204 president's address. 



worked out a definite problem. By inspection you may see that 

 the aberration is positive, but it is only when you work out an 

 example that you find the smallness of the positive aberration 

 at a single surface by the cubic equation, and tbis is what they 

 have not done. 



In conclusion, I must apologise for having, on this second 

 occasion, brought such a dry subject before you.* 



Appendix. 



Sir John Herschel's doublet (high power form), as given in 

 " Ency. Metrop.," art. " Light," p. 391, transposed to a com- 

 bination whose focus is -f 1*0. Refractive index 1*50 

 1st lens crossed r = + 1'644 



s = — 9-866 / = + 2-819 

 2nd lens, meniscus r = + "579 



s= + 2-291 /= + l-55 



Aberration = — '296 — 

 F. 



* The following information may be of service to those beginning to com- 

 pute the curves of lenses : — 



1st. One of the greatest labour-saving machines is a good slide rule. An 

 ordinary 12-inch slide rule may be obtained for 10s. or 12s. These are 

 accurate to two places, and the third may be approximated. By far the 

 best slide rule is that of Prof. Puller. It has a logarithmic scale nearly 42 

 feet long ; its price is £3, and it is accurate to four places ; a fifth may be 

 approximated. A smaller one is made with a scale nearly 17 feet long ; its 

 price is £1. Both these are sold by Stanley. Turnstile, Lincoln's Inn 

 Fields, W.C. 



2nd. Logarithm Tables. — An excellent five-place logarithm table by E. 

 Sang, published by Blackwood ; price is, I think, -Id. A seven-place 

 table, published by Chambers, price 2s. 6d. ; this is sufficient for all pur- 

 poses. A very fine table by Sang of numbers up to 200,000, to seven places, 

 published by Williams and Norgate, price £1 Is. 



3rd. One of the most useful books for optical work is Barlow's tables, 

 published by Spon, price 4s. 6d. It contains squares, cubes, square roots, 

 cube roots, and reciprocals of all numbers up to 10,000. 



A very fine but more elaborate reciprocal table is that of Oake's of all num- 

 bers from 1 to 100,000 to seven places. Published by Laytou, price £1 Is. 



Of these the smaller Fuller slide rule, Chambers' and Barlow's tables are 

 sufficient for most practical purposes. For accurate work the larger 

 Fuller slide rule is best, and O. ike's reciprocal tables are very useful. 



