1822.] a Body in Motion with Dead Weight. 167 
Loading the circular plate, and by this means compressing the 
spring, being both tedious and troublesome, a table was formed, 
containing the requisite weight to press the rod every half inch. 
In Table I, column 1 shows the compression of the spring in 
half inches. Column 2, the pounds, ounces, and drachms, that 
produced the effect. Column 3, the pounds, with the ounces 
and drachms reduced to the decimals of a pound. Column 4, 
the difference between the numbers in Column 3. The sum of 
these differences 1:708, divided by 9, gives the mean effort when 
compressed half an inch; and this last quotient divided by 5, 
and afterwards further reduced by decimal division, are the num- 
bers placed in the remaining columns of the same Table. The 
weights employed in these experiments were globes of lead, the 
larger one weighing one pound, the smaller eight ounces ; the 
lesser sphere was dropped from the height of 6, 12, and 18 
inches; but the larger one, for want of sufficient strength in the 
spring, was limited to the elevation of six inches. 
Column 1, of Table II, If, [1V, and V, contains the number of 
times the ball struck the brass plate, it being requisite to continue 
the experiment till the effort of the spring counterbalanced the 
momentum of the falling weight. Column 2, the depression of 
the vernier after each blow ; and Column 3, the difference of the 
numbers in Column 2. The asterisk denotes the numbers 
included in taking the mean. 
From these experiments, a globe of lead weighing one pound 
avoirdupoise, and falling from the height of six inches, has an 
impetus of 15,143 lbs. ; a leaden ball weighing half the former, 
_ or eight ounces, and falling through the respective altitudes of 
6, 12, and 18 inches, acquired a momentum of 6,600, 12,899, 
and 19,600 pounds avoirdupoise. Half 15,143 is 7,572, which 
exceeds 6,600 by 972, or nearly one pound. This difference 
may be partly attributed to error in the experiments, and partly 
to elasticity, which may have a greater proportionable effect on 
the smaller sphere than on the larger. The resistance of the air 
in these experiments is so trifling as to be unworthy of notice. 
It is demonstrable that if a body falls through any space, and 
moves afterwards with the velocity gained in falling, it will 
describe twice that space in the time of its falling. Assuming, 
therefore, that a body in this latitude falls in the first second of 
time, a space of 193,144 inches, or 16,095 feet, by a well-known 
theorem v = 2 / gs: g representing 16:095, the space a body 
falls in the first second of time; s the height of 6, 12, and 18. 
inches. 
The uniform velocity acquired by a body falling through the 
spaces of 6, 12, and 18 inches, will be 5,6736, 8,0238, and 
9,827 feet. On the supposition that the impetus is proportional 
to some power of the velocity represented by m, V and v being 
symbols of the velocity, I and 7 those of the impetus. V™: v™ :: 
log. I — log. i 
log. V — log. v" 
I :7; and the exponent m = By comparing the 
