410 



MOTION SICKNESS, II 



tion are fully as important as the maximum 

 amplitude developed during the cycle. In 

 his final paper (5) dealing with physical 

 characteristics Wendt concludes that the 

 incidence of sickness can be described in 

 terms of the response of "a resonant 

 mechanical system with a natural period of 

 3.75 to 2.72 sec." He expresses the view, 

 however, that such a system is not knowTi 

 (in the anatomical sense), and considers 

 the vestibular system, for example, as being 

 of "a very short period, heavily damped." 

 It thus appears that at least in the broad 

 sense Wendt was led by his experiments to 

 form a model of the responsive system rather 

 similar to the model of the receptors con- 

 sidered above. We shall here take issue 

 with his second conclusion, which seems to 

 exclude the vestibular apparatus as the 

 responding system, but this is more a matter 

 of detail. Aside from the question of the 

 identity of the responding system, we shall 

 suggest the possible general usefulness of 

 the quantity, a, in the analysis of experi- 

 ments of the sort undertaken by Wendt. 



It must be noted in connection with 

 Wendt's experiments that, although they 

 represent one of the best efforts in the field, 

 the criterion — i.e., "sickness" — used to 

 assess the nauseating power of the wave is 

 an intrinsically unreliable one. This is 

 evident from the varying results obtained 

 with the same wave form (e.g., compare 

 waves A and A', and H and H' in Fig. 4). 

 The author is not prepared to offer a better 

 suggestion, particularly because from the 

 military operational point of view it is 

 "sicloiess" which is the real criterion; none- 

 theless it is true that for purposes of physical 

 evaluation the sickness index has to be re- 

 garded as a crude measure, and its variations 

 are only rough indications of the response. 

 A second point of caution to be observed in 

 connection with the experiments of Fig. 4 

 is that the relation between incidence and 

 the time of exposure to the wave has not been 



studied,^^ and one does not know where in 

 the dose-response curve the 20-minute ex- 

 posure lies. 



Assuming, in accordance with considera- 

 tions of the previous section and with the 

 hypothesis of Wendt, that the imposed ac- 

 celeration activates a responsive system 

 consisting of a linear vibrator (this can of 

 course be generalized to a spectrum of 

 vibrators), we obtain v (i) from equation 

 (3) as soon as f{t) is specified. In Wendt's 

 case /(/) represents a "square wave"; such 

 waves can be given analytic expression by 

 means of a Fourier series. When the proper 

 series is substituted into (3) the resulting 

 equation yields v (t) also in series form. 

 Putting this v (t) into equation (5) gives 

 finally the series for a^. This last series 

 (for 0-2) converges rapidly when 2X and k^ 

 are of about the size calculated (23) for the 

 canals; we can therefore base a qualitative 

 discussion of the properties of cr on the square 

 of the first term, which is proportional to 



a sin' (t^/T) 



[k' - (27r/r)2]2 + 4X2(27r/T)2 



(6) 



in the case of a symmetrical wave.^^ Some 

 of the relevant features of expression (6) 

 are the following: (a) Increasing the period 

 from a minimum value (of 2/3) to infinity, 

 holding amplitude and pulse duration con- 

 stant, reduces the numerator of cr^ from a 

 maximum to as the sine^ (1/^), and also 

 reduces the denominator as (1/T^) + (1/T^). 

 However, since at first the numerator de- 

 creases more slowly than the denominator 

 the result is an increase in a"^; eventually, 

 the numerator tends to while the de- 

 nominator tends to k^, so a^ finally decreases 

 to 0. This behavior can be paraphrased 

 by saying that when one applies brief, 



'^ It is the author's understanding that Pro" 

 fessor Wendt has carried out experiments along 

 these lines, but they have not yet appeared in the 

 general literature and were not available to the 

 author at the time of this WTiting. 



'^ Analogous expressions for asymmetrical 

 waves can be derived without difficulty. 





