18 Proceedings of the Royal Society' 
the motion of the original parts of the system. This method applies 
with perfect generality whether the external masses he themselves 
free, constrained, or resisted. 
(15) Another method of applying the same principles is then 
given. Starting from the definition dA = '^mSpdp, the kinematical 
properties of A are developed. Then, by the help of § 2, these are 
exhibited in their physical translations. 
(16) The. paper concludes with a brief comparison of the funda- 
mental principles of the science as they have been introduced by 
hfewton, Lagrange, Hamilton, Peirce, Kirchhoff, and Clerk-Maxwell, 
respectively ; and also as they appear in the unique Vortex-system 
of Thomson. 
2. On Illegitimacy in Scotland. By Mr Geo. Seton, 
M.A. Oxon. 
In the year 1860, at the meeting of the Social Science Association 
in Glasgow, I read a paper on “The Causes of Illegitimacy in Scot- 
land,’’ which was published shortly afterwards; and eleven years 
later (1871), at the meeting of the British Association in Edinburgh, 
I read another paper on “ The Illegitimacy of Banffshire,” which was 
privately printed. On the present occasion I intend to confine my ob- 
servations to the facts exhibited by the Eegistrar-General’s returns. 
Eor a good many years a perceptible improvement has been going 
on in England in the matter of illegitimacy ; and I am glad to be 
able to add that in Scotland also we have evidence of a gradual, and 
nearly as satisfactory, diminution in the number of illegitimate births. 
During the two decades, ending 1870 and 1880 respectively, the 
decrease in England was rather more, and in Scotland rather less, 
than 1 per cent. 
Percentage of Illegitimacy. 
1861-70. 
1871-80. 
Decrease. 
England 
6-1 
5-0 
11 
Scotland, .... 
9-7 
8-8 
0-9 
From the Forty-second Annual Report of the English Registrar- 
