1841.] 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



301 



Cisalpine Gaul has mines which are not worked so much as they 

 used to be, perhaps because they produce less than those of the 

 Transalpine Celts and of Iberia, but formerly they were worked very 

 much, since a mine of gold was wrought even in the territory of Ver- 

 celli.* 



In the territory of Poplonium (Capo di Campana) are some aban- 

 doned mines, and the forges in which is wrought the iron of Elba, 

 ■which, as it can only be reduced in the furnaces, is transported to the 

 continent, as soon as it is brought out of the mine. Strabo says that 

 the excavation of these mines grew up.'" 



Pithecusa (Procida) has gold mines.! 



Near Luna in Tyrrhenia are the quarries of marble, white, and 

 spotted with green, of which tables and columns are made of a single 

 block. These quarries are so numerous and so well supplied, that 

 they are sufficient for most of the fine works which are made at Rome 

 and throughout Italy. 



The Pisan territory has an abundance of marbles.^ 



Gabii near Palestrina is in the midst of the quarries most used by 

 the Romans. 



At Tibura (Tivoli) are quarries of those different kinds of stones 

 known under the names of Tiburtines, Gabians, red stones, of which 

 most of the Roman buildings are constructed. || 



B. 



* E, 5, ch. 

 , ch. 2. 



§B. 



t B. 5, ch. 4. 

 ch. 4. II B. 5, ch. 7. 



ON THE FORMS AND PROPORTIONS OF STEAM VESSELS. 



Sir — Among the numerous opinions which have been advanced, as 

 to the causes of the failure in point of speed which has attended the 

 voyages of the British Queen and President, a subject to which the 

 non-arrival of the latter vessel has given a most painful interest, I 

 have not met with one which appears at all conclusive or satisfactory. 

 Deficiency of power is always the first reason assigned ; and a writer 

 in a professional periodical, assuming that the models of these vessels 

 are as perfect as any in existence, has gone the length of asserting 

 that the power necessary to produce the same speed in vessels of 

 similar form, but different dimensions, must increase in a larger ratio 

 than the tonnage. His first position as to the forms of the vessels 

 could, I think, be easily proved untenable, and his conclusion tends to 

 subvert a plain physical principle ; as he would make it appear that 

 to overcome the resistance of the water, in which the surface of the 

 immersed portion of the vessel alone is concerned, requires power in- 

 creasing in a greater proportion than is requisite to conquer the iner- 

 tia; the latter being always directly as the mass. Yet similar opinions 

 are avowed by most persons who place reliance on the popular notions 

 prevalent respecting the models of these steamers. — The nearest ap- 

 proach to the true manner of considering this question which I have 

 yet seen, is, I think, made by a correspondent signing himself E., in 

 the number of your Journal for last January ; where he remarks that 

 of the vessels lie mentions, the best have the most beam in proportion 

 to their length ; and afterwards, that more seems to depend on model 

 than power. Taking somewhat similar ground, I shall endeavour to 

 show that as regards the several points of speed, capacity for carrying 

 fuel to advantage, efficient working of the paddles, good qualities as 

 seaboats, and power of carrying sail on an emergency; one essential 

 requisite for seagoing steamers is a good breadth of beam in propor- 

 tion both to their length and depth ; and out of these considerations 

 will arise others as respects the most advantageous modifications of 

 form in the fore and after body. On all these points I shall confine 

 myself, as much as jiossiible, to such remarks as arise from known 

 facts, my intention being merely to state opinions resulting from a good 

 deal of observation, on a subject which I do not think has ever received 

 the attention it deserves, from those more practically interested in it 

 than myself. The first point to which I would call attention is that of 

 speed. In all the comparisons which I have ever seen drawn as to the 

 relative merits of dill'erent steam vessels, the principal data have 

 always been the power of their engines, and the sectional area of the 

 immersed parts of their bodies ; and the comparison so far as regards 

 the latter particular has always proceeded simply on the superficial 

 area of these sections, no regard being paid to the increased pressure 

 of the water w ith an increased depth : so that supposing two vessels 

 have their immersed sectional surfaces parallellograms severally 40 

 feet wide by 15 feet deep, and 30 feet wide by 20 feet deep, these 

 giving the same result as to area, their resistances are in the abstract 

 considered equal, and any advantage which one such vessel may have 

 in point of speed over the other, supposing their power, speed of en- 

 gines, S;c. tu be equal, is always referred to some supposed superiority 

 of form in the entrance and run of the faster vessel. Such a mode of 



calculation is founded, I believe, on the experiments of M. Bossut, 

 who gives as a rule that any plane surface moving with a given speed 

 perpendicularly against a fiiiid, suffers a resistance equal to the weight 

 of a column of the fluid, with a base equal to the area of the moving 

 surface, and of such a height as a body must fall to acquire the given 

 velocity. I have never seen the details of these experiments, nor do 

 I know whether they are within my reach, but I feel pretty certain 

 that the surfaces made use of must have been immersed in all cases 

 the same depth in the fluid, and the difference of dimension must have 

 been made in breadth only, or such results could never have been 

 arrived at. Suppose the "two above named surfaces were those of 

 flood gates ; to ascertain the jtressure of water on each, GOO square 

 feet, the common result of 40 x 15, and 30 x 20, must be multiplied 

 into the pressure at the mean depth of each. The pressure of water 

 at the depth of 7-2 feet, the mean of 15, may be taken as 3-75 lb. per 

 square inch : and that at 10 feet, the mean of '20, as 5 lb. These num- 

 bers multiplied into S6400 the number of square inches in each surface 

 give the results of 325000 lb. =i 145 tons 1 cw t. &S lb. for the first named, 

 and 432000 lb. =r 192 tons 17 cwt. 6 lb. for the second, being about as 

 7 to 9 ; and yet if the rule applied to calculate the resistances of ves- 

 sels be correct, these two surfaces when put in motion at the same 

 speed, immediately have their amounts of resistance equalized, be- 

 cause their areas are equal !— Such a result is manifestly absurd; and 

 as the increased pressure of water in the proportion of its depth is an 

 established fact, I shall proceed on these premises to inquire into the 

 manner in which these vessels would be affected by the alteration of 

 form necessary to reduce their resistance in moving through the water. 

 We will suppose, for simplicity of argument, that their transverse 

 sections are uniform throughout, and that both in plan and elevation 

 they are also parallellograms : that they are each of the length of 200 

 feet, and their cubic contents consequently the same, viz., 120,000 feet. 



Fig. 1. 



Fig. 2. 



L/?«.j i/yii^. 



—t^ 



a 



Suppose it were required to reduce their resistance by one half, pre- 

 serving to the wider vessel her advantage of 7 to 9. Let fig. 1 repre- 

 sent the vessel of 40 feet beam, and fig. 2 that of 30. To effect the 

 required reduction, we have simply to employ the principle of the 

 wedge, and making a 6 in each figure equal to c d, in the same we 

 have 6 a, the velocity of the vessel, equal to twice be, the velocity 

 of the weight which represents the resistance of the water to the mo- 

 tion of the vessel in the direction ba. For the weight or resistance 

 of the whole surface cd \s divided into two equal parts on the sur- 

 faces a c, a d, and these two halves being each moved the distance 

 be or b d, while the vessel moves the distance a 6, a power is shown 

 exactly equivalent to that of a wedge c a e iu fig. 1. I state this thus 

 fully because some writers on mechanics, as Emerson for example, 

 make it appear that though the direction of the power be that of the 

 line a b, it is to be calculated on the proportion which ed bears to ab, 

 instead of that borne by c 6 or 6 d, the half of c d. 



The vessels are thus reduced in their bulk or tonnage by the amount 

 of a rectangular prism equal in its upper surface to the parallelogram 

 c 6, 6 a, and, (as we are at present considering only the immersed 

 portion of their hulls,) of the immersed depths of each, viz., 15 feet in 

 fig. 1, and 20 feet in fig. 2. Now a 6 is in each equal to the beam of 

 the vessel, and c b equal to half a b, therefore the cubic contents of 

 the parts removed are in fig. 1, 40 X 20 x 15 = 12,000 cubic feet, 

 and in fig. 2, 30 X 15 X 20 = 9000 feet, giving a difference of 3000 

 feet, which divides exactly 40 times into ]2u,000, the total cubic 

 contents of each vessel; thus by the sacrifice of ^th part of the im- 

 mersed portion of her body, we preserve to the vessel of greatest 

 breadth her advantage in point of speed of 7 to 9, together with the 



