514 Transactions. — Chemistry and Physics. 



The motion of the sun, as deduced from the proper motion of 

 the stars, is, according to Proctor (" The Sun "), 150,000,000 

 miles per year— that is, 25,154-38 ft. per second, the line of 

 motion being inclined to the earth's orbit at about 53° in 

 longitude 285°. This is about 60° to the earth's axis. Resolv- 

 ing along the equatorial plane, this gives — 

 u = 21.784ft. per second; 

 and, as<D = 0000073 rad. per second, 



we get / = —1-584 = — ^ (about) when 0=0. 



Similarly, this would be the acceleration along the radius at 



= 90° ; so that the weight of a body at the equator should 



vary by 10 per cent, every twelve hours. The motion of the 



earth in space, therefore, cannot be as great as deduced from 



the proper motions of stars. 



If A be the angle through which a plumb-bob is deflected 



by this spacial acceleration, we have — 



— uu cos. 6 

 tan. A = Uu sin e cos> x + g 



Perhaps this in some part reconciles the seismological tides 

 found by Milne with Lord Kelvin's value of the rigidity of the 

 earth. 



From an experimental point of view the method is very 

 accommodating. Being a harmonic quantity, it does not 

 matter when we set our instruments, which may, for the same 

 reason, measure variations in pressures. Being an accelera- 

 tion, it may be magnified to any extent by using large masses. 

 With sufficiently delicate apparatus, and observations extend- 

 ing over a long period, it might be possible to deduce the rela- 

 tive motion and distance of a star for which the earth's orbit 

 failed to show any parallax. 



Abt. LII. — Mathematical Treatment of the Problem of Pro- 

 duction, Bent, Interest, and Wages. 



By Douglas Hector. 



[Read before the Wellington Philosophical Society, 11th February, 



1902.] 



The following attempt at a mathematical treatment of some 

 of the problems of political economy was not origiually in- 

 tended for publication, but I have been persuaded to submit 

 it as a paper to the Wellington Philosophical Society. I have 

 not solved all the interesting points in the subject, but merely 



