Nov. 25, 1881.] 



KNOWLEDGE 



81 



AXXIVERSARY MEETING OF THE BIRMING- 

 HAM AND MIDL.\.ND INSTITUTE UNION OF 

 TEACHERS AND STUDENTS. 



By W. M.vttiec Willums. 



IN the first namber of Knowi,edge I communicated a skct''" 

 of the history of the Scientific Department of the Midland 

 Institute, so far as the classes are concerned. But there is another 

 tienient, viz., the Students' own Associations for Mutual Improvo- 

 ineut, which is well worthy of notice and imitation. 



One of these, the Institute Scientific Society, has been remarkably 

 successful. It possesses a scientific library of no mean character, 

 :ind its members read admirable papers and carry on discussions of 

 considerable interest. Some of these papers or lectures on the 

 Birmingham trades, written by practical workers who, at the classes, 

 have attained sufficient scientific knowledge to discuss the philo- 

 fophy of their daily avocations, supply a kind of information not 

 t'asily attainable from books or the lectures of ordinary professors. 



The Union of Teachers and Students, another and larger society, 

 I'.eld its anniversary gathering on Tuesday evening, Nov. 22. The 

 programme included a tea-party, the whole arrangements of which 

 were conducted by the female students, without external aid of 

 contractor or pnrveyor. This was followed by a meeting in the 

 new theatre, under the presidency of the Mayor, where an address 

 was read by the retiring President of the Union, Mr. C. J. Wood- 

 ivard. The subject was the history of the institute. I must not be 

 temjitcd to quote any more than the following — viz., that when Mr. 

 liickard commenced the Penny Arithmetic Classes, he had six pupils 

 to tlie first lessons. This session the attendance to the first lesson 

 was two hundred, and there are now held every week no less than 

 sixty-five " Penny " classes on different subjects in the central 

 institute and its branches, besides all the other classes. 



Then followed a general coni'ersazione, distributed through the 

 various class-rooms and lecture-theatres, including an exhibition of 

 m'croscopes contributed by the members of the Institute Scientific 

 Society, scientific experiments by students of the Chemistry and 

 Physic Classes, vocal music by members of the Singing Classes, 

 German recitations, a French play — '' Un Quartier Tranquillo " — 

 by members of the Institute French Dramatic Club, with the usual 

 social and loyal conclusion of " Auld Lang Syne " and " God Save 

 the Queen " by everj-body. 



Criticism would be out of place here, and description of details 

 possibly tedious. I need only add that the whole programme was 

 successfully carried out. 



The attendance, which commenced with 450 at the tea-party, 

 grew to above a thoasand later in the evening, i.e., after working 

 liours. 



The feature to which I wish to direct particular attention is the 

 sjiontaneous, self-originating, and self-supporting character of these 

 proceedings, and of all the other doings of these student associa- 

 tions. They constitute what appears to me to be a most important 

 adjunct to the classes and public lecttires of the Midland Institute, 

 and one which may be very advantageously introduced in other 

 kindred institutions, especially those of London. One of the most 

 shallow and mischievous of popular delusions on the subject of 

 education is the supposing that ivhen we have completed a certain 

 jirescribed course of study, and passed our examinations on any 

 subject, we have completed that part of our education — the fact 

 being that all class teaching and all book reading is but the first 

 stage of true, comprehensive education ; self -teaching, original 

 thought, the digesting and co-ordination cf such school knowletlge, 

 must follow, to render it truly fruitful, and social cooperation in 

 such supplementary work is most desirable. The meeting of old 

 students with their younger successors, the revisiting of the old 

 teachers, and sustaining of the old friendships between them and 

 their former pupils, gives vitality and moral warmth to the whole 

 institution, prevents the possibilitj- of that decay which too often 

 falls upon such institutions, when their existence is allowed to de- 

 pend upon the efforts of outside patrons and the beneficence of mere 

 endowments. Besides all this, the governing body is kept justly 

 informed of the real requirements of the students— those who have 

 good reason to be grateful to it, and know its workings by their own 

 experience as former pupils, remain attached to it, join in its 

 management, and otherwise substantially express their gratitude. 



The genuine enthusiasm and hard-working efforts in carrj-ing out 

 the evening's programme, the genial friendship and high moral tone 

 which I witnessed as pervading all the proceedings of Tuesday's 

 meeting, convinces me that if such unions and friendly gatherings 

 of teachers and students, old and young, male and female, should 

 become one of the essential elements of all our literary and scientific 

 institutions, their general prosperity and practical effectiveness 

 would be greatly promoted. 



(Bw iHatbrmatiral Column. 



PRACTICAL USE OF LOGARITUMIC TABLES. 



LET us now take a few examples of the practical use of a table 

 of logarithms, noting that the former paper was intended to 

 explain all that is necessary to be known respecting the theory of 

 logarithms. I did not then think it necessary to draw any distinc- 

 tion between the logarithms of our tables and logarithms to any 

 other base than 10; for the computers who mostly employ 

 logarithms, tise the decimal notation. 



Let us first take the example afforded by Mr. Harding's calcula- 

 tion at p. 55, noting that the result, corrected for a " printer's 

 error," is 



.21.0012. Ii552i 



loSOW 

 We have to take out the logarithms of these three numbers. 

 Take first 21'9912. We turn to the number 2199 in the table and 

 ran our eye to the second column above which is the next digit, 1, 

 getting the logarithm 3-122150. (The first three digits of this are 

 shown in the first column, the other columns only giving the next 

 four for each number). But we still hare to provide for the last 

 digit, 2. Xow we might do this from the part of the tables already 

 used. Thus they show : — 



logarithm of 21991 is 3422450, 



and logarithm of 21992 is 3422647, or 197 more. 

 Xow, we see that 219912 is only two-tenths of the way from 

 21991 to 21992, so that we should add only two-tenths of 197 to 

 the logarithm of 21991 to get the logarithm of 219912, assuming 

 that the logarithm increases, for such small differences, propor- 

 tionately with the number of which it is the logarithm — which is 

 shown to be true by tlie circumstance that we have the difference 

 197 or 19S (oftener the latter) for several logarithms on either side 

 of the one we are using. Manifestly if in passing from 219E0 to 

 to 21991 and thence to 21992, 21993, and so forth, we have the 

 same difference*, the logarithm is hero growing in the same pro- 

 portion as the anti-logarithm (that is, as the number of which it is 

 the logarithm). Hence, we take two-tenths of 198 (note italicised 

 words above), or 396 (the nearest whole number to which is 40), 

 and add this to 3422450, the logarithm of 21991, to get the 

 logarithm of 2-19912. Thus 



log. 219912 = 1-3422490. 

 But we are saved even this slight labour by good tables. All tables 

 give the difference as 198 in our example ; but in good tables there 

 is sho^vn on the right the table of proportional parts, giving the 

 amount to be added for digits 1, 2, 3, 4, 5, &c., respectively, and 

 opposite 2 is set 40, the amount to be added. 



Let us proceed in the same way with 143303 and 153664. Wc 

 find in the tables, logarithm 1-4330 is 1562462, the '-difference" 

 is 303, and 3-lOths of tins are 91, which added to 1562402 gives us 



log. 143303=5-1502552. 

 Again, we find in the tables, logarithm of 1-5366 is 1865608, " dif- 

 ference " is 283, and 4-lOths of this are 113, which added to 186560,S 

 gives 



log. 153664=5-1865721 

 Thus, according to the principles on which logarithms are used, our 

 " sum " is worked thus -. — 



log. 21-9912 = 1-3422490 



log. 143303 = 5-1502552 



Sum = 6-4985042 

 log. 153064 = 5-1805721 



Difference = 1-3119321 [ = Iog. 20508]. 

 We now turn to the tables, and looking first along the left hand 

 column of logarithms (next to the column of numbers) for the pai-t 

 311 of the logarithm we have found. This comes next the number 

 2047, but running along this part of the tables for the remaining 

 part, 9321, or what comes nearest to it, we find it opposite 2050 

 under the ninth column, corresponding to digit 8 (shown at the top 

 of this column). The logarithm given here is 3119233 while that 

 next larger is 3119445 ; the former is nearest to the logarithm 

 above obtained. 3119321. Thus, if we are content with this degree 

 of approximation to the result we want we write down 20508 as the 

 digits representing that result, but as in the bracketed part of above 

 computation we set the decimal point after the second digit, because 

 our logarithm has 1 on the left of the decimal point. As a matter 

 of fact, it would be absurd not to be content with this degree of 

 approximation, simply because we cannot get more out of the 



• The same difference, for though the actual difference alternate? hereabouts 

 between 197 and 198, this is only due to the circumstance that the last digit has to 

 be the nearett to the true value, and cannot represent the exact vahie. 



