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ART. IV. An Essay on the comparative Advantages of Vertical and
Horizontal Wind-Mills : Containing a Description of an Hori. zontal Wind-Mill and Water-Mill, upon a new Construction; and explaining the Manner of applying the same Principle to Pumps, Sluices, Methods for moving Boats or Vessels, &c. &c.' With Plates. By Robert Beatson, Esq. F.R.S. E. Honorary Member of the Board of Agriculture, Member of the Society of London for the Encouragement of Arts, Manufactures and Commerce, and of the Royal Highland Society of Scotland, and late of his Majesty's Corps of Royal Engineers. 8vo. 2s. 6d. I. and J. Taylor. 1798. The principle on which the horizontal mill is constructed by
1 Mr. Beatson is, we think, very simple, and the method of getting the sails back seems ingenious and practicable. In stating, however, the velocity with which the sails of an horizontal mill may move, we are of opinion that the author has not attended to a circumstance which will restrict the velocity, and confine it within certain limits : we mean the resistance of the air against the back part of the sail, which must always take place when any point in the sail moves with a velocity greater than that of the wind. Let us attend to the author's statement:
• Those who have only been accustomed to vertical wind-mills, and who have never seen a proper horizontal one, argue in favour of the former, that they will sometimes revolve with greater velocity than even the wind itself; consequently that they must have more power then the horizontal mill, which, say they, cannot be made to move so fast as the wind. This is another proof how little the power and principles of the horizontal mill have hitherto been under. stood or attended to.
• That the vertical mill will sometimes move with greater velocity than the wind, is not disputed; but that can only happen when the mill is going empty or uploaded, or at least when meeting with but little resistance; nor can it ever be the case excepting at or near the outer extremities of the sails, or at a considerable distance from the centre of motion. At those parts the sails may often move with greater velocity than the wind, and it is most likely they generally do so, otherwise the mill must be going very slow indeed ; that how. ever can be no argument in favour of the superiority of the vertical mill, as it proves nothing more than what every other mill or wheel possesses in a similar manner, whether vertical or horizontal; for it may be demonstrated, that any such wheel may be made to move with more velocity than the power that moves it. Suppose, for example, a fly-wheel, thirty feet in diameter, turned by a handle placed eighteen inches from its centre; every revolution that handle makes round the axis of the wheel, it will describe an imaginary circle three feet in diameter, which is only one-tenth of the diameter of the wheel, any point in the circumference of which revolves in the same time, through ten times the space that the handle does; and therefore it moves ten times faster than the power that sets it in motion. If the handle or moving power were placed at three feet from the centre, the circumference of the wheel would move five times faster ; and if placed at seven feet and a half (the double of which is equal to the radius, or semi-diameter of the wheel) it would then move at only twice the velocity of the acting power. So it may happen with a vertical or any other mill; for as the power of the wind acting upon the sail of a wind-mill increases upon every point of that sail, as it recedes from the centre, there must be a certain point or line (which I shall call the line of action) where the power acting at that part of the sail is sufficient to turn the mill; and if the remaining part of the sail between that line and the extremity of the arms is, for experiment, taken away, the mill will still continue to go round ; if that line is supposed to be at one-fourth the length of the arm from the centre, and moving at only one half the velocity of the wind, that point of the arms at one half the distance from the centre will be moving with the same velocity as the wind, and the extremities will at the same time be moving with double that velocity: if the remaining part of the sail is supposed to be now added, the velocity will be increased; if it is doubled, then the fourth part from the centre will move with the same velocity as the wind, and the extremities will be moving with four times that velocity. It is therefore evident, that at whatever part of the sails of a vertical windmill the line of action may be, those parts between that line and the extremities will move progressively faster, in proportion as they recede from the centre. The same argument will hold as to horizontal wind-mills of a proper construction ; for if a horizontal wind-mill is going empty or unloaded, as in the former case, and is so constructed that there is little or no resistance on the returning side, the wind will act in a direct manner upon every part of each vane, when at right angles to its line of direction; as in the former case, there will also be a certain line of action on the vane, at which the power acting is sufficient to turn the mill; the velocity of the different parts of the vane between that line and the extremities will likewise increase in proportion to their distance from the centre ; whatever additional sail is put between that line of action and the extremities, will of course add to the power and to the velocity of the mill. Supposing, therefore, that part of the vane at one-fourth the distance from the centre is moving with a velocity equal to the wind, the part at half the distance to the ex. tremities will be moving with twice the velocity, and the extremities at four times the velocity of the wind ; that is, twice or four times its direct impulse : whereas in the vertical mills, in similar cases, it moves at the rate of only twice or four times its lateral impulse.'
Mr. B. here supposes that, if a part of the vane at one fourth of the distance be moving with a velocity equal to the wind, the part at half the distance to the extremities will be moving with twice the velocity, and the extremities at four times the volocity of the wind ; which would undoubtedly be the case were there no resistance against the back part of the vane :- but the fact is that, if a point moves with a velocity double that of the wind, it must move against the air with a
relative velocity equal to that with which the wind moves; or (which is the same thing in other words) with a velocity equal to that with which the air is impelled on the fore part of the vane.-Let us take a more simple case. --Suppose it possible that a vane moves so that a point, bisecting the distance between its extremity and axis, should have a velocity equal to that of the wind :—then all the points between the middle axis and the extremity would move faster than the wind; and the differences of their velocities and that of the wind would forma a series of relative velocities, where the lowest term would be 0, and the highest term a quantity equal to that which represents the velocity of the wire:--but, with these relative velocities, the * back part of the vane would act against the air, and produce a resistance greater than the power acting on the fore part:-for, to the resistance and power belong equal velocities, and surfaces, but the former acts on a part at a greater distance from the axis than that on which the power acts. We have used the words resistance and power for the sake of clear. ness alone, and not to designate effects of a different class.
Although we think that Mr. B. has failed in establishing his position that a horizontal mill, like a vertical one, may be made to move with any velocity,- yet his essay well des serves notice for the simplicity of his principle, for its extensive application, and for the perspicuity with which he has explained the machinery necessary to its action.
ART. V. The Works of Horatio Walpole Earl of Orford.
[Article concluded from p. 189.] The fifth volume of this extensive collection contains the
I author's epistolary correspondence ; and here we must own that, in spite of his lordship's singularities, prepossessions, and weaknesses, which we have freely pointed out, his letters, as well as his narrations vivâ voce, were extremely original, often comic, and always amusing.
The first of a long series of letters in this volume, "To the Honourable Henry Seymour (afterward Field Marshal) Conway,' written in the year 1740, when Mr. Walpole was 23 and Mr. Conway 21 years old, has a peculiar cast of affection and drollery. We have at times been rather out of humour with our noble author : but we have pretty well made it up with him, in perusing the chief part of his letters to various persons ; in which - his friendliness must conciliate esteem, while his
* We mean only that part of the back of the vane which is in tercepted between the iniddle and the extremity,
descriptions, descriptions, his knowlege of the world, his playful satire, wit, and humour, will fascinate the reader's attention. A little coolness, however, returned on observing (page 25) the contempt with which he treats The Pleasures of Imagination, and The Art of preserving Health : poems which we loved in our youth, and of which, in age, we have more clearly seen the merit.
Being unable to allow space for many whole letters, as specimens of the writer's peculiar wit and humour, which often depend on the application of common words and phrases to yncommon purposes, we shall extract some of the happiest of bis bons mots and pleasantries, from the several series of his letters in the course of this most entertaining volume; the only one, of which the whole contents are new to the public.
We cannot, however, prevail on ourselves to curtail the following letter to his cousin Conway, dated Twickenham, June 8th, 1747'; the former part of it is jocosely descriptive of his house at Strawberry-Hill, which he had then just entered, and . which has since been so famous : . . You perceive by my date that I am got into a new camp, and have left my tub at Windsor. It is a little play-thing-house that I got out of Mrs. Chenevix's * shop, and is the prettiest bawble you ever saw. It is set in enamelled meadows, with philigree hedges :
A small Euphrates through the piece is roll’d,
And little finches wave their wings in gold, Two delightful roads, that you would call dusty, supply me continually with coaches and chaises : barges as solemn as barons of the exchequer move under my window ; Richmond-hill and Ham-walks bound my prospect; but, thank God! the Thames is between me and the duchess of Queensberry. Dowagers as plenty as founders inhabit all around, and Pope's ghost is just now skimming under my window by a most poetical moonlight. I have about land enough to keep such a farm as Noah's, when he set up in the ark with a pair of each kind; but my cottage is rather cleaner than I believe his was after they had been cooped up together forty days. The Chenevixes had tricked it out for themselves : up two pair of stairs is what they call Mr. Chenevix's library, furnished with three maps, one shelf, a bust of Sir Isaac Newton, and a lamne telescope without any glasses. Lord John Sackville predecessed me here, and insituted certain games called cricketalia, which have been celebrated this very evening in honour of him in a neighbouring mcadow.
- You will think I have removed my philosophy from Windsor with my tea-things hither ; for I am writing to you in all this tranquillity while a parliament is bursting about my ears. You know it is going to be dissolved : I am told, you are taken care of, though I don't know where, nor whether any body that chooses you will
6 * A famous toy-Shop.'
quarrel with me because he does choose you, as that little bug =- did; one of the calamities of my life which I have bore [borne] as abominably well as I do most about which I don't care. They say the Prince has taken up two hundred thousand pounds, to carry elections which he won't carry : - he had much better have saved it to bay the parliament after it is chosen. A new set of peers are in embryo, to add more dignity to the silence of the house of lords.
I'make no reinarks on your campaign *, because, as you say, you do nothing at all; which, though very proper nutriment for a thinking head, does not do quite so well to write upon. If any one of you can but contrive to be shot upon your post, it is all we desire, shall look upon it as a great curiosity, and will take care to set up a monument to the person so slain, as we are doing by vote to captain
----, who was killed at the beginning of the action in the Mediterranean four years ago. In the present dearth of glory, he is canonized ; though, poor man ! he had been tried twice the year before for cowardice.
• I could tell you much election-news, none else; though not being thoroughly attentive to so important a subject, as to be sure one ought to be, I might now and then mistake, and give you a candidate for Durham in place of one for Southampton, or name the returning-officer instead of the candidate. In general, I believe, it is much as usual--those gold in detail that afterwards will be sold in the representation the ministers bribing jacobites to choose friends of their own- the name of well-wishers to the present establishment, and patriots, outbidding ministers that they may make the better market of their own patriotism :-in short, all England, under fome name or other, is just now to be bought and sold ; though, whenever we become posterity and forefathers, we shall be in high repute for wisdom and virtue. My great great grand-children will figure me wi:h a white beard down to my girdle ; and Mr. Pitt's will believe him unspotted enough to have walked over nine hundred hot plough. shares, without hurting the sole of his foot. How merry my ghost will be, and shake its ears to hear itself quoted as a person of con. summate prudence ! - Adieu, dear Harry! Yours ever,
"HOR. WALPOLE.'. P. 32. Comic and sarcastic reflections on the peace of 1748; after which, he says:
Then Charles Frederick has turned all his virtù into fire-works, and by his influence at the Ordnance, has prepared such a spectacle for the proclamation of the peace as is to surpass all its predecessors of bouncing memory. It is to open with a concert of fifteen hundred hands, and conclude with so many hundred thousand crackers all set to music, that all the men killed in the war are to be wakened with the crash, as if it was the day of judgment, and fall a dancing, like the troops in the Rehearsal. I wish you could see him making squibs of his papillotes, and bronzed over with a patina of gunpowder, and talking himself still hoarser on the superiority that his firework will have over the Roman naumachia. * Mr. Conway was in Flanders with William duke of Cumberland.” Rev. Nov. 1798.