SECT. 13.] Averages. 449 



very possibly does not agree with any one of them. If I find 

 the temperature in different parts of a room to be different, 

 but say that the average temperature is 61, there may per 

 haps be but few parts of the room where this exact tempera 

 ture is realized. And if I say that the average stature of 

 a certain small group of men is 68 inches, it is probable that 

 no one of them will present precisely this height. 



The principal way in which accuracy can be thus secured 

 is when what we are really aiming at is not the magnitudes 

 before us but something else of which they are an indication. 

 If they are themselves inaccurate, we shall see presently 

 that this needs some explanation, then the single average, 

 which in itself agrees perhaps with none of them, may be 

 much more nearly what we are actually in want of. We shall 

 find it convenient to subdivide this view of the subject into 

 two parts ; by considering first those cases in which quantita 

 tive considerations enter but slightly, and in which no deter 

 mination of the particular Law of Error involved is demanded, 

 and secondly those in which such determination cannot be 

 avoided. The latter are only noticed in passing here, as a 

 separate chapter is reserved for their fuller consideration. 



13. The process, as a practical one, is familiar enough 

 to almost everybody who has to work with measures of any 

 kind. Suppose, for instance, that I am measuring any object 

 with a brass rod which, as we know, expands and contracts 

 according to the temperature. The results will vary slightly, 

 being sometimes a little too great and sometimes a little too 

 small. All these variations are physical facts, and if what 

 we were concerned with was the properties of brass they 

 would be the one important fact for us. But when we are 

 Joncerned with the length of the object measured, these facts 

 Become superfluous and misleading. What we want to do is 

 o escape their influence, and this we are enabled to effect by 

 v. 29 



