486 ON CERTAIN APPROXIMATE FORMULA, ETC. [59 



latter. Also, the resistance varies nearly as the cube of the velocity, both 

 when v lies between 850 f.s. and 1040 f.s., and also when it lies between 

 1100 f.s. and 1300 f.s., but the coefficient increases from 74'4 in the former 

 to 108'8 in the latter case. Again, for velocities which are nearly equal 

 to that of sound in air, the proportionate increase of the resistance is much 

 greater than that of the velocity. 



Mr Bashforth remarks that the points of transition from one law of 

 resistance to another, as stated above, are somewhat arbitrary, but that, if 

 they were changed a little in either direction, the practical error would 

 not be large. 



Of course, if we had at our disposal much more numerous and still 

 more accurate observations, it would be possible to represent the experi- 

 mental results with any degree of exactness that might be desired, by 

 subdividing the observations into a larger number of groups, so that the 

 limiting velocities in any one group should be closer together, and that 

 the change of the index of the power of the velocity in passing from one 

 group to the next should be less abrupt. 



