536 Scientific Proceedings^ Royal Dublin Society. 



and my object will be attained if the contrivance I have proposed 

 helps in any degree to bring about a better balance of thought 

 relatively to the cosmos in which we find ourselves : it is so diffi- 

 cult to avoid making the small range of our senses a universal scale 

 with which to measure all nature. Where, for instance, is the 

 justification for our alleging that any visible speck of protoplasm is 

 undifferentiated ? And, in fact, are not subsequent events perpe- 

 tually rebuking this rashness ? 



A convenient object to help in connecting visible with ultra- 

 visible magnitudes is the marking on the frustule of the Pleiiro- 

 sigma angiilatimi (or, Gyrosigma angulatum) , one of the commonest of 

 test objects. The little brown specks are easily seen with the higher 

 powers of a microscope if a good condenser and the proper stop be 

 used, and their distance asunder from centre to centre is somewhere 

 between '64 and '65 of a micron according to the best determina- 

 tions I can make. This is a trifle more than the spacing deduced 

 from Professor Smith's measurement of the interval between the 

 rows. It is the ordinate of our gauge at about six and a-half 

 metres from its end, and is the wave-length of a ray of red' 

 light not far from the a hydrogen line, the line C of the solar 

 spectrum ; so that the brown dots succeeding one another in a row 

 mark off in the field of the microscope the successive waves of this 

 particular ray of red light. 



The dots are arranged in i"Ows parallel to the sides of an equi- 

 lateral triangle, and with oblique light coming at right angles to 

 any one of these sets of rows, the dots will elongate and almost run 

 into one another in a way that makes the rows look like a ruling 

 of parallel lines. These parallel lines are at shorter distances 

 asunder than the dots in the ratio of v^3 to 2, and accordingly 

 present to the eye intervals equal to the wave-length of a green 

 ray less refrangible than the line E of the solar spectrum. Tlie 

 interval in this case is the ordinate of our gauge at a distance of 

 about five metres and a third from its apex. 



Furthermore what we have 'found above to be the minimum 

 visibile is a little more than one-third of the interval from centre to 

 centre of the dots, or a little less than half the interval of the rows. 

 It is well illustrated by the Pleurosigma markings. In fact, 

 judging from similar markings on other scales, the round dots 

 would be seen as rings were it not for their small size, which 



