210 TUE PRINCIPLES OF SCIENCE. 



considerably exceeded that obtained by any other method, 

 being no less than 6-566, or 6-623 as finally corrected. 



In 1844 Sir John Herschel remarked in his Memoir of 

 Francis Baily f , that the mean specific gravity of this our 

 planet is, in all human probability, quite as well deter 

 mined as that of an ordinary hand-specimen in a mine- 

 i alogical cabinet, a marvellous result, which should teach 

 us to despair of nothing which lies within the compass of 

 number, w r eight, and measure/ But at the same time he 

 pointed out that Baily s final result, of which the probable 

 error was only 0*0032, was the highest of all determina 

 tions then known, and Airy s investigation has since given 

 a much higher result, quite beyond the limits of probable 

 error of any of the previous experiments. If we treat all 

 determinations yet made as of equal weight, the simple 

 mean is about 5-45, the mean error nearly 0*5, and the 

 probable error almost O 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 AiryB, 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. In this case we learn an impressive 

 lesson concerning the value of repeated determinations by 

 distinct methods in disabusing our minds of the reliance 

 which we are only too apt to place in results which show 

 a certain degree of coincidence. 



Since the establishment of the dynamical theory of heat 

 it has become a matter of the greatest importance to 

 determine with accuracy and high probability the mecha 

 nical equivalent of heat, or the quantity of energy which 



f Monthly Notices of the Royal Astronomical Society for 8th Nov. 

 1844, No. X, vol. vi. p. 89. 

 * Philosophical Magazine, 2nd Series, vol. xxvi. p. 61. 



