TRANSACTIONS OP THE SECTIONS. WS 



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as to indicate such a difficulty as that which exists higher in the social scale, of 

 obtaining a position in society ; but that, to counterbalance this, there are sudden 

 and repeated augmentations of the rates of mortality occurring at irregular periods, 

 and produced most probably by the pressure of numbers and the varying demands 

 for labour, as well perhaps as by circumstances not well understood in the nature of 

 particular employments. Thus, among agricultural labourers the mortality comes to 

 a maximum at 23, and declines to a minimum at 30, just as among the Government 

 annuitants. Among country workmen (not labourers) there is a maximum at 19 and 

 a minimum at 25, and another maximum at 30 and a minimum at 32. Among miners 

 there is a first maximum at 22 and a minimum at 29, and a second maximum at 34 

 and a minimum at 37- Among clerks, the first maximum is at 28 and the minimum 

 at 35 ; the second maximum is at 44 and the minimum at 47. Among plumbers and 

 painters the first maximum is at 18 and the minimum at 25, the second maximum at 

 33 and the minimum at 33. Among bakers, there are three maxima, at 18, 31, and 

 49, and three minima, at 22, 38, and 54. Among the female workers the course of 

 mortality is very anomalous, decreasing from the earliest period till 24 years of age, 

 and then increasing till 28 and decreasing till 33. 



On a Mechanical Process, by which a Life Table commencing at Birth may be 

 converted into a Table, in every respect similar, commencing at any other 

 period of Life, By Professor A. Buchanan, M.D., University of Glasgow. 



The process consists in the use of a calculating diagram, which performs, mecha- 

 nically, all the calculations required ; and can be made to answer the four following 

 sets of questions by mere inspection of the diagram and the life table annexed to it. 



1st. Of 10,000 persons entering upon any year or month of life, it tells the 

 number which will survive at any subsequent period, or conversely. 



2nd. Of 10,000 persons entering on any year or month of life, it tells at what sub- 

 sequent period any per-centage or less given number will survive. 



3rd & 4th. It will answer the same two sets of questions, giving the results not in 

 the number of survivals, but in the number of deaths. 



It is thus not only true that the diagram converts the life table, on which it is 

 based, into a life table having the same radix but commencing at any given sub- 

 sequent period of life, but it bestows on all of these tables properties which the 

 original table does not possess ; for it gives its indications either in terms of the 

 deaths, or of the survivals, out of the original number of persons entering on any 

 given period of life. 



The diagram by which these calculations are performed is a right-angled triangle, 

 so drawn that one of the sides forming the right angle is perpendicular, and the 

 other horizontal. The perpendicular side or base is divided into 10,000, or any 

 other number of equal parts corresponding to the radix of the table ; and from the 

 points of division a series of horizontal lines are drawn to the opposite, or long side 

 of the triangle, each tenth line being more prominent, so as more readily to catch 

 the eye. The radical number of the table is inscribed on the margin opposite to the 

 top of the base, and the successive terms of the table are placed below it, at unequal 

 intervals, so that each indicates the number of divisions of the base opposite to it, 

 counting from the bottom ; and on the same line is marked also the year of life to 

 which the term corresponds. The horizontal side of the triangle is also divided into 

 100 equal parts, and from the points of division a series of perpendicular lines are 

 drawn intersecting the horizontal ones, each tenth line being made more conspicuous. 



The diagram being thus constructed, the mechanism by which the calculations are 

 effected is exceedingly simple. A thread or fine cord is attached to the vertex of 

 the triangle, and the cord being stretched to any point of the base, whatever be the 

 age marked at that point, it converts the table on the margin into a life table com- 

 mencing at that age. 



The principle upon which the results depend, is that the cord, being a line drawn 

 from the vertex of the triangle to the base, divides the base and all the lines parallel 

 to it into proportional parts, and we have therefore the lower segment of the base to 

 the lower segment of any parallel, as the whole base is to the whole parallel. Now 

 these are exactly the four proportionals involved in the questions proposed above 



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