THE ROLLING CARRIAGE. 09 



The resulting values of k m for the 6, 8, and 12 inch square planes are not 

 entirely accordant, as the successive sets of observations with the 12-inch plane 

 all give considerably larger values than those obtained with the smaller planes. 

 I am not disposed, however, to consider this as a real effect due to an actual 

 difference in the pressure per unit area on these planes. Such a difference, if one 

 exists, is in all probability quite small, and much within the degree of accuracy 

 possessed by these experiments. The resulting differences in the mean values of 

 k m I consider, therefore, as discrepancies in the observations, the cause of which 

 has not become apparent. In recognition, however, of the fact that other experi- 

 menters have claimed to discover a difference in the pressure per unit area on 

 planes of different sizes, I have, in general, in the preceding chapters, taken pains 

 to specify the area of the plane to which all my experimental results apply. 

 That there should be a real, though perhaps a small, difference between the 

 pressure per unit area on planes of different sizes seems in fact quite probable, 

 when we consider that the ratio of perimeter to area varies for similar shaped 

 planes of different sizes. If the side of a square plane be a and that of another 



4 . 4 . 



be na, the ratio of perimeter to surface is - in the one case and - in the other, 



which is not mei'ely an expression of a mathematical relation, but calls attention 

 to a possibly important physical fact, for it seems probable that this relation 

 between perimeter and area has a considerable influence in determining the 

 pressure on the plane, especially that part of it produced by the diminution of 

 pressure on its posterior face. 



The general weighted mean of all the values of k m is .0087, or, in English 

 measures, k = .00166, and I believe this result is within 10 per cent, of the true 

 value. These experiments lead me to place the lijpits of the value of k m for a 

 1-foot square plane between 0078 (k = .0015) and 0.0095 (A = .0018) for the 

 assumed temperature of 10° C, and pressure 736 mm., and, made as they were 

 in the open air and subject to wind currents, they are not sufficiently precise to 

 give more contracted limits. It may be noted that the value of k m obtained from 

 the experiments with the Resultant Pressure Recorder, viz., k m = .0080, falls 

 between the probable limits above assigned, and is within the probable uncertainty 

 (10 per cent.) of the mean of the results with the Rolling Carriage. The Rolling 

 Carriage, therefore, although a very sensitive and delicate piece of apparatus, has 

 not been able under the conditions of experiment to yield a sensibly better 

 result than the rougher instrument. 



