48 Messrs. Ayrton and Perry on the Determination 



less than the tenth of a millimetre per second per second — that 

 is, by less than the one hundred thousandth part of the value of 

 g ; so that, seeing that local circumstances would probably 

 make the real value of g differ by more than the one hundred 

 thousandth part from the calculated value, Major Herschel's 

 correction is of absolutely no importance for the object of our 

 paper, which concerned the value of g in Tokio. 



But Major Herschel says, in disparagement of our experi- 

 mental determination of the value of g for Tokio, Japan, that 

 the formula " no more belongs to Clairaut than to Coper- 

 nicus." In the table of contents, however, of Thomson and 

 Tait's standard work on Natural Philosophy wo find " Clai- 

 rault's formula for the amount of Gravity;" and in section 

 222, page 167, there referred to, it is stated : — 



" The formula deduced by Clairault from observation, and 

 a certain theory regarding the figure and density of the earth 

 may be employed to calculate the most probable value of the 

 apparent force of gravity. This formula, with the two coeffi- 

 cients which it involves, corrected according to the best pen- 

 dulum observations (Airy, Encyc. Metr., Figure of the Earth) 

 is as follows : — 



" Let G be the apparent force of gravity on a unit mass at 

 the equator, and g that at any latitute X ; then 



# = G (1 + -005133 sin 2 X)." 



If, then, Clairault proposed any formula of the form 



a + b sin 2 \, 



it will still, it appears to us, be Clairault's formula when put 

 in the form 



(a + ^)- 2 cos2\; 



nor do we think that the unit of length, English, French, 

 Japanese, &c, which may be involved in the expression for 

 the acceleration due to gravity at different latitudes affects the 

 name of the formula. 



That our having compared the value of g obtained from a 

 long course of experiments, with the approximate value calcu- 

 lated from the standard formula, should have caused Major 

 Herschel to be unable to " find words to represent adequately 

 the state of dazed astonishment created by such an appeal," is to 

 be regretted, but, we are afraid, cannot be helped, seeing that 

 the comparison of results obtained experimentally with those 

 previously calculated from theoretical considerations is the 

 ordinary method of procedure in physical investigations ; and, 

 indeed, we may add that in Col. Clarke's l Geodesy ' the great 



