EXPERIMENTS ON SURFACE-FRICTION. 121 



friction per iiuit of surface were uniform, as is common] j' supiwscd, through- 

 out the length of the surface, and consequently the total resistance of a plane 

 of given Avidth varied simply as the length, the diagrams M'ould be straight 

 lines, originating at the zero-point of both horizontal and vertical scale. If, 

 again, these lines were straight, but apparently originated at a point above 

 the zero, this would indicate that there was a constant clement of resistance 

 throughout (such as head-resistance might be), in addition to the element 

 varying as the length. If, however, the lines were concave towards the base, 

 this would indicate that the friction per unit of surface decreased with in- 

 creasing length of surface. 



Since each plane, when once mounted, was, for convenience, tried through- 

 out the intended series of velocities, the results primarily shaped themselves 

 in the first-mentioned form. Some transcripts of the resuUs as originally so 

 '^lotted are shown on Plate IV., the lines on which represent the actual resist- 

 ances for any veloci'y of certain planes under certain differences of condition 

 as specified in the margin of the sheet. The cross mprks upon the lines show 

 the actual spots decided by the individual experimei cs made, and from which. 

 the curves drawn were deduced. It may be remarked that, wi.h the excep- 

 tions which will be subsequently noticed (the lines marked b' b', c' c') , there 

 is scarcely any difference between any of the lines in respect to the law of 

 variation of resistance in terms of velocity, the resistance varying throughout 

 nearly as the power 1-8 of the velocity. 



From the great multiplicity of the experiments tried, it would have been 

 confusing to show even a tolerable large proportion of the origiual reductions. 

 Those given are selected, partly as exhibiting the results of certain sligl tly 

 varied conditions which will be presently referred to, and partly as fairly 

 averaged specimens which instructively attest the accuracy of the experiments. 

 This is shown, not only by the fairness of the curves passing strictly through. 

 all the spots, but also by the consistency of the contiguous lines. 



The results which had been thus reduced to diagram according to the first 

 of the two methods supplied the data for constructing a general diagram 

 according to the second method, as shown in Plate VII. The black Hues on 

 this figure express the finally analyzed and complete results, for one quality 

 of surface only, up to a length of 50 feet, that beijig the greatest length that 

 the apparatus can command. It appeared desirable to ascertain the effect of 

 length of surface (at any rate provisionally) before proceeding to try various 

 qualities of surface ; and the process by which these results, as given in the 

 diagram, were finally arrived at requires some explanation. 



I commenced by a series of experiments on planes of various lengths, from 

 one foot to fifty feet, having all a similar surface. 



The results of this first series of experiments, when analyzed, gave lines 

 similar to the dotted line (« a) on Plate VII. This, it will be seen, is con- 

 cave towards the base, thus indicating that the friction per unit of surface 

 does actually diminish as the length of surface increases. At the same time 

 its form, as it approached the zero of speed, seemed to show, either that this 

 effect was very much more marked in the first two feet of surface, or that 

 there was considerable body-resistance involved. Moreover, the line obtained, 

 if drawn strictly through all the spots determined by experiment, did not 

 give a fair curve. 



This might have been thought to be owing to inaccuracy in the apparatu.?, 

 were it not that experiments, when repeated, always gave identical results, 

 and that, as has been already mentioned, the results for each individual plane 

 were perfectly harmonious, thus indicating that the discrepancy in question 



1872. K 



