August 4, 1916] 



SCIENCE 



159 



head in a water or gas pipe systematic 

 errors (due to "the particular details of 

 roughness, etc., in the pipe) are not in evi- 

 dence when a particular pipe is used, and 

 extrinsic errors may be made negligible by 

 using a precision device for measuring pres- 

 sure; but the loss of head (or pressure) re- 

 mains nevertheless extremely variable on 

 account of eddy action which grows out of 

 unstable vortex sheets; that is to say, very 

 large "errors" persist, the thing which is 

 being measured is inherently subject to 

 erratic variation. 



DESCRIPTIVE SCIENCE AND STATISTICAL 

 SCIENCE 



The greater part of physical science as 

 applied in the arts and as used by the inves- 

 tigator is essentially descriptive. Thus we 

 may wish to determine how the members of 

 a bridge stretch or shorten as a car passes 

 across the bridge; how electromotive force, 

 current strength and all the changing vari- 

 ables play in the operation of a dynamo; 

 how the pressure and temperature of the 

 steam vary during the successive stages of 

 admission, expansion and exhaust of a 

 steam engine; and so on. But everything 

 that takes place in this world has associated 

 with it a substratum of complex action 

 which baffles description. Consider, for ex- 

 ample, a simple thing like the movement of 

 a train of cars. The engineer is concerned 

 only with certain broad features of what 

 takes place, the amount of coal and water 

 used, the draw-bar pull of the locomotive, 

 and the forward motion of the cars as af- 

 fected by steepness of grade, and the oppos- 

 ing force of friction. But who could de- 

 scribe in detail the rocking and rattling mo- 

 tion of the cars and the whirling and eddy- 

 ing motion of the surrounding air, and who 

 could trace the motion of every particle of 

 dust and smoke ! This indescribably com- 

 plex action we call by the name of turbu- 



lence — it exists everywhere and in every- 

 thing that goes forward in this world of 

 ours, and it is never twice alike in detail 

 even when the conditions are what one 

 would consider exactly the same. All of 

 which suggests two postulates concerning 

 turbulence, namely (a) that it is infinitely 4 

 complicated, and (b) that it is essentially 

 erratic in character. Let it be understood, 

 however, that we are not speaking in terms 

 of ordinary values in making these two 

 statements. It is not a question, for ex- 

 ample, as to whether a brakeman loses his 

 hat every time he makes a trip from Albany 

 to Buffalo, but it is a question as to whether 

 his hat is lost every time at identically the 

 same place because of a gust of wind of 

 precisely the same character when he lets 

 go of it in the same way because of a sud- 

 den jerk of the train which always occurs 

 at the same place in exactly the same man- 

 ner, and so on in endless detail of specifica- 

 tion — if such specification were possible ! 



In the motion of a simple mechanism like 

 the sun and planets, or in the operation of 

 a simple machine like a dynamo the accom- 

 panying erratic action is practically negli- 

 gible. Thus one does not consider even the 

 tremendous storm movements in the sun in 

 the study of planetary motion, and one 

 does not consider the minute details of the 

 motion which takes place in a lubricated 

 bearing in the study of the operation of a 

 dynamo. In many phenomena, however, 

 erratic action is dominant, and in the study 

 of such phenomena the statistical method 

 must be used. Consider, for example, the 

 motion of the water in a brook. This mo- 

 tion presents a fairly definite average char- 

 acter at each point, and a fairly typical 

 rhythmic variation from this average exists 

 at each point, but there is an erratic depar- 



* The idea of infinity which comes from counting, 

 one, two, three, four and so on ad infinitum, is as 

 nothing compared with the intimation of infinity 

 that comes from things that are seen and felt! 



