COMPENSATION PENDULUM. 



J9§ 



The difficulty therefore stated in both my former letters 

 is thus explained, uuaiely, that we have considered quanti- 

 ties as equal, because they are represented by ttse same sym- 

 bols ; whereas, in consv^queuce of thus entering under ra- 

 d'ca's, and beina;- restricted with regard to their roots, all 

 equnlity between ihem ceases. 



Vv'iih regard to the proper criterion, by which such ano- Method ©f 

 roalies may be guarded ai^ainst in other cases, there appears ^'^^'^ "'" , 

 to be none more general than the following, viz. — that, in anomalies. 

 the invoiu'iion of qaaiitities under radicals, the operation 

 should noL be wo.ked cut at length, but indicated by the 

 sign of the particular power, to which it is to be raised, 



I have thus endeavouied to fuihl the promise which I 

 made in my former letter ; but how far what 1 have said 

 may be considered as satisfactory must be left to others to 

 decide, I shall only observe, that if any of your corre- 

 spondents should perceive any defect in the reasoning em- 

 ployed in the preceding pages, I shall be extremely happy 

 to see it corrected in a subseque^it number of this Journal ; 

 if not, I may probably at some future time trouble you 

 with a few other remarks on this subject. 



Yours, 



MATHEMATICUS. 



VIL 



Description of a Compensation Pendulum for a Clock : hif 

 Mr. Adam Reid, of Greenes End, Woolwich*. 



SIR, 



j[ OU will have the goodness to lay before the Society of Half-second 

 ArtR &c> a half-second compensating pendulum of my in- compensation 

 vention ; which is so simple in its construction, that it will ^^^ ^ ""** 

 be fully understood by viewing either the pendulum, or the 



* Trans, of the Soc of Arts, vol. XXVIII, p. 230. Fifteen guineas 

 were voted to Mr. Reid for this invention* 



drawing 



