( 250 ) 



rr^ Hlh 

 m,=—mX . . . i . . . (32) 



The accuracy with which m^ can be calculated in grammes depends 

 of course in the first place upon the accuracy with which m is known 

 in [min — {.lA) units and further upon the accuracy of the values of 

 H, I, h and V. TJie latter quantity occurs in formula (32) squared 

 and so would \\u\q a preponderant importance. But the time-record- 

 ing arrangement which we used, works, as we saw formerly, with 

 so great an accuracy that we may neglect errors in the value of V. 



Also / and h can be measured with sufticient accuracy, while for 

 H the value has been taken which we found in chapter IV, namely 

 17600 [C. G. S.]. 



The error in the absolute value of m.^ I estimate at a few percent. 



In formula (32) we have. 



/ƒ= 17600, 

 1= 12,7, 

 & = 660, 



Fr=500, 



from which follows that ???! = 7,28 X -10-4 ?« (33) 



In chapter III we found that : 



for string W. 10 m = 9,4 X 1Ö-3 [mm — iiA] 

 „ „ 13 m = 6,9x10-3 „ 

 „ „ 14 m = 3,6 X 10-3 ^^ 



By formula (33) we calculate from this the mass of the strings in 

 absolute measure : 



for string N". 10 m, = 6,85 X lO-e gram. 

 „ „ 13 VI, = 5,02 X 10-6 ,^ 

 „ „ 14 m, = 2,62 X 10-^ „ 



We passingly remark that for recording sounds we use a very 

 light short string: a 2,5 cM. long, 1 ft thick quartz thread, of which 

 the weight may be estimated at about 1,5x10-" grammes. 



From the length /, the diameter d of the naked quartz thread and 

 the specific gravity of quartz s, the weight of the quartz may be 

 calculated as 



•^ 4 

 This weight is only inaccurately known on account of the uncer- 

 tainty in (I. But combined with the value of m, it may serve us 

 to obtain a rough idea of the relative weights of quartz and silver 

 in the string. Calculated in this manner we find this ratio 



