430 THE PRINCIPLES OF SCIENCE. 



erroneous in one direction as ^ (& + c) in the other, so 

 that the mean of these two means, or what is the same, 

 J (a + 2 ~b + c), will be exceedingly near to the point of 

 rest . A still closer approximation may be made by 

 taking four readings and reducing them by the formula 

 4 (a + 2 b + 2 c + d). 



The accuracy of Baily's experiments, directed to deter- 

 mine the density of the earth, entirely depended upon this 

 mode of observing oscillations. The balls whose gravi- 

 tation was measured were so delicately suspended by a 

 torsion balance that they never came to rest. The ex- 

 treme points of the oscillations were observed both when 

 the heavy leaden attracting ball was on one side and on the 

 other. The difference of the mean points when the leaden 

 ball was on the right hand and that when it was on the 

 left hand gave double the amount of the deflection. 



A most beautiful instance of the mode of avoiding the 

 use of a zero point is to be found in Mr. E. J. Stone's 

 observations on the radiated heat of the fixed stars. The 

 great difficulty in these observations arose from the com- 

 paratively great amounts of heat which were sent into the 

 telescope from the atmosphere, and which were sufficient 

 almost entirely to disguise the feeble heat rays of a star. 

 But Mr. Stone fixed at the focus of his telescope a double 

 thermo-electric pile of which the two parts were reversed 

 in order. Now any disturbance of temperature which 

 acted upon both piles uniformly produced no effect 

 upon the galvanometer needle, and when the rays of the 

 star were made to fall alternately upon one pile and 

 the other, the total amount of the deflection represented 

 double the heating power of the star. Thus Mr. Stone 

 was able to detect with much certainty a heating effect 

 of the star Arcturus, which even when concentrated 

 by the telescope amounted only to roo* n f a 



Gauss. Taylor's ' Scientific Memoirs,' vol. ii. p. 43, &c. 



