520 Proceedings of Royal Society of Edinburgh. [sbss. 
A.— Table of the Constants of the Theoretical Curves 
type IV. 
Disease. 
Locality. 
Date. 
Cases 01 
Deaths. 
r Unit of 
Time. 
M2 
* 
ft 
1. Miliary 
Oise . . 
1821 
Cases 
1 week 
7-0285 
-4-0867 
226*366 
*0479 
2. Plague 
1665 
Deaths 
4 weeks 
1*7758 
1*3117 
14*3663 
*3072 
3. ,, 
6-1454 
3-0194 
123-7395 
•0393 
4. Cholera . 
1832 
1 week 
9-3849 
120-1387 
*6223 
5. „ 
Exeter . 
1832 
Cases 
2 weeks 
3-5318 
10*1086 
98-9950 
2-3411 
1891 
Deaths 
2-4678 
3*08748 
27*9962 
•6342 
7. „ 
1891-2 
2*3093 
30-5716 
1*2217 
8. Smallpox . 
Warrington . 
1743 
” 
1 month 
3*1149 
*7893 
38-4964 
*0206 
9. „ 
Boston, 
U.S.A. 
1721 
1-3010 
-1-2993 
8*7323 
■7636 
10. 
Glasgow 
1784 
1 
1 week 
7-8888 
2*8044 
1-5082 
•0161 
11. 
; Gloucester . 
Cases 
21-9069 
- 5-3486 
1640-46 
•00272 
12. „ . , 
Severe 
cases 
4 weeks 
5*7644 
*1938 
105*39 
•00196 
13. „ 
London 
Deaths | 
5*6492 
1-4905 
102*115 
*01322 
14. „ 
1902 
Cases 1 
6-9321 
-2-4550 
192-8322 
•01794 
15. „ . | 
Orsett Union 
” 
3-3240 
- -68839 
36-5115 
*0129 
16. ■ , 
Liverpool . 
(local epi- 
demic) 
1901 
2 weeks 
2-5540 
*9005 
27*8201 
*0487 
Sheffield . 
1887-8 
7*2097 
- *68647 
174*6607 
*12574 
18. Measles . 
Glasgow 
1808 
Deaths 
1 month 
1-7039 
1-13235 
12*7061 
*25920 
19. Zymotic 
1890-1903 
” 
2 weeks 
6-0870 
•21329 
115-4617 
*00020 
20. „ . 
London 
1854-1903 
4-5056 
2-9978 
68-2995 
*09825 
21. „ 
Manchester . 
1878-1887 
Cases 
1 month 
1-4458 
■04423 
6*2549 
Islington 
Deaths 
1-62106 
- *16702 
10-8032 
•006 
23! \\ \ 
1857-62 
Cases 
(1-5) 
4 weeks 
2-3797 
•47904 
217134 
*01703 
24. „ 
Cases ' 
ages 1 
2*10781 
- -90387 
19 7548 
*08724 
25. Enteric 
Coventry . 
1900 
LJ 
1 week 
1*76744 
1*95543 
11*71872 
*3471 
26. 
Rotherham . 
1892 
5-27047 
5-14338 
94-1654 
*17811 
27. Scarlet 
Halifax 
1880-1 
2 weeks 
1-35199 
- 1-13994 
9*55176 
*52582 
28. „ 6 . 
Thorshavn . 
1873-4 
1 month 
1*83684 
3-28100 
22-22123 
1-7371 
Glasgow 
1 day 
3-08965 
3*18762 
43-03616 
•34451 
Wimbledon . 
2 days 
1-92734 
2-60173 
26-30963 
*94548 
TYPE I. 
M2 
M3 
M4 
* 
31. Enteric 
Fever 
32. Yellow 
Fever 
33. Zymotic 
Diarrhoea 
Maidstone . 
Demerara 
Islington . . 
1900 
1840-1 
1857-62 
Cases 
Cases 
under 
3 days 
1 month 
12-0281 
3-6612 
1-45193 
26-7769 
-3-0409 
*57488 
472-168 
37-5459 
4*61391 
■4121 
*1883 
•10797 
B.— Table giving the Constants of the Theoretical Curves 
1. Smallpox . 
2. „ 
j 4. Relapsing 
Fever 
London 
Liverpool 
Glasgow 
N.W. to 
S.E. 
E. & W. 
N. &S. 
E. & W. 
T 
7-4279 
4-1247 
1*6609 
7*6882 
2*6121 
2*1155 
*2124 
196-6696 
66-1562 
13-0490 
97323 
*1442 
*0972 
•9771 
■01025 
1905-6.] Studies in Immunity : Theory of an Epidemic. 521 
CORRESPONDING TO THE COURSES OF EPIDEMICS. 
TYPE IV. 
02 
d 
rnd 
- 
• 
No of 
Diagram. 
Remarks. 
4-583 
*14798 
•6527 
6-8217 
•9470 
5*0493 
I. 
4-5526 
4-2209 
4-4240 
4-5863 
5 7329 
111 Pi 
6-8129 
5*5113 
8-9635 
8-2141 
17*1334 
9*6667 
13*9478 
11-6988 
18 931 
106-175 
11-7934 
61659 
*50655 
4-4195 
:: 
II. 
IV. 
V. 
III. 
/These epidemics are 
| almost identical al- 
J though the max. of 
| the first waB in May 
I and the second in 
3-9677 
5-1578 
•0824 
- -3342 
*4712 
1-3523 
9-4378 
10-0932 
•8711 
4-9054 
61049 
2-7823 
VII. 
VI. 
V. January. 
3-5593 
3-4183 
3-1718 
•0479 
1-2434 
*8825 
•9715 
14-2556 
17-4959 
38*551 
1-7394 
•8133 
2*5513 
10*1675 
14-601 
IX. 
31997 
4-01274 
3- 3046 
4- 2688 
*1181 
- -11288 
- -0897 
2-2574 
■62727 
1-17172 
36-2085 
9-1130 
24-1147 
5-8743 
•7625 
3-2589 
13*94 
7- 4959 
8- 6703 
X. 
VIII. 
VIIlA. 
3-35995 
4*3664 
3*11622 
•4328 
- -2172^ 
1*25287 
*47918 
9-53494 
54-7740 
3*55635 
1*4512 
3-35904 
18*0862 
" 
xi. 
XII. 
3*36441 
2-99658 
4-1111 
•29294 
- *0318 
•06834 
4-87785 
•42676 
31*3251 
8-4564 
10*45943 
■405896 ! 
•76214 
10*6226 
3*4727 
4-7257 
XV. 
XIII. 
XIV. 
Normal curve. 
4-44641 
- *12539 
•60384 
7-6313 
1-2489 
3-6896 
3-7514 
■34452 
5-7297 
31-26136 
3-94458 
4*5408 
XX. 
3-38995 
5-2256 
*2482 
1*2067 
7*7248 
3*3742 
2*7633 
xviii. 
6- 5863 
4*5083 
7- 08272 
*5151 
•34823 
•32812 
1-27706 
11-7664 
9*5718 
6*78413 
4-8054 
4-05043 
2-68123 
•86803 
2-75496 
XIX. 
XXIII. 
XXII. 
TYPE I. 
ft 
r 
in. 
<*2 
d 
3-2638 
15-6768 
XXI. 
2-7998 
10-0166 
2-1776 
5*8390 
3-708 
9-942 
*6224 
XVI. 
2 7010 
3*33101 
1-7606 
6-6703 
1*7773 
6*7345 
*6824 
CORRESPONDING TO THE DISTRIBUTION 
of Epidemics in Cities. 
r 
d 
- 
a 
3-5645 
20-8514 
■4269 
4-8780 
9-1466 
11*1204 
XXVI. 
Type IV. 
3- 8885 
4- 7303 
4-0435 
7*3258 
8*8507 
•0440 
*2388 
3*451 
Type IV. 
Type VI. 
Type IV. 
