[ 99 ] 



fupporting it, is fcrewed to a tree &c. be made fleady enough 



by a weight, thousjh it be not fufpended in water ; and fince a 



N 2 flone 



weight (hould be kept raifed in tlie water, and that the interval between the point 

 of fufpenfion and the weight fliould be thus (hortened, than that the ftrong wire 

 with which I connedled it to the fttrn, fliould be ftretched : hence fince fuch vi- 

 brations of mufical firings are greatefl juft after the impulfe which produces them, 

 and die away quickly, perhaps if fuch a compound pendulum were applied to a 

 clock, and the ftroke of the pallet applied near the end of its afcent, it would be 

 likely to acquire the cycloidal properties, by being fliortened towards the extremities 

 of its arch, dnring moft of the inftants of time it fpends there ; efpecially fince the 

 fame force or maintaining power, would enlarge or diminifli the muCcal and pen- 

 dulous vibrations together, and might therefore adjuft the length of the pendulum 

 in every part of its vibration, fo as to make its accelerating force as its diftance 

 from the point of reft. 



As the extent of the difadvantagcs which would attend an enlargement of the 

 fize or weight of the inftrument beyond what is neceflary, may not be obvious, I 

 mud obferve, that the accuracy of obfervations made by it chiefly depends on its 

 lleadinefs in refifting the wind -, and fince the action of the wind is not momentary 

 but continued, its effefl: will be probably proportional to the extent ef furface 

 expofed to it, and alfo to the quantity of matter it impels, and will be in a ratio 

 compounded of both thefe, i. e. of the furface of the mirror and frame which is in 

 the duplicate ratio of the diameters or dimenfions of the feveral parts; and of the 

 folid content of the inftrument, which is in the triplicate ratio of the fame 

 diameters : fo that if the diameter of each part be made twice greater in one of 

 thefe inftruments than in another, the adtion of the wind on the former will be 

 exerted on four times a greater furface than js expofed to it by the latter, and on 

 eight times a greater mafs : it will therefore elevate the extremity of the ftem, and 

 with it the appended weight, in each tremulous vibration, four times high.r, in the 

 larger than in the fmaller inftrument : and fince the momentum of each is pro- 

 portional to the verfed fine of the arch of its vibration (which is the height to 

 which the weight is raifed), and alfo to its quantity of matter-, and the magnitude 

 and duration conjointly of the tremors are as the momentum ; fo the difadvantage 



