482 Prof. A, Schuster. [Mar. 28, 



rential coefficient with regard to the distance from the earth to the 

 centre, each single term in the series is of opposite sign according to 

 the location of the cause ; hut what is true for each single term need 

 not be time for the sum of the series. By a curious combination of 

 terms the vertical forces might possibly be of the same sign on 

 whichever of the two hypotheses it is calculated. In any case, how- 

 ever, the differences between the two results will be of the same 

 order of magnitude as the vertical force itself. If it were then a 

 question simply of deciding whether the cause is outside or inside, 

 without taking into account a possible combination of both causes, 

 the result should not be doubtful, even if we have only an approxi- 

 mate knowledge of the vertical forces. 



Two years ago I showed that the leading features of the horizontal 

 components for diurnal variation could be approximately represented 

 by the surface harmonic of the second degree and first type, and that 

 the vertical variation agreed in direction and phase with the calcula- 

 tion on the assumption that the seat of the force is outside the earth. 

 The agreement seemed to me to be sufficiently good to justify the 

 conclusion that the greater part of the variation is due to causes 

 outside the earth's surface. Nevertheless, it seemed advisable to 

 enter more fully into the matter, as in the first approximate treat- 

 ment of the subject a[number of important questions had to be left 

 untouched. I now publish the results of an investigation which has 

 been carried out, as far as the observations at my disposal have 

 allowed me to do. My^original conclusions have been fully confirmed, 

 and some further information has been obtained, which I believe to 

 be of importance. 



I have made use of the observations taken at Bombay, Lisbon, 

 Greenwich, and St. Petersburg. The horizontal components of the 

 diurnal variation during the year 1870 were in the first place reduced 

 to the same system of coordinates and to the same units. If we 

 remember that experience has shown the diurnal variation to be very 

 nearly the same for places in the same latitude, except near the 

 magnetic pole, and also that it is symmetrical north and south of the 

 equator, we may for a given time of day assume the horizontal 

 components known over eight circles of latitude, four of which are 

 north and four south of the equator. If we chose the period of the 

 year for which the reduction is made to be that corresponding to the 

 summer months in the northern hemisphere, we must take the 

 variation in the southern hemisphere to be the same as that found 

 during the winter months north of the equator. This was done in 

 one part of the inquiry ; in the other the mean of the whole year was 

 taken, and in that case the same values hold north and south of the 

 equator, with the same sign for the force towards geographical north, 

 and opposite sign for the force towards the geographical west. 



