486 
PROFESSOR A. SCHUSTER OH THE DIURNAL 
IV, Comparison of Observed and Calculated Vertical Forces. 
I'he complete potential can be written down from the value at its surface in the 
usual manner, either on the supposition that the potential is zero at an infinite 
distance, or that it is zero at the centre of the Earth, the first supposition 
corresponding to the hypothesis that the seat of the magnetic variation is outside 
the Earth. If Y,j is a surface harmonic of degree n occurring in the expansion of 
V/a, the solid harmonic will either be Y„(r/a)" or The vertical force 
is given by 0V/0r, as the force is considered positive when it aces downwards. At 
the surface, therefore, we have a term for the vertical force which is either nY,, or 
— (w + l) Y„. 
Before we proceed to discuss the comparisen between the observed and calculated 
values of the vertical force, a few words are necessary regarding the available 
observations. 
The only station for which we have complete records for 1870 is Lisbon. It is 
therefore impossible to obtain a satisfactory series for the vertical force which 
would give us, if our information was more complete, directly the two terms, one 
due to outside, the other due to inside, effects. But I shall show that even from the 
existing data we can draw important conclusions. 
At Bombay no vertical force determinations are published, as far as I know, before 
1873, when the magnetograjih came into operation; but we have complete records 
between 1873 and 1878. During these years the general type of the vertical force 
remained practically the same, only the range varying. Figs. 5 and 6, for instance, 
Fig. 5. Fig. 6. 
are tracings of the curves given by Mr. Chambers in the years 1873 and 1877, the 
two years which differ most in range. The other years show curves vaiying between 
these two extremes. As far as the general form of the curve is concerned, we cannot 
go far wrong, therefore, if we make use of the 1873 observations, especially as the 
horizontal components show no marked difference (except as regards range) in 1873 
and 1870. 
Similar remarks apply to Greenwich. Although published records exist for 1870, 
there is an uncertainty about the temperature correction, which makes the vertical 
force observations previous to 1882 useless for our present purpose. 
I’able XI. will give an idea of the changes which the vertical force variation is 
