370 THE PRINCIPLES OF SCIENCE. [chap. 



points of three excursions of the beam from the zero of the 

 scale, then | (a + b) will be about as much erroneous in 

 one direction as | (b + c) in the other, so that the mean 

 of these two means, or ^ (« -f 2 h + c), will be exceedino;ly 

 }iear to the point of rest.^ A still closer approximation 

 may be made by taking four readings and reducing them 

 by the formula ^(a + 2& + 2 c ■\- (I). 



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 extreme 

 points of the oscillations were observed both when the 

 lieavy leaden attracting ball was on one side and on the 

 otlier. 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 beautiful instance of avoiding the use of a zero point 

 is found in Mr. E. J. Stone's observations on the radiant 

 heat of the fixed stars. The difficulty of these observations 

 arose from the comparatively great amounts of heat which 

 were sent into the telescope from the atmosphere, and which 

 were sufficient to disguise almost entirely 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 uniformly upon both piles pro- 

 duced 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 o'''02 Fahr., and which 

 represents a heating effect of the direct ray of only about 

 o°oooooi37 Fahr., equivalent to the heat which would be 

 received from a three-inch cubic vessel full of boiling 

 water at the distance of 400 yards.^ It is probable that 



' G.auss, Taylor's Scicntijtc Memoirs, vol. ii. p. 43, &c. 

 ^ Proci'Mwgs of the Boyal l'<ociety, vof. xviii. p. 159 (Jiin. 13, 1870) 

 Philosophical Magazine (4tli Series), vol. xxxix. p. 376. 



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