J 



BOB 



has obtained in cannon balls, intendtd to pafs through the 

 air with as little obllruftion as poffible, and has fometimes, 

 for the fame reafoii, been applied as a bob for a pendulum. 

 Such a ihape is better adapted for a large bob than a imall 

 one ; for the incrcafe of the furface is in proportion to the 

 fquare of the diameter, whereas tlie increafe of weight or 

 quantity of matter is as the cube. Mr. B. Martin (Mathe- 

 matical lullitutions, vol. ii. p. 417.) propofed two equal 

 frufta of fimilar cones, to be joined together at the bafes, as 

 a ligure approximating nearly to a folid of leail rcfiftance, 

 and recommended it as that out of which the middle one of 

 three fegmcnts, cut longitudinally, will conftitute the belt 

 (hape for an appended weight, to anfwer the purpofe of avoid- 

 ing refiftance. Such a fedion, he conceived, would difplace 

 but a fmall quantity of air in one vibration, and the inipulfes 

 of that quantity, being made obliquely on the floping fur- 

 faces of the ends, would produce but a fmall effect. The 

 lenticular {hape, however, compofed of two fegments of a 

 large globe joined to the line of feftion, has been generally 

 adopted by clock-makers, probably becaufe two plates ot 

 brafs of that (liape can be eafily foldered together, and left 

 hollosv, fo as to be filled with lead, or other heavy metal, 

 in order to obtain a due degree of weight without adding to 

 the thickuefs, which is an advantage that brafs or copper 

 cannot have of itfclf in any fhape. M Ferdinand Berthoud 

 (ElTai fur I'Horlorgerie, tome. ii. chap, xiii.) made fome 

 experiments with bobs of both a fpherical and lenticular 

 Ihape, of equal weight, attached fucceffivcly to the fame free 

 pendulum, from which it appeared, that, in the fame tem- 

 perature, the latter continued to vibrate ieconds much longer 

 than the former before they arrived at the quiefcent ftate, 

 which experiment was confidered as a proof that the lenticu- 

 lar ihape has the advantage in efcaping the effeft of refiftance; 

 it was difcovered, however, on a repetition of the experi- 

 ment, with feconds and half-feconds pendulums, that the 

 friftion at the point of fufpenfion occaiioned by heavy 

 weights, particularly when vibrating in long arcs, made con- 

 iiderable alterations in the refults, and proved itfelf a fecond 

 fource of refiftance to the free motion of the pendulum. 



The fecond confideration to be attended to in making the 

 bob, as has been faid, is the weight which a given pendu- 

 lum requires, with a given maintaining power. No theory 

 is adequate to determine this defideratum of itfelf, becaufe 

 the diminution of the maintaining power by the friction of 

 the pivots and the ftate of the oil, the duration of the im- 

 pulfe on the pallets, the nature of the efcaptments in other 

 relpetls, the refiftance of the air, and at the point of fufpen- 

 fion, and particularly the nature and quantity of momentum 

 of the pendulum, muft all enter into tlie calcr.lation ; and 

 thefe are data, many of which are conlfantly varying. The 

 momentum, or whole quantity of motion of any pendulum, is 

 the weight multiplied into the fquare of its velocity, fo that 

 a large arc with a fmall weight, and a fmall arc with a corrtf- 

 ponding large weight, cxterls paribus, ought to have an equal 

 effetl upon the ifochronilm of the fame pendulum ; but the 

 theory is not perfeft ; for firrt, large circular arcs deviate 

 confiderably from cycloidal ones, which, it has been de- 

 mon llrated by Huygens and others fincc, are thofe which 

 have the ifochronal property in an uniformly denie medium ; 

 and fecondly, they require a greater maintaining power than 

 calculation gives : for inllancc, where the arc is 10° from the 

 point of reft, the addition to be made to the maintaining 

 power beyond calculation is 5^ parts in 100, according to 

 Berthoud's experinieiits, wiiich colifideration induces him to 

 conclude, thatirregulatiticain the maintaining power will affcft 

 the momentum principally corrpofed of velocity, more than 

 the momentum principally compofed of weight ; each kind 

 of monientuni, however, has its peculiar difad vantage j for 



I 



BOB 



great velocity is fubjeft to great refiftance from the air, and 

 great weight to much friftion at the point of fufpenfion. 

 ^Ir. Alexander Cummings was an advocate for a large arc with 

 a fmall bob ; but modern pra6tice is in favour of a large ball or 

 bob with a fliort arc of vibration. It feems to be generally 

 allowed, that the momentum of a pendulum ought to be as 

 great as poffible for a given maintaining power, provided the 

 latter be iufticient to overcome all obftacles to conftant mo- 

 tion ; but as the momentum is obtained in two different 

 ways, it may be proper to fubjoin here an ilhiltration of them. 

 If a pendulum, moving in an arc of one degree from the 

 quiefcent point, with a bob or ball of fix pounds, have its 

 momentum denominated by unity, then the fquare of any given 

 momentum will give its correlponding weight for another 

 bob, moving in the fame arc ; or the fquare root of the given 

 momentum will give the arc of femivibration with the fame 

 weight; for inftance, a momentum 4 will require 6x4 = 24 

 for the weight where the arc remains unaltered ; but the root 

 of 4=2 will be the arc from the point of reft with the fame 

 weight ; again, if the momentum be required to be 9 for a 

 given maintaining power, the weight muft be 54, or the 

 arc 3° from the point of reft, and in the fame proportion 

 for any other momentum ; but, in faft, both the weight and 

 arc may be varied according to circumftancts, which lati- 

 tude affords great variety in the adjuftment of the bob, and 

 matter for multiplied experiments to determine what weight 

 and arc ftiall be moft defirable, taken conjointly under dif- 

 ferent circumftaiices. 



The moft practicable method of adjuftment of the mo- 

 mentum of a pendulum, where a weight is ufedasthe main» 

 taining power, feems to be, to vary this power iuftead of the 

 weight of the bob or ball, which, when once finiftied of the 

 requifite (hape, is not fo eafily altered. In pendulum clocks, 

 aftuated by a fpring as a maintaining power, fuch adjuft- 

 ment cannot indeed be made in the power properly without 

 changing the fpring, or altering the fufee after they are ad- 

 jufted to each other; but as thefe inftruments are not intend- 

 ed to meafure time with great nicety, the adjuftmt h of the 

 bob to the maintaining power is exadtly done by gucfs. In 

 Huygens's beft clock, the maintaining power was equal to 

 three pounds, falling about go inches in 24 hours, and the 

 ball of its feconds pendulum, together with the pendulum 

 itfclf, was alfo three pounds ; but the nature of his cfcapcment 

 required the vibrations to be performed in long arcs. Cum- 

 mings tried different weights for his pendulums from 6 to 16 

 pounds, and various arcs from 3° to 6° from the point of 

 reft ; but it does not appear that any other ftandard has 

 been adopted by clock-makers than what accords with the 

 individual opinion of each. See Maintaining Power. 



Bob, in Ringing, denotes a peal confifting of feveral courfes, 

 or fets of changes. 



BoB^iTy, in Sea-Language, a rope ufed to confine the 

 bowfprit of a ftiip downward to the ftem, or cut-water, and 

 to counteraft the force of the ftays of the fore-maft, which 

 draw It upwards. 



It is fixed by thrufting one of its ends through a hole 

 bored in the fore-part of the cut-water, and then fplicing 

 both ends together, fo as to make it two-fold, or like the 

 link of a chain ; a dead-eye is then feized into it, and a lan- 

 iard pafling through this, and communicating with another 

 dead-eye upon the bowfprit, is drawn extremely tight by help 

 of mechanical powers. The bob-ftay is the firft part of a ftiip's 

 rigging, which is drawn tight to fupport the mafts. With 

 this view, it is ufual to fufpend a boat, anchor, or other 

 weighty body, at the bowfprit end, to prefs it downwards 

 during the operation. 



BoTi-Jlay-ho/es, are thofe holes in the ftem, or fore-part of 

 the knee of the head, to which the bob-ftay is fattened. 



BQBAC, 



