26 
MR. J. J. WATERSTOX OX THE PHYSICS OF MEDIA COMPOSED OF 
and assuming the specific heat of air to be 0‘238 that of water, # we may ascertain the 
mechanical value of 1 applied to 1 lb. of water, which is equal to degree applied 
to 1 lb. of air. Since 820 cubic feet of air at 60° and 30 in. tension weigh as much as 
o 
one cubic foot of water, we have — 3444 cubic feet of air which, heated one 
degree without being allowed to change its volume, requires as much beat as one 
cubic foot of water to raise it one degree. The absolute temperature at 60° is 520°, 
and one degree added augments by part the absolute heat or molecular vis viva of 
the air. But the whole vis viva in 3444 cubic feet of air at the temperature 60° and 
pressure 30 in., is equal to the whole pressure of the atmosphere on a square foot, 
acting through three times 3444 feet in height, or 10,332 feet (XIII.). The pressure 
of a column of 30 inches of mercury on a base of 1 square foot or 144 square inches 
is equal to 14722 lbs. X 144 = 2120 lbs. This weight raised through 10,332 ft., 
corresponds to 21,904,000 lbs. raised one foot high, and 'part of this, or 
42,043 lbs., raised one foot high represents the absolute mechanical effect of 1° of 
heat applied to one cubic foot of water. Dividing this by 62^, the number of lbs. in 
a cubic foot of water, we get G73 lbs. raised one foot high equal to the mechanical 
effect corresponding to 1° of heat applied to 1 lb. of water. This compared with 
Mr. Joule’s result is not unsatisfactory considering the difficulties that attend the 
experiments that afford the data.tj 
Section IY.—On the Resistance op Media to a Moving Surface.^ 
26. The simplest case of resistance is that attending the motion of a rigid and 
perfectly elastic plane moving in the direction of its perpendicular. 
Let the velocity of its motion be z, which we must at first assume to be indefinitely 
smaller than v, the square root of the mean square molecular velocity. Let a molecule 
with velocity u, impinge on the front surface of the moving plane at an angle 6 ; 
the impinging velocity is u sin 6 ; and applying the formula for the meeting 
impact (§ 2) the velocity of reflexion is u sin 6 + 2z, and the square of this is 
u 9 sin 3 6 + u sin 0 4z fl- 4z 2 . The increment of molecular vis viva received from the 
* Xote E (specific heat of air). 
f Xote F (M. Clapeyron’s view of the motive power of lreat examined). 
X [This is an independent calculation of the mechanical equivalent of heat, quite distinct from that of 
Mayer.— R.] 
§ [The weak point in the argument of this section appears to he the neglect of the effect of the altered 
velocities of the reflected molecules in disturbing the condition of those about to impinge. The results 
can only apply when the dimensions of the obstacle are small in comparison with the free path of the 
molecules. 
The non-agreement of his theory with observations upon the resistance experienced by obstacles which 
do not comply with the above condition, unfortunately led the author to take the step in the wrong 
direction explained in §§ 27, 28. But it is proper to note that the author speaks with hesitation (§ 29). 
-R.] 
