218 Mr. G. King and Dr. A. Newsholme. 





of Actuaries/ vol. xxiv and vol. xxx. As showing the application of 

 the method to the present inquiry, the accompanying diagram, No. 1, 

 relating to England and Wales, is submitted, of which a very few 

 words of explanation will suffice. Along the abscissa axis are marked 

 off equal lengths to represent each of the periods of seven years 

 under review, with a portion of proportionate length for the three 

 years 1888-90 ; and along the ordinate axis the rates of mortality per 

 million are marked off. Rectangles are then erected, the areas of 

 which are to represent the number of deaths from cancer in each of 

 the septennial periods. Thus the area of the rectangle for the 

 septennium 1860-66 is 4,375 for males, as its base is 7 and its alti- 

 tude 625. Similarly for the other rectangles. 



Through the tops of the rectangles must then be drawn 

 continuous curve in such a way that the area cut off is exactly 

 equal to the area added. The length of the ordinate of the 

 curve which is central to any particular year will then give- 

 the deaths from cancer in that year; and the accuracy of the 

 drawing of the curve will be proved, if there be no sudden 

 change of direction, and if the sum of the numbers for the seven 

 years of a septennium is equal to the area of the rectangle for that 

 septennium. Diagram No. I shows the curves for England and 

 Wales, that for males being in an unbroken line, and that for 

 females in a dotted line. Similar curves were prepared for all the 

 observations so far discussed, and they are collected in Diagram 

 No. 3, so that they may be easily compared. The curves for males 

 are in continuous lines, while those for females are broken, and that 

 for the Scottish Widows' Fund is marked by crosses. 



The only curve which proved at all intractable was that for 

 the Scottish Widows' Fund in its earlier portion. It will be seen 

 from Table X that the death-rate from cancer in the first septennium 

 was very light, while in the second it was comparatively heavy, very 

 nearly equal to that in the third, and that the rates in the third, 

 fourth, and fifth exhibit an almost uniform upward progression. 

 These peculiarities are better seen by the help of Diagram No. 2,. 

 where the deaths are represented by the rectangles. The second and 

 third rectangles being of nearly the same altitude, while the first is 

 much lower, and the fourth considerably higher, there is indication 

 of a rapid rise in the curve between the first and second periods and 

 of a slight fall between the second and the third, and effect has been 

 given to this in the undulating curve shown in the diagram. The 

 most unpractised eye will, however, at once perceive that the un- 

 dulating line cannot represent the real law of the curve, and more 

 especially so when the other six curves are examined (Diagram 3), 

 Except for the one bend in the Scottish Widows' Fund curve, they 

 all partake of One character, and the conclusion is forced upon us 



