VALUE OF COPYHOLDS. 



which is thus found: take 2J of the square of a. If 

 greater accuracy be required, add to the result one less 

 than its 7@0th part, which is sure to make it correct 

 within a single game. Thus if the number of his stakes 

 be 100, 100xlOOx2f is 23750, the ?60th part of 

 which is 31, whence 23750 + 30, or 23780, is within 

 one of the number of games required. 



APPENDIX THE SECOND. 



ON THE RULE FOR DETERMINING THE VALUE OF 

 SUCCESSIVE LIVES, AND OF COPYHOLD ESTATES. 



THE rule given in the work is in a different form from 

 that of any writer with whom I am acquainted, though 

 it agrees with that given by Mr. Milne, as will be shown. 

 This Appendix has been rendered necessary by the fact 

 that no writer has solved the question of the value of 

 copyhold estates with absolute correctness except Mr. 

 Milne, whose solution is in a form of unnecessary diffi- 

 culty. The writers with whom I am acquainted, who 

 give the old rule, or one involving an omission of the 

 same kind, are De Moivre, Dodson, Thomas Simpson, 

 Stonehouse, Morgan, Baily, and the French translator 

 of the latter. Mr. Milne stands alone in proposing a 

 somewhat different rule, which like many results of 

 independent investigation, differs more than need have 

 been the case from the form of preceding results. 



Let there be an estate held on a single life, and 

 renewable for ever upon payment of a fine of II. Let 

 it be a condition, that each renewal is to be made on the 

 1st of January next following the extinction of the 

 previous life ; it is required to find the present value of 

 all the fines. 



Firstly, To find the value on the 1st of January, the 

 moment after a fine has been received, and the best life 

 which can be found has been put in. Let P be the 

 y 



