Vol. 7, 1921 
PATHOLOGY: FLEXNER AND A MOSS 
319 
where p— (xjWj-i), q= (y/uuj-i). But this congruence is found to imply 
Aq — Bp \wj-i> wj for sufficiently high values of /. Hence, either 
| or | Bp | or both are > wj/wj-i. 
7. Reverting now to the equations (3), we take any approximate solu- 
tion in integers, say x, y, z, w. Assuming for our purpose that \w\ > 
2 141 " [3J , we determine the positive integer j such that 
2 [j-i]-y-2] < | w | < 2 u)-\j-u 
We have 
wjei = \A + (w + r)£j\, Wj€ 2 = \B+(w.+ s)7ij\, Wje 3 = \C+(p + t){j\, 
and it follows from the results above that at least one of the three prod- 
ucts ei€ 2 , € 2 € 3 , «3€i is of magnitude M.2~ 4[j ~ 2] for sufficiently large values 
of /. But, under the same condition, 
M. 2-^-2] > 2 -eU-21 > /(2W- 1 l J 'W-«)4/( H ). 
Hence, when / exceeds a certain number, the condition (2) is not fulfilled. 
That is, the values of w satisfying this condition are limited. 
1 Throughout this paper the term "integer" means "a positive or negative integer 
or zero," when it is not specially defined. 
2 Kronecker, Monatsberichte Kgl. Preuss. Aka. Wiss., 1884 (1179ff., 1271fL); 
Werke, 3 1 , Leipzig, 1899 (49-109). 
3 See Dickson, L. E-, History of the Theory of Numbers, 2; Carnegie Institution, Wash., 
1920 (93-99), for references. 
A PHYSICAL BASIS FOR EPIDEMIOLOGY 
By Simon Flkxnkr and Harold L. Amoss 
Laboratories op the Rockefeller Institute for Medical Research 
Read before the Academy, April 26, 1921 
In the autumn of 1918 there swept through one of the mouse breeding 
rooms of the Rockefeller Institute a destructive epidemic of mouse 
typhoid — an infection of mice with a bacillus of the enteritidis group of 
organisms to which the name of Bacillus typhi murium has been given. 
The history of the epidemic is instructive : the original mice of the popu- 
lation, numbering about 3000 at the time of the epidemic, came from a 
breeder in Massachusetts and had been purchased some time before and 
moved en masse to the Rockefeller Institute. In the meantime many new 
mice had been born of this stock, and many of the original mice had died 
or been employed for experiment, so that only a small residue of the origi- 
nal population remained. In other words, the epidemic of mouse typhoid 
arose among chiefly a new stock of mice, the offspring of an old stock 
believed on good grounds to have passed through previous outbreaks of 
the disease. 
There is still another reason for supposing that the epidemic arose from 
within and was not imported from without this stock. Besides the breed- 
