Rev, J, B. Emmett on (he [June, 



BC, be, and complete the parallelograms CD, cd; join AB, ab. 

 By the nature of centripetal force, it is in each as I) B : c? 6. 



Naw A C : chord A B :: chord A B : A G /. A C = ±2I^L±?^ 

 similarly a c = 



AG 



chord^ a b 



Since the evanescent chord is equal to its arc, the centripetal 

 •force with which A tends to S : that with which a tends \joh r. 



A B« ah* 



ag ' ag' 



Again, since the arcs described in the same time are as 

 the velocities V and v, centripetal force at A : that at a :: 



AG • JI7 ^^ *• R*r* 



■ If T and t be the periodic times, centripetal force of A (F) : 



centripetal force of a (f) :: ^ : ^. 



Hence if the times T and t are respectively as R" and r", the 

 velocities are as -^^^ and -p;^ or V and jr;^^ and the centri- 

 petal forte F is as j^^„_t . 



If, therefore, the velocity of a particle be increased by heat, it 

 is greater at a remote than at a nearer distance from its centre 



offeree; and in this case ^737 must have a negative index, or 



2 n must be less than 1 ; therefore - ^ _ ^ must be as 1 at the 



least, or centripetal force must increase with increased distance. 

 If such a force as this existed in the particles of matter, its 

 effects upon the moon would be very great, as may be proved by 

 phenomena 2, 3, and 4. If the force of gravity vary inversely 

 as the square or cube of the distance, the greater velocity attains 

 in the smaller orbits ; which is highly inconsistent with the 

 phenomena of the solidification of liquids by cold. And in all 

 cases, if the motion be obstructed, i. e. if part of the centripetal 

 force be removed, the consequence is a diminution of the orbit, 

 "which is changed into a spiral, in which all motion soon ceases^ 

 as the bodies ultimately come into contact. If, therefore, this 

 were the cause of heat, the pressure of the atmosphere would 

 soon destroy the motion, and the body would arrive at the true 

 zero of temperature. 



The phenomena of combustion furnish us with another argu- 

 ment wnich is fatal to this hypothesis. Warm a grain of sand^ 

 not to ignition, and let it fall upon a piece of dry phosphorus ; it 

 will set it on fire, and the whole will be consumed ; intense heat 

 will be liberated ; this may communicate heat to larger masses 



