314 Intelligence and Miscellaneous Articles. 



correction z. Instead of 



(m) + ( g )U+Q3)V 



2— ; —f 



I 



I ought to have written as follows : 



z= _ (m) + («)U+(0)V (£) _ t> 

 i i 



a constant quantity as before. 



This alteration will make the following changes in paragraph 6 of 

 my paper in your July Number. To z v z 2 , z 3 must be added 



w_, oy_, oy_, 



I I I 



This will lead to the following results : — 



W=-0"-05, (il=0"-54, (M = _0"'05. 

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These angles, therefore, — 0"*05, 0"*54, — 0"*05, are not the local- 

 attraction-deflections at the reference- stations of the Anglo-Gallic, 

 Russian, and Indian arcs, but are the averages of the deflections 

 caused by local attraction at all the stations of the several arcs. 



2. I will not occupy your pages by showing how I come to this 

 result, as I purpose taking up this very important subject elsewhere, 

 and more at length than your space will allow. I will merely add 

 that it will appear that in every case the unknown quantity which 

 enters into the formulas for the axes of the earth, derived from the 

 measurement of any arc, when local attraction is taken account of, is 

 the average local deflection of all the stations of the arc, and not 

 the deflection at the reference- station merely. It may appear from 

 this that my revised method for using the principle of least squares 

 introduces several unknown quantities instead of one, viz. the local 

 deflections at all the stations of the arc instead of at the reference- 

 station only. But as the difference of local deflection at any two 

 stations on the arc is exactly measured by the difference between the 

 astronomical and geodetical amplitudes of the stations, one of which 

 is known by observation, and the second by calculation, the average 

 of all the local deflections can always be expressed in terms of the 

 deflection at the reference-station, or at any other single station of 

 the arc. 



3. The calculation of the semiaxes in my paper in No. 64 of the 

 Royal Society's ' Proceedings ' remains as before, and makes them 



20,926,189 and 20,855,316 feet. 



4. As — 0"'05, 0"'54, — 0"*05 are now the average local deflec- 

 tions of the whole arc and not merely of the reference-station, the 

 actual local deflections at the several stations will have to be rede- 

 termined. 



5. The data for doing this for the Indian arc I have at hand (see 

 my ' Figure of the Earth/ 3rd edit. p. 148). Let t, t', t", t'" be the 



