6. _A number of small divided openings are not collectively equal in ventilating power to one large one having the same area._ Thus, when a ventilating orifice is divided into four parts, which have the same collective area as the original orifice, it is found that only half as much air passes through these as through the original orifice. In order to obtain as much air, therefore, each opening must be equal in size to half the original opening. This is in accordance with the rule that the friction for air passing through openings is inversely to the diameter of these openings, _i.e._ inversely to the square-root of the area of the openings. 7. The most important requirements of perfect ventilation may be recapitulated as follows:— 1st. The maximum impurity of air vitiated by respiration should not exceed 6 parts carbonic acid per 10,000 volumes. 2nd. To ensure the maintenance of this standard, 3,000 cubic feet of pure air must be supplied per head per hour. 3rd. In order to supply this amount of pure air, with ordinary means of ventilation, 1,000 cubic feet at least must be allowed per head in buildings always occupied. CHAPTER XXI. PROBLEMS AS TO VENTILATION. The following formula enables many problems relating to ventilation to be solved. Let p = the amount of poison (carbonic acid) in every cubic foot of fresh air, viz. ·0004 cubic foot. Let A = the number of cubic feet of fresh air delivered or available, P = the amount of carbonic acid exhaled, and x = the amount of carbonic acid per cubic foot in the room at the end of a given time. Then— x = p + P/A, whence A = P/(x - p). _If the carbonic acid in the air of a room is ·75 per 1,000 volumes (that in the outer air being ·4 per 1,000 volumes), and there are five persons in the room, how much air is entering the room per hour?_ Here x = ·00075. p = ·0004. P = ·6 (_i.e._ number of cubic feet of carbonic acid expired by each person per hour). Now x = p + P/A. ·00075 = ·0004 + ·6/_A_. Therefore _A_ = about 1,700. Thus 1,700 cubic feet are required for each individual to keep the air within the given limit, and five times this amount will be required for five persons = +8,500+ cubic feet. _A room has been occupied for one hour, at the end of which the total carbonic acid present was found to be 1·1 per 1,000 parts. The carbonic acid in the open air amounting to ·0004 per cubic foot, find the quantity of air supplied per hour._ Here x = ·0011. p = ·0004 and P = ·6. Hence ·0011 = ·0004 + ·6/A. Therefore A = +857+ cubic feet. _If six persons are in a room containing 3,000 cubic feet, and there is a supply of 2,000 cubic feet of air per head per hour; how much carbonic acid is there in the air of the room at the end of 4 hours?_