50

DEDUCTIONS from the

TRACT 34.

the radius was constantly 10 feet, or 120 inches,. which wasdivided into 1000 equal parts, and the chords of vibrationmeasured in thousandth parts of the radius, each part beingof an inch. It will therefore be convenient to reducethe recoils of the first year, to the same radius and partsas those of the other two years: which may be done asfollows:

Let r = any radius of the first year in inches,

and c = a corresponding chord of recoil, in inches andparts.

120 c

Then r : 120 :: c : —- the chord corresponding to

the radius 120, and mea-sured in inches;

, 120c 1000c , i ,

and 120 : 1000 :: —: ——- the same chord as express-ed in thousandth parts of 120 inches.

Hence then, to reduce any chord of recoil, in the firstyear, multiply it by 1000, and divide the product by itsown radius in inches ; so shall the quotient bet he corre-sponding chord answering to the radius 120 inches, andexpressed in thousandth parts of that radius.

106. By the foregoing rule then having reduced all thechords of recoil to the radius 10 feet, and denoted them inthousandth parts of that radius ; the mediums of every day’sexperiments, collected and arranged, are as follow.