Fruit-walls improved, by inclining them to the horizon, or, A way to build walls for fruit-trees whereby they may receive more sun shine, and heat, than ordinary / by a member of the Royal Society. Fatio de Duillier, Nicolas, 1664-1753. 1699 Approx. 239 KB of XML-encoded text transcribed from 83 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2007-10 (EEBO-TCP Phase 1). A40990 Wing F557 ESTC R5191 11794058 ocm 11794058 49276 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A40990) Transcribed from: (Early English Books Online ; image set 49276) Images scanned from microfilm: (Early English books, 1641-1700 ; 492:1) Fruit-walls improved, by inclining them to the horizon, or, A way to build walls for fruit-trees whereby they may receive more sun shine, and heat, than ordinary / by a member of the Royal Society. Fatio de Duillier, Nicolas, 1664-1753. xxviii, [2], 128 p., 2 leaves of plates (folded) : ill. Printed by R. Everingham, London : 1699. Attributed to Nicolas Fatio de Duillier. Cf. Halkett & Laing (2nd ed.). Reproduction of original in Cambridge University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Fruit-culture -- Early works to 1800. 2006-11 TCP Assigned for keying and markup 2006-11 Aptara Keyed and coded from ProQuest page images 2006-12 Emma (Leeson) Huber Sampled and proofread 2006-12 Emma (Leeson) Huber Text and markup reviewed and edited 2007-02 pfs Batch review (QC) and XML conversion FRUIT-WALLS IMPROVED , By Inclining them TO THE HORIZON : OR , A WAY TO BUILD WALLS FOR FRUIT-TREES ; Whereby they may receive more Sun Shine , and Heat , than ordinary . By a Member of the Royal Society . LONDON : Printed by R. Everingham ; and are to be sold by John Taylor , at the Sign of the Ship , in St. Paul's Church-Yard . MDCXCIX . Imprimatur Liber cui Titulus , Fruit-Walls Improved , by inclining them to the Horizon . John Hoskyns , V. P. R. S. August 31. 1698. TO THE RIGHT HONOURABLE THE MARQUISS OF TAVISTOCK . MY LORD , WHile Your Lordship fits Your Self , in Your Travels , to follow the Footsteps of so many glorious Ancestors , I prepare for You , in the Culture of Fruits , a Diversion to those great Occupations , which Your Birth will hereafter bring upon Your Lordship . I was walking with Your Lordship , when I first thought of this Way , to make our Gardens yield better Fruits . Besides , My Lord , I cannot forget what other Titles you have , to look upon this as a domestick Production . I shall think my self happy , if I can add something to the Innocent Pleasures of many Nations ; especially this ; for which , as well as most of the Neighbouring Countries , what I have to propose seems to be of most Use . However , My Lord , I shall be satisfied , if , by thus indeavouring to become useful to Your Lordship , I express my most sincere Gratitude , for all the Obligations I have to Your Illustrious Family . I am with all manner of Respect , My LORD , Your Lordship 's Most humble , most obedient , and most obliged Servant , N. F. D. The PREFACE . THE Reader may , perhaps , think it strange to find , in this Discourse , a mixture of Gardening and Geometry ; these having had hitherto but little communication with each other . But such is the wonderful extent of Mathematicks , that very few Arts can be named , but what may be , by a due Application of them , in a great measure improved . At least I hope Experience will make this plain , in the very case we have under consideration . I might have published only that part of this Discourse , which could be understood by every body ; or else have placed the Mathematical part , wholy by it self . But it was hard to separate them , without an injury to both . And I thought it better , that whoever dos not care , for what relates to Geometry , should be desired , from hence , to read only what the Table , or Margin , will shew him to be most for his use . And , lest the nicest Reader should have yet any occasion to complain , and think it too great a trouble , for him to chuse what he may read , and what he may pass over , I have all along set , in the Margin , some Commas , over against such places , as any one , not skilled in the Mathematicks , may freely avoid . I must however except the two or three first Sheets , which were already Printed , before I thought of this Distinction . The remaining Discourse , tho some few Words in it may not be understood , by such as are unacquainted with the common Terms of ordinary Arts , will , I hope , neither prove tedious , nor offensive , to any Lovers , of Gardening ; even Ladies themselves not excepted . Where I have used a double row of Commas , I desire to have no other Readers , but such as have studyed , to a great degree , either Natural Philosophy , or Mathematicks , or both . It was requisite that this Theory should not appear , without its Demonstration ; that so the Curious might know the Ground , it is built upon ; and satisfie the rest of the World , that here is no design laid , to impose upon them ; but , on the contrary , such hopes offered , of an extraordinary Success , in raising good and early Fruits , unless the Seasons be too much wanting , as amount almost to an intire certainty . Neither could the Directions , that were to be given , be fitly expressed , without borrowing from Geometry , and some other Mathematical Sciences , their proper Language . I have endeavoured to be as short , as I possibly could : and there are some places , where , if one reads fast , he will hardly conceive the whole extent of the Discourse . Such are , for instance , the places , where I speak of Remedies against Winds . That very brevity , for which discerning Men are used to express so great an Esteem , will make a second reading pleasanter , less troublesom , and more profitable , whenever it will be necessary : and will help to find easily , and within a little compass , the Directions useful to Practice . As to the Style , I am sorry to find so very few Words , and not one Sentence , to have been altered , by such , as were at the trouble to peruse my Manuscript . But the Example of the Illustrious Monsieur Hugens , who published in French his Theories of Light and Gravity , tho he was no perfect Master of that Language , makes me hope that any faults , in the Style , will be forgiven me , especially by English Men ; who , of all Nations , have least to reproach me withal , that I should offer to write this Treatise in English . If it be well received , perhaps a second Edition may be more accurately penned . Most Countries may reap some Advantage , by the Theory , which I shall propose : but especially such , as have more than 45 Degrees Latitude . This comprehends , in our Europe , all England , Scotland , and Ireland ; most part of France ; Holland , Flanders , Germany , Switzerland ; the North part of Italy ; Hungary , Sclavonia , Transilvania , Moldavia Poland , Denmark , Sweden , Muscovy ; and several other Countries of less note : but with some difference . Of these Countries , such , as lie more to the South , may expect to have , with our Walls , some excellent Figs , and Grapes , &c. with some of the Fruits of hotter Climates . But as one goes more Northwards , tho here and there some new Sorts of Fruits be met withal , yet fewer and fewer good Fruits will , by degrees , be left , especially of those Kinds that require a great deal of Heat ; till at last most Fruits , by the help of Sloping Walls , will only shew better their Shape and Bigness , and perhaps something of their Flavour , without ever coming to a perfect maturity . For I do not doubt but that , even in those unhappy Climates , the natural Productions , which they have , will be much mended , by our Inclining Walls . Southwards of 45 Degrees Latitude , I can no more reckon , in the North Hemisphere , whole Countries , as concerned in this Discourse ; but only some particular places , upon Hills and Mountains ; or else some peculiar sorts of Fruits ; of which some may be made forwarder , without any prejudice from the Increase of Heat ; and others may be transported , from hotter Countries : Or lastly , some peculiar Expositions ; which being yet too cold , as , for instance , the North Expositions , may be helped , as much , as one pleases , by duly inclining their Walls . As our Theory is not restrained to Europe , nor to Countries on this side the Equinoctial Line ; so it is not proper only to Men of great Estates : but whoever is able to have a Wall , about his Garden , may , in some proportion , injoy the Advantage , that arises from it . 'T is true I have principally considered how large Gardens , for Fruit , might be made useful , handsome , and stately . And this being the hardest part , and including all the Directions , necessary to those , that can be but at a small Expence , what I had more to say , in reference to them , was the less considerable . No body therefore ought to complain , that I forgot his Case . It is not just that we should lay open those rich Presents , which the Author of Nature offers us , without expressing a due Sense of His Magnificence and Greatness . Who can avoid admiring that Supream and Infinite Wisdom , which makes every where such an immense variety , of most graceful and excellent Productions , to cover the whole Face of the Earth , and to spring out of the very Ground ? From thence it is that , notwithstanding their different Proprieties , they all draw wonderfully their Life , and the Spirit that animates them ; to the Amazement of any , that considers this surprising Operation . THE TABLE . IDEA of Sloping Walls for Fruit. Pag. 1 Defects of perpendicular South Walls . p. 2 Perpendicular South Walls , East Walls and West-Walls compared together . ibid. Perpendicular Walls compared with Sloping Walls . p. 4 The same done in a particular Example for the Equinox : p. 5 And for the Summer Solstice . p. 6 The result of which shews the great advantage of Sloping Walls . ibid. What Countries they are best for . ibid. A good Culture is necessary for them to have their full effect . p. 7 An instance from Experience of the usefulness of Sloping Walls . ibid. How Sloping Walls may be built with little charge . p. 9 And how far the Roofs of Houses might serve instead of Sloping Walls . p. 10 The advantage of their having no Foundation . p. 11 Rule for determining the quantity of the Inclination of Sloping South Walls . p. 12 Of Sloping Walls in very hot Countries . p. 14 A Table giving the Limits of the Elevation of South Walls in temperate Countries . p. 15 It is difficult to determine those Limits in very hot Countries . p. 16. The Vse of the Table . p. 17 Vines are commonly planted upon a rising Ground well exposed . ibid. A Hill well exposed cut into Terrasses , with Sloping Walls for Fruit. p. 18. Something like this done in China , but for another reason . p. 19 A considerable Declivity to the South , in a large Garden , may be turned to much advantage . p. 20. A perpendicular Wall in no Country so hot , as a Sloping Wall , proper to the Place and Exposition . p. 21. The North Exposition is made tolerable by a Sloping Wall. ibid. Vse of Sloping Walls for having Fruits , Melons &c , early and thoroughly ripe . p. 22 Walls of Bricks are best in England . p. 23 Of Walls of Slate , or of any dark coloured Stone , whether natural or painted . p. 23 Sloping Walls not to be clogged with any Shade , except perhaps in Winter , or when the Sun is very low . p. 24 Sloping Walls may ascend obliquely upon a Hill ; and the use of making them so . ibid. Many Slopes in several Gardens are ready made , and fit for Sloping Walls . ibid. The goodness of a Wall proved owing in a great measure to the Exposition . p. 25 The Author's design in commending this Theory . ibid. The advantage for Vegetation of a close and warm Air , and of small and narrow Gardens . p. 26 How to make some Terrasses , running from East to West , so that the Air between be extreamly warm : p. 28 And that they be not exposed to Winds . p. 29 Terrasses to be made higher when they are far asunder . p. 30 Roofs may be used instead of Terrasses . p. 31 Of Plants of hotter Countries . ibid. Of Orange Trees . ibid. Of some Objections against Sloping Walls . ibid. Sloping South Walls exposed to the mischiefs of latter Frosts , unless prevented . p. 32 Of Remedies against an early Vegetation and Winds . ibid. Sloping Walls are exposed to one sort of White Frosts . p. 33 They are much exposed to Hail . p. 34 Of the Trees growing obliquely to the Ground . ibid. Of the dampness that may be objected against Sloping Walls . p. 35 Of their being exposed to Mice , and Ants , &c. p. 36 Of all other Objections against them . ibid. Calculation shewing for an Example the proportion of Heat , at the Solstice , in the Latitude of 52½ , upon a perpendicular Wall , and a Sloping smooth South Wall , passing thrô the Pole. p. 38. The Ground and Method of this Calculation . ibid. The result of it . p. 42 Other Examples to the same purpose for the Latitude of 51½ : ibid. And 45 Degrees . p. 43 Sloping Walls are more necessary in colder Countries ; but the Increase of Heat , they give , is greater , in warmer Climates . ibid. Sloping South Wall passing thrô the Pole less hot , in the Solstice , than the South Wall passing thrô the lower point of the Polar Circle . p. 44 A more accurate Method of comparing the Sun's Heat , upon two plane Walls , in any Situation . p. 45 This Method depends upon the Quadrature , and Center of Gravity , of the Line of Sines and its Segments : ibid. And is general : p. 48 And in some few Cases capable of a very easie Approximation ; ibid. Notwithstanding the Effects of the Air. p. 49 A Corollary for finding the Heat of the Sun , upon a Plane parallel to the Horizon . ibid. A Table shewing the Sun's Heat upon a Plane , for each Degree of the Sun's Elevation upon it . ibid. The Vse of the Table . p. 51 The Diminution of Heat occasioned by the Air is considerable ; ibid. But hardly to be found by Meditation ; and why . ibid. A Method for finding it by some Experiments , with a Burning Speculum . ibid. A Table giving the Length of a Beam of Light in the Air , supposing the Height of the Atmosphere given &c. p. 52 How to find , in an Air of an uniform Density , the Diminution of Heat , for the several Altitudes of the Sun. p. 54 Of Movable Walls , in order to receive the Light of the Sun almost perpendicularly for the whole Day . p. 56 Description of an Engine for that purpose . ibid. Advantage of Movable Walls against Storms and Winds . p. 59 Their use for early Fruits . ibid. Of the Rain falling upon Sloping Walls . ibid. Terrasses so shaped as to give some more Advantages , in reference to Rain and Heat . p. 60 Idea of a Paved Sloping Ground upon a Hill , to be used instead of Terrasses with Sloping Walls . p. 62 It will prevent the Dissipation of the Spirits of the Earth . p. 63 What the Author finds said by others , particularly by Monsieur La Quintinye , that may have some relation to Sloping Walls . ibid. An Account of what Monsieur La Quintinye calls des Ados . p. 64 And of his Slopes of Earth , exposed to the South or East , and purposely made for Fruit. p. 65 Reflexion upon this contrivance : p. 66 Which is here compared with Sloping Walls . ibid. Our Gardens , thô Square , may at once injoy the Sun upon their four Walls . p. 67 In Monsieur La Quintinye's Ground Plat of the French King's Garden , no Footstep found of Sloping Walls . ibid. To what degree they may be unpleasant to the Eye . ibid. Objection from Monsieur La Quintinye's English Translation solved . p. 68 Account of an Amphitheater with Sloping Walls . ibid. And of some Melons , and other Fruits , heated with Convex Glasses . p. 69 The Fault of Vines that are commonly made to grow against a Roof , or the Coping of a Wall. ibid. Judgement of those and all other such Tryals , in order to make the most of the Sun's Heat . p. 70 Caution against too much Heat Sloping Walls are like to procure . ibid. Frames called Espaliers by the French recommended , to take off some of the Sun's Heat , and to give more liberty to Trees . p. 71 A Method for chusing the Elevation of a Sloping Wall in any Exposition whatsoever . p. 72 The Heat sensibly the same upon a South or upon a North Sloping Wall , thô a little declining from the true North or South . p. 75 A singular sort of Maximums and Minimums , very different from those that are commonly considered . ibid. The same in some measure already observed by others . ibid. The Ground of the foregoing Method . p. 76 Experience must also be consulted . ibid. Of Walls that are not smooth . ibid. There can be no such thing as a Wall giving the Heat proportional to the Sine of the Sun's Elevation upon it . ibid. But if there was , the Method of calculating the Heat upon it would be easie . p. 77 And Sloping Walls would be yet very advantagious , even in that Supposition , thô less than before . p. 77 Of a Wall giving a mean proportional Heat , between such a Wall as this and a Plane Wall. ibid. A smooth Wall compared with a rough Wall. p. 78 How to make a Brick Wall smooth . ibid. Of a Sloping Wall with Semi-cylindrical Furrows upon it . p. 79 These Furrows compared with a plane Wall of the same breadth with them . ibid. Measure of the Heat upon a Semi-cylindrical Space . p. 81 An Account of a Table giving , from 40 to 67 Degrees Latitude , the proportion of the Sun's Heat , in the Solstice , upon a perpendicular and a Sloping South Wall. ibid. The use of Sloping Walls in very hot Countries , in such Situations as , being high , are naturally temperate or cold . ibid. The Table it self , and its Explication p. 82 The Vse of the Table . Example for Paris . p. 84 Of South Walls that are more inclined to the Horizon , than the Wall that passes thrô the Pole of the World. p. 85 Perpendicular and Sloping South Walls may be well compared together in the same , but not in different Climates . ibid. Of some other Advantages of Sloping Walls . p. 86 In reference to Dew and Rain ; especially as to the East Wall : ibid. In reference to Frost , occasioned by the Earth's transpiring some moisture ; p. 87 Or by the cold Vapours in the Air driving with the Wind and sticking upon Trees . ibid. The growing of Fruits extended to more Countries and Places : ibid. And the time of their Ripeness and Vse for Men to more Days in the Year . p. 88 Ordinary Walls compared among themselves and with Sloping Walls , as to the Forwardness of their Fruits . ibid. The Certainty made greater of our Latter Fruits coming to Perfection . p. 89 Slopes of Earth for smaller Plants . ibid. Of the dividing a main Slope into many small ones . ibid. Of shaping the Level or ordinary Ground , into very large Furrows running East and West , with a gentle Slope Southwards , and a steep one Northwards , or contrary wise , in order to increase or diminish a little the Sun's Heat . ibid. Application of this Practice to Vse . p. 91. Of the Difference of Heat upon the North and South side of Mountains , Hills and Downs . ibid. The Heat of the Air in any place dos not very easily spread into the next Air. p. 92 Nor the reflected Heat spend it self so fast but that it may be strongly felt . ibid. Our European Plants grow naturally , upon the Mountains in the West-Indies , in such places where the Heat is fitted to their several Natures . p. 93 An Account of a Slope where extraordinary Strawberries are said to grow . ibid. Advantage of Sloping Walls in such days as the Sun is seen for some Hours only . p. 94 Advantage of inclining Sloping Walls more or less , according to the Climate , Situation , and Exposition . ibid. Advantage of Terrasses with Sloping Walls , in reference to a sufficient quantity of good Earth , which is easily procured . p. 95. Description of a Garden for Fruit , according to the present Theory . ibid. The Vse of making the outside Wall thicker at bottom than at top . p. 96 A kind of Canal or Ditch , to keep the Garden from too much Water . ibid. Measures of the Slopes , which are respectively made equal . But being made different they may be better fitted for several Fruits . p. 98 A Table shewing the Heights , Elevations , and Bases of the Walls . p. 99 Measures for the Ground Plat taken across the Garden . p. 100 Of a Garden for Vines only . It requires but small Terrasses . p. 103 Of the Number of ordinary Trees the Garden could hold ; from whence is to be estimated the Number of its Fruits . ibid. A Table shewing the Heights and Lengths and Expositions of the Walls . p. 104 Short Table giving the Result of the former . p. 105 Some Suppositions taken from Monsieur La Quintinye ; ibid. By which a Table is made of the number of ordinary Trees the Garden would have . p. 106 3½ Vines to be substituted for one Tree . p. 107 General Sum of ordinary Trees and Vines in the Garden . ibid. Of Terrasses for Vines only . ibid. Vines ought to be kept very low . ibid. Of a large Terrasse , parted into two , for Vines . p. 108 The Garden will not hold so many Trees as it would , if they were to keep within the ordinary Sizes . ibid. The Trees in it will grow very large , and why : ibid. And must be far asunder : ibid. Yet will not yield a less Crop of Fruits . p. 109 They will be more lasting . ibid. A Guess at their Distances . ibid. Proportion of the London Foot to that of Paris . ibid. A Draught of the Garden in Perspective . ibid. Division of a large Garden by some Canals into four or sixteen little Gardens , or any other number . p. 110 This will yield the Earth necessary for the Terrasses . ibid. And either give different Ponds for several sorts of Fishes : or else open the way by Boats among the Gardens . 111 And leave also a Foot-way into them all p. 111 Any ordinary Gentleman may have a few Terrasses or Slopes well exposed . p. 112 A Tryal of Sloping Walls not to be depended upon , unless made by a very good Artist . ibid. A good Culture more significant than a good Exposition . p. 113 Sloping Walls very necessary , while our Summers continue to be so cold . ibid. The Cause of that Change , in our Seasons , referred to a Phenomenon , like Smoak , that incompasses the Body of the Sun , and is seen to spread an exceeding great way from it . p. 114 The Origine of that Smoak . p. 115 How to determine the Figure of the Space it lies in . ibid. It may grow thicker and yet not be perceived to have changed , except perhaps by its Effects . p. 117 Some Directions relating to Fruit-Walls . Directions about Garden Walls ought to be taken from Monsieur La Quintinye , and the present Discourse . p. 118 Let your Walls be Straight . ibid. How they must be if they stand by themselves , without any Earth on either side . ibid. How if they rest against a Terrasse or Slope of Earth . p. 119 Let the Earth of the Terrasses be throughly setled . ibid. The Perpendicular Height of Sloping Walls . p. 120 Their Inclination . ibid. Of a broad Terrasse , and how it may be made ; ibid. When its sides are almost equally leaning ; ibid. And when the Terrasse runs from East to West . p. 121 The Ground of Alleys for Fruit may be made sloping towards the South . ibid. The North Wall may be left bare , and Herbs sown at the Foot of it : ibid. Or else the Earth be kept resting , in order to renew that of the South Wall. ibid. Slopes preferred to Walls . p. 122 If you can have but one Slope , give it the best Exposition . ibid. Of a Slope round the Garden . ibid. Of a Terrasse round the Garden . ibid. Of more Terrasses in the Garden . ibid. Of flat and sharp Terrasses ibid. Description of a Wall very well secured from Winds . p. 123 Of the Disposition the Roots ought to have , in a Tree that is to be planted against a Sloping Wall. p. 124 Description of a Ladder to be used about Sloping Walls . p. 125 Of Harbours and Summer Houses , in our large Gardens . p. 126 Of Ornaments of Architecture , in a Wall altogether smooth . p. 127 THE END OF THE TABLE . ERRATA . PAG. xviij . l. 14. THE. p. xxj . l. 21. Latitudes . p. 4. l. 28. Neighbourhood . p. 14. l. 30. err . p. 15. In the Note A Table . p. 16. l. 22. dos . p. 19. l. 27. China tells us , how . p. 23. l. 2. we should gather from . p 26. l. 23. not to be . p. 29. l. 18. Terrasse . p. 33. l. 21. Ridings for Fruit might . p. 37. l. 27. proceed . p. 38. l. 10. smooth South Wall. p. 43. l. 4. 10593. p. 50. In the Column of Degrees read 55. p. 53. In the Column of Degrees read 41. p. 54. l. 5. Add in the Margin the following Note if it be wanting : How to find , in an Air of an uniform Density , the Diminution of Heat , for the several Altitudes of the Sun. p. 60. l. 6. B A is the Slope . p. 67. In the Notes La Quintinye's . l. 27. Begin a new Paragraph . p. 69. l. 2. tryed , about 53. p. 78. l. 5. would . p. 96. l. 29. Canal . And so in the Marginal Note . p. 104. l. 17. 16. 6¾ . l. 19. 10. 2¾ and. p. 115. l. 4. that it has . p. 121. l. 2. In the Notes read when . p. 122. l. ult . and. p. 124. l. 29. judgement . p. 127. l. 8. fear yet lest . p. 128. l. 4. Frontispice . ADVERTISEMENT . A Mistake of one Degree , in the supposed Latitude of Paris , which ought to have been 48 Degrees 50 Minutes , has spread thrô the Numbers in the whole 85th Page , and the beginning of the next . But it is easie to rectifie this mistake , which is not very material . If you are minded to correct it ; Instead of 49. 183. 781. 427. 548. 427. 121. 548. 121. 487. 4⅚ . 2 Degrees . 49. Write 48. 169. 773. 460. 595. 460. 135. 595. 135. 527. 5¼ . 1 Degree . 48. IN the Latin Mathematical Treatise , which will be bound at the end of some Copies of the present Discourse , the last Number in the 21th Page , ought to be 2●302584 . To the BOOK-BINDER . ☞ THE Frontispice and the Title Half-sheets ought to be folded so , one within another , as to have first two white Leafs ; then the Frontispice and the Title facing each other . The Garden in Perspective ought to face the first Page ; and the large Mathematical Cut ought to face the last Page , that is the 128th Page . Both these Cuts must be so disposed , as to lie , when unfolded , altogether out of the Book . After the same way must also be folded the small Mathematical Cut. It belongs to the Latin Mathematical Treatise , and it must face the 24th Page , which is the last Page of the said Treatise . Horti Fructuum edilium feracis Orthographica Delineatio , Spectatore versus Occidentem Acquinoctialem prospiciente Hac Tabula Murorum ad Horizontem inclinatorum . Arboribus pandendis ac plenius diutiusque Soli exponendis , exhibetur vsus . S : Gribelin sculp . FRUIT-WALLS IMPROVED , BY INCLINING THEM TO THE HORIZON : OR A WAY TO BUILD WALLS FOR FRUIT-TREES , Whereby they may receive more Sun-shine and Heat than ordinary . AFTER all the Application of so many Men in all Times and Countries to Agriculture , one would scarce have thought there was yet left so notable and so very obvious an Improvement of it as that I am a going to propose . It consists in building Walls for Fruits , Grapes &c , not in a perpendicular Situation , as is commonly done , but so sloping , thô otherwise straight and plane , as to receive the Beams of the Sun , not only for a longer time , but also with a much fuller and better Exposition . It will appear that this way of building Fruit-Walls will be very advantagious , if we compare perpendicular Walls in several Countries and Expositions with one another , and with sloping Walls : examining withal some of their most considerable Proprieties . South-Walls are commonly reckoned to be the best for Fruits . But in these Climates , and much more in hotter Countries , when the Days are something long , and the Heat of the Summer is in its greatest strength , it is late before the Sun shines upon them , and the Sun leaves them as early in the Afternoon . When it is about Mid-day the Sun is so high , that it shines but faintly and very sloping upon them ; which makes the Heat to be much the less ; both because a small quantity of Rays falls then upon these Walls ; and because that very quantity acts with a kind of glancing ; and not with full force . Before or after Noon the Rays come yet upon our ordinary South-walls with more obliquity . In the North part of France East Walls are looked upon as almost of the same goodness for Fruit as South-walls : which proceeds more from the Defect I have noted in South-walls , than from any particular Excellency in those facing the East . And accordingly South-walls are here , and in all other cold Climates , much the best of the two . West-walls in France , as well as here , are but indifferent , thô they have the like Exposition to the Sun as East-walls . I take the reason of this difference between East-walls and West-walls to be partly because in the Morning the Air is purer , and that the Sun shines oftener and stronger than in the Afternoon ; and meets with the Dew while it is yet fresh upon Plants , whose motion it revives after a long rest , and as it were a refreshing Sleep . But the chief cause of it must be attributed to the coldness of the Air in the Morning , that checks the Vegetation , till the presence of the Sun revives it ; which it dos much sooner and much more effectually on the East-wall than on the Westerly . In the Afternoon the Heat of the Air is great every where ; and Heat alone , without any Sun-shine , is able to make Plants vegetate , thô not so perfectly . Which , if it were not sufficiently known , might be easily evinced from what is observed in Summer in the Fields , when the Sun happens not to be seen for some Weeks together . I said that the Sun shines stronger in the Morning than in the Afternoon , thô it be hotter in the Afternoon than in the Morning . But this is not because the Sun in the Afternoon shines with more force ; but because it continues to act upon an Air already warmed with the impression of the Morning Sun. In order to be satisfied in it , one may , when the Days are long , compare nicely the Effects of a burning Speculum at 5 , 6 and 7 a Clock in the Morning , with its Effects at 7 , 6 and 5 in the Afternoon . For the like reason it is much warmer a Month or two after than a Month or two before the Summer Solstice ; thô we cannot but suppose the Sun to shine sensibly with the same force at equal distances from the Tropick . Conceive a perpendicular Wall with Trees against it . It is evident that it is exposed only to one half of the visible Sky . And the point to which it is directly exposed falls upon the Horizon . To which point should we suppose the Sun to be something near , one half of the time it would be under the Horizon , and the other half it would shine but weakly thrô so great a depth of Air. But if we suppose the said Wall remaining on the same place to be inclined , with the Trees against it , so as to become elevated only 45 Degrees upon the Horizon , and to have the Trees on its upper side ; the Wall in that situation will be exposed to three quarters of the visible Sky : and the point to which it is directly exposed will be 45 Degrees high . To all the Neigbourhood of which place if the Sun happens to come , it must needs act from thence upon the Wall with a considerable force . And so far the advantage of sloping Walls is already plain and obvious , without any Calculation . Now if we proceed farther , and bring the matter to a Calculation , according to some Principles , which shall be explained in a proper place , and which most Mathematicians will admit of ; we shall not only say that there is a great advantage in sloping Walls ; but we may also shew in Numbers , sometimes exactly , sometimes by a near Computation , the Increase of Heat we shall have , by using them rather than perpendicular Walls . Thus , for Instance , if in the Latitude of 52½ Degrees , which is more Northerly by one Degree than London , a South-wall , very smooth and even , be so leaning as to have its Plane passing thrô the Pole of the World ; which sloping for many Fruits is not altogether the best that might be assigned ; the Action of the Sun upon it in an Equinoctial Day will be to the Action of the Sun in the same Day upon an ordinary upright South-wall ( supposing it also to be smooth and even ) as 100 to 63. And these Numbers we can easily continue with exactness to many more places at pleasure . So then here the Heat of the Sun is increased something more than in the proportion of 3 to 2 ( not to say of 11 to 7 ) above what it is in the perpendicular Wall ; which is very considerable . But that Increase will be yet greater and greater , as the Sun comes to have a greater Northerly Declination . For in the Summer Solstice the Action of the Sun , upon that even and smooth sloping Wall , will be increased so as to be upon one account more than 3½ times greater than the Action upon the perpendicular Wall. Besides another very considerable addition of Heat , which would make that Action from 3½ to become 4½ times greater , were it not that something is to be substracted from this last number , upon the account of the Light of the Sun not coming so freely thrô a greater depth of Air : which Correction has no place in the Equinoctial Day . However we may suppose the Heat , in the Summer Solstice , to be about fourfold what it would have been upon the perpendicular Wall. This Increase of Heat is so extraordinary , and for above two Months the Sun keeps so very near the Tropick , viz. within a distance from it of 3½ Degrees , that seeing what our South-walls are already able to do , I do not doubt but such a Wall as this would make Grapes , and Figs , and other Fruits equal here in goodness to those of some much hotter Climates . Yet I confess this improvement for Fruit-Walls is not like to be so useful here as in France , or those other Countries where they enjoy the sight of the Sun oftener than we use to do ; a due regard being had every where to the natural productions of the place . Nor do I look for any excellent effect from it , unless the Trees or Grapes be raised from the best Kinds , and the Soil be good and deep , and the Trees and Vines be governed and cultivated by a skilful Artist . It is too common here to leave these Plants to themselves , and in a manner without any Culture . Whereas , besides the necessary care of Pruning them duly , they do not think it too much , even in Latitudes where they have not the same occasion for those foreign helps , to dig very frequently about them , or to do it at least four or five times in a Year . Lest those that desire good Fruits , and are no proper Judges in an Inquiry that depends so much on Geometry , should look upon what I have said as a bare Speculation , I will make them acquainted with the following Story . By which it will appear , that as we have already our Reflexions and Calculations of our side , so we are not altogether destitute of Experience . Having explained to a Person of Quality the present Invention of Sloping Walls , I received for answer , that upon a Sloping Wall , which I saw since , and I will describe by and by , there grew some Years ago Grapes equal in Goodness to those that grow in France . This Wall was nothing but a facing of Bricks laid flat ( and by consequence only two or three Inches thick ) upon a natural slope of Earth , about seven or eight Foot high . It was of very many Years standing , yet extreamly sound and intire ; except in some few places , where the Brick it self was mouldered away . It had been made only because ( being very near and directly opposite to the House ) it was thought to be handsomer than the naked Earth . It made an Angle of about 60 Degrees with the Horizon ; and was exposed not directly to the South , but several Degrees Westward . The Soil is not extraordinary . The House was but low , but it must needs shade that place a great part of the Day . There has been added since some pretty high Buildings to both ends of the House , which Buildings by their shade have intirely spoiled the said Vine , so that it has been pulled up . I felt the Bricks of that Slope one Day , when the Sun shone almost perpendicularly upon them , and they were exceeding hot . But those Noble Persons , to whom the House belonged , thought the goodness of the Grapes might arise from the Soil ; and forgetting the Exposition , they never tryed to recover their loss by another Sloping Wall , for which the Ground would have afforded them abundance of convenient places . And thus we have not only a notable Experience for us ; but we see also how easily and how cheap our Sloping Walls may be built , without any danger of their tumbling down , as our Garden-walls are apt to do . But this being a very material Point , and considering that most People may think it either very chargeable , or very impracticable , to build a Sloping Wall , let us a little inlarge upon it . I conceive then that the facing the Slope of Terrasse Walks , either with a Brick-wall , such as I just now described , or else with a Wall twice , or at most three or four times as thick is the best , easiest , and handsomest way of building our Inclining Walls . Whose name ought not therefore to mislead one so far , as to make him think , that we would propose the building of a thick Wall sloping and incompassed on both sides with Air. The thicker Walls are properest when they are less sloping : for so their strength may better serve to keep the Terrasses from breaking out . It is not required we should lay the flat sides of the Bricks perpendicularly to the plane of our Wall : but it will be more proper to lay them parallel to it : So that each Bed or Floor of Bricks , of which our Wall is composed , may be only two or three Inches thick . And thus the Joynts of the Bricks may be so disposed as to leave no room for Plants or Insects to come out of the Ground . After having explained a better way , 't is hardly worth our while to observe that the Roofs of long and low Buildings in the Country , and even the Roofs of Houses in great Towns , might also conveniently be made to serve for Sloping Walls ; especially if some regard were had to it in building . So , for instance , in the Country the Roof of a long Building might on one side be brought as low as the very Ground . And thus Trees and Vines , especially the last , might be made to grow against the Roof , without spending their very strength in growing up to an immoderate height . In Cities , where they use sometimes to make one Roof to serve many Houses of one side the Street , one might , between the Garret Windows , cut out in the Roof a rectangular Space , of the same height and breadth with the Space the Windows take up ; and from within one might slide up to that Space a square Box full of Earth , of a fit Figure and bigness to stand handsomly between the Windows . This Box being supported at some height from the Floor , one need not fear any inconveniency from the Water 's dropping out : which , in case it should do , might be received in some Vessels . It is so easie to prevent the Rain from running in , between the Roof and the Box , that it is to no purpose to inlarge upon it . Out of these Boxes one might raise some excellent Trees and Vines , and spread them upon some Frames disposed against the Roof . And this , besides the more substantial Advantage of yielding a considerable quantity of Fruit , would also prove a delightful Ornament to that part of our Buildings , which seems to want it most . However at London the Smoak of Sea-coal is much to be feared ; since it both takes off the strength of the Sun , and dos settle upon Trees , where its great acrimony must needs be unnatural and pernicious . But I must give over and leave the Application of this Doctrine to every body's Industry . I need not mention that , in the making our Bricks , some holes may be made in them to receive Pegs of Wood to serve as necessity shall require : unless you chuse rather to use those Frames the French call des Espaliers ; which indeed seem to be much better . But it is worth observing , that such Walls as these , having no Foundation , leave in the Earth more room for the Roots of our Trees ; and are cheaper built and less apt to fall . If they be not made both exceeding heavy and little sloping , I do not think that they will compress so much the Ground under them as to obstruct the growing and spreading of the Roots . And thus much is sufficient as to the manner of building our Walls . Let us now see , as far as we can , how we may chuse , in any Latitude , the properest Elevation for our South Wall , and for the Fruit we design to raise . In order then to determine what Slope is best to give , in cold and temperate Countries , to our South-wall , I look for the Sun's Meridian Altitude at least ten Days , or a Fortnight , or three Weeks , &c. before the latter half of the Fruit of the Kind I design to have uses to be ripe : and then I make the Complement of that Altitude , to 90 Degrees , the measure of the Elevation of the Wall above the Horizon . However I would not be tyed by this Rule , but that I might alter , upon the least consideration , the sloping of the Wall by several Degrees ; especially if one be afraid of taking in too much Heat . And if the Sun's Declination , belonging to the Meridian Altitude found by the Rule aforesaid , should be otherwise , I commonly reduce it so ( in our Northern Climates ) as to make it fall in the Space , which is from the Equator to the Parallel that goes thrô the 16th or 20th Degree of North Latitude . The longer the Fruit is a growing ripe , and also the more distance of time there is between the first and the last ripe Fruit of the same Tree , the more Days would I allow backwards in the finding the Sun's Meridian . Altitude , and Declination : Indeavouring by this to make , for the most part , the strongest Heat of all to fall something before the middle of the ripening time . For the Degree of Heat , that arises barely from the Exposition , is during many Days sensibly the same , and as it were at a stay , when it is at the greatest . And we must , for the most part , indeavour that , when our Tree makes an end of yielding its Fruit , especially if this be about the latter end of the Year , the Sun may already , by changing its Declination , have been withdrawing it self some 5 , or 10 , or 15 Degrees from the Line perpendicular to our inclined Plane . Thus all the while the Fruit is growing ripe it will injoy the greatest Heat . But let us inquire more particularly after the Limits of the Elevations of South-walls : so that we may resolve to keep them , in each Climate , within the two Extreams we shall find . I should not easily chuse to make any where , except perhaps in extraordinary high Grounds , the South-wall more sloping than an Elevation of about 30 or 40 Degrees upon the Horizon would make it to be . For , thô a great obliquity of the Wall would not hinder . Vegetation , but rather , for ought I know , forward it ; yet , our experience in this kind being so very narrow I cannot know otherwise , than by guess , how the Elevations of only 10 or 20 Degrees upon the Horizon would agree with Plants . However such small Elevations are not fit for South-walls , in these Countries . But , if there were any use for our South-walls in the Torrid Zone , as there may possibly be for those Fruits , which , being peculiar to that Climate , require also a great deal of Sun-shine to bring them to perfection , especially in the higher Situations , upon some Hills or some Mountains , I should even there chuse not to give these Walls less than 40 , or 45 Degrees Elevation : which sloping would perhaps give but too much Heat . For there is some reason to doubt whether it would not scorch any Plant whatsoever , that is set , in these hot Countries , against a Wall very much inclined . So I should leave the most sloping South-walls for the Climates that have about 40 , or 45 Degrees Latitude : and not use them there neither , but upon Mountains , or for the Plants of hotter Countries . In Iseland , which is placed under the Polar Circle , the inclined South-walls must make an Angle of more than 46 Degrees , and less than 66½ Degrees with the Horizon . Generally , in all the temperate Zone , I should limit the Elevation of the South-wall between 30 and 66 Degrees . These several Considerations must be duly weighed together , as well as the tenderness of your Plants , in order to chuse a properer Elevation . But a small errour in this is not of great consequence , if you intend to raise all the Heat possible . For you can indeed erre considerably but one way , to wit , in procuring too much Heat . If you do not fear to exceed in this , you may follow the Numbers of this Table ; where the first Column gives the Latitude or Elevation of the Pole ; Latitude . Deg. Greatest Elevation of the South Wall. Deg. Least Elevation of the South Wall. Deg. Least Elevation corrected . Deg. Middle Elevation . Deg. 40 40 20 30 35 50 50 30 35 42½ 60 60 40 40 50 70 70 50 50 60 I II III IV V The second Column gives the greatest , and the third Column the least Elevation of the South Wall upon the Horizon . The fourth Column gives the same least Elevation , with some Corrections , that are not made in order to increase the Heat , but , at the expense of some Heat , to give ( in smaller Latitudes ) more Elevation to the Wall. The fifth Column gives only the middle Numbers between those of the second and fourth ; never differing from them one way or another more than 10 Degrees . The Table was made from this Rule , That the Elevation of the South Wall , in temperate Countries , ought , in order to make the most of the Sun's Heat , neither to be more than the Height of the Pole , nor less than the Height of the Pole wanting 20 Degrees . So then the second and fourth Column may pretty well serve , especially in great Latitudes , for Limits of the Elevations of our warmest South Walls . But the Elevations , for hottest Countries , cannot be so well determined , till Experience has taught what may and what may not be done there . In those hot Climates the Rule I gave just now is of little or no use . For it supposes that Fruits are ripe by the end of October , or long before . But in the Torrid Zone we may have Fruits all the Year round . In great Latitudes the Sun in Autumn and Winter shines seldom , and always thrô a great depth of Air ; which inclines one to neglect that insignificant Sun-shine , and to make the most of the Sun-shine in the Spring and Summer ; by keeping the South Walls , as our Rule does , rather more sloping than they needed have been otherwise . But pretty near the Equator the Sun comes every Day to a considerable Height . And that invites one not to neglect the Sun-shine so much during Autumn and Winter , and by consequence to make there the Walls rather less sloping . Which the scorching Heat requiring also , all these Reasons seem to prove that the South Walls must again grow rather more upright , as one comes nearer the Equator . For let it ever be remembred to consider whether the Climate , the height of the Situation , the Soil , the Exposition , the Nature of your Plants , and the Season of their growing be such as to permit you to give your Sloping Walls the most Heat you can procure . As to the Use of the Table , the Fruits that ripen in Autumn , and very late in the Year , require the greatest Elevations ; those that ripen in June , or July the least . Such as grow ripe in May will have almost the least Elevations : and such as grow ripe in April , August , and September , require some middling ones . But if any Fruit , such as Pease &c , are to grow ripe in March , they require again the greatest Elevations . Now all this is said upon supposition that you are in no fear of procuring too much Heat . And this is what we can at present determine about the Limits of the Elevations of South Walls . Before we proceed farther , should not we relate , as an Experiment favouring our Inclined Walls , that where Vines do grow in the open Air , they chuse to Plant them not upon a flat , but upon a rising Ground , exposed to the East , or South-East , or South ? Which sloping of the Ground , consonant to the Theory I have been proposing , is found by Experience to be of an extraordinary Advantage . And to this must also be referred what Monsieur La Quintinye has writ concerning the Exposition and Declivity of the Ground for great Gardens . But , if after all there should be left some Scruples in the Reader 's Mind , let him either examine the Demonstrations I shall give in this Discourse , or cause some proper Judge to tell him how far he may rely upon them . Having then no reason to think , but that our Theory will be found agreeable to Nature , we may see farther how it can be brought to an extended and easie Practice . If any body therefore is desirous , particularly in a Country not exposed to some returns of Frost in the Spring , and to blasting Winds , to raise a pretty deal of good Fruit , either for his own use or for the Market , I would advise him , both as the best and the least chargeable , to chuse , in a very good Soil , especially in the side of a narrow Vale , a convenient Hill or Rising , with a pretty strong Ascent , and exposed to the South South East , or to the South and by East , or to the South , or to the South and by West , or at least not far from these Expositions : and to dispose his Ground by Terrasses , one above another , so that , in the Latitude of London , the sloping of the Terrasses be elevated upon the Horizon , for the South Wall , neither less than 36 , nor more than 52 Degrees . See the Figure I , where the Section of those Terrasses is represented , in two several Places , to the Eye . And here you may take notice that , if the Ground be not very steep , the less the Sloping Wall is elevated upon the Horizon , the less Room , all things being alike , each Terrasse will take , and the less charge will be required . In the making of these Terrasses a sufficient quantity of the good Earth must be carefully gathered along the Ridge of each Walk , there to receive and nourish the Roots of our Trees . Neither is it necessary to be very curious in keeping your Terrasses , or Sloping Grounds , straight and parallel . But you may follow the winding of the Hill , provided it keeps within the extent of good Expositions : and take every where so much breadth as dos most conveniently give your Terrasses the Height you require . Thus the Expence will not be considerable ; and even the plain Countrey Man may not think it above his power ; especially if he dos his Work by parts , and in several Years . And I am much mistaken , if even those irregular Terrasses do not prove very pleasant and entertaining to the Eye . A late ingenious Account of China , tells us how agreeable the prospects of their Hills are , which the Country Men divide into several Levels , parted by a Sloping Ground between . All this trouble is taken , in that industrious Country , in order to keep the Rain from running off their Fields . But here we shall have probably more occasion to think how we may not be troubled with too much Water ; and how that of the upper Terrasses may be prevented from falling into the lower ones : which being always easie to be done , and the Remedy depending , in a great measure , upon the Extent of the Ground , I must here forbear any farther Discourse . Thus have I brought our Theory to some consistence , and shewn how it might easily be reduced to Practice . But while the first Figure is under our Eyes , I cannot but observe , that instead of looking with others upon a great Declivity towards the South as a considerable inconveniency in the Ground for a great Garden , I should rather admire it , for the multitude of Sloping Walls , well exposed , it would afford from place to place ; besides the pleasantness of many Walls breast high , and of a good prospect abroad . And as to the shade for Walks , one might have it at the top of all from some rows of Trees . I will here add some Reflexions , I chuse among a great many , by which we may farther compare Inclined Walls with perpendicular ones . For I should swell this to an unreasonable Bulk , should I speak of all the Calculations I have made relating to this matter . I shall only then observe that , from the Equator to the very Pole , that is in the whole Terrestrial Globe , I find not one Place , and not one Exposition whatsoever , in which a perpendicular Wall is so hot as a Wall sloping to a proper Degree for the Exposition . And , whereas the North Exposition is utterly naught , in our ordinary manner of building perpendicular Walls , if in the Latitude of 51½ Degrees a North Wall be elevated only 38½ Degrees upon the Horizon , it will injoy the Sun , thô much sloping , for every Minute it can shine in the whole half Year , from the Spring Equinox to the Autumn Equinox . But during the two Months and three Days about the Summer Solstice it will injoy the Sun with an Elevation , or Inclination , ever greater than of 20 Degrees : which gives more than the ninth part of the full Action of the Sun. And for ought I see that may be near as much as our ordinary South Walls do then receive . This might serve for the Summer Fruits that are ripe about the end of July , and for raising of Pease , &c. For thô one would not chuse to build such a Wall without some necessity , or some other considerable advantage , yet having it at hand one would not leave it without use . The North Exposition dos mend very fast as the Countrey lies more Southerly : And above all others it dos require , in temperate Countries on this side the Equator , Walls with a very small Elevation , such as 25 , or 30 , or 35 Degrees . So then we find that even the very worst of perpendicular Walls may become tolerably good , if they be made sloping . It will appear , by the sequel of this Discourse , how many Advantages , besides the bare Increase of Heat , do follow our building of Sloping Walls : But one of them lies already too obvious not to be spoken of here . I say then that this Contrivance seems to be of an extraordinary consequence , for the raising of all sorts of Fruits something earlier than we use to have them , and for their perfect ripening : And that it may prevent some of those , that are fond of Fruits , from falling into the Diseases that usually follow the eating Fruit not thoroughly ripe . I expect from these Walls such Melons , and Figs , and Grapes , as , I think , have never been seen in this Country . I forbear speaking of other Fruits ; but shall only say that , if we had once some excellent Kinds of Trees raised by this Method , we might not need to send for new Graffs again to France . And if , the Summer being extraordinary wet and cloudy , our Sloping South Wall should bring forth but indifferent Fruits , yet even then those Fruits will be more tolerable than such as we gather from our ordinary Walls . But all this will become more evident , when the Principles I build upon shall be laid down . There is yet something I have to say , both in reference to the properest matter to build our Walls withal , and to some other circumstances in the manner of building . As to the properest Matter for our Walls , I think Brick to be much better , in this Countrey , than Stone : because they grow hotter , and keep much longer the Heat . By which means they do still warm the Plants a good while after the Sun is hid under a Cloud , and , in a manner , lost to other Walls . I know nothing ▪ that is more convenient than they are , or of a better Shape for our purpose . The biggest and thickest Bricks will be best : And I should chuse , as I said before , to dispose them so that they might appear by their broadest sides . Thus the Wall will be cheaper , the Bricks will be apt to grow warmer , and , their Interstices being fewer and less deep , there will be less room to take care of against Insects finding a shelter there . Walls of Slate , or of any dark coloured Stone , whether natural or painted , will also be very good . For these Colours imbibe the Light , or Heat , much more than Colours that are whiter . Our Walls ought not to have any Building raised from the top of them ; nor any other Shade cast upon them in Vegetating time , by the Interposition of any thing standing , on either side of them , between them and the Sun. But if they be deprived of the sight of the Sun , while it is only within a few Degrees from the Horizon , the loss is not considerable , and abundantly made up , if , at the same time , they be secured from Winds . The Foundation , or rather Bottom of Sloping Walls needs not be horizontal ; but it may ascend obliquely upon a Hill by some Degrees . Which is of some conveniency for the running off of the Water , and for the chusing a South Exposition upon a Hill that looks to the South-East , or South-West , or to any other point , either between , or , at least , not much above 45 Degrees distance from these places . For the most part of the Spring and Summer such a Wall will injoy as much Sun , as if the Foundation had been horizontal ; but the Ground at the Foot of it will injoy less . And this is what I had further to mention as to the way of building our Sloping Walls . I have seen , in many Gardens , and other places , some Slopes of Earth ready made , and fit every way for Trees to grow against them , if they had been but faced with Bricks . But they lay neglected , perhaps because the good Use that might be made of them was unknown . If any were apt yet to think that there can be no great difference between two South Walls , of which the one receives the Light of the Sun much fuller and longer than the other ; let them consider that , upon the very same Soil , the South-side of a Wall is as good for Fruit as the North-side is bad . That the East-side of another Wall is very good , at least in France , and the West-side but indifferent . Which diversity can certainly be attributed to nothing but the Exposition ; and makes it more than probable that by so much as this is mended , by so much Fruits ought to be more perfect . I have given to this Theory some of the Commendations it justly deserves , knowing how hard a matter it is to persuade People to go out of their ordinary way : And I wish I may have said enough to bring it into common Practice . I hope this is not out of any vain Ostentation , since I chuse to publish here what I know to be much inferiour to some Meditations of another Kind , I have had these many Years by me . And thus much I beg leave to say ; lest a thing that might be useful should be neglected and thrown by , before it be understood . If the vegetation of Plants did only depend upon the Sun-shine coming freely to them , there would be but little occasion left for any farther Improvement . But it is well known that a warm and pretty close Air , well sheltered from Winds , thô not so much exposed to the Sun , in a word , such an Air as is found in the Gardens at Paris , and other great Cities where they do not burn Sea Coal , dos often bring forth better Fruit than will be found in other places , in the Neighbourhood , thô better exposed . However , at the same time that we get wholly the advantage of Sloping Walls , we may also keep all others , and secure those Walls from cold and dangerous Winds . This makes me recommend Gardens of but an indifferent bigness , with high Walls to them : being willing to purchase a close Air with some little loss of Sun-shine . But if the Gardens be very narrow , as I should for the most part chuse , the Walls may be less high . The breadth of your Gardens ought not be the same in all Expositions . And it is of great consequence that the length of very narrow Gardens be from East to West , and not from North to South . In disposing thus the length of the Garden , the Wall may be from 8 or 10 , to 15 Foot , or a little more , in the Slope : the breadth of the Garden , or Earth , between the Walls , from 11 or 12 , to 50 or 100 Foot : and the length as great as you please . But the smallest Breadths are best : And those , as I said , do not so much require high Walls : and by consequence will not be so chargeable . In Gardens that run from North to South , a very small Breadth will be as prejudicial as it is good in Gardens that run from East to West . For it is easie to see that , in these last , the Shade of the long Walls upon each other is but little , in vegetating time ; and falls either upon the shortest Days , or upon such Moments as the Sun is but low and weak . But , in Gardens that run from North to South , and are of the same breadth with the former , the Shade is more considerable . And I find that such Gardens , having an East Wall and a West Wall , each with an Elevation of 30 Degrees , and each of 7 Foot in perpendicular Height , must be 68 Foot wide , from Wall to Wall , if you will that neither Wall should take from the other the sight of the Sun , but when it is less than 5 Degrees high . Lest any one should wonder at this extraordinary narrowness , which dos often turn what we called a Garden into a narrow Walk , I will shew that I do not chuse it without securing that great advantage of a warm and close Air : In order to which I give here the Section of a Walk , or narrow Garden for Trees , whose length runs East and West . Let the South Wall AB have a proper Elevation for your Climate , and for the Fruits you design to have ; suppose at London an Elevation of 45 Degrees . That Elevation is good for those Trees , whose latest Fruits are ripe near the 20th of September , when the Sun is about 3 or 4 Degrees South Declination : at which time the Sun is already withdrawn about 10 Degrees from the perpendicular to the Wall AB . Let the perpendicular Height BC of your Wall be for Instance , of 7 or 10 Foot ; which will give 9 ⌊ 9 , or 14 ⌊ 1 Foot in the Slope AB , and 7 or 10 Foot in the horizontal Line AC . Let the Line AD be in the Plane of the Equator : and it will make here at London an Angle of 38½ Degrees with the horizontal Line AE . Make the Breadth of your Walk the narrowest you can . Allow , for Instance , four Foot to the Ground that is to receive the Trees , and to be now and then cultivated : three Foot to the Walk or Path ; which ought , of right , to be dug up every Winter : four Foot more to another Line of cultivated Ground . So you will have 11 Foot for the whole Breadth of your Walk AE . Draw from the top B of your Sloping Wall an horizontal Line BDG . Draw also the Sloping Line EG , representing your North Wall , and make it , if you please , parallel to the Plane of the Equator ; or rather , if you think fit , make it yet more inclined to the Horizon , I mean more approaching to it , by some 10 Degrees . Make the tops of your Terrasses GH , BI , of what Breadth you please ; suppose of 1 , 2 , or 3 Foot. But they must be broader if you intend them for Walks . Draw the new Slopes HK , IL , either parallel to BA , GE , or else with what alteration you think convenient . And so you have two Terrasses ; to which you may , upon the same Level , and at convenient Distances , add as many more as you please . Now it is evident that the Heat of the Sun , being at the same time reflected , in the Spring and Summer , by both the Walls , will warm extreamly the Air ABGE ; and , in all probability , give a much closer Heat than is in great Cities : especially if , to break the Winds , you have , from distance to distance , another Terasse running from North to South , between those I have described . These Terrasses have a double advantage against Winds , in that they receive them more sloping , and also reflect them upwards : So that the first Terrasses are a pretty good Shelter to defend the following ones . If the Ground be falling or hanging towards the South , the top GH might be kept lower than the top BI ; or the contrary done if the falling be to the North and but little . For I would chuse , except in hot Countries , to avoid any other North Exposition . In case you should desire to make your Walls higher , you might , for instance , increase by a quarter the Lines in each of the Figures ; or else increase them in any other such proportion ; and keep the same Inclinations as before . So you might make AB of 13 ⌊ 2 Foot , and AE of 14 ⌊ 7 Foot ; or else AB of 18 ⌊ 8 Foot , and AE of 14 ⌊ 7 or 20 Foot. Only the cultivated Ground needs not exceed 5 or 6 Foot ; and the Path may be accordingly increased as it lights . On the other hand , in case your Walk be made a pretty deal wider , it would , at the same time , be proper that your Sloping Walls should be made higher , thô in a less proportion than the Walk is increased . And this is in order to procure more closeness to your Air , and to have both more Sun-shine and a better Shelter against Winds . So , for instance , if you make your Walk four times as broad as it was supposed in the second and third Figures , and your Wall higher only in the proportion of 4 to 3 than it was already , the Foot of your Wall would not , after that change , lose half the Sun-shine it should have lost before . And the Sun , of which it would be deprived , being ever very low and oblique , it would yet amount to much less as to the loss of Heat : Especially almost all that loss falling upon the shortest Days , and coming to nothing near the Equinox . But those extraordinary Banks would perhaps be more chargeable , as they would also be more lasting , than two bare Roofs , like those of Houses , and supporting , instead of Tiles , a Brick Wall. Which Roofs would also yield under them a Space that might be turned to some use . The greater those Banks or Roofs are , the greater is the quantity of Rain brought to the Foot of them ; and the closer and stronger is the Heat . Unless , for the conveniency of a Garden between , you should remove them farther asunder . Such a Walk as I have described would also be good for raising in it those rare foreign and Medicinal Plants , that require more Heat than the Climate dos give . And I don't doubt but Orange Trees may grow there in the nature of Standards , provided , in Winter , the place be secured from Cold : which is not impracticable . However we have what we aimed at , the closeness of Air , and Walls pretty well secured against dangerous Winds . I cannot here dissemble some faults of our Sloping Walls . For , as they have several very great advantages , so on the other hand there is in them some inconveniencies , which I could heartily wish were otherwise . However these last are not at all able to ballance the former ; as will easily appear to any one that reads impartially this whole Discourse . Let me first mention one very considerable Objection , against our Sloping South Walls , in those cold Countries , where the passage , from cold to fair Weather , is not , as in Denmark , quick and certain ; but the Air is subject , as here , to some returns of Frost , after it has been fair for a good while . And that is , that the Heat of these Walls will probably make the Blossoms of some Trees to come out too soon , and expose them to an evident danger of being spoiled by the latter Frosts . To this Objection I have little to say , but that it dos already grant a great deal in favour of our Walls : and that we may take our chance , as others do ; there being but a few Days more of danger , for our South Walls , than for those of other people ; whose Blossoms are like enough to be spoiled when ours are . Let us also remember that , in those Climates , a kindly and natural forwardness , together with a perfect maturity , owing not to our artificial Fires , but to the light of the Sun , is hardly to be had , but at the rate of running that hazard . Let us then , as I said , try our Fortune ; and in the mean while use , if we think fit , all the Remedies Agriculture dos afford , to keep back this early Vegetation , and to prevent the mischiefs of Frost : for which I refer you to the proper Authors . * However here is an easie Remedy we may use , not only against this too great forwardness , but also against Winds . Suppose we make but few parallel Terrasses , all of them running from East to West , for instance , but two , or four , &c. Let , in the II Figure , AB represent the South Wall of the Northermost Terrasse , and EG the North Wall of the Southermost Terrasse . Prolong upwards , indefinitly , the Lines AB , EG , in M and N ; and prolong also the Horizontal Line EA Northwards in O , and Southwards in P. You may fill all the Angle MAO with Trees , and very tall and thick Hedges &c , without any injury to the South Wall AB , and the Angle NEP , without any injury to the North Wall GE. And yet both the Walls AB and EG will , for six Months together , enjoy the Sun-shine , for twelve Hours or more . Now this Remedy is better against Winds , and against the forwardness of blossoming , than against the forwardness of Fruits ; and , by consequence , is so much more to be valued . Thus several Ridings might be made in a large Forest ; provided the Ground were not already worn out ; or that it were put in heart again . Another Objection against our Sloping Walls , is , that in the Spring , in some cold Mornings , the Dew may sometimes fall , in great plenty , upon the Blossoms , and there freeze , as it falls ; which might endanger them , and blast all our hopes . I confess , I do not know how far this mischief is to be feared . But this I may say , that , in the coldest part of the Spring , the Sun shines upon our Terrasses , from the time it begins to be some few degrees high ; and , by consequence , soon after the Dew is fallen . So that there will be no time , at least in fair Weather , without which we have commonly no Dews , for much harm to be done : Especially the Vapours , or Steams , that arise from the Ground , being more like to disperse in the Air , than to condense against our Trees ; as I shall explain hereafter . However this inconveniency being already too much felt in ordinary Gardens , the Remedies against it are found , and well known ; at least by such as raise some early and tender Plants , at the latter end of Winter . Our Walls are also more exposed to Storms , and Hail , than ordinary Walls . Yet this ought not to deter us . For we shall not have this accident every Year , at such times , when we may fear it . And , if we should have it , yet it is to be supposed that many of our Fruits will escape being spoiled . Neither is it impossible to cover such Trees , as are most precious , when there is any prospect of a Storm . I expect some will object also , that , the natural posture of Trees being to grow upright , their leaning against a Bank will be like to disagree with their Vegetation . But this Objection has not that strength in it , which is in the former ; and might well have passed under silence . For it is a common thing , in our Gardens , to force Trees into a Figure not at all natural to them . And even Trees , that grow in the open Air , have some of their Branches bending downwards ; and most of them in a manner parallel to the Horizon . It was ordered wisely , for the beauty and stability of Trees , but not for their fruitfulness , that they should naturally grow upright . Now these first considerations ceasing , in an Inclined Wall , I do not doubt but that , as to the production of Fruit , Vegetation will have there its ordinary course . It has been twice objected to me that the dampness of the Ground would probably spoil the Fruits growing against our Sloping Walls . Which makes me take notice of this Objection , for otherwise I should have neglected to give it an answer . I say then that either this inconvenience is not at all to be feared ; or , if it be , that the Remedies are obvious and easie . I do not fear it in such Terrasses as those of the II , III , and XIth Figures ; especially when they are well exposed . For I cannot see what mighty store of Dampness can come , or be kept there ; since water naturally runs off of such heaps . But as to the lower Terrasses of the first Figure , if one or two beds of Bricks be not enough , at least three or four such Beds , and what else one pleases underneath , will be sufficient to make the Wall remain dry at the outside . Moreover it is not necessary that the Fruit should touch the very Wall. But in case it should grow too close against it , a thin Slate , or a small Ring , of any proper matter and shape , will easily keep it from the Terrasse . After all I think Experience , to which I must appeal , will add no strength to this Objection . Some have urged , against our Walls , that our Fruit will be eaten up by Mice , or by Ants , &c. Thô I might say that all other Trees are exposed to this very mischief ; for 't is known that those Mice and Ants can easily creep upon them , yet to this , and all other Objections , I will give but one general Answer . I ask whether the inconvenience that is objected be real , necessary , general , and unavoidable ? or else whether it be not , in a great measure , imaginary ? I ask whether there be no Remedy left against it to our Care and Industry ? I ask , when all is granted to the Objection that can be given it , whether there will be nothing at all left for us , but Trees without Fruit ? 'T is true that I ought by so much more to fear the resort of Insects to our Fruits , as they are like to prove more excellent than others are . But it is well for us that the first Inventers and Improvers of Arts have not at all been moved by such Objections as these . Are they greater than such as may be made against a Countrey-man , who would sow his Grounds ? How is he secured against the vexations of troublesom Neighbours , against the Invasions of an Enemy , the mischiefs of Civil Wars , the unfaithfulness of Servants ? How can he depend upon fair and seasonable Weather ; without too much Drought or Rain , without Hail and Storms and strong Winds ? May not his Seed be eaten up in the Fields ; may not his increase be stolen away from him ; or destroyed by numberless sorts of Insects ? What shall I say of the mischiefs of Fire ? What of Taxes and Tithes ? What of the price of Rents and Leases ? What of selling one's increase to such as will not , or cannot , pay their Debts ? What of all other fears and troubles that may come upon this poor Countrey-man ? Yet for all this our Fields are ploughed , we are nourished , and our Barns are filled with Grain . Such is the Profusion , with which God Almighty provides for us , that , after all deductions made , we have enough to bless his Munificence , and to live with plenty . Now having , in some measure , satisfied the curiosity and impatience of the Reader , I may proeeed to shew how I calculate the proportion of Heat , I gave before , between a Perpendicular and a Sloping South Wall ; and treat at large of the Principles and Method , upon which those , and the like Calculations , are grounded : endeavouring to make our Doctrine as general and as exact as the Nature of the Subject will bear . I begin with Calculating , for the Parallel that lies one Degree North of London , the proportion between the Actions of the Sun , in the Summer Solstice , upon a Perpendicular , and upon an Inclined smooth Wall , with an Elevation of 52¼ Degrees ; which is an Inclination very good there , for the Fruits that are ripe in the Month of October , or the latter end of September . For other Fruits that Elevation is rather of the greatest . The Circle PTEP described from the Center C represents the Celestial Sphere . CH is the Horizon ; P the Pole ; CE the Equator ; IT a Parallel to the Equator , as suppose here the Tropick of Cancer . CIP is the Plane of the Inclined Wall Ci CM the Plane of the perpendicular Wall Cm. Upon the Circumference of the Parallel TI I suppose a right Cylindrical Surface elevated and prolonged of each side as far as is necessary : Which I do in order to find upon it the proportion of the Sun's Heat . ; Now it is easily known that the Quantity of Rays , falling from the Sun upon any Plane , is as the Sine of the Sun's Altitude on that Plane . And that the Force of each Ray , coming from the Sun upon a Plane , is also as the Sine of the Sun's Altitude on that Plane . From whence it follows that the whole Action of the Rays , upon a Plane , is as the Square of the Sine of the Sun's Altitude on the Plane , and the time that Action lasts , joyntly : neglecting the Effects of the Atmosphere . Let now the whole perpendicular Force of the Sun , upon a Plane directly exposed to it , be expressed by the Radius CE , which is Unity divided into 10000 parts . The Force of the Sun at the Meridian in T upon the Wall C i , will be as the Square of the Sine TI ; that is , supposing still CE for Unity , as the Line TV equal to 8410 parts ; which I take upon the Cylindrical Surface Northward . Now from the Vertex I , upon the Axis IP , I draw thrô the Point V the Parabola INV. And the Lines or Ordinates as TV , MN &c , drawn parallel to the Axis IP , from any Point as T or M in the Line IT , till they meet the Parabola IV , express by their Lengths TV , MN the Action of the Sun in the Tropick , in T or M &c , upon the Sloping Wall Ci. The Sum of all those Lines till Noon is the Cylindrical Surface ITVI , which gives the whole Heat of the Morning Sun upon the Sloping Wall Ci , secluding , as before , the Effects of the Atmosphere . Now from the Point T drawing a Parallel to the Horizon , till it meets with the Line CmM , make the Line TL opposite to TV equal to the Square of that Parallel ; supposing still Unity to be expressed by CE. And in our Example you will find TL equal to 2350 parts . Draw the Parabola ML , of which M is the Vertex , MT the Tangent at the Vertex , and L a Point thrô which that Parabola passes . The Ordinates , such as TL , will give , for every correspondent point of the Circle TM , the Action of the Sun upon the perpendicular Wall Cm. And the Cylindrical Surface MTLM will give the whole Heat of the morning Sun , upon that perpendicular Wall , excepting only the Effects of the Atmosphere . Make the Point M the Vertex of another Parabola , of which MT is the Tangent at the Vertex , and V a point thrô which the said Parabola passes . It is evident that the Cylindrical Spaces MTV , MTL are to one another as TV to TL , that is as 8410 to 2350 , or as 3 ⌊ 58 to 1. And that proportion obtaining for every Point in the Arc MT , it is clear the Heats arising from thence keep that very proportion upon the Walls ; notwithstanding any variety you may suppose in the Thickness and Effects of the Air , thrô which the Light is to come from different Altitudes . But there is yet all the Heat expressed by the Cylindrical Surface MVI to be accounted for . The Proportion between the Arcs TM , TI will be found , by the help of their Versed Sines , to be as 100 to 127 ⌊ 6. And the Proportion between the very small Arcs tm , ti will be found as 100 to 122½ : which depends upon the Proportion of the Line TM to TI being as tm is to ti . And if upon TV you take the Point τ , which is three times farther from v than from T , and thrô that Point you conceive the Circle τμι parallel to TMI , and meeting the two Parabolas in μ and ι , you will find the Proportion , between the Arcs τμ and τι , as 100 to 124½ . So then one cannot err sensibly with supposing the whole Cylindrical Space MTVM to the Cylindrical Space ITVI as 100 to 125 , or thereabouts ; that is as 8410 to 10512 ; which stands for the Cylindrical Space ITV , supposing the Cylindrical Space MTL , MTV to be 2350 and 8410. And the Number 10512 being divided by 2350 , you find the Cylindrical Space MTL to the Cylindrical Space ITV as 1 to 4 ⌊ 47. But this Number is to be something diminisht , because of the different Transparency of the Air for different Altitudes . IMN is very considerably less than the 1 / 27 of the Cylindrical Space ITV : and it is upon IMN , and the neighbouring parts , that the greatest Diminution of the Heat of the Sun dos fall . From whence it appears that the said Diminution cannot be very great : Especially , in our present Inquiry , not the whole Diminution of the Sun's Heat being to be accounted for ; but the Diminution or Difference only from what the Heat of the Sun is , when as high as in T. However the Number 3 ⌊ 58 being certainly too small , and the Number 4 ⌊ 47 certainly too great , to express the whole Heat upon the Sloping Wall , it cannot but be pretty near 4 times as great as the Heat upon the perpendicular Wall : the middle Number between those being 4 ⌊ 02. This Method , which is clear and easie , is sufficiently exact for our purpose : and it can be easily transfered to other Latitudes , and to the Cases where the Wall is more or less sloping : not to mention those where the Wall has indifferently any other Exposition . Thus if we leave the Latitude of 52½ Degrees , which is about the middle of England and Holland , and make the like Calculations for the Latitude of London , LT will become 2204 ; TV will remain 8410. The Space MTL will be to the Space MTV as 2204 to 8410 ; or as 1 to 3 ⌊ 82. The Arc τμ will be 47° 38′ . τι is of 60 Degrees , as it was before . Now as 47° 38′ to 60° , so is 8410 to 10593 , which comes for the Space ITV . And dividing 10595 by 2204 the Quotient is 4 ⌊ 81 ; which is too great to express the Heat upon the Sloping Wall , as 3 ⌊ 82 is too little . The middle Number is 4 ⌊ 31 , which was only 4 ⌊ 02 before . So here the Disproportion is considerably greater , between the Heat for the Sloping and the perpendicular Wall. On the Equinoctial Day the Heats are as 1000 to 614. In the Latitude of 45 Degrees TL becomes 1344 , which gives MTL to MTV as 1 to 6 ⌊ 26. So the Heat is already 6¼ times greater for the Sloping than the Perpendicular Wall : besides the Addition of Heat MVI , which is very considerable . For the whole Space ITV is about 8½ times bigger than MTL . The Middle between those two Numbers is 7⅜ . On the Equinoctial Day the Heat is exactly doubled . The immediate Action of the Sun upon the Walls , without any regard to the Heat reflected from the Ground , or occasioned by the Warmth of the Air , dos not become equal for both the Perpendicular and Sloping Wall , till the Sun has got a considerable South Latitude . By this it appears that our Walls are not only good for the Climates of cold Countries , but that they will have the greatest Effect farther from the Poles . In England and Holland , and all the North , they are almost necessary ; because without them Fruits can hardly be very good . In France &c , they cannot fail of producing most excellent Fruits , of the Kinds that require a great deal of Heat , they being able there to outdo so much ordinary South Walls ; than which confessedly there is among perpendicular Walls no hotter Exposition . Hitherto I have not compared Sloping and Perpendicular South Walls to the best Advantage of the former . For in our first Latitude of 52½ if the Sloping Wall was at Noon exposed directly to the Sun in the Tropick , there would already be above 4¼ times the Heat from the Comparison of the two opposite Parabolas . Besides that Addition I have so often mentioned , which would make the Heat about 6⅙ . times greater , were it not for the Interposition of the Atmosphere . The middle Number is 5⅕ or thereabouts . In the Equinox the Proportion of Heats would be found as 1000 to 748. So then a little loss of Heat near the Equinox is here very largely made up about the Solstice . And this may invite ( instead of giving to the South Walls the same Elevation , as the Pole has above the Horizon ) to give them rather a smaller Elevation by 15 or 20 Degrees . If you desire a more accurate Method of comparing the Sun's Heat upon two different Walls , but with neglecting the Effects of the Air , you will have it in the Solution of the following Probleme ; which depends upon the Quadrature and the Center of Gravity of the Line of Sines . The Latitude being given , for Instance that of London , to find for a given Day , suppose that of the Summer Solstice , the Heat of the Sun upon any Plane Wall whatsoever ; suppose a Sloping Wall that lies , for Instance , North-East and North-West , and has an Elevation of 48 Degrees upon the Horizon , going obliquely from the North-East Point towards he North. The great variety of Cases , into which this Problem may be branched , obliges me thus to fix my Discourse , by applying it , in a great measure , to a particular Example . Conceive , in the fifth Figure , the Sphere POBD αβGAP , projected about the Center C , for an Eye placed at an infinite Distance , in the common Section of the Planes of the Sloping Wall , and of the Equator , or its Parallels . Let ακCNKA be the Plane of the Sloping Wall ; βXCEξB the Plane of the Equator ; P the Pole of the World ; DEZKHζκD the Horizon ; OTZNζG the Tropick or Parallel ; N the common Section of its Plane , with the Plane of the Wall , whether this Section fall within or without the Sphere ; Z , ζ the two Intersections of the Tropick or Parallel with the Horizon , if they meet each other . In the Triangle CKE the side EK being given , as here of 45 Degrees , and the Angle E being of 38½ , and the Angle K of 48 Degrees , you will easily find the side EC and the Angle C. Take upon the Equator CX equal to the Complement of CE ; and thrô the Point X conceive the Meridian XHPTξX . In the Rectangular Triangle EBD find BD ; and so draw thrô the Point E the Horizon DEZKHζκD , cutting , as I said , if it lights so , the Tropick or Parallel OG in the Points Z , ζ ; and draw the Indefinite Lines ZY , ζυ perpendicular to OG . Take the Radius of the Sphere for Unity ; and make OV , perpendicular to OG , equal to the Square of the Sine of the Arc OA . From the Point N as Vertex draw thrô the Point V the Parabola NYV υ , making NO to be a Tangent at the Vertex . Transfer as much of the Cylindrical Surface NVNON into the sixth Figure , ( where it is opened , and the Parallel or Tropick becomes a straight Line ) as there is of it that is seen from the Wall. And thus having drawn from the Points Z , ζ duly transfered , if they be seen by the Sloping Wall , the Ordinates ZY . ζυ , the Space between them ZYVNZ , after it is increased in the proportion of the Circumference or Radius of the Tropick or Parallel to the Circumference or Radius of the Equator , will give you the measure of the Heat upon the Sloping Wall. But this is with neglecting the Effects of the Atmosphere . Now that Space , or a Solid proportional to it , is found by having the Quadrature and Center of Gravity of the Line of Sines , and of its Segments ; all which are already known . The Truth of this Assertion is obvious without any farther Demonstration of it ; and will appear to agree with the following Construction , which also dos solve the Problem . To the Circle ONG , Fig. V. conceive the correspondent Line of Sines AOYBZGA Fig. VII . In which the Axis AB is equal to the Semi circumference , and the other Axis OG is equal to the Diameter of the Parallel or Tropick . Thrô the Point N duly transfered upon OG , to wit , with making GN , GN equal in both Figures , draw the Parallel NNN to the Axis AB , till it meets in N , N with the Curve AOB continued for that purpose as far as is necessary . And having also duly trasfered the Point Z , by taking the Line NZ equal to the Arc NZ , and having drawn ZY perpendicular to NNN , and meeting with the Line of Sines AOB in Y , upon NNZ as the Edge , and ZYOANZ as Basis , erect a Semi-quadrantal Ungula ; and find its Solidity or bigness , by those Rules Dr. Wallis has publisht in his Mechanicks ; where he has given the Quadrature and the Center of Gravity of the Line of Sines and its Segments . Then depress that Ungula , or make it smaller , in the Proportion of the Square of NO to the Square of the Sine of the Arc OA . When the Solid of this new Ungula is found , correct it again , increasing it in the Proportion of the Circumference or Radius of the Tropick or Parallel to the Circumference or Radius of the Equator . The new resulting Solid will be proportional to the Heat of the Sun upon the Sloping Wall , if we neglect the Effects of the Air. After the same way might be found the Solid expressing the Heat MTMLM of the IV. Figure , upon a perpendicular South Wall ; for the Solution is general . But if the Cylindrical Surface MTMLM be also duly transfered into the VI. Figure , as you see it done ; and upon the Basis MTM , when it falls intire between the Points N , N , you draw the Curve Line MAM , whose Ordinates upon MM are every where proportional to the correspondent Ordinates of the Curve MLM , and whose swelling comes just to touch the Curve NVN , the Heats expressed by the Surfaces MLMM , MAMM will be as TL to TA , notwithstanding the Effects of the Air. Which consideration may be of some Use , where the begness of the remaining part is but small , and to be guessed at , as we did heretofore , by some easie Approximation . But this by the by . This Solution gives , as a Corollary , the Method of measuring the Heat of the Sun upon the Horizon , any Day in the Year , for any proposed Climate ; thô it remains yet to account for the Diminution of Heat arising from the Atmosphere . I do not expect that the whole crowd of Geometers will see that our Constructions carry with themselves the Strength and Evidence of a Demonstration . But this Discourse being intended to be , in a great measure , popular , I am loth to fill it with a long Digression , only to make our Proofs evident to a greater number of Mathematicians . Let it be enough that some of them may perceive that we have advanced here nothing but what is exactly true . Having calculated a Table of the Sun's Heat upon a Plane , for each Degree of the Sun's Elevation upon the said Plane , I thought it might be acceptable to some if I transcribed it here . In this Table the Heats to an Elevation and to its Complement make always the same Sum : Which depends upon the Squares of the Sides being , in a Rectangular Triangle , equal to the Square of the Hypotenuse . The Sun's Elevation upon a Plane . The Sun's Heat upon the Plane . The Sun's Elevation upon a Plane . The Sun's Heat upon the Plane . The Sun's Elevation upon a Plane . The Sun's Heat upon the Plane . Deg. Parts . Deg. Parts . Deg. Parts . 1 3 31 2653 61 7650 2 12 32 2808 62 7796 3 27 33 2966 63 7939 4 49 34 3127 64 8078 5 76 35 3290 65 8214 6 109 36 3455 66 8346 7 149 37 3622 67 8473 8 194 38 3790 68 8597 9 245 39 3960 69 8716 10 302 40 4132 70 8830 11 364 41 4304 71 8940 12 432 42 4477 72 9045 13 506 43 4651 73 9145 14 585 44 4825 74 9240 15 670 45 5000 75 9330 16 760 46 5175 76 9415 17 855 47 5349 77 9494 18 955 48 5523 78 9568 19 1060 49 5696 79 9636 20 1170 50 5868 80 9698 21 1284 51 6040 81 9755 22 1403 52 6210 82 9806 23 1527 53 6378 83 9851 24 1654 54 6545 84 9891 25 1786 45 6710 85 9924 26 1922 56 6873 86 9951 27 2061 57 7034 87 9973 28 2204 58 7192 88 9988 29 2350 59 7347 89 9997 30 2500 60 7500 90 10000 Degrees . Squares of their Sines Degrees . Squares of their Sines . Degrees . Squares of their Sines . If the Sun's Altitude be given , and you expose to its Rays a Plane , with more or less Obliquity ; the Sun's Heat upon it will be , in any Obliquity , as the Table shews . But if the Sun's Altitude be supposed to change , the Effects of the Atmosphere ought also to come under consideration . I need not say that I make no allowance for the Sun 's apparent Diameter being of a pretty great bigness , and not insensible like the Stars . As to the Diminution of the Sun's Heat , occasion'd by the Interposition of a greater or less depth of Air , it is certainly very great . We cannot bear the Sight of the Sun when it is something high ; much less if it was in the very Zenith . But it is no hard matter to bear it , when the Sun is within three or four Degrees of the Horizon . It is not easie to find by bare Study the Laws of that Diminution ; not only because of the different Density and continual Refraction of the Air , at several Heights from the Center of the Earth ; but especially because of that wonderful Propriety of Light , that makes it go thrô , and among Terrestrial Bodies , under a certain and determinate Degree of smallness , depending upon their Density , without being affected at all in its Passage . However I see how that Diminution might be found , by some Experiments made with a large burning Speculum constantly turned to the Sun for a whole Summer-Day , and with a Thermometer kept by it always at the same degree of Heat . The middle of the Speculum must be shaded by a round Plate , supported exactly over against it . In the Shade of this Plate , and not far from the Focus of the Speculum , the Thermometer , which ought to be but small , must be duly fastened . The Speculum ought to have a graduated Circle about it . And by the different opening of an Arched Ruler , that is to move about the Center of the Speculum , and to be every where pretty near its Surface , it ought to have an Opaque Vail spread , more or less , before it : So that a greater or smaller Sectour be uncovered , according as the strength of the Sun's Heat requires . That Heat will be reciprocal to the Arc or Sectour uncovered . So then keeping , in one of the longest Days , a Table of the Quantity of this Arc , for the several Minutes , or other Intervals of Time , of which the Day is composed , one may easily gather the Proportion of the Sun's Heat it-self , such as is transmitted thrô the Atmosphere . The following Table , which is very short and easie to make , or , instead of it , some other Table made upon the like Principles , might help us also to guess a little , in so dark an Inquiry . This Table gives , upon some Suppositions , the Length of the Way of the Sun-Beams thrô the Air , to every apparent Altitude of the Sun. Apparent Altitude of the Sun. Length of the Way of the Sun-Beams thrô the Air. Deg. Min Parts . 0. 0 20. 0. 18 19. 0. 37 18. 0. 57 17. 1. 18 16. 1. 41 15. 2. 6 14. 2. 33½ 13. 3. 4 12. 3. 39 11. 4. 19 10. 5. 6 9. 6. 3 8. 7. 13 7. 8. 45 6. 10. 51 5. 13. 55 4 19. 4 3 29. 45 2 31. 31 1 ⌊ 9 33. 32 1 ⌊ 8 35. 51 1 ⌊ 7 38. 30 1 ⌊ 6 31. 39 1 ⌊ 5 45. 26 1 ⌊ 4 50. 9 1 ⌊ 3 56. 21 1 ⌊ 2 65. 19 1 ⌊ 1 90. 0 1. Let 2r be the Diameter of the Earth , equal , for instance , to 400 Parts : a the Perpendicular Height of the Air that is able to obstruct sensibly the Light of the Sun : this I suppose , for an Example , equal to 1 Part. Let the Indeterminate q be the Length of the Way of the Sun-Beams thrô that Air : s the Sine of the Sun 's Apparent Altitude to the Radius r : and neglect the Effects of Refraction . In these Suppositions you will find . Which Equation is the Ground , upon which the Table was calculated . And if you give any other Value to the Quantity a , you will easily make such another Table , at your pleasure , by the help of the same Equation . If we suppose the Air every where of an Uniform Density ; and its Perpendicular Height given ; which will be easily determined in that Supposition : and the whole Refraction of the Rays of Light to be , at their coming into the Atmosphere : and that the same Quantity of Light penetrates into the Air , whether it comes with more , or with less Obliquity ; it will be easie to make a Table shewing the loss of Light occasioned by the Air , for any given Apparent Altitude of the Sun. And this may , perhaps , serve well enough for Use . From Experience find the Proportion of Light , suppose as a to b , for any two Apparent Altitudes of the Sun ; suppose 62 and 30 Degrees . Let the Length of the Rays in the Air for those Apparent Altitudes be as n to m. Draw , in the eighth Figure , the Assymptote OAB , of an Indefinite Length . Take in it OB equal to m OA equal to n and AB will be equal to m — n. Draw to the Assymptote the perpendicular . Lines AD , BC , equal respectively to a and b. Thrô the Points C and D draw the Logarithmic Line FCDQ : and draw the Ordinate OQ . If ▪ you suppose OQ for the whole Light , that enters the Atmosphere ; and , upon the Assymptote , you take , from the Point O , the Line OE equal to the Length of the Rays of Light in the Air ; the correspondent Ordinate EF will give the Quantity of Light remaining , after the Passage thrô so much Air , as the Length of the Rays dos expose : And a Table of its Diminution will easily be calculated . The Ground , I proceed upon , is that if two Solid Rays of Light pass , thrô a given Thickness of Air equally dense , they will lose of their Quantity , or Strength , in the same Proportion , as they have to one another . By the like Method you may find how much more Light there is , at any time , near the Surface of a Calm Water , than in any given Depth . ; ; And this is what we had to say of the Diminution of Heat , occasioned by the Rays of Light crossing the Atmosphere . Let us now take our leave of these Mathematical Speculations , and go on to consider what Advantage we can make of Movable Walls . As there are some Countries , or some sorts of Fruits , for which the best is not always the hottest Exposition ; so there are some other Countries , or some other sorts of Fruits , for which we cannot well procure too much Heat . But it will be a hard matter to outdo much the South Walls of our second , or third , or eleventh Figure ; of which last I shall speak hereafter ; unless it be perhaps by a Movable Wall. I shall not mention here the placing some Earth , and having a Sloping Wall built , all along in a kind of Boat ; or otherwise built , in any other sort of floating Vessel ; as suppose a round one . Thô with the turning of the Vessel , so as to follow the Sun , and making it , and the Wall at the same time , lean more or less , one might be sure to injoy almost all the Sun's Heat . I will only describe a kind of movable Box , which having an Inclined Brick Wall fastened to it , will , without any Water , which both is difficult to procure , and rots Vessels too easily , have the same advantage of being constantly turned towards the Sun ; and may , in Winter time , be laid up in an Orange House . In the IX and X Figures AB is a strong Post fastened upright in the Ground ; whose upper end B is shaped into an Hemisphere , or rather into a Part of a Sphere , yet something bigger . Upon B there rests a strong piece of Oak , CC ; in the middle of which there is a concave Place , so made as to fit the Figure of B , and to leave the liberty of turning and inclining the Box several Degrees to and fro . The concave Surface will be great enough , if it contains the half of the Surface of an Hemisphere . D is the Box it self ; which is somewhat long , and so shaped that the Sun may shine pretty fully upon the foreside of it . To the two sides of the Box , and to the Piece CC , are fastened two inclined Pieces of Timber EF , EF , almost parallel to one another ; and upon these , close by the Box , another pretty long horizontal Piece of Timber GG . The remaining Pieces GF , GF ; GF , GF ; FF ; EG , EG ; EE , are so disposed as to give much Strength to the whole Frame . Upon the Part GFFG I place a Floor of Boards , and the Piece GG jets out some two or four Inches , from that Floor . I use both the Piece GG , and the Floor of Boards , for the Foundation of my inclined Brick Wall ; to which I give a thickness equal to once or twice the thickness of a Brick , according to the Weight as I desire it should have . Under the Box are yet two strong parallel Pieces of Timber HH , running on each side close by the Post AB ; and made firm together , at both their Ends , by two cross Pieces . From the back End of HH there rises several Pieces HK , HI ; which being fastened to the Pieces EF , some near the Middle , some at or near the upper End of the Floor or Frame , help to bear it up . In the Pieces HH there might be some holes , at proper distances from each other , for two Iron Pegs , one of each side the Post AB , to keep , at your pleasure , the whole Box in a proper Elevation . But this might be done more conveniently with Cords . For from the Ends E , E ; F , F ; G , G ; H , H , you might have some Cords fastened to some pretty great Weights of Metal or Stone , or else to some Buckles , to keep the whole Engine firm in any position . In the making of it it must be so proportioned , in all its Parts , that the Center of Gravity may fall under B , but withal near it . And so it will be proper that the Floor be not exactly flat , but convex . The Addition of some movable Weight like P might also help to alter the Center of Gravity , and to manage the Engine more easily . And it is to be observed , that the farther ●C is from the Box , the wider you may make it at bottom . Such an Engine as this will easily be defended from Ants and other creeping Insects . About the Floor GFFG one might have a kind of plain Border , with an Inclination to the Floor , of about 45 Degrees every where : which Border , by its Reflexion , would much increase the Heat , and make it closer ; giving besides some Shelter from Winds : And upon it one might spread a Net , to keep off the Birds and Flys . If , by an easie change , you should desire to have two Boxes and two Trees , in one single Engine , the Boxes being something distant from each other , there would be room for the Post AB between them ; and you might make them as broad as you would at Bottom ; and fix the bearing Place much lower , if you thought it convenient so . Instead of Bricks the Floor might perhaps be covered with Lead , either painted dark or black , or not painted at all . But I am apt to think it would give , in some Climates not far from this , and at some Seasons in the Year , too great a Heat for Vines , and such other tender Trees . One advantage of Movable Walls is that they may , at any time , be turned from Storms , and from cold or blasting Winds ; and take in as much , or as little , of the Sun-shine , as one pleases . They might besides , when the Sun is strong , and the Fruit grown large , be sometimes presented side ways to the Sun , that it may shine fully upon the Sides of the Fruits ; and give them also that fine Colour which becomes the whole Fruit so well . But after all these Walls may better serve the turn of some Curious Body , than the Publick . They will be good particularly for Melons , Vines , Figs &c , and for raising early most sorts of Fruits . As to our former Sloping Walls , it remains yet to order them so that we may not be troubled with the Rain , they are apt to bring in abundance to the Root of our Trees . But this certainly can be no fault in a dry Season , or light Ground , or Easterly Wall , or hot Countrey ; especially considering the great force of the Sun upon our Terrasses , which will quickly dry the Ground . In other places , besides what may be done , by receiving and turning off the Rain , the Walk might be made as you see in the XIth Figure ; where it is pretty deep in the middle of it . is the Slope of the South Wall ; AM the Cultivated Ground , some three , four , or five Foot broad : MN another thin Sloping Wall , parallel to BA , and some three or four Foot high : NO the Walk , or Path ; which may be five or six Foot broad , and paved , if you think fit . OP , PE , EG are the correspondent Sloping North Walls and Cultivated Ground . The great Depth of NO will keep the Grounds AMN , EPO pretty dry : and the Path NO may be made falling , in order to bring the Water to some Drains , where it may be lost . In an extraordinary wet Weather , one might use some slight Boards , like QR , and place them so , near the Foot of the Sloping Wall , that they might receive the Rain at their upper end , in order to convey it to the bottom NO . For this purpose it is proper that there be a very small jetting out in the Wall , to which the Boards may be closely applyed . Or rather one might , at first , fix in the Wall a long and narrow piece of beaten Lead , which necessarily receiving the Rain , would easily bring it to the upper Surface of the Boards , or to some Gutters placed along the Wall , which would be much convenienter than the Boards ; and would easily convey the Water to some other Gutters that should make it fall upon the Bottom NO . The Slope MN , receiving so directly the Sun-shine upon it , will help very much to heat the Ground NMA ; and by consequence will , in some measure , forward Vegetation . The Bottom NO , which is to serve for a Path or Walk , must be raising near the middle in a round Figure , to keep it dry there . The two Terrasses being farther from one another , than in the second or third Figure , the Heat will accordingly be less close . Now we have begun to propose , for our Terrasses , a Shape something different from that excellent one , in the second and third Figure ; we may farther observe that there would perhaps be some small Advantage to shape our cultivated Ground so as to have it better exposed to the Sun , and grow warmer . We might , for Instance , let the Section of our Walk , in the eleventh Figure , be according to the Lines BRMNOTEG ; and order matters so , as not to be troubled with the Rain , especially in the Ridge E. And by these means we should also get a Sloping Wall OT , of a tolerable bigness , and very well sheltered , but ill placed , and of an indifferent Exposition . You may remember how , speaking to the first Figure , I did chuse , in the side of a narrow Vale , a pretty steep Hill well exposed ; which I did shape into several Terrasses , one above another . I don't know but that , keeping to the like Idea , it may succeed pretty well , especially about 45 Degrees Latitude , to chuse that Hill very steep , to take it almost as Nature dos give it us , and to pave it all over with Brick laid flat , except some Holes of an Oval Figure , about six or seven Foot long , and about four Foot broad . These Holes are each to receive at the Top of them a Tree , whose Branches must be made to spread upon the paving of Bricks . The greatest Diameter of the Ovals ought to be horizontal . They must be disposed with as much regularity as possible . They will look handsomer , and will be more equally divided , and lie more convenient for the spreading of the Tree , and to receive all the Rain , if they be Checker-wise ; as you see them in the twelth Figure . But they will lie something more conveniently to turn off the Rain , if they be above one another . However it seems there is no great danger to be feared , from too much Rain , in a Hill so well exposed to the Sun ; and where an extraordinary quantity of Rain will not fail to find its way down , or will ever be easily turned off . The uncovered Earth must be dug as often , as it is convenient . The Bricks will grow very hot , by the Sun shining so fully upon them : And , for ought I know , they may hinder the too great and useless Dissipation of the Spirits of the Earth , that secret and precious Fire of Nature , not only by preventing the growth of Grass , but also by intercepting their way , and making them come out , in greater abundance , at the place where the Trees and their Roots are . The good Earth must have been gathered to a sufficient Depth about the Ovals . It is easie to order it so that either all the Rain shall run into the Ovals , or most of it run down at the sides of them , according as your Climate or the Season requires . As to the Charge , both in Bricks and Mortar and Day-labour , it will come , for each Tree , to much less than half the correspondent Charge , in building of a perpendicular Wall ; thô we should suppose this to have Trees on both sides . Since I began this Treatise , I have often inquired whether our Sloping Walls had been used any where : And particularly I have indeavoured to find , in Monsieur la Quintinye's Book , what he says that may relate to this matter . It is very plain that they are in no common use , if used at all , in these Northern Climates , where they are most wanted . And probably they have have had no occasion to think of them in hotter Climates , where , for the most part , Heat is as much feared , as here it is desired . But I would fain have known whether ever they had been designedly built , on purpose to injoy the Sun longer , and to increase its Heat . Monsieur la Quintinye speaks * of some Sloping Grounds , which he calls des Ados . These , he says , are an Earth raised up , with a Slope , along a well exposed Wall , in order to sow upon it , in Winter time and in the Spring , some Plants , that are designed to be more forward , than in the open Ground . So Pease and Beans are sown , and Artichokes , Vines , Rasberries &c , are planted upon an Ados ; the Reflexion of the Sun , probably from the Wall above , and from the Ground before , heating these Slopes , as if they were real Walls . What I find said of them , in the rest of the Work , is much to the same purpose . By this contrivance , the Origine of which I do not at present inquire into , one dos considerably increase the Heat , at all times in the Year ; and I do not see that one can out-do it much in Winter or Autumn . But , in the Spring and Summer , the Wall hides the Sun from the Slope for some time ; which perhaps the Reflexion from the said Wall is not a sufficient recompence for . To which must be added , that the Heat is perhaps better , being divided to a greater part of the Day , than crowded together about Noon . However by this Disposition of the Wall the Heat is made closer . In another Place * he dos mend the hanging of the Ground , in a large Garden , but without admiring at all the Remedy , by dividing it into several Parts , of different heights , and making each of them level , and parting them , either by some little Walls , or only by some Slopes of Earth closely beaten together . And being satisfied , as he has it somewhere else , that there is no place , in a Garden , but what may be of some use ; he says , That these little Walls may serve for several things he mentions : and that the little Slopes will not be useless neither ; but on the contrary , when they are exposed to the South or East , they may either be used to raise at first some early Plants , for the Spring ; as Winter Lettuce , Pease , Beans , Strawberries , Artichokes and after the Spring they may serve to raise some Seeds of Purslain , Basil &c : or else , if there be a great quantity of those Slopes well exposed , a part of them may be imployed for good and all to bring forth good Grapes and other Fruits ; as it has been done in the King of France's Fruit or Kitchen Garden , in certain Slopes purposely made for that use . I guess , by these Passages , that the worthy Author , who is ever very particular and full in what he writes , thô he says no more in this matter , used these Slopes no otherwise than as Grounds , and as they do chuse some Hills well exposed for their Vines , or even for their Gardens . But thô this be something a-kin to the main Idea I follow , in this Discourse , and a Confirmation of it , yet I believe there remain some considerable differences , between what Monsieur La Quintinye has writ , and what I propose . The Gardens of his making may justifie whether or no he had left any room for our Meditations . Which would indeed be only a fuller Explication of his Thoughts , if he had covered his Slopes with Bricks or Stones ; and had made his Trees to grow against them obliquely to the Ground ; and had used them in any Exposition rather than perpendicular Walls ; and had made them sometimes more , sometimes less Sloping ; and had defended them , as I do , against Winds ; and had likewise procured the closeness of Air , with no loss of either Sun or Rain , for the six or seven hottest Months , from Equinox to Equinox : Not to mention some other Improvements you will find in this Treatise . However those Ados of Earth have a peculiar advantage for all Herbs ; and particularly for those early Plants , that are to be gathered in February , March , or April . To this I might add the Account Monsieur La Quintinye gives of Square or Rectangular Gardens ; where he explains how the Sun never shines upon more than two Walls at once ; and in some Moments upon one only ; without ever shining upon two opposite Walls together . But near the Summer Solstice one might see , for a good while together about Noon , the Sun to shine at once pretty full upon the four Walls of a Rectangular Garden built after our way : and seldom , in the rest of the Day , to shine upon less than three Walls , except the Sun be very low . There is in Monsieur La Quintinye's Book a Ground Plat of the Kitchen Garden , or Fruit Garden , of Versailles . Thô there be in that Garden a high and very long Terrasse , with Trees on both sides against it , yet the Ground Plat shews that the Walls of it are perpendicular . So this Terrasse having at once the disadvantages of being more chargeable , and less solid or lasting , and worse for Vegetation than a Terrasse with Sloping Walls would be , I cannot but conclude also from thence that Monsieur La Quintinye knew no other Walls than perpendicular ones . As to the Beauty , I acknowledge indeed our Sloping Walls not to be altogether so handsome as the others are : And yet I do not doubt but the Eye will soon be accustomed to them ; especially when it may look upon them more as Terrasses , than as Walls ; so that their leaning may not seem to threaten a fall . In the English Translation of Monsieur La Quintinye , I find a place , that seems peremptorily to condemn our Sloping Walls . It is near the end of the fifth Chapter of the third Part of the first Volume . There you may read , By all I have newly said , about the Height of Walls , it appears that I have little value for those leaning Walls , to pretend to make them Fruit Walls for Pears , Peaches , Apricocks but they may serve for something else . And in the Margin you find also writ , Leaning Walls not proper . But the Sense , in the French Original , is that such Walls as are only breast high ( des Murs d'appui ) are not good for Fruit. Neither was the Author speaking of Sloping Walls before , but of the Height of perpendicular Walls . I have also heard of a large round Pit , like an Amphitheater , built here in England with Sloping Walls all about it . The Ground in the middle was , as they said , several Yards Diameter , perhaps about 50 or 100 or more . And upon all that Ground there grew Vines , both sheltered from Winds , and cherished with a closer Heat , than they could have in the open Air. A Person of Quality has tryed about , 53 Degrees Latitude , in the present Year 1697 , to increase the Sun's Heat upon his Melons , by some pretty large Convex Glasses . These being placed , between the Sun and the Melons , did gather the Rays in a pretty small Focus each . And we have been told , to our admiration , that the Melons thus helpt have been tolerably good , and much better than others that did grow in the Neighbourhood , which were generally bad ones . As if it were enough to heat any one part of the Fruit , to make the Effects of it to spread over the whole . But I hear also that the like Tryals having been made upon several Fruits , in other places , have had no other success than the giving them some unkindly precocity , leaving withal to them a harsh and unpleasant taste . In some places , they make a Vine to grow as high as the Roof of some ordinary Building ; and there to spread its Branches over the whole Roof . In other places , they make the Vines to grow first as high as the top of a Garden Wall ; and there to part into two Branches , running on each side , for 25 or 30 Foot together , upon the small Coping of Bricks , they do sometimes end their Garden Walls withal . Thô I have been told that , with the first of these two ways , they have had some good Grapes in England ; yet I find , in both of them , this capital fault , that the Roots having work enough to feed so long a Stock , and to garnish such a large extent with Leaves , and a thousand other little useless Shoots , there can remain no strength in the Sap , for the production of Grapes ; unless perhaps they be some few and ill favoured ones . All these and the like Trials were indeavours towards what is here more fully stated : for I do not doubt but a great deal more besides has been attempted , in many places , in order to make the most of the Sun's Heat . Whether I have done any thing more towards it than others , let either Experience justifie , or those determine , that are able to understand the Mathematical part of this Discourse . But after all I acknowledge readily that our Invention required but an ordinary Capacity , to light upon it ; and even but an indifferent Skill in Geometry , to examine and establish it upon its true Principles . I must here repeat again and again , that I have , in this Discourse , indeavoured to increase the Sun's Heat to an extraordinary degree : and this , I hope , I have found how to do effectually . But it is easie in hot Climates , and in some light and dry Grounds , and in the governing of tender Plants , to err by an excess of Heat . If any body should fall into that Errour , it must be by his own fault . He may take as much and as little , as he pleases , of that degree of Heat , which is to be had by our Sloping Walls . Thô accommodating my self to the Climate of England , where too much Heat is hardly to be feared , I may perhaps have sometimes spoke , as if one were always to take the most . However a pretty good Remedy , against too much Heat , is to keep constantly the Ground sufficiently watered : So that the Trees being conveniently full of moisture , their Fruits may be so much the farther from being scorched and dryed up . And here I may observe by the by , that if our Terrasses be so broad as to have , at the top of them , a little Rivulet , or Aqueduct , it will be very easie from thence to water them on both sides . But this is perhaps above the Circumstances of an ordinary Gentleman's Estate . The same conveniency for watering would be found , in the steep Hill of the twelfth Figure , provided there were some Water at hand , above the uppermost Ovals . If you have a Sloping Wall ready built , and you are unwilling to have all the Heat it dos give , you may keep your Trees upon some Frames or Espaliers , at some little distance from the Wall , as half a Foot , or a Foot , or a Foot and a half , more or less , as you intend to take off more or less of the Sun's Heat . Those Frames , thô not much used in England , are yet better than the bare Wall , because they leave more room and liberty to Trees . Perhaps you may desire to have some Method , for the chusing of the Elevations of your Walls , when they have any other Exposition than to the South , or to the North. I do for this make use , in our Climates , of the following Construction ; which I do not give as a Geometrical one , but only as a Mechanical Approximation , for the Solution of a Problem perhaps too hard , to be solved , in its full Extent , with any great exactness . An Exposition being given , in a given Climate , it is easily understood , by what I said before , that all Fruits do not require the Sloping Wall should have the same Elevation : but that some Fruits will have it great , some little : and that among these Elevations there is two Extreams , to wit , the highest Elevation and the lowest , that stand , as it were , for Limits of the rest . I call the highest Elevation , the Sloping Wall can have , in the given Exposition , simply the greatest or highest Elevation ; and its proper Wall the highest Wall. And I call the lowest Elevation , the same Wall can have , in the same Exposition , the smallest or least Elevation ; and its proper Wall the lowest Wall. Let HA be the Horizon , AOP the Meridian ; AO an Arc equal to the Elevation you chuse to give to your Sloping Wall , when it looks to the North : AP the Height of the Pole. And you may find thus the greatest Elevation of your Declining Wall ; whether it declines to the East , or to the West . Draw the Line PO , whose middle is D ; and determine how much more you would take , for the greatest Elevation of your East Wall , than for the greatest Elevation of your West Wall. For I do chuse to give the East Wall a greater Elevation , that it may injoy the Morning Sun more fully : and to the West Wall a smaller Elevation ; that the Sun may come the sooner to shine upon it . Suppose , for instance , you chuse 5 Degrees , or 10 Degrees , for the difference of Elevations , between the highest East Wall , and the highest West Wall. Place those 10 Degrees , for instance , in the middle of the Arc PO , from S to T ; and let S be higher than T. And draw the Lines DS , DT . Make the little Circle PDO to serve as a Compass ; where the Point O will answer to the North Exposition , and the Point P to the South Exposition . Let your proposed Expositions look , for instance , towards the 60th Degree , taken on both sides the North : and upon the Circle ODP take OE equal to 60 Degrees . The Lines E σ , E τ , parallel to DS , DT , will give , upon the Arc AP , the greatest Elevations A σ , A τ , for the two Walls : to wit , A σ for the Wall that looks 60 Degrees East-ward , from the North Point of the Horizon ; and A τ for the Wall that looks 60 Degrees Westward , from the same Point . The smallest Elevations , belonging to the same Expositions , will be found with taking AQ equal to the smallest Elevation of the South Wall , and proceeding , with the little Circle OQ , as was done , with the little Circle OP . Now the Point Q cannot be lower than the Point O. For whatever be the least Elevation you can give to the South Wall , the North Wall requires either the same , or a lower : and never the same , but when it seems inconvenient , for Vegetation , to give a lower . If the Point Q happens to be very near the Point O , as suppose within 5 Degrees from it ; you may , upon the little Circle OQ , take O● of 60 Degrees , as before ; and draw to OQ the perpendicular eh , meeting with the Arc AP in h and so you will have the Arc Ah , for the least Elevation . And , if you think fit , you may add to and substract a little from it , at your pleasure ; if you intend to give more Elevation to the East Wall , than to the Westerly . But let it be so that you may still remain , between the Limits O , Q. However much Niceness , in so wide a Construction , is probably superfluous . ; The Heat remains sensibly the same , for the South Wall , and for the North Wall too , if , keeping their Elevation each , they are made to decline some few Degrees , from the North or from the South . This is partly plain , because the Heat , upon a Wall , whose Elevation is given , is a Maximum , when the Exposition is to the South , and a Minimum , when it is to the North. And , this not being a sufficient Proof , it is also further evident , by some Calculations , which I forbear to insert here . For thô a Maximum , or a Minimum , dos not , for the most part , alter its bigness sensibly , when the Elements , from which it results , are but a little changed ; yet it happens sometimes , as in the Points of Retrogression of Curves , that a Maximum , or a Minimum will alter very much , upon the least change in its Elements ; as suppose in the Abscisse . And not only a Maximum , or Minimum , may be found , where the Fluxions of the Abscisse and Ordinate are either of them infinitely greater than the other ; but where those very Fluxions have any determinate and finite Proportion among themselves . But a part of this has already been observed by others . This Equality of Heat is the Ground of the Construction I have given , for determining the Elevation of declining Walls . For it follows easily from it , that the Elevation of the South Wall will remain sensibly the same , thô it declines , some few Degrees , from the true South ; and that the Elevation of the North Wall will also remain sensibly the same , thô it should decline , some few Degrees , from the true North. But Experience will be , in all Climates , the properest way to determine , for each Fruit , and each Exposition and Situation , and each sort of Materials , our Walls may be made withal , the Elevation that should be given to Sloping Walls . We must now compare , as well as we can , a smooth and plane Wall , with a rough irregular Wall , and with some other Walls , that are not plane . In this Theory I have supposed hitherto the Walls to be very smooth and plane . And in that Supposition the Heat is as the Square of the Sine of the Sun's Elevation , upon the Plane of the Wall. But , if it was possible to have a Wall , of an uniform and determinate roughness every where , that could perpetually fold its rough Surface into larger and straight prismatical Furrows , so as to have always one side of the Furrows parallel to the Rays of Light , and the other side perpendicular to them , the Heat would then be , and only then , as the Sine of the Sun's Elevation upon the Wall. Which must be so understood , as not to exclude a Wall , whose roughness vanishes into an exact Plane . I am apt to think that our ordinary Walls , thô very rough and uneven , come nearer the first Supposition , than the second . But , if the second was to take place , TV , TL must , in the fourth Figure , be made equal to the Sines of their proper Arcs TP , TZ : And the Parabolas MV , ML , IV , must be turned into straight Lines , and the rest of the Calculation must be altered accordingly . The result of which would be a much smaller disproportion of Heat than before , between the Sloping and the perpendicular Wall. But , notwithstanding this , there would be yet left a very considerable Increase of Heat for Sloping Walls ; which would give a sufficient incouragement for the building of them : As will soon appear to you , by an easie Calculation , too obvious after all I have said , for me to explain it any farther . However it is not possible that the Heat should follow this Proportion . If the Heat was supposed as S½ , which is the mean proportional , between the Heats in the two former Suppositions , taking S for the Sine of the Sun's Elevation upon the Wall ; then , TV , TL being duly determined , the Parabolas would be turned into Parabolas of another Kind , where the Cube of the Ordinate would be as the Square of the Abscisse . And the Calculations woud be made after a Method like that I followed before . And the result would come much nearer my first Supposition : thô it would perhaps yet fall short of the true Increase of Heat , upon the Wall. A smooth South Wall seems to receive more Heat in all , than a rough irregular Wall. But the rough Wall receives more Heat , while the Sun shines very obliquely upon it , than a smooth South Wall would do : And it receives less Heat than the smooth Wall , when the Sun shines near full upon both . For my part I think the smooth Wall to be preferable ; not only because it seems to have more Heat in all , and looks much neater , but because it gives no shelter to Insects . The very sloping of a Brick Wall will give an advantage for the polishing or making of it smooth , by the drawing to and fro of a rough and hard Stone sufficiently plane upon it , the Stone being large and suspended from above , to some convenient place for that purpose . But we have one sort of very large and thin Bricks , whose Figure is an exact Square , already polished to our Hands . Neither should I be very fond of a Sloping South Wall , with some smooth semi-cylindrical Furrows upon it , running from top to bottom , in all the Wall ; as in Architecture some Pilasters are often made ; the flat part between the Furrows being also very smooth ; unless the Furrows were very small indeed ; which would bring the Wall so much the nearer a Plane . Any other Furrows would prove too convenient a Nest for Insects . I have calculated , more out of Curiosity , than for any real Use , the Proportion of Heat , for an Equinoctial Day , upon such a Furrow , and upon the Plane Wall , or Fascia , that could fill it up to the very Axis ; supposing the Atmosphere not to act upon the Rays of Light , and the Elevation of the Walls to be the same , with that of the Pole ; and these Walls to be turned directly to the South . And I have also calculated the Heat , that the like Fascia would receive , if it was turned directly to the Sun , for the whole Day . In the seventh Figure , where C is the Center of the Lines of Sines OA , AG , make up the Rectangles OCAD and GCAE ; and upon the Axis AC conceive the Solid formed by the Revolution of the Space OAGO , as well as the Cylinder formed by the Revolution of the Space DEGOD . The Heat of the Sun , upon the Fascia always perpendicular to its Rays , will be , at the Days end , as the Moment or Weight of the Cylinder ODEG , in reference to the Line OD ; suppose as the Number 9870. And the Heat upon the Cylindrical Surface , will be as the Moment of the Solid OAG , in reference to the Line DE , that is as 2723. And the Heat upon the inclined Fascia , will be as the Moment of the Solid OAG , in reference to the Line OD ; that is as 2467. But the inclined Fascia , or the Plane Wall , receives , in proportion to its Surface , much more Heat than the Semi-cylindrical Cavity ; as appears both by the very Numbers I have just now given ; and by taking upon the Semi-cylindrical Surface a small Space , equal to the like Space upon the inclined Plane Wall. For the Space , taken in the Cylindrical Surface , will be seen by the Sun , only for six Hours : And the most it can receive of the Sun's Heat dos but equal the Heat , that the Space taken in the Plane Wall dos receive , from Nine in the Morning to Three in the Afternoon . The Wall with the Cylindrical Furrows has some Advantage , in that the Solid , between the Furrows , not being thick , it may be heated from side to side , and in that the Reflexion of the Sun-Beams makes the Heat something closer . But the advantage will be greater if the Furrows be very close , and very small , as suppose six or ten or more in an Inch : In which case they seem to be even preferable to a Plane Wall , thô the difference between them can be but little . The whole direct or unreflected Heat , upon a Semicylindrical Space ADB , is as the Sectour DAB , the Line DA being directed to the Sun , and the perpendicular Heat being expressed by a Height equal to the Radius of the Cylinder . From whence it follows that the Heat , upon the Plane AB , is equal to the Heat , or Action of the Rays of Light , upon the Cylindrical Space ADB , when the Angle DAB is of 59 Degrees 4 Minutes , and about 50 Seconds . And so we leave off considering of Walls that are not Plane . I have , for the Reader 's satisfaction , calculated , according to the Principles that have been laid down , the following Table , which gives for all Countries , from 40 to 67 Degrees Latitude , the proportion of Heat , in the Summer Solstice , upon a Perpendicular South Wall , and a Sloping Wall passing thrô the Pole of the World. This Space dos comprehend almost all Europe . But , in the South parts of it , I should not much care for our Sloping South Walls , unless it were for some Plants of the hottest Countries , or in a place naturally temperate or cold , upon the side of some little Vale duly chosen in a high Hill or Mountain . And thus those many Habitations , which , being placed very high , are , in all times of the Year , much colder than the neighbouring Plains , and unfit upon that account , even in hot Countries , for the production of good Fruits , may hereafter injoy that blessing . And this so much the more , that the Heat of the South Wall may , perhaps without danger , be extremely increased there . So , for instance , in the middle of Spain , which is a Mountainous Kingdom , the Heat may be made , in the Solstice , ten or fifteen times greater , upon our Wall , than upon a perpendicular South-Wall . And this , or rather a part of it , will give a very good help against the coldness of a Situation , proceeding from its Height . Suppose that , in the fourth Figure , the Point τ is , as before , three times nearer to T than to V : and that the Cylindrical Surface TMV is to the Cylindrical Surface TIV as the Arc τμ to the Arc τι : You will find the Proportion , between the Cylindrical Surfaces TML , TMV , TIV , to be , at the Solstice , as in the following Table . The first Column gives the Elevation of the Pole in Degrees from 40 to 67. The fourth Column gives the Heat TIV , upon a smooth South Wall , so much inclined to the Horizon as to pass thrô the Pole of the World ; and it makes it always equal to 1000. HP TML TMV TIV MN TML TMV TIV M. N. 40 65 677 1000 838 100 1043 1540 1291 41 74 690 1000 845 100 930 1348 1139 42 84 702 1000 851 100 835 1189 1012 43 95 714 1000 857 100 755 1057 906 44 106 725 1000 863 100 686 946 816 45 118 736 1000 868 100 626 851 738 46 130 746 1000 873 100 574 770 672 47 143 756 1000 878 100 529 700 614 48 157 765 1000 883 100 489 639 564 49 171 774 1000 887 100 454 586 520 50 185 783 1000 891 100 422 540 481 51 201 791 1000 896 100 394 499 447 52 216 799 1000 900 100 369 462 416 53 233 807 1000 903 100 347 430 388 54 249 814 1000 907 100 327 401 364 55 267 821 1000 911 100 308 375 342 56 284 829 1000 914 100 291 352 321 57 303 835 1000 918 100 276 33O 303 58 321 842 1000 921 100 262 311 287 59 340 848 1000 924 100 249 294 272 60 360 855 1000 927 100 238 278 258 61 379 861 1000 930 100 227 264 245 62 399 867 1000 933 100 217 250 234 63 420 873 1000 936 100 208 238 223 64 441 878 1000 939 100 199 227 213 65 462 884 1000 942 100 191 217 204 66 483 890 1000 945 100 184 207 196 67 504 895 1000 947 100 177 198 188 I II III IV V VI VII VIII IX The Explication of the TABLE . I. Elevation of the Pole in Degrees . II. Heat upon the perpendicular South Wall , in the Summer Solstice . III. That part of the Heat , upon the Sloping Wall , that is not affected by the Air. IV. Heat upon the Sloping South Wall , in the Solstice ; its Elevation being the same as that of the Pole. V. Middle Numbers , between those of the third and fourth Column . VI. Heat upon the perpendicular South Wall , in the Summer Solstice . VII . That part of the Heat , upon the Sloping Wall , that is not affected by the Air. VIII . Heat upon the Sloping South Wall , in the Solstice . IX . Middle Numbers , between those of the seventh and eighth Column . And indeed that Heat would be always the same , if it was not for the different Effects of the Atmosphere , in several Climates , and for the various communication of Heat from the Ground to the Air , and so to the Sloping Wall. The second Column gives , in the same proportion , the Heat TML , upon a smooth perpendicular South Wall : And the third Column gives that part TMV , of the total Heat TIV , upon the Sloping Wall , that is not affected by the Air. The fifth Column gives the middle Numbers between those of the third and fourth . The three following Columns give the same Heats , and with the same Proportions ; but the Heat , upon the South Wall , is always exprest by 100. The ninth Column gives the middle Numbers , between those of the seventh and eighth . The real direct or unreflected Heats , upon the Sloping Wall , being determined , by the Atmosphere , to some Number between TMV and TIV , they cannot be very far from the Strength exprest in the fifth and ninth Column . The Use of the Table is as follows . Suppose I would know what might be at Paris , in the Solstice , the Proportion of Heat , between a perpendicular plane South Wall , and a Sloping plane South Wall , passing thrô the Pole of the World. I take the Height of the Pole at Paris , which is 49 Degrees 50 Minutes . And over against this Number I find TML , TMV , TIV must be 183 , 781 and 1000. Or else that they must be 100 , 427 and 548. I will use these last Numbers , as being more convenient . I conclude therefore that , the Heat , upon the perpendicular South Wall , being supposed of 100 Parts , the Heat , upon the Sloping Wall , is already , upon a consideration , which is not at all subject to the Effects of the Atmosphere , of 427 Parts . Besides an additional Heat of 121 Parts , that would raise it to 548 Parts , were it not that from this Number , 121 , something is to be substracted , because of the Effects of the Air. The last Column gives the middle Number 487 ; which we may suppose is not far from the real Heat upon the Sloping Wall. And this is about 4⅚ times greater than the Heat upon the perpendicular Wall. But if we go about to calculate the Heat , upon the Sloping South Wall , that passes thrô the lowest Point of the Polar Circle , we shall find the Increase of Heat , upon it , to be yet much greater . And in general a Sloping South Wall , elevated at Paris , upon the Horizon , by so much as is the Height of the Pole , wanting the whole Distance between the two Tropicks , being much hotter in the Solstice , than the Sloping South Wall , that passes thrô the Pole : it follows that any South Wall whatsoever , whose Elevation , upon the Horizon , is there between 2 Degrees 50 Minutes , and 49 Degrees 50 Minutes , must be hotter also . This comparing together of perpendicular and Sloping South Walls proceeds well enough , for the same Climate , whether it be often cloudy or often fair : provided the Clouds do not use to come more at some certain hours of the Day than at others : suppose more about Noon than in the Morning . But we cannot , from the Table , determine safely the Proportion of Heat , between the perpendicular and Sloping South Walls of several Countries ; the Interposition of the Air , and especially the difference of Weathers being almost an insuperable Obstruction against it . In the Tract of this Discourse , I have , in several places , shewn some of the Advantages we get by using Sloping instead of perpendicular Walls . I will now run over some other Advantages , that are yet untouched , or else not fully treated of . Our Sloping Walls injoy much more the benefit of the Dew and Rain's falling , than other Walls can do . And the East Sloping Wall will not have , as the perpendicular , that great fault of keeping the Rain from its Trees . The consequence of this will easily be perceived , by those that complain so much of the Drought incident to their East Walls . It is a common fault , in all perpendicular Walls , that the Ground being wet , and transpiring much humidity , this will stick upon the tender Blossoms , and in cold weather cover them with Frost , and destroy them . If our Sloping Walls do not intirely prevent this , they cannot but do it at least in a great measure : the very sloping of the Tree turning it from those Steams , and giving room for them to dissipate themselves in the Air. In like manner our Terrasses will have an advantage in reference to Frost , occasioned by the cold Vapours in the Air driving with the Wind and sticking upon Trees . For one Terrasse dos defend , in a great measure , the following Terrasses against this Accident . By our Theory the Extent of those Places , where several Fruits do grow , will be much inlarged . And not only two Zones of some Miles , or perhaps of some Degrees , round the whole Earth , one of each side the Equator , will be made able to produce , for instance , some good Grapes , whereas they afforded before only some bad or indifferent ones . But in Countries , where Vines do grow plentifully , if you mark upon the Hills , or Mountains , those Limits , where Vines do begin to be but bad or indifferent , even against Walls built after the ordinary way ; you may often take in yet a great deal more of Ground , with several Country Houses and Towns in it , and have there some excellent Vines , by the help of Sloping Walls . What is here said of Vines is , in like manner , easily understood of other Trees . So then whereas every Climate in Europe begins to lose some sorts of Fruits , for want of Heat and Time to ripen them ; we may every where open our Gardens to receive those Fruits , which hitherto we have been unable to have , thô our near Neighbours Southwards did raise them , with no extraordinary trouble . And not only the Places for the growing of Fruits are inlarged , but so are the Times also , in which we may injoy them . This advantage arising from our Walls giving probably their Fruits a Week , or perhaps a Fortnight , sooner than we could have them otherwise . For since at Paris the Fruits of good Espaliers are something sooner ripe , than those of Standard Trees ; and these last are sooner ripe , than those of Dwarf Trees : And , among the Espaliers , those of the South and of the East begin to give some ripe Fruits about eight or ten Days sooner than those of the West , and about , at least , fifteen or twenty Days sooner than those of the North ; is it not easie , from thence , to conclude that our Sloping South Walls and East Walls will give their Fruits considerably sooner , than ordinary Walls can do ? The Certainty of our latter Fruits coming to Ripeness is also much greater ; since , by our having them early , we need not fear so much the beginnings of cold and wet Weather , that might hinder them from coming to Perfection . Walls may not only be so exposed , and so inclined , as to make several sorts of Trees , growing against them , to bear early some excellent Fruits ; but , according to the same Idea , the Ground it self may be so shaped , into Slopes and Terrasses , as to bring early some of the smallest sorts of Plants , as Strawberries , Sallets &c. And as for such Plants , as cast a pretty deal of Shade , thô the same Sloping Ground might serve very well for them , yet one might also use , with some more advantage , a main Slope cut by Stories into several small ones faced with Bricks , as you see in the fifteenth Figure . In the like manner we might easily so shape the large Furrows of our Fields , or the Surface of our other Grounds , as to have them exposed to the Sun , with the same Obliquity , as the level Ground of any Country , not above 10 or 15 Degrees more to the South , or North , than we are our selves . For instance , in the Latitude of London , the Ground will have the same Exposition to the Sun , as the level Ground , in the Latitude of 45 Degrees , if going from South to North , you make , suppose for five Yards together , your Ground to rise by an Angle of 6½ Degrees , in a Slope exposed exactly to the South ; and then you make your Ground to fall as much towards the North , by a Slope as steep as it can conveniently be , suppose of 35 or 40 Degrees : and then you begin again another long and gentle Slope towards the South , for five Yards together , to be followed as before , by a short and steeper Slope towards the North ; and so on . See the eighteenth Figure . Thô we do not , by this , give the same Weather , or Heat , to the Climate , nor the same Strength , or Weakness , to the Sun , as there is in a Country , where its Rays do not pass thrô so much or so little Air ; yet at first sight it seems to be of some consequence for Agriculture , both in cold and in hot Countries ; and I could not forbear proposing it to the consideration of the Curious . If , in our Example , we do not get that degree of Heat , they have naturally in the Latitude of 45 , supposing both Countries equally cloudy ; yet , with the very Numbers I gave , we may possibly reach , upon our Ground , the Heat , which they have in 48 Degrees Latitude ; and we may yet come nearer the Heat , which the Ground has in the Latitude of 45 , if we make our Slope , that looks to the South , a little steeper ; raising it , for instance , 10 or 12 Degrees above the Horizon . There is some Ground lost here , thô not very much . As to the Trouble it is not greater than we see Countrey-men take , to make the Water to run off their Fields . And we have this conveniency , that we may give our Slopes only what Breadth we please ; suppose as much as will result from the strength of a Man to throw , with a Shovel , the Earth from him . But the broadest Slopes are best . Thus we may help and increase a little , by the shape of our Ground , the Heat of the Sun ; or else we may abate a little from it . And by consequence we may fit our Lands the better , to bear any Plants we have a mind to raise . This may serve to guide such as would plant some Vines in their Country , whether it be naturally a little too hot or too cold . For it will either lead them , as daily Experience dos others , to chuse a Ground fitly exposed and inclined for their purpose : or else , if their Ground be not proper , it will let them see a possibility and a Method , with a little trouble , to make it so . Every body knows what great difference of Heat and Vegetation there is , in the same Climate , between the North and South side of great Mountains ; and the like is , in some measure , observed , at much smaller distances , in our Hills . I remember that travelling once in England , in Summer , over some Downs , which had but an ordinary Declivity , one could plainly perceive , by turns that the Air became of a suddain much warmer , when the Declivity was towards the Sun ; and colder , when it lay from it . Yet the Sun being high then did shine upon the whole Ground . In any Shade , and even in our Woods , thô the communication be so open with the very next Air , warmed immediately by the Sun , and its Rays are let in at several places , yet the coolness is very sensible ; the Heat spreading from the ambient Air , with less ease , than one is apt to think . These considerations incline me to believe that , by this shaping the Ground , there may be something done for the benefit of smaller Plants , especially in a close place , or calm weather , when the reflected Heat may not be blown away from the Ground that reflects it . For it seems each Surface of Ground makes then , close about it , as it were a peculiar Climate . And this is farther confirmed , by the common Experiment we have , how much hotter it is , in Summer , near a South Wall , or a row of Houses , that look to the South , when the Sun shines full against them , than in any other place , where the Light of the Sun comes with the same Liberty . For it is plain the reflected Heat , being thus perpetually supplied from the Sun , dos not so much spend it self , into the open Air , but that it may be strongly felt , at some distance , all along the place that reflects it . I cannot here but mention what I heard a learned Gentleman say , who has been in the West-Indies . He assured that upon their Mountains , according as one goes up higher and higher , and the Heat dos become less , one finds , by degrees , very many of our European Plants naturally growing ; the Mountains always giving them , in some peculiar places , as it were different Climates , fitted to their several Natures . So then , as the Diminution of Heat makes the Ground naturally to bring forth the Plants of colder Countries : so , on the other side , the Increase of Heat , which in a great measure lyes in our power , must needs fit our Grounds , and Gardens , for an easie and natural Production of the Plants of such Countries , as are hotter , only to a certain degree , than ours . The use of Sloping Grounds , for smaller Plants , is pretty well known already ; especially beyond Sea. And as for these Climates , not to mention what they call in French des Ados , I have heard that a Gentleman , who lives at Dublin , has in his Garden a pretty easie Slope well exposed ; which furnishes him with Straw berries , long before they be ripe in other Gardens ; and with such Strawberries too , as have a colour , smell and taste , to which the others are not to be compared . It happens pretty often that the Sun dos shine only some part of the Day ; which makes , at such times , perpendicular Walls , in the Spring and Summer , to be frequently altogether without it . But Sloping Walls , having before them a much greater part of the Sky , are so much the more likely to injoy the Sun , if it comes at all to be seen . This advantage , as well as that of injoying more fully the Sun , at any Moment it happens to shine , is so much the more to be valued , when the Climate is apt to be Cloudy , and subject to much Rain . In pretty hot Countries , or in Climates , where their perpendicular South Walls are already as hot , as they desire to have them , one may often , by inclining another Wall , to a proper quantity , make any Exposition , from the North East Southwards to the North West , to be equal in Heat to a perpendicular South Wall. The like may be said of a perpendicular South East Wall , &c : If it be the best perpendicular Wall , in your Climate , you may make several other Expositions not to be inferiour to it , by inclining the Walls , as much as is necessary . And further , suppose Experience has taught , in your Country and Situation , the best East-South-East Wall , for instance , to be , for such a kind of Fruits , that , which is elevated 75 Degrees upon the Horizon ; you may give such an Elevation to another Wall , in another given Exposition , as will receive an equal Degree of Heat with the former . Very few Grounds have so much good Earth , as is necessary for Fruit Gardens . The charge of bringing some , from another Place , is very great : And , unless one fetches it from far , there will probably be , too near the Garden and the House , some large unsightly place left in a manner barren and desolate . Neither is it practicable to take away the good Earth , from some Parts of your Garden , to bring it to some other Parts ; except as far as your Alleys , and such other Places , will give leave . But , in a Garden for Fruit , made as I shall presently describe , one may find , upon the Spot , so much good Earth , as will much more than double the natural Depth , there was of it before ; thô you should plant your Lines of Wall Trees , in the middle of a plat of good Ground , eight or nine Foot wide . And all this may be done , without altering at all the Beauty or Symmetry , of your Disposition . The sixteenth Figure is the Ground Plat of a Garden for Trees , made up into Terrasses . It is an exact Square of 470 Foot on each side : that Figure not being so offensive , in our Disposition , as it is in that which is common . If you would have a bigger Garden you may keep the same Breadth , and add two , or four , or six , or eight Terrasses more &c , and order it so that the Door may still remain in the middle . If you design to have a smaller Garden , you may make the Length of your Terrasses less , by 50 , or 100 , or 150 Foot. And if you would have it smaller yet , you may , instead of ten Terrasses , make only eight , or six , &c. The outside Wall is about 10 Foot high ; and broader at bottom , than at top . The Breadth at bottom is 3 or 4 Foot. The Breadth at top might be made of 8 Inches ; and it would be better yet , if the Wall ended there into a sharp Edge . The sides of the Wall are plane ; and so they must needs be somewhat Sloping . Thô this may perhaps seem to be of little consequence , yet I do not doubt but it will be a considerable advantage for this Wall , to injoy thus the Sun , near the Solstice , for about half an hour , or an hour , longer of each side , than it could otherwise ; and at the same time to injoy it more fully . To which advantage there must also be added that of a greater Solidity ; which will make the Wall to be more lasting , and seldom to want any Reparations . On the inside of this Wall is a Line of four or five Foot of cultivated Ground ; then an Alley round the Garden , and a Chanel , or deep Trench , that may serve for a Drain to the Garden . I did suppose in the Figure that this Canal was faced on each side , with a competent perpendicular Brick Wall. But it should always have some Water , whose Surface ought to be about three or four Foot lower than the Level of the little Walks . One or two of those little Wind Mills , that turn alone towards the Wind , and are so common in the Fields in Holland , might serve to empty this Ditch , lest it should grow too full ; and , if one would , they might also serve to distribute the Water of it to any other place , or to the Alleys , in order to water the Trees . Those Wind Mills might be placed either within or without the Garden ; as you think it most convenient . The Breadth of the Canal must be considerable , if you design it for state and ornament ; but it may be little , if you design it chiefly for use . Unless the necessity of having some Earth from thence , for the Terrasses , makes you to chuse a large Canal . Under the Middle of the Alleys , a cross the whole Garden , should be as it were a Common-shore , to receive all the superfluous Water of the Alleys , and to carry it into the Ditch . And , if one such Common-shore was not sufficient , one might have two placed at equal distances , from the Middle of the Alleys ; so as to leave between them about half the length of the Alleys , or very little more . After the Ditch comes a little Path , and a Line of cultivated Ground . Then the Slope of the main Terrasse round the Garden . Then an Alley at the top of it . Then the inner Slope of the main Terrasse . The rest are the lesser Terrasses , with their respective Slopes on each side ; their Thicknesses at top ; the cultivated Grounds at the foot of them , and the little Walks between . The Door , and Bridge , and main Staires , to get up the main Terrasse , and lesser Staires , to go down from it into the Alleys , are easily perceived in the Figure ; whose particular measures are as follows hereafter . Thô the Sloping , in all the little Terrasses , have been made the same , and such as are properest for latter Fruits , yet it would be more convenient to have them something different . The perpendicular Height of the Terrasses is 8 Foot. The Slopes that look to the South are elevated 51 Degrees 30 Minutes , above the Horizon . Those that look to the East 45 Degrees . Those that look to the West 35 Degrees 22 Minutes . And those that look to the North 28 Degrees 53 Minutes . The Height of the South Walls taken along the Slope is 10 Foot 2¾ Inches . That of the East Walls 11 Foot 3¾ Inches . That of the West Walls 13 Foot 10 Inches . And that of the North Walls 16 Foot 6¾ Inches . The Bases of the Slopes that look to the South , to the East , to the West , and to the North have in Breath 6 Foot 4⅓ Inches , 8 Foot , 11 Foot 3¼ Inches , and 14 Foot 6 Inches . The Door is towards the East . Expositions of the Walls . Height of the Walls in the Slope . Elevations of the Walls above the Horizon . Bases of the Walls or their Talus . Perpendicular Height of the Walls .   Feet . Inches . Deg. Min. Feet . Inches . Feet . Inches . South . 10. 2¾ 51. 30 6. 4⅓ 8. 0 East . 11. 3● 45. 0 8. 0 8. 0 West . 13. 10 35. 22 11. 3¼ 8. 0 North. 16. 6¾ 28. 53 14. 6 8. 0 Here I bring into one Table the several Heights , Elevations and Bases I said did belong to our Sloping Walls . I go on to give the Measures of two several Sections cross our Garden . Measures taken across the Garden , going from South to North. Feet . Inch : 1. 6 EXternal Slope of the Wall. 0. 0 Breadth of the Wall at Top. 1. 6 Internal Slope of the Wall. 4. 8 Cultivated Ground . 16. 4 Alley . 19. 4 Ditch or Canal . 2. 0 Path. 4. 8 Cultivated Ground . 6. 4⅓ Slope looking towards the South . 13. 0 Alley at the Top of the main Terrasse . 14. 6 Slope looking towards the North. Sums . 4. 8 Cultivated Ground . 4. 9⅔ Path or Alley . Feet . Inch : 4. 8 Cultivated Ground . 98. 0 — 6. 4⅓ Slope looking towards the South . 1. 0 Thickness of the Terrasse at Top. 14. 6 Slope looking towards the North. 4. 8 Cultivated Ground . 4. 9⅔ Path or Alley . 4. 8 Cultivated Ground . 36. 0 — Feet . Inch : 36. 0 Divided as before , or with what Alterations one pleases . 36. 0 Divided as before , &c. 36. 0 Divided as before , &c. 36. 0 Divided as before , &c. 36. 0 Divided as before , &c. 36. 0 Divided as before , &c. 36. 0 Divided as before , &c. Feet . Inch : 6. 4⅓ Slope looking towards the South . 13. 0 Alley at the Top of the main Terrasse . 14. 6 Slope looking towards the North. 4. 8 Cultivated Ground . 2. 0 Path. 19. 5⅔ Ditch or Canal . 16. 4 Alley . 4. 8 Cultivated Ground . 1. 6 Internal Slope of the Wall. 0. 0 Breadth of the Wall at Top. 1. 6 External Slope of the Wall. 84. 0 — — 470. 0 Total Sum. Measures taken across the Garden , along one of the small Alleys , going from East to West . Feet . Inch. 7. 8 Wall and Cultivated Ground . 42. 4 Alley , Ditch , Path , Cultivated Ground . 8. 0 Slope looking towards the East . 13. 0 Alley . 11. 3¼ Slope looking towards the West . 305. 5½ Length of the Alley and small Cultivated Ground . 8. 0 Slope looking towards the East . 13. 0 Alley . 11 3¼ Slope looking towards the West . 42. 4 Cultivated Ground , Path , Ditch , Alley . 7. 8 Cultivated Ground and Wall. — 470. 0 Total Sum. But , with increasing the Breadth of the Canal every where , by 15 Foot more , the whole Breadth and Length of the Garden would be 500 Foot each . If the Garden be designed for Vines only , the Terrasses need not , I suppose , have more than 4 or 5 , or at most 6 Foot , in the Slope that looks to the South ; and accordingly they will be smaller , and nearer one another ; and by consequence they will be less chargeable ; and the same Extent of Ground will yield more Fruit. Supposing the Ground not to be of the very best sort , but of a middling kind , between that , and the sort of Ground Monsieur La Quintinye calls indifferent ; the Garden , whose Measures I have just now given , would hold almost 1600 ordinary Fruit Trees ; taking in those that may be placed against the outside of the Wall , that goes round the Garden . This will appear upon examining the three following Tables , where I make yet no allowance for the Trees growing bigger , against our Walls , than against the ordinary ones . But the Tables however will very well serve , to guess at the Quantity of Fruits , that will be produced . And this must be with allowing for each Tree according to the common rate of their Fruitfulness . Height of the Wall taken along the Slope . Length of the Wall. Exposition of the Wall to the Heavens . The Walls spoken of in this Table . Feet . Inches . Feet . Inches .     10. 0 456. 0 East . Outside of the Wall that goes round the Garden . 10. 0 468. 0 South . 10. 0 468. 0 West . 10. 0 468. 0 North. 10. 0 458. 8 East . Inside of the Wall that goes round the Garden . 10. 0 458. 8 South . 10. 0 446. 8 West . 10. 0 458. 8 North. 11. 3¾ 347. 6 East . Outside of the main Terrasse round the Garden . 10. 2¾ 360. 4 South . 13. 10 359. 6 West .   16. 6 360. 4 North.   11. 3¾ 27 Trees East . The Nine little Walls , at the Bottom of the Nine Alleys . 20. 2¾ and 9 Trees South and West . The Nine Corners at the right hand , at the going into the Alleys . 13. 10 16. 6¾ and 9 Trees North and West The Nine Corners at the left hand , at the going into the Alleys . 13. 10 16. 6¾ 297. 0 North. One of the North Walls of the little Alleys . 16. 6¾ 2376. 0 North. The remaining 8 North Walls . 10. 2¾ 297. 0 South . One of the South Walls of the little Alleys . 10. 2¾ 2376. 0 South . The remaining 8 South Walls . This first Table allows twelve Foot to the Gate and Pillars ; and makes the Length of a Sloping Wall middlemost , between its Length at Bottom , and its Length at Top. Only , as to the long Slopes of the little Alleys , observe that they are set down less by 8½ Foot , than what they really are at Bottom : So much being allowed , for the spreading of the Trees in the Corners . The Result of the first Table is here set down in the second . East . South . South and West . West . North and West . North. Length and Height of the Walls . Length and Height of the Walls . Length and Height of the Walls . Length and Height of the Walls . Length and Height of the Walls . Length and Height of the Walls . 914. 8 10. 0 926. 8. 10. 0 9 Trees . 10. 2● ; 914. 8. 10. 0 9 Trees . 16. 6¾ 926. 8. 10. 0 247. 6. 11. 3¾ 3033. 4. 10. 2¾ and 359. 6 13. 10 and 3033. 4. 16. 6¾ 27 Trees 11. 3¾         13. 10         13. 10         Monsieur La Quintinye divides our Wall Trees into two Classes : and , according to him , if the Ground be between very good and indifferent Soil , the Walls , whose Height is in the Table 10 Foot and 10 Foot 2¾ Inches , require the Trees of the first Class to be at eight Foot six Inches distance asunder ; and the Trees of the second Class to be at seven Foot three Inches distance asunder . The middle Number between those is about 8 Foot. But the Walls , whose Height is in the Table 11 Foot 3● ; Inches , and 13 Foot 10 Inches , and 16 Foot 6● ; Inches , require to have their Trees alternately intermixt , with making them by turns a high one and a low one : and their Distances must be about five Foot three Inches , one with another . According to these Determinations , the last Table will give the following Numbers of ordinary Trees . East . South . South and West . West . North and West . North. Trees . Distance . Trees . Distance . Trees . Trees . Distance . Trees . Trees . Distance 114 8 116 8   114 8   116 8 66 5¼ 379 8 9 68 5¼ 9 577 5¼ 27 5¼                 The total Sum of Trees is 1595. And for one Tree , that takes up 8 Foot Space , you may substitute , if you please , 3● Vines . But if the Ground be very good the Number of Trees will be less . So then our Garden might hold 1300 ordinary Trees , and 1000 ordinary Vines ; or 1400 ordinary Trees , and 680 ordinary Vines . And from thence must be estimated the Number of its Fruits . But it would be very unwise to make such high Terrasses , to serve for Vines only . For that Plant being of such a Nature , as not to do well in these Countries , if it be suffered , as it is too often done , to spend its strength in nourishing an overgrown Stock ; we may follow their Directions , that advise us to keep it so low , as to give , for instance , to Muscat only the Height from three Foot to five . A Terrasse for Vines would then be great enough , unless I mistake in drawing this conclusion , if it was but half as high as those I have described . Neither would it be necessary to allow more than half the Breadth , we did give to our Alleys , or very little besides . And since this great narrowness might prove troublesome , because of the Rain , I would in building the Terrasses spare , within , and at a good Depth under each of them , a little paved Ditch , to carry off the Rain at both Ends , and to keep the Alleys clear of too much Water . The same might also be conveniently done , in building any Terrasses , thô never so big . But , if you think it too improper , to have in one Garden a mixture of large and small Terrasses , you might cut one great Terrasse so , as to afford , in the middle of its Height , a Step for another row of Vines ; as you see in the seventeenth Figure . I should however , upon many other Accounts , and also for fear of the Vines of the lower part of the Terrasse intangling with those of the upper part , rather chuse to have a whole Garden for Vines , excepting only the bad Walls in it : And such might be , after some few changes , the sixteenth Figure ; if we suppose the outside to be only of 240 , or 300 Foot. Now , as I did already intimate once before , our Garden will probably not hold so many Trees , as are set down in the last Table . For there being more room with our Walls , than with the ordinary ones , for the spreading and growing of the Roots round about , they will make their Trees undoubtedly to grow bigger , and larger every way . The best Fault , in determining the Distances , between the Trees , is to make them too big at first ; for fear of the Confusion , and want of Fruitfulness , that attends those Distances , when they are made too small . However in this we find a new advantage of our Gardens ; since a smaller Number of Trees will garnish the same Extent of Walls , and give no fewer Fruits , than a greater Number would have done ; and will be withal more vigorous and lasting . But the Difficulty lies in guessing at the Distances we must chuse . For my part I would , for the first Tryal , if the Ground be good , not only make them as great , as the Distances , Monsieur La Quintinye determines , for the very best sort of Ground ; but make them yet , by about one sixth or one fifth part bigger . Neither would I begin to mix alternately big Trees and little Trees together ; unless the Wall were , at least , twelve Foot high . We must take notice here that the Paris Foot , used by Monsieur La Quintinye , and after him by me , is to that of London as 16 to 15. So that to the London Foot one must add ⅘ of an Inch , to make it a Paris Foot. I have drawn , with a great deal of care , according to the Rules of Perspective , in a large Print by it self , the Elevation of the South-West Corner of our Garden . Any body may judge , by the effect of this Figure , particularly with hiding the lower part , whether Sloping Walls and Sloping Trees will be much offensive to the Eye . For my part I think it may be a question whether an ordinary Fruit-Garden , with perpendicular Walls , can ever be made to look so pleasant , and so full of a regular and stately variety , as I find the Figure to be . That stateliness is altogether owing to those great and massy Terrasses , which , in our Draught , overrule , as it were , and master the whole ; and have an effect like to that of very large Columns , in our Buildings . They have besides , from so many Trees set against them , in a regular order , that Airiness and Gayity , which arise in our Architecture , from abundance of proper Ornaments . The Canal is made broader than according to the measures of the Ground Plat. It will not only be nobler , if it be very broad ; but , if you have no natural rising , in the midst of your Ground , it may yield also the Earth necessary for the Terrasses , without sinking the level of the Garden . The Figure will help to conceive how some Roofs might be used , instead of Terrasses . If the Garden be very large , and you are at a loss where to have all the Earth , that would be required ; even thô you should pretty much increase the breadth of your Canal ; keep the outermost square Terrasse untouched ; and in the middle of your Ground Plat , draw , from side to side , a large Canal , like a Cross , ending at the four ends perpendicularly against the main Terrasse . This new Canal will give the Earth you want : And each of the four Divisions of the Garden must be finished by it self , according to the Idea I have followed , in the sixteenth Figure . Only the new Terrasses , that go round the inner half of the four Divisions of the Garden , and make up the Banks of the new Canal , should not be so large , as the main Terrasse . After the same way , if the Extent of the Ground was extraordinary great , and there was yet some Earth wanting one might again , by four new Canals like a Cross , subdivide each of the four last Divisions : which would give sixteen small Gardens in all . If these Canals be designed for several Ponds , where you may keep different sorts of Fishes , they need not have any communication one with another . But if you would have the liberty of going every where , with Boats , among the Gardens , it will be sufficient , if all the Canals be opened , and continued into one another , along that Branch of the main Cross , which the Bridge dos come up to : excepting only that part of the main Terrasse , the Bridge ends against . Thus you might go , at your pleasure , either with a Boat , or walking , to any one particular Garden . As the outer Terrasses are made less and less , according as their Length decreases , so should also the Canals be made less and less broad . Now , by such Canals , your Garden might be divided , not only into four or sixteen smaller Gardens , but into any other Number . Thô such large and magnificent Gardens can only be the Work of Princes , and other Great Men , or of powerful Societies ; yet there is no ordinary Gentleman , that is able to have a Garden , but may , according to his ability , and the Directions I have given in other places of this Discourse , have one or more Terrasses , or Slopes , well exposed , of what length he can afford : So that he may have , against them , a competent number of Vines , and other Trees . And whereas they say now , for instance , I have got fifty Yards of very good Wall ; they may say hereafter , to a greater commendation of their Gardens , I have raised 30 or 40 Yards of a Sloping South Wall. It may happen that , upon some Tryals made by an unskilful Artist , our Walls may seem not to be of any use , for the Production of good Fruits . But ordinary Agriculture dos not now thrive equally , in everybody's hands . And whilst a diligent and understanding Country Man is largely repaid for his Care and Industry , the unskilful often sees himself deceived in his hopes . There will ever be a just distinction , between those that act by the certain Principles of an Art grounded upon Nature , and such as act in a great measure by chance . The same Instruments , according to the several Applications that are made of them , being managed by two several Hands , produce often both what is deservedly admired of one side , and what is as deservedly despised on the other . In a word , I do not hope , by this Theory , to make all Gardeners equal among themselves . But I give them , in all Countries , an easie , and natural , and very great Increase of the Sun's Heat ; which may often assure them of an extraordinary Success ; thô without excluding the necessary Care and Skill , which after all is the most significant Part. If what I have been proposing might , at any time , have been acceptable and useful to Mankind , it must certainly be so now . Every body has been sensible , for these twelve or fifteen Years , of a very great , and , as some think , unaccountable Change in our Seasons . Our Summers are much colder than they were ; and 't is but seldom they bring us any Thunder . Their Influence is felt in many of the Productions of the Earth ; particularly in all sorts of Fruits , that come late in the Year : for such have no Heat to bring them to perfection . And the unsettledness of our Springs commonly destroys the very first hopes we have , at the blossoming of our Trees . The cause of this Change , in our Seasons , is often the Subject of common Discourse : And it is no wonder to see how wide and empty the guesses of most people are , upon that matter . This is certain , and was made out heretofore past dispute , that from the Year 1683 downwards , and I say now even to the present time , the Sun has been in the very Middle , or Center , of a thin Mist of a prodigious Extent ; which , incompassing the whole Body of the Sun , spreads near the Plane of the Ecliptick , so as to reach almost the great Orb of the Earth ; resembling much , in its Figure , an ordinary Ocular Glass , or Lens , equally convex on both sides . It s Thickness or Opacity ( not where it is greatest , but where we may begin to see it , when the Night is already become dark ) is like that of the Tail of a Comet , or the Milky Way . But it is yet considerably greater , just in the Line that passes from the Earth thrô the Body of the Sun. Whoever has seen this Vail , that is spread between the Sun and us , will easily grant that it must needs take off some part of its Heat . There has not yet been found , at least as far as I know , any other old Footstep of this strange Phenomenon , but that in 1660 , Mr. J. Childrey , in his Britannia Baconica , has printed that he had observed it several Years together , and he desired Astronomers to mind it . Thus much seems very possible , that it might be many Years unobserved in the Sky , and perhaps have continued for some Ages , without being minded . But the very change in our Seasons seems now to be a Proof , that it has either not been at all , in former times , unless we should find in History such another Series of cold Summers , or at least that it is has not been so thick , or has not lasted so long , as at present . The true System of the World having at length been discovered , by the immortal Mr. Newton , we may perhaps guess more exactly , than heretofore , at the natural Causes of this Appearance . It seems then , at least , the outside of it , to arise from some Fumes , or Exhalations , which the Sun throws up , with an equal Strength , and the greatest it can , all about its Body , perpendicularly to the several points of its Surface . And the Sun revolving at the same time , about its Axis , in some 25 Days , occasions the spreading of that Smoak , near the Plane of the Sun 's Equator , much farther than it dos towards the Poles . The Parts of Smoak , whose Swiftness is not so great , do not rise so high ; and perform all their Motions , within the Body of the Phenomenon ; not being able ever to come near its Extremity . And , supposing several Degrees of Swiftness in those Particles , the Phenomenon ought to grow much denser , as one approaches the Sun : which our Observations also do confirm . From the Supposition that the Particles of Smoak , that fly out at the Sun 's Equator , perpendicularly to its Surface , are able to rise so far , as to reach , as by Observation they are seen to do , the Circumference of a Circle , that seems , at its Extremity , to be removed from the Sun by about 70 Degrees , I have calculated how high would rise the Particles that should , with the same perpendicular Velocity , fly out of the Poles of the Sun. And the Calculation gave me that Height , as agreed very well with the Breadth , the Phenomenon seems to have in all its Parts . It would have been easie , upon the same Grounds , to make the like Calculations , for so many points in the Section thrô the Axis , as would have made it sufficiently known ; and by consequence have served to establish , or overthrow my Conjectures . But as yet I have neglected to do it . And this is no proper place to handle this Subject more exactly . I shall only say that I look upon each Particle of Smoak , that rises from the Sun , as having its Motion as free , as if it was a Planet : The same being observed also in the Smoak , that composes the Tayl of Comets . So then each of our Particles revolves in an Ellipsis , till being near the end of its Revolution it falls into the Sun again . The whole Body of the Phenomenon is thus perpetually supplyed afresh , somewhat in the nature of those Jets d'Eau , or Water Spouts , they call in French , des Gerbes . The extraordinary small number of Spots , that appear for these many Years so seldom in the Sun , whereas in the first half of this Age they were so very numerous and so frequent , leads us to suspect that the matter of those Spots has , for several Years , been kept evaporated and dispersed , in all the Space I have just now described . For ought we know yet this Phenomenon may , at sometimes , by the supervention of a thicker and heavier Smoak , grow denser about the Sun , than at other times ; thô the outside of it spreads but to the same place , and seems not to increase in thickness . So that our Heat , in our Summers , may very much alter , without our being able to perceive any Change , in the outermost Part of the Phenomenon ; which is the only Part visible to us ; unless the Sun should be totally Eclipsed ; and give us , in the middle of the Day , an Image of a dark Night . Some Directions relating to Fruit Walls . LET the Rules and Directions given by Monsieur La Quintinye be supposed here , as the main Foundation of our Hopes , in raising Fruit Trees . To which Rules must be joyned those , that may be gathered , from the present Discourse . And to the whole the following Maxims may be yet added ; some of them being only an Abridgment of what I have already treated of more at large , and some others being yet untouched . Let all your Walls be plain , and straight on both sides . If they are to stand by themselves , without any Earth or Terrasse on either side , let them be thicker at bottom than at top , where they must end as it were into an Edge . That Edge , which is at the Top of the Wall , should stand over the Middle of its Thickness at Bottom , if you would have the Wall to be most solid and lasting . But , if you intend to favour the Trees of one side , more than those of the other side , where perhaps it is not in your power to have any Trees , the Top of the Wall may be removed , going from that side , you intend to favour , towards the other ; provided it dos yet bear directly over some part of the Bottom . And this will make that side the steeper , which probably you design for the outside of your Garden . The broader your Wall is at Bottom the better it is for Vegetation ; but the charge is also greater . 2½ or 3 Foot may be a competent Thickness . The Height will be well from 8 to 10 or 11 Foot. A higher Wall would be more chargeable , and , unless the Breadth at bottom be also increased , it would be less hot , and would not last so long . Walls of darkest Colours are best . If your Wall is to rest against a Terrasse , or Earth , having a Slope faced with Bricks on the other side , it will be well that the Plane , which parts the Earth and the Wall , be perpendicular to the Horizon ; which will make the other side of the Wall so much the more Sloping . And let the several Beds of Bricks , which make up your Wall , be , not Horizontal , but a little leaning towards the Terrasse . So the Wall will be able to witstand better the Pression of the Earth . Let the Earth of all your Terrasses , or other Sloping Grounds , which you intend to face , be throughly setled , or well beaten , before you face them . Lest that Earth , by coming to sink , should spoil the Regularity of your Wall. The perpendicular Height of such a Wall as this needs not be more than 8 Foot. If you would have a Terrasse , with solid Walls on both sides , they must be built after the same way . Let the Inclinations of all your Terrasses be made , according to the Directions , I have given at large , in the present Discourse . If your Terrasse be very Sloping on both sides , let it have some little Thickness at top ; that the Earth coming more and more to settle , the two Walls , that face it , may not come to touch one another . Terrasses that are flat at top , with a Walk there , are very Noble and neat . But if this Walk be broad , you may consider whether you had rather build two Walls breast high , on both sides of the Terrasse , so that the facing of it be not altered by them . This will save the charge of bringing so much Earth , and is capable of the Ornaments of Architecture , or else may be performed after a very plain way , and with little charge . It is most proper for such Terrasses , as have both their sides almost equally leaning . Such are those that run from North to South , or from North West to South East . You might also have a Wall breast high , only of one side of the Terrasse ; which would spare some charge , and be pleasanter in walking . This is very proper , when your Terrasse runs from East to West : for thus your South Wall , having at the Top of it the Wall breast high , your North Wall will have a more proportionable Height for Trees . See the Figures quoted in the Margin . The Ground of your Alleys may be made Sloping by some 5 or 10 Degrees &c , towards the South : which will expose it better to the Sun ; and cause the Water to run more towards the North Wall , or worst side ; and make the Ground near the South Wall to be the dryer . This will be particularly proper for Vines , which thrive best in a pretty dry Ground ; and for a Country subject to much Rain . Your North Wall might be left bare , without any Trees ; which would make the reflected Heat to be much the stronger , upon the South Wall. And then , at the Foot of the North Wall , might be sown some Plants that require , in your Climate , in the Spring and Summer , much Sun Shine , and a Ground not very dry . Such might be some Strawberries , or any other smaller Plants , that are common in Gardens . So then one side of your Alleys may be for Fruit , and the other side for all sorts of Herbs . But , if you think fit , the Earth of the North side may wholly rest , and be kept in store , to renew the Earth of the South side , as there shall be occasion . You may order , after the manner I have said , whatever Walls , or Terrasses , you build ; prefering always a Terrasse , with a Slope on each side , faced with Bricks , to an Earth , or Slope , walled on one side , and only faced on the other : as this must be preferred to a simple Wall , without any Earth . I need not say that , if in your Garden you will have but one Slope , it should be against the best Wall , and reach the very Top. A Garden may very properly be surrounded by a Slope of Earth , walled on one side , and faced on the other ; the Wall being at the outside of the Garden . But , if you please , you may not make the Slope , that would look to the North. If you will be at a greater Expence , you may have a flat Terrasse round your Garden . Or else , before your Slope , that looks to the South , build a sharp Terrasse , having the whole length of your Garden . The same you might do along your Slope , that looks to the North. And so you might have as many Terrasses , as you please . But it is best not to part them , by a Garden between , but to keep them all together ; because they will be thus better sheltered against Winds . A flat Terrasse is that , which has a convenient Walk at the Top of it ; whether it be walled or only faced on both sides . A sharp Terrasse is , for the most part , only faced on both sides , and ends at Top , as it were into an Edge ; there not being Room enough for a Walk . It may also be walled on one side , and only faced on the other . The same may be said of a Flat Terrasse . A Sharp Terrasse is preferable to a Flat Terrasse for Cheapness . A Flat Terrasse is preferable to a Sharp Terrasse for State , and for the convenience of the Walk it affords . If your Climate be subject to very dangerous Winds ; from which your Walls must be secured at any rate ; the best will be to make , in a convenient place , two Terrasses , running exactly from East to West , like those of the second and third Figure . I have no new Directions to give , about the Insides of those Terrasses . They must be faced with Bricks ; and , the Side exposed to the South being used for Fruit , the North Side may either wholly rest , or be employed as you think fit . But , as to the Outsides , these not being designed for any use , you may make them as steep as you please . Then you may fill the whole Spaces , comprehended by the indefinite Lines , or rather Planes , AM , AO ; EN , EP , continued as far as you think fit , with Trees , and very tall and thick Hedges or with Buildings , and whatever else is able to stop the Wind. Both the Ends of the Alley must be stopped , by a cross Terrasse each ; and , at their outside , the same care must be taken for a Shelter , of very tall Hedges and Trees , against Winds . Thus the Walk , between your Terrasses , will be sheltered , as much as possible , and the Heat in it will be very close , and the Sun Shine , that is lost , will be inconsiderable . I do not mean only that such Buildings and Plantations , as I spoke of , may be made about your Walk , to secure it from Winds : but that you may also take your advantage of Buildings already made , and of Trees already planted , even of those of a Forest , to make your Alley between them , and to secure it , by the Shelter they will afford . The Roots of the Trees , we are to plant against our Sloping Walls , should not be disposed after the same way , as if the Walls were perpendicular . If there be but one Root , it is best placed , when it makes an Angle , with the Body of the Tree , equal to the Angle of the Sloping Wall , with the Cultivated Ground . And then such a Root , being turned from the Wall , will be Horizontal . But , thô the Root made a smaller Angle with the Tree , yet there will be commonly some position , where it will naturally place it self , in your Cultivated Ground , in an Horizontal Situation . But this must be done with judgment , so that the Roots , of different Trees , may not too much intermix . If there be but two Roots in your Tree , when they are opposite , and both Horizontal , place them parallel to your Sloping Wall. If they be not directly opposite , they will be best , when they both bend a little downwards , from the Body of the Tree . And you will easily find what Situation is best , for the Tree , with keeping its Body parallel to the Situation it is to have , and , at the same time , turning the Tree about its own Axis . After the same way , whatever be the number of your Roots , and their Situation , you will know how to place the Tree , if you indeavour to find how all the Roots , without running too deep ; from the places , which are heated by the Sun , can best remain under Ground : especially under the Cultivated Ground , which receives more the benefit of the Dew and Rain and Sun Shine , than that which is under the Wall. And , when the Roots are long and pliant , you may place them ; at your pleasure , in a Situation parallel to the Surface of the Ground , or to the Plane of the Wall ; according as they are near the one or the other of those . The Fruits that grow pretty high , from your Cultivated Ground , will require that you should have ▪ in order to gather them , a Ladder somewhat particular , with two Arms at the upper End , by which it may be kept from the Wall , and from the Trees . And such a Ladder , being once fixed , will be near parallel to the Wall ; and will serve to gather at once all the ripe Fruits in that place ; or to do all the necessary Work about the Trees , be the Wall never so high ; till you remove the Ladder , to another part of the Wall. Some Harbours , Cabinets , or Summer Houses , in our large Garden , might be very well placed at the four Corners . They should have the full Breadth of the Alleys , or rather more ; so that they may face the middle of them directly . And the Walks may be continued into one another , by cutting a round Space , from the Corner of the Canal . I have drawn , in one of the Corners of the sixteenth Figure , some pointed Lines , which shew how I mean those Summer Houses should be made ; and what changes they will give , both in the Alleys and Canal , and in the Corners of our main Terrasse . Smaller Harbours , or Grottos , may be made under the Terrasses ; and may serve for shelter against Storms , and for Store-Houses for our Fruits : not to keep them there for a good while ; but to lay them up , till they be carried to a more convenient Place . They may be of about ten Foot Square ; and have their Floor lower than the Ground : and cause no other change , in the outer Part of the Terrasses , but that a Way must be cut to them , along that Corner of the Walk , which is exposed to the North West . They must have a good deal of Air from the Door &c. And , according as you would have them dry , you may have , under your Trees , in the South Wall , a small Window , of a convenient bigness , so much raising from the Wall , as to exclude the Rain . And , if you fear lest you Harbour , or Store-House , might prove too damp , you may make it narrower , and spread it under a greater length of the Terrasse . This will give you the liberty of making the Floor higher , and level with your Alley , or raised above it , by two or three Inches , or more . One is not apt to think that a Brick Wall , altogether smooth , and without any jetting out , and Windows , should be capable of some pretty Ornaments of Architecture . Yet I find it may be very much imbellisht , barely by the different Disposition of the Bricks : And I have given an Instance of it , in the Frontispice . There I made use only of Bricks , whose Measures are as follows . Ordinary Brick ; Length 4 Parts ; Breadth 2. Double Brick ; 4. 4. Half Brick square ; 2. 2. Half Brick long ; 4. 1. Quarter Brick ; 2. 1. But one might also imploy Bricks of different Colours and Sizes . What is done in the Frontispiece , for imitating an Architrave , Freese and Cornish , might also be done for Pilasters , and for large Partitions between them , like the Square Frames of our Wainscot , or like our Windows . I say this , after having tried it , and perceived that even the Schizzos I made looked noble and pretty ; and imitated our good Architecture , beyond what I could have expected , without having any thing either Gottick or Fanciful . The Example you have , in the Frontispice , is very much inferiour to what might have been done , if there had been more Room . And not only the Modillons , of the finest orders , might be easily imitated ; but so might also the Triglyphes , and Metopes , of the Dorick . F.I. F.II. F.III. F.IV. F.V. F.VI. F.VII. F. VIII . F.IX. F.X. F.XI. F.XII. F. XIII . F.XIV. F.XV. F.XVI. F. XVII . F. XVIII . F.XIX. F.XX. F.XXI. F. XXII . S : G : sculp : Notes, typically marginal, from the original text Notes for div A40990-e4800 Idea of sloping Walls for Fruit. Defects of perpendicular South-walls . Perpendicular South-walls , East-walls , and West-walls compared together . Perpendicular Walls compared with Sloping Walls . The same done in a particular Example for the Equinox ; and for the Summer Solstice . The result of which shews the great advantage of Sloping Walls . What Countries they are best for . A good Culture is necessary for them to have their full effect . An Instance from Experience of the usefulness of Sloping Walls . How Sloping Walls may be built with little charge : And how far the Roofs of Houses might serve instead of Sloping Walls . The Advantage of their having no Foundation . Rule for determining the quantity of the Inclination of Sloping South-Walls . Of Sloping-Walls in very hot Countries . A Table giving the Limits of the Elevation of South Walls in Temperate Countreys . It is difficult to determine those Limits in very hot Countries . The Use of the Table . Vines are commonly planted upon a rising Ground well exposed . A Hill well exposed cut into Terrasses with Sloping Walls for Fruit. Fig. I. Something like this done in China , but for another reason . Fig. I. A considerable Declivity to the South in a large Garden may be turned to much advantage . A perpendicular Wall in no Countrey so hot as a Sloping Wall proper to the Place and Exposition . The North Exposition is made tolerable by a Sloping Wall. Vse of Sloping Walls for having Fruits , Melons &c , early and thoroughly ripe . Walls of Bricks are best in England . Of Walls of Slate , or of any dark coloured Stone , whether natural or painted . Sloping Walls not to be clogged with any Shade , except perhaps in Winter , or when the Sun is very low . Sloping Walls may ascend obliquely upon a Hill ; and the use of making them so . Many Slopes in several Gardens are ready made , and fit for Sloping Walls . The goodness of a Wall proved owing in a great measure to the Exposition . The Author's Design in commending this Theory . The Advantage for Vegetation of a close and warm Air ; and of small and narrow Gardens . Fig. II , III. How to make some Terrasses running from East to West , so that the Air between be extreamly warm ; and that they be not exposed to Winds . Terrasses to be made higher when they are far asunder . Roofs may be used instead of Terrasses . Of Plants of hotter Countries . Of Orange Trees . Of some Objections against Sloping Walls . Sloping South Walls exposed to the mischiefs of latter Frosts , unless prevented . Of Remedies against an early Vegetation and Winds . * See La Quintinye . Fig. II. Sloping Walls are exposed to one sort of white Frosts . They are much exposed to Hail . Of the Trees growing obliquely to the Ground . Of the dampness that may be objected against Sloping Walls . Of their being exposed to Mice and Ants , &c. Of all other Objections against them . Calculation shewing for an Example the proportion of Heat at the Solstice , in the Latitude of 52½ upon a perpendicular Wall , and a sloping smooth South Wall , passing thrô the Pole. Fig. IV. The Ground and Method of this Calculation . The Result of it . Other Examples to the same purpose for the Latitudes of 51½ ; and 45 Degrees . Sloping Walls are more necessary in colder Countries ; but the Increase of Heat they give is greater in warmer Climates . Sloping South Wall passing thrò the Pole less hot , in the Solstice , than the South Wall passing thrô the lower point of the Polar Circle . A more accurate Method of comparing the Sun's Heat upon two plane Walls in any Situation . This Method depends upon the Quadrature and Center of Gravity of the Line of Sines and its Segments : Fig. V 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Fig. VI. Fig. V. Fig. VII . Fig. IV. and is general : and in some few Cases Fig. VI. capable of a very easie Approximation ; notwithstanding the Effects of the Air. A Corollary for finding the Heat of the Sun upon a Plane , parallel to the Horizon . A Table shewing the Sun's Heat upon a Plane for each Degree of the Sun's Elevation upon it . The Vse of the Table . The Diminution of Heat occasioned by the Air is considerable ; but hardly to be found by Meditation ; and why . A Method for finding it by some Experiments with a burning Speeulum . A Table giving the Length of a Beam of Light in the Air , supposing the Height of the Atmosphere given , &c. Fig. VIII . Of Movable Walls , in order to receive the Light of the Sun almost perpendicularly for the whole Day . Description of an Engine for that purpose . Fig. IX . X. Advantage of movable Walls against storms and winds . Their Vse for early Fruits . Of the Rain falling upon Sloping Walls . Fig. XI . Terrasses so shaped as to give some more Advantages in reference to Rain and Heat . Idea of a paved sloping Ground upon a Hill , to be used instead of Terrasses with Sloping Walls . Fig. XII . It will prevent the dissipation of the Spirits of the Earth . What the Author finds said by others , particularly by Monsieur la Quintinie , that may have some relation to Sloping Walls . * Tom. 1. p. 20. Edition of Amsterdam , 1692. An Account of what Monsieur la Quintinye calls des Ados . * Pag. 92. And of his Slopes of Earth exposed to the South or East , and purposely made for Fruit. Reflexion upon this Contrivance ; which is here compared with Sloping Walls . Part 1. pag. 205. Our Gardens , thô square , may at once injoy the Sun upon their four Walls . In Monsieur La Quintinei's Ground Plat of the French King's Garden no footstep found of Sloping Walls . To what degree they may be unpleasant to the Eye . Objection from Monsieur la Quintinye's English Translation solved . Account of an Amphitheater with Sloping Walls . And of some Melons , and other Fruits , heated with Convex Glasses . The fault of Vines that are commonly made to grow against a Roof , or the Coping of a Wall. Judgement of those and all other such Trials , in order to make the most of the Sun's Heat . Caution against too much Heat Sloping Walls are like to procure . Fig. XII . Frames called Espaliers by the French recommended , to take off some of the Sun's Heat , and to give more liberty to Trees . A Method for chusing the Elevation of a Sloping Wall , in any Exposition whatsoever . Fig. XIII . The Heat sensibly the same , upon a South or upon a North Sloping Wall , thô a little declining from the true North or South . A singular sort of Maximums and Minimums , very different from those that are commonly considered . The same , in some measure , already observed by others . The Ground of the foregoing Method . Experience must also be consulted . Of Walls that are not smooth . There can be no such thing as a Wall giving the Heat proportional to the Sine of the Sun 's . Elevation upon it . But if there was , the [ Fig. IV. ] Method of calculating the Heat upon it would be easie . And Sloping Walls would be yet very advantagious , even in that supposition ; thô less than before . Of a Wall giving a mean proportional . Heat , between such a Wall as this and a Plane Wall. A smooth Wall compared with a rough Wall. How to make a Brick Wall smooth . Of a Sloping Wall with Semi-cylindrical Furrows upon it . These Furrows compared with a Plane Wall of the same breadth with them . Fig. VII . Fig. XIV . Measure of the Heat upon a Semicylindrical Space . An Account of a Table giving , from 40 to 67 Degrees Latitude , the Proportion of the Sun's Heat , in the Solstice , upon a perpendicular and a Sloping South Wall. The Use of Sloping Walls , in very hot Countries , in such situations as being high , are naturally temperate or cold . The Table it self , and its Explication . The Vse of the Table . Example for Paris . Of South Walls that are more inclined , to the Horizon , than the Wall that passes thrô the Pole of the World. Perpendicular and Sloping South Walls may be well compared together in the same , but not in different Climates . Of some other Advantages of Sloping Walls : In reference to Dew and Rain ; especially as to the East Wall. In reference to Frost occasioned by the Earths transpiring sonte moisture : Or by the cold Vapours in the Air driving with the Wind , and sticking upon Trees . The growing of Fruits extended to more Countries and Places . And the time of their Ripeness , and use for Men , to more Days in the Year . Ordinary Walls compared among themselves , and with Sloping Walls , as to the forwardness of their Fruits . The Certainty made greater of our latter Fruits coming to Perfection . Slopes of Earth for smaller Plants . Of the dividing a main Slope into many small ones . Fig. XV. Of shaping the Level or ordinary Ground , into very large Furrows running East and West , with a gentle Slope Southwards , and a steep one Northwards , or contrarywise ; in order to increase or diminish a little the Sun's Heat . Fig. XVIII . Application of this Practice to Vse . Of the difference of Heat , upon the North and South side of Mountains , Hills and Downs . The Heat of the Air in any place dos not very easily spread into the next Air. Nor the reflected Heat spend it self so fast , but that it may be strongly felt . An Account of a Slope where extraordinary Strawberries are said to grow . Advantage of Sloping Walls , in such Days as the Sun is seen for some Hours only . Advantage of inclining Sloping Walls more or less , according to the Climate , Situation and Exposition . Advantage of Terrasses with Sloping Walls , in reference to a sufficient quantity of good Earth , which is easily procured . Fig. XVI . Description of a Garden for Fruit , according to the present Theory . The Vse of making the outside Wall thicker at bottom than at top . A kind of Chanel , or Ditch , to keep the Garden from too much Water . Measures of the Slopes , which are respectively made equal . But being made different they may be better fitted for several Fruits . A Table shewing the Heights , Elevations and Bases of the Walls . Measures for the Ground Plat taken across the Garden . Of a Garden for Vines only . It requires but small Terrasses . Of the Number of ordinary Trees the Garden could hold : From whence is to be estimated the Number of its Fruits , A Table shewing the Heights and Lengths and Expositions of the Walls . Short Table giving the Result of the former . Some Suppositions taken from Monsieur La Quintinye : By which a Table is made of the Number of ordinary Trees , the Garden would have . 3½ Vines to be substituted for one Tree . General Sum of ordinary Trees and Vines in the Garden . Of Terrasses for Vines only . Vines ought to be kept very low . La Quintinye . Of a large Terrasse parted into two for Vines . Fig. XVII . Fig. XVI . The Garden will not hold so many Trees , as it would , if they were to keep within the ordinary Size . The Trees in it will grow very large and why : And must be far asunder : Yet will not yield a less Crop of Fruits . They will be more lasting . A guess at their Distances . See La Quintinye Vol. II. p. 294. and Vol. l. p. 208. &c. Proportion of the London Foot to that of Paris . A Draught of the Garden in Perspective . Pag. 1. Division of a large Garden , by some Canals , into four or sixteen little Gardens , or any other Number . This will yield the Earth necessary for the Terrasses . And either give different Ponds for several sorts of Fishes : Or else open the Way , by Boats , among the Gardens : Aud leave also a Foot Way into them all . Any ordinary Gentleman may have a few Terrasses , or Slopes , well exposed . A Tryal of Sloping Walls not to be depended upon , unless made by a very good Artist . A good Culture more significant than a good Exposition . Sloping Walls very necessary , while our Summers continue to be so cold . The cause of that change in our Seasons referred to a Phenomenon like Smoak , that incompasses the Body of the Sun , and is seen to spread an exceeding great way from it . The Origine of that Smoak . How to determine the Figure of the Space it lies in . It may grow thicker , and yet not be perceived to have changed , except perhaps by its Effects . Directions about Garden Walls ought to be taken from Monsieur . La Quintinye , and the present Discourse . Let your Walls be straight . How they must be if they stand by themselves , without any Earth on either side . Fig. XIX . How if they rest against a Terrasse or Slope of Earth . Fig. XX. Let the Earth of the Terrasses be throughly setled . The perpendicular height of Sloping Walls . Their Inclination . Of a broad Terrasse and how it may be made ; Fig. XXI . Fig. XXII . When its sides are almost equally leaning ; Fig. XXIII . Fig. XXIV . And when the Terrasse runs from East to West . The Ground of Alleys for Fruit may be made Sloping towards the South . The North Wall may be left bare , and Herbs sown at the foot of it : Or else the Earth be kept resting , in order to renew that of the South Wall. Slopes preferred to Walls . If you can have but one Slope , give it the best Exposition . Of a Slope round the Garden . Of a Terrasse round the Garden . Of more Terrasses in the Garden . Of Flat and Sharp Terrasses . Description of a Walk very well secured from Winds . Fig. II. III ▪ Of the Disposition the Roots ought to have , in a Tree that is to be planted against a Sloping Wall. Description of a Ladder to be used about Sloping Walls . Of Harbours and Summer Houses , in our large Gardens . Fig. XVI . Of Ornaments of Architecture , in a Wall altogether smooth .