324 Prof. Spencer U. Pickering, on Experimental 



variations of tan - is 

 a 



1 1 



extending from +co to -co. 



In such cases the general proof of the law of error breaks 

 down. The general formula for the modulus, that it is the 

 double sum of squares of the apparent errors, is apt to yield 

 an infinite result. We must fall back upon the explicit 

 methods. If, for instance, the law of facility above written, 

 or rather the more general form 



1 8 



V <irs 2 +y* 



held good for any species of phenomena, then, in order to 

 determine the improbability of a chance deviation to the extent 

 of y', we must integrate y from go to y f . 



In view of the rarity of such cases, I think we are justified 

 in concluding that the received formula enounced at the outset 

 is in general either accurate or at least safe; and that, in 

 the exceptional case where it is neither correct nor safe, it is still 

 corrigible, so far as the laws of error which exist in nature 

 may be regarded as binomials. 



XLIY. Experimental Error in Calorimetric Work. By 

 Spencer Umfeeville Pickering, M.A., Professor oj 

 Chemistry at Bedford College*. 



THE determination of the heat of dissolution of a solid in 

 water is an operation which will always occupy a most 

 important position in the majority of calorimetric determina- 

 tions ; and it is therefore desirable to ascertain what the 

 experimental error involved in this process is, and in what 

 direction we must look for a reduction of this error. The 

 large number of these determinations which I have had occa- 

 sion to make during the last two years will give the means 

 requisite for an investigation of this error. 



The modus operandi in the experiments was as follows : — 

 The given salt was weighed out into test-tubes on feet, which 

 were placed in an open metal beaker carefully guarded from 

 radiation and draughts by screens ; in this was suspended 

 a delicate thermometer, a companion instrument to that used 

 in the calorimeter itself, the exact difference in the readings 



* Communicated by the Physical Society : read February 13, 1886. 



