RAILWAV CONSTANTS. 21/ 



resistance of a body could be calculated from its form and mag- 

 nitude. The results obtained were merely negative^, showing 

 that the resistance could not be calculated on such or such data, 

 but that it depended on some principle not yet discovered, and 

 which the experiments themselves of Dr. Hutton did not de- 

 velop. 



These experiments also were made on bodies of very limited 

 magnitude : the bases of the cones, cylinders and hemispheres 

 were less than a quarter of a square foot. It will therefore be 

 apparent, that they furnish no just grounds by which the resist- 

 ance to bodies of the form and magnitude of railway trains can 

 be computed independently of experiment. How strongly Dr. 

 Hutton himself was impressed with the imperfect nature of his 

 results, and with the necessity for further experimental inquiry 

 before any i-eal or satisfactory determination of the atmospheric 

 resistance could be obtained, will be collected from the fol- 

 lowing observations, with which he closes this part of the in- 

 quiry : 



'' On a review of the whole of the premises, we find that the 

 resistance of the air, as determined fi'om the foregoing experi- 

 ments, differs very widely, both in respect to its quantity on all 

 figures, and in regard to the proportion of its action on oblique 

 surfaces, from the same actions and resistances, as assigned by 

 the most plausible and imposing theories which have been hitherto 

 delivered and confided in by philosophers. Hence it may be con- 

 cluded that all the speculative theories on the resistance of the 

 air hitherto laid down are very erroneous, and that it is from 

 experiments only, carefully and skilfully executed, that a rational 

 hope can be grounded of deducing and establishing a true and 

 useful theory of the action of forces so intimately connected with 

 the numerous and important concerns of human life." 



Since the only two sources of resistance to moving bodies 

 with which we are acquainted, are the friction of the parts mo- 

 ving upon and against one another, and the resistance of the at- 

 mosphere through which the body moves ; and since all scientific 

 experiments which have been directed to ascertain the law of 

 the former agree in showing it to be proportional to the weight 

 or pressure and independent of the velocity, and that the latter, 

 within moderate limits of speed, varies in a proportion, cceteris 

 paribus, not much departing from that of the square of the velo- 

 city ; the form which may with most probability be assigned to 

 the expression for the resistance of a railway train will be one 

 consisting of two terms, one of which is proportional to the load 

 and the same at all velocities, while the other for the same train 

 will vary as the square of the velocity. If, then, R express the 



