NATURE 729 



to those which have been observed, but it also gives me the observed 

 values more accurately than direct observation does; that is why I 

 make the curve pass near the points and not through the points 

 themselves. 



Here, then, is a problem in the probability of causes. The effects 

 are the measurements I have recorded; they depend on the com- 

 bination of two causes the true law of the phenomenon and errors 

 of observation. Knowing the effects, we have to find the probability 

 that the phenomenon shall obey this law or that, and that the observa- 

 tions have been accompanied by this or that error. The most probable 

 law, therefore, corresponds to the curve we have traced, and the most 

 probable error is represented by the distance of the corresponding point 

 from that curve. But the problem has no meaning if before the observa- 

 tions I had an a priori idea of the probability of this law or that, 

 or of the chances of error to which I am exposed. If my instruments 

 are good (and I knew whether this is so or not before beginning the 

 observations), I shall not draw the curve far from the points which 

 represent the rough measurements. If they are inferior, I may draw 

 it a little farther from the points, so that I may get a less sinuous 

 curve; much will be sacrificed to regularity. 



Why, then, do I draw a curve without sinuosities? Because I 

 consider a priori a law represented by a continuous function (or 

 function the derivatives of which to a high order are small), as 

 more probable than a law not satisfying those conditions. But for 

 this conviction the problem would have no meaning; interpolation 

 would be impossible ; no law could be deduced from a finite number 

 of observations; science would cease to exist. 



Fifty years ago physicists considered, other things being equal, a 

 simple law as more probable than a complicated law.- This prin- 

 ciple was even invoked in favor of Mariotte's law as against that of 

 Regnault. But this belief is now repudiated; and yet, how many 

 times are we compelled to act as though we still held it! However 

 that may be, what remains of this tendency is the belief in continuity, 

 and as we have just seen, if the belief in continuity were to disap- 

 pear, experimental science would become impossible. 



VI. The Theory of Errors. We are thus brought to consider the 

 theory of errors which is directly connected with the problem of the 

 probability of causes. Here again we find effect* to wit, a certain 

 number of irreconcilable observations, and we try to find the causes 

 which are, on the one hand, the true value of the quantity to be 

 measured, and, on the other, the error made in each isolated observa- 

 tion. We must calculate the probable a posteriori value of each error, 

 and therefore the probable value of the quantity to be measured. 

 But, as I have just explained, we cannot undertake this calculation 

 unless we admit a priori i.e., before any observations are made 



