AnousT 24, 1SS3.] 



SCIENCE. 



•2-29 



cenieil. Some of us have known you personally be- 

 fore, and most of us have long been more or less 

 familiar at second hand with your state and city; 

 and yet, I think, to many of us it is something like 

 a new revelation to see for ourselves what a few 

 years have accomplished. I am not enough of a 

 Latin scholar to quote my "Virgil well; but I have 

 been all the time most forcibly reminded of the pas- 

 sage in which JCneas first comes in sight of rising 

 Carthage. Most emphatically the work 'hails' 

 here. We see no drones or sluggards; but every 

 .shoulder is at the wheel, and every thing is moving. 

 It may, perhaps, seem to you sometimes, when in our 

 sectional meetings we discuss some question about 

 the stars, or some hypothesis as to the formation of 

 rock-strata, or the structure of some worm or insect, 

 that we are out of the current, and contributing 

 no,thing to the advancement of the world. But you 

 know it is not so, and your invitation to hold our 

 meeting here shows that you know it. The world 

 advances, not on one line only, but on many, — on 

 lines material, intellectual, spiritual. To some ex- 

 tent, the movements are indeed independent, but 

 not very far. Any true advance on either line im- 

 plies corresponding movement on each of the others. 



if not absolutely simultaneous, yet surely oonsoquent. 

 There is no need to ask you here how much this city 

 owes to modi'rn science, when I see on every side, in 

 your streets and storehouses and mills, the practical 

 ap]>lication of the highest engineering, mechanical, 

 and electric art; and in the future it is almost certain 

 that science is to contribute still more liberally to 

 business. But not mainly ftir this reason do I claim 

 your regard to science ; but because, made in the im- 

 age of God as we are, knowledge and understanding 

 are as truly wealth and power as lands and food and 

 money. 



I need not add that, as you have invited us here, so 

 we on our part cordially invite you to attend all our 

 meetings, to listen to the papers and their discus- 

 sion. We cannot promise that every paper will be 

 interesting to all, but each one, I think, will be able 

 to select certain ones he will be glad to hear; and if 

 any of you choose to join us, and enroll yourselves as 

 promoters of the a<lvancement of science, our mem- 

 bership is open on easy terms. Once more, gentlemen, 

 we thank you for the cordial welcome, ami address 

 ourselves to our business, in the hope and confidence 

 that our meeting here is to be in the highest degree 

 pleasant and successful. 



PROCEEDINGS OF SECTION A. — MATHEMATICS AND ASTRONOMY. 



ADDRESS OF WILLTAM A. ROGERS, 

 OF CAMBRIDGE. MASS., VICE-PRESI- 

 DENT OF THE SECTION, AUG. 15, 1SS3. 



THE GERMAIN SURVEY OF THE NORTH- 

 ERN HEAVE>fS. 



The illustrious Argelamler was accustomed to say, 

 in the quaint form of speech which he often em- 

 ployed, '■ The attainable is often not attained if the 

 range of inquiry is extended too far." In no under- 

 taking is there greater need of a judicious application 

 of this sound maxim than in the systematic determi- 

 nation of the exact positions of all the stars in the 

 visible heavens which fall within the reach of tele- 

 scopes of moderate power. 



The first subject which engaged the attention of 

 the Astrononiische gesellschaft, at its formation in 

 186.1, was the proposition to determine accurately the 

 co-ordinates of all the stars in the northern heav- 

 ens down to the ninth magnitude. To this associa- 

 tion of astronomers (at first national, but since 

 become largely international, in its character and or- 

 ganization) belongs the credit of arranging a scheme 

 of observations by which, through the co-operation of 

 astronomers in different parts of the world, it has 

 been possible to accomplish the most important piece 

 of astronomical work of modern times. With a fea- 

 sible plan of operations, undertaken with entire luiily 

 of purpose on the part of the observers to whom the 

 several divisions of the labor were assigned, this great 

 work is now approaching completion. While it is yet 

 too early to speak with confidence concerning the 

 dcfluiiive results which the discussion of all the ob- 



servations are expected to show, we may with profit 

 consider the object sought in the undertaking, the 

 general plan of the work, the difficulties which have 

 been encountered, and the probable bearing which 

 the execution of the present work will have upon the 

 solution of a problem concerning which we now 

 know absolutely nothing with certainty, — a problem 

 of which what we call universal gravitation is only 

 one element, if, indeed, it be an element, — a problem 

 which reaches farther than all others into the mys- 

 teries of the universe, — the motion of the solar and 

 the sidereal systems in space. 



Our first inquiry will be with respect to the con- 

 dition of the question of stellar positions at the time 

 when this proposal was made by the gesellschaft in 

 18(i.5. All the observations which had been made up 

 to this time possess one of two distinct characteris- 

 tics. A portion of them were made without direct 

 reference to any assumed system of stellar co-ordi- 

 nates as a base, but by far the larger part are differ- 

 ential in their character. This remark holds more 

 especially with reference to right ascensions. 'Nearly 

 all of the observations of the brighter stars made pre- 

 vious to about 18:ro were referred to the origin from 

 which stellar co-ordinates are reckoned by correspond- 

 ing observations of the sun ; but since that date it has 

 been the custom to select a sufficient nuiijber of ref- 

 erence stars, symmetrically distributed both in right 

 ascension and declination, and whose co-ordinates 

 were supposed to be well known. The unequalled 

 Pulkova observations for the epoch 1^.5 form, I be- 

 lieve, the only exception to this statement. From the 

 assumed system of primary stars .are derived the clock 

 errors and instrumental constants which are employed 



