Musschenbroek, Petrus van - Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae

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Corol 2. Quoniam ſinus 3 ? graduum æqualis eſt dimidio radio, adſcen-
ſus Acus Inclinatoriæ ſecundum lineam vel planum A D, in diſtan-
tia 60 graduum a Meridiano Magnetico A I, erit hic dimidium ma-
ximi adſcenſus.

Londini, ubi Inclinatio Acus pedis unius eſt 73 {3/4} graduum, &
adſcenſus ejus â Nadir 16 {1/4} graduum: ſed Inclinatio Acus 4 pedum
eſt 75 {1/6} graduum, adeoque ejus adſcenſus eſt â Nadir 14 {1/6} graduum:
Ideo adſcenſus in diſtantia 60 graduum abhinc, erit 8 {1/8} grad. per-
Acum unius pedis, & 7 {5/12} graduum per Acum 4 pedum. Notat Whi-
ſtonus ſe hoc variis temporibus exploraſſe, an experientia compro-
baretur, ſeſeque eam reſpondere demonſtrationi non modo in hoc
angulo, ſed in aliis deprehendiſſe.

Corol. 3. Conſtructio præcedens ſupponatur in plano perpendicu-
lari ad horizontem, ſupra eandem A I, tanquam ſemidiametrum
ejuſdem circuli: tum id ſupponatur locari a centro Acus Inclinato-
riæ ſecundum Magneticam directionem, ita ut ſinus A c, A d & c,
repræſentent vires obliquas, ut antea: tum inde ſupputare poſſumus
quantitatem iſtarum virium, tam in horizontali, quam in verticali
ſitu Acuum; uti una enim linea exhibet vires Acus horizontalis, ita
altera exhibebit vires Acus Inclinatoriæ, cujus planum eſt in Ma-
gnetico æquatore. Si quantitatem virium deſideramus in plano verti-
cali, prout Londini eſt, in Acubus unum pedem longis, hoc eſt
reſpectu totius virtutis ſecundum Magneticum Meridianum, hæc
eſt, uti ſinus 73 {3/4} graduum ad ſinum totum, qui eſt uti 96 ad 100.
adeoque tempora oſcillationum duarum Acuum Londini, vel in
Meridiano poſitarum Magnetico ſunt, uti hi numeri, vel proxime, ut
98 ad 100, vel 49 ad 50, quod congruit cum experientia. Si eo-
dem modo deſideramus quantitatem virium in plano horizontali,
erit hæc reſpectu virium abſolutarum in Meridiano Magnetico, po-
ſita Acu unius pedis, uti ſinus 16 {1/4} graduum ad Sinum totum, ſive
ut 28 ad 100, & poſita Acu 4 pedum, uti ſinus 14 {5/6} graduum ad
Sinum totum, vel ut 2560 ad 10000, ſive proxime uti 1 ad 4. ad-
eoque tempora vibrationum ab his A cubus peractarum, quæ ſunt in
ſubduplicata proportione horum numerorum, ſunt in primo caſu
uti 52 {9/19} ad 100, & in ſecundo proxime, uti 500 ad 1000, hoc eſt
uti 1 ad 2, quod convenit cum Experientia.

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