192 MORTEN SIMONSEN 



Having calculated the slope, the position of the 2 parallel lines 

 is determined by the mean dose and mean response for the normal 

 curve, and similarly for the immune one. 



Readers interested in the statistical theory of parallel-line 

 assays may refer to the textbook by Finney (1952). 



We now come to the question of calculating the Factor of 

 Immunization, i.e. the potency ratio between immune and 

 normal cells. This factor is the horizontal distance between the 2 

 parallel lines. No matter where the horizontal line is drawn, this 

 distance is obviously the same and represents, for a given response, 



log dose N-log dose /=log j ^, 



The antilogarithm to the distance gives therefore (dose 

 N/dose /), the Factor of Immunization, indicating how many 

 more normal cells than immune cells are needed to give the same 

 degree of spleen enlargement. 



As seen from Fig. i, where the horizontal distance has been 

 drawn through the point of mean response on the immune 

 curve, the distance is easy to calculate as the sum of ^D and DB, 

 AD is simply the difference between the mean doses employed 

 (measured on the logarithmic scale); that is, in this experiment, 

 log 3 -log I =log 3. DB is a little more laborious to calculate, but 

 it only amounts to dividing DC (the difference between mean 

 responses) with the earlier calculated slope b. This is easily seen 

 from the triangle BCD, where (DC/DJB) = the tangent to the 

 angle v ( = the angle of the parallel lines with the .v-axis); the 

 tangent to v being the definition of the slope. 



Calculation of the Factor of Immunization can be made on a 

 purely arithmetical basis, according to the general formula 



log ¥.l. = xN-xI-^^^^j^, 



where x represents the mean log dose and y the mean response 

 (Finney, 1952). 



