568 THE PRINCIPLES OF SCIENCE. [CHAP. 



the previous experiments. If we treat all determinations 

 yet made as of equal weight, the simple mean is about 

 5 -4 5, the mean error nearly 0*5, and the probable error 

 almost 0'2, so that it is as likely as not that the truth lies 

 between 5-65 and 5-25 on this view of the matter. But it 

 is remarkable that the two most recent and careful series 

 of observations by Baily and Airy, 1 lie beyond these limits, 

 and as with the increase of care the estimate rises, it seems 

 requisite to reject the earlier results, and look upon the 

 question as still requiring further investigation. Physicists 

 often take 5f or 5 '67 as the best guess at the truth, but it 

 is evident that new experiments are much required. I 

 cannot help thinking that a portion of the great sums of 

 money which many governments and private individuals 

 spent upon the transit of Venus expeditions in 1874, and 

 which they will probably spend again in 1882 (p. 562), 

 would be better appropriated to new determinations of 

 the earth's density. It seems desirable to repeat Baily's 

 experiment in a vacuous case, and with the greater me- 

 chanical refinements which the progress of the last forty 

 years places at the disposal of the experimentalist. It 

 would be desirable, also, to renew the pendulum experi- 

 ments of Airy in some other deep mine. It might even 

 be well to repeat upon some suitable mountain the obser- 

 vations performed at Schehallien. All these operations 

 might be carried out for the cost of one of the superfluous 

 transit expeditions. 



Since the establishment of the dynamical theory of heat 

 it has become a matter of the greatest importance to 

 determine with accuracy the mechanical equivalent of 

 heat, or the quantity of energy whieh must be given, or 

 received, in a definite change of temperature effected in a 

 definite quantity of a standard substance, such as water. 

 No less than seven almost entirely distinct modes of 

 determining this constant have been tried. Dr. Joule first 

 ascertained by the friction of water that to raise the tem- 

 perature of one kilogram of water through one degree 

 centigrade, we must employ energy sufficient to raise 424 

 kilograms through the height of one metre against the 

 force of gravity at the earth's surface. Joule, Mayer, 



1 Philosophical Magazine, 2nd Series, voL xxvi. p. 61. 



