January 23, 1920] 



SCIENCE 



89 



Among the comparative recent develop- 

 ments in geodesy that are especially well 

 stated in the book are (1) the importance of 

 determining the relative strength of different 

 proposed chains of triangulation as fixed by 

 the geometrical relations, and the methods 

 for quickly doing so; (2) the relation between 

 the average length of the lines in a triangula- 

 tion and the rapidity, economy, and accuracy 

 of that triangulation and its convenience to 

 the user; (3) the advantages of the light and 

 rapidly built towers such as are now used in 

 the Coast and Geodetic Survey; (4) the ad- 

 vantages of the transit micrometer on portable 

 instruments for determining time accurately; 

 (5) the application of the interferometer to 

 determination of the flexure of the support of 

 a pendulum used to determine the relative 

 values of gravity at different points. These 

 things are stated forcefully and with good 

 judgment as to their relation to older ideas 

 and methods. 



Though he has looked carefully for errors 

 of omission, the reviewer, who has a back- 

 ground of experience which naturally tends 

 to make him keenly critical, finds only three 

 that are, in his opinion, important. 



1. On its best direction theodolites the 

 Coast and Geodetic Survey uses two sets of 

 double parallel lines in the micrometer micro- 

 scopes with which the horizontal circle is 

 read, the two sets being so placed that the 

 observer moves the micrometer screw only one 

 turn between a forward and the corresponding 

 backward reading, instead of five turns. This 

 is a time-saving convenience which also in- 

 creases the accuracy, and surely should have 

 been mentioned in the book. 



2. The necessity of tracing back the adopted 

 field length of a base measuring tape to the 

 standard meter and the methods of doing so 

 are inadequately treated in the book. The 

 developments of the past twenty years have 

 made it clear that one must concentrate much 

 more keenly on this part of the work than 

 the book indicates. 



3. The area method of computing the figure 

 of the earth from geodetic and astronomic 

 observations is barely referred to on page 204 

 without explanation. In view of the fact that 



this method gives a much higher degree of 

 accuracy from the same observations than the 

 traditional arc method, it certainly deserves a 

 page of general exposition in the book, even 

 if it is possibly too difficult for the student to 

 grasp in full. The student and the engineer 

 should know that the more accurate method 

 exists, should know its general character, and 

 in a general way why it is more accurate than 

 the arc method. 



The author of the book has shown such 

 ability to see with the eye of an expert, and to 

 exercise the judgment of a practicing geodetic 

 engineer, that one may confidently expect that 

 even these three omissions will not occur in a 

 second edition. 



John F. Hayford 



SPECIAL ARTICLES 



CONCERNING APPLICATION OF THE PROB- 

 ABLE ERROR IN CASES OF EXTREMELY 

 ASYMMETRICAL FREQUENCY CURVES 



In a study of the fecal pollution of shell- 

 fish. Dr. James Johnstone^ raises an im- 

 portant question : that of determining the 

 most probable value of a measure from a 

 series whose frequency distribution is highly 

 asymmetrical. In such instances it is evi- 

 dent, although prevailing practise contradicts 

 the statement, that it is illegitimate to apply 

 the probable error in the usual manner. For 

 such application presupposes a symmetrical 

 (Gaussian) distribution, and, since a wide 

 range of biological measurements is char- 

 acterized by an asymmetrical distribution, the 

 matter merits consideration. 



Dr. Johnstone lists the following counts of 

 colonies of bacteria growing on twenty plates, 

 each having been incubated a standard length 

 of time after being inoculated with 1 c.c. of 

 an emulsion, in 250 c.c. of water, of five 

 muscles collected at random from the polluted 

 area: 7, 24, 40, 15, 22, 20, 17, 9, 16, 29, 7, 9, 

 10, 26, 15, 11, 21, 17, 10, and 41. Dr. John- 

 stone assumes each count to be an estimate of 

 the number of bacteria per c.c. of the emul- 



1 ' ' The Prolbable Error of a Bacteriological 

 Analysis," Eept. Lane. Sea-Fisli. Lab., 1919, No. 

 XXVII., p. 64-85. 



