12 



NATURE 



[May 5, \\ 



that the principal Guyou formulce may be deduced with 

 little difficulty from the well-known Napier's analogies as 

 follows. 



Let us suppose, as before, that in a spherical triangle 

 the three sides «, h, c being given, it is required to de- 

 termine the angles A, B. 



We have 



A - B.._ c 



A + B 



cos- COS - 4- sin — sin - 



2 2 2 2 



A B 



I + tan - tan - 



2 2,_ ^. 



A, B 2 



I - tan - tan — 



2 2 



Let 



Then 

 tan 



A B 



tan - tan- = tan: 

 2 2 : 



tan _ = tan I a^ + - j tan -. 

 2 V 2/ 2 



Whence 



]MP(a-) = MP(90° - c) - MP(90° - ^TT) . 



An equation which determines x. 

 While from equation (i) it may be deduced that 



MP(9o° - A) + MP(9o' - B) = MP(90° - x) 

 Proceeding in the same manner to expand 



(2) 



(3) 



in the expression 



.„ A + B •„ A - B 

 sin , sm 



2 2 



and assuming that 



tan — cot — = tan- 



we arrive at the equations 



MP(j) = MP(90° - a - b) - MP(90° - c) . 

 MP(90° - B) - MP(9o° - A) = MP(9o° -y) 



(4) 



(5) 

 (6) 



By adding and subtracting each side of the two equa- 

 tions (3) and (6), we obtain equations which will enable 

 us to determine the values of A and B respectively. 



In place of the notation " MP," M. Guyou adopts the 

 Greek letter X (lambda). Thus, ineridional parts for an 

 angle = X(^). 



He also indicates the meridional parts of the comple- 

 ment of an angle by the symbol Co-X, so that meridional 

 parts for the angle (90°- 6) = Co-X {6). 



And in his excellent collection of tables the values of 

 X and Co-X are given for each angle side by side, an 

 arrangement which much facilitates the work of com- 

 putation. 



The ordinary employment of Napier's analogies in 

 practical work is limited to finding the remaining two 

 «ides when two angles and the included side are given, 

 or to finding the remaining angles when two sides and 

 the included angle are known. It is a somewhat remark- 

 able extension of their functions to find that they suffice 



NO. 1488, VOL. 58] 



also to furnish satisfactory logarithmic formulce for 

 solving a triangle where the three sides are the given 

 parts. In a similar manner formulae may be found which 

 will determine the sides when the three angles are given, 



so that formuliE of the type which gives tan - in terms 



of functions of the sides, or tan - in terms of functions of 



2 

 the angles may be dispensed with altogether. 



It would be premature at present to hazard a con- 

 jecture as to whether the new processes will come into 

 general use in England. In these matters we move 

 slowly. The British mariner does not easily surrender 

 the methods upon which he has been brought up, the 

 practice of which becomes almost automatic with him, and 

 he looks with feelings of doubt, tempered with suspicion, 

 upon any novelties that may be brought to his notice. 

 But some advantages, at least, of a system of rules in- 

 volving the use of only one table of logarithms must be 

 obvious to all. In the first place, as has been already 

 mentioned, we have that of the greater siinplicity in the 

 statement of rules, and the diminished risk of error 

 through the taking out of a logarithm from a wrong 

 column. But even more important than these is the 

 saving of time lost at present in turning over the leaves 

 of tables in hunting for sines and cosines in different 

 parts of a somewhat bulky book. In the table of meri- 

 dional parts we have but 5400 logarithins, occupying 

 some nine pages of Inman's collection, not more than 

 might be printed on a sheet of cardboard of moderate 

 size, so as to save the turning over of leaves altogether. 



These logarithms furnish results correct to the nearest 

 minute of arc, which is the usual limit of accuracy 

 aimed at by the practical navigator. 



As the case stands at present, the new system is well 

 thought of in Fiance ; it has excited considerable atten- 

 tion in Italy, and has won the approbation of at least one 

 distinguished authority in Spain ; so that, perhaps, M. 

 Guyou is not over-sanguine in his expectation that "the 

 table of meridional parts is destined to become sooner or 

 later the universal instrument of computation amongst 

 mariners.'' H. B. G. 



THE NEW PHYSICAL RESEARCH LABOR- 

 ATORY AT THE SORBONNE. 



AN interesting account of the new physical laboratory 

 at the Sorbonne recently appeared in La Nature. 



This laboratory, originally situated in the old Sor- 

 bonne, was founded in 1868 by M. Jamin, who was its 

 director until his death in 1886. In 1894 it was trans- 

 ferred to the new Faculty of Sciences, and was recon- 

 structed by the architect M. Nenot. At the present 

 time M. Lippmann, member of the Institute, is the 

 director. Although this change took place in 1894, the 

 work has only recently been carried on in the usual 

 manner. 



The new buildings are surrounded by other buildings 

 connected with the Sorbonne, and are therefore away 

 from any disturbances caused by passing vehicles. On 

 the ground floor, after passing an entrance hall with a 

 cloak-room, there is a large room (Fig. i) two stories 

 high, and measuring 16 metres (about 52 feet) long by 

 12 metres broad (about 39 feet). Six physicists can 

 work here, provided their work does not require any 

 special conditions with regard to light and isolation. 

 In the middle of the room, and at the corners there are 

 solid stone pillars isolated from the floor ; a " compar- 

 ateur" is attached to the one in the middle. Each of 

 the six places has four jets of gas, two incandescent 

 lamps, one arc lamp, and a water-tap. About two yards 

 above each table there is a joist, thus making it possible 



