Vol. 4] Thelen. — Thermal Conductivities of Certain Schists. 217 



other turn. Then the motion was reversed. As the lost motion of 

 the instrument was considerable, readings were obtained at C 

 and D which were numerically different from those at A and 

 B. I f the two values of the differences of the readings agreed 

 within ten units, as they easily did, no further measurements 

 were taken on that axis. 



It was found in the early stages of the work that the prob- 

 able error of the mean of a number of observations on different 

 figures on the same face could be kept under one per cent., with- 

 out taking an unreasonably large number of readings, — not that 

 the homogeneity of the rock was sufficient to give the same results 

 on spots a few cm. apart, but the mean value represents the 

 average ratio over a large portion of the specimen. One per 

 cent., then, was set as the limit of the probable error of the 

 mean value of any one ratio, and the number of readings was 

 increased where necessary till this accuracy was obtained. 

 Columns 4 and 5 of the table show that this intention was prob- 

 ably realized. 



Senarmont, working with the largest obtainable monoclinic 

 crystals, said: "Selten sind die drei Beobaehtungen einer 

 solchen Genauigkeit fahig dass sie einer numerischen Vergleich 

 gestatten." But his material was not always satisfactory. 

 With a good specimen of calcite, he obtained on one face ten 

 values varying from 1.09 to 1.19. Such is about the range ob- 

 tained in the most unfavorable cases by the writer. The end 

 section of the W ranged schist yielded 19 results varying in value 

 from .773 to .892. The probable error of the mean, .808, com- 



puted by the familiar formula I—. 67-15-. /— ; -.was .009. 



\ n (n — 1 ) 



A rhombic section parallel to A of the same rock, yielded as 

 the most favorable case, seven values ranging from .810 to 

 .835, with a probable error of the mean, .823, of .002. Of 

 course the term probable error is really a misnomer, for this is 

 not a ease of measuring the same quantity a number of times, 

 since neither the homogeneity of the rock, as before suggested, 

 nor its uniformity of structure, as will be shown later, are such 

 as to lead one to expect the same ratios at all points of any one 

 surface. (A fresh crystal, however, might be expected to do this.) 



