four times greater than the linear dimensions of the other. Thus if the length of the first is taken as 400 feet the length of the other is taken at 100 feet, the

breadth of the first being 40 feet that of the second is 10 feet, and if the draft of water of the first steamer is fixed at 20 feet the second will be 5 feet; the appropriate speed for these vessels will therefore be 2/4-2, that

Τ

is, the speed of the larger vessel should be twice the speed of the small vessel. And so Mr. Denny says: "What Mr. Froude would have predicted of these two steamers is that if the speed of the smaller steamer were 10 knots, then the similar appropriate speed of the larger steamer would be 20 knots." At these speeds Mr. Froude proved that the resistance, with some allowance, would be as the cube of the steamer's dimensions, which would give for comparative resistance with these figures, as

64

(7)=(4)=1/1 or as 64 is to 1.

This, as Mr. Denny points out, "means practically that the resistance would vary as the displacement of the two steamers;" so that, in the case illustrated, the speed is doubled without adding to the resistance per ton of weight, and that consequently at a lower speed the large steamer would have a very much less comparative resistance; hence, "in the same type of steamer, by simply increasing all the dimensions proportionately, the same speed can be obtained with much less resistance per ton of weight driven through the water-that is, since the speed remains unchanged, much less expenditure of horse-power, and consequently much less expenditure of coal per ton of weight driven."

R

P

The relation of the powers required to drive the ship and model can also be shown by another power of the ratio of the lineal dimensions, viz.: (), where P and p are the powers required for the ship and model respectively.

Р

These powers are the effective powers required to overcome the fluid resistance. The gross power is much in excess of this, as there are losses by friction of the working parts. Dr. Froude found that the thrust or effective power is 37 per cent of the indicated power.

CHAPTER VII.-COMMERCIAL AND INDUSTRIAL.

Much has been written and spoken in connection with the Union of 1707, in respect to its effect on the industrial condition of Scotland, and more especially with reference to the rise and progress of the commercial life of Glasgow. The union of the crowns, in 1603, was one of inheritance on the part of the Scottish king, but this was not necessarily, as the event proved, of special advantage to Scotland; and it was not until many changes had taken place that the treaty, whereby a legislative union was established, removed certain restrictions on the foreign trade which enabled the Scottish merchants —more especially on the west coast-to open up enterprises which formerly had been closed to them. But, after all, what could have been expected in the way of commercial operations in the earlier times? The country had been for centuries in a state of turmoil; a condition

of things which is prejudicial to that peace, security, and recognition of law which encourages and gives confidence to commercial undertakings.

After the death of Alexander III., throughout whose reign the country was becoming consolidated after the earlier struggles, a long period of turmoil arose during the contention for the crown and the armed interference of the English monarch, Edward I. The Scottish nation, without a king to lead them, found in the patriot hero Wallace one who carried on the cause of national liberty boldly and unselfishly for several years. Then it was taken up by the Bruce himself, who fought against the power of both the first and second Edwards, finally rolling back the tide of usurpation on the field of Bannockburn.

During the next two centuries we read in history of almost nothing but war and turmoil, Scotch and English invading each other's country, and fighting desperately with equal courage and valour. In James IV.'s reign we find that not only on land, but also at sea, the old fighting was kept up; and it says a great deal for the resources of the country at that time, and for the skill of the eastcoast ship-builders, that they could turn out such ships as enabled Sir Andrew Wood successfully to cope with the English vessels.

The great nobles and the monarch watched each other, trying who was the stronger. Sometimes the former had the advantage, and laid hands on royalty itself. Another half-century, and the career of the unfortunate Mary ended. The Reformation, both in Scotland and England, had taken place. Knox, with an early enlighten

ment in scholastic matters, endeavoured to provide in a systematic manner for the welfare of the people, by founding schools, and establishing the means for a proper religious training; but political contention was now for a time united with religious zeal, and, in the earlier part of the reign of James VI., the country was in a state of civil war. In 1603 that monarch succeeded to the English crown, and it is stated wished to unite the two kingdoms; but however well meant his aims were, his method of procedure was unfortunate, as, by attempting to rule the religious instincts of the people, he stirred up opposition, and the strife became renewed, and was continued in the reign of his son, whose further attempts to impose the southern liturgy upon his subjects in the north was met with a robust Presbyterian defiance, which took a public shape in the well-known scene in St. Giles' Church in Edinburgh. The National Covenant was signed by all ranks, and thus we are brought to the Covenanting times, when again the religious aspirations of the country were attempted to be dominated by force, and for years we read of little but strife with tongue and sword, English, Scottish, Highland, and Irish troops all marching and countermarching about the country.

In the reign of the English Commonwealth, Cromwell invaded the country, and, it is said, conceived the idea of uniting the three kingdoms. The restoration of Charles II. took place, but unfortunately the same religious spirit of intolerance was abroad, so that an Archbishop of Glasgow, in 1662, gave orders to shut up the churches until Episcopal incumbents could be got to fill them; fines and

imprisonment were now common for religious nonconformity, and the Covenanting struggle was renewed with special severity in the west country. The Bass Rock was a state prison; torture was applied to refractory prisoners, for these were days of rude and ready methods to effect their objects, when men's passions were aroused.

Later on we find the tide of battle rolling in the North and in the West Highlands, ending for a time in the battle of Killiecrankie, in 1689. The reign of William III., Prince of Orange, began to have an influence in quieting the country, Glasgow being granted-for its loyalty a new charter, whereby the citizens were conferred the power of self-government in the choosing of "their own magistrates, provost, bailies, and other officers." In reference to the troublous times in Scotland, in the latter part of the seventeenth century, Woodrow, in his Church History, says: "This rising in the west of Scotland, like many other considerable turns, had but very small beginnings; and it is scarce to be thought that the persons concerned in them had any prospect that what they did would have been followed with what succeeded." Woodrow then goes on to recount that about eighty armed persons, avoiding Glasgow in consequence of hearing that the king's troops had come there from Lanark, went to Rutherglen, "a small royal burgh two miles from Glasgow," where they affixed to the market cross a declaration, entitled "The declaration and testimony of some of the Presbyterian party in Scotland; published at Rutherglen, May 29th, 1679." This declaration, after referring to the "testimony of faithful witnesses from the beginning against adversaries to the church and king