120 REPORT — 1H72. 



The lower edge consisted of a quasi keel of lead of the same thickness as the 

 plane, and made heavy enough to nearly neutralize the flotation of the light 

 Avood of which the planes were made. But though thus made stahle, and 

 approximately neutralized as to flotation, the jjlane under experiment required 

 control to keep it resolutely vertical, and the line of its length correctly 

 horizontal, while, nevertheless, it required perfect liberty in the line of motion, 

 in order that the whole towing-strain might be accurately delivered to the 

 dynamometer. 



For this purpose a light but stiffened wooden bar (Plate II. c c) Avas hung 

 longitudinally beneath the dynamometer truck, just clear of the surface of the 

 water. To this the planes were rigidly attached. This bar was carried at 

 each end by a light swing or rocking-frame (e e and e e) , thus forming a 

 parallel motion perfectlj* free longitudinally, and perfect^ unyielding trans- 

 versely. It was of course necessary to extend one of the swings above the 

 point of suspension to carry a weight adjusted so as to counterbalance the 

 weight of the bar, together with any sinking or floating force that the plane 

 might exert ; otherwise the frame would not have been in equilibriimi in the 

 line of motion except in one position, and in any other position would have 

 exerted a positive or negative force on the dynamometer. 



The rigid connexion between the planes (which were of course imder 

 water) and the swinging bar or parallel motion (which was above water) 

 consisted of a kind of sheath or cutwater (n d), which received the forward 

 edge of the plane, and had a long upper end, extending out of the water, and 

 fastened to an upright on the swinging bar with three strong pins or bolts. 

 The plane was rebated to receive tlie sides of the sheath, so that the outside 

 surface at the juncture was flush as far as possible. 



Tlie investigation of surface-friction may be separated into three primary 

 divisions : — (1) the law of the variation of resistance witli the velocity ; (2) 

 the differences in resistance due to differences in the quality of surface ; (3) 

 the differences in the resistance per unit of surface due to differences in the 

 length of surface. 



The necessity of investigating the latter of these conditions may not be at 

 once apparent, it having been generallj' held that surface-friction varies 

 directly with the area of surface, and will be the same for a given area, 

 wliether the surface be long and narrow or short and broad. It has always 

 seemed to me to be impossible that this should be the case, because the por- 

 tion of surface that goes fii'st in the line of motion, in experiencing resistance 

 from the water, must in turn communicate to the water motion in the direc- 

 tion in which it is itself travelling ; and consequently the portion of siirface 

 which succeeds the first will be rubbing, not against stationary water, but 

 against water partially moving in its own direction, and cannot therefore 

 experience as much resistance from it. If this reasoning holds good, it is 

 certain that doubling, for instance, the length of a surface, though it doubles 

 the area, would not double the resistance, for the resistance of the second 

 half would not be as great as that of the first. 



In order to reduce the results obtained to the most serviceable form for 

 determining the three separate conditions of resistance enumerated above, 

 it was convenient to represent them graphicallj^, by diagram, in two methods ; 

 in both methods the ordinates represent resistance, whUe the abscissfc repre- 

 sent in the one case velocities, and in the other lengths of surface. Plates VI. and 

 VII. are instances^of the two kinds. In the former, if the friction proved to 

 vary as the square of the velocity, the diagrams would be ordinarj^ parabola; 

 originating at the zero-point of resistance and velocity; in the latter, if the 



