Results of Experiments. 419 



hurry of modern life are apt to omit the test of accuracy 

 afforded by obtainiDg the same results by several different 

 methods. Thus long rows of figures are frequently given 

 which have in reality no experimental basis to rest upon. 

 On the other hand, mathematicians obtain formulae which 

 require experimental results of unattainable accuracy, and 

 frequently immense arithmetical labour in the course of which 

 the experimentalist is led into bewilderment and error. 



There are only three possible methods of finding an equa- 

 tion to connect two or more physical quantities, of which one 

 has been recently applied in a manner open to very grave 

 suspicion. 



(i.) By deduction from a general law assumed to connect 

 the phenomena the form of the required function is obtained 

 and the constants are then determined by experiment. Too 

 little is known about the ultimate constitution of matter to 

 allow of the safe application of this method in the cases which 

 ordinarily occur in physics and chemistry. It is, however, 

 used not unfrequently in astronomy and practical mechanics, 

 e. g. in determining heights by the fall of the barometer, and 

 the variation in gravity with latitude. 



(ii.) In the graphical method the experimental results are 

 plotted on a sheet of paper or metal, and a curve drawn 

 through these points is assumed to give the most reliable 

 expression for the general law. The problem of drawing a 

 curve through any given points is essentially an indetermi- 

 nate one, hence the following further assumptions are gener- 

 ally made : — (a) the simplest curve (i. e. with the fewest 

 changes of curvature) which fairly fulfils the given conditions 

 is to be chosen ; (6) nearly an equal number of experimental 

 results should lie on each side of each portion of the curve. 



No one can deny the great value of this method in all cases 

 in which minute accuracy is not required. Thus it gives a 

 ready solution of the efficiency of engines and machines, the 

 volume of earthwork, and the best shape of roof and bridges ; 

 but when it is applied to the solution of certain theoretical 

 questions, it is apparently pressed at times beyond its power. 



Regnault made use of a copper sheet divided into small 

 squares, in which the intersection of the experimental ordinate 

 and abscissa was drawn by a special dividing-engine. Among 

 these points a curve was drawn by the " free hand" and 

 engraved. 



Experimentalists now prefer squared paper. In some of 

 French manufacture a sheet is divided into 1,000,000 milli- 

 metre squares by dotted lines, with five dots to the millimetre. 

 In the middle part of such a sheet one part in 2500 can be 



2H2 



