Dr. Schroder van der Kolk on the Velocity of Sound. 47 



In order to be able to compare approximately the values of 

 these determinations, the probable errors of each are calculated. 

 For the 27th of June this calculation is made from the column s, 

 and for the 28th of June from the last column. The sum of the 

 squares is thus found to be 



27th June. 28th June. 



2210, 18715; 



whence it follows that the probable error of one observation in 

 seconds is 



0069, 0-256; 



and for the mean values, 



0-0147, 0-0684. 



This is the probable amount of the errors in the determina- 

 tions of the velocity during 52 seconds ; therefore upon one 

 second they would be 



0-00028, 0-0684*; 



and in metres, 



0-096, 0-442. 



In consequence of this difference in the probable errors, we 

 must not take the arithmetical mean of the two determinations, 

 but must calculate the relative weight to be given to each. 

 These are to each other as 



11 _ : 



96 2 442 2 



icaii y. 





Hence we have 









Probable error. 



Value. 



27th of June . . . 332'82 



0096 



20, 



28th „ ... 331-91 



0-442 



h 



and this gives for the velocity of sound in dry air at 0° C, and 

 under 0*760 metre pressure, 



332-77 + 0-093 metre. 



The result is accordingly 0*72 metre higher than was given 

 by the previous calculation. 



In one respect the probable error that has been found is still 

 a little too great. During each day's observations the tempera- 

 ture and pressure were not constant, but slightly variable. If 

 we take the mean of all the readings, the final result remains the 



* [Should apparently be 0-00132.— Transl.] 



