1 1 8 Sou ntific [intelligence. 



."). American Lubricants, by 1j. IS. Lookhaet. 8vo, pp. '-'•!(>. 

 Gaston, Pa., 1918 (The Chemical Publishing Company).- This 

 hook is intended particularly as an aid to users in the selection 

 of lubricants. II gives interesting data in regard to the produc- 

 tion and refining of petroleum, descriptions of the products, and 

 ilic physical tests for examining them. Lubrication is discussed 

 in a great variety of special eases, especially in connection with 

 viscosity. Animal and vegetable Eats and oils ace also exten- 

 sively discussed, and physical and chemical tests for them are 

 given. A large number of copies of specifications for various 

 commercial oils are given, and several tallies relating to viscosity, 

 specific gravity, temperatures, prices of oils and heavy chemicals, 

 and petroleum statistics are appended. It should be said that 

 the hook is not wholly devoted to lubricants, for other petroleum 

 products such as gasoline, fuel-oil and kerosene are dealt with. 

 The book wall be useful not only to those who are interested in 

 machinery, but also to chemists who have occasion to examine. 

 oils, greases and other lubricants. H. L. w. 



6. Prime Numbers. — For obvious reasons, the last anniver- 

 sary address of the President of the Royal Society, Sir J. J. 

 Thomson, contains practically nothing of interest for the phys- 

 icist. His comments, however, on a certain investigation rela- 

 tive to a rule for prime numbers merit quotation. "If we take 

 the numbers in order 1, 2, 3, . . . we see that there are some, 

 such as 3, 5, 7, 11, which cannot be divided by any number smaller 

 than themselves; these are called prime numbers; the number 

 of such primes which are less than a given number is a matter 

 of very considerable importance, and Gauss, many years ago, 

 gave, without any rigorous proof, a rule about it. The rule was 

 tested by actual trial for numbers up to a thousand millions, 

 and, as it was found to be true over that immense range, it was 

 accepted as universally correct in spite of the absence of a satis- 

 factory proof. Quite recently, however, Mr. Littlewood, one of 

 our Fellows, has shown that, in spite of this apparently over- 

 whelming evidence in its favour, the result is not general, but 

 the numbers for which it breaks down are so enormous that, it 

 would be quite beyond the powers of human endurance to detect 

 its failure by actual trial. I may say, in passing, that, enormous 

 as these numbers are, they are mere nothings, compared with whal 

 we have to deal with in many branches of Physics. Here, then, 

 we have a result which has satisfied, and apparently always will 

 satisfy, any direct test that can be applied to it, and yet is not 

 generally true ; there seems to me to be something of a tragedy, 

 perhaps the suspicion of a sermon, in this investigation, which 

 is in a paper of a highly technical character, quite unintelligible 

 to anyone who was not an expert mathematician." — Proc. Roy. 

 Soc, 94A, 187, 1918. h. s. u. 



7. Polarimetry. Second Edition. Pp. 196, 12 figures. 

 Washington, 1918 (Circular No. 44 of the Bureau of Stand- 



