406 



MOTION SICKNESS, II 



and return to its application in the next 

 section. 



We have said that, granting the model of 

 receptor action described above, integration 

 of equation (3) for a given f(t) yields v(t), 

 or, in the event that there is a rest fre- 

 quency, vo, it yields v — vo; in any case one 

 has a measure of the instantaneous rate 

 of stimulation of the central nervous system 

 by the receptor. The average rate of stim- 

 ulation over a time interval, ^2 — 4, we shall 

 take to be cr, where, 



= 1/(^2 - ^1) |/^'' {v - v,y d6. 



(4) 



For periodic imposed motions of period, T, 

 we have the special case of equation (4), 



(5) 



= (i/D N) {v-voYdt 



where <v indicates integration over one com- 

 plete cycle. In the next section we shall 

 evaluate cr^ by integrating equation (3) and 

 substituting the resulting value of v into 

 equation (5), 



To this point we have dealt with the 

 mechanical problems posed by the action of 

 the receptor mechanism when the imposed 

 motion is especially simply directed with 

 respect to the receptor in question. Very 

 little attention has been paid in the past to 

 the geometrical arrangement of the recep- 

 tors in the head. This is excusable if the 

 imposed motion is a pure vertical accelera- 

 tion and the receptor supposed to be in- 

 volved in the process is the utricle. In the 

 case of arbitrarily directed linear accelera- 

 tions, and especially in the case of rotations 

 such as those attending roll and pitch, there 

 is no question but that the imposed accel- 

 erations must be resolved into appropri- 

 ate effective components. Resolution into 

 linear horizontal and vertical components 

 is simple, but it is interesting to note that 

 the components of the acceleration which 

 act upon the linear receptors in the "adapt- 

 ing head" — that is, a head which is under- 



going no rotation even though the ship is 

 rolling or pitching — have a rather com- 

 plicated time dependence, certainly a very 

 different one from that of the angular dis- 

 placement (23). A more complicated case 

 is that of the resolution of an imposed 

 angular velocity into components normal 

 to the planes of the six semicircular canals 

 (41). Specifically, one has a vector angular 

 velocity co, whose instantaneous components 

 in some fixed rectangular reference, (X, F, 

 Z) frame are loiown. It is desired to know 

 the components of w in another rectangular 

 (^, 77, f) frame which moves relative to the 

 first in pure rotation. In the case in point 

 the ^, 77, f axes are taken normal to the 

 planes of the canals. The most convenient 

 coordinates to describe the position of this 

 moving frame are the Euler angles (see 

 Osgood's Mechanics, 29, p. 216), 1/', d, (p. 

 When the (human) head is still, we may take 

 the X-Y plane as the horizontal, the Y 

 axis as the intermeatal line, and the positive 

 Z axis along the upward vertical. Re- 

 ferred to this frame the Euler angles of the 

 frame whose axes are normal to the planes 

 of the canals are: \p = 0, 6 = 30°, and 

 <p = 45° (Fig. 3). The equations of the 

 transformation a5 {x, y, z) —^ oj (^, rj, f) are 

 given by Osgood (29) and also by Summers 

 et al. (41). It is conceivable, of course, that 

 motion out of the plane of a canal may never- 

 theless be capable of deflecting the cupula 

 and thus of stimulating. In such a case, 

 rotation in the plane of a canal would evoke 

 an afferent frequency not only in the fibers 

 from that canal, but in those of the other 

 canals as well, and the central effect would 

 be the resultant of all three effects. Such 

 results have been reported (1, 16, 21). It 

 seems to the author, however, that these 

 are adequately explained by noting that 

 because of the geometric disposition of the 

 canals in the (human) head it is possible to 

 choose an axis of rotation such that only the 

 two horizontal canals will be stimulated, but 

 it is impossible to choose an axis such that 

 only the two anterior or the two posterior 



