Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ſtentiam fili, quæ certe permagna erat, ac de pendulorum inventa
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reſiſtentia ſubduci debet. </
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>Hanc accurate definire non potui, ſed
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majorem tamen inveni quam partem tertiam reſiſtentiæ totius mi
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noris penduli; & inde didici quod reſiſtentiæ Globorum, dempta
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fili reſiſtentia, ſunt quam proxime in duplicata ratione diametro
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rum. </
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>Nam ratio 7 1/3-1/3 ad 1-1/3, ſeu 10 1/2 ad 1, non longe abeſt a
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diametrorum ratione duplicata (11 11/16) ad 1.
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DE MOTU
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CORPORUM</
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>Cum reſiſtentia fili in Globis majoribus minoris ſit momenti,
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tentavi etiam experimentum in Globo cujus diameter erat 18 1/4 di
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gitorum. </
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>Longitudo penduli inter punctum ſuſpenſionis & cen
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trum oſcillationis erat digitorum 122 1/2, inter punctum ſuſpenſionis
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& nodum in filo 109 1/2 dig. Arcus primo penduli deſcenſu a no
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do deſcriptus, 32 dig. Arcus aſcenſu ultimo poſt oſcillationes
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quinque ab eodem nodo deſcriptus, 28 dig. Summa arcuum ſeu
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arcus totus oſcillatione mediocri deſcriptus, 60 dig. Differentia
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arcuum 4 dig. Ejus pars decima ſeu differentia inter deſcenſum &
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aſcenſum in oſcillatione mediocri 2/5 dig. Ut radius 109 1/2 ad radi
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um 122 1/2, ita arcus totus 60 dig. oſcillatione mediocri a nodo de
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ſcriptus, ad arcum totum 67 1/8 dig. oſcillatione mediocri a centro
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Globi deſcriptum: & ita differentia 2/5 ad differentiam novam 0,4475.
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Si longitudo penduli, manente longitudine arcus deſcripti, augere
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tur in ratione 126 ad 122 1/2; tempus oſcillationis augeretur & velo
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citas penduli diminueretur in ratione illa ſubduplicata, maneret
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vero arcuum deſcenſu & ſubſequente aſcenſu deſcriptorum diffe
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rentia 0,4475. Deinde ſi arcus deſcriptus augeretur in ratione
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(124 1/31) ad 67 1/8, differentia iſta 0,4475 augeretur in duplicata illa ra
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tione, adeoque evaderet 1,5295. Hæc ita ſe haberent, ex hy
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potheſi quod reſiſtentia Penduli eſſet in duplicata ratione velo
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citatis. </
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>Ergo ſi pendulum deſcriberet arcum totum (124 1/31) di
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gitorum, & longitudo ejus inter punctum ſuſpenſionis & cen
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trum oſcillationis eſſet 126 digitorum, differentia arcuum de
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ſcenſu & ſubſequente aſcenſu deſcriptorum foret 1,5295 digito
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rum. </
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>Et hæc differentia ducta in pondus Globi penduli, quod erat
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unciarum 208, producit 318,136. Rurſus ubi pendulum ſuperius
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ex Globo ligneo conſtructum, centro oſcillationis, quod a puncto
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ſuſpenſionis digitos 126 diſtabat, deſcribebat arcum totum (124 1/31)
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digitorum, differentia arcuum deſcenſu & aſcenſu deſcriptum fuit
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(126/121) in (8/9 2/3), quæ ducta in pondus Globi, quod erat unciarum (57 1/22),
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producit 49,396. Duxi autem differentias haſce in pondera Glo
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borum ut invenirem eorum reſiſtentias. </
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<
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