General Cattle Mutual Insurance Fund. 4G7 



sum allowed as compensation for cattle slauglitered by authority 

 as would make up the full sum insured. 



To avoid tediousness, I do not enter into a multitude of ad- 

 ministrative details, on which the success of the measure depends. 



(1.) Peoblems in Cattle Insukance. 



Allowing nothing for expenses, or profits of speculation, or 

 interest, — What premium (p) should be paid to insure a cow of 

 the value of (5) pounds sterling, for any unit of time during 

 which (d) of such cows will die out of (e) living at the beginning 

 of the time ? 



The aggregate of the premiums payable for (c) cows will be 

 p c ; and the aggregate of the payments for the cows dying 

 will he d s by hypothesis. By the conditions of the question 

 p c = s d. 



d 



. • ]} = S = fX s 



c 

 It will be convenient to write -^ = ^ =z the probability of 

 dying within the time. 



If p is the premium for a week, then two premiums will be 

 required for two Aveeks, fifty-two for fifty-two weeks, and n for n 

 weeks. 



Examples. 



(1.) If 5000 cattle die in a week out of 10,000,000 head, 

 {hen to insure an animal worth 15/. the weekly premium is 



^ — oQQO'^- ^ -0005 X 15 = £-0075 

 ^ 10,000,000 



or a little more than l^d. 



(2.) If the probability that cows attacked by Rinderpest 

 will die of that disease is correctly expressed hy pb = "85, then 

 J) = fjb X s = '85 X 15 = 12'75Z. at least is required to insure 

 1 ~jI. on the death by Rinderpest of a cow attacked with the de- 

 cisive symptoms. 



Note. — The mean duration of the disease appears to be 



about ten days, and the premium is consequently 



8"925Z. for a week of seven days. 



(3.) If among the 200,000 cattle on farms that suffer from 



Rinderpest, 7000 will die weekly, the premium to insure a cow 



on such farms, worth 15Z. will be half a guinea a week: 



73 = M s = = '035 X 15 = '525 



'^ ^ 200 



Thus the premium ranges from 7 farthings to 10s. Gd., and to 

 •8/. I85. 6t?. a week. 



Hence the power of selecting cases against an office on the 

 voluntary principle in time of plague is enormous. 



