ON THE VIBRATION OF PENDULUMS. 35 



if ftraight, would have met the original furface ; for on account 

 of the rounding off of this angle, it extends nearly twice as far. 

 The effect of reducing the breadth of a river may be determin- 

 ed in a manner nearly fimilar. The author remarks, that a 

 confiderable diminution of breadth produces but a fmall eleva- 

 tion, a refult which appears to be conformable to experience; 

 but that where depth is required for navigation, it may often 

 be obtained by a projection built out from the bank, which may- 

 be fufficient to increafe the river's velocity, and to caufe it to 

 excavate* its bed . 



(To be concluded.) 



VI. 



Experimental Proof, that Corrections deduced from the Arcs of 

 Vibration of a Pendulum in Vacuo, are practically ufeful. By 

 Mr. Ezekiel Walker. 



To Mr. NICHOLSON. 



SIR, Lymi, Aug. 20, 18Q2. 



Y OUR annotation on my laft paper * convinces me, that I Introduction* 

 ought to have given you my reafons, derived either from theory 

 ©r experience, for troubling you on the fubject which it con- 

 tains. 



Though theory may be too uncertain a guide to be depend- Arguments 

 ed on, in a matter fo complicated as the vibration of a pendu- ™ ^J^ ^ r * d 

 lum in a variable refitting medium, yet I think that fome philo- plying the theory 

 fophical arguments might be advanced in its favour; butthefe of Pendulums to 

 I fhall not at prefent enter into, as I mean to confine myfelf to 

 mere matters of experience. 



The clock which I ufed formerly was made by the late Mr. but at prefent 

 John Arnold, in his belt manner. It had a dead beat, with a the author con-* 

 compound pendulum that vibrated in the arc of a circle. This e xltr{meatol° 

 pendulum frequently varied in its arc; and as the (hort vibra- facH. 

 tions were performed in lefs time than the long ones, I was led 

 to fuppofe that it might be governed by the fame law, which 



* See Vol. III. p. 273. 



D 2 obtains 



