614 DR THOMAS R. FRASER ON THE ANTAGONISM BETWEEN 



A combined representation of the results of the three series, involving, as it 

 must, three variable quantities, will be best effected by means of a model in 

 three dimensions. Such a model may be constructed by bending wires into the 

 shape of the plane curves separating the pink and blue regions of Diagrams 

 1, 3, and 6, and fixing them in the manner to be described to two boards placed 

 at right angles to one another. The wire of Diagram 1 may be called a, that of 

 Diagram 3 b, and that of Diagram 6 c, and the boards may be distinguished as 

 A and B. Wire a is to be so fixed to the boards that its plane shall be at 

 right angles to both of them, and intersect A in the position of the left-hand 

 margin, and B in that of the lower margin of Diagram 1. Wire b is to be so fixed 

 to the boards that its plane shall be parallel to, and at a distance corresponding 

 to an interval of ten minutes from that of a, and intersect A in the position of the 

 left-hand margin, and B in that of the lower margin of Diagram 3. Lastly, wire 

 c is to be so attached to wires a and b, that its plane shall be parallel to, and at 

 a distance corresponding to one and a half times the minimum-lethal dose of 

 physostigma from B, and intersect A in the position of the left-hand margin of 

 Diagram 6 and a plane parallel to and half way between the planes of a and b, 

 which may be called plane C, in the position of the line of simultaneous adminis- 

 tration. 



The conditions represented by any point in the model may be found by draw- 

 ing from it perpendiculars to the planes A, B and C. The perpendicular upon A 

 represents the dose of atropia ; that upon B the dose of physostigma ; and that 

 upon C the interval of time between the administration of the two doses, 

 atropia being administered first where the point is on the one side, and physo- 

 stigma first when it is on the other side of the plane C. 



Diagram 7 is an orthogonal projection of such a model, in which the 

 three variables are represented on a scale somewhat different from that of 

 Diagrams 1, 3, and 6 ; but this difference does not cause any difficulty in the re- 

 cognition of the corresponding parts. The continuous line a a' represents the 

 boundary of the region of recovery in the experiments where atropia was 

 administered five minutes before physostigma (Series 1) ; the continuous line b V 

 the boundary of this region where atropia was administered five minutes after 

 physostigma (Series 2) ; and the dotted line c a! b' b a d the boundary of this 

 region where atropia was administered in various doses and at various intervals 

 of time before and after one and a half times the minimum-lethal dose of physo- 

 stigma (Series 3). It is obvious that these lines lie upon a curved surface, on 

 whose one side every point represents conditions leading to death, and on whose 

 other side every point represents conditions leading to recovery. The surface, 

 of course, cannot be fully known from the three sections of it that have been 

 obtained by these experiments. It could be known only by greatly increasing 

 the number of the experiments, so as to obtain a number of other curves of 



