Dec. 23, 1881.] 



KNOWLEDGE 



169 



lace anterior to the historical life of the country." Mariette says, 

 ■ tlio O30 of stone and flint tools extended nearly 1,000 years, 

 tlirough thirty dynasties." Brugsch tells us, " Kjryptian history 

 llirows scorn on the supposed periods of stone, bronze, and iron ; " 

 and Chabas shows that similar tools were in use at the latest 

 historical period, and even now are not uncommon among the Arabs. 

 — A Membku of the SofiETY OF Biblical Arch.eology. 



[84] — Aktiquity of JI.vx, .\s Shown by the Works of Art in 



Nile Mud. — Your coiTcspondent " Clio " may find Mr. Horner's 



H'soarches in the "Philosophical Ti-ansactions," 1855-8, or ptrhaps 



-he will do better by consulting an admirable summary i,n Lyell's 



Antiquity of Man," p. 35 and 11, Ith edition, 1873. The result 



,1 simple rule of three sum. As is the thickness of Xile mud de- 



: '>>ited by the annual inundations over certain historical monuments 



!'■ their known age, so is the greatest depth at which the works of 



art occur in like mud liard by to their approximate age. — A Tramp. 



[89] — CoLLODio.N" Plates. — "Persevere" does not say whether 



the red stains appear after tlio plate is developed, or whether they 



are on the plates as received f«om the maker. In either case, it 



would be almost impossible to detei*miue cause without inspection. 



The vagaries of gelatine plates are innumerable. If the negatives 



are not varnished, they are very liable to be spoiled by the silver 



i from the paper ; the gelatine readily absorbs moisture. The remedy 



i- obvious. Evidently " Persevere " has not tried to answer his own 



i|UC3tJon as to developing gelatine plates; let him trj', and give liis 



• \|)erience, if successful. — A. Brothers. 



31] — " Missing LasK." — Dr. Andi-ew liVilson's article is on 

 -Missing Links " (not on the "Missing Link"). It appeared in 

 :u' Gentleman's ilayaxine for September, 1879.— Ed. 



fioU^ on 2vt anti Jriniff. 



A.MOXG recent finds at Pompeii were several amphorae, on some 

 of the largest of whicli was written the exact date of the extraction 

 of the wine contained within, and on smaller ones the names of the 

 wine. 



Ir is announced that Dr. King, in charge of the Government 

 cinchona factory at British Sikkim, has succeeded in manu- 

 facturing, for the first time in India, sulphate of quinine from local 

 cinchona bark. I'he samples produced are said to bear com- 

 parison, on analysis, with the pure sulphate of quinine of commerce, 

 and preparations are being made for undertaking the manufacture 

 on a large scale. 



The famous spring of boiling water in the middle basin of Hell's 

 Half Acre, in the Yellowstone region, has lately become still more 

 wonderful as a geyser. Four or five times every twenty-four hours 

 it discharges a great column of water, freighted with stones and ob- 

 scured by a dense volume of steam. The hollow formation for 

 hundreds of yards around the orifice trembles under the upheaval, 

 and the water is thrown to a height of a hundred feet. 



The six healthiest cities of the United States are said to be in 

 the order following : — Utica, Dayton, New Haven, Portland, San 

 Francisco, and Lawrence. Tlie unhealthiest are Charleston, 

 Memphis, Cleveland, Chicago, and Lynn. St. Petersburg is the 

 unhealthiest city in the woi'ld. and is followed by Charleston, 

 Malaga, Alexandria, Warsaw, and Buda-Pesth. 



M. Macag.vo, in Les ilondes, states that he has been making ex- 

 periments on the influence of electricity upon the gi'ov/th of the 

 vine. An electric circuit was formed by copper wire between the 

 extremity of a bra»ich beai-ing fniit and its origin near the soil. 

 More wood was formed in the branch, which contained less potash 

 than the other parts, and the grapes ripened more readily, containing 

 an excess of sugar. 



It is said that a marked improvement has been noticed in the 

 acoustic properties of the Grand Opera House, Paris, since the 

 introduction of the electric light. A layer of heated gases acts as 

 a screen for sound, hence the volumes of hot fumes arising from the 

 old gas footlights obstructed and marred, to some extent, the voices 

 of the singers. With the electric light, inclosed in air-tight bulbs, 

 no fumes can be emitted, and very little heat is given off. Hence its 

 benefits to the ear as well as to the eye. — Frank Leslie's Magazine. 



The question of the existence of volcanoes in Central Asia, esjie- 

 pecially on the Kuldja frontier, has always- been a matter of doubt 

 and discussion among geologists and Bussian explorers. The 

 GoveiTior of Semfretchinsk, General Kolpakofsky, had already 

 fitted out expeditions to settle the question — one in 1878, and again 

 in 1879 ; btit owing to the difficulties of reaching the mountains, 

 which the Chinese considered impassable, and also to disorders 

 which were then taking place in Kashgar, both expeditions were 



unsnccessful. This year General Kolpakofsky again set himself to 

 the task, and now rei)orts that ho has at last discovered the per- 

 petual files in the Thinn Shan range of mountains. Ho telegra|)hs 

 that the mountain Bai Shan has been found t«T?lve miles north-east 

 of the City of Kukija, in a basin surrounded by tho massive Ailak 

 Mountains, and that the fires which have been burning there from 

 time immemorial are not volcanic, but proceed from burning coal. 

 On the sides of the mountain there are caves emitting smoke and 

 .suliihuious gas. — Frank Leslie's Magazine. 



0\\x iWatlKinntiral Column. 



THE USE OF LOGARITHMS. 



IX our last, we took a simjile case of the multiplicatiou of two 

 numbers, each of six digits, and the division of tlie products by 

 another number, also of six digits. Working this sum by logarithms 

 seemed rather long, just as in practice nearly every one finds the first 

 two or three sums he works by logarithms requii'O more care and 

 watchfulness than he afterwards finds necessary. We may now, 

 however, proceed more freely. 



Let us consider a few cases of taking powers, or extracting roots 

 of numbers. 



Take first the familiar problem of tho horse with 24 shoe-nails, 

 for which a price of id. for first nail, Jd. for second, Id. for thu-d, 

 2d. for fourth nail, and so on, doubling to the twenty-fourth nail, 

 was to be paid : to find his price by the aid of logarithms. This 

 is a case somewhat unlike those \isually dealt with, ivherc an answer 

 exact to so many decimal places is required, not an answer abso- 

 lutely exact. However, it can be readily solved by logarithms. 

 Thus, for the first nail, amount is ^d. ; for fii"st and second, Jd. ; for 

 first three, \\A. ; for first four, 3|d. Start from the fifth, for 

 which nail 4d., or a third of a shilling, was to be paid, and let the 

 third of a shilling be our unit (the reason being that if we take 

 pence or farthings, we should not be likely to get an exact result). 

 Then there is to be paid for fifth naU 1, for the sixth 2, for the 

 seventh 4, or 2 to power 2 ; for the eiglith 8, or 2 to power 3 ; and 

 so on : and for the twenty-fourth, 2 to the power 19, while wo know 

 that the total paid for all the nails from the fifth to the last is twice 

 this, less 1, or 2''" — 1. 



Now, turning to the tables we find — ■ 

 log. 2 = 0-3010300 

 Multiply by 20 20 



log. : 



= 60200000 = log. 10485G 



log. 10485 = ■0205684~| 



difference for 70 = 



316 I This part of tho calculation 



292 y is simply working out 



the logarithm. 



240 



IdifEerence for G = 250J 



We know that 2™ must be a whole number, and can end 

 on'y with one of the digits 2, 4, 6, or 8; so we take with confidence 

 the number 1048576. This, less 1, is the number of 3rds of a shilling 

 for the nails from 5th to 24th inclusive, and the first four give us 

 one-thu-d of a shUling, less a farthing. So the answer is 1048576 

 thirds of a shilling, less a farthing. 



Or 349,525s. 3|d. 



Or £17,476. 5s. 3p. 



This is an unfavourable example, because of the necessity for an 



exact instead of an approximate result. If we had only required to 



know the amount rouglily, that is, within a shilling or two, we 



might have proceeded thus : — The amount in farthings is 2'* — 1, Or 



in shillings tho amount is 75, neglecting the farthing. 



Now log. 2 = -3010300 

 log. 2^ = 7-2247200 

 log. 48 = 1-6812412 



log. (2°-<+48) =5-5434788 



log. 34952 -5434720 



difference for 50 62 



5 6 



5-5434788 = log. 349525 

 Ans. = 34952-5 shillings. 



=£17,476. 5s. 6d. ; and the conditions of 

 the problem show that the pence really amount only to Z\d. 



