Intelligence and Miscellaneous Articles. 407 



re-examination. In consequence of this recommendation, a well- 

 practised computer in the Nautical Almanac Office was employed to 

 read three thousand of the logarithms of numbers and eight degrees 

 of the trigonometrical portion (all chosen at hazard), and compare 

 them with tables of undoubted accuracy. The consequence was, the 

 detection of only three errors, one in the numbers, two in the sines, 

 &c. ; of these three there was only one which an expert user of the 

 tables could not have detected at sight. This being considered, and 

 also the number of errors which were detected in Hassler's book du- 

 ring the printing, it is certain that the work before us must be very 

 correct ; as correct, indeed, as any table is likely to be unless it have 

 been first stereotyped and then re-examined, and much more so 

 than most others of the same size. 



The work is an imitation of Hassler's, and has the same small oc- 

 tavo form. All the logarithms are to seven decimals. The loga- 

 rithms of numbers are as usual : in the trigonometrical portion the 

 first and last five degrees are to every ten seconds, all the rest to every 

 half minute, with differences for ten seconds annexed. In the first two 

 degrees is added a factor for facilitating the determination of the 

 logarithmic sine or tangent of the fractional part of a second. The 

 type is clear and the paper good. We can decidedly recommend the 

 work, and have we think shown reasons for our confidence. 



LXXI. Intelligence and Miscellaneous Articles. 



On itie Law of Double Refraction. By James MacCullagh, 

 Fellow of Trinity College, and Professor of Mathematics in 

 the University qf Dublin *. 

 IT AV1NG mentioned, in an articlef which I sent a few days 

 -*•-*• ago for insertion in the Philosophical Magazine, that I 

 had been led, in following out an hypothesis, to a law of 

 double refraction more general than that of Fresnel, I think 

 it may be well to state very briefly the nature of that law, and 

 to point out the difference between it and the law of Fresnel, 

 especially as I have since observed that the difference is one 

 of a very extraordinary kind, and one which, if it has a real 

 existence (a question which experiment only can decide), may 

 serve to account for phaenomena that have seemed hitherto 

 inexplicable. 



I have said, in the article referred to, that when the poten- 

 tial V, which is a function of the second degree, is supposed 

 to contain only the squares and products of the derivatives 

 X, Y, Z, X 2 , Y 2 , Z 2 , X 4 , &c, we get the law of Fresnel, as well 

 as the law of crystalline dispersion ; but if we make the more 

 general, and apparently the more natural supposition, that it 



* Communicated by the Author. 



+ On the Dispersion of the Optic Axes, and of the Axes of Elasticity, in 

 Biaxal Crystals. [Inserted in the last Number, p. 293.] 



