546 REPOKT — 1888. 



the tail produced a force of 140 lbs. at the head, whereas at 180 ft. per 

 minute 5^ lbs. was required to obtain the same result. With a very short 

 coil of section c, having only five convolutions, the sleeve inside the coil 

 could be rapidly revolved, with no apparent resistance ; but directly the 

 speed was reduced below a certain limit, the coil gripped with its full 

 force. ^ It may be that further experiments in this direction will throw 

 some light on frictional resistance at high velocities. 



The foregoing results, which are a brief resume of the experiments 

 upon the four typical coils, at first appear to be contradictory.' Two of 

 the coils behave in a very different manner to the other two. Thus, with 

 a and c, after allowing for the stiffness of the spring, the experiments 

 agree with the usual theory, which assumes that the forces at the two 

 ends of the coil are directly proportional to each other when the arc of 

 contact and coefficient of friction are constiint, as was the case in the 

 experiment. This is not so evident with the former of the two. in which 

 the 8tifi"nes.s of the coil and the manner in Avhich it acted prevented very 

 accurate results being obtained. With the latter it is easy to see that an 

 equation of the form 



represents the results, F being the force on the tail, R being the resistance 

 on the head, while k and m are constants. The exact value of m is 3-625, 

 this being a measure in lbs. of the stiffness of the spring, since when the 

 resistance is zero, m is equal to the force on the tail in lbs., and it will be 

 seen that for each increase of i lb. on the tail there must be an increased 

 resistance of 80 lb. on the head. With the coils h and d there is no such 

 proportion between the two effects, but when once the coil comes into 

 operation the grip is sudden and absolute. The explanation is found by 

 reference to the dimensions of the coils themselves, when it will be seen 

 that the section towards the tail in the case of b and d is much less than 

 that in the case of d and c ; thus, when the initial resistance in the latter 

 case to closing the coil due to its stiffness is overcome, the bearing is 

 continuous, and the force then on the tail is probably far in excess of 

 that which would be required to even tear off the head of the coil. It 

 will thus be evident that on attempting to make use of metal coils for 

 practical purposes two distinct modes of operation are available, which, 

 although so very different, can be obtained by merely varying the 

 relation between the number of convolutions and cross section of the coil. 

 Where a definite ratio is required between force and resistance, then the 

 number of coils must be reduced or the cross section towards the tail 

 increased; but if small constant force only is available to put into 

 operation, whatever be the resistance at the head, then the convolutions 

 must be sufficiently numerous and the tail end of the coil sufficiently 

 flexible. The objection to the former is that any variation in the 

 coefficient of friction makes a considerable difference in the result; 

 but in the latter case, where the force required to start the coil is so 

 extremely small, some effective means of releasing the grip when it 

 reaches a certain definite amount would enable such coils to be effectively 

 applied for purposes such as clutches and brakes. 



Note. — In the discussion which followed the reading of the paper, 

 various suggestions were made to account for the peculiar effect of the 

 lubricant in increasing the effective action of the coil. The authors, upon 

 further consideration, believe the true reason to be as follows. At times, 



