremity, because six cubic metres of air, half saturated at 60°, can absorb the thirty-five or forty grammes of vapor given out by transpiration. The fresh air containing already a proportion of 0·0004 of carbonic acid, to which respiration adds 0*0033, we find that the proportion limit will be 0*0037. This limit will be almost reached and the regime will be constant when the air has been renewed three times, for the proportion of air will then exceed 0·0035. If the allotted space is only one cubic metre, as we know happens sometimes to be the case in theatres and other assembly-halls, a half an hour will be long enough to bring about this state of things; if the cubic space is increased to ten cubic metres, five hours will be required, and ten hours if it is increased to twenty cubic metres, to reach the same degree of alteration. Such, then, would be the effect of a ventilation at the rate of six cubic metres an hour, according to the capacity of the building. By raising the ration of air to thirty cubic metres, the proportion-limit becomes 0·0011, and we may assume that this has been reached when the air has been renewed twice (the real proportion being then 0·0010). This will happen at the end of four minutes in a space of one cubic metre, after forty minutes in ten cubic metres, etc. But the prolongation of time obtained under these circumstances is not of the same importance as in the preceding case, for the limit of 0·001 is a characteristic of respirable air. With so energetic a ventilation as this, the consideration of cubic space becomes a minor affair; but it