20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



sist most simply in measuring, by the aerodynamic balance, the force 

 R exerted on a given body at various values of the wind speed vS". 



Variations of may equally well be produced by varying D while 5" 



is constant, i. e., by experimenting at a fixed speed but with a series 

 of models of different sizes ; or, D, S, p, and v may all be varied simul- 

 taneously. But while such experiments furnish a desirable check 

 on the results obtained when 6^ alone is varied, they are not neces- 



DS 

 sary, if compressiblity is negligible ; for it is immaterial whether 



is changed by changing D, S, or v. 



If the plotted points obtained in any of these ways do not all lie on 

 a single curve, within their experimental errors, equation (8) is not 

 accurate enough. And if the models have been exactly geometrically 

 similar, we must conclude that compressibility has played some part 

 in the phenomenon. This means that in the more general equation 



~'l>{-^'rl (9) 



pD^S^~^\ V ' C 



obtained by applying (6) to geometrically similar bodies, the effects 



6" • • • 



of varying -^ are not of entirely negligible nnportance. 



Head Resistance Proportional to 6"^ ; Viscosity Negligible 



At ordinary speeds and for bodies that are not too small, experi- 

 ment shows that in air of standard density, R is very nearly pro- 

 portional to vS^. It follows that, to the degree of approximation to 



which equation (8) is valid, \\i i — ] is merely a constant and is 



independent of the values of D, S, and v. If we write 



equation (8) reduces to 



R = KpD^S\ (lo) 



As is seen by referring to equation (7), K depends on the values of 

 r', r",...., etc.; it is a shape factor for the given series of geo- 

 metrically similar bodies in the given attitude. 



It is to be noted that viscosity does not appear at all in equation 

 (10), so that when the resistance is found to be proportional to the 

 square of the speed, if compressibility is negligible the value of the 

 viscosity is of no importance. This is not equivalent to saying that 

 viscosity plays no part at all in the phenomena ; for if viscosity did 



