May 30, 1889] 



NATURE 



115 



togetlier in such a way as to render taking down and removal a 



comparatively easy matter. In addition to the circular inclosure 

 supporting the dome, the height of which is about 20 feet, the 

 dome itself being 40 feet diameter, there are two or three rooms 

 and an entrance porch, available as a dark room and computing 

 room. The mechanism for moving the dome and the dome itself 

 are in good order, but in the opinion of the Committee, it would 

 be advisable to go to some expense in providing brackets for the 

 wheels on which the dome runs with horizontal rollers as guides 

 instead of the flanges on the wheels. The observing platform 

 is a first-rate one and will need no alteration. It is suitable 

 for general observational work, or for work where the use of a 

 large spectroscope renders considerable space necessary in any 

 direction. 



The shutters of the dome will require some slight repair. 



As regards the apparatus with this telescope there are the 

 usual battery of eye-piece-; suitable to the telescope ; a series of 

 parallel bar, ring, and other fixed micrometers, a very fine 

 parallel wire micrometer, all complete in mahogany boxes ; a 

 fine barrel chronograph in glass case, and a good sidereal clock 

 with compensated pendulum. These with sundry apparatus 

 belonging to the telescope complete the outfit. 



We had no opportunity of thoroughly testing the clockwork. 

 We consider that it might be advisable to add an electric control 

 and slow- motion gear of the modern pattern in order to render 

 the telescope more efficient in this respect. 



II. We have drawn up a specification showing more fully the 

 work required to be done in order to put the telescope simply 

 into an efficient state, but we would recommend that the 

 opportunity be taken to add electric lighting to the circles and 

 micrometer, to provide an electric control to the clock and an 

 electric slow-motion gear. We would further recommend that 

 12 cast-iron brackets be added to the dome as supports for the 

 wheels, that one or both of the flanges be turned off these wheels, 

 and that horizontal rollers carried by the brackets be added as 

 guides to keep the wheels on the rail. This, we think, would 

 render the turning of the dome much more easy. We would 

 retain the iron circular wall under the dome in preference to a 

 brick or stone wall, as offering more favourable conditions for the 

 telescope. We have added in the appendix our estimate of the 

 cost of this work. 



III. When erected and in working order, this telescope will 

 be specially adapted to any work in observational astronomy for 

 which a large aperture is required, and if it is decided to restrict 

 the use of the telescope to micrometric measures of faint satellites, 

 or to the scrutiny of planetary details, no outlay will be required 

 for additional apparatus, beyond an efficient system of lighting 

 the circles and micrometer with small electric lamps. Should it 

 be determined, however, 10 undertake work in stellar physics, 

 which we understand, from the letter published in Nature, is 

 the wish of the donor, and which we would strongly recommend 

 as the most useful systematic work to take up, then the necessary 

 spectroscopic outfit, at present wanting, would have to be pro- 

 vided. We estimate the cost of this at about ^100. So equipped 

 the telescope would at once be capable of commencing systematic 

 work of first-class importance that would amply repay the cost 

 of keeping such an instrument regularly employed, and in carry- 

 ing on such systematic work no further outlay in buildings would 

 be required, the computing and dark rooms attached to the 

 dome being sufficient for the work to be done at the telescope. 

 But in our view it would greatly increase the usefulness of this 

 instrument for spectroscopic research if it were placed within easy 

 reach of a physical laboratory where apparatus would be avail- 

 able for experimental investigations in connection with the 

 telescopic observations. As regards the selection of a site we con- 

 sider it a matter of great importance that the instrument should be 

 located where it would be easy of access to members of the 

 University engaged in making observations with it. It is 

 essential for the effective use of an instrument in a variable 



observer should be as near his work as 



climate that 

 practicable. 



the 



W. H. M. Christie. 



A. AiNSLIE C0M.MON. 



A. Graham. 



April 3, 1889. 



The previous experience of these gentlemen has also enabled 

 theai to give an approximate estimate of the expense of the 

 removal and re erection of the telesope at Cambridj;e. It 

 appears unnecessary to quote the details of their estimate, but the 

 total sum is given by them as £770. 



At the time when Mr. Nevvall had in contemplation his offer 



to the University, he was already veiy ill, and the Syndicate 

 heard with deep regret of his dcaih on the 2ist of April. They 

 have reason to believe that he wes gratified, before his death, 

 with the prospect that his valuable instrument would probably 

 contribute to the advancement of astronomical science at 

 Cambridge. 



Since his death, the executors, with the full approval of his 

 family, have renewed the offer to the University. The- 

 Syndicate are of opinion that the University should avail itself 

 of the opportunity of possessing this fine instrument, and they 

 are at present occupied with schemes for its proper maintenance 

 and use. 



C. E. Searle, Vice- Chancellor. 



E. J. ROUTH. 



J. W. L. Glaisher. 



J. C. Adams. 



G. D. LiVEING. 



G. H. Darwin. 

 May iS, 1889. J. J. Thomson. 



SOME PROPERTIES OF THE NUMBER 7. 



I. IV/rY attention was recently drawn by a pupil to the fol- 

 -^'-'- lowing property, which will be best illustrated by 

 working out a particular example : 



Let N = 342544 3 



if any one of the quantities u.^, Wj, u^, &c., is divisible by 7, 

 then N is so divisible.^ 



For, let N = loPj -f /o 

 M2 = 10P2 + qi 



«3 = IOP3 + (J-i 



ti^ = 10P4 -f q-i 

 U„ — I = ioP„ _ I + qn -2 



tin = loP« -I- q,,- 1 — 7Q, by hypothesis. 



Now, loPi -. 10-P2 -f- io[q-^ + 2/0) 

 lO'Pa = lO^Pg -f {6\q^ + 2^1) 

 lo-Pa = IO^P4 + lo\q^ + 2q^) 



IC-'P;,-, = IO"P„ + lO» -'(qn-x + 2qn-^); 



.-. N = loPi -f A = 2i[A) + loi'i + • . . + 10"--^,, -2] 



-f lo«-'(ioP„ -h qn--^) 

 - 21M -f 10"- '(7Q) = 7Q\ 



Or we may proceed thus : — 



u.;, = Pi - 2/0 ; ••• N = io(«2 + 2/0) + A = iO''2 + 21/0 J 

 hence, if N is divisible by 7, so also is ti», and so on. 



If for 2 we substitute i, 3, 4, 5) ■ • • «, then if N is divis- 

 ible by II, 31, 41, 51(3, 17), . . . ion + I, so also are (the 

 corresponding) ti^, «3, . . . w«- 



In like manner, if we strike off 2, 3, ... « figures, then if N 

 is divisible by (loi, 201, . . . io"« -i- i), (looi, 2001, . . . 

 id^n + i), . . . and so on, so are ti.^, u-^, . . . u„. 



2. This property was suggested by the question, " Prove 

 that a number consisting of six like figures (riiiil) is 

 divisible by 7." 



Let X be the digit, and let it be repeated n times, then if N 

 be of the form (7/ - «;r)io'' 4- (lo«-' -I- JO»-^+.. . +io+i)x, 

 i.e. such a number as 5733, in which \\q have 57 -I- 2 x 3 

 = multiple of 7, it will be divisible by 7, if - « . 10" -f 

 (10" - i)/9 is, i.e. if (9« - 1)10" -f- i is, i.e. if (2« - 1)10" 

 -f I is, i.e. if (k =) (2« - l) y + I. is. 



Omitting the case of six like digits, we write down the fol- 

 lowing table for an inferior number, the use of which is explained 

 subsequently. 



I In fact, 21 may be substituted for 7. 



