Determination of the Acceleration of Gravity for Tokio. 447 



of which were found of any practical consequence, on account 

 of the very small angle through which the pendulum usually 

 swung, and that the decrement of the amplitude of the vibra- 

 tions was imperceptible even after many swings. Although, 

 however, such a pendulum as we were using approaches very 

 nearly a perfect simple pendulum, there are certain causes of 

 possible error arising from its flexibility and slight elasticity 

 which would not affect a rigid compound pendulum." 



Perhaps I ought to regard this as dust thrown into the 

 pupils' eyes, to prevent their attending to such well-known 

 reductions as those for arc, buoyancy, resistance, &c. But is 

 it possible not to suspect another explanation, when we have 

 just before heard that long-continued experiments with two 

 of u Kater's pendulums" (the convertible form is meant) 

 were at last abandoned as having proved " always unsatisfac- 

 tory"? How could they possibly be otherwise, in the ab- 

 sence of any knowledge of, or care about, the instrumental 

 constants ? Also we have been told that these results differed 

 too much from the value " calculated by a formula developed 

 by Clairault, who, from pendulum-experiments made at a 

 variety of latitudes on the earth's surface, has shown that, ap- 

 proximately, for any latitude X, and any height h centimetres 

 above the level of the sea, 



^=980-6056-2-5028 cos X-0-000003 A." 



To say nothing of the misprint (of cos X for cos 2X) and the 

 anachronism of assigning to Clairaut a formula metrically 

 expressed, I cannot find words to represent adequately the 

 state of dazed astonishment created by such an appeal. Not 

 only is the formula wrong, numerically, but it no more belongs 

 to Clairaut than to Copernicus. And even admitting that, in 

 demonstrating or elucidating some point in connexion with 

 the law of increase of gravity, Clairaut may have had recourse 

 to numerical exposition analogous to the above, the idea of 

 testing a modern experiment thereby is perfectly astounding, 

 when regarded as part of academical instruction. 



The force of gravity may be expressed, with all the preci- 

 sion at present justifiable, in metres, thus : — 



# = 9-8063-0-02553 cos 2\. 



If Clairaut is here credited with what he would not claim, 

 Colonel Clarke is scarcely more fortunate : — " Clairault's for- 

 mula assumes a circular equator ; Captain Clarke has found 

 that the equator is elliptical." Colonel Clarke will not thank 

 the authors for that raw statement. What he has taught is in 

 effect this : Assuming an equator more or less elliptical, the 



