( 235 ) 



The third method, the only one that conhl be applied with good 

 results, as was remarked ahove, consists in measuring tlie angles of 

 inclination in two points of the curve, situated near each other. 



Let /?! and p.^ he two near points of a curve, the radius of curv- 

 ature of which keeps the same value q in all points between p^ and 

 j^j, the angle of inclination at p^ being represented l\y « and that 

 in p^ by ^. 



MX is an absciss in the coordinate system which was recorded 

 as a net of square millimetres together with the curve, but has been 

 omitted in the tignre, while MY, p^q^ and p.,q.^ are ordinates. 



It is seen from the tigure that 



sin a =r ana sin p = . 



9 Q 



Putting Mq.^ — Afq^ = xh we have 



. - (27) 



sin ^ — sin it 



The value of ^ can be read otF in a simple manner on the net 

 of square millimetres, while the angles « and /5 must be measured 

 by means of the eye-piece with cross-wires. This arrangement and 

 the accuracy that can be obtained by it, have already been dealt 

 with in the preceding chapter ; we now put the question in what 

 cases Ihe determination of ^ may or may not be practically useful. 



Let us once more consider formula (11) 



q zziz crv -\- cm , , . (11) 



this time as the expression of a curve, representing the damped 

 oscillations of a strongly stretched quartz-thread. For each reversing 

 point the value of t? must be put =0. Hence for a reversing point 

 the formula becomes 



cm 



Q 



m = ~Q, (28) 



c 



in which the sensitiveness c is an accurately known quantity. So it 

 would only be necessary to determine q and q in order to be able 

 to calculate at once a value for m from every reversing point. 



But here the pra-ctical difficulty lies in the quick variations which 

 Q shows already for moderate values of q. The time & has now to 

 be taken so small that it can no longer be measured with sufficient 



