ON PROBABILITY. 
Py, (2,) En > (D) —_ 
me 08 12D) } 
log. r °° 
In this manner, when 7 is taken at 1:005, m is found, from the Chester 
Observations, Table I., to be somewhere about 40. This result agrees, 
within the errors of observation, with the period given by an actual compa- 
rison of burials and baptisms. 
61. The difficulty has been seen of applying mathematical reasoning to the 
and we apg valuation of risks which are connected with the duration of life, but the 
feiency, |i difficulty with fire and sea insurances is greater, from the number of circum- 
ng from ap stances which are necessary to be taken into account. If underwriters only 
ete cop insured against total losses, the question would be comparatively easy, for 
lo each it would only be necessary to ascertain the number of houses out of a given 
ld done be number which are annually burnt to the ground, or the number of vessels 
 Risedent which have been lost out of a given number making the same voyage. 
dying the But by far the greater part of the claims on the underwriters arises from 
) divided by partial losses, as when a house is damaged by fire, or a cargo is partially 
py injured by sea water, &c. : 
ot of Yeuly 62. In insurances upon lives the observations which we have referred to 
furnish data which serve to ascertain the value of the risk, but in insurances 
against loss by fire and sea no similar data have been published, and so 
various and complicated are the contingencies to which they are subject, that 
it would be difficult to form any tables of the values of these risks, A regis- 
ter might be made out by each individual underwriter, or company of under- 
writers, showing the result of their respective experience, which would, 
ie b= doubtless, be useful to them in the conduct of their business. There are 
4 b many important facts which might be collected and systematically arranged, 
. the knowledge of which would also be useful to the underwriter. Thus a 
ulfs require register of the weather in different parts of the world, for a sufficient number 
of years, would be some guide in ascertaining the relative value of the risk 
\, the births in maritime insurances, as far as it is affected by season. The Society for 
the Registry of Shipping appoints competent persons to survey every ship 
which enters any of the principal ports in this kingdom ; their detailed report, 
which contains the name of the ship, captain, owners, her tonnage, the port 
where built, the materials of which, she is made, &c., is published by sub- 
otal num scription, and an office is kept for the purpose of posting it up to the latest 
gression. period. Such a plan adopted in the principal maritime ports of foreign 
countries would, in the course of time, give a complete register of the com- 
mercial shipping of Europe. The preceding remarks apply to maritime 
insurances, and although the difficulty of obtaining sufficient data to deter- 
mine the risk in fire insurances is considerable, it is not so great as in sea 
insurances. 
It is foreign to our purpose to offer any further remarks upon these ques- 
tions, the solution of which is the continual business of the underwriter, 
ch in (he and which requires great skill and experience. : 
We, . 63. The principal use that has hitherto been made practically of the 
our at theory of probability has been in the solution of questions connected with 
from anf the valuation of annuities and reversionary payments. 
The method of least squares, which is of very extensive application in 
astronomy, was proposed by M. Legendre in 1805;* it has since been 
shown by Laplace} to be preferable to every other, when the number of 
* Nouvelles Méthodes pour la Détermination des Orbites des Cometes. 
i Théorie des Probabilités. 
39