THE 



PHILOSOPHICAL MAGAZINE 

 AND JOURNAL. 



:1 st OCTOBER 1826. 



XXXVI. On the Methods proper to be used for deducing a 

 general Formida for the Length of the Seconds Pendulum, 

 from a Number of Experiments 'made at different Latitudes. 

 By J. Ivory, Esq. M.J. F.R.S.* 



nPHE determination of the figure of the earth by means of 

 -*- terrestrial experiments, is a problem of extreme delicacy. 

 The solution of it requires the measurement of magnitudes 

 nearly equal, such as a degree of the meridian, or a pendulum 

 that oscillates in a given time ; and as the investigation turns 

 on the differences of those magnitudes, the greatest precision 

 is necessary, because errors inconsiderable in respect of the 

 magnitudes themselves, may nevertheless bear a great propor- 

 tion to the small differences. But even granting that the de- 

 sired degree of accuracy has been attained in the experiments, 

 yet the difficulties of the problem are not entirely overcome. 

 When the data of a mathematical question are exact, the re- 

 sult is rigorously accurate ; and thei'e can be no reason for 

 preferring one mode of solution to another, except easiness in 

 the calculation, or elegance in the process of deduction. But 

 if the data be liable to error, as in most physical researches, 

 the effect of the probable errors must be scrupulously ex- 

 amined in every proposed solution. Every method of investi- 

 gation must be rejected as uncertain and unsafe, when small 

 changes in the data would produce great variations in the re- 

 sult. Unless care be taken in this respect, it is evident that a 

 deficiency of mathematical science might be attended with the 

 same consequences as the want of accuracy in the experi- 

 ments. 



It is usual to employ the method of the least squares in de- 

 ducing the ellipticity of the earth from a number of pendu- 

 lum experiments made at different latitudes. Now this prac- 

 tice would seem at a first view to be very unexceptionable, 

 whether we regard the certainty of the general principles of 

 the method, or its great practical utility, or its extensive ap- 



* Communicated by the Author. 

 Vol. 68. No. 342. Oct. 1826. 2 H plication. 



