336 



♦ KNOWLEDGE ♦ 



[April 17, 1885. 



miles per second. And from the well-known formula connecting 

 the velocity in an elliptical orbit with the axis, '2a, viz., 



We tnow that 



(vel.)- at dist. r in cii-c. orbit 



e- 



^J) 



(vel.)' at dist. 



: 1 : 2: 



in parabolic orbit 



.'. Tel. at earth's distance in a parabolic orbit, which is the same as 

 the velocity of a body arriving from an infinite distance, under 

 solar gravity, when at the earth's distance, exceeds the earth's mean 

 velocity as v'ij exceeds 1, or as 1-414 exceeds lOOO. This makes u, 

 for earth's distance, R, from the sun, in case of a body arriving 

 from infinity, equal to 26 miles per second. 



Thus equation (ii), above, becomes 



.= =(26)^.2,(1-1) (iii) 



and since, when x = infinity, vel. = 0, we have from (ii) and (iii) 

 i' = ?^(iv); and (20) = = ?^; 



whence /i = 338 x 92,600,000 = 31,298,800,000 



This, being interpreted, means that the sun's attractive energy 

 all concentred in a point would at the distance of a mile (the unit 

 of distance) exert a force whicli, continued constant for a second 

 (the unit of time), would generate a velocity of 31,298,800,000 

 miles per second! 



From (iv.) we can determine v for any given distance from the 

 sun's centre. Thus at a distance of 425,000 miles — or at the appa- 

 rent surface of the sun (the real surface, I am satisfied, lies tens of 

 thousands of miles lower down) — we have 



, 2 X 31,298,800,000 , , < qaa 1 



v= '— .' = 144,900 nearly 



432,000 ^ 



r=380, nearly enough. 



Hence a body reaching our sun's surface from outer space under 

 his sole attraction would have a velocity of 380 miles per second if 

 it had come from rest at a distance such as separates star from 

 star. 



But now suppose that in interstellar space, when so far from the 



2 u 

 solar system that —C may be regarded as evanescent, or may at 



r 

 any rate be neglected, the velocity of a meteoric body is V. Then 

 we have 



t^ = V'-H^ ^"^ 



We may conveniently apply this to the case of the solar system, 

 in order to determine the velocities with which bodies starting from 

 interstellar space with various velocities, outstanding let us suppose 

 after their retreat from the domain of some other sun, would pass 

 definite distances from our own sun, — noting that, by a well-known 

 law, the velocity acquired in passing from a very great distance 

 towards the sun, is the same at a given distance from him, whether 

 the motion is directly towards his centre or such as to carry the 

 body on a parabolic or hyperbolic course around him. We may 

 also apply (iv) to determine the velocities of bodies at given dis- 

 tances from the sun, which have been ejected from him so as to 

 cross his apparent surface with such and such velocities exceeding 

 that of 380 mUes per second which is the greatest he can impart or 

 control. 



Thus suppose a body moving in interstellar space with a velocity 

 of (1) 100 miles per second, (2) 500 miles per second, and (3) 1,000 

 miles per second, then since, at the earth's distance, R, from the 

 sun, 2/1 -f- R = 676, we have, in these three cases, respectively, — 



(1) r'' = (100)= -I- 676; whence v •= 103 j approximately 



(2) I- = (500)= + 676; whence v = 500j approximately 



(3) (■= = (1000)= + 676 ; whence v = lOOOJ approximately. 



We see then that in the first case, instead of imparting a velocity 

 of 26 miles per second by the time the body is at the earth's distance 

 the sun adds only a velocity of 3} miles per second ; in case (2) the 

 sun adds a velocity of only § miles per second ; and in case (3) onlj' 

 a velocity of J mile per second. 



Suppose next we inquire what must be the velocity of a body in 

 interstellar space that entering the solar domain under the sun's 

 attraction it may acquire an additional velocity of 10 miles per 

 second at the earth's distance. For this, we require to determine 

 V from the following equation : — 



Y= + 676 = (V + 10)= = V= + 20 V + 100 



whence V = 284 miles per second. 



So that if a meteor entered our sun's domain (by which I mean 

 a much larger sphere than Neptune's orbit would girdle) with a 

 velocity of 30 miles a second the sun would not raise its velocity 

 to 40 miles a second by the time it reached the earth's distance 

 from him. 



Suppose next we try the effect of the same interstellar velocities 

 in modifying the velocity with which a body would reach the sun's 

 surface. Here our equation becomes 



\' + 676 



92,600,00 

 432,0l0~ 



144,900. 



Whence if T = 100, r= = 10,000 + 144,000 = 154,900 



I- = 393 ; a gain of 293 miles per second. 

 If V = 500, V- = 250,000 + 144,900 = 394,900 



V = 628 ; a gain of 128 miles per second. 

 If V = 1,000, )!» = 1,144,900 



V = 1,070; a gain of only 70 milespersecond. 



Observe that it follows from these results that if the velocity of 

 ejection from the sun, at the photosphere, be 393 miles per second, 

 or 13 miles per second more than the 380 which the sun's attrac- 

 tion can give, or master, the velocity of recession never sinks 

 below 100 miles per second. If the velocity of recession be 628 

 at the sun's surface, or 248 more than the sun's attraction can give 

 or master, the velocity of recession never sinks below 500 miles 

 per second. If the velocity of recession be 1,070 at the sun's 

 surface, or 690 beyond what the sun's attraction can master, the 

 velocity of recession never sinks below 1,000 miles per second. 



We may as easily consider the problem from the other side. 

 Thus, suppose we wish to ascertain what the ultimate velocity of 

 recession will be for a body leaving the sun's surface with a 

 velocity of 390 miles per second, 10 beyond the greatest which the 

 sun can impart or master. We have 



(390)= = V= - 14-1,900 

 /. V= = 152,100 - 144,900 = 7,200 

 or V = 85 nearly. 



A body, then, which left the sun with a velocity of 390 miles per 

 second at his apparent surface would reach interstellar space with 

 a velocity of 85 miles per second. With a velocity of 4C0 miles 

 per second at the sun's apparent surface, the velocity in mid-space 

 would be ^/(400)=-144,900 = v/16,Tob = 127. 



{To he continued.) 



A BRIDGE crossing Lake Ponchartrain, near New Orleans, is 22 

 miles long. It is of trestle-work on piles of cypress wood treated 

 with creosote oil. 



The Electric Light in' Brussels. — The lowest estimates for 

 lighting the new Theatre Flamand in Brussels are : — Gas, £1,509; 

 electricity, £1,846. 



In New York a special committee has been inquiring into the 

 question of public gas supply. It is found that for some years a 

 profit of about Idol per 1,000 ft. has been made. This shows a 

 gain to the companies of about two-thirds the cost of the material, 

 and it is computed that the excess profits extorted from the people 

 of New York during the last ten years have been from six to eight 

 millions sterling. 



At a recent meeting of the Commercial Gas Company, the 

 chairman stated that during the last half-year they had carbonised 

 88,407 tons of coal, against 87,017 tons, and the gas made and sold 

 had been 833 millions of cubic feet, as compared with 826 millions 

 in the same period of the previous year. The gas rental had been 

 £113,333, or a decrease of £6,003, but had the price of the gas been 

 tbe same there would have been an increase of .£6,943. He was 

 happy to state that the receipts from residual products had been 

 £40,009, showing the substantial increase of £3,194. 



Shocks ix W.\ter-Pipes. — The water-pipes in a building often 

 prove a nuisance by transmitting with noisy effect the various 

 shocks and vibrations in the water-pressure. A pump used for the 

 purpose of supplying the hydraulic pressure which operated the 

 elevators in a building in New York, could be heard over the 

 building, each water-pipe giving a sympathetic tremor with every 

 stroke of the pump. After the failure of many attempts to reduce 

 the noise by changing the mechanism of the pump, the difficulty 

 was solved by removing about 2 ft. of the discharge-pipe, and sub- 

 stituting a piece of rubber hose, which seemed to appropriate to 

 its dilatation the variations of water pressure. — Engineering. 



