432 



PROBANG 



ruonrs 



between the moral and mathematical value* of 

 'expectation,' owing to the assumption that in 

 such speculations the loss of money |>aid for tickets 

 is not to be regarded. If one man of moderate 

 means risks i'.'itxi in order to gain 5 when the 

 il'l- are 100 to 1 in his favour, anil another rinks 

 5 to gain 500 when the odds are 100 to 1 against, 

 the apecnlation in the former ca*e appears much 

 more reckless and immoral than in tin* latter, 

 although in lioth cases the stake is exactly equal 

 to the expectation. 



We now reach the most iin]x>rtant of all the 

 applications of the theory of probability, its use 

 in the calculation of life insurances and annuities. 

 During the early part of the 18th century the cele- 

 brated Ijondon mathematician De Moivre con- 

 structed a formula of great simplicity which is 

 still available, although largely rapemded by 

 elaborate 'tables of mortality' which have since 

 been compiled in all commercial countries. By De 

 Moivre's hypothesis, out of 86 children Imrn at the 

 same time'l dies every year until all are extinct. 

 Thus, for a man 40 years' old, 86 - 40 = 46, 46 years 

 on an average are still before him and 45 others ; 

 and his chance of life is the average number be- 

 tween and 46 i.e. 4 x 46 = 23. Generally a per- 

 son's probability of life or expectation is i(86 - ), 

 where n is the present age. Actuarial writers have 

 found that this simple formula agrees with their 

 official tables, except in the cose of young chil- 

 dren and aged persons. The tables are based 

 upon long-continued observations of the mortality 

 in the class of persons dealt with, and from them 

 the theory of probability is easily applied in calcu- 

 lating annuities, reversionary payments, and other 

 results. 



For ascertaining the various life contingencies 

 the Institute of Actuaries employ a table giving 

 all the ages from 10 upwards, and, l>egiiining with 

 100,000 persons alive at the age of 10, place oppo- 

 site each succeeding age the number of survivors, 

 till at 98 years none are left. At 40, survivors = 

 82,284 ; at 50, survivors = 72,726 ; therefore the 

 chance that a man of 40 shall live to 50 is 

 72,726 4- 82,284 = '884. The Belgian tables give 

 s.'i'-' for the same event in the cose of a married 

 man living in town ; and if liis wife is 30 years old 

 her chance of surviving for ten years is "862. 

 These data give the following calculation of the 

 chances of the four double events occurring 10 years 

 hence : 







-717 



Both being alive 



]tollidea<r (1- -832) x (1- -882) = -023 



Hiwhanil alive only '882 X (1 - -862)= -115 



alive only (1-'832)X '862 = '145 



As we have seen already the sum of these four 

 probabilities must = 1, which verifies the reckon- 

 ing. The chance of both these persons being alive 

 is evidently more than /j i.e. the odds in favour 

 are better ihan 7 to 3. 



Some of the higher applications of the doctrine 

 of probability require a knowledge of the inlin- 

 itesimal calculus, and are of interest only to 

 experts. It is proved, for example, by integration 

 and the theory of averages that the mean latitude 

 of all places north of the equator is 32704 ; and 

 when lour |mints in the circumference of any 

 circle (radius = r) are taken at random, the 

 mean area of the quadrilateral so determined is 



^ = r x -955. 



There are worki on the snbject by De Morgan (1837), 

 Boole (1854), Todhunter (1865), Venn (1866), Whit- 

 worth (1886), and Procter (1887). 



Probang, an instrument of various shape and 

 material, for pushing obstructions down the oeso- 

 phagus of a choking animal. See CHOKING. 



Proliatr Court, a court created in Kngland 

 in IS.'iS. in lieu of the old Prerogative Coiiits, to 

 exercise jurisdiction in matters touching the MO- 

 ces-ion to (M-rsonal estate. Since the Judicature 

 Acts of IS73 75 the Probate Court is included in 

 the Probate, Divorce, ami Admiralty Division of 

 the High Court of Justice. If a man at his death 

 leaves a will, then it must be produced and verilied 

 so as to prove that it is an authentic will, duly 

 executed and signed in presence of witnesses, 

 and therefore that the right to the personal estate 

 is vested in the executors named by the will. The 

 will is proved in common form by deposit ing it in 

 one of the registries of the couri, by making alii 

 davit of the amount of the property, and by paying 

 the probate duly (varying from 1 per >~>0 to 3 

 ]M?r 100, according to the amount of the pro 

 perty). The executors receive a copy of the 

 will, accompanied by a grant of administra- 

 tion ; and this probat >py is usually shown to 



bankers, &e. when the executors lay claim to the 

 property of the deceased. If the authenticity of 

 tin' will is disputed it must be proved by witnesses 

 in court. If there is no will the personal estate 

 devolves on the next of kin and widow, if any ; 

 and it is necessary that an application be made to 

 the court to appoint an administrator. This is 

 called taking out administration, and the act of the 

 court appointing administrators is called letters of 

 administration. See Dixon on J'rulxi/,- (2d ed. 1885). 



Probationer, one who is on probation ; 

 especially, in Scotland, a divinity student who, 

 having completed his studies and performed the 

 prescribed exercises, is licensed to preach bv the 

 presbytery, and is entitled to become a candidate 

 for a pastoral charge. 



Proboscidea. See ELEPHANT, Vol. IV. p. 291. 



Proboscis Monkey (A'(/w/.v im-mtus), a 

 native of Borneo, one of the dog like ( Cynotnorph ) 

 Catarrhines, nearly allied to the genus Semno- 

 pithecus. The nose is very long, especially in the 

 old males, and is mobile and retractile like a 

 proboscis. In the young monkeys it is short and 



Proboscis Monkey (A'tumlit lareatut). 



blunt. There are bushy whiskers, which, with the 

 long hair on the l>ack of the head, encircle tin- neck. 

 The colours brown, red, yellow, and gray are 

 bright. The adult males arc about :i feet in 

 height; the Inxly is lank, and the tail is MTV long. 

 In habit these animals are arlmreal and gregarious. 



rollS. MARCUS Al'ltKI. ITS, emperor of Koine. 

 was l>orn at Sirmium, in Pannonia, early entered 

 the army, and hod the good fortune to attract the 

 favourable notice of the Emperor Valerian. His 

 subsequent conduct justified his rapid promotion, 

 for he greatly distinguished himself on the Danube, 

 and in Africa, Egypt, Asia, Germany, and Gaul. 

 l.y the Emperor Tacitus he was appointed governor 



