W. A. Norton— Experiments on Contact Resistance. 445 



to the pressure. The fractions of an inch that would answer to 

 this law are as follows : For 2 oz. O'OOOIT in., for 4 oz. 0-00025 

 m., for 8 oz. 0-00033 in., for 16 oz. 0-00041 in., for 24 oz 

 0-00046 in. These values differ but little from those given in 

 the table as the reliable averages. The only material discrep- 

 ancies occur in the results for 8 oz. and 24 oz. Now the table 

 of results shows that in a few cases some cause was in opera- 

 tion to reduce the diminution of contact distance for 8 oz. to 

 nearly the value observed for 5 oz. The same tendency was 

 also often manifest in the individual experiments. If we reject 

 the results for 8 oz. in these cases, that occur in the table, the 

 average diminution of contact distance for a pressure oi S oz., 

 comes out 0'00032 in., and the discrepancv is reduced to 

 0-00001 in. Again the experimental result for the case of 24 

 oz, is 0-00003 in. larger than the law above stated calls for; but 

 the individual micrometer readings were liable to this amount 

 of error, and hence if the support had been depressed by this 

 amount, by the 24 oz. weight, it would have escaped detection. 



That the law of diminution of the contact distance which has 

 been stated is very nearly, if not the exact law of Nature in the 

 case, may also be inferred from the fact already stated, that 

 the variation of contact distance is nearly if not entirely inde- 

 pendent of the extent of the surface of contact. For if the con- 

 tact area be diminished in any ratio, say 2 to 1, under the 

 pressure of the same weight the pressure at each individual 

 point of contact would be doubled, and the increment of pres- 

 sure at each point, resulting from an additional weight of one 

 ounce, would also be doubled. Now if we suppose the law, 

 just referred to, to hold good for a given surface of contact, the 

 diminution of contact distance at each point should be inversely 

 proportional to the pressure on it, and therefore be half as 

 great for the same increment of pressure there, as in the case of 

 the larger area of contact ; but in fact the additional pressure 

 at a single point, resulting from an additional weight of one 

 ounce, is doubled, and hence the diminution of distance should 

 be the same as in the case of the larger area of contact. 



We may conclude, therefore, that in the contact of surfaces, 

 the force of molecular repulsion, in which the force of contact 

 resistance consists, conforms in its variations very nearly, if not 

 exactly, to the law that the decrement of the distance between 

 the molecules, for the same small increment of pressure, is in- 

 versely proportional to the effective pressure by which the 

 molecules are urged into closer proximity. If then we suppose 

 the distance between the molecules to be denoted by x, and the 

 effective molecular repulsion by r, and observe that x is a de- 

 creasing function of r, we may put dx=-m-. This gives, 



