via PREFACE. 



many persons the present volume should, therefore, provide all the 

 logarithmic and trigonometric tables needed for the entire ran 



I'cr \vork of greater precision than the above limit, 

 the more bulky Vega, or seme similar reliable seven-place table 

 would be required. It is exceedingly rare that more than six or 

 re necessary, while for most work five are sufficient. 

 although a striking chapter of absurd illustrations might be gleaned 

 a r ions text-books and tables where ten- and even twenty-place 

 '.thins are given, often for quantities uncertain in their fourth 

 or fifth place. Persons doing much work with squares, cubes, square 

 roots, cube roots, or reciprocals of more than four places would natu- 

 rally make use of the Barlow Tables. 



The rules for significant figures (pages xi to xv) are intended to 

 be terse, direct, and simple, so that they may be easily acquired and 

 retained. The strong type emphasizes the leading portions. The 

 ordinary and finer types give details and explanations. For the sake 

 of affording still greater prominence to the main working portions, 

 some explanatory matter which will be unnecessary to many per- 

 sons has been transferred from its more logical position of precedence 

 to the latter part of the text. These rules in various forms have 

 been in successful use by large classes of students, in connection 

 with the author's "Physical Laboratory Notes" (printed, but not 

 published, by the Massachusetts Institute of Technology), and his 

 " Precision of Measurements." The recognition of the need of such 

 rules amongst engineers and others whose practical work demands 

 rapid and reliable computations was the cause of their general intro- 

 duction into this laboratory instruction. It is therefore hoped that 

 they may render effective service to others besides the students for 

 whom they have been more directly designed. 



In the arrangement of the tables, the effort has been exerted to 

 make them correct, legible, systematic, and convenient in use. A 

 new set of tables is, of course, liable to contain mistakes ; notices of 

 errata will therefore be thankfully received. 



The special indexing of the corners of pages, the use of heavy 

 type at points to be made conspicuous, the employment of spaces 

 rather than rules for the partition of lines and columns, and the 

 style of type and kind of paper used, are believed to conduce to 

 legibility. As to system of arrangement, there are few novelties 

 other than the insertion of the logs, cplogs, and reciprocals of i .000 

 to 1. 1 oo at the top of the respective four-place tables, and the division 



