VOL. XXXII.] PHILOSOPHICAL TRANSACTIONS 641 



to c at the same time. Here the equal forces will agree with the product of the 

 masses into the velocities, or into the squares of the velocities; because a X 12 

 = B X 12, as well as a X 144 is equal to b X 144. 



2. If A be taken of 4 ounces weight, and let go from d, or 6 inches, while 

 B, still equal to 2, moves from 12 inches; both bodies will again meet at c: 

 therefore here the equal forces must be expressed by the masses into the veloci- 

 ties, and not into their squares; for though a X 6 be equal to b X 12, or 4 X 6 

 = 2 X 12, yet A X 6 X 6, or 144 is but half of b X 12 X 12, or 288. 

 Whereas if the forces had been as Poleni affirms, b should have been let loose 

 only from 8,4 inches. 



3. When a is 6 ounces, it is let loose only from e, or 4 inches, to meet at c 

 with B, let loose from 12; for then a X 4 = b X 12, while a X 4 X 4, or 96, 

 is 3 times less than b X 12 X 12, or 288. So that according to Poleni, b must 

 have been let loose from 7 ; but in that case it comes sooner to c than a. 



N. B. The weight w must be greater than the weight of both balls, lest the 

 friction of the table should spoil the experiment. 



An Account of an Experiment, made to ascertain the Proportion of the Expan- 

 sion of the Liquor in the Thermometer, with Regard to the Degrees of heat. 

 By Brook Taylor, LL.D., R.S.S. N« 376, p. 291. 



It has been generally supposed, though not proved, that the expansion of the 

 liquor in the thermometer, is proportional to the increase of heat. To deter- 

 mine this matter with certainty, I made the following experiment. 



I provided a good linseed oil thermometer, which I marked with small divi- 

 sions, not equal in length, but equal according to the capacity of the tube in 

 the several parts of it, as all thermometers ought to be graduated. I likewise 

 provided 2 vessels of thin tin, of the same shape, and equal in capacity, con- 

 taining each about a gallon. Then, observing in every trial, that the vessels 

 were cold, before the water was put in them, as also that the vessel I measured 

 the hot water with, was well heated with it, I successively filled the vessels with 

 one, two, three, &c. parts of hot boiling water, and the rest cold; and at last 

 with all the water boiling hot; and in every case I immersed the thermometer 

 into the water, and observed to what mark it rose, making each trial in both 

 vessels for the greater accuracy. And having first observed where the thermo- 

 meter stood in cold water, I found that its rising from that mark, or the expan- 

 sion of the oil, was accurately proportional to the quantity of hot water in the 

 mixture, that is, to the degree of heat. 



VOL. VI. 4 N 



