388 



PHILOSOPHICAL TRANSACTIONS. 



ITS '55 o5 



[anno 1794. 



1) = 



127", n = -jSgW* '•he alteration of the daily rate 



+ 2".62. 



It here appears, that a very minute alteration in the law of the force's variation, 

 amounting to no more than -ruhru P^rt of the entire ratio of the distances, causes 

 an acceleration in the daily rate of more than 24-'', when the diminution of the 

 semi-arc of vibration is 8°. It may therefore be of some use to inquire, what 

 are the differences of the weights to be observed in experiments from which the 

 law of the spring's elastic force is derived; first, supposing that law to be the 

 precise ratio of the distances from the quiescent position ; and 2dly, supposing 

 the law of the force to deviate from that ratio by a small difference of , „\ „ , so 

 as to become the -fi/o%- power of the distances from the quiescent position ; from 

 the result a judgment may be formed how far experiments may be relied on for 

 ascertaining the precise law according to which the elastic force of a spring varies. 



Values of 



Angular distances from the quies 

 cent position when the spring's 

 elastic force is counterpoised by 

 the weights in the 2d and 3d co 

 lumns. (Fig. 14). 



10° 



20 



30 



40 



50 



60 



70 



80 



90 



Values of 



P = 9 gr. X 



90° 



Weiglits p, expressed in grains, 

 which counterpoise the spring's 

 elastic force when wound to the 

 several distances from die quies 

 cent position in tlie first column, 

 if the force varies in the precise 

 ratio of the angular distances 

 from the quiescent point. 



1 Grains. 



2 



3 



4 



5 



6 



7 



8 



9 



Values of 



p = 9 gr. X 





Weights p, expressed in grains, 

 which counterpoise the spring's 

 elastic force when wound to the 

 several distances from quiescence 

 in the first column, if die force 

 varies in the -^^0 power of the 



distances 

 point. 



from the quiescent 



1.002 199 Grains, 



2.003010 



3.003298 



4.00324.5 



5.002940 



6.00:433 



7.001759 



8.000942 



9.000000 



The differences of weights expressed in the 2d and 3d columns of this table 

 are evidently too small to admit of being observed experimentally, and yet their 

 effect on the daily rate of a time-keeper amounts to a quantity far from insen- 

 sible. This effect on the rate might probably be augmented to 20 or 30 seconds 

 daily, and yet the corresponding differences of weights arising from the deviation 

 of the spring's force from the law of isochronism might be too minute to become 

 sensible by any statical counterpoise of the spring's forces; and it would be still 

 less possible to measure the said differences of weights with the exactness required 

 for the determination of the law observed by the spring's forces. Experiments 

 of this kind should not therefore be absolutely relied on for ascertaining practi 



