On another hand, and reciprocally, that whatever might be the reaction of the medium exerted for this motion, the amount of power transmitted in the line of the axis, could also never be more than the quantity of motion imparted and evolved around the axis. Hence, the positive quantity p2 —c2 which for the points below the line of equation, having c2 less than p2, raises the reaction equal to c2 the imparted power from c2 to c2 + p2-c2-p2, can never consist in an addition to the quantity of motion transmitted in a linear direction. But, as an inclined plane lessens the weight of, and lengthens the space run through, by a falling body, thus the reaction of the effort p2-c2 to fly off from the trajectory of least resistance, decomposes the imparted circular impulse c2 into the ratio of force and velocity given by the linear speed p, from which speed follows p2 as the reaction exerted for the motion of least resistance.

Therefore, any quantity of motion imparted around the axis, will be transmitted to a steamship in the line of the axis, without any loss of steam power, but decomposed in another ratio of velocity and pressure, by a helix which has been described with a radius cut off at the point of equation, and which is moving in a case of motion of least resistance.

PRACTICAL REMARKS.

This solution answers to the first part of the great problem: how to introduce more suitable proportions between the size and expenses of, and the services and receipts expected from, a steam vessel. And although the intention of the author is not to enter here upon the second part, or upon any description of the practical methods, which he could have to propose for building such a propeller of that size, strength, and geometrical accuracy, which would be essential and peculiar to it, the matter suggests some other remarks of a practical nature.

The length of radius, that of pitch, the linear speed of least resistance, and the transmissible quantity of motion, are correlative quantities in a helix propeller. A short inquiry would then render apparent, that a helix would always form a propelling apparatus of a pretty large size and surface, and that the ordinary speed of the steam-engine would be rather too high for a slow sailing, whilst it would be sufficient with any size of tonnage and rate of speed for a fast-sailing helix steamship.

Thus a complete saving of waste of steam power, a rowing surface of a large area, a high speed, and a steam-engine working in its ordinary and most economical conditions, would be the preeminent features of a well proportioned helix steamer. These features are entirely different from, and almost the reverse of, those of the screw propellers. And such are indeed the prospects for ocean steam navigation, opened by the principles from which this outline has been drawn, that although these principles bear their truth within themselves, one would still place less reliance upon them, if they were not altogether a consequence of, and key to, the practical results and infinitely various defectuosities of the screw propellers.

DIFFERENCE BETWEEN A HELIX AND A PADDLE-WHEEL PROPeller.

The curved surface of a helix can be made use of as a propeller without generating any waste of power. The plane which enters into the contrivance called a paddle-wheel, on the contrary, can never be employed for such a purpose, without wasting a certain amount of power.

It is a well-known fact, that, independently from these circumstances which

attend each practical combination of mechanics, a paddle-wheel propeller is, by a consequence of its own nature, subject to a waste of power in the ratio of the linear speed of the vessel, to the circular speed of the paddles, or the propelling plane.

The ultimate limit of this ratio depends upon the segment of the circle of the wheel which is dipped into the water. And a new waste of power arises from the changes and variations undergone by the segment of immersion, during a long voyage, and upon a surface of water like that of the

ocean.

The nature of such causes relieves us from the arduous task of penetrating farther into the labyrinth of the theory of a paddle-wheel steamship; since the amount of waste of power of such a vessel, could in every case be only ascertained with some certitude from the experimental results of ocean steam navigation. This amount being affected by a quantity which is as variable as the oscillations of the sea, from a gentle swell, furling a perfect level, up to the highest and most whimsical waves of the tempest, the number of it can be but an average, being altogether at variance for the same vessel in each different voyage. Taking, then, the instances of the most favorable sailing of vessels, which may be considered as the most perfect among merchantmen steamers, and it will be found that 1: 1,45 would still be the waste of power for staeamship propelled by a paddle-wheel.

Being deduced from entire voyages, the number of the waste of power includes all these minor losses of each combination of existing forces. And as the least waste is of great importance in ocean steam navigation, these losses cannot be neglected for a helix steamer. For a vessel of this kind, they could almost be ascertained in advance; consisting chiefly in the friction taking place on the surface upon which the shaft of the helix exerts the propelling pressure, and in the stuffing box through which the same enters into the vessel, and in the resistance encountered by the vertical edges of the helix, and by the rudder-rake of the ship, partly insulated from the body of the vessel, in their motion through the water. The preference may, however, be given also to more experimental methods. Thus, and taking the facts from a screw propeller sailing between the old and new continent, 1: 1,07 will be found as the ratio of these losses for a helix steamer.

CONCLUSION.

V3 f d
6364,5

Let now the speed of a steam vessel be set down at the rate of 21,2 feet per second, or at 12,5 marine miles per hour, making 300 per day, and the length of voyage at 12 days, giving 3,600 marine miles for the length of route; or full 400 miles more than the distance between New York and the principal Atlantic ports of Europe. By introducing this speed and number of days into the formula 2A, and making f=1,45 for a paddle wheel, f=1,07 for a helix steam vessel, it will appear that the performance of such a voyage requires, at least, a paddle-wheel steamer of a tonnage of 106,080 cubic feet, or 2,960 tons measured by the displacement of water, and 736 horse steam power, or a helix steamer of a tonnage of 41,960 cubic feet, or 1,170 tons, measured in the same manner, and 293 horse steam power.

Such numbers would not require any farther explanation, if, notwithstanding the difference in tonnage and steam power, the sailing qualities of both .vessels should yet be the same.

But this could never be the fact. The waste of power of a paddle-wheel

steamer is a variable quantity, depending upon the state of the surface of the sea. Hence, 1,45 being the waste of only the most favorable cases of sailing, the average speed of the vessel must necessarily be below the designed speed of 1,25 marine miles per hour, for which the proportions of the steamship have been laid out. A paddle-wheel steamer of 2,960 tons, and 736 horse steam power is, then, still too small for ever attaining 1,25 miles per hour during a voyage of 3,200 miles, as a mean for an entire voyage; otherwise, as by very few exceptions, and by a fortunate concourse of the most favorable circumstances. Such are indeed pretty near the facts of these few paddle-wheel steamers, which, by their performances and proportions, approach the nearest to the speed taken for our point of comparison, and to the tonnage and steam power, which have been found indispensable for a vessel of this kind sailing with such a speed.

The waste of power of a helix steamer being on the contrary a constant quantity depending very little, if ever, for anything at all, from the state of the surface of the sea, the average speed of the vessel would almost constantly be the same as her designed speed. And far from attaining the latter only by exception, the departure from it could only take place by a concourse of circumstances entirely exceptional for her completely submerged propelling apparatus.

As a steamship advances in her voyage, the resistance of the vessel decreases, by her rising out of the water, in consequence of the consumption of the stock of fuel. A helix steamer may have the whole benefit of this, by saving a corresponding quantity of steam power, and thus of coal. A paddle-wheel steamer, on the contrary, gains nothing, or very little, from the decreasing resistance of the vessel; for in this case, the area of the segment of immersion decreases in a greater ratio than the area of the immerged midship section, and as the propelling pressure is proportional to the first, the propeller must make up by an increase of circular speed the reduction of pressure, if the ship shall continue at the same rate of sailing; wasting, thus, by an increase of the ratio between the circular and linear speed, the best part of the power saved by a decrease of the resistance of the vessel.

Hence, towards the end of the voyage, when the approach of land produces again, to their fullest extent, the obstacles of contrary winds, tides, and currents, a helix steamer would have more steam power in store, or, what is the same, a larger remainder of the stock of coal, than a paddle-wheel steamer, with which to make head against these obstacles. Thus, the first would then not sail simply at a higher and more equal rate of speed during the Voyage, but altogether enter with a greater precision than the second, into the port of her destination.

Now, as the same number of passengers, the same mail matters, and the same quantity of freight worth the shipping of an ocean steamer, which, in the present state of commercial intercourse, are transported by paddle-wheel steamships, could be as well accommodated and carried on board of vessels of much less tonnage and steam power, this final conclusion may at least be drawn from the researches above, that the receipts of the most stupendous existing steamers could be reaped; and altogether all the services of these vessels be performed with more dispatch and greater regularity, at the expense of building and keeping afloat helix steamships of 300 horse steam power, and 1,200 tons displacement of water.

Art. IV.-COMMERCE AND RESOUCES OF CANADA.

PROGRESS OF CANADA-LANDS OF THE PROVINCE-PROGRESS OF POPULATION-RELIGIOUS CENSUSAGRICULTURAL AND OTHER PROPERTY-MANUFACTURES-SHIPPING-REVENUE-PUBLIC DEBT-EXPORTS AND IMPORTS-ARTICLES OF CONSUMPTION, ETC.

Most of our readers are aware that the attainment of a correct account of the material progress of the country has been long a subject of solicitude with enlightened Canadians. This has not been effected hitherto, in a manner to afford very ample or reliable details; nor is this to be wondered at, since in the older countries of Europe the great advantages of an accurate census have been, up to a recent period, but feebly appreciated. In the United States, perhaps, this information has been more carefully collected than in any other country. Upper Canada, too, has paid considerable attention to the business of numbering the people; and it is probable we should have had, by this time, a satisfactory enumeration of the resources of the eastern part of the Province, but for the rebellion of 1837-8. Causes of an analagous character, have, since the union, retarded the work of the census; but the subject has never been lost sight of, and one of the papers laid before Parliament during the present session, is the first fruit of the renewed effort made in this direction.

paper is the appendix to the first report of the Board of Registration and Statistics. It is creditable alike to the Board, consisting of the Hon. Messrs. Hincks, Viger, and Leslie, and to their Secretary, Mr. W. C. Crofton, on whom no doubt the chief labor of the work must have fallen. The report comprises a number of tables, illustrating almost every subject of which figures can be the exponents, and affording a very favorable view of our increase in all the elements of material prosperity. Many of these tables extend to details, relating to localities and other particulars, which are highly important for some purposes, but are unnecessary to the appreciation of the general condition of the province. Our design is to reduce this mass of information to a more popular form, so as to render it available to those who may be interested in the results, but do not care to wade through the calculations.

LANDS. The lands of the Province, being the chief source of its prosperity, as well as the chief inducement to settlers, we shall begin with them. The total number of surveyed acres in Lower Canada, according to Bouchette's last survey, was 18,871,040; but the return of lands disposed of is made with reference to a previous survey of 17,685,942 acres, and is dated in 1845. Of this quantity of land, 2,377,733 acres have been set apart for Clergy Reserves. The Jesuits' Estates, now employed in promoting education in the United Province, and other lands disposed of for charitable purposes, amount to 3,424,213 acres; and the grants en seigneurie, and free and common soccage to 11,343,629 acres. The surveyed lands, therefore, four years ago, stood thus :

From Canada West the return is as follows for 1848:

If we take the entire Province, therefore, and add the difference between the survey of 1845, and the latter one of Bouchette, amounting to 1,185,098 acres, we have 6,710,322 acres for the quantity of unsurveyed land still in the hands of the government, less the sales in Canada East since 1845, which probably amount to 500,000 acres 6,210,322 acres. During the present session, the Provincial Parliament has set apart a specific quantity of 100,000 acres for the endowment of Common Schools, with the further provision that the money received for all future sales of crown lands shall be applied to the same purpose, until a school fund of £1,000,000 shall have been formed.

Between the years 1836 and 1847, both inclusive, 933,229 acres of land were disposed of by the crown, in Canada East, by sale or gift, and 2,145,502 acres in Canada West. These figures, however, furnish little indication of the actual amount of settlement in either section, as they include large grants or sales to individuals far beyond the capacity of the granters to occupy or cultivate; and, on the other hand, do not include the sales of wild land made by individuals to settlers. The average price of public lands in Canada West, is given for several years, down to 1840, in which year the prices are reported at 11s. 2d. per acre for crown lands; 12s. 8d. for clergy reserves, and 12s. 6d. for school lands-the two latter classes being often found in detatched lots in settled parts of the country. The price has not varied very considerably since that period. There are still vast wildernesses unsurveyed.

POPULATION. The population of Canada East is estimated according to the mean of the calculation, by Colonel Taché, Mr. Cauchon, and Mr. Crofton, founded on previous censuses. The result shows a population of 768,334 in Canada East, in 1848. The census for Canada West, for the same year, give 723,292 souls; so that the population of the Province is about 1,491,626 souls. The ratio of increase has been very different at different periods, owing to the fluctuations of the volume of the stream of emigration. The following figures will give some idea of the progress of population respectively, in the two sections:

In 1825......

CANADA EAST.

423,630 | In 1848....... 768,334 | Increase, 23 years 334,704 At this rate the population of Eastern Canada will require about thirty years to double itself.

CANADA WEST.

In 1825....... 158,027 | In 1848 ....... 723,292 | Increase, 23 years 565,265

So that in Western Canada the population doubled itself in about eleven years. It is obvious, however, that this method of estimating the increment of population, however appropriate for countries which depend entirely upon the natural mode of reproducing the species, is of little use in countries sparsely inhabited, and receiving their largest augmentation of population from without. The report gives the following comparative statement of the progress of population in ten years, in the two sections of the Province, in

VOL. XXI.-NO. III.

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