APPENDIX B. 221 



of maintaining trustworthy life-histories that shall be of medical service in after- 

 life to the person who keeps them. The Record shows how the life histories of 

 members of the same family may be collated and used to forecast the development 

 in mind and body of the younger generation of that family. Both works are 

 intended to promote the registration of a large amount of information that has 

 hitherto been allowed to run to waste iu oblivion, instead of accumulating and 

 forming stores of recorded experience for future personal use, and from which 

 future inquirers into heredity may hope to draw copious supplies. 



problems by j. d. hamilton dickson, fellow and tutor op 

 st. peter's college, Cambridge. 



(Reprinted from Proc. Royal Sbc, No. 242, 1886, p. 63.) 



Problem 1. — A point P is capable of moving along a straight line 

 P'OP, making an angle tan _1 | with the axis of y, which is drawn 

 through the mean position of P ; the probable error of the pro- 

 jection of P on Oy is 1'22 inch : another pointy, whose mean posi- 

 tion at any time is P, is capable of moving from P parallel to the 

 axis of x (rectangular co-ordinates) with a probable error of 

 P50 inch. To discuss the "surface of frequency" of p. 



1. Expressing the " surface of frequency " by an equation in 

 x, y, z, the exponent, with its sign changed, of the exponential 

 which appears in the value of z in the equation of the surface is, 

 save as to a factor, 



.V 2 , (3x--2y)2 m 



(1-22) 2 y(l-5U) 2 



hence all sections of the "surface of frequency" by planes parallel 

 to the plane of xy are ellipses, whose equations may be written in 

 the form, 



^ on In! ~ C ' a constant ... (2) 



(P22) 2 9(1 -50) 2 

 2. Tangents to these ellipses parallel to the axis of y are found, 



