100 Letter from Peter Barlow, Esq., to Dr. Lardner. 
By the solution of this equation, we obtain 
pos 1 = 2 
( and v being taken in the same measure,) and the last ac- 
quired velocity v' will be 
v= f/(v+4gh). 
Taking now the first example given in my letter, that is to 
say, a plane sloping 16 feet in a mile, and let the length of 
the plane be half a mile, (which is one of the cases in the 
Basing line given by Dr. Lardner in his table): Here, since 
v = 25 miles, and h = 8 feet: we find v’ = 29:29 miles per 
hour for the greatest velocity, and 27:11 miles per hour for 
the mean velocity; whereas, Dr. Lardner’s formula gives the 
uniform velocity of descent 103:09 miles per hour. 
The time of descent will, in like manner, by my 1™ ¢ 
formula be Seeceeseeces ess eeseese esessteseeeseesees 6 
By Dr. Lardner’s formula.......scsscssesseeseseers 0 17 
Taking the second example, of a slope of 1 in 250, and the 
length of plane half a mile, we have 
h = 103 feet nearly. 
Whence v, the greatest velocity ... ... +. = 303 miles. 
Mean velocity = 271 
Time of descenté = 1™ 5%. 
By Dr. Lardner’s formula the velocity = infinity. 
Time of descent = zero. 
With these very wide differences in our results, it must be 
that one of the two solutions is wrong, and without saying 
which, I am, on my part, quite content to leave the decision 
to those whose minds have not already received a bias from 
preconceived notions of the forces. A locomotive power is 
rather a novel consideration in mechanics; and either Dr. 
Lardner or I have certainly taken a wrong view of the subject, 
that is, of the * fundamental law of gravitations.” ‘That the 
results as computed by Dr. Lardner’s formula are inconsistent 
with practice there can be no doubt, and how that can be theo- 
retically right which is practically wrong is rather difficult to 
conceive. 
