INTRODUCTION 7 



The use of formulae represents a great step forwards in 

 the study of this portion of the science of immunisation. 

 Formerly investigators were content to state that the 

 quantity of antitoxin in the blood decreases gradually, 

 and in the first stages more rapidly than later on. The 

 application of the formula of Madsen teaches us much 

 more. It shows that the phenomenon is a regular one, and 

 we are impelled to seek for a cause for the differences of 

 the values of the constants n and const 2 . For instance, the 

 different values of const. 2 for the three days in the experi- 

 ments of Bomstein are they really different or do the 

 observed differences depend only upon experimental errors? 

 This and other questions suggest themselves after the use 

 of such an equation, and they lead to improvement in the 

 experimental methods, and to very sharp and well-defined 

 ideas of the natural phenomena themselves. With the 

 help of formulas, which may be empiric or rational, scien- 

 tific progress will be much more rapid than without them; 

 and as the experimental material increases, the empiric 

 formulae will probably be converted into rational ones, i.e. 

 we shall detect new laws of nature. It is therefore very 

 much to be regretted that efforts have been made, espe- 

 cially recently, to reject the use of formulae in the treat- 

 ment of questions of serum-therapy. These efforts may 

 be regarded as a last desperate struggle against the strin- 

 gent conclusions that may be reached by means of the 

 application of mathematical treatment a struggle that 

 cannot be greatly prolonged. 



The injection of toxins or cells into the blood of an ani- 

 mal can be done in different ways. Perhaps the most used 

 of them is the "intravenous injection" directly into the 



