178 REPORT—1862. 
depends ability to pay, no one will object to the same rate being applied to all in- 
comes, It is only because injustice is committed by taxing the whole income, that 
an attempt is made to repair the injustice by demanding that a lower rate be im- 
posed than would be proper if only part were taxed. 
A third objection to Mr. Mill’s suggestion is the opposite of the second. It has 
been said that to exempt savings would be to favour the rich at the expense of the 
poor, inasmuch as it is by the comparatively rich that the greater part of savings 
are made, To this Mr. Thornton answers, that if the rich pay on all they spend, 
and are exempted only on what they save, they obtain the exemption only on that 
part of their income with respect to which they abdicate the advantage of riches, 
not consuming it themselves, but making it over to be consumed by the poor. 
Moreover, if they pay on all they spend, they pay on all they enjoy; and the prin- 
ciple that every man should pay on what he enjoys, whether the sum be great or 
small, is fully carried out. 
On Expectation of Life. 
By Cuarzes M. Wituicu, Actuary, Unwersity life Assurance Society. 
The author showed that the following hypothesis agrees very nearly with Dr. 
Farr’s English Life Table, which was obtained from Returns made by every parish 
in England and Wales. 
If a=age in years, 
then 3 (80 — a) = expectation. 
Also, that by an extension of the hypothesis we obtain the expectation of life closely 
agreeing with the result of the laborious investigation made by the late Mr, Fin- 
laison as to the duration of the lives of female Government annuitants. 
If a=age in years, 
then 3 (86 — a) = expectation. 
MECHANICAL SCIENCE. 
Address of Wrtitam Fairpatrn, Esq., LL.D., F.RS., President of the Section. 
Every succeeding year presents to our notice some new feature of construction, 
or some new application of science to the useful arts. Last year we had to record 
several new discoveries in chemical as well as mechanical science; and this year 
is fruitful of machinery and the industrial developments, as exhibited in the 
courts of the International Exhibition. It is not my intention to oceupy your time 
with a history of these Exhibitions, but I may be permitted to notice some of the 
most interesting objects, and some of the ingenious contrivances which we are 
called upon to witness, and which do honour to the age in which we live. Before 
I venture on a description of these objects, I must, however, crave your indulgence 
whilst I endeavour to notice some of the more important improvements which have 
taken place in mechanical science during some of the past years. i 
It may be stated that there is no period of the past history of science so fruitful 
in discoveries as the present century. Within the last fifty years we are enabled 
to enumerate the application of steam as a motive power to every description of 
manufacture, as also to navigation, locomotion, and agriculture, At the close of 
the eighteenth century the power of steam and its now almost universal applica- 
tion was, with the exception of a few engines by Boulton and Watt, comparatively 
unknown. Now it is the handmaid of all work, from our domestic requirements 
to the ocean-steamer of a thousand horses’ power. This we may consider as the 
present state of steam and the steam-engine, and we have only to compare the 
small but beautiful construction of engines for private and domestic use, as seen in 
the Exhibition of this year, with those which propel our fleets, drain our mines, 
and move with clockwork precision the innumerable machines of our manufacto-. 
ries. To these we may add the use of steam to locomotion, and we realize the law. 
of heat reciprocally convertible into mechanical force, or the dynamic theory of 
nel 
