158 



SCIENCE 



[N. S. Vol. XLIV. No. 1127 



special fluids as the cerebro-spinal fluid, 

 the aqueous humor and the fluids of the 

 serous cavities, as well as the general fluid 

 of the less specialized tissue-spaces. 



The study of the lymphatic system throws 

 emphasis on the importance of tissue-spaces. 

 I am convinced that the understanding of 

 lymphatic capillaries as definite struc- 

 tures, definitely placed in restricted areas, 

 forms a secure basis from which the varied 

 problems of absorption may be solved. 

 Florence R. Sabin 



The Johns Hopkins University 



STATISTICAL PHYSICS 1 



Evert physical measurement must be 

 made in a region in equilibrium, 2 and nearly 

 all of the correlations which have been 

 established in physics, that is, nearly all 

 physical laws, relate to substances in steady 

 states or to substances in equilibrium. 

 Furthermore, nearly all physical laws are 

 one-to-one correspondences, and they are 

 expressible as analytical functions. Thus 

 the pressure of a given amount of a gas is 

 an analytical function of the volume and 

 temperature of the gas. 



In every field of measurement, however, 

 extreme refinement and care lead an inves- 

 tigator into a region of erratic action. This 

 is evident when we consider that refined 

 measurements are always subject to erratic 

 error, and the atomic theory of the consti- 

 tution of matter suggests that erratic action 

 is always present everywhere, even in sub- 

 stances in complete thermal equilibrium. 



i The substance of a lecture delivered by "W. S. 

 Franklin before the Department of Terrestrial 

 Magnetism of the Carnegie Institution, Washing- 

 ton, D. C, December 20, 1915. 



2 Thermal equilibrium is here referred to; cer- 

 tain quasi states of thermal equilibrium being in- 

 cluded. The only exception is the kind of meas- 

 urement which consists of simple counting, like the 

 counting of cattle as they pass through a gate or 

 the counting of electrons as they enter an ioniza- 

 tion chamber. 



It has long been the custom to speak of 

 the probable error of a precise measurement 

 as if perfect precision would be possible if 

 our measuring devices were perfect and 

 free from erratic variations. It is impor- 

 tant, however, to recognize two distinct 

 types of erratic error, namely, extrinsic 

 error due to uncontrollable variability of 

 the measuring device or system, and intrin- 

 sic error due to inherent variability of the 

 thing or system which is being measured. 

 Every physical measurement involves an 

 operation of congruence, a standard of some 

 kind is fitted to or made congruent with, suc- 

 cessive parts (which parts are thereby 

 judged to be equal parts) of the thing or 

 system which is being measured; and the 

 standard system and the measured system 

 are both subject to erratic variations. 



There is, perhaps, no case in which intrin- 

 sic error and extrinsic error can be clearly 

 distinguished and separated from each 

 other ; but when the errors of one kind are 

 much larger than the errors of the other 

 kind they can, of course, be recognized. It 

 is proper to speak of the probable error of 

 a single measurement when the variations 

 of the measuring device or system are domi- 

 nant, but one should speak of the probable 

 departure of the measured system from a 

 certain mean condition at any time when 

 the "errors" of observation are due chiefly 

 to variability of the thing or system which 

 is being measured. Thus in measuring the 

 coefficient of sliding friction extrinsic 

 error may be made negligible by making 

 the measurements carefully, but very large 

 "errors" persist. The thing which is being 

 measured is inherently indefinite, and it 

 may at any time depart widely from its 

 average value. 3 In measuring the loss of 



s A very brief but comprehensive statement of 

 the proper precision method for the study of an 

 erratic thing like friction is given by W. S. Frank- 

 lin, Transactions of American Institute of Elec- 

 trical Engineers, Vol. 20, pp. 285-286. 



