Connected ivith the Earth's Field of Force. 143 



the same forces that make one end of Lake Michigan 

 apparently higher than the other and that tend to draw 

 the rolling sphere or the floating body towards the equa- 

 tor. With forces of this type are connected the deriva- 

 tives 



and 



9x 9z 9,1/ 9z 



and a balance of the second type enables ns to find the 

 numerical value of these derivatives. 



What may be surprising at first is that the observed 

 values of the second derivatives seem to bear absolutely 

 no relation to the theoretical values. Here is a compari- 

 son expressed in two tables. The rr-axis is in the meri- 

 dian with its positive end towards the north ; the i/-axis 

 has its positive end toward the east. One table gives the 

 theoretical values for our assumed normal case with 

 maximum curvature in the meridian, minimum in the 

 prime vertical, and with a line of force lying in the meri- 

 dian plane and convex toward the equator. The other 

 table gives the values at several stations near Padua, 

 Italy, as observed by Professor Soler in his '^Seconda 

 Campagna'' (footnote, p. 139, reference H). The stations 

 are fairly close together, so we might expect the values of 

 the derivatives to agree pretty well with one another and 

 with the theoretical values for latitude 45° (the latitude 

 of Padua is 45° 24'). The unit of the table is one lO'^ 

 C. G. S. unit, that is, the tabular values are the real 

 values multiplied by an American billion (10'^): 



Normal Values of the Second Derivatives of the Gravity Poten- 

 tial, V. 

 [Unit = one 10"^ C. G. S. Unit.] 



9'y 9'y 9'Y 9'Y 9'Y 



'Ji' ~ ~9x' 9x9y 



Lat. 



0° + 10.1 



15° + 0.7 



30° + 7.6 



45° + 5.0 



60° + 2.5 



75° -}- 9.4 



90° -f 0.0 



9x 9z 



91/ 9z 











+ 4.1 







+ 7.0 







+ 8.1 







+ 7.0 







+ 4.1 















