i873-] Notices of Books. 521 



introduced by the irregular numbers will be compensated by the 

 very process of taking the arithmetical mean, for, as single ones 

 among a greater number, they have small influence upon the 

 mean value." This is, no doubt, good advice, but very difficult 

 to follow ; if, for example, in a series of twenty observations, 

 seventeen agree very closely, and three are altogether anomalous, 

 or at least differ more widely, the conclusion seems to be almost 

 irresistible that, in these three divergent results, the " personal 

 equation " of the observer has, by some unknown means, been 

 unduly exalted, or some unseen or unremembered error of manipu- 

 lation has crept into the observation. If made absolutely under 

 the same conditions, of course every determination, however 

 anomalous it may be, and however the series may be prolonged, 

 is subject to equal credence. 



The first section is devoted to an account of " Weighing and 

 the Determination of Density." In this, full rules are given for 

 the adjustment and testing of a balance and of the weights ; 

 also various modes of weighing, and the determination of the 

 density of solids, liquids, and gases. This is followed by 

 measurements relating to heat ; the calibration of a thermometer, 

 and determination of its fixed points ; the various methods of 

 calorimetry, &c. 



The determination of the modulus of elasticity of a body is 

 discussed under various forms, as by stretching, and by the 

 complex and somewhat unusual method by longitudinal vibra- 

 tions, in which the necessary factors are (a) the length of the 

 wire, (/3) its specific gravity, (y) the acceleration by gravity, (#) 

 the number of longitudinal vibrations per second. The time of 

 vibration is determined by a tuning-fork of known pitch, and the 

 longitudinal vibrations are produced in the usual manner, by 

 rubbing the rod with woollen cloth sprinkled with resin. The 

 determination of the modulus by bending a rod, and by swinging 

 under torsion, is also described. 



The optical measurements include various determinations 

 connected with spectroscopy, the wave-length of a ray of light, 

 the focal length of a lens, the magnifying power of optical 

 instruments, the operations of saccharimetry by polarised light. 

 Finally, a number of magnetic and electrical measurements are 

 described in detail. 



The tables at the end of the volume will be found of consider- 

 able service; here we find, among others, the density of certain 

 gases given to seven places of decimals, the density of water 

 to five places of decimals between o° and 30° C, the expansion 

 of water, the density of -air at various temperatures, and the 

 capillary depression of mercury in a glass tube of from 1 to 10 

 millimetres diameter. Table 19 gives the lines of flame- 

 spectra of the most important light metals, according to the 

 scale of Bunsen and Kirchhoff, in which the slit is considered to 

 have the breadth of one division, while the sodium line is taken 



