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b'.:".;b!e? nfcefTarv to fill vlicin being found nlmoft evaj tliat if the J'ameterof a balloon be 35 feet, its circwtrfL-rence 

 wii:rL-, fo that when the nrovlGon of fuel is cxliaufted, the will be I !0 feet. If tlie diameter be multiplied by tii; cir- 

 aeronaut may defccud ;ma recruit liis fuel, in order to pro- 

 ceed on his vf.yage. But thty nuift be larger than balloons 

 of til.- other fort, in order to lake up the fame wei^'ht ; and 

 the prefence of Crc is a continual trouble and a continual 



danj^cr. Experience has, in many inftances, envinced the 

 difalirous comequences that have attended them. On the 

 other hand, the inflammable air balloon mull be made of a 

 fnbftance irapenneable to the fubtile gas ; the gas it fclf can- 

 not b: produced without a confiderable expence ; and it is 

 not eafy to find the materials and apparatus neecfTaiT- for 

 the prod'.'.Aion of it in eveiy place. Improvements, how- 

 ever, daily occur in the preparation of the coverings of 

 thefe balloons, fo as to render them nearly impermeable to 

 the inflammable air : and it has been found that an in- 

 flammable air-balloon, 30 feet in diameter, may be fo made 

 as to fuftain two pcrfons and a confidcrable quantity of 

 ballail in the air for more than 24 hours, when properly 

 managed ; and one man might poflibly be fupported by the 

 fame machine for three day.i. 



Afrostatios, piiiclice of. The (liape of the balloon is 

 •ne of the firft objecls of confideration in the conftruftion 

 ©f this machine. As a fphere admits the greateft capacity 

 tinder the Icaft furface, the fpherical figure, or that which 

 approaches nearell to it, has been generally preferred. 

 However, fince bodies of thii form oppofe a greater furface 

 to tiie air, and conftqucntly a greater obibiiftion to the 

 aclioii of the oar or wings than thofe of fome otlier form, 

 and tlierefore cannot be fo well guided in a calm, or in 

 a courfe different from the direction of the wind, it has been 

 prdpofed to conllruft balloons of a conical or oblong figure, 

 and to make them proceed with their narrov/ er-d forward. 

 Mr. Hoole, an ingenious writer, who is now publifliing a 

 tranflation of the works of Leeuwenhoek, in his Thoughts 

 on the farther Improvement of Aeroftation, fuggeils the 

 Ihape of a filTi as the mod proper ; the fliarp head, under 

 fuch a form, will ferve to divide the refifting iluid, 

 and open a paflage, and the tail will ferve as a rud- 

 der to fteer its courfe. He alfo propofes to fix a feat 

 for the traveller in the lower part of the body of the 

 fi(h, or in tlie centre of gravity of the whole mafs, fo 

 that the machine may be always horizontal, and that 

 the impulfe of any force ufed there may aftuate the whole 

 body. And he farther fuggefts, that the traveller fiaould 

 be furniflied with inilruments of fufficient furface to take 

 hold of the air, and of fufficient ftrength to bear the whole 

 exertion of his mufcular force, analogous in their form and 

 Situation to the fins of fiflies. But by adopting the oblong 

 fhape, the furface, and confequently die weight of the 

 cover, muft be augmented, in order to obtain the fame 

 lifting power with that of a fphere, both becavife its capa- 

 city will be lefs under the fame furface, and becaufe its 

 capacity muft be made greater in order to compeniate for 

 the augmentation of weight. Befides, an oblong machine 

 cannot eafily be kept with the fmallefl: part forward in the 

 atmofphere ; and if it ihould turn fideways, as it probably 

 might, the propofed advantage would thereby be loft : not 

 to add, that accidental circumitances might occur which 

 would endanger its overturning. 



In order to expedite the calculations that relate to the 

 «onftruftion of a balloon <3f a fpherical form, it fhould 

 be remembered, that the circumferences of fpheres are 

 as their diameters ; their furfaces as the fquares ; and their 

 fohd contents as the cubes of the diameters. The pro- 

 portion of the diameter to the circumference of a cir- 

 «k, i. t, 7 to 22, or I to 31, fhould be rccolkfted ; lj» 



cumfereuce, the produtSl will be the furfiice of the fphere ; 

 i.e. ^5 X 1 10=3850 fquare feet. If this furface be divided 

 by the breadth (in feet) of the (luff of wiiicl; the b::lloon 

 is made, the quotient wiil be the number of feet in length 

 neceflary for conftrudling the balloon : thus, if the ituft" be 



3 feet wide, — ^ = 1283] feet, or 428 yards nearly, which 



is the quantity for a balloon of 35 feet in diameter. By 

 knowing the v/eight of a given piece of the ituiT, as of » 

 fquare yard or fquare foot, it is eafy to find the weight of 

 the whole bag, by multiplying the furface in fquare feet m 

 yards by the weight of a fquare foot or yard ; c. g. if each 

 fquare yard weigh 16 ounces, or one pound, the whole 

 bag wiU weigh 42S pounds. Agam, the capacity, or folid 

 content of the fphere, may be found by multiplying -K of t!ie 

 furface by the diameter, or by taking \\ of the cube of 

 the diameter ; thus, in the prefent inftance, we (hall have- 

 22458 cubic feet for the capacity of the balloon, or the 

 number of cubic feet of air which it will difplace. From 

 the content and furface of the balloon, we may deduce its 

 power of afceufion or levity in the following manner : — a 

 cubic foot of air vreighs, at an average, about l\ ounce, 

 and adding to the number 22458, its fifth part, we flii'd 

 have 26950 ounces, or 1684 pounds, for the weight of the 

 common air difplaced by the balloon. From this weigiit, 

 dedufting the weight of the bag, or 428 pounds, tliere 

 will remain 1256 pounds expreffing the levity of the bal- 

 loon, independently of the contained air. If this be Inflam- 

 mable air, its weight varies from 5- to -jJ,; the weight of 

 common air ; if it be taken at -g- of the weight of common 



air, then — - — =r 280 pounds will denote the weight of the 



air filling the balloon ; and taking this from 1256, /. e> 

 1256 — 280, will leave 976 pounds, the power of afcenfion 

 of the balloon, or the weight which it will carry up, con- 

 fifting of the car, ropes, palfengei-s, ballaft, and other 

 neceifaries. If heated air be ufed, the denlity of this is 

 diminiflied about one-third ; and therefore, taking from 

 1684 one-third of itfeif, there will remain 1123 for the 

 weight of the contained warm air, and this fubtraclcd from 

 1256, leaves 133 pounds for the levity of the balloon ; but 

 as this is not fufiicient for carrying up the car, paflengers, 

 &c. it is evident that a larger balloon, on Montgolfier's 

 principle, is neceflarv for the fame purpofe that may be 

 effedled by a fmaller one of inflammable air. To eftimate 

 the power of afcenfion correfponding to any given weight, 

 e.g. 1000 pounds ; fince the levities are nearly as the cubes 

 of the diair,<;ters, and confequently the diameters as the 

 cube roots of the levities ; and the levities being as 133 to 

 1000, i.e. nearly as I to 8, the cube-roots are as i to 2 ;. 

 confequently I : 2 : : 35 : 70 feet, the diameter of a 

 Montgolfier, made of the fame thicknefs of ftuff a; the 

 former, and capable of hfting 1000 pounds. Purfuing the 

 fame kind of calculation, it is eafy to eftimate the fize of a 

 balloon, made of iluif of a given thicknefs, and filled with, 

 air of a given denfity, that will juft float in air. From the 

 weight of a cubic foot of common air, fubtracl that. of a 

 cubic foot of the lighter or contained air ; then divide 

 6 times the weight of a fquare foot of the ftuft" by the 

 remainder, and the quotient will be the diameter, in feet, of 

 the balloon that will juft float at the furface of the earth. 

 Suppofe the ftuft' to be l pound to the fquare yard, or 

 •^ ounces to the fquare foot, and this multiphed b)* 6 gives 

 ^l ; then the cubic foot of common air weighing i-l ounce, 

 and of heated air f of the fame, the difference being -^ ; 



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