NOVEJIBEK 1, 1889.] 



KNOWLEDGE 



tory note on the subject mil be read at the nest 

 (November) meeting of the Society. There are three 

 hirge drawings in all, one showing a little more than the 

 northern half of the Galaxy down to about 10 deg. to the 

 soutli of the equator on either side of the map, and two 

 other drawings on double the scale of the first, each repre- 

 senting a half of the part of the Milky Way shown in the 

 first map. Dr. Boeddicker's drawings differ in character 

 from the drawmgs of the Milky Way which have been 

 made by other observers. Heis and Gould may be said to 

 show the Galaxy as made up of cloud-like lumps or masses 

 of light and curiously shaped areas of fainter brightness, 

 whereas Dr. Boeddicker shows it as composed of whisps 

 and streams of light with very numerous dark channels, 

 having more or less sharply defined edges. Every one 

 must have noticed the great dark channel which divides 

 the Milky Way into two nearly parallel streams from 

 Cygnus to Scorpio ; but Dr. Boeddicker sees innumerable 

 smaller channels of a similar character liranching away 

 fi'om the main channel and frequently followin.L; the central 

 line of outlying streams of nebulous light, which curve so 

 as to include stream lines of brighter stars. If the exis- 

 tence of such cur\'ing streams are confirmed by other 

 observers, and by the mierring eye of the camera (which 

 has not as yet given us any trace of the nebulous light of 

 even the brighter parts of the ]\Iilky Way) we shall not be 

 able to resist the conclusion that the nebulous streams are 

 associated with, and are not more distant than, the bright 

 stars which lie ujjon them ; and that associated with the 

 Galaxy there are streams of opaque matter, dust clouds or 

 fog-filled space, which cut out the light of the bright 

 streams, and in most cases follow their curvmgs, so as to 

 lie upon the central parts of the bright streams. A sup- 

 position which seems somewhat unlikely. 



The production of these maps has occupied Dr. 

 Boeddicker for the last five years. They have evidently 

 been executed with extreme care. The accurate delinea- 

 tion of faint masses of nebulous light is a much more 

 difficult and laborious task than would be supposed by 

 those who have not attempted such work. The relative 

 intensity of the various parts, as well as the shapes of ihe 

 nebulous structures, have to be continually altered and 

 compared under difficult conditions, and the ultimate 

 result presented to the world generally only represents a 

 small part of the work that has been done. 



Thei'e can be no doubt as to the importance of the 

 great problem which has been attacked by Dr. J5oeddicker 

 and the J'lai'l of Rosse ; but it is rather curious that tlie 

 owner of tlu! largest telescope in the world should have 

 devoted so much of the time of his observatory to a class 

 of work which can be done with the naked eye, and needs 

 no instrument larger than an opera-glass. We shall see 

 what the very numerous owners of such connnonplace in- 

 struments have to say in confirmation or contradiction of 

 the Parsonstown work. A. C. 1!. 



SOME PROPERTIES OF NUMBERS. 



By Itor.T. \\ . I). CiiuiSTiK. 



IT is a fact well known to all who are engaged in the 

 education of the young that the rule of arithmetic 

 known as long division is one of the most difficult to 

 be comprehended by learners ; and it has occurred 

 to me that an alternative method of arriving at the 

 same results would be appreciated. The proposed method 

 possesses one or two advajitages peculiar to itself. The 

 figures of the quotient are given in the reverse of the usual 

 order, and. when the remainder is known, the quotient is 



obtained surprisingly quickly. The chief difficulty by this 

 method is to obtam the true remainder, but this is by no 

 means insuperable. I shall first give one or two examples 

 having no remamder, and afterwards deal with the question 

 of remainders. It is to be luiderstood that the method 

 particularly applies to all dinsors ending in the digits 1, 3, 

 7, and 9, and therefore to all prime numbers, and conse- 

 quently to any divisor whatever, since all numbers are 

 compounded of prime numbers. 



Example I. — Find the quotient of 80-119753^-7. 



Biilc. — Multiply both dindend and thvisor by 3. 



(N.B. — TJiire is the multiplier for all di\isors ending in 

 the digit 7. Multiplication is preferable but not absolutely 

 necessary.) 



Thus 2592.59259-=-21. 



Now multiply tliis di\ideud by the tens' digit of the 

 divisor, \dz. 2, as follows, and pomt off the quotient. 



25925923.9 



18 



306.4 

 20 



728.6 

 30 



569.8 

 40 

 252.9 

 45 



920.7 

 35 



G88.5 

 25 



66.3 



15 



5.1 



5 



The required (juotient is 135798642. 



Though the nu^thod is here given at full length, a good 

 deal could, in actual practice, be done mentally. It will 

 be noticed that the figures (>9257, c<;c. are '• brought 



