of Latitudes for Local Attraction. 32 5 



be 6 //# 52, and on the southern side 5 //# 14. We have signified 

 above our assent to the employment of corrections to the ob- 

 served latitudes corresponding to these deflections, viz. 6"-5 

 and W'l, should they be used to deduce the figure of the earth; 

 relying on the fact that the value 4*7 resulting from these 

 same numbers for the mean density of the earth agrees 

 pretty closely with the value given by repeated and entirely 

 independent experiments with the torsion balance ; namely, 

 5*48 according to Cavendish, 5'48 and 5*58 by the two ex- 

 periments of Reich, 5*66 according to Baily. Although it 

 cannot be doubted that by the application of these corrections 

 the individual latitudes are brought notably nearer to the 

 mean, yet the figures themselves show that, even in this case, 

 the accuracy so attained is only moderate. For if 8=5*5 in- 

 stead of the aforesaid 4*7, we have £=048, and therefore a 



deflection on the northern side 5 //# 6, on the southern side 4 //# 4; 

 or together only lO^'O, instead of the observed amount ll //# 66. 

 The missing l //# 66 mast be assigned (together with actual 

 errors of observation) to disturbances unknown to us; and we 

 have not the slightest reason to divide this amount between 

 the two points in the same proportion as the attraction of the 

 mountain, as we really do if we apply the corrections 6"'5 and 

 5 /, "l. Is it not clear now that we gain quite as much, and 

 perhaps more, for the determination of the figure of the earth, 

 by adhering firmly to the directly observed latitudes, without 

 any corrections whatever ? and w T ill it not always be so, if only 

 the two stations are so chosen as to have the disturbing mass, 

 with the consideration of which we have to do, between them, 

 so that they shall presumably be affected about equally and in 

 opposite directions, — a condition for the fulfilment of which at 

 most a general knowledge of the surroundings of the place 

 will suffice ? But it is needless to insist further on the 

 practical importance of this consideration. 



" Let us now turn back to the interrupted course of our 

 argument to indicate the third and, to all appearance, the 

 shortest and safest way, in which the said correction of lati- 

 tude might bo justified. It is by appeal to experience, that 

 supreme judge in all matters relating to the study of nature. 

 Could we succeed in obtaining an unmistakable decision from 

 that tribunal, the matter would at once be set at rest. 

 Indeed all the pains bestowed in the foregoing arguments to 

 justify particular cases would be comparatively worthless, at 

 any rate for the purpose in hand, could it be shown that 

 by these corrections the observed latitudes are on the whole 

 really assimilated to the mean ones. For in truth it seems to 



